1,1,10,9,0.397000," ","int(x/(x^2-1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$2 \left(x^{2}-1\right)^{\frac{1}{4}}$&$10$\\ default&$2 \left(x^{2}-1\right)^{\frac{1}{4}}$&$10$\\ trager&$2 \left(x^{2}-1\right)^{\frac{1}{4}}$&$10$\\ risch&$2 \left(x^{2}-1\right)^{\frac{1}{4}}$&$10$\\ gosper&$\frac{2 \left(-1+x \right) \left(1+x \right)}{\left(x^{2}-1\right)^{\frac{3}{4}}}$&$16$\\ meijerg&$\frac{\left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{3}{4}} x^{2} \hypergeom \left(\left[\frac{3}{4}, 1\right], \left[2\right], x^{2}\right)}{2 \mathrm{signum}\left(x^{2}-1\right)^{\frac{3}{4}}}$&$33$\\ \hline \end{longtable}"," ",0,"2*(x^2-1)^(1/4)","A"
2,1,11,10,0.357000," ","int((3*x^2+1)/(x^3+x-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$2 \sqrt{x^{3}+x -1}$&$11$\\ derivativedivides&$2 \sqrt{x^{3}+x -1}$&$11$\\ default&$2 \sqrt{x^{3}+x -1}$&$11$\\ trager&$2 \sqrt{x^{3}+x -1}$&$11$\\ risch&$2 \sqrt{x^{3}+x -1}$&$11$\\ elliptic&$2 \sqrt{x^{3}+x -1}$&$11$\\ \hline \end{longtable}"," ",0,"2*(x^3+x-1)^(1/2)","A"
3,1,11,10,0.106000," ","int((x^8-1)/(x^4-1)^(1/2)/(x^8-2*x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{x}{\sqrt{x^{4}-1}}$&$11$\\ default&$-\frac{x}{\sqrt{x^{4}-1}}$&$11$\\ trager&$-\frac{x}{\sqrt{x^{4}-1}}$&$11$\\ risch&$-\frac{x}{\sqrt{x^{4}-1}}$&$11$\\ elliptic&$-\frac{x}{\sqrt{x^{4}-1}}$&$11$\\ \hline \end{longtable}"," ",0,"-x/(x^4-1)^(1/2)","A"
4,1,10,9,0.072000," ","int(x/(x^2-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{3 \left(x^{2}-1\right)^{\frac{2}{3}}}{4}$&$10$\\ default&$\frac{3 \left(x^{2}-1\right)^{\frac{2}{3}}}{4}$&$10$\\ trager&$\frac{3 \left(x^{2}-1\right)^{\frac{2}{3}}}{4}$&$10$\\ risch&$\frac{3 \left(x^{2}-1\right)^{\frac{2}{3}}}{4}$&$10$\\ gosper&$\frac{3 \left(-1+x \right) \left(1+x \right)}{4 \left(x^{2}-1\right)^{\frac{1}{3}}}$&$16$\\ meijerg&$\frac{\left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}} \hypergeom \left(\left[\frac{1}{3}, 1\right], \left[2\right], x^{2}\right) x^{2}}{2 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}}}$&$33$\\ \hline \end{longtable}"," ",0,"3/4*(x^2-1)^(2/3)","A"
5,1,10,9,0.066000," ","int(x/(x^2-1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{2 \left(x^{2}-1\right)^{\frac{3}{4}}}{3}$&$10$\\ default&$\frac{2 \left(x^{2}-1\right)^{\frac{3}{4}}}{3}$&$10$\\ trager&$\frac{2 \left(x^{2}-1\right)^{\frac{3}{4}}}{3}$&$10$\\ risch&$\frac{2 \left(x^{2}-1\right)^{\frac{3}{4}}}{3}$&$10$\\ gosper&$\frac{2 \left(-1+x \right) \left(1+x \right)}{3 \left(x^{2}-1\right)^{\frac{1}{4}}}$&$16$\\ meijerg&$\frac{\left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[\frac{1}{4}, 1\right], \left[2\right], x^{2}\right) x^{2}}{2 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{4}}}$&$33$\\ \hline \end{longtable}"," ",0,"2/3*(x^2-1)^(3/4)","A"
6,1,10,9,0.069000," ","int(x*(x^2-1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{2 \left(x^{2}-1\right)^{\frac{5}{4}}}{5}$&$10$\\ default&$\frac{2 \left(x^{2}-1\right)^{\frac{5}{4}}}{5}$&$10$\\ risch&$\frac{2 \left(x^{2}-1\right)^{\frac{5}{4}}}{5}$&$10$\\ gosper&$\frac{2 \left(-1+x \right) \left(1+x \right) \left(x^{2}-1\right)^{\frac{1}{4}}}{5}$&$16$\\ trager&$\left(\frac{2 x^{2}}{5}-\frac{2}{5}\right) \left(x^{2}-1\right)^{\frac{1}{4}}$&$16$\\ meijerg&$\frac{\mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{1}{4}, 1\right], \left[2\right], x^{2}\right) x^{2}}{2 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{4}}}$&$33$\\ \hline \end{longtable}"," ",0,"2/5*(x^2-1)^(5/4)","A"
7,1,10,9,0.063000," ","int(x*(x^2-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{3 \left(x^{2}-1\right)^{\frac{4}{3}}}{8}$&$10$\\ default&$\frac{3 \left(x^{2}-1\right)^{\frac{4}{3}}}{8}$&$10$\\ risch&$\frac{3 \left(x^{2}-1\right)^{\frac{4}{3}}}{8}$&$10$\\ gosper&$\frac{3 \left(-1+x \right) \left(1+x \right) \left(x^{2}-1\right)^{\frac{1}{3}}}{8}$&$16$\\ trager&$\left(\frac{3 x^{2}}{8}-\frac{3}{8}\right) \left(x^{2}-1\right)^{\frac{1}{3}}$&$16$\\ meijerg&$\frac{\mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{1}{3}, 1\right], \left[2\right], x^{2}\right) x^{2}}{2 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}}}$&$33$\\ \hline \end{longtable}"," ",0,"3/8*(x^2-1)^(4/3)","A"
8,1,10,9,0.063000," ","int(x*(x^2-1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{3 \left(x^{2}-1\right)^{\frac{5}{3}}}{10}$&$10$\\ default&$\frac{3 \left(x^{2}-1\right)^{\frac{5}{3}}}{10}$&$10$\\ risch&$\frac{3 \left(x^{2}-1\right)^{\frac{5}{3}}}{10}$&$10$\\ gosper&$\frac{3 \left(-1+x \right) \left(1+x \right) \left(x^{2}-1\right)^{\frac{2}{3}}}{10}$&$16$\\ trager&$\left(\frac{3 x^{2}}{10}-\frac{3}{10}\right) \left(x^{2}-1\right)^{\frac{2}{3}}$&$16$\\ meijerg&$\frac{\mathrm{signum}\left(x^{2}-1\right)^{\frac{2}{3}} \hypergeom \left(\left[-\frac{2}{3}, 1\right], \left[2\right], x^{2}\right) x^{2}}{2 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{2}{3}}}$&$33$\\ \hline \end{longtable}"," ",0,"3/10*(x^2-1)^(5/3)","A"
9,1,10,9,0.066000," ","int(x*(x^2-1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{2 \left(x^{2}-1\right)^{\frac{7}{4}}}{7}$&$10$\\ default&$\frac{2 \left(x^{2}-1\right)^{\frac{7}{4}}}{7}$&$10$\\ risch&$\frac{2 \left(x^{2}-1\right)^{\frac{7}{4}}}{7}$&$10$\\ gosper&$\frac{2 \left(-1+x \right) \left(1+x \right) \left(x^{2}-1\right)^{\frac{3}{4}}}{7}$&$16$\\ trager&$\left(\frac{2 x^{2}}{7}-\frac{2}{7}\right) \left(x^{2}-1\right)^{\frac{3}{4}}$&$16$\\ meijerg&$\frac{\mathrm{signum}\left(x^{2}-1\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{3}{4}, 1\right], \left[2\right], x^{2}\right) x^{2}}{2 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{3}{4}}}$&$33$\\ \hline \end{longtable}"," ",0,"2/7*(x^2-1)^(7/4)","A"
10,1,10,9,0.050000," ","int(x/(x^2+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{3 \left(x^{2}+1\right)^{\frac{2}{3}}}{4}$&$10$\\ derivativedivides&$\frac{3 \left(x^{2}+1\right)^{\frac{2}{3}}}{4}$&$10$\\ default&$\frac{3 \left(x^{2}+1\right)^{\frac{2}{3}}}{4}$&$10$\\ trager&$\frac{3 \left(x^{2}+1\right)^{\frac{2}{3}}}{4}$&$10$\\ risch&$\frac{3 \left(x^{2}+1\right)^{\frac{2}{3}}}{4}$&$10$\\ meijerg&$\frac{\hypergeom \left(\left[\frac{1}{3}, 1\right], \left[2\right], -x^{2}\right) x^{2}}{2}$&$17$\\ \hline \end{longtable}"," ",0,"3/4*(x^2+1)^(2/3)","A"
11,1,10,9,0.056000," ","int(x/(x^2+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{2 \left(x^{2}+1\right)^{\frac{3}{4}}}{3}$&$10$\\ derivativedivides&$\frac{2 \left(x^{2}+1\right)^{\frac{3}{4}}}{3}$&$10$\\ default&$\frac{2 \left(x^{2}+1\right)^{\frac{3}{4}}}{3}$&$10$\\ trager&$\frac{2 \left(x^{2}+1\right)^{\frac{3}{4}}}{3}$&$10$\\ risch&$\frac{2 \left(x^{2}+1\right)^{\frac{3}{4}}}{3}$&$10$\\ meijerg&$\frac{\hypergeom \left(\left[\frac{1}{4}, 1\right], \left[2\right], -x^{2}\right) x^{2}}{2}$&$17$\\ \hline \end{longtable}"," ",0,"2/3*(x^2+1)^(3/4)","A"
12,1,10,9,0.048000," ","int(x*(x^2+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{2 \left(x^{2}+1\right)^{\frac{5}{4}}}{5}$&$10$\\ derivativedivides&$\frac{2 \left(x^{2}+1\right)^{\frac{5}{4}}}{5}$&$10$\\ default&$\frac{2 \left(x^{2}+1\right)^{\frac{5}{4}}}{5}$&$10$\\ risch&$\frac{2 \left(x^{2}+1\right)^{\frac{5}{4}}}{5}$&$10$\\ trager&$\left(\frac{2}{5}+\frac{2 x^{2}}{5}\right) \left(x^{2}+1\right)^{\frac{1}{4}}$&$16$\\ meijerg&$\frac{\hypergeom \left(\left[-\frac{1}{4}, 1\right], \left[2\right], -x^{2}\right) x^{2}}{2}$&$17$\\ \hline \end{longtable}"," ",0,"2/5*(x^2+1)^(5/4)","A"
13,1,10,9,0.045000," ","int(x*(x^2+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{3 \left(x^{2}+1\right)^{\frac{4}{3}}}{8}$&$10$\\ derivativedivides&$\frac{3 \left(x^{2}+1\right)^{\frac{4}{3}}}{8}$&$10$\\ default&$\frac{3 \left(x^{2}+1\right)^{\frac{4}{3}}}{8}$&$10$\\ risch&$\frac{3 \left(x^{2}+1\right)^{\frac{4}{3}}}{8}$&$10$\\ trager&$\left(\frac{3}{8}+\frac{3 x^{2}}{8}\right) \left(x^{2}+1\right)^{\frac{1}{3}}$&$16$\\ meijerg&$\frac{\hypergeom \left(\left[-\frac{1}{3}, 1\right], \left[2\right], -x^{2}\right) x^{2}}{2}$&$17$\\ \hline \end{longtable}"," ",0,"3/8*(x^2+1)^(4/3)","A"
14,1,10,9,0.048000," ","int(x*(x^2+1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{2 \left(x^{2}+1\right)^{\frac{7}{4}}}{7}$&$10$\\ derivativedivides&$\frac{2 \left(x^{2}+1\right)^{\frac{7}{4}}}{7}$&$10$\\ default&$\frac{2 \left(x^{2}+1\right)^{\frac{7}{4}}}{7}$&$10$\\ risch&$\frac{2 \left(x^{2}+1\right)^{\frac{7}{4}}}{7}$&$10$\\ trager&$\left(\frac{2}{7}+\frac{2 x^{2}}{7}\right) \left(x^{2}+1\right)^{\frac{3}{4}}$&$16$\\ meijerg&$\frac{\hypergeom \left(\left[-\frac{3}{4}, 1\right], \left[2\right], -x^{2}\right) x^{2}}{2}$&$17$\\ \hline \end{longtable}"," ",0,"2/7*(x^2+1)^(7/4)","A"
15,1,10,9,0.077000," ","int(x^2/(x^3-1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{4 \left(x^{3}-1\right)^{\frac{3}{4}}}{9}$&$10$\\ default&$\frac{4 \left(x^{3}-1\right)^{\frac{3}{4}}}{9}$&$10$\\ trager&$\frac{4 \left(x^{3}-1\right)^{\frac{3}{4}}}{9}$&$10$\\ risch&$\frac{4 \left(x^{3}-1\right)^{\frac{3}{4}}}{9}$&$10$\\ gosper&$\frac{4 \left(-1+x \right) \left(x^{2}+x +1\right)}{9 \left(x^{3}-1\right)^{\frac{1}{4}}}$&$19$\\ meijerg&$\frac{\left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[\frac{1}{4}, 1\right], \left[2\right], x^{3}\right) x^{3}}{3 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}}}$&$33$\\ \hline \end{longtable}"," ",0,"4/9*(x^3-1)^(3/4)","A"
16,1,10,9,0.069000," ","int(x^2*(x^3-1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{4 \left(x^{3}-1\right)^{\frac{5}{4}}}{15}$&$10$\\ default&$\frac{4 \left(x^{3}-1\right)^{\frac{5}{4}}}{15}$&$10$\\ risch&$\frac{4 \left(x^{3}-1\right)^{\frac{5}{4}}}{15}$&$10$\\ trager&$\left(\frac{4 x^{3}}{15}-\frac{4}{15}\right) \left(x^{3}-1\right)^{\frac{1}{4}}$&$16$\\ gosper&$\frac{4 \left(-1+x \right) \left(x^{2}+x +1\right) \left(x^{3}-1\right)^{\frac{1}{4}}}{15}$&$19$\\ meijerg&$\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{1}{4}, 1\right], \left[2\right], x^{3}\right) x^{3}}{3 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}}}$&$33$\\ \hline \end{longtable}"," ",0,"4/15*(x^3-1)^(5/4)","A"
17,1,10,9,0.069000," ","int(x^2*(x^3-1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{4 \left(x^{3}-1\right)^{\frac{7}{4}}}{21}$&$10$\\ default&$\frac{4 \left(x^{3}-1\right)^{\frac{7}{4}}}{21}$&$10$\\ risch&$\frac{4 \left(x^{3}-1\right)^{\frac{7}{4}}}{21}$&$10$\\ trager&$\left(\frac{4 x^{3}}{21}-\frac{4}{21}\right) \left(x^{3}-1\right)^{\frac{3}{4}}$&$16$\\ gosper&$\frac{4 \left(-1+x \right) \left(x^{2}+x +1\right) \left(x^{3}-1\right)^{\frac{3}{4}}}{21}$&$19$\\ meijerg&$\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{3}{4}, 1\right], \left[2\right], x^{3}\right) x^{3}}{3 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{3}{4}}}$&$33$\\ \hline \end{longtable}"," ",0,"4/21*(x^3-1)^(7/4)","A"
18,1,10,9,0.115000," ","int(x^2/(x^3+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{2 \sqrt{x^{3}+1}}{3}$&$10$\\ default&$\frac{2 \sqrt{x^{3}+1}}{3}$&$10$\\ trager&$\frac{2 \sqrt{x^{3}+1}}{3}$&$10$\\ risch&$\frac{2 \sqrt{x^{3}+1}}{3}$&$10$\\ elliptic&$\frac{2 \sqrt{x^{3}+1}}{3}$&$10$\\ gosper&$\frac{2 \left(1+x \right) \left(x^{2}-x +1\right)}{3 \sqrt{x^{3}+1}}$&$21$\\ meijerg&$\frac{-2 \sqrt{\pi}+2 \sqrt{\pi}\, \sqrt{x^{3}+1}}{3 \sqrt{\pi}}$&$24$\\ \hline \end{longtable}"," ",0,"2/3*(x^3+1)^(1/2)","A"
19,1,10,9,0.057000," ","int(x^2/(x^3+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{4 \left(x^{3}+1\right)^{\frac{3}{4}}}{9}$&$10$\\ default&$\frac{4 \left(x^{3}+1\right)^{\frac{3}{4}}}{9}$&$10$\\ trager&$\frac{4 \left(x^{3}+1\right)^{\frac{3}{4}}}{9}$&$10$\\ risch&$\frac{4 \left(x^{3}+1\right)^{\frac{3}{4}}}{9}$&$10$\\ meijerg&$\frac{\hypergeom \left(\left[\frac{1}{4}, 1\right], \left[2\right], -x^{3}\right) x^{3}}{3}$&$17$\\ gosper&$\frac{4 \left(1+x \right) \left(x^{2}-x +1\right)}{9 \left(x^{3}+1\right)^{\frac{1}{4}}}$&$21$\\ \hline \end{longtable}"," ",0,"4/9*(x^3+1)^(3/4)","A"
20,1,10,9,0.053000," ","int(x^2*(x^3+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{4 \left(x^{3}+1\right)^{\frac{5}{4}}}{15}$&$10$\\ default&$\frac{4 \left(x^{3}+1\right)^{\frac{5}{4}}}{15}$&$10$\\ risch&$\frac{4 \left(x^{3}+1\right)^{\frac{5}{4}}}{15}$&$10$\\ trager&$\left(\frac{4}{15}+\frac{4 x^{3}}{15}\right) \left(x^{3}+1\right)^{\frac{1}{4}}$&$16$\\ meijerg&$\frac{\hypergeom \left(\left[-\frac{1}{4}, 1\right], \left[2\right], -x^{3}\right) x^{3}}{3}$&$17$\\ gosper&$\frac{4 \left(1+x \right) \left(x^{2}-x +1\right) \left(x^{3}+1\right)^{\frac{1}{4}}}{15}$&$21$\\ \hline \end{longtable}"," ",0,"4/15*(x^3+1)^(5/4)","A"
21,1,10,9,0.059000," ","int(x^2*(x^3+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\left(x^{3}+1\right)^{\frac{4}{3}}}{4}$&$10$\\ default&$\frac{\left(x^{3}+1\right)^{\frac{4}{3}}}{4}$&$10$\\ risch&$\frac{\left(x^{3}+1\right)^{\frac{4}{3}}}{4}$&$10$\\ trager&$\left(\frac{x^{3}}{4}+\frac{1}{4}\right) \left(x^{3}+1\right)^{\frac{1}{3}}$&$16$\\ meijerg&$\frac{\hypergeom \left(\left[-\frac{1}{3}, 1\right], \left[2\right], -x^{3}\right) x^{3}}{3}$&$17$\\ gosper&$\frac{\left(1+x \right) \left(x^{2}-x +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}}{4}$&$21$\\ \hline \end{longtable}"," ",0,"1/4*(x^3+1)^(4/3)","A"
22,1,10,9,0.046000," ","int(x^2*(x^3+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{2 \left(x^{3}+1\right)^{\frac{3}{2}}}{9}$&$10$\\ default&$\frac{2 \left(x^{3}+1\right)^{\frac{3}{2}}}{9}$&$10$\\ risch&$\frac{2 \left(x^{3}+1\right)^{\frac{3}{2}}}{9}$&$10$\\ trager&$\left(\frac{2}{9}+\frac{2 x^{3}}{9}\right) \sqrt{x^{3}+1}$&$16$\\ gosper&$\frac{2 \left(1+x \right) \left(x^{2}-x +1\right) \sqrt{x^{3}+1}}{9}$&$21$\\ meijerg&$-\frac{\frac{4 \sqrt{\pi}}{3}-\frac{2 \sqrt{\pi}\, \left(2 x^{3}+2\right) \sqrt{x^{3}+1}}{3}}{6 \sqrt{\pi}}$&$31$\\ \hline \end{longtable}"," ",0,"2/9*(x^3+1)^(3/2)","A"
23,1,10,9,0.048000," ","int(x^2*(x^3+1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\left(x^{3}+1\right)^{\frac{5}{3}}}{5}$&$10$\\ default&$\frac{\left(x^{3}+1\right)^{\frac{5}{3}}}{5}$&$10$\\ risch&$\frac{\left(x^{3}+1\right)^{\frac{5}{3}}}{5}$&$10$\\ trager&$\left(\frac{1}{5}+\frac{x^{3}}{5}\right) \left(x^{3}+1\right)^{\frac{2}{3}}$&$16$\\ meijerg&$\frac{\hypergeom \left(\left[-\frac{2}{3}, 1\right], \left[2\right], -x^{3}\right) x^{3}}{3}$&$17$\\ gosper&$\frac{\left(1+x \right) \left(x^{2}-x +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}}{5}$&$21$\\ \hline \end{longtable}"," ",0,"1/5*(x^3+1)^(5/3)","A"
24,1,10,9,0.053000," ","int(x^2*(x^3+1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{4 \left(x^{3}+1\right)^{\frac{7}{4}}}{21}$&$10$\\ default&$\frac{4 \left(x^{3}+1\right)^{\frac{7}{4}}}{21}$&$10$\\ risch&$\frac{4 \left(x^{3}+1\right)^{\frac{7}{4}}}{21}$&$10$\\ trager&$\left(\frac{4}{21}+\frac{4 x^{3}}{21}\right) \left(x^{3}+1\right)^{\frac{3}{4}}$&$16$\\ meijerg&$\frac{\hypergeom \left(\left[-\frac{3}{4}, 1\right], \left[2\right], -x^{3}\right) x^{3}}{3}$&$17$\\ gosper&$\frac{4 \left(1+x \right) \left(x^{2}-x +1\right) \left(x^{3}+1\right)^{\frac{3}{4}}}{21}$&$21$\\ \hline \end{longtable}"," ",0,"4/21*(x^3+1)^(7/4)","A"
25,1,10,9,0.075000," ","int((3*x^2+1)*(x^3+x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{3 \left(x^{3}+x \right)^{\frac{4}{3}}}{4}$&$10$\\ default&$\frac{3 \left(x^{3}+x \right)^{\frac{4}{3}}}{4}$&$10$\\ gosper&$\frac{3 \left(x^{2}+1\right) x \left(x^{3}+x \right)^{\frac{1}{3}}}{4}$&$16$\\ trager&$\frac{3 \left(x^{2}+1\right) x \left(x^{3}+x \right)^{\frac{1}{3}}}{4}$&$16$\\ risch&$\frac{3 \left(\left(x^{2}+1\right) x \right)^{\frac{1}{3}} \left(x^{2}+1\right) x}{4}$&$18$\\ meijerg&$\frac{3 \hypergeom \left(\left[-\frac{1}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], -x^{2}\right) x^{\frac{4}{3}}}{4}+\frac{9 \hypergeom \left(\left[-\frac{1}{3}, \frac{5}{3}\right], \left[\frac{8}{3}\right], -x^{2}\right) x^{\frac{10}{3}}}{10}$&$34$\\ \hline \end{longtable}"," ",0,"3/4*(x^3+x)^(4/3)","A"
26,1,12,11,0.076000," ","int(1/x^2/(x^4-1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{4}-1\right)^{\frac{1}{4}}}{x}$&$12$\\ risch&$\frac{\left(x^{4}-1\right)^{\frac{1}{4}}}{x}$&$12$\\ gosper&$\frac{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}{x \left(x^{4}-1\right)^{\frac{3}{4}}}$&$23$\\ meijerg&$-\frac{\left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{3}{4}} \left(-x^{4}+1\right)^{\frac{1}{4}}}{\mathrm{signum}\left(x^{4}-1\right)^{\frac{3}{4}} x}$&$33$\\ \hline \end{longtable}"," ",0,"(x^4-1)^(1/4)/x","A"
27,1,10,9,0.070000," ","int(x^3/(x^4-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{3 \left(x^{4}-1\right)^{\frac{2}{3}}}{8}$&$10$\\ default&$\frac{3 \left(x^{4}-1\right)^{\frac{2}{3}}}{8}$&$10$\\ trager&$\frac{3 \left(x^{4}-1\right)^{\frac{2}{3}}}{8}$&$10$\\ risch&$\frac{3 \left(x^{4}-1\right)^{\frac{2}{3}}}{8}$&$10$\\ gosper&$\frac{3 \left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}{8 \left(x^{4}-1\right)^{\frac{1}{3}}}$&$21$\\ meijerg&$\frac{\left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{3}} \hypergeom \left(\left[\frac{1}{3}, 1\right], \left[2\right], x^{4}\right) x^{4}}{4 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{3}}}$&$33$\\ \hline \end{longtable}"," ",0,"3/8*(x^4-1)^(2/3)","A"
28,1,10,9,0.069000," ","int(x^3*(x^4-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{3 \left(x^{4}-1\right)^{\frac{4}{3}}}{16}$&$10$\\ default&$\frac{3 \left(x^{4}-1\right)^{\frac{4}{3}}}{16}$&$10$\\ risch&$\frac{3 \left(x^{4}-1\right)^{\frac{4}{3}}}{16}$&$10$\\ trager&$\left(\frac{3 x^{4}}{16}-\frac{3}{16}\right) \left(x^{4}-1\right)^{\frac{1}{3}}$&$16$\\ gosper&$\frac{3 \left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right) \left(x^{4}-1\right)^{\frac{1}{3}}}{16}$&$21$\\ meijerg&$\frac{\mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{1}{3}, 1\right], \left[2\right], x^{4}\right) x^{4}}{4 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{3}}}$&$33$\\ \hline \end{longtable}"," ",0,"3/16*(x^4-1)^(4/3)","A"
29,1,10,9,0.068000," ","int(x^3*(x^4-1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{3 \left(x^{4}-1\right)^{\frac{5}{3}}}{20}$&$10$\\ default&$\frac{3 \left(x^{4}-1\right)^{\frac{5}{3}}}{20}$&$10$\\ risch&$\frac{3 \left(x^{4}-1\right)^{\frac{5}{3}}}{20}$&$10$\\ trager&$\left(\frac{3 x^{4}}{20}-\frac{3}{20}\right) \left(x^{4}-1\right)^{\frac{2}{3}}$&$16$\\ gosper&$\frac{3 \left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right) \left(x^{4}-1\right)^{\frac{2}{3}}}{20}$&$21$\\ meijerg&$\frac{\mathrm{signum}\left(x^{4}-1\right)^{\frac{2}{3}} \hypergeom \left(\left[-\frac{2}{3}, 1\right], \left[2\right], x^{4}\right) x^{4}}{4 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{2}{3}}}$&$33$\\ \hline \end{longtable}"," ",0,"3/20*(x^4-1)^(5/3)","A"
30,1,10,9,0.080000," ","int(x^3*(x^4-1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\left(x^{4}-1\right)^{\frac{7}{4}}}{7}$&$10$\\ default&$\frac{\left(x^{4}-1\right)^{\frac{7}{4}}}{7}$&$10$\\ risch&$\frac{\left(x^{4}-1\right)^{\frac{7}{4}}}{7}$&$10$\\ trager&$\left(\frac{x^{4}}{7}-\frac{1}{7}\right) \left(x^{4}-1\right)^{\frac{3}{4}}$&$16$\\ gosper&$\frac{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right) \left(x^{4}-1\right)^{\frac{3}{4}}}{7}$&$21$\\ meijerg&$\frac{\mathrm{signum}\left(x^{4}-1\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{3}{4}, 1\right], \left[2\right], x^{4}\right) x^{4}}{4 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{3}{4}}}$&$33$\\ \hline \end{longtable}"," ",0,"1/7*(x^4-1)^(7/4)","A"
31,1,12,11,0.118000," ","int((x^4-1)/x^2/(x^4+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{\sqrt{x^{4}+1}}{x}$&$12$\\ default&$\frac{\sqrt{x^{4}+1}}{x}$&$12$\\ trager&$\frac{\sqrt{x^{4}+1}}{x}$&$12$\\ risch&$\frac{\sqrt{x^{4}+1}}{x}$&$12$\\ elliptic&$\frac{\sqrt{x^{4}+1}}{x}$&$12$\\ meijerg&$\frac{\hypergeom \left(\left[\frac{1}{2}, \frac{3}{4}\right], \left[\frac{7}{4}\right], -x^{4}\right) x^{3}}{3}+\frac{\hypergeom \left(\left[-\frac{1}{4}, \frac{1}{2}\right], \left[\frac{3}{4}\right], -x^{4}\right)}{x}$&$33$\\ \hline \end{longtable}"," ",0,"(x^4+1)^(1/2)/x","A"
32,1,10,9,0.052000," ","int(x^3/(x^4+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{3 \left(x^{4}+1\right)^{\frac{2}{3}}}{8}$&$10$\\ derivativedivides&$\frac{3 \left(x^{4}+1\right)^{\frac{2}{3}}}{8}$&$10$\\ default&$\frac{3 \left(x^{4}+1\right)^{\frac{2}{3}}}{8}$&$10$\\ trager&$\frac{3 \left(x^{4}+1\right)^{\frac{2}{3}}}{8}$&$10$\\ risch&$\frac{3 \left(x^{4}+1\right)^{\frac{2}{3}}}{8}$&$10$\\ meijerg&$\frac{\hypergeom \left(\left[\frac{1}{3}, 1\right], \left[2\right], -x^{4}\right) x^{4}}{4}$&$17$\\ \hline \end{longtable}"," ",0,"3/8*(x^4+1)^(2/3)","A"
33,1,10,9,0.065000," ","int(x^3*(x^4+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{\left(x^{4}+1\right)^{\frac{5}{4}}}{5}$&$10$\\ derivativedivides&$\frac{\left(x^{4}+1\right)^{\frac{5}{4}}}{5}$&$10$\\ default&$\frac{\left(x^{4}+1\right)^{\frac{5}{4}}}{5}$&$10$\\ risch&$\frac{\left(x^{4}+1\right)^{\frac{5}{4}}}{5}$&$10$\\ trager&$\left(\frac{x^{4}}{5}+\frac{1}{5}\right) \left(x^{4}+1\right)^{\frac{1}{4}}$&$16$\\ meijerg&$\frac{\hypergeom \left(\left[-\frac{1}{4}, 1\right], \left[2\right], -x^{4}\right) x^{4}}{4}$&$17$\\ \hline \end{longtable}"," ",0,"1/5*(x^4+1)^(5/4)","A"
34,1,10,9,0.050000," ","int(x^3*(x^4+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{3 \left(x^{4}+1\right)^{\frac{4}{3}}}{16}$&$10$\\ derivativedivides&$\frac{3 \left(x^{4}+1\right)^{\frac{4}{3}}}{16}$&$10$\\ default&$\frac{3 \left(x^{4}+1\right)^{\frac{4}{3}}}{16}$&$10$\\ risch&$\frac{3 \left(x^{4}+1\right)^{\frac{4}{3}}}{16}$&$10$\\ trager&$\left(\frac{3}{16}+\frac{3 x^{4}}{16}\right) \left(x^{4}+1\right)^{\frac{1}{3}}$&$16$\\ meijerg&$\frac{\hypergeom \left(\left[-\frac{1}{3}, 1\right], \left[2\right], -x^{4}\right) x^{4}}{4}$&$17$\\ \hline \end{longtable}"," ",0,"3/16*(x^4+1)^(4/3)","A"
35,1,10,9,0.049000," ","int(x^3*(x^4+1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{3 \left(x^{4}+1\right)^{\frac{5}{3}}}{20}$&$10$\\ derivativedivides&$\frac{3 \left(x^{4}+1\right)^{\frac{5}{3}}}{20}$&$10$\\ default&$\frac{3 \left(x^{4}+1\right)^{\frac{5}{3}}}{20}$&$10$\\ risch&$\frac{3 \left(x^{4}+1\right)^{\frac{5}{3}}}{20}$&$10$\\ trager&$\left(\frac{3}{20}+\frac{3 x^{4}}{20}\right) \left(x^{4}+1\right)^{\frac{2}{3}}$&$16$\\ meijerg&$\frac{\hypergeom \left(\left[-\frac{2}{3}, 1\right], \left[2\right], -x^{4}\right) x^{4}}{4}$&$17$\\ \hline \end{longtable}"," ",0,"3/20*(x^4+1)^(5/3)","A"
36,1,10,9,0.084000," ","int(x^4*(x^5-1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{3 \left(x^{5}-1\right)^{\frac{5}{3}}}{25}$&$10$\\ default&$\frac{3 \left(x^{5}-1\right)^{\frac{5}{3}}}{25}$&$10$\\ risch&$\frac{3 \left(x^{5}-1\right)^{\frac{5}{3}}}{25}$&$10$\\ trager&$\left(\frac{3 x^{5}}{25}-\frac{3}{25}\right) \left(x^{5}-1\right)^{\frac{2}{3}}$&$16$\\ gosper&$\frac{3 \left(-1+x \right) \left(x^{4}+x^{3}+x^{2}+x +1\right) \left(x^{5}-1\right)^{\frac{2}{3}}}{25}$&$25$\\ meijerg&$\frac{\mathrm{signum}\left(x^{5}-1\right)^{\frac{2}{3}} \hypergeom \left(\left[-\frac{2}{3}, 1\right], \left[2\right], x^{5}\right) x^{5}}{5 \left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{2}{3}}}$&$33$\\ \hline \end{longtable}"," ",0,"3/25*(x^5-1)^(5/3)","A"
37,1,10,9,0.066000," ","int(x^4*(x^5+1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{3 \left(x^{5}+1\right)^{\frac{5}{3}}}{25}$&$10$\\ default&$\frac{3 \left(x^{5}+1\right)^{\frac{5}{3}}}{25}$&$10$\\ risch&$\frac{3 \left(x^{5}+1\right)^{\frac{5}{3}}}{25}$&$10$\\ trager&$\left(\frac{3}{25}+\frac{3 x^{5}}{25}\right) \left(x^{5}+1\right)^{\frac{2}{3}}$&$16$\\ meijerg&$\frac{\hypergeom \left(\left[-\frac{2}{3}, 1\right], \left[2\right], -x^{5}\right) x^{5}}{5}$&$17$\\ gosper&$\frac{3 \left(1+x \right) \left(x^{4}-x^{3}+x^{2}-x +1\right) \left(x^{5}+1\right)^{\frac{2}{3}}}{25}$&$29$\\ \hline \end{longtable}"," ",0,"3/25*(x^5+1)^(5/3)","A"
38,1,10,9,0.075000," ","int(x^5/(x^6-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\left(x^{6}-1\right)^{\frac{2}{3}}}{4}$&$10$\\ default&$\frac{\left(x^{6}-1\right)^{\frac{2}{3}}}{4}$&$10$\\ trager&$\frac{\left(x^{6}-1\right)^{\frac{2}{3}}}{4}$&$10$\\ risch&$\frac{\left(x^{6}-1\right)^{\frac{2}{3}}}{4}$&$10$\\ gosper&$\frac{\left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right)}{4 \left(x^{6}-1\right)^{\frac{1}{3}}}$&$30$\\ meijerg&$\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} \hypergeom \left(\left[\frac{1}{3}, 1\right], \left[2\right], x^{6}\right) x^{6}}{6 \mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}}}$&$33$\\ \hline \end{longtable}"," ",0,"1/4*(x^6-1)^(2/3)","A"
39,1,10,9,0.088000," ","int(x^5*(x^6-1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{2 \left(x^{6}-1\right)^{\frac{5}{4}}}{15}$&$10$\\ default&$\frac{2 \left(x^{6}-1\right)^{\frac{5}{4}}}{15}$&$10$\\ risch&$\frac{2 \left(x^{6}-1\right)^{\frac{5}{4}}}{15}$&$10$\\ trager&$\left(\frac{2 x^{6}}{15}-\frac{2}{15}\right) \left(x^{6}-1\right)^{\frac{1}{4}}$&$16$\\ gosper&$\frac{2 \left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right) \left(x^{6}-1\right)^{\frac{1}{4}}}{15}$&$30$\\ meijerg&$\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{1}{4}, 1\right], \left[2\right], x^{6}\right) x^{6}}{6 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{4}}}$&$33$\\ \hline \end{longtable}"," ",0,"2/15*(x^6-1)^(5/4)","A"
40,1,10,9,0.072000," ","int(x^5*(x^6-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\left(x^{6}-1\right)^{\frac{4}{3}}}{8}$&$10$\\ default&$\frac{\left(x^{6}-1\right)^{\frac{4}{3}}}{8}$&$10$\\ risch&$\frac{\left(x^{6}-1\right)^{\frac{4}{3}}}{8}$&$10$\\ trager&$\left(\frac{x^{6}}{8}-\frac{1}{8}\right) \left(x^{6}-1\right)^{\frac{1}{3}}$&$16$\\ gosper&$\frac{\left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right) \left(x^{6}-1\right)^{\frac{1}{3}}}{8}$&$30$\\ meijerg&$\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{1}{3}, 1\right], \left[2\right], x^{6}\right) x^{6}}{6 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}}}$&$33$\\ \hline \end{longtable}"," ",0,"1/8*(x^6-1)^(4/3)","A"
41,1,10,9,0.075000," ","int(x^5*(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\left(x^{6}-1\right)^{\frac{3}{2}}}{9}$&$10$\\ default&$\frac{\left(x^{6}-1\right)^{\frac{3}{2}}}{9}$&$10$\\ risch&$\frac{\left(x^{6}-1\right)^{\frac{3}{2}}}{9}$&$10$\\ trager&$\left(\frac{x^{6}}{9}-\frac{1}{9}\right) \sqrt{x^{6}-1}$&$16$\\ gosper&$\frac{\left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right) \sqrt{x^{6}-1}}{9}$&$30$\\ meijerg&$\frac{\sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(\frac{4 \sqrt{\pi}}{3}-\frac{2 \sqrt{\pi}\, \left(-2 x^{6}+2\right) \sqrt{-x^{6}+1}}{3}\right)}{12 \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$51$\\ \hline \end{longtable}"," ",0,"1/9*(x^6-1)^(3/2)","A"
42,1,10,9,0.075000," ","int(x^5*(x^6-1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{2 \left(x^{6}-1\right)^{\frac{7}{4}}}{21}$&$10$\\ default&$\frac{2 \left(x^{6}-1\right)^{\frac{7}{4}}}{21}$&$10$\\ risch&$\frac{2 \left(x^{6}-1\right)^{\frac{7}{4}}}{21}$&$10$\\ trager&$\left(\frac{2 x^{6}}{21}-\frac{2}{21}\right) \left(x^{6}-1\right)^{\frac{3}{4}}$&$16$\\ gosper&$\frac{2 \left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right) \left(x^{6}-1\right)^{\frac{3}{4}}}{21}$&$30$\\ meijerg&$\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{3}{4}, 1\right], \left[2\right], x^{6}\right) x^{6}}{6 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{3}{4}}}$&$33$\\ \hline \end{longtable}"," ",0,"2/21*(x^6-1)^(7/4)","A"
43,1,12,11,0.076000," ","int((x^6-2)/x^3/(x^6+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}+1}}{x^{2}}$&$12$\\ risch&$\frac{\sqrt{x^{6}+1}}{x^{2}}$&$12$\\ gosper&$\frac{\left(x^{4}-x^{2}+1\right) \left(x^{2}+1\right)}{x^{2} \sqrt{x^{6}+1}}$&$27$\\ meijerg&$\frac{\hypergeom \left(\left[\frac{1}{2}, \frac{2}{3}\right], \left[\frac{5}{3}\right], -x^{6}\right) x^{4}}{4}+\frac{\hypergeom \left(\left[-\frac{1}{3}, \frac{1}{2}\right], \left[\frac{2}{3}\right], -x^{6}\right)}{x^{2}}$&$33$\\ \hline \end{longtable}"," ",0,"(x^6+1)^(1/2)/x^2","A"
44,1,10,9,0.053000," ","int(x^5/(x^6+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\left(x^{6}+1\right)^{\frac{2}{3}}}{4}$&$10$\\ default&$\frac{\left(x^{6}+1\right)^{\frac{2}{3}}}{4}$&$10$\\ trager&$\frac{\left(x^{6}+1\right)^{\frac{2}{3}}}{4}$&$10$\\ risch&$\frac{\left(x^{6}+1\right)^{\frac{2}{3}}}{4}$&$10$\\ meijerg&$\frac{\hypergeom \left(\left[\frac{1}{3}, 1\right], \left[2\right], -x^{6}\right) x^{6}}{6}$&$17$\\ gosper&$\frac{\left(x^{2}+1\right) \left(x^{4}-x^{2}+1\right)}{4 \left(x^{6}+1\right)^{\frac{1}{3}}}$&$25$\\ \hline \end{longtable}"," ",0,"1/4*(x^6+1)^(2/3)","A"
45,1,10,9,0.070000," ","int(x^5*(x^6+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{2 \left(x^{6}+1\right)^{\frac{5}{4}}}{15}$&$10$\\ default&$\frac{2 \left(x^{6}+1\right)^{\frac{5}{4}}}{15}$&$10$\\ risch&$\frac{2 \left(x^{6}+1\right)^{\frac{5}{4}}}{15}$&$10$\\ trager&$\left(\frac{2}{15}+\frac{2 x^{6}}{15}\right) \left(x^{6}+1\right)^{\frac{1}{4}}$&$16$\\ meijerg&$\frac{\hypergeom \left(\left[-\frac{1}{4}, 1\right], \left[2\right], -x^{6}\right) x^{6}}{6}$&$17$\\ gosper&$\frac{2 \left(x^{2}+1\right) \left(x^{4}-x^{2}+1\right) \left(x^{6}+1\right)^{\frac{1}{4}}}{15}$&$25$\\ \hline \end{longtable}"," ",0,"2/15*(x^6+1)^(5/4)","A"
46,1,10,9,0.054000," ","int(x^5*(x^6+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\left(x^{6}+1\right)^{\frac{4}{3}}}{8}$&$10$\\ default&$\frac{\left(x^{6}+1\right)^{\frac{4}{3}}}{8}$&$10$\\ risch&$\frac{\left(x^{6}+1\right)^{\frac{4}{3}}}{8}$&$10$\\ trager&$\left(\frac{1}{8}+\frac{x^{6}}{8}\right) \left(x^{6}+1\right)^{\frac{1}{3}}$&$16$\\ meijerg&$\frac{\hypergeom \left(\left[-\frac{1}{3}, 1\right], \left[2\right], -x^{6}\right) x^{6}}{6}$&$17$\\ gosper&$\frac{\left(x^{2}+1\right) \left(x^{4}-x^{2}+1\right) \left(x^{6}+1\right)^{\frac{1}{3}}}{8}$&$25$\\ \hline \end{longtable}"," ",0,"1/8*(x^6+1)^(4/3)","A"
47,1,13,12,0.090000," ","int((x^3-4)/x^2/(x^3-1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{4 \left(x^{3}-1\right)^{\frac{1}{4}}}{x}$&$13$\\ risch&$-\frac{4 \left(x^{3}-1\right)^{\frac{1}{4}}}{x}$&$13$\\ gosper&$-\frac{4 \left(-1+x \right) \left(x^{2}+x +1\right)}{x \left(x^{3}-1\right)^{\frac{3}{4}}}$&$22$\\ meijerg&$\frac{\left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[\frac{2}{3}, \frac{3}{4}\right], \left[\frac{5}{3}\right], x^{3}\right) x^{2}}{2 \mathrm{signum}\left(x^{3}-1\right)^{\frac{3}{4}}}+\frac{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{1}{3}, \frac{3}{4}\right], \left[\frac{2}{3}\right], x^{3}\right)}{\mathrm{signum}\left(x^{3}-1\right)^{\frac{3}{4}} x}$&$66$\\ \hline \end{longtable}"," ",0,"-4*(x^3-1)^(1/4)/x","A"
48,1,11,10,0.287000," ","int(1/x/(x^3+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 \arctanh \left(\sqrt{x^{3}+1}\right)}{3}$&$11$\\ elliptic&$-\frac{2 \arctanh \left(\sqrt{x^{3}+1}\right)}{3}$&$11$\\ trager&$-\frac{\ln \left(-\frac{x^{3}+2 \sqrt{x^{3}+1}+2}{x^{3}}\right)}{3}$&$23$\\ meijerg&$\frac{\left(-2 \ln \left(2\right)+3 \ln \left(x \right)\right) \sqrt{\pi}-2 \ln \left(\frac{1}{2}+\frac{\sqrt{x^{3}+1}}{2}\right) \sqrt{\pi}}{3 \sqrt{\pi}}$&$37$\\ \hline \end{longtable}"," ",0,"-2/3*arctanh((x^3+1)^(1/2))","A"
49,1,13,12,0.069000," ","int((x^3+4)/x^2/(x^3+1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{4 \left(x^{3}+1\right)^{\frac{1}{4}}}{x}$&$13$\\ risch&$-\frac{4 \left(x^{3}+1\right)^{\frac{1}{4}}}{x}$&$13$\\ gosper&$-\frac{4 \left(1+x \right) \left(x^{2}-x +1\right)}{x \left(x^{3}+1\right)^{\frac{3}{4}}}$&$24$\\ meijerg&$\frac{\hypergeom \left(\left[\frac{2}{3}, \frac{3}{4}\right], \left[\frac{5}{3}\right], -x^{3}\right) x^{2}}{2}-\frac{4 \hypergeom \left(\left[-\frac{1}{3}, \frac{3}{4}\right], \left[\frac{2}{3}\right], -x^{3}\right)}{x}$&$34$\\ \hline \end{longtable}"," ",0,"-4*(x^3+1)^(1/4)/x","A"
50,1,11,10,0.070000," ","int((3*x^2+2)*(x^3+x)^(1/3)/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{3 x \left(x^{3}+x \right)^{\frac{1}{3}}}{2}$&$11$\\ trager&$\frac{3 x \left(x^{3}+x \right)^{\frac{1}{3}}}{2}$&$11$\\ risch&$\frac{3 \left(\left(x^{2}+1\right) x \right)^{\frac{1}{3}} x}{2}$&$13$\\ meijerg&$\frac{3 \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], -x^{2}\right) x^{\frac{4}{3}}}{2}+\frac{9 \hypergeom \left(\left[\frac{2}{3}, \frac{5}{3}\right], \left[\frac{8}{3}\right], -x^{2}\right) x^{\frac{10}{3}}}{10}$&$34$\\ \hline \end{longtable}"," ",0,"3/2*x*(x^3+x)^(1/3)","A"
51,1,13,12,0.106000," ","int((-2+x)/(-1+x)/(x^3-x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{4 x}{\left(\left(-1+x \right) x^{2}\right)^{\frac{1}{4}}}$&$13$\\ gosper&$\frac{4 x}{\left(x^{3}-x^{2}\right)^{\frac{1}{4}}}$&$15$\\ trager&$\frac{4 \left(x^{3}-x^{2}\right)^{\frac{3}{4}}}{x \left(-1+x \right)}$&$22$\\ meijerg&$\frac{4 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{4}} \hypergeom \left(\left[\frac{1}{2}, \frac{5}{4}\right], \left[\frac{3}{2}\right], x\right) \sqrt{x}}{\mathrm{signum}\left(-1+x \right)^{\frac{1}{4}}}-\frac{2 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{4}} \hypergeom \left(\left[\frac{5}{4}, \frac{3}{2}\right], \left[\frac{5}{2}\right], x\right) x^{\frac{3}{2}}}{3 \mathrm{signum}\left(-1+x \right)^{\frac{1}{4}}}$&$54$\\ \hline \end{longtable}"," ",0,"4*x/((-1+x)*x^2)^(1/4)","A"
52,1,13,12,0.083000," ","int((2+x)/(1+x)/(x^3+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{4 x}{\left(x^{3}+x^{2}\right)^{\frac{1}{4}}}$&$13$\\ risch&$\frac{4 x}{\left(x^{2} \left(1+x \right)\right)^{\frac{1}{4}}}$&$13$\\ trager&$\frac{4 \left(x^{3}+x^{2}\right)^{\frac{3}{4}}}{x \left(1+x \right)}$&$20$\\ meijerg&$4 \hypergeom \left(\left[\frac{1}{2}, \frac{5}{4}\right], \left[\frac{3}{2}\right], -x \right) \sqrt{x}+\frac{2 \hypergeom \left(\left[\frac{5}{4}, \frac{3}{2}\right], \left[\frac{5}{2}\right], -x \right) x^{\frac{3}{2}}}{3}$&$30$\\ \hline \end{longtable}"," ",0,"4*x/(x^3+x^2)^(1/4)","A"
53,1,13,12,0.055000," ","int(1/x^2/(x^4+1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{\left(x^{4}+1\right)^{\frac{1}{4}}}{x}$&$13$\\ trager&$-\frac{\left(x^{4}+1\right)^{\frac{1}{4}}}{x}$&$13$\\ meijerg&$-\frac{\left(x^{4}+1\right)^{\frac{1}{4}}}{x}$&$13$\\ risch&$-\frac{\left(x^{4}+1\right)^{\frac{1}{4}}}{x}$&$13$\\ \hline \end{longtable}"," ",0,"-(x^4+1)^(1/4)/x","A"
54,1,13,12,0.062000," ","int((x^4+3)/x^4/(x^4+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{\sqrt{x^{4}+1}}{x^{3}}$&$13$\\ default&$-\frac{\sqrt{x^{4}+1}}{x^{3}}$&$13$\\ trager&$-\frac{\sqrt{x^{4}+1}}{x^{3}}$&$13$\\ risch&$-\frac{\sqrt{x^{4}+1}}{x^{3}}$&$13$\\ elliptic&$-\frac{\sqrt{x^{4}+1}}{x^{3}}$&$13$\\ meijerg&$\hypergeom \left(\left[\frac{1}{4}, \frac{1}{2}\right], \left[\frac{5}{4}\right], -x^{4}\right) x -\frac{\hypergeom \left(\left[-\frac{3}{4}, \frac{1}{2}\right], \left[\frac{1}{4}\right], -x^{4}\right)}{x^{3}}$&$31$\\ \hline \end{longtable}"," ",0,"-(x^4+1)^(1/2)/x^3","A"
55,1,13,12,0.903000," ","int((4*x^3-1)/(2*x^4-2*x-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\sqrt{2 x^{4}-2 x -1}$&$13$\\ default&$\sqrt{2 x^{4}-2 x -1}$&$13$\\ trager&$\sqrt{2 x^{4}-2 x -1}$&$13$\\ risch&$\sqrt{2 x^{4}-2 x -1}$&$13$\\ elliptic&$\sqrt{2 x^{4}-2 x -1}$&$13$\\ \hline \end{longtable}"," ",0,"(2*x^4-2*x-1)^(1/2)","A"
56,1,13,12,0.082000," ","int((x^5-4)/x^2/(x^5+1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{5}+1\right)^{\frac{1}{4}}}{x}$&$13$\\ risch&$\frac{4 \left(x^{5}+1\right)^{\frac{1}{4}}}{x}$&$13$\\ gosper&$\frac{4 \left(1+x \right) \left(x^{4}-x^{3}+x^{2}-x +1\right)}{x \left(x^{5}+1\right)^{\frac{3}{4}}}$&$32$\\ meijerg&$\frac{\hypergeom \left(\left[\frac{3}{4}, \frac{4}{5}\right], \left[\frac{9}{5}\right], -x^{5}\right) x^{4}}{4}+\frac{4 \hypergeom \left(\left[-\frac{1}{5}, \frac{3}{4}\right], \left[\frac{4}{5}\right], -x^{5}\right)}{x}$&$34$\\ \hline \end{longtable}"," ",0,"4*(x^5+1)^(1/4)/x","A"
57,1,13,12,0.093000," ","int((x^5+4)/x^2/(x^5-1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{5}-1\right)^{\frac{1}{4}}}{x}$&$13$\\ risch&$\frac{4 \left(x^{5}-1\right)^{\frac{1}{4}}}{x}$&$13$\\ gosper&$\frac{4 \left(-1+x \right) \left(x^{4}+x^{3}+x^{2}+x +1\right)}{x \left(x^{5}-1\right)^{\frac{3}{4}}}$&$28$\\ meijerg&$\frac{\left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[\frac{3}{4}, \frac{4}{5}\right], \left[\frac{9}{5}\right], x^{5}\right) x^{4}}{4 \mathrm{signum}\left(x^{5}-1\right)^{\frac{3}{4}}}-\frac{4 \left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{1}{5}, \frac{3}{4}\right], \left[\frac{4}{5}\right], x^{5}\right)}{\mathrm{signum}\left(x^{5}-1\right)^{\frac{3}{4}} x}$&$66$\\ \hline \end{longtable}"," ",0,"4*(x^5-1)^(1/4)/x","A"
58,1,60,12,0.413000," ","int((5*x^3+2)/(x^3+1)^(1/2)/(x^5+x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{5}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 x \sqrt{x^{3}+1}+\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{5}+x^{2}+1}\right)$&$60$\\ default&$-\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{5}+\textit{\_Z}^{2}+1\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{3}+1\right) \left(\underline{\hspace{1.25 ex}}\alpha^{4}-\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha^{2}\right) \left(3-i \sqrt{3}\right) \sqrt{\frac{1+x}{3-i \sqrt{3}}}\, \sqrt{\frac{-1+2 x -i \sqrt{3}}{-3-i \sqrt{3}}}\, \sqrt{\frac{-1+2 x +i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{3 \underline{\hspace{1.25 ex}}\alpha^{4}}{2}+\frac{3 \underline{\hspace{1.25 ex}}\alpha^{3}}{2}-\frac{3 \underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{i \underline{\hspace{1.25 ex}}\alpha^{4} \sqrt{3}}{2}-\frac{i \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{3}}{2}+\frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}}{2}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}\right)$&$197$\\ elliptic&$-\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{5}+\textit{\_Z}^{2}+1\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{3}+1\right) \left(\underline{\hspace{1.25 ex}}\alpha^{4}-\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha^{2}\right) \left(3-i \sqrt{3}\right) \sqrt{\frac{1+x}{3-i \sqrt{3}}}\, \sqrt{\frac{-1+2 x -i \sqrt{3}}{-3-i \sqrt{3}}}\, \sqrt{\frac{-1+2 x +i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{3 \underline{\hspace{1.25 ex}}\alpha^{4}}{2}+\frac{3 \underline{\hspace{1.25 ex}}\alpha^{3}}{2}-\frac{3 \underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{i \underline{\hspace{1.25 ex}}\alpha^{4} \sqrt{3}}{2}-\frac{i \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{3}}{2}+\frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}}{2}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}\right)$&$197$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2+1)*ln(-(-RootOf(_Z^2+1)*x^5-RootOf(_Z^2+1)*x^2+2*x*(x^3+1)^(1/2)+RootOf(_Z^2+1))/(x^5+x^2+1))","C"
59,1,7,10,0.381000," ","int(1/x/(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\arcsin \left(\frac{1}{x^{3}}\right)}{3}$&$7$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{3}$&$28$\\ meijerg&$\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(\left(-2 \ln \left(2\right)+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}-2 \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right) \sqrt{\pi}\right)}{6 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$61$\\ \hline \end{longtable}"," ",0,"-1/3*arcsin(1/x^3)","A"
60,1,13,12,0.083000," ","int((x^6-2)/x^2/(x^6+1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{6}+1\right)^{\frac{1}{4}}}{x}$&$13$\\ risch&$\frac{2 \left(x^{6}+1\right)^{\frac{1}{4}}}{x}$&$13$\\ gosper&$\frac{2 \left(x^{2}+1\right) \left(x^{4}-x^{2}+1\right)}{x \left(x^{6}+1\right)^{\frac{3}{4}}}$&$28$\\ meijerg&$\frac{\hypergeom \left(\left[\frac{3}{4}, \frac{5}{6}\right], \left[\frac{11}{6}\right], -x^{6}\right) x^{5}}{5}+\frac{2 \hypergeom \left(\left[-\frac{1}{6}, \frac{3}{4}\right], \left[\frac{5}{6}\right], -x^{6}\right)}{x}$&$34$\\ \hline \end{longtable}"," ",0,"2*(x^6+1)^(1/4)/x","A"
61,1,17,10,0.215000," ","int(1/x/(x^6+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(\frac{\sqrt{x^{6}+1}-1}{x^{3}}\right)}{3}$&$17$\\ default&$\frac{\ln \left(\frac{\sqrt{x^{6}+1}-1}{\sqrt{x^{6}}}\right)}{3}$&$19$\\ meijerg&$\frac{\left(-2 \ln \left(2\right)+6 \ln \left(x \right)\right) \sqrt{\pi}-2 \ln \left(\frac{1}{2}+\frac{\sqrt{x^{6}+1}}{2}\right) \sqrt{\pi}}{6 \sqrt{\pi}}$&$37$\\ \hline \end{longtable}"," ",0,"1/3*ln(((x^6+1)^(1/2)-1)/x^3)","A"
62,1,13,12,0.095000," ","int((x^6+2)/x^2/(x^6-1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{6}-1\right)^{\frac{1}{4}}}{x}$&$13$\\ risch&$\frac{2 \left(x^{6}-1\right)^{\frac{1}{4}}}{x}$&$13$\\ gosper&$\frac{2 \left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right)}{x \left(x^{6}-1\right)^{\frac{3}{4}}}$&$33$\\ meijerg&$\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[\frac{3}{4}, \frac{5}{6}\right], \left[\frac{11}{6}\right], x^{6}\right) x^{5}}{5 \mathrm{signum}\left(x^{6}-1\right)^{\frac{3}{4}}}-\frac{2 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{1}{6}, \frac{3}{4}\right], \left[\frac{5}{6}\right], x^{6}\right)}{\mathrm{signum}\left(x^{6}-1\right)^{\frac{3}{4}} x}$&$66$\\ \hline \end{longtable}"," ",0,"2*(x^6-1)^(1/4)/x","A"
63,1,36,12,0.190000," ","int((2*x^6-1)/(x^6+1)^(1/2)/(x^6-x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\ln \left(-\frac{x^{6}+2 \sqrt{x^{6}+1}\, x +x^{2}+1}{x^{6}-x^{2}+1}\right)}{2}$&$36$\\ \hline \end{longtable}"," ",0,"-1/2*ln(-(x^6+2*(x^6+1)^(1/2)*x+x^2+1)/(x^6-x^2+1))","B"
64,1,62,12,0.332000," ","int((2*x^6+1)/(x^6-1)^(1/2)/(x^6+x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \sqrt{x^{6}-1}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{6}+x^{2}-1}\right)}{2}$&$62$\\ \hline \end{longtable}"," ",0,"-1/2*RootOf(_Z^2+1)*ln(-(RootOf(_Z^2+1)*x^6-RootOf(_Z^2+1)*x^2+2*(x^6-1)^(1/2)*x-RootOf(_Z^2+1))/(x^6+x^2-1))","C"
65,1,12,11,0.079000," ","int((3*x^2-1)/(x^3-x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{3 \left(x^{3}-x \right)^{\frac{2}{3}}}{2}$&$12$\\ default&$\frac{3 \left(x^{3}-x \right)^{\frac{2}{3}}}{2}$&$12$\\ trager&$\frac{3 \left(x^{3}-x \right)^{\frac{2}{3}}}{2}$&$12$\\ risch&$\frac{3 x \left(x^{2}-1\right)}{2 \left(x \left(x^{2}-1\right)\right)^{\frac{1}{3}}}$&$18$\\ gosper&$\frac{3 \left(1+x \right) \left(-1+x \right) x}{2 \left(x^{3}-x \right)^{\frac{1}{3}}}$&$19$\\ meijerg&$-\frac{3 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{2}\right) x^{\frac{2}{3}}}{2 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}}}+\frac{9 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{4}{3}\right], \left[\frac{7}{3}\right], x^{2}\right) x^{\frac{8}{3}}}{8 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}}}$&$66$\\ \hline \end{longtable}"," ",0,"3/2*(x^3-x)^(2/3)","A"
66,1,12,11,0.079000," ","int((3*x^2-1)*(x^3-x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{3 \left(x^{3}-x \right)^{\frac{4}{3}}}{4}$&$12$\\ default&$\frac{3 \left(x^{3}-x \right)^{\frac{4}{3}}}{4}$&$12$\\ trager&$\frac{3 x \left(x^{2}-1\right) \left(x^{3}-x \right)^{\frac{1}{3}}}{4}$&$18$\\ risch&$\frac{3 \left(x \left(x^{2}-1\right)\right)^{\frac{1}{3}} x \left(x^{2}-1\right)}{4}$&$18$\\ gosper&$\frac{3 \left(1+x \right) \left(-1+x \right) x \left(x^{3}-x \right)^{\frac{1}{3}}}{4}$&$19$\\ meijerg&$-\frac{3 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], x^{2}\right) x^{\frac{4}{3}}}{4 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}}}+\frac{9 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{5}{3}\right], \left[\frac{8}{3}\right], x^{2}\right) x^{\frac{10}{3}}}{10 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}}}$&$66$\\ \hline \end{longtable}"," ",0,"3/4*(x^3-x)^(4/3)","A"
67,1,37,13,0.951000," ","int((-x^3+x+2)/(x^3+x+1)^(1/2)/(x^3-x^2+x+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(-\frac{x^{3}+2 \sqrt{x^{3}+x +1}\, x +x^{2}+x +1}{x^{3}-x^{2}+x +1}\right)$&$37$\\ default&$\text{Expression too large to display}$&$1905$\\ elliptic&$\text{Expression too large to display}$&$1905$\\ \hline \end{longtable}"," ",0,"ln(-(x^3+2*(x^3+x+1)^(1/2)*x+x^2+x+1)/(x^3-x^2+x+1))","B"
68,1,16,13,0.320000," ","int((x^4+1)/(-x^4+1)/(x^4+x^2-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\arctanh \left(\frac{\sqrt{x^{4}+x^{2}-1}}{x}\right)$&$16$\\ trager&$\frac{\ln \left(-\frac{x^{4}+2 \sqrt{x^{4}+x^{2}-1}\, x +2 x^{2}-1}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)}{2}$&$46$\\ default&$-\frac{2 \sqrt{1-\left(\frac{1}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \sqrt{1-\left(\frac{1}{2}+\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{2-2 \sqrt{5}}}{2}, \frac{i}{2}+\frac{i \sqrt{5}}{2}\right)}{\sqrt{2-2 \sqrt{5}}\, \sqrt{x^{4}+x^{2}-1}}+\frac{\sqrt{1-\left(\frac{1}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \sqrt{1-\left(\frac{1}{2}+\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{1}{2}-\frac{\sqrt{5}}{2}}\, x , \frac{1}{\frac{1}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}}}{\sqrt{\frac{1}{2}-\frac{\sqrt{5}}{2}}}\right)}{\sqrt{\frac{1}{2}-\frac{\sqrt{5}}{2}}\, \sqrt{x^{4}+x^{2}-1}}+\frac{\sqrt{1-\frac{x^{2}}{2}+\frac{\sqrt{5}\, x^{2}}{2}}\, \sqrt{1-\frac{x^{2}}{2}-\frac{\sqrt{5}\, x^{2}}{2}}\, \EllipticPi \left(\sqrt{\frac{1}{2}-\frac{\sqrt{5}}{2}}\, x , -\frac{1}{\frac{1}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}}}{\sqrt{\frac{1}{2}-\frac{\sqrt{5}}{2}}}\right)}{\sqrt{\frac{1}{2}-\frac{\sqrt{5}}{2}}\, \sqrt{x^{4}+x^{2}-1}}$&$265$\\ \hline \end{longtable}"," ",0,"arctanh((x^4+x^2-1)^(1/2)/x)","A"
69,1,13,12,0.109000," ","int((x^3-4)/x^4/(x^3-1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{4 \left(x^{3}-1\right)^{\frac{3}{4}}}{3 x^{3}}$&$13$\\ risch&$-\frac{4 \left(x^{3}-1\right)^{\frac{3}{4}}}{3 x^{3}}$&$13$\\ gosper&$-\frac{4 \left(-1+x \right) \left(x^{2}+x +1\right)}{3 x^{3} \left(x^{3}-1\right)^{\frac{1}{4}}}$&$22$\\ meijerg&$\frac{2 \sqrt{2}\, \Gamma \left(\frac{3}{4}\right) \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}} \left(\frac{\pi  \sqrt{2}}{\Gamma \left(\frac{3}{4}\right) x^{3}}-\frac{\left(3-3 \ln \left(2\right)-\frac{\pi}{2}+3 \ln \left(x \right)+i \pi \right) \pi  \sqrt{2}}{4 \Gamma \left(\frac{3}{4}\right)}-\frac{5 \hypergeom \left(\left[1, 1, \frac{9}{4}\right], \left[2, 3\right], x^{3}\right) \pi  \sqrt{2}\, x^{3}}{32 \Gamma \left(\frac{3}{4}\right)}\right)}{3 \pi  \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \Gamma \left(\frac{3}{4}\right) \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}} \left(\frac{\left(-3 \ln \left(2\right)-\frac{\pi}{2}+3 \ln \left(x \right)+i \pi \right) \pi  \sqrt{2}}{\Gamma \left(\frac{3}{4}\right)}+\frac{\hypergeom \left(\left[1, 1, \frac{5}{4}\right], \left[2, 2\right], x^{3}\right) \pi  \sqrt{2}\, x^{3}}{4 \Gamma \left(\frac{3}{4}\right)}\right)}{6 \pi  \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}}}$&$172$\\ \hline \end{longtable}"," ",0,"-4/3*(x^3-1)^(3/4)/x^3","A"
70,1,13,12,0.074000," ","int((x^3-1)^(1/3)/x^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{3}-1\right)^{\frac{4}{3}}}{4 x^{4}}$&$13$\\ gosper&$\frac{\left(-1+x \right) \left(x^{2}+x +1\right) \left(x^{3}-1\right)^{\frac{1}{3}}}{4 x^{4}}$&$22$\\ risch&$\frac{x^{6}-2 x^{3}+1}{4 \left(x^{3}-1\right)^{\frac{2}{3}} x^{4}}$&$23$\\ meijerg&$-\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \left(-x^{3}+1\right)^{\frac{4}{3}}}{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x^{4}}$&$33$\\ \hline \end{longtable}"," ",0,"1/4*(x^3-1)^(4/3)/x^4","A"
71,1,13,12,0.063000," ","int((x^3-1)^(2/3)/x^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{3}-1\right)^{\frac{5}{3}}}{5 x^{5}}$&$13$\\ gosper&$\frac{\left(-1+x \right) \left(x^{2}+x +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}}{5 x^{5}}$&$22$\\ risch&$\frac{x^{6}-2 x^{3}+1}{5 x^{5} \left(x^{3}-1\right)^{\frac{1}{3}}}$&$23$\\ meijerg&$-\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}} \left(-x^{3}+1\right)^{\frac{5}{3}}}{5 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} x^{5}}$&$33$\\ \hline \end{longtable}"," ",0,"1/5*(x^3-1)^(5/3)/x^5","A"
72,1,13,12,0.067000," ","int((x^3+1)^(1/3)/x^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(x^{3}+1\right)^{\frac{4}{3}}}{4 x^{4}}$&$13$\\ meijerg&$-\frac{\left(x^{3}+1\right)^{\frac{4}{3}}}{4 x^{4}}$&$13$\\ risch&$-\frac{x^{6}+2 x^{3}+1}{4 \left(x^{3}+1\right)^{\frac{2}{3}} x^{4}}$&$23$\\ gosper&$-\frac{\left(1+x \right) \left(x^{2}-x +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}}{4 x^{4}}$&$24$\\ \hline \end{longtable}"," ",0,"-1/4*(x^3+1)^(4/3)/x^4","A"
73,1,13,12,0.046000," ","int((x^3+1)^(2/3)/x^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(x^{3}+1\right)^{\frac{5}{3}}}{5 x^{5}}$&$13$\\ meijerg&$-\frac{\left(x^{3}+1\right)^{\frac{5}{3}}}{5 x^{5}}$&$13$\\ risch&$-\frac{x^{6}+2 x^{3}+1}{5 x^{5} \left(x^{3}+1\right)^{\frac{1}{3}}}$&$23$\\ gosper&$-\frac{\left(1+x \right) \left(x^{2}-x +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}}{5 x^{5}}$&$24$\\ \hline \end{longtable}"," ",0,"-1/5*(x^3+1)^(5/3)/x^5","A"
74,1,23,12,0.134000," ","int((x^3-2)*(x^3+1)^(3/2)/x^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{6}+2 x^{3}+1\right) \sqrt{x^{3}+1}}{5 x^{5}}$&$23$\\ gosper&$\frac{2 \left(1+x \right) \left(x^{2}-x +1\right) \left(x^{3}+1\right)^{\frac{3}{2}}}{5 x^{5}}$&$24$\\ risch&$\frac{\frac{2}{5} x^{9}+\frac{6}{5} x^{6}+\frac{6}{5} x^{3}+\frac{2}{5}}{x^{5} \sqrt{x^{3}+1}}$&$28$\\ meijerg&$\frac{2 \hypergeom \left(\left[-\frac{5}{3}, -\frac{3}{2}\right], \left[-\frac{2}{3}\right], -x^{3}\right)}{5 x^{5}}-\frac{\hypergeom \left(\left[-\frac{3}{2}, -\frac{2}{3}\right], \left[\frac{1}{3}\right], -x^{3}\right)}{2 x^{2}}$&$34$\\ default&$\frac{2 \sqrt{x^{3}+1}}{5 x^{5}}+\frac{4 \sqrt{x^{3}+1}}{5 x^{2}}+\frac{2 x \sqrt{x^{3}+1}}{5}$&$36$\\ elliptic&$\frac{2 \sqrt{x^{3}+1}}{5 x^{5}}+\frac{4 \sqrt{x^{3}+1}}{5 x^{2}}+\frac{2 x \sqrt{x^{3}+1}}{5}$&$36$\\ \hline \end{longtable}"," ",0,"2/5*(x^6+2*x^3+1)/x^5*(x^3+1)^(1/2)","A"
75,1,13,12,0.086000," ","int((x^3+4)/x^4/(x^3+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{4 \left(x^{3}+1\right)^{\frac{3}{4}}}{3 x^{3}}$&$13$\\ risch&$-\frac{4 \left(x^{3}+1\right)^{\frac{3}{4}}}{3 x^{3}}$&$13$\\ gosper&$-\frac{4 \left(1+x \right) \left(x^{2}-x +1\right)}{3 x^{3} \left(x^{3}+1\right)^{\frac{1}{4}}}$&$24$\\ meijerg&$\frac{2 \sqrt{2}\, \Gamma \left(\frac{3}{4}\right) \left(-\frac{\pi  \sqrt{2}}{\Gamma \left(\frac{3}{4}\right) x^{3}}-\frac{\left(3-3 \ln \left(2\right)-\frac{\pi}{2}+3 \ln \left(x \right)\right) \pi  \sqrt{2}}{4 \Gamma \left(\frac{3}{4}\right)}+\frac{5 \hypergeom \left(\left[1, 1, \frac{9}{4}\right], \left[2, 3\right], -x^{3}\right) \pi  \sqrt{2}\, x^{3}}{32 \Gamma \left(\frac{3}{4}\right)}\right)}{3 \pi}+\frac{\sqrt{2}\, \Gamma \left(\frac{3}{4}\right) \left(\frac{\left(-3 \ln \left(2\right)-\frac{\pi}{2}+3 \ln \left(x \right)\right) \pi  \sqrt{2}}{\Gamma \left(\frac{3}{4}\right)}-\frac{\hypergeom \left(\left[1, 1, \frac{5}{4}\right], \left[2, 2\right], -x^{3}\right) \pi  \sqrt{2}\, x^{3}}{4 \Gamma \left(\frac{3}{4}\right)}\right)}{6 \pi}$&$133$\\ \hline \end{longtable}"," ",0,"-4/3*(x^3+1)^(3/4)/x^3","A"
76,1,13,12,0.050000," ","int(1/x^2/(x^3+x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{3 \left(x^{3}+x \right)^{\frac{2}{3}}}{4 x^{2}}$&$13$\\ meijerg&$-\frac{3 \left(x^{2}+1\right)^{\frac{2}{3}}}{4 x^{\frac{4}{3}}}$&$13$\\ gosper&$-\frac{3 \left(x^{2}+1\right)}{4 x \left(x^{3}+x \right)^{\frac{1}{3}}}$&$18$\\ risch&$-\frac{3 \left(x^{2}+1\right)}{4 x \left(\left(x^{2}+1\right) x \right)^{\frac{1}{3}}}$&$20$\\ \hline \end{longtable}"," ",0,"-3/4*(x^3+x)^(2/3)/x^2","A"
77,1,18,12,0.095000," ","int((x^2+1)*(x^2+3)/x^6/(x^3+x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{4 \left(x^{2}+1\right) \left(x^{3}+x \right)^{\frac{3}{4}}}{7 x^{6}}$&$18$\\ gosper&$-\frac{4 \left(x^{2}+1\right)^{2}}{7 x^{5} \left(x^{3}+x \right)^{\frac{1}{4}}}$&$20$\\ risch&$-\frac{4 \left(x^{4}+2 x^{2}+1\right)}{7 x^{5} \left(\left(x^{2}+1\right) x \right)^{\frac{1}{4}}}$&$25$\\ meijerg&$-\frac{4 \hypergeom \left(\left[-\frac{21}{8}, \frac{1}{4}\right], \left[-\frac{13}{8}\right], -x^{2}\right)}{7 x^{\frac{21}{4}}}-\frac{16 \hypergeom \left(\left[-\frac{13}{8}, \frac{1}{4}\right], \left[-\frac{5}{8}\right], -x^{2}\right)}{13 x^{\frac{13}{4}}}-\frac{4 \hypergeom \left(\left[-\frac{5}{8}, \frac{1}{4}\right], \left[\frac{3}{8}\right], -x^{2}\right)}{5 x^{\frac{5}{4}}}$&$50$\\ \hline \end{longtable}"," ",0,"-4/7/x^6*(x^2+1)*(x^3+x)^(3/4)","A"
78,1,13,12,0.049000," ","int((x^3+x)^(1/3)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{3 \left(x^{2}+1\right)^{\frac{4}{3}}}{8 x^{\frac{8}{3}}}$&$13$\\ gosper&$-\frac{3 \left(x^{2}+1\right) \left(x^{3}+x \right)^{\frac{1}{3}}}{8 x^{3}}$&$18$\\ trager&$-\frac{3 \left(x^{2}+1\right) \left(x^{3}+x \right)^{\frac{1}{3}}}{8 x^{3}}$&$18$\\ risch&$-\frac{3 \left(\left(x^{2}+1\right) x \right)^{\frac{1}{3}} \left(x^{4}+2 x^{2}+1\right)}{8 x^{3} \left(x^{2}+1\right)}$&$32$\\ \hline \end{longtable}"," ",0,"-3/8*(x^2+1)^(4/3)/x^(8/3)","A"
79,1,13,12,0.066000," ","int(1/x^4/(x^4-1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{4}-1\right)^{\frac{3}{4}}}{3 x^{3}}$&$13$\\ risch&$\frac{\left(x^{4}-1\right)^{\frac{3}{4}}}{3 x^{3}}$&$13$\\ gosper&$\frac{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}{3 x^{3} \left(x^{4}-1\right)^{\frac{1}{4}}}$&$24$\\ meijerg&$-\frac{\left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \left(-x^{4}+1\right)^{\frac{3}{4}}}{3 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}} x^{3}}$&$33$\\ \hline \end{longtable}"," ",0,"1/3*(x^4-1)^(3/4)/x^3","A"
80,1,13,12,0.074000," ","int((x^4-1)^(3/4)/x^8,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{4}-1\right)^{\frac{7}{4}}}{7 x^{7}}$&$13$\\ risch&$\frac{x^{8}-2 x^{4}+1}{7 x^{7} \left(x^{4}-1\right)^{\frac{1}{4}}}$&$23$\\ gosper&$\frac{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right) \left(x^{4}-1\right)^{\frac{3}{4}}}{7 x^{7}}$&$24$\\ meijerg&$-\frac{\mathrm{signum}\left(x^{4}-1\right)^{\frac{3}{4}} \left(-x^{4}+1\right)^{\frac{7}{4}}}{7 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{3}{4}} x^{7}}$&$33$\\ \hline \end{longtable}"," ",0,"1/7*(x^4-1)^(7/4)/x^7","A"
81,1,18,12,0.092000," ","int((x^4-1)/x^2/(x^3+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{2}+1\right) \sqrt{x^{3}+x}}{3 x^{2}}$&$18$\\ gosper&$\frac{2 \left(x^{2}+1\right)^{2}}{3 \sqrt{x^{3}+x}\, x}$&$20$\\ default&$\frac{2 \sqrt{x^{3}+x}}{3}+\frac{2 \sqrt{x^{3}+x}}{3 x^{2}}$&$23$\\ elliptic&$\frac{2 \sqrt{x^{3}+x}}{3}+\frac{2 \sqrt{x^{3}+x}}{3 x^{2}}$&$23$\\ risch&$\frac{\frac{2}{3} x^{4}+\frac{4}{3} x^{2}+\frac{2}{3}}{x \sqrt{\left(x^{2}+1\right) x}}$&$25$\\ meijerg&$\frac{2 \hypergeom \left(\left[\frac{1}{2}, \frac{5}{4}\right], \left[\frac{9}{4}\right], -x^{2}\right) x^{\frac{5}{2}}}{5}+\frac{2 \hypergeom \left(\left[-\frac{3}{4}, \frac{1}{2}\right], \left[\frac{1}{4}\right], -x^{2}\right)}{3 x^{\frac{3}{2}}}$&$34$\\ \hline \end{longtable}"," ",0,"2/3*(x^2+1)/x^2*(x^3+x)^(1/2)","A"
82,1,13,12,0.047000," ","int(1/x^4/(x^4+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{\left(x^{4}+1\right)^{\frac{3}{4}}}{3 x^{3}}$&$13$\\ trager&$-\frac{\left(x^{4}+1\right)^{\frac{3}{4}}}{3 x^{3}}$&$13$\\ meijerg&$-\frac{\left(x^{4}+1\right)^{\frac{3}{4}}}{3 x^{3}}$&$13$\\ risch&$-\frac{\left(x^{4}+1\right)^{\frac{3}{4}}}{3 x^{3}}$&$13$\\ \hline \end{longtable}"," ",0,"-1/3*(x^4+1)^(3/4)/x^3","A"
83,1,13,12,0.097000," ","int((x^4-3)*(x^4+1)^(1/3)/x^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{3 \left(x^{4}+1\right)^{\frac{4}{3}}}{4 x^{4}}$&$13$\\ trager&$\frac{3 \left(x^{4}+1\right)^{\frac{4}{3}}}{4 x^{4}}$&$13$\\ risch&$\frac{\frac{3}{2} x^{4}+\frac{3}{4}+\frac{3}{4} x^{8}}{\left(x^{4}+1\right)^{\frac{2}{3}} x^{4}}$&$23$\\ meijerg&$\frac{\frac{3 \Gamma \left(\frac{2}{3}\right)}{x^{4}}-\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+4 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)+\frac{\hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 3\right], -x^{4}\right) \Gamma \left(\frac{2}{3}\right) x^{4}}{3}}{4 \Gamma \left(\frac{2}{3}\right)}-\frac{-3 \left(3+\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)-\hypergeom \left(\left[\frac{2}{3}, 1, 1\right], \left[2, 2\right], -x^{4}\right) \Gamma \left(\frac{2}{3}\right) x^{4}}{12 \Gamma \left(\frac{2}{3}\right)}$&$103$\\ \hline \end{longtable}"," ",0,"3/4*(x^4+1)^(4/3)/x^4","A"
84,1,13,12,0.093000," ","int((x^2-1)*(x^2+1)*(x^4+1)^(1/2)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{\left(x^{4}+1\right)^{\frac{3}{2}}}{3 x^{3}}$&$13$\\ trager&$\frac{\left(x^{4}+1\right)^{\frac{3}{2}}}{3 x^{3}}$&$13$\\ elliptic&$\frac{\left(x^{4}+1\right)^{\frac{3}{2}}}{3 x^{3}}$&$13$\\ risch&$\frac{x^{8}+2 x^{4}+1}{3 x^{3} \sqrt{x^{4}+1}}$&$23$\\ default&$\frac{\sqrt{x^{4}+1}\, x}{3}+\frac{\sqrt{x^{4}+1}}{3 x^{3}}$&$24$\\ meijerg&$\frac{\hypergeom \left(\left[-\frac{3}{4}, -\frac{1}{2}\right], \left[\frac{1}{4}\right], -x^{4}\right)}{3 x^{3}}+\hypergeom \left(\left[-\frac{1}{2}, \frac{1}{4}\right], \left[\frac{5}{4}\right], -x^{4}\right) x$&$31$\\ \hline \end{longtable}"," ",0,"1/3*(x^4+1)^(3/2)/x^3","A"
85,1,13,12,0.080000," ","int((x^4-3)*(x^4+1)^(2/3)/x^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{3 \left(x^{4}+1\right)^{\frac{5}{3}}}{5 x^{5}}$&$13$\\ trager&$\frac{3 \left(x^{4}+1\right)^{\frac{5}{3}}}{5 x^{5}}$&$13$\\ risch&$\frac{\frac{3}{5} x^{8}+\frac{6}{5} x^{4}+\frac{3}{5}}{x^{5} \left(x^{4}+1\right)^{\frac{1}{3}}}$&$23$\\ meijerg&$\frac{3 \hypergeom \left(\left[-\frac{5}{4}, -\frac{2}{3}\right], \left[-\frac{1}{4}\right], -x^{4}\right)}{5 x^{5}}-\frac{\hypergeom \left(\left[-\frac{2}{3}, -\frac{1}{4}\right], \left[\frac{3}{4}\right], -x^{4}\right)}{x}$&$34$\\ \hline \end{longtable}"," ",0,"3/5*(x^4+1)^(5/3)/x^5","A"
86,1,13,12,0.055000," ","int((x^4+1)^(3/4)/x^8,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{\left(x^{4}+1\right)^{\frac{7}{4}}}{7 x^{7}}$&$13$\\ trager&$-\frac{\left(x^{4}+1\right)^{\frac{7}{4}}}{7 x^{7}}$&$13$\\ meijerg&$-\frac{\left(x^{4}+1\right)^{\frac{7}{4}}}{7 x^{7}}$&$13$\\ risch&$-\frac{x^{8}+2 x^{4}+1}{7 x^{7} \left(x^{4}+1\right)^{\frac{1}{4}}}$&$23$\\ \hline \end{longtable}"," ",0,"-1/7*(x^4+1)^(7/4)/x^7","A"
87,1,13,12,0.106000," ","int((x^4-1)^(2/3)*(x^4+3)/x^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(x^{4}-1\right)^{\frac{5}{3}}}{5 x^{5}}$&$13$\\ risch&$\frac{\frac{3}{5} x^{8}-\frac{6}{5} x^{4}+\frac{3}{5}}{x^{5} \left(x^{4}-1\right)^{\frac{1}{3}}}$&$23$\\ gosper&$\frac{3 \left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right) \left(x^{4}-1\right)^{\frac{2}{3}}}{5 x^{5}}$&$24$\\ meijerg&$-\frac{\mathrm{signum}\left(x^{4}-1\right)^{\frac{2}{3}} \hypergeom \left(\left[-\frac{2}{3}, -\frac{1}{4}\right], \left[\frac{3}{4}\right], x^{4}\right)}{\left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{2}{3}} x}-\frac{3 \mathrm{signum}\left(x^{4}-1\right)^{\frac{2}{3}} \hypergeom \left(\left[-\frac{5}{4}, -\frac{2}{3}\right], \left[-\frac{1}{4}\right], x^{4}\right)}{5 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{2}{3}} x^{5}}$&$66$\\ \hline \end{longtable}"," ",0,"3/5*(x^4-1)^(5/3)/x^5","A"
88,1,13,12,0.093000," ","int((x^4+1)^(1/3)*(x^4+3)/x^9,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{3 \left(x^{4}+1\right)^{\frac{4}{3}}}{8 x^{8}}$&$13$\\ trager&$-\frac{3 \left(x^{4}+1\right)^{\frac{4}{3}}}{8 x^{8}}$&$13$\\ risch&$-\frac{3 \left(x^{8}+2 x^{4}+1\right)}{8 \left(x^{4}+1\right)^{\frac{2}{3}} x^{8}}$&$23$\\ meijerg&$-\frac{\frac{3 \Gamma \left(\frac{2}{3}\right)}{x^{4}}-\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+4 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)+\frac{\hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 3\right], -x^{4}\right) \Gamma \left(\frac{2}{3}\right) x^{4}}{3}}{12 \Gamma \left(\frac{2}{3}\right)}-\frac{\frac{3 \Gamma \left(\frac{2}{3}\right)}{2 x^{8}}+\frac{\Gamma \left(\frac{2}{3}\right)}{x^{4}}+\frac{\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)}{3}-\frac{5 \hypergeom \left(\left[1, 1, \frac{8}{3}\right], \left[2, 4\right], -x^{4}\right) \Gamma \left(\frac{2}{3}\right) x^{4}}{27}}{4 \Gamma \left(\frac{2}{3}\right)}$&$115$\\ \hline \end{longtable}"," ",0,"-3/8*(x^4+1)^(4/3)/x^8","A"
89,1,13,12,0.217000," ","int(1/x^2/(x^4+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 \sqrt{x^{4}+x}}{3 x^{2}}$&$13$\\ trager&$-\frac{2 \sqrt{x^{4}+x}}{3 x^{2}}$&$13$\\ meijerg&$-\frac{2 \sqrt{x^{3}+1}}{3 x^{\frac{3}{2}}}$&$13$\\ elliptic&$-\frac{2 \sqrt{x^{4}+x}}{3 x^{2}}$&$13$\\ risch&$-\frac{2 \left(x^{3}+1\right)}{3 x \sqrt{x \left(x^{3}+1\right)}}$&$20$\\ gosper&$-\frac{2 \left(1+x \right) \left(x^{2}-x +1\right)}{3 x \sqrt{x^{4}+x}}$&$24$\\ \hline \end{longtable}"," ",0,"-2/3*(x^4+x)^(1/2)/x^2","A"
90,1,18,12,0.084000," ","int((x^3+1)/x^6/(x^4+x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{4 \left(x^{3}+1\right) \left(x^{4}+x \right)^{\frac{3}{4}}}{21 x^{6}}$&$18$\\ risch&$-\frac{4 \left(x^{6}+2 x^{3}+1\right)}{21 x^{5} \left(x \left(x^{3}+1\right)\right)^{\frac{1}{4}}}$&$25$\\ gosper&$-\frac{4 \left(1+x \right) \left(x^{2}-x +1\right) \left(x^{3}+1\right)}{21 x^{5} \left(x^{4}+x \right)^{\frac{1}{4}}}$&$29$\\ meijerg&$-\frac{4 \left(1-\frac{4 x^{3}}{3}\right) \left(x^{3}+1\right)^{\frac{3}{4}}}{21 x^{\frac{21}{4}}}-\frac{4 \left(x^{3}+1\right)^{\frac{3}{4}}}{9 x^{\frac{9}{4}}}$&$33$\\ \hline \end{longtable}"," ",0,"-4/21*(x^3+1)/x^6*(x^4+x)^(3/4)","A"
91,1,18,12,0.096000," ","int((x^3-2)*(x^4+x)^(1/3)/(x^3+1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{3 x \left(x^{4}+x \right)^{\frac{1}{3}}}{2 \left(x^{3}+1\right)}$&$18$\\ trager&$-\frac{3 x \left(x^{4}+x \right)^{\frac{1}{3}}}{2 \left(x^{3}+1\right)}$&$18$\\ risch&$-\frac{3 \left(x \left(x^{3}+1\right)\right)^{\frac{1}{3}} x}{2 \left(x^{3}+1\right)}$&$20$\\ meijerg&$-\frac{3 \hypergeom \left(\left[\frac{4}{9}, \frac{5}{3}\right], \left[\frac{13}{9}\right], -x^{3}\right) x^{\frac{4}{3}}}{2}+\frac{3 \hypergeom \left(\left[\frac{13}{9}, \frac{5}{3}\right], \left[\frac{22}{9}\right], -x^{3}\right) x^{\frac{13}{3}}}{13}$&$34$\\ \hline \end{longtable}"," ",0,"-3/2*x*(x^4+x)^(1/3)/(x^3+1)","A"
92,1,13,14,0.073000," ","int((x^4+x^2)^(1/4)/x^2/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{2 \left(x^{2}+1\right)^{\frac{1}{4}}}{\sqrt{x}}$&$13$\\ gosper&$-\frac{2 \left(x^{4}+x^{2}\right)^{\frac{1}{4}}}{x}$&$15$\\ trager&$-\frac{2 \left(x^{4}+x^{2}\right)^{\frac{1}{4}}}{x}$&$15$\\ risch&$-\frac{2 \left(x^{2} \left(x^{2}+1\right)\right)^{\frac{1}{4}}}{x}$&$17$\\ \hline \end{longtable}"," ",0,"-2*(x^2+1)^(1/4)/x^(1/2)","A"
93,1,13,12,0.142000," ","int((x^5-6)*(x^5-1)^(2/3)/x^11,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{3 \left(x^{5}-1\right)^{\frac{5}{3}}}{5 x^{10}}$&$13$\\ risch&$-\frac{3 \left(x^{10}-2 x^{5}+1\right)}{5 x^{10} \left(x^{5}-1\right)^{\frac{1}{3}}}$&$23$\\ gosper&$-\frac{3 \left(-1+x \right) \left(x^{4}+x^{3}+x^{2}+x +1\right) \left(x^{5}-1\right)^{\frac{2}{3}}}{5 x^{10}}$&$28$\\ meijerg&$\frac{2 \mathrm{signum}\left(x^{5}-1\right)^{\frac{2}{3}} \Gamma \left(\frac{2}{3}\right) \sqrt{3}\, \left(\frac{\pi  \sqrt{3}}{2 \Gamma \left(\frac{2}{3}\right) x^{10}}-\frac{2 \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right) x^{5}}+\frac{\left(\frac{3}{2}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+5 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{4 \hypergeom \left(\left[1, 1, \frac{7}{3}\right], \left[2, 4\right], x^{5}\right) \pi  \sqrt{3}\, x^{5}}{81 \Gamma \left(\frac{2}{3}\right)}\right)}{5 \left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{2}{3}} \pi}+\frac{\mathrm{signum}\left(x^{5}-1\right)^{\frac{2}{3}} \Gamma \left(\frac{2}{3}\right) \sqrt{3}\, \left(-\frac{\pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right) x^{5}}-\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+5 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}-\frac{\hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 3\right], x^{5}\right) \pi  \sqrt{3}\, x^{5}}{9 \Gamma \left(\frac{2}{3}\right)}\right)}{15 \left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{2}{3}} \pi}$&$207$\\ \hline \end{longtable}"," ",0,"-3/5*(x^5-1)^(5/3)/x^10","A"
94,1,13,12,0.100000," ","int((x^5-4)*(x^5+1)^(3/4)/x^8,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{5}+1\right)^{\frac{7}{4}}}{7 x^{7}}$&$13$\\ risch&$\frac{\frac{4}{7} x^{10}+\frac{8}{7} x^{5}+\frac{4}{7}}{x^{7} \left(x^{5}+1\right)^{\frac{1}{4}}}$&$23$\\ gosper&$\frac{4 \left(1+x \right) \left(x^{4}-x^{3}+x^{2}-x +1\right) \left(x^{5}+1\right)^{\frac{3}{4}}}{7 x^{7}}$&$32$\\ meijerg&$\frac{4 \hypergeom \left(\left[-\frac{7}{5}, -\frac{3}{4}\right], \left[-\frac{2}{5}\right], -x^{5}\right)}{7 x^{7}}-\frac{\hypergeom \left(\left[-\frac{3}{4}, -\frac{2}{5}\right], \left[\frac{3}{5}\right], -x^{5}\right)}{2 x^{2}}$&$34$\\ \hline \end{longtable}"," ",0,"4/7*(x^5+1)^(7/4)/x^7","A"
95,1,13,12,0.109000," ","int((x^5-1)^(3/4)*(x^5+4)/x^8,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{5}-1\right)^{\frac{7}{4}}}{7 x^{7}}$&$13$\\ risch&$\frac{\frac{4}{7} x^{10}-\frac{8}{7} x^{5}+\frac{4}{7}}{x^{7} \left(x^{5}-1\right)^{\frac{1}{4}}}$&$23$\\ gosper&$\frac{4 \left(-1+x \right) \left(x^{4}+x^{3}+x^{2}+x +1\right) \left(x^{5}-1\right)^{\frac{3}{4}}}{7 x^{7}}$&$28$\\ meijerg&$-\frac{\mathrm{signum}\left(x^{5}-1\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{3}{4}, -\frac{2}{5}\right], \left[\frac{3}{5}\right], x^{5}\right)}{2 \left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{3}{4}} x^{2}}-\frac{4 \mathrm{signum}\left(x^{5}-1\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{7}{5}, -\frac{3}{4}\right], \left[-\frac{2}{5}\right], x^{5}\right)}{7 \left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{3}{4}} x^{7}}$&$66$\\ \hline \end{longtable}"," ",0,"4/7*(x^5-1)^(7/4)/x^7","A"
96,1,13,12,0.112000," ","int((x^5+1)^(2/3)*(x^5+6)/x^11,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{3 \left(x^{5}+1\right)^{\frac{5}{3}}}{5 x^{10}}$&$13$\\ risch&$-\frac{3 \left(x^{10}+2 x^{5}+1\right)}{5 x^{10} \left(x^{5}+1\right)^{\frac{1}{3}}}$&$23$\\ gosper&$-\frac{3 \left(1+x \right) \left(x^{4}-x^{3}+x^{2}-x +1\right) \left(x^{5}+1\right)^{\frac{2}{3}}}{5 x^{10}}$&$32$\\ meijerg&$-\frac{\Gamma \left(\frac{2}{3}\right) \sqrt{3}\, \left(\frac{\pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right) x^{5}}-\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+5 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}+\frac{\hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 3\right], -x^{5}\right) \pi  \sqrt{3}\, x^{5}}{9 \Gamma \left(\frac{2}{3}\right)}\right)}{15 \pi}-\frac{2 \Gamma \left(\frac{2}{3}\right) \sqrt{3}\, \left(\frac{\pi  \sqrt{3}}{2 \Gamma \left(\frac{2}{3}\right) x^{10}}+\frac{2 \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right) x^{5}}+\frac{\left(\frac{3}{2}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+5 \ln \left(x \right)\right) \pi  \sqrt{3}}{9 \Gamma \left(\frac{2}{3}\right)}-\frac{4 \hypergeom \left(\left[1, 1, \frac{7}{3}\right], \left[2, 4\right], -x^{5}\right) \pi  \sqrt{3}\, x^{5}}{81 \Gamma \left(\frac{2}{3}\right)}\right)}{5 \pi}$&$166$\\ \hline \end{longtable}"," ",0,"-3/5*(x^5+1)^(5/3)/x^10","A"
97,1,18,12,0.102000," ","int((x^4-3)*(x^4+1)/x^6/(x^5+x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{4}+1\right) \left(x^{5}+x \right)^{\frac{3}{4}}}{7 x^{6}}$&$18$\\ gosper&$\frac{4 \left(x^{4}+1\right)^{2}}{7 x^{5} \left(x^{5}+x \right)^{\frac{1}{4}}}$&$20$\\ risch&$\frac{\frac{4}{7} x^{8}+\frac{8}{7} x^{4}+\frac{4}{7}}{x^{5} \left(x \left(x^{4}+1\right)\right)^{\frac{1}{4}}}$&$25$\\ meijerg&$\frac{4 \hypergeom \left(\left[-\frac{21}{16}, \frac{1}{4}\right], \left[-\frac{5}{16}\right], -x^{4}\right)}{7 x^{\frac{21}{4}}}+\frac{8 \hypergeom \left(\left[-\frac{5}{16}, \frac{1}{4}\right], \left[\frac{11}{16}\right], -x^{4}\right)}{5 x^{\frac{5}{4}}}+\frac{4 \hypergeom \left(\left[\frac{1}{4}, \frac{11}{16}\right], \left[\frac{27}{16}\right], -x^{4}\right) x^{\frac{11}{4}}}{11}$&$50$\\ \hline \end{longtable}"," ",0,"4/7*(x^4+1)*(x^5+x)^(3/4)/x^6","A"
98,1,15,14,0.089000," ","int((x^2-1)*(x^5+x^3)^(1/4)/x^2/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{4 \left(x^{5}+x^{3}\right)^{\frac{1}{4}}}{x}$&$15$\\ trager&$\frac{4 \left(x^{5}+x^{3}\right)^{\frac{1}{4}}}{x}$&$15$\\ risch&$\frac{4 \left(x^{3} \left(x^{2}+1\right)\right)^{\frac{1}{4}}}{x}$&$17$\\ meijerg&$\frac{4 \hypergeom \left(\left[-\frac{1}{8}, \frac{3}{4}\right], \left[\frac{7}{8}\right], -x^{2}\right)}{x^{\frac{1}{4}}}+\frac{4 \hypergeom \left(\left[\frac{3}{4}, \frac{7}{8}\right], \left[\frac{15}{8}\right], -x^{2}\right) x^{\frac{7}{4}}}{7}$&$34$\\ \hline \end{longtable}"," ",0,"4*(x^5+x^3)^(1/4)/x","A"
99,0,0,14,0.030000," ","int((3*a*x^5-2*b)/(a*x^5+b)^(1/2)/(a*x^5+x^2+b),x)","\[\int \frac{3 a \,x^{5}-2 b}{\sqrt{a \,x^{5}+b}\, \left(a \,x^{5}+x^{2}+b \right)}\, dx\]"," ",0,"int((3*a*x^5-2*b)/(a*x^5+b)^(1/2)/(a*x^5+x^2+b),x)","F"
100,1,13,12,0.059000," ","int(1/x^4/(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}-1}}{3 x^{3}}$&$13$\\ risch&$\frac{\sqrt{x^{6}-1}}{3 x^{3}}$&$13$\\ gosper&$\frac{\left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right)}{3 x^{3} \sqrt{x^{6}-1}}$&$33$\\ meijerg&$-\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{-x^{6}+1}}{3 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, x^{3}}$&$33$\\ \hline \end{longtable}"," ",0,"1/3*(x^6-1)^(1/2)/x^3","A"
101,1,13,12,0.084000," ","int((x^6-1)^(1/3)/x^9,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{6}-1\right)^{\frac{4}{3}}}{8 x^{8}}$&$13$\\ risch&$\frac{x^{12}-2 x^{6}+1}{8 \left(x^{6}-1\right)^{\frac{2}{3}} x^{8}}$&$23$\\ gosper&$\frac{\left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right) \left(x^{6}-1\right)^{\frac{1}{3}}}{8 x^{8}}$&$33$\\ meijerg&$-\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}} \left(-x^{6}+1\right)^{\frac{4}{3}}}{8 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} x^{8}}$&$33$\\ \hline \end{longtable}"," ",0,"1/8*(x^6-1)^(4/3)/x^8","A"
102,1,13,12,0.071000," ","int((x^6-1)^(1/2)/x^10,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{6}-1\right)^{\frac{3}{2}}}{9 x^{9}}$&$13$\\ risch&$\frac{x^{12}-2 x^{6}+1}{9 x^{9} \sqrt{x^{6}-1}}$&$23$\\ gosper&$\frac{\left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right) \sqrt{x^{6}-1}}{9 x^{9}}$&$33$\\ meijerg&$-\frac{\sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(-x^{6}+1\right)^{\frac{3}{2}}}{9 \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, x^{9}}$&$33$\\ \hline \end{longtable}"," ",0,"1/9*(x^6-1)^(3/2)/x^9","A"
103,1,13,12,0.044000," ","int(1/x^4/(x^6+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\sqrt{x^{6}+1}}{3 x^{3}}$&$13$\\ meijerg&$-\frac{\sqrt{x^{6}+1}}{3 x^{3}}$&$13$\\ risch&$-\frac{\sqrt{x^{6}+1}}{3 x^{3}}$&$13$\\ gosper&$-\frac{\left(x^{2}+1\right) \left(x^{4}-x^{2}+1\right)}{3 x^{3} \sqrt{x^{6}+1}}$&$28$\\ \hline \end{longtable}"," ",0,"-1/3*(x^6+1)^(1/2)/x^3","A"
104,1,13,12,0.055000," ","int(1/x^5/(x^6+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(x^{6}+1\right)^{\frac{2}{3}}}{4 x^{4}}$&$13$\\ meijerg&$-\frac{\left(x^{6}+1\right)^{\frac{2}{3}}}{4 x^{4}}$&$13$\\ risch&$-\frac{\left(x^{6}+1\right)^{\frac{2}{3}}}{4 x^{4}}$&$13$\\ gosper&$-\frac{\left(x^{2}+1\right) \left(x^{4}-x^{2}+1\right)}{4 x^{4} \left(x^{6}+1\right)^{\frac{1}{3}}}$&$28$\\ \hline \end{longtable}"," ",0,"-1/4*(x^6+1)^(2/3)/x^4","A"
105,1,13,12,0.075000," ","int((x^6-2)/x^4/(x^6+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{6}+1\right)^{\frac{3}{4}}}{3 x^{3}}$&$13$\\ risch&$\frac{2 \left(x^{6}+1\right)^{\frac{3}{4}}}{3 x^{3}}$&$13$\\ gosper&$\frac{2 \left(x^{2}+1\right) \left(x^{4}-x^{2}+1\right)}{3 x^{3} \left(x^{6}+1\right)^{\frac{1}{4}}}$&$28$\\ meijerg&$\frac{2 \hypergeom \left(\left[-\frac{1}{2}, \frac{1}{4}\right], \left[\frac{1}{2}\right], -x^{6}\right)}{3 x^{3}}+\frac{\hypergeom \left(\left[\frac{1}{4}, \frac{1}{2}\right], \left[\frac{3}{2}\right], -x^{6}\right) x^{3}}{3}$&$34$\\ \hline \end{longtable}"," ",0,"2/3*(x^6+1)^(3/4)/x^3","A"
106,1,13,12,0.053000," ","int((x^6+1)^(1/2)/x^10,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(x^{6}+1\right)^{\frac{3}{2}}}{9 x^{9}}$&$13$\\ meijerg&$-\frac{\left(x^{6}+1\right)^{\frac{3}{2}}}{9 x^{9}}$&$13$\\ risch&$-\frac{x^{12}+2 x^{6}+1}{9 x^{9} \sqrt{x^{6}+1}}$&$23$\\ gosper&$-\frac{\left(x^{2}+1\right) \left(x^{4}-x^{2}+1\right) \sqrt{x^{6}+1}}{9 x^{9}}$&$28$\\ \hline \end{longtable}"," ",0,"-1/9*(x^6+1)^(3/2)/x^9","A"
107,1,13,12,0.094000," ","int((x^6-2)*(x^6+1)^(3/4)/x^8,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{6}+1\right)^{\frac{7}{4}}}{7 x^{7}}$&$13$\\ risch&$\frac{\frac{2}{7} x^{12}+\frac{4}{7} x^{6}+\frac{2}{7}}{x^{7} \left(x^{6}+1\right)^{\frac{1}{4}}}$&$23$\\ gosper&$\frac{2 \left(x^{2}+1\right) \left(x^{4}-x^{2}+1\right) \left(x^{6}+1\right)^{\frac{3}{4}}}{7 x^{7}}$&$28$\\ meijerg&$\frac{2 \hypergeom \left(\left[-\frac{7}{6}, -\frac{3}{4}\right], \left[-\frac{1}{6}\right], -x^{6}\right)}{7 x^{7}}-\frac{\hypergeom \left(\left[-\frac{3}{4}, -\frac{1}{6}\right], \left[\frac{5}{6}\right], -x^{6}\right)}{x}$&$34$\\ \hline \end{longtable}"," ",0,"2/7*(x^6+1)^(7/4)/x^7","A"
108,1,13,12,0.107000," ","int((x^6-1)^(1/3)*(x^6+1)/x^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{6}-1\right)^{\frac{4}{3}}}{4 x^{4}}$&$13$\\ risch&$\frac{x^{12}-2 x^{6}+1}{4 \left(x^{6}-1\right)^{\frac{2}{3}} x^{4}}$&$23$\\ gosper&$\frac{\left(x^{6}-1\right)^{\frac{1}{3}} \left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right)}{4 x^{4}}$&$33$\\ meijerg&$\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{6}\right) x^{2}}{2 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}}}-\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{2}{3}, -\frac{1}{3}\right], \left[\frac{1}{3}\right], x^{6}\right)}{4 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} x^{4}}$&$66$\\ \hline \end{longtable}"," ",0,"1/4*(x^6-1)^(4/3)/x^4","A"
109,1,13,12,0.094000," ","int((x^6+2)/x^4/(x^6-1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{6}-1\right)^{\frac{3}{4}}}{3 x^{3}}$&$13$\\ risch&$\frac{2 \left(x^{6}-1\right)^{\frac{3}{4}}}{3 x^{3}}$&$13$\\ gosper&$\frac{2 \left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right)}{3 x^{3} \left(x^{6}-1\right)^{\frac{1}{4}}}$&$33$\\ meijerg&$-\frac{2 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{1}{2}, \frac{1}{4}\right], \left[\frac{1}{2}\right], x^{6}\right)}{3 \mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{4}} x^{3}}+\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[\frac{1}{4}, \frac{1}{2}\right], \left[\frac{3}{2}\right], x^{6}\right) x^{3}}{3 \mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{4}}}$&$66$\\ \hline \end{longtable}"," ",0,"2/3*(x^6-1)^(3/4)/x^3","A"
110,1,13,12,0.109000," ","int((x^6-1)^(3/4)*(x^6+2)/x^8,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{6}-1\right)^{\frac{7}{4}}}{7 x^{7}}$&$13$\\ risch&$\frac{\frac{2}{7} x^{12}-\frac{4}{7} x^{6}+\frac{2}{7}}{x^{7} \left(x^{6}-1\right)^{\frac{1}{4}}}$&$23$\\ gosper&$\frac{2 \left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right) \left(x^{6}-1\right)^{\frac{3}{4}}}{7 x^{7}}$&$33$\\ meijerg&$-\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{3}{4}, -\frac{1}{6}\right], \left[\frac{5}{6}\right], x^{6}\right)}{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{3}{4}} x}-\frac{2 \mathrm{signum}\left(x^{6}-1\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{7}{6}, -\frac{3}{4}\right], \left[-\frac{1}{6}\right], x^{6}\right)}{7 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{3}{4}} x^{7}}$&$66$\\ \hline \end{longtable}"," ",0,"2/7*(x^6-1)^(7/4)/x^7","A"
111,1,13,12,0.093000," ","int((2*x^5-3)/x^3/(x^6+x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{6}+x \right)^{\frac{3}{4}}}{3 x^{3}}$&$13$\\ risch&$\frac{\frac{4 x^{5}}{3}+\frac{4}{3}}{x^{2} \left(x \left(x^{5}+1\right)\right)^{\frac{1}{4}}}$&$20$\\ gosper&$\frac{4 \left(1+x \right) \left(x^{4}-x^{3}+x^{2}-x +1\right)}{3 x^{2} \left(x^{6}+x \right)^{\frac{1}{4}}}$&$32$\\ meijerg&$\frac{4 \hypergeom \left(\left[-\frac{9}{20}, \frac{1}{4}\right], \left[\frac{11}{20}\right], -x^{5}\right)}{3 x^{\frac{9}{4}}}+\frac{8 \hypergeom \left(\left[\frac{1}{4}, \frac{11}{20}\right], \left[\frac{31}{20}\right], -x^{5}\right) x^{\frac{11}{4}}}{11}$&$34$\\ \hline \end{longtable}"," ",0,"4/3*(x^6+x)^(3/4)/x^3","A"
112,1,23,12,0.105000," ","int((x^4+x)^(1/3)*(x^6-x^3-2)/x^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(x^{6}+2 x^{3}+1\right) \left(x^{4}+x \right)^{\frac{1}{3}}}{7 x^{5}}$&$23$\\ gosper&$\frac{3 \left(x^{3}+1\right) \left(x^{4}+x \right)^{\frac{1}{3}} \left(1+x \right) \left(x^{2}-x +1\right)}{7 x^{5}}$&$29$\\ risch&$\frac{3 \left(x \left(x^{3}+1\right)\right)^{\frac{1}{3}} \left(x^{9}+3 x^{6}+3 x^{3}+1\right)}{7 x^{5} \left(x^{3}+1\right)}$&$37$\\ meijerg&$\frac{3 \hypergeom \left(\left[-\frac{1}{3}, \frac{4}{9}\right], \left[\frac{13}{9}\right], -x^{3}\right) x^{\frac{4}{3}}}{4}+\frac{3 \hypergeom \left(\left[-\frac{5}{9}, -\frac{1}{3}\right], \left[\frac{4}{9}\right], -x^{3}\right)}{5 x^{\frac{5}{3}}}+\frac{3 \hypergeom \left(\left[-\frac{14}{9}, -\frac{1}{3}\right], \left[-\frac{5}{9}\right], -x^{3}\right)}{7 x^{\frac{14}{3}}}$&$50$\\ \hline \end{longtable}"," ",0,"3/7*(x^6+2*x^3+1)/x^5*(x^4+x)^(1/3)","A"
113,1,42,14,0.201000," ","int(x*(x^6+2)/(x^6-1)^(1/2)/(x^6-x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(-\frac{-x^{6}-x^{4}+2 x^{2} \sqrt{x^{6}-1}+1}{x^{6}-x^{4}-1}\right)}{2}$&$42$\\ \hline \end{longtable}"," ",0,"1/2*ln(-(-x^6-x^4+2*x^2*(x^6-1)^(1/2)+1)/(x^6-x^4-1))","B"
114,1,13,12,0.102000," ","int((x^8-1)/x^4/(x^4-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{4}-1\right)^{\frac{3}{2}}}{3 x^{3}}$&$13$\\ elliptic&$\frac{\left(x^{4}-1\right)^{\frac{3}{2}}}{3 x^{3}}$&$13$\\ risch&$\frac{x^{8}-2 x^{4}+1}{3 x^{3} \sqrt{x^{4}-1}}$&$23$\\ gosper&$\frac{\sqrt{x^{4}-1}\, \left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}{3 x^{3}}$&$24$\\ default&$\frac{x \sqrt{x^{4}-1}}{3}-\frac{\sqrt{x^{4}-1}}{3 x^{3}}$&$24$\\ meijerg&$\frac{\sqrt{-\mathrm{signum}\left(x^{4}-1\right)}\, \hypergeom \left(\left[\frac{1}{2}, \frac{5}{4}\right], \left[\frac{9}{4}\right], x^{4}\right) x^{5}}{5 \sqrt{\mathrm{signum}\left(x^{4}-1\right)}}+\frac{\sqrt{-\mathrm{signum}\left(x^{4}-1\right)}\, \hypergeom \left(\left[-\frac{3}{4}, \frac{1}{2}\right], \left[\frac{1}{4}\right], x^{4}\right)}{3 \sqrt{\mathrm{signum}\left(x^{4}-1\right)}\, x^{3}}$&$66$\\ \hline \end{longtable}"," ",0,"1/3*(x^4-1)^(3/2)/x^3","A"
115,1,13,12,0.102000," ","int((x^8-1)*(x^8+1)^(1/2)/x^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{\left(x^{8}+1\right)^{\frac{3}{2}}}{6 x^{6}}$&$13$\\ trager&$\frac{\left(x^{8}+1\right)^{\frac{3}{2}}}{6 x^{6}}$&$13$\\ risch&$\frac{x^{16}+2 x^{8}+1}{6 x^{6} \sqrt{x^{8}+1}}$&$23$\\ meijerg&$\frac{\hypergeom \left(\left[-\frac{3}{4}, -\frac{1}{2}\right], \left[\frac{1}{4}\right], -x^{8}\right)}{6 x^{6}}+\frac{\hypergeom \left(\left[-\frac{1}{2}, \frac{1}{4}\right], \left[\frac{5}{4}\right], -x^{8}\right) x^{2}}{2}$&$34$\\ \hline \end{longtable}"," ",0,"1/6*(x^8+1)^(3/2)/x^6","A"
116,1,45,15,0.338000," ","int((2*x^2+x+2)/(-1+2*x)/(x^4+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(-\frac{2 x^{3}+2 x \sqrt{x^{4}+x}-4 x^{2}-4 \sqrt{x^{4}+x}+4 x +1}{\left(-1+2 x \right)^{2}}\right)$&$45$\\ default&$-\frac{2 \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}-\frac{2 \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{2 \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+2 \EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{3}{2}+\frac{3 i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$781$\\ elliptic&$-\frac{2 \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}-\frac{2 \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{2 \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+2 \EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{3}{2}+\frac{3 i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$781$\\ \hline \end{longtable}"," ",0,"ln(-(2*x^3+2*x*(x^4+x)^(1/2)-4*x^2-4*(x^4+x)^(1/2)+4*x+1)/(-1+2*x)^2)","B"
117,1,16,15,0.417000," ","int((x^2-1)/(x^2+1)/(x^4+x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\arctan \left(\frac{\sqrt{x^{4}+x^{2}+1}}{x}\right)$&$16$\\ trager&$\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x +\sqrt{x^{4}+x^{2}+1}}{x^{2}+1}\right)$&$36$\\ default&$\frac{2 \sqrt{1-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{-2+2 i \sqrt{3}}}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}-\frac{2 \sqrt{1+\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}}\, \sqrt{1+\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , -\frac{1}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+x^{2}+1}}$&$188$\\ \hline \end{longtable}"," ",0,"arctan(1/x*(x^4+x^2+1)^(1/2))","A"
118,1,18,15,0.289000," ","int((x^4-1)/(x^4+1)/(x^4+x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\arctanh \left(\frac{\sqrt{x^{4}+x^{2}+1}}{x}\right)$&$18$\\ trager&$\frac{\ln \left(-\frac{-x^{4}+2 \sqrt{x^{4}+x^{2}+1}\, x -2 x^{2}-1}{x^{4}+1}\right)}{2}$&$38$\\ default&$\frac{2 \sqrt{1-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{-2+2 i \sqrt{3}}}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2}+1\right) \left(-3 \underline{\hspace{1.25 ex}}\alpha^{2}+5 x^{2}+4\right)}{10 \sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{x^{4}+x^{2}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{\sqrt{2}\, \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{x^{2}+2-i \sqrt{3}\, x^{2}}\, \sqrt{x^{2}+2+i \sqrt{3}\, x^{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , \frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}}{2}+\frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{2}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{i \sqrt{3}-1}\, \sqrt{x^{4}+x^{2}+1}}\right)\right)}{4}$&$250$\\ \hline \end{longtable}"," ",0,"-arctanh(1/x*(x^4+x^2+1)^(1/2))","A"
119,1,32,15,0.243000," ","int((2*x^4+2*x^2-1)/(2*x^2+1)/(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(-\frac{2 x^{4}+2 \sqrt{x^{6}-1}\, x +1}{2 x^{2}+1}\right)}{2}$&$32$\\ \hline \end{longtable}"," ",0,"1/2*ln(-(2*x^4+2*(x^6-1)^(1/2)*x+1)/(2*x^2+1))","B"
120,1,15,14,0.070000," ","int(x^3/(x^2-1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{2 \left(x^{2}-1\right)^{\frac{1}{4}} \left(x^{2}+4\right)}{5}$&$15$\\ trager&$\left(\frac{2 x^{2}}{5}+\frac{8}{5}\right) \left(x^{2}-1\right)^{\frac{1}{4}}$&$16$\\ gosper&$\frac{2 \left(-1+x \right) \left(1+x \right) \left(x^{2}+4\right)}{5 \left(x^{2}-1\right)^{\frac{3}{4}}}$&$21$\\ meijerg&$\frac{\left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[\frac{3}{4}, 2\right], \left[3\right], x^{2}\right) x^{4}}{4 \mathrm{signum}\left(x^{2}-1\right)^{\frac{3}{4}}}$&$33$\\ \hline \end{longtable}"," ",0,"2/5*(x^2-1)^(1/4)*(x^2+4)","A"
121,1,15,14,0.092000," ","int((3+x)/(-1+x)^2/(x^2-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{3 \left(x^{2}-1\right)^{\frac{2}{3}}}{2 \left(-1+x \right)^{2}}$&$15$\\ gosper&$-\frac{3 \left(1+x \right)}{2 \left(-1+x \right) \left(x^{2}-1\right)^{\frac{1}{3}}}$&$18$\\ risch&$-\frac{3 \left(1+x \right)}{2 \left(-1+x \right) \left(x^{2}-1\right)^{\frac{1}{3}}}$&$18$\\ \hline \end{longtable}"," ",0,"-3/2*(x^2-1)^(2/3)/(-1+x)^2","A"
122,1,15,14,0.046000," ","int(x^3/(x^2+1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{3 \left(x^{2}-3\right) \left(x^{2}+1\right)^{\frac{1}{3}}}{8}$&$15$\\ risch&$\frac{3 \left(x^{2}-3\right) \left(x^{2}+1\right)^{\frac{1}{3}}}{8}$&$15$\\ trager&$\left(\frac{3 x^{2}}{8}-\frac{9}{8}\right) \left(x^{2}+1\right)^{\frac{1}{3}}$&$16$\\ meijerg&$\frac{\hypergeom \left(\left[\frac{2}{3}, 2\right], \left[3\right], -x^{2}\right) x^{4}}{4}$&$17$\\ \hline \end{longtable}"," ",0,"3/8*(x^2-3)*(x^2+1)^(1/3)","A"
123,1,15,14,0.060000," ","int(1/x^2/(x^3-x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(x^{3}-x \right)^{\frac{2}{3}}}{4 x^{2}}$&$15$\\ risch&$\frac{\frac{3 x^{2}}{4}-\frac{3}{4}}{x \left(x \left(x^{2}-1\right)\right)^{\frac{1}{3}}}$&$20$\\ gosper&$\frac{3 \left(-1+x \right) \left(1+x \right)}{4 x \left(x^{3}-x \right)^{\frac{1}{3}}}$&$21$\\ meijerg&$-\frac{3 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}} \left(-x^{2}+1\right)^{\frac{2}{3}}}{4 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}} x^{\frac{4}{3}}}$&$33$\\ \hline \end{longtable}"," ",0,"3/4*(x^3-x)^(2/3)/x^2","A"
124,1,20,14,0.066000," ","int((x^3-x)^(1/3)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(x^{2}-1\right) \left(x^{3}-x \right)^{\frac{1}{3}}}{8 x^{3}}$&$20$\\ gosper&$\frac{3 \left(-1+x \right) \left(1+x \right) \left(x^{3}-x \right)^{\frac{1}{3}}}{8 x^{3}}$&$21$\\ risch&$\frac{3 \left(x \left(x^{2}-1\right)\right)^{\frac{1}{3}} \left(x^{4}-2 x^{2}+1\right)}{8 x^{3} \left(x^{2}-1\right)}$&$32$\\ meijerg&$-\frac{3 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}} \left(-x^{2}+1\right)^{\frac{4}{3}}}{8 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}} x^{\frac{8}{3}}}$&$33$\\ \hline \end{longtable}"," ",0,"3/8*(x^2-1)/x^3*(x^3-x)^(1/3)","A"
125,1,11,16,0.079000," ","int((x^2-1)/(x^2+1)/(x^3+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{2 x}{\sqrt{x^{3}+x}}$&$11$\\ default&$-\frac{2 x}{\sqrt{\left(x^{2}+1\right) x}}$&$13$\\ risch&$-\frac{2 x}{\sqrt{\left(x^{2}+1\right) x}}$&$13$\\ elliptic&$-\frac{2 x}{\sqrt{\left(x^{2}+1\right) x}}$&$13$\\ trager&$-\frac{2 \sqrt{x^{3}+x}}{x^{2}+1}$&$17$\\ meijerg&$\frac{2 \hypergeom \left(\left[\frac{5}{4}, \frac{3}{2}\right], \left[\frac{9}{4}\right], -x^{2}\right) x^{\frac{5}{2}}}{5}-2 \hypergeom \left(\left[\frac{1}{4}, \frac{3}{2}\right], \left[\frac{5}{4}\right], -x^{2}\right) \sqrt{x}$&$34$\\ \hline \end{longtable}"," ",0,"-2*x/(x^3+x)^(1/2)","A"
126,1,11,14,0.051000," ","int(1/x/(x^3+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{3 \left(1+x \right)^{\frac{2}{3}}}{2 x^{\frac{2}{3}}}$&$11$\\ gosper&$-\frac{3 \left(1+x \right)}{2 \left(x^{3}+x^{2}\right)^{\frac{1}{3}}}$&$15$\\ trager&$-\frac{3 \left(x^{3}+x^{2}\right)^{\frac{2}{3}}}{2 x^{2}}$&$15$\\ risch&$-\frac{3 \left(1+x \right)}{2 \left(x^{2} \left(1+x \right)\right)^{\frac{1}{3}}}$&$15$\\ \hline \end{longtable}"," ",0,"-3/2*(1+x)^(2/3)/x^(2/3)","A"
127,1,15,14,0.064000," ","int((2+x)/x^2/(x^3+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{4 \left(x^{3}+x^{2}\right)^{\frac{3}{4}}}{3 x^{3}}$&$15$\\ gosper&$-\frac{4 \left(1+x \right)}{3 x \left(x^{3}+x^{2}\right)^{\frac{1}{4}}}$&$18$\\ risch&$-\frac{4 \left(1+x \right)}{3 x \left(x^{2} \left(1+x \right)\right)^{\frac{1}{4}}}$&$18$\\ meijerg&$-\frac{4 \hypergeom \left(\left[-\frac{3}{2}, \frac{1}{4}\right], \left[-\frac{1}{2}\right], -x \right)}{3 x^{\frac{3}{2}}}-\frac{2 \hypergeom \left(\left[-\frac{1}{2}, \frac{1}{4}\right], \left[\frac{1}{2}\right], -x \right)}{\sqrt{x}}$&$30$\\ \hline \end{longtable}"," ",0,"-4/3*(x^3+x^2)^(3/4)/x^3","A"
128,1,15,14,0.358000," ","int((a*x^3-2*b)*(a*x^3+b)^(1/2)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{2 \left(a \,x^{3}+b \right)^{\frac{3}{2}}}{3 x^{3}}$&$15$\\ trager&$\frac{2 \left(a \,x^{3}+b \right)^{\frac{3}{2}}}{3 x^{3}}$&$15$\\ risch&$\frac{2 \left(a \,x^{3}+b \right)^{\frac{3}{2}}}{3 x^{3}}$&$15$\\ elliptic&$\frac{2 b \sqrt{a \,x^{3}+b}}{3 x^{3}}+\frac{2 a \sqrt{a \,x^{3}+b}}{3}$&$29$\\ default&$a \left(\frac{2 \sqrt{a \,x^{3}+b}}{3}-\frac{2 \sqrt{b}\, \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{3}\right)-2 b \left(-\frac{\sqrt{a \,x^{3}+b}}{3 x^{3}}-\frac{a \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{3 \sqrt{b}}\right)$&$73$\\ \hline \end{longtable}"," ",0,"2/3*(a*x^3+b)^(3/2)/x^3","A"
129,1,15,14,0.116000," ","int((x^2+x+1)/(-1+x)^2/(x^4-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{x^{4}-1}}{2 \left(-1+x \right)^{2}}$&$15$\\ trager&$-\frac{\sqrt{x^{4}-1}}{2 \left(-1+x \right)^{2}}$&$15$\\ elliptic&$-\frac{\sqrt{x^{4}-1}}{2 \left(-1+x \right)^{2}}$&$15$\\ gosper&$-\frac{\left(1+x \right) \left(x^{2}+1\right)}{2 \left(-1+x \right) \sqrt{x^{4}-1}}$&$23$\\ risch&$-\frac{x^{3}+x^{2}+x +1}{2 \left(-1+x \right) \sqrt{x^{4}-1}}$&$24$\\ \hline \end{longtable}"," ",0,"-1/2*(x^4-1)^(1/2)/(-1+x)^2","A"
130,1,20,14,0.111000," ","int((x^4-1)/x^2/(x^3-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{2}-1\right) \sqrt{x^{3}-x}}{3 x^{2}}$&$20$\\ risch&$\frac{\frac{2}{3} x^{4}-\frac{4}{3} x^{2}+\frac{2}{3}}{x \sqrt{x \left(x^{2}-1\right)}}$&$25$\\ gosper&$\frac{2 \left(x^{2}-1\right) \left(-1+x \right) \left(1+x \right)}{3 \sqrt{x^{3}-x}\, x}$&$26$\\ default&$\frac{2 \sqrt{x^{3}-x}}{3}-\frac{2 \sqrt{x^{3}-x}}{3 x^{2}}$&$27$\\ elliptic&$\frac{2 \sqrt{x^{3}-x}}{3}-\frac{2 \sqrt{x^{3}-x}}{3 x^{2}}$&$27$\\ meijerg&$\frac{2 \sqrt{-\mathrm{signum}\left(x^{2}-1\right)}\, \hypergeom \left(\left[\frac{1}{2}, \frac{5}{4}\right], \left[\frac{9}{4}\right], x^{2}\right) x^{\frac{5}{2}}}{5 \sqrt{\mathrm{signum}\left(x^{2}-1\right)}}+\frac{2 \sqrt{-\mathrm{signum}\left(x^{2}-1\right)}\, \hypergeom \left(\left[-\frac{3}{4}, \frac{1}{2}\right], \left[\frac{1}{4}\right], x^{2}\right)}{3 \sqrt{\mathrm{signum}\left(x^{2}-1\right)}\, x^{\frac{3}{2}}}$&$66$\\ \hline \end{longtable}"," ",0,"2/3*(x^2-1)/x^2*(x^3-x)^(1/2)","A"
131,1,15,14,0.219000," ","int(1/x^2/(x^4-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 \sqrt{x^{4}-x}}{3 x^{2}}$&$15$\\ trager&$\frac{2 \sqrt{x^{4}-x}}{3 x^{2}}$&$15$\\ elliptic&$\frac{2 \sqrt{x^{4}-x}}{3 x^{2}}$&$15$\\ risch&$\frac{\frac{2 x^{3}}{3}-\frac{2}{3}}{x \sqrt{x \left(x^{3}-1\right)}}$&$20$\\ gosper&$\frac{2 \left(-1+x \right) \left(x^{2}+x +1\right)}{3 x \sqrt{x^{4}-x}}$&$24$\\ meijerg&$-\frac{2 \sqrt{-\mathrm{signum}\left(x^{3}-1\right)}\, \sqrt{-x^{3}+1}}{3 \sqrt{\mathrm{signum}\left(x^{3}-1\right)}\, x^{\frac{3}{2}}}$&$33$\\ \hline \end{longtable}"," ",0,"2/3*(x^4-x)^(1/2)/x^2","A"
132,1,15,14,0.079000," ","int(1/x^3/(x^4-x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{4}-x \right)^{\frac{3}{4}}}{9 x^{3}}$&$15$\\ risch&$\frac{\frac{4 x^{3}}{9}-\frac{4}{9}}{x^{2} \left(x \left(x^{3}-1\right)\right)^{\frac{1}{4}}}$&$20$\\ gosper&$\frac{4 \left(-1+x \right) \left(x^{2}+x +1\right)}{9 x^{2} \left(x^{4}-x \right)^{\frac{1}{4}}}$&$24$\\ meijerg&$-\frac{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}} \left(-x^{3}+1\right)^{\frac{3}{4}}}{9 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}} x^{\frac{9}{4}}}$&$33$\\ \hline \end{longtable}"," ",0,"4/9*(x^4-x)^(3/4)/x^3","A"
133,1,20,14,0.074000," ","int((x^3-1)/x^6/(x^4-x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{3}-1\right) \left(x^{4}-x \right)^{\frac{3}{4}}}{21 x^{6}}$&$20$\\ risch&$\frac{\frac{4}{21} x^{6}-\frac{8}{21} x^{3}+\frac{4}{21}}{x^{5} \left(x \left(x^{3}-1\right)\right)^{\frac{1}{4}}}$&$25$\\ gosper&$\frac{4 \left(-1+x \right) \left(x^{2}+x +1\right) \left(x^{3}-1\right)}{21 x^{5} \left(x^{4}-x \right)^{\frac{1}{4}}}$&$29$\\ meijerg&$\frac{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}} \left(1+\frac{4 x^{3}}{3}\right) \left(-x^{3}+1\right)^{\frac{3}{4}}}{21 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}} x^{\frac{21}{4}}}-\frac{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}} \left(-x^{3}+1\right)^{\frac{3}{4}}}{9 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}} x^{\frac{9}{4}}}$&$73$\\ \hline \end{longtable}"," ",0,"4/21*(x^3-1)*(x^4-x)^(3/4)/x^6","A"
134,1,20,14,0.072000," ","int((x^4-x)^(1/4)/x^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{3}-1\right) \left(x^{4}-x \right)^{\frac{1}{4}}}{15 x^{4}}$&$20$\\ gosper&$\frac{4 \left(-1+x \right) \left(x^{2}+x +1\right) \left(x^{4}-x \right)^{\frac{1}{4}}}{15 x^{4}}$&$24$\\ risch&$\frac{4 \left(x \left(x^{3}-1\right)\right)^{\frac{1}{4}} \left(x^{6}-2 x^{3}+1\right)}{15 x^{4} \left(x^{3}-1\right)}$&$32$\\ meijerg&$-\frac{4 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}} \left(-x^{3}+1\right)^{\frac{5}{4}}}{15 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}} x^{\frac{15}{4}}}$&$33$\\ \hline \end{longtable}"," ",0,"4/15*(x^3-1)/x^4*(x^4-x)^(1/4)","A"
135,1,20,14,0.115000," ","int((x^3+2)*(x^4-x)^(1/3)/(x^3-1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{3 x \left(x^{4}-x \right)^{\frac{1}{3}}}{2 \left(x^{3}-1\right)}$&$20$\\ trager&$-\frac{3 x \left(x^{4}-x \right)^{\frac{1}{3}}}{2 \left(x^{3}-1\right)}$&$20$\\ risch&$-\frac{3 \left(x \left(x^{3}-1\right)\right)^{\frac{1}{3}} x}{2 \left(x^{3}-1\right)}$&$20$\\ meijerg&$\frac{3 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[\frac{4}{9}, \frac{5}{3}\right], \left[\frac{13}{9}\right], x^{3}\right) x^{\frac{4}{3}}}{2 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}}}+\frac{3 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[\frac{13}{9}, \frac{5}{3}\right], \left[\frac{22}{9}\right], x^{3}\right) x^{\frac{13}{3}}}{13 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}}}$&$66$\\ \hline \end{longtable}"," ",0,"-3/2*x*(x^4-x)^(1/3)/(x^3-1)","A"
136,1,20,14,0.100000," ","int((x^4-x)^(1/2)/x^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{3}-1\right) \sqrt{x^{4}-x}}{9 x^{5}}$&$20$\\ gosper&$\frac{2 \left(-1+x \right) \left(x^{2}+x +1\right) \sqrt{x^{4}-x}}{9 x^{5}}$&$24$\\ risch&$\frac{\frac{2}{9} x^{6}-\frac{4}{9} x^{3}+\frac{2}{9}}{x^{4} \sqrt{x \left(x^{3}-1\right)}}$&$25$\\ default&$-\frac{2 \sqrt{x^{4}-x}}{9 x^{5}}+\frac{2 \sqrt{x^{4}-x}}{9 x^{2}}$&$30$\\ elliptic&$-\frac{2 \sqrt{x^{4}-x}}{9 x^{5}}+\frac{2 \sqrt{x^{4}-x}}{9 x^{2}}$&$30$\\ meijerg&$-\frac{2 \sqrt{\mathrm{signum}\left(x^{3}-1\right)}\, \left(-x^{3}+1\right)^{\frac{3}{2}}}{9 \sqrt{-\mathrm{signum}\left(x^{3}-1\right)}\, x^{\frac{9}{2}}}$&$33$\\ \hline \end{longtable}"," ",0,"2/9/x^5*(x^3-1)*(x^4-x)^(1/2)","A"
137,1,7,14,0.182000," ","int(x/(x^4+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{2 \arcsinh \left(x^{\frac{3}{2}}\right)}{3}$&$7$\\ trager&$-\frac{\ln \left(2 x^{3}-2 x \sqrt{x^{4}+x}+1\right)}{3}$&$21$\\ default&$-\frac{2 \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$290$\\ elliptic&$-\frac{2 \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$290$\\ \hline \end{longtable}"," ",0,"2/3*arcsinh(x^(3/2))","A"
138,1,11,16,0.076000," ","int((x^3-2)/(x^3+1)/(x^4+x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{3 x}{\left(x^{4}+x \right)^{\frac{1}{3}}}$&$11$\\ risch&$-\frac{3 x}{\left(x \left(x^{3}+1\right)\right)^{\frac{1}{3}}}$&$13$\\ trager&$-\frac{3 \left(x^{4}+x \right)^{\frac{2}{3}}}{x^{3}+1}$&$17$\\ meijerg&$-3 \hypergeom \left(\left[\frac{2}{9}, \frac{4}{3}\right], \left[\frac{11}{9}\right], -x^{3}\right) x^{\frac{2}{3}}+\frac{3 \hypergeom \left(\left[\frac{11}{9}, \frac{4}{3}\right], \left[\frac{20}{9}\right], -x^{3}\right) x^{\frac{11}{3}}}{11}$&$34$\\ \hline \end{longtable}"," ",0,"-3*x/(x^4+x)^(1/3)","A"
139,1,15,14,0.074000," ","int((x^2-1)/x/(x^4+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(x^{4}+x^{2}\right)^{\frac{2}{3}}}{2 x^{2}}$&$15$\\ gosper&$\frac{\frac{3 x^{2}}{2}+\frac{3}{2}}{\left(x^{4}+x^{2}\right)^{\frac{1}{3}}}$&$17$\\ risch&$\frac{\frac{3 x^{2}}{2}+\frac{3}{2}}{\left(x^{2} \left(x^{2}+1\right)\right)^{\frac{1}{3}}}$&$19$\\ meijerg&$\frac{3 \hypergeom \left(\left[-\frac{1}{3}, \frac{1}{3}\right], \left[\frac{2}{3}\right], -x^{2}\right)}{2 x^{\frac{2}{3}}}+\frac{3 \hypergeom \left(\left[\frac{1}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], -x^{2}\right) x^{\frac{4}{3}}}{4}$&$34$\\ \hline \end{longtable}"," ",0,"3/2*(x^4+x^2)^(2/3)/x^2","A"
140,1,13,14,0.055000," ","int(1/x^2/(x^4+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{2 \left(x^{2}+1\right)^{\frac{3}{4}}}{3 x^{\frac{3}{2}}}$&$13$\\ trager&$-\frac{2 \left(x^{4}+x^{2}\right)^{\frac{3}{4}}}{3 x^{3}}$&$15$\\ gosper&$-\frac{2 \left(x^{2}+1\right)}{3 x \left(x^{4}+x^{2}\right)^{\frac{1}{4}}}$&$20$\\ risch&$-\frac{2 \left(x^{2}+1\right)}{3 x \left(x^{2} \left(x^{2}+1\right)\right)^{\frac{1}{4}}}$&$22$\\ \hline \end{longtable}"," ",0,"-2/3*(x^2+1)^(3/4)/x^(3/2)","A"
141,1,13,14,0.051000," ","int((x^4+x^2)^(1/4)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{2 \left(x^{2}+1\right)^{\frac{5}{4}}}{5 x^{\frac{5}{2}}}$&$13$\\ gosper&$-\frac{2 \left(x^{2}+1\right) \left(x^{4}+x^{2}\right)^{\frac{1}{4}}}{5 x^{3}}$&$20$\\ trager&$-\frac{2 \left(x^{2}+1\right) \left(x^{4}+x^{2}\right)^{\frac{1}{4}}}{5 x^{3}}$&$20$\\ risch&$-\frac{2 \left(x^{2} \left(x^{2}+1\right)\right)^{\frac{1}{4}} \left(x^{4}+2 x^{2}+1\right)}{5 x^{3} \left(x^{2}+1\right)}$&$34$\\ \hline \end{longtable}"," ",0,"-2/5*(x^2+1)^(5/4)/x^(5/2)","A"
142,1,20,14,0.079000," ","int((x^2-1)*(x^4+x^2)^(1/3)/x^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{3 \left(x^{2}+1\right) \left(x^{4}+x^{2}\right)^{\frac{1}{3}}}{4 x^{2}}$&$20$\\ trager&$\frac{3 \left(x^{2}+1\right) \left(x^{4}+x^{2}\right)^{\frac{1}{3}}}{4 x^{2}}$&$20$\\ meijerg&$\frac{3 \hypergeom \left(\left[-\frac{2}{3}, -\frac{1}{3}\right], \left[\frac{1}{3}\right], -x^{2}\right)}{4 x^{\frac{4}{3}}}+\frac{3 \hypergeom \left(\left[-\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{2}\right) x^{\frac{2}{3}}}{2}$&$34$\\ risch&$\frac{3 \left(x^{2} \left(x^{2}+1\right)\right)^{\frac{1}{3}} \left(x^{4}+2 x^{2}+1\right)}{4 x^{2} \left(x^{2}+1\right)}$&$34$\\ \hline \end{longtable}"," ",0,"3/4*(x^2+1)*(x^4+x^2)^(1/3)/x^2","A"
143,1,11,14,0.055000," ","int(1/x/(x^4+x^3)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{4 \left(1+x \right)^{\frac{3}{4}}}{3 x^{\frac{3}{4}}}$&$11$\\ gosper&$-\frac{4 \left(1+x \right)}{3 \left(x^{4}+x^{3}\right)^{\frac{1}{4}}}$&$15$\\ trager&$-\frac{4 \left(x^{4}+x^{3}\right)^{\frac{3}{4}}}{3 x^{3}}$&$15$\\ risch&$-\frac{4 \left(1+x \right)}{3 \left(x^{3} \left(1+x \right)\right)^{\frac{1}{4}}}$&$15$\\ \hline \end{longtable}"," ",0,"-4/3*(1+x)^(3/4)/x^(3/4)","A"
144,1,20,14,0.060000," ","int((1+x)*(x^4+x^3)^(1/4)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{4 \left(1+x \right)^{2} \left(x^{4}+x^{3}\right)^{\frac{1}{4}}}{9 x^{3}}$&$20$\\ trager&$-\frac{4 \left(x^{2}+2 x +1\right) \left(x^{4}+x^{3}\right)^{\frac{1}{4}}}{9 x^{3}}$&$23$\\ meijerg&$-\frac{4 \left(-\frac{4}{5} x^{2}+\frac{1}{5} x +1\right) \left(1+x \right)^{\frac{1}{4}}}{9 x^{\frac{9}{4}}}-\frac{4 \left(1+x \right)^{\frac{5}{4}}}{5 x^{\frac{5}{4}}}$&$32$\\ risch&$-\frac{4 \left(x^{3} \left(1+x \right)\right)^{\frac{1}{4}} \left(x^{3}+3 x^{2}+3 x +1\right)}{9 \left(1+x \right) x^{3}}$&$33$\\ \hline \end{longtable}"," ",0,"-4/9/x^3*(1+x)^2*(x^4+x^3)^(1/4)","A"
145,1,39,16,6.077000," ","int((2*x^4-x-2)/(x^4+x+1)/(x^4+x^2+x+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(-\frac{x^{4}+2 \sqrt{x^{4}+x^{2}+x +1}\, x +2 x^{2}+x +1}{x^{4}+x +1}\right)$&$39$\\ default&$\text{Expression too large to display}$&$4880$\\ elliptic&$\text{Expression too large to display}$&$4880$\\ \hline \end{longtable}"," ",0,"-ln(-(x^4+2*(x^4+x^2+x+1)^(1/2)*x+2*x^2+x+1)/(x^4+x+1))","B"
146,1,15,14,0.107000," ","int((x^4+3)/x^3/(x^5-x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{5}-x \right)^{\frac{3}{4}}}{3 x^{3}}$&$15$\\ risch&$\frac{\frac{4 x^{4}}{3}-\frac{4}{3}}{x^{2} \left(x \left(x^{4}-1\right)\right)^{\frac{1}{4}}}$&$20$\\ gosper&$\frac{4 \left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}{3 x^{2} \left(x^{5}-x \right)^{\frac{1}{4}}}$&$26$\\ meijerg&$-\frac{4 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{9}{16}, \frac{1}{4}\right], \left[\frac{7}{16}\right], x^{4}\right)}{3 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}} x^{\frac{9}{4}}}+\frac{4 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[\frac{1}{4}, \frac{7}{16}\right], \left[\frac{23}{16}\right], x^{4}\right) x^{\frac{7}{4}}}{7 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}}}$&$66$\\ \hline \end{longtable}"," ",0,"4/3*(x^5-x)^(3/4)/x^3","A"
147,1,20,14,0.095000," ","int((x^4-1)*(x^4+3)/x^6/(x^5-x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{4}-1\right) \left(x^{5}-x \right)^{\frac{3}{4}}}{7 x^{6}}$&$20$\\ risch&$\frac{\frac{4}{7} x^{8}-\frac{8}{7} x^{4}+\frac{4}{7}}{x^{5} \left(x \left(x^{4}-1\right)\right)^{\frac{1}{4}}}$&$25$\\ gosper&$\frac{4 \left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right) \left(x^{4}-1\right)}{7 x^{5} \left(x^{5}-x \right)^{\frac{1}{4}}}$&$31$\\ meijerg&$\frac{4 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{21}{16}, \frac{1}{4}\right], \left[-\frac{5}{16}\right], x^{4}\right)}{7 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}} x^{\frac{21}{4}}}-\frac{8 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{5}{16}, \frac{1}{4}\right], \left[\frac{11}{16}\right], x^{4}\right)}{5 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}} x^{\frac{5}{4}}}+\frac{4 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[\frac{1}{4}, \frac{11}{16}\right], \left[\frac{27}{16}\right], x^{4}\right) x^{\frac{11}{4}}}{11 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}}}$&$98$\\ \hline \end{longtable}"," ",0,"4/7*(x^4-1)/x^6*(x^5-x)^(3/4)","A"
148,1,11,16,0.085000," ","int((x^4-3)/(x^4+1)/(x^5+x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{4 x}{\left(x^{5}+x \right)^{\frac{1}{4}}}$&$11$\\ risch&$-\frac{4 x}{\left(x \left(x^{4}+1\right)\right)^{\frac{1}{4}}}$&$13$\\ trager&$-\frac{4 \left(x^{5}+x \right)^{\frac{3}{4}}}{x^{4}+1}$&$17$\\ meijerg&$-4 \hypergeom \left(\left[\frac{3}{16}, \frac{5}{4}\right], \left[\frac{19}{16}\right], -x^{4}\right) x^{\frac{3}{4}}+\frac{4 \hypergeom \left(\left[\frac{19}{16}, \frac{5}{4}\right], \left[\frac{35}{16}\right], -x^{4}\right) x^{\frac{19}{4}}}{19}$&$34$\\ \hline \end{longtable}"," ",0,"-4*x/(x^5+x)^(1/4)","A"
149,1,20,14,0.095000," ","int((2*x^3-1)*(x^5+x^2)^(1/3)/x^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(x^{3}+1\right) \left(x^{5}+x^{2}\right)^{\frac{1}{3}}}{4 x^{2}}$&$20$\\ gosper&$\frac{3 \left(x^{2}-x +1\right) \left(1+x \right) \left(x^{5}+x^{2}\right)^{\frac{1}{3}}}{4 x^{2}}$&$26$\\ meijerg&$\frac{3 \hypergeom \left(\left[-\frac{4}{9}, -\frac{1}{3}\right], \left[\frac{5}{9}\right], -x^{3}\right)}{4 x^{\frac{4}{3}}}+\frac{6 \hypergeom \left(\left[-\frac{1}{3}, \frac{5}{9}\right], \left[\frac{14}{9}\right], -x^{3}\right) x^{\frac{5}{3}}}{5}$&$34$\\ risch&$\frac{3 \left(x^{2} \left(x^{3}+1\right)\right)^{\frac{1}{3}} \left(x^{6}+2 x^{3}+1\right)}{4 x^{2} \left(x^{3}+1\right)}$&$34$\\ \hline \end{longtable}"," ",0,"3/4*(x^3+1)/x^2*(x^5+x^2)^(1/3)","A"
150,1,15,14,0.070000," ","int((x^2-1)/x/(x^5+x^3)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}}{3 x^{3}}$&$15$\\ gosper&$\frac{\frac{4 x^{2}}{3}+\frac{4}{3}}{\left(x^{5}+x^{3}\right)^{\frac{1}{4}}}$&$17$\\ risch&$\frac{\frac{4 x^{2}}{3}+\frac{4}{3}}{\left(x^{3} \left(x^{2}+1\right)\right)^{\frac{1}{4}}}$&$19$\\ meijerg&$\frac{4 \hypergeom \left(\left[-\frac{3}{8}, \frac{1}{4}\right], \left[\frac{5}{8}\right], -x^{2}\right)}{3 x^{\frac{3}{4}}}+\frac{4 \hypergeom \left(\left[\frac{1}{4}, \frac{5}{8}\right], \left[\frac{13}{8}\right], -x^{2}\right) x^{\frac{5}{4}}}{5}$&$34$\\ \hline \end{longtable}"," ",0,"4/3*(x^5+x^3)^(3/4)/x^3","A"
151,1,22,14,0.094000," ","int((x^4-1)*(x^5+x^3)^(1/4)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{4 \left(x^{2}+1\right)^{2} \left(x^{5}+x^{3}\right)^{\frac{1}{4}}}{9 x^{3}}$&$22$\\ trager&$\frac{4 \left(x^{4}+2 x^{2}+1\right) \left(x^{5}+x^{3}\right)^{\frac{1}{4}}}{9 x^{3}}$&$25$\\ meijerg&$\frac{4 \hypergeom \left(\left[-\frac{9}{8}, -\frac{1}{4}\right], \left[-\frac{1}{8}\right], -x^{2}\right)}{9 x^{\frac{9}{4}}}+\frac{4 \hypergeom \left(\left[-\frac{1}{4}, \frac{7}{8}\right], \left[\frac{15}{8}\right], -x^{2}\right) x^{\frac{7}{4}}}{7}$&$34$\\ risch&$\frac{4 \left(x^{3} \left(x^{2}+1\right)\right)^{\frac{1}{4}} \left(x^{6}+3 x^{4}+3 x^{2}+1\right)}{9 x^{3} \left(x^{2}+1\right)}$&$39$\\ \hline \end{longtable}"," ",0,"4/9*(x^2+1)^2*(x^5+x^3)^(1/4)/x^3","A"
152,1,17,14,0.150000," ","int(x^2/(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\ln \left(x^{3}-\sqrt{x^{6}-1}\right)}{3}$&$17$\\ meijerg&$\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \arcsin \left(x^{3}\right)}{3 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}$&$25$\\ \hline \end{longtable}"," ",0,"-1/3*ln(x^3-(x^6-1)^(1/2))","A"
153,1,7,14,0.135000," ","int(x^2/(x^6+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\arcsinh \left(x^{3}\right)}{3}$&$7$\\ trager&$-\frac{\ln \left(x^{3}-\sqrt{x^{6}+1}\right)}{3}$&$17$\\ \hline \end{longtable}"," ",0,"1/3*arcsinh(x^3)","A"
154,1,20,14,0.124000," ","int((x^5-1)*(2*x^5+3)/x^6/(x^6-x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{5}-1\right) \left(x^{6}-x \right)^{\frac{3}{4}}}{7 x^{6}}$&$20$\\ risch&$\frac{\frac{4}{7} x^{10}-\frac{8}{7} x^{5}+\frac{4}{7}}{x^{5} \left(x \left(x^{5}-1\right)\right)^{\frac{1}{4}}}$&$25$\\ gosper&$\frac{4 \left(-1+x \right) \left(x^{4}+x^{3}+x^{2}+x +1\right) \left(x^{5}-1\right)}{7 x^{5} \left(x^{6}-x \right)^{\frac{1}{4}}}$&$35$\\ meijerg&$\frac{4 \left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{21}{20}, \frac{1}{4}\right], \left[-\frac{1}{20}\right], x^{5}\right)}{7 \mathrm{signum}\left(x^{5}-1\right)^{\frac{1}{4}} x^{\frac{21}{4}}}-\frac{4 \left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{1}{20}, \frac{1}{4}\right], \left[\frac{19}{20}\right], x^{5}\right)}{\mathrm{signum}\left(x^{5}-1\right)^{\frac{1}{4}} x^{\frac{1}{4}}}+\frac{8 \left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[\frac{1}{4}, \frac{19}{20}\right], \left[\frac{39}{20}\right], x^{5}\right) x^{\frac{19}{4}}}{19 \mathrm{signum}\left(x^{5}-1\right)^{\frac{1}{4}}}$&$98$\\ \hline \end{longtable}"," ",0,"4/7*(x^5-1)/x^6*(x^6-x)^(3/4)","A"
155,1,13,14,0.058000," ","int(1/x^3/(x^6+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{3 \left(x^{4}+1\right)^{\frac{2}{3}}}{8 x^{\frac{8}{3}}}$&$13$\\ trager&$-\frac{3 \left(x^{6}+x^{2}\right)^{\frac{2}{3}}}{8 x^{4}}$&$15$\\ gosper&$-\frac{3 \left(x^{4}+1\right)}{8 x^{2} \left(x^{6}+x^{2}\right)^{\frac{1}{3}}}$&$20$\\ risch&$-\frac{3 \left(x^{4}+1\right)}{8 x^{2} \left(x^{2} \left(x^{4}+1\right)\right)^{\frac{1}{3}}}$&$22$\\ \hline \end{longtable}"," ",0,"-3/8*(x^4+1)^(2/3)/x^(8/3)","A"
156,1,15,14,0.088000," ","int((x^4-1)/x^2/(x^6+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{3 x^{3}}$&$15$\\ gosper&$\frac{\frac{2 x^{4}}{3}+\frac{2}{3}}{\left(x^{6}+x^{2}\right)^{\frac{1}{4}} x}$&$20$\\ risch&$\frac{\frac{2 x^{4}}{3}+\frac{2}{3}}{x \left(x^{2} \left(x^{4}+1\right)\right)^{\frac{1}{4}}}$&$22$\\ meijerg&$\frac{2 \hypergeom \left(\left[-\frac{3}{8}, \frac{1}{4}\right], \left[\frac{5}{8}\right], -x^{4}\right)}{3 x^{\frac{3}{2}}}+\frac{2 \hypergeom \left(\left[\frac{1}{4}, \frac{5}{8}\right], \left[\frac{13}{8}\right], -x^{4}\right) x^{\frac{5}{2}}}{5}$&$34$\\ \hline \end{longtable}"," ",0,"2/3*(x^6+x^2)^(3/4)/x^3","A"
157,1,20,14,0.091000," ","int((x^4-1)*(x^6+x^2)^(1/4)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{2 \left(x^{4}+1\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}}}{5 x^{3}}$&$20$\\ trager&$\frac{2 \left(x^{4}+1\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}}}{5 x^{3}}$&$20$\\ meijerg&$\frac{2 \hypergeom \left(\left[-\frac{5}{8}, -\frac{1}{4}\right], \left[\frac{3}{8}\right], -x^{4}\right)}{5 x^{\frac{5}{2}}}+\frac{2 \hypergeom \left(\left[-\frac{1}{4}, \frac{3}{8}\right], \left[\frac{11}{8}\right], -x^{4}\right) x^{\frac{3}{2}}}{3}$&$34$\\ risch&$\frac{2 \left(x^{2} \left(x^{4}+1\right)\right)^{\frac{1}{4}} \left(x^{8}+2 x^{4}+1\right)}{5 x^{3} \left(x^{4}+1\right)}$&$34$\\ \hline \end{longtable}"," ",0,"2/5*(x^4+1)*(x^6+x^2)^(1/4)/x^3","A"
158,0,0,14,0.016000," ","int((1+(x^2+1)^(1/2))^(1/2)/(x^2+1)^(1/2),x)","\[\int \frac{\sqrt{1+\sqrt{x^{2}+1}}}{\sqrt{x^{2}+1}}\, dx\]"," ",0,"int((1+(x^2+1)^(1/2))^(1/2)/(x^2+1)^(1/2),x)","F"
159,1,13,17,0.270000," ","int((x^2-2*x-2)/(x^2+x+1)/(x^3-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{2 \left(-1+x \right)}{\sqrt{x^{3}-1}}$&$13$\\ risch&$-\frac{2 \left(-1+x \right)}{\sqrt{x^{3}-1}}$&$13$\\ default&$-\frac{2 \left(-1+x \right)}{\sqrt{\left(-1+x \right) \left(x^{2}+x +1\right)}}$&$18$\\ trager&$-\frac{2 \sqrt{x^{3}-1}}{x^{2}+x +1}$&$18$\\ elliptic&$-\frac{2 \left(-1+x \right)}{\sqrt{\left(-1+x \right) \left(x^{2}+x +1\right)}}$&$18$\\ \hline \end{longtable}"," ",0,"-2*(-1+x)/(x^3-1)^(1/2)","A"
160,1,18,17,0.126000," ","int((a*x^2+b)/x/(a*x^3-b*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \sqrt{a \,x^{3}-b x}}{x}$&$18$\\ gosper&$\frac{2 a \,x^{2}-2 b}{\sqrt{a \,x^{3}-b x}}$&$24$\\ risch&$\frac{2 a \,x^{2}-2 b}{\sqrt{x \left(a \,x^{2}-b \right)}}$&$25$\\ elliptic&$\frac{2 a \,x^{2}-2 b}{\sqrt{x \left(a \,x^{2}-b \right)}}$&$25$\\ default&$\frac{\sqrt{a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \left(-\frac{2 \sqrt{a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{\sqrt{2}}{2}\right)}{a}+\frac{\sqrt{a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{\sqrt{2}}{2}\right)}{a}\right)}{\sqrt{a \,x^{3}-b x}}+b \left(\frac{2 a \,x^{2}-2 b}{b \sqrt{x \left(a \,x^{2}-b \right)}}-\frac{\sqrt{a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \left(-\frac{2 \sqrt{a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{\sqrt{2}}{2}\right)}{a}+\frac{\sqrt{a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{\sqrt{2}}{2}\right)}{a}\right)}{b \sqrt{a \,x^{3}-b x}}\right)$&$322$\\ \hline \end{longtable}"," ",0,"2*(a*x^3-b*x)^(1/2)/x","A"
161,1,46,17,0.375000," ","int((2*x^2-2*x-1)/(2*x^2+1)/(x^4+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) x +2 \sqrt{x^{4}+x}-\RootOf \left(\textit{\_Z}^{2}+1\right)}{2 x^{2}+1}\right)$&$46$\\ default&$\text{Expression too large to display}$&$13532$\\ elliptic&$\text{Expression too large to display}$&$14832$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2+1)*ln((2*RootOf(_Z^2+1)*x+2*(x^4+x)^(1/2)-RootOf(_Z^2+1))/(2*x^2+1))","C"
162,1,18,17,0.412000," ","int((x^4+1)/(x^4-1)/(x^4-x^2-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\arctan \left(\frac{\sqrt{x^{4}-x^{2}-1}}{x}\right)$&$18$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-2 x \sqrt{x^{4}-x^{2}-1}-\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)}{2}$&$73$\\ default&$\frac{2 \sqrt{1-\left(-\frac{1}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{-2-2 \sqrt{5}}}{2}, \frac{i \sqrt{5}}{2}-\frac{i}{2}\right)}{\sqrt{-2-2 \sqrt{5}}\, \sqrt{x^{4}-x^{2}-1}}-\frac{\sqrt{1-\left(-\frac{1}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}-\frac{\sqrt{5}}{2}}\, x , \frac{1}{-\frac{1}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}}}{\sqrt{-\frac{1}{2}-\frac{\sqrt{5}}{2}}}\right)}{\sqrt{-\frac{1}{2}-\frac{\sqrt{5}}{2}}\, \sqrt{x^{4}-x^{2}-1}}-\frac{\sqrt{1+\frac{x^{2}}{2}+\frac{\sqrt{5}\, x^{2}}{2}}\, \sqrt{1-\frac{\sqrt{5}\, x^{2}}{2}+\frac{x^{2}}{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}-\frac{\sqrt{5}}{2}}\, x , -\frac{1}{-\frac{1}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}}}{\sqrt{-\frac{1}{2}-\frac{\sqrt{5}}{2}}}\right)}{\sqrt{-\frac{1}{2}-\frac{\sqrt{5}}{2}}\, \sqrt{x^{4}-x^{2}-1}}$&$273$\\ \hline \end{longtable}"," ",0,"arctan(1/x*(x^4-x^2-1)^(1/2))","A"
163,1,16,15,0.051000," ","int(x/(x^4-4*x^3+6*x^2-4*x+1)^(1/5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{5 \left(-1+x \right) \left(5+x \right)}{6 \left(\left(-1+x \right)^{4}\right)^{\frac{1}{5}}}$&$16$\\ gosper&$\frac{5 \left(-1+x \right) \left(5+x \right)}{6 \left(x^{4}-4 x^{3}+6 x^{2}-4 x +1\right)^{\frac{1}{5}}}$&$29$\\ trager&$\frac{5 \left(5+x \right) \left(x^{4}-4 x^{3}+6 x^{2}-4 x +1\right)^{\frac{4}{5}}}{6 \left(-1+x \right)^{3}}$&$31$\\ \hline \end{longtable}"," ",0,"5/6*(-1+x)*(5+x)/((-1+x)^4)^(1/5)","A"
164,1,16,15,0.075000," ","int((x^6-2)/x^4/(x^6+x^4+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{2 \left(x^{6}+x^{4}+1\right)^{\frac{3}{4}}}{3 x^{3}}$&$16$\\ trager&$\frac{2 \left(x^{6}+x^{4}+1\right)^{\frac{3}{4}}}{3 x^{3}}$&$16$\\ risch&$\frac{2 \left(x^{6}+x^{4}+1\right)^{\frac{3}{4}}}{3 x^{3}}$&$16$\\ \hline \end{longtable}"," ",0,"2/3*(x^6+x^4+1)^(3/4)/x^3","A"
165,1,16,15,0.072000," ","int((x^8+1)/x^4/(x^8+x^4-1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{\left(x^{8}+x^{4}-1\right)^{\frac{3}{4}}}{3 x^{3}}$&$16$\\ trager&$\frac{\left(x^{8}+x^{4}-1\right)^{\frac{3}{4}}}{3 x^{3}}$&$16$\\ risch&$\frac{\left(x^{8}+x^{4}-1\right)^{\frac{3}{4}}}{3 x^{3}}$&$16$\\ \hline \end{longtable}"," ",0,"1/3*(x^8+x^4-1)^(3/4)/x^3","A"
166,1,16,15,0.080000," ","int((x^8-1)/x^4/(x^8+x^4+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{8}+x^{4}+1\right)^{\frac{3}{4}}}{3 x^{3}}$&$16$\\ risch&$\frac{\left(x^{8}+x^{4}+1\right)^{\frac{3}{4}}}{3 x^{3}}$&$16$\\ gosper&$\frac{\left(x^{2}+x +1\right) \left(x^{2}-x +1\right) \left(x^{4}-x^{2}+1\right)}{3 \left(x^{8}+x^{4}+1\right)^{\frac{1}{4}} x^{3}}$&$40$\\ \hline \end{longtable}"," ",0,"1/3*(x^8+x^4+1)^(3/4)/x^3","A"
167,1,13,18,0.125000," ","int((x^2+1)/(x^2-1)/(x^3-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{2 x}{\sqrt{x^{3}-x}}$&$13$\\ risch&$-\frac{2 x}{\sqrt{x \left(x^{2}-1\right)}}$&$13$\\ elliptic&$-\frac{2 x}{\sqrt{x \left(x^{2}-1\right)}}$&$13$\\ trager&$-\frac{2 \sqrt{x^{3}-x}}{x^{2}-1}$&$19$\\ default&$\frac{x^{2}-x}{\sqrt{\left(1+x \right) \left(x^{2}-x \right)}}-\frac{x^{2}+x}{\sqrt{\left(-1+x \right) \left(x^{2}+x \right)}}$&$41$\\ meijerg&$-\frac{2 \sqrt{-\mathrm{signum}\left(x^{2}-1\right)}\, \hypergeom \left(\left[\frac{1}{4}, \frac{3}{2}\right], \left[\frac{5}{4}\right], x^{2}\right) \sqrt{x}}{\sqrt{\mathrm{signum}\left(x^{2}-1\right)}}-\frac{2 \sqrt{-\mathrm{signum}\left(x^{2}-1\right)}\, \hypergeom \left(\left[\frac{5}{4}, \frac{3}{2}\right], \left[\frac{9}{4}\right], x^{2}\right) x^{\frac{5}{2}}}{5 \sqrt{\mathrm{signum}\left(x^{2}-1\right)}}$&$66$\\ \hline \end{longtable}"," ",0,"-2*x/(x^3-x)^(1/2)","A"
168,1,11,18,0.058000," ","int(1/(x^2+1)/(x^3+x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{3 x}{2 \left(x^{3}+x \right)^{\frac{1}{3}}}$&$11$\\ meijerg&$\frac{3 x^{\frac{2}{3}}}{2 \left(x^{2}+1\right)^{\frac{1}{3}}}$&$13$\\ risch&$\frac{3 x}{2 \left(\left(x^{2}+1\right) x \right)^{\frac{1}{3}}}$&$13$\\ trager&$\frac{3 \left(x^{3}+x \right)^{\frac{2}{3}}}{2 \left(x^{2}+1\right)}$&$17$\\ \hline \end{longtable}"," ",0,"3/2*x/(x^3+x)^(1/3)","A"
169,1,15,16,0.067000," ","int(1/x/(x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{-\frac{3}{2}+\frac{3 x}{2}}{\left(\left(-1+x \right) x^{2}\right)^{\frac{1}{3}}}$&$15$\\ gosper&$\frac{-\frac{3}{2}+\frac{3 x}{2}}{\left(x^{3}-x^{2}\right)^{\frac{1}{3}}}$&$17$\\ trager&$\frac{3 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}}{2 x^{2}}$&$17$\\ meijerg&$-\frac{3 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{3}} \left(1-x \right)^{\frac{2}{3}}}{2 \mathrm{signum}\left(-1+x \right)^{\frac{1}{3}} x^{\frac{2}{3}}}$&$27$\\ \hline \end{longtable}"," ",0,"3/2*(-1+x)/((-1+x)*x^2)^(1/3)","A"
170,1,17,16,0.297000," ","int(x^2/(a*x^3-b)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{2 \sqrt{a \,x^{3}-b}}{3 a}$&$17$\\ derivativedivides&$\frac{2 \sqrt{a \,x^{3}-b}}{3 a}$&$17$\\ default&$\frac{2 \sqrt{a \,x^{3}-b}}{3 a}$&$17$\\ trager&$\frac{2 \sqrt{a \,x^{3}-b}}{3 a}$&$17$\\ risch&$\frac{2 \sqrt{a \,x^{3}-b}}{3 a}$&$17$\\ elliptic&$\frac{2 \sqrt{a \,x^{3}-b}}{3 a}$&$17$\\ \hline \end{longtable}"," ",0,"2/3*(a*x^3-b)^(1/2)/a","A"
171,1,17,16,0.046000," ","int(x^2*(a*x^3-b)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{2 \left(a \,x^{3}-b \right)^{\frac{3}{2}}}{9 a}$&$17$\\ derivativedivides&$\frac{2 \left(a \,x^{3}-b \right)^{\frac{3}{2}}}{9 a}$&$17$\\ default&$\frac{2 \left(a \,x^{3}-b \right)^{\frac{3}{2}}}{9 a}$&$17$\\ trager&$\frac{2 \left(a \,x^{3}-b \right)^{\frac{3}{2}}}{9 a}$&$17$\\ risch&$\frac{2 \left(a \,x^{3}-b \right)^{\frac{3}{2}}}{9 a}$&$17$\\ \hline \end{longtable}"," ",0,"2/9*(a*x^3-b)^(3/2)/a","A"
172,1,17,16,0.102000," ","int((a*x^3-b)^(1/2)*(a*x^3+2*b)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{2 \left(a \,x^{3}-b \right)^{\frac{3}{2}}}{3 x^{3}}$&$17$\\ trager&$\frac{2 \left(a \,x^{3}-b \right)^{\frac{3}{2}}}{3 x^{3}}$&$17$\\ risch&$\frac{2 \left(a \,x^{3}-b \right)^{\frac{3}{2}}}{3 x^{3}}$&$17$\\ elliptic&$-\frac{2 b \sqrt{a \,x^{3}-b}}{3 x^{3}}+\frac{2 a \sqrt{a \,x^{3}-b}}{3}$&$33$\\ default&$a \left(\frac{2 \sqrt{a \,x^{3}-b}}{3}+\frac{2 b \arctanh \left(\frac{\sqrt{a \,x^{3}-b}}{\sqrt{-b}}\right)}{3 \sqrt{-b}}\right)+2 b \left(-\frac{\sqrt{a \,x^{3}-b}}{3 x^{3}}-\frac{a \arctanh \left(\frac{\sqrt{a \,x^{3}-b}}{\sqrt{-b}}\right)}{3 \sqrt{-b}}\right)$&$90$\\ \hline \end{longtable}"," ",0,"2/3*(a*x^3-b)^(3/2)/x^3","A"
173,1,17,16,0.079000," ","int(1/x^2/(x^4-x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{4}-x^{2}\right)^{\frac{3}{4}}}{3 x^{3}}$&$17$\\ risch&$\frac{\frac{2 x^{2}}{3}-\frac{2}{3}}{x \left(x^{2} \left(x^{2}-1\right)\right)^{\frac{1}{4}}}$&$22$\\ gosper&$\frac{2 \left(-1+x \right) \left(1+x \right)}{3 x \left(x^{4}-x^{2}\right)^{\frac{1}{4}}}$&$23$\\ meijerg&$-\frac{2 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{4}} \left(-x^{2}+1\right)^{\frac{3}{4}}}{3 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{4}} x^{\frac{3}{2}}}$&$33$\\ \hline \end{longtable}"," ",0,"2/3*(x^4-x^2)^(3/4)/x^3","A"
174,1,22,16,0.071000," ","int((x^4-x^2)^(1/4)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{2}-1\right) \left(x^{4}-x^{2}\right)^{\frac{1}{4}}}{5 x^{3}}$&$22$\\ gosper&$\frac{2 \left(-1+x \right) \left(1+x \right) \left(x^{4}-x^{2}\right)^{\frac{1}{4}}}{5 x^{3}}$&$23$\\ meijerg&$-\frac{2 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{4}} \left(-x^{2}+1\right)^{\frac{5}{4}}}{5 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{4}} x^{\frac{5}{2}}}$&$33$\\ risch&$\frac{2 \left(x^{2} \left(x^{2}-1\right)\right)^{\frac{1}{4}} \left(x^{4}-2 x^{2}+1\right)}{5 x^{3} \left(x^{2}-1\right)}$&$34$\\ \hline \end{longtable}"," ",0,"2/5*(x^2-1)*(x^4-x^2)^(1/4)/x^3","A"
175,1,22,16,0.104000," ","int((x^2+1)*(x^4-x^2)^(1/3)/x^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(x^{2}-1\right) \left(x^{4}-x^{2}\right)^{\frac{1}{3}}}{4 x^{2}}$&$22$\\ gosper&$\frac{3 \left(-1+x \right) \left(1+x \right) \left(x^{4}-x^{2}\right)^{\frac{1}{3}}}{4 x^{2}}$&$23$\\ risch&$\frac{3 \left(x^{2} \left(x^{2}-1\right)\right)^{\frac{1}{3}} \left(x^{4}-2 x^{2}+1\right)}{4 x^{2} \left(x^{2}-1\right)}$&$34$\\ meijerg&$-\frac{3 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{2}{3}, -\frac{1}{3}\right], \left[\frac{1}{3}\right], x^{2}\right)}{4 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}} x^{\frac{4}{3}}}+\frac{3 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{2}\right) x^{\frac{2}{3}}}{2 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}}}$&$66$\\ \hline \end{longtable}"," ",0,"3/4*(x^2-1)/x^2*(x^4-x^2)^(1/3)","A"
176,1,15,16,0.075000," ","int(1/x/(x^4-x^3)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{-\frac{4}{3}+\frac{4 x}{3}}{\left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}}}$&$15$\\ gosper&$\frac{-\frac{4}{3}+\frac{4 x}{3}}{\left(x^{4}-x^{3}\right)^{\frac{1}{4}}}$&$17$\\ trager&$\frac{4 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}}{3 x^{3}}$&$17$\\ meijerg&$-\frac{4 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{4}} \left(1-x \right)^{\frac{3}{4}}}{3 \mathrm{signum}\left(-1+x \right)^{\frac{1}{4}} x^{\frac{3}{4}}}$&$27$\\ \hline \end{longtable}"," ",0,"4/3*(-1+x)/(x^3*(-1+x))^(1/4)","A"
177,1,22,16,0.073000," ","int((-1+x)*(x^4-x^3)^(1/4)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{4 \left(-1+x \right)^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}}{9 x^{3}}$&$22$\\ trager&$\frac{4 \left(x^{2}-2 x +1\right) \left(x^{4}-x^{3}\right)^{\frac{1}{4}}}{9 x^{3}}$&$25$\\ risch&$\frac{4 \left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}} \left(x^{3}-3 x^{2}+3 x -1\right)}{9 \left(-1+x \right) x^{3}}$&$33$\\ meijerg&$\frac{4 \mathrm{signum}\left(-1+x \right)^{\frac{1}{4}} \left(-\frac{4}{5} x^{2}-\frac{1}{5} x +1\right) \left(1-x \right)^{\frac{1}{4}}}{9 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{4}} x^{\frac{9}{4}}}-\frac{4 \mathrm{signum}\left(-1+x \right)^{\frac{1}{4}} \left(1-x \right)^{\frac{5}{4}}}{5 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{4}} x^{\frac{5}{4}}}$&$64$\\ \hline \end{longtable}"," ",0,"4/9/x^3*(-1+x)^2*(x^4-x^3)^(1/4)","A"
178,1,20,16,0.065000," ","int((x^4-x^3)^(1/4)/x^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{4 \left(-1+x \right) \left(x^{4}-x^{3}\right)^{\frac{1}{4}}}{5 x^{2}}$&$20$\\ trager&$\frac{4 \left(-1+x \right) \left(x^{4}-x^{3}\right)^{\frac{1}{4}}}{5 x^{2}}$&$20$\\ meijerg&$-\frac{4 \mathrm{signum}\left(-1+x \right)^{\frac{1}{4}} \left(1-x \right)^{\frac{5}{4}}}{5 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{4}} x^{\frac{5}{4}}}$&$27$\\ risch&$\frac{4 \left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}} \left(x^{2}-2 x +1\right)}{5 x^{2} \left(-1+x \right)}$&$28$\\ \hline \end{longtable}"," ",0,"4/5/x^2*(-1+x)*(x^4-x^3)^(1/4)","A"
179,1,17,16,0.048000," ","int(x*(2*x^2+1)*(2*x^4+2*x^2-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{\left(2 x^{4}+2 x^{2}-1\right)^{\frac{3}{2}}}{6}$&$17$\\ default&$\frac{\left(2 x^{4}+2 x^{2}-1\right)^{\frac{3}{2}}}{6}$&$17$\\ risch&$\frac{\left(2 x^{4}+2 x^{2}-1\right)^{\frac{3}{2}}}{6}$&$17$\\ trager&$\left(\frac{1}{3} x^{4}+\frac{1}{3} x^{2}-\frac{1}{6}\right) \sqrt{2 x^{4}+2 x^{2}-1}$&$28$\\ \hline \end{longtable}"," ",0,"1/6*(2*x^4+2*x^2-1)^(3/2)","A"
180,1,22,16,0.112000," ","int((2*x^3+1)*(x^5-x^2)^(1/3)/x^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(x^{3}-1\right) \left(x^{5}-x^{2}\right)^{\frac{1}{3}}}{4 x^{2}}$&$22$\\ gosper&$\frac{3 \left(x^{2}+x +1\right) \left(-1+x \right) \left(x^{5}-x^{2}\right)^{\frac{1}{3}}}{4 x^{2}}$&$26$\\ risch&$\frac{3 \left(x^{2} \left(x^{3}-1\right)\right)^{\frac{1}{3}} \left(x^{6}-2 x^{3}+1\right)}{4 x^{2} \left(x^{3}-1\right)}$&$34$\\ meijerg&$-\frac{3 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{4}{9}, -\frac{1}{3}\right], \left[\frac{5}{9}\right], x^{3}\right)}{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x^{\frac{4}{3}}}+\frac{6 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{5}{9}\right], \left[\frac{14}{9}\right], x^{3}\right) x^{\frac{5}{3}}}{5 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}}}$&$66$\\ \hline \end{longtable}"," ",0,"3/4*(x^3-1)/x^2*(x^5-x^2)^(1/3)","A"
181,1,22,16,0.106000," ","int((x^4-1)/x^2/(x^5-x^3)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{2}-1\right) \left(x^{5}-x^{3}\right)^{\frac{3}{4}}}{7 x^{4}}$&$22$\\ risch&$\frac{\frac{4}{7} x^{4}-\frac{8}{7} x^{2}+\frac{4}{7}}{x \left(x^{3} \left(x^{2}-1\right)\right)^{\frac{1}{4}}}$&$27$\\ gosper&$\frac{4 \left(x^{2}-1\right) \left(-1+x \right) \left(1+x \right)}{7 \left(x^{5}-x^{3}\right)^{\frac{1}{4}} x}$&$28$\\ meijerg&$\frac{4 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{7}{8}, \frac{1}{4}\right], \left[\frac{1}{8}\right], x^{2}\right)}{7 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{4}} x^{\frac{7}{4}}}+\frac{4 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[\frac{1}{4}, \frac{9}{8}\right], \left[\frac{17}{8}\right], x^{2}\right) x^{\frac{9}{4}}}{9 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{4}}}$&$66$\\ \hline \end{longtable}"," ",0,"4/7*(x^2-1)/x^4*(x^5-x^3)^(3/4)","A"
182,1,27,16,0.110000," ","int((x^4-1)*(x^5-x^3)^(1/4)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{4}-2 x^{2}+1\right) \left(x^{5}-x^{3}\right)^{\frac{1}{4}}}{9 x^{3}}$&$27$\\ gosper&$\frac{4 \left(x^{5}-x^{3}\right)^{\frac{1}{4}} \left(x^{2}-1\right) \left(-1+x \right) \left(1+x \right)}{9 x^{3}}$&$28$\\ risch&$\frac{4 \left(x^{3} \left(x^{2}-1\right)\right)^{\frac{1}{4}} \left(x^{6}-3 x^{4}+3 x^{2}-1\right)}{9 x^{3} \left(x^{2}-1\right)}$&$39$\\ meijerg&$\frac{4 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{9}{8}, -\frac{1}{4}\right], \left[-\frac{1}{8}\right], x^{2}\right)}{9 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{4}} x^{\frac{9}{4}}}+\frac{4 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{1}{4}, \frac{7}{8}\right], \left[\frac{15}{8}\right], x^{2}\right) x^{\frac{7}{4}}}{7 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{4}}}$&$66$\\ \hline \end{longtable}"," ",0,"4/9*(x^4-2*x^2+1)/x^3*(x^5-x^3)^(1/4)","A"
183,1,19,18,0.068000," ","int((2*x^4-2*x^2-1)/x^2/(x^2+1)/(x^6+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}+1}}{x \left(x^{2}+1\right)}$&$19$\\ gosper&$\frac{x^{4}-x^{2}+1}{x \sqrt{x^{6}+1}}$&$22$\\ risch&$\frac{x^{4}-x^{2}+1}{x \sqrt{x^{6}+1}}$&$22$\\ \hline \end{longtable}"," ",0,"(x^6+1)^(1/2)/x/(x^2+1)","A"
184,1,17,16,0.072000," ","int(1/x^3/(x^6-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(x^{6}-x^{2}\right)^{\frac{2}{3}}}{8 x^{4}}$&$17$\\ risch&$\frac{\frac{3 x^{4}}{8}-\frac{3}{8}}{x^{2} \left(x^{2} \left(x^{4}-1\right)\right)^{\frac{1}{3}}}$&$22$\\ gosper&$\frac{3 \left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}{8 x^{2} \left(x^{6}-x^{2}\right)^{\frac{1}{3}}}$&$28$\\ meijerg&$-\frac{3 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{3}} \left(-x^{4}+1\right)^{\frac{2}{3}}}{8 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{3}} x^{\frac{8}{3}}}$&$33$\\ \hline \end{longtable}"," ",0,"3/8*(x^6-x^2)^(2/3)/x^4","A"
185,1,17,16,0.102000," ","int((x^4+1)/x^2/(x^6-x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{6}-x^{2}\right)^{\frac{3}{4}}}{3 x^{3}}$&$17$\\ risch&$\frac{\frac{2 x^{4}}{3}-\frac{2}{3}}{x \left(x^{2} \left(x^{4}-1\right)\right)^{\frac{1}{4}}}$&$22$\\ gosper&$\frac{2 \left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}{3 x \left(x^{6}-x^{2}\right)^{\frac{1}{4}}}$&$28$\\ meijerg&$-\frac{2 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{3}{8}, \frac{1}{4}\right], \left[\frac{5}{8}\right], x^{4}\right)}{3 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}} x^{\frac{3}{2}}}+\frac{2 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[\frac{1}{4}, \frac{5}{8}\right], \left[\frac{13}{8}\right], x^{4}\right) x^{\frac{5}{2}}}{5 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}}}$&$66$\\ \hline \end{longtable}"," ",0,"2/3*(x^6-x^2)^(3/4)/x^3","A"
186,1,22,16,0.103000," ","int((x^4+1)*(x^6-x^2)^(1/4)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{4}-1\right) \left(x^{6}-x^{2}\right)^{\frac{1}{4}}}{5 x^{3}}$&$22$\\ gosper&$\frac{2 \left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right) \left(x^{6}-x^{2}\right)^{\frac{1}{4}}}{5 x^{3}}$&$28$\\ risch&$\frac{2 \left(x^{2} \left(x^{4}-1\right)\right)^{\frac{1}{4}} \left(x^{8}-2 x^{4}+1\right)}{5 x^{3} \left(x^{4}-1\right)}$&$34$\\ meijerg&$-\frac{2 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{5}{8}, -\frac{1}{4}\right], \left[\frac{3}{8}\right], x^{4}\right)}{5 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} x^{\frac{5}{2}}}+\frac{2 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{1}{4}, \frac{3}{8}\right], \left[\frac{11}{8}\right], x^{4}\right) x^{\frac{3}{2}}}{3 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}}}$&$66$\\ \hline \end{longtable}"," ",0,"2/5*(x^4-1)*(x^6-x^2)^(1/4)/x^3","A"
187,1,22,16,0.102000," ","int((x^8-1)/x^4/(x^6-x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{4}-1\right) \left(x^{6}-x^{2}\right)^{\frac{3}{4}}}{7 x^{5}}$&$22$\\ risch&$\frac{\frac{2}{7} x^{8}-\frac{4}{7} x^{4}+\frac{2}{7}}{x^{3} \left(x^{2} \left(x^{4}-1\right)\right)^{\frac{1}{4}}}$&$27$\\ gosper&$\frac{2 \left(x^{4}-1\right) \left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}{7 \left(x^{6}-x^{2}\right)^{\frac{1}{4}} x^{3}}$&$33$\\ meijerg&$\frac{2 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{7}{8}, \frac{1}{4}\right], \left[\frac{1}{8}\right], x^{4}\right)}{7 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}} x^{\frac{7}{2}}}+\frac{2 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[\frac{1}{4}, \frac{9}{8}\right], \left[\frac{17}{8}\right], x^{4}\right) x^{\frac{9}{2}}}{9 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}}}$&$66$\\ \hline \end{longtable}"," ",0,"2/7*(x^4-1)/x^5*(x^6-x^2)^(3/4)","A"
188,1,13,18,0.128000," ","int((x^8+1)/(-x^8+1)^(1/4)/(x^8-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{x}{\left(-x^{8}+1\right)^{\frac{1}{4}}}$&$13$\\ risch&$-\frac{x}{\left(-x^{8}+1\right)^{\frac{1}{4}}}$&$13$\\ trager&$\frac{x \left(-x^{8}+1\right)^{\frac{3}{4}}}{x^{8}-1}$&$19$\\ meijerg&$-\hypergeom \left(\left[\frac{1}{8}, \frac{5}{4}\right], \left[\frac{9}{8}\right], x^{8}\right) x -\frac{\hypergeom \left(\left[\frac{9}{8}, \frac{5}{4}\right], \left[\frac{17}{8}\right], x^{8}\right) x^{9}}{9}$&$28$\\ \hline \end{longtable}"," ",0,"-x/(-x^8+1)^(1/4)","A"
189,1,26,16,0.453000," ","int(1/(x^8-x^2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{x \sqrt{x^{6}-1}\, \arcsin \left(\frac{1}{x^{3}}\right)}{3 \sqrt{x^{8}-x^{2}}}$&$26$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x +\sqrt{x^{8}-x^{2}}}{x^{4}}\right)}{3}$&$35$\\ meijerg&$\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(\left(-2 \ln \left(2\right)+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}-2 \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right) \sqrt{\pi}\right)}{6 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$61$\\ \hline \end{longtable}"," ",0,"-1/3/(x^8-x^2)^(1/2)*x*(x^6-1)^(1/2)*arcsin(1/x^3)","A"
190,0,0,16,0.011000," ","int((1+(x^2+1)^(1/2))^(1/2)/(x^2+1),x)","\[\int \frac{\sqrt{1+\sqrt{x^{2}+1}}}{x^{2}+1}\, dx\]"," ",0,"int((1+(x^2+1)^(1/2))^(1/2)/(x^2+1),x)","F"
191,1,74,17,0.352000," ","int((-1+x)/(2+x)/(x^3-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-12 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-6 \RootOf \left(\textit{\_Z}^{2}+1\right) x -6 \sqrt{x^{3}-1}\, x -10 \RootOf \left(\textit{\_Z}^{2}+1\right)+6 \sqrt{x^{3}-1}}{\left(2+x \right)^{3}}\right)}{3}$&$74$\\ default&$\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{i \sqrt{3}}{6}+\frac{1}{2}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}$&$240$\\ elliptic&$\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{i \sqrt{3}}{6}+\frac{1}{2}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}$&$240$\\ \hline \end{longtable}"," ",0,"1/3*RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)*x^3-12*RootOf(_Z^2+1)*x^2-6*RootOf(_Z^2+1)*x-6*(x^3-1)^(1/2)*x-10*RootOf(_Z^2+1)+6*(x^3-1)^(1/2))/(2+x)^3)","C"
192,1,28,19,0.206000," ","int((x^2-2*x-2)/(x^2+2)/(x^3-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(\frac{x^{2}+2 \sqrt{x^{3}-1}+2 x}{x^{2}+2}\right)$&$28$\\ default&$\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{3 i \sqrt{2}\, \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{1-i \sqrt{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(1-i \sqrt{2}\right)}+\frac{\sqrt{2}\, \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{1-i \sqrt{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}\, \left(1-i \sqrt{2}\right)}+\frac{3 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{1-i \sqrt{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(1-i \sqrt{2}\right)}+\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{1-i \sqrt{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}\, \left(1-i \sqrt{2}\right)}+\frac{3 i \sqrt{2}\, \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{1+i \sqrt{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(1+i \sqrt{2}\right)}-\frac{\sqrt{2}\, \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{1+i \sqrt{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}\, \left(1+i \sqrt{2}\right)}+\frac{3 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{1+i \sqrt{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(1+i \sqrt{2}\right)}+\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{1+i \sqrt{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}\, \left(1+i \sqrt{2}\right)}$&$1656$\\ elliptic&$-\frac{3 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}+\frac{3 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{1-i \sqrt{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(1-i \sqrt{2}\right)}+\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{1-i \sqrt{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}\, \left(1-i \sqrt{2}\right)}-\frac{3 i \sqrt{2}\, \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{1-i \sqrt{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(1-i \sqrt{2}\right)}+\frac{\sqrt{2}\, \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{1-i \sqrt{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}\, \left(1-i \sqrt{2}\right)}+\frac{3 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{1+i \sqrt{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(1+i \sqrt{2}\right)}+\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{1+i \sqrt{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}\, \left(1+i \sqrt{2}\right)}+\frac{3 i \sqrt{2}\, \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{1+i \sqrt{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(1+i \sqrt{2}\right)}-\frac{\sqrt{2}\, \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{1+i \sqrt{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}\, \left(1+i \sqrt{2}\right)}$&$1865$\\ \hline \end{longtable}"," ",0,"-ln((x^2+2*(x^3-1)^(1/2)+2*x)/(x^2+2))","A"
193,1,47,19,0.381000," ","int((x^2-2*x-2)/(x^2+2*x)/(x^3-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \sqrt{x^{3}-1}}{x \left(2+x \right)}\right)$&$47$\\ default&$\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{2 \arctan \left(\sqrt{x^{3}-1}\right)}{3}-\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{i \sqrt{3}}{6}+\frac{1}{2}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}$&$250$\\ elliptic&$-\frac{3 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}-\frac{2 \arctan \left(\sqrt{x^{3}-1}\right)}{3}+\frac{3 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{i \sqrt{3}}{6}+\frac{1}{2}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{i \sqrt{3}}{6}+\frac{1}{2}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}$&$676$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2+1)*ln(-(RootOf(_Z^2+1)*x^2+2*RootOf(_Z^2+1)-2*(x^3-1)^(1/2))/x/(2+x))","C"
194,1,18,19,0.207000," ","int((2*x^2+2*x-1)/(-1+x)/x/(x^4-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{2 \left(x^{2}+x +1\right)}{\sqrt{x^{4}-x}}$&$18$\\ trager&$-\frac{2 \sqrt{x^{4}-x}}{\left(-1+x \right) x}$&$20$\\ default&$\frac{2 x^{3}-2}{\sqrt{x \left(x^{3}-1\right)}}-\frac{2 \left(x^{3}+x^{2}+x \right)}{\sqrt{\left(-1+x \right) \left(x^{3}+x^{2}+x \right)}}$&$42$\\ elliptic&$\frac{2 x^{3}-2}{\sqrt{x \left(x^{3}-1\right)}}-\frac{2 \left(x^{3}+x^{2}+x \right)}{\sqrt{\left(-1+x \right) \left(x^{3}+x^{2}+x \right)}}$&$42$\\ \hline \end{longtable}"," ",0,"-2*(x^2+x+1)/(x^4-x)^(1/2)","A"
195,1,46,19,0.386000," ","int((2*x^2+2*x-1)/(2*x^2+1)/(x^4-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) x +\RootOf \left(\textit{\_Z}^{2}+1\right)+2 \sqrt{x^{4}-x}}{2 x^{2}+1}\right)$&$46$\\ default&$\text{Expression too large to display}$&$13534$\\ elliptic&$\text{Expression too large to display}$&$14836$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2+1)*ln((2*RootOf(_Z^2+1)*x+RootOf(_Z^2+1)+2*(x^4-x)^(1/2))/(2*x^2+1))","C"
196,1,28,19,0.239000," ","int((2*x^2-2*x-1)/(-1+2*x)/(x^4+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(\frac{-2 x^{2}+2 \sqrt{x^{4}+x}-1}{-1+2 x}\right)$&$28$\\ default&$\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}-\frac{2 \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+2 \EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{3}{2}+\frac{3 i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$780$\\ elliptic&$\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}-\frac{2 \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+2 \EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{3}{2}+\frac{3 i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$780$\\ \hline \end{longtable}"," ",0,"-ln((-2*x^2+2*(x^4+x)^(1/2)-1)/(-1+2*x))","A"
197,1,14,19,0.205000," ","int((2*x^2-2*x-1)/(x^2-x+1)/(x^4+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{2 x \left(1+x \right)}{\sqrt{x^{4}+x}}$&$14$\\ trager&$-\frac{2 \sqrt{x^{4}+x}}{x^{2}-x +1}$&$20$\\ default&$-\frac{2 \left(x^{2}+x \right)}{\sqrt{\left(x^{2}-x +1\right) \left(x^{2}+x \right)}}$&$24$\\ elliptic&$-\frac{2 \left(x^{2}+x \right)}{\sqrt{\left(x^{2}-x +1\right) \left(x^{2}+x \right)}}$&$24$\\ \hline \end{longtable}"," ",0,"-2*x*(1+x)/(x^4+x)^(1/2)","A"
198,1,11,19,0.052000," ","int(1/(1+x)/(x^4+x^3)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{4 x^{\frac{1}{4}}}{\left(1+x \right)^{\frac{1}{4}}}$&$11$\\ gosper&$\frac{4 x}{\left(x^{4}+x^{3}\right)^{\frac{1}{4}}}$&$13$\\ risch&$\frac{4 x}{\left(x^{3} \left(1+x \right)\right)^{\frac{1}{4}}}$&$13$\\ trager&$\frac{4 \left(x^{4}+x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(1+x \right)}$&$20$\\ \hline \end{longtable}"," ",0,"4/(1+x)^(1/4)*x^(1/4)","A"
199,1,20,19,0.317000," ","int((2*x^4+1)/(2*x^4-1)/(2*x^4-x^2-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\arctan \left(\frac{\sqrt{2 x^{4}-x^{2}-1}}{x}\right)$&$20$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \sqrt{2 x^{4}-x^{2}-1}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right)}{2 x^{4}-1}\right)}{2}$&$69$\\ default&$-\frac{i \sqrt{2}\, \sqrt{2 x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticF \left(i x \sqrt{2}, \frac{i \sqrt{2}}{2}\right)}{2 \sqrt{2 x^{4}-x^{2}-1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(2 \textit{\_Z}^{4}-1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\left(4 \underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \left(-9 \underline{\hspace{1.25 ex}}\alpha^{2}+7 x^{2}-4\right)}{14 \sqrt{-\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{2 x^{4}-x^{2}-1}}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{2 i \sqrt{2}\, \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{2 x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticPi \left(\sqrt{-2}\, x , -\underline{\hspace{1.25 ex}}\alpha^{2}, \frac{\sqrt{-2}}{2}\right)}{\sqrt{2 x^{4}-x^{2}-1}}\right)\right)}{4}$&$179$\\ \hline \end{longtable}"," ",0,"arctan(1/x*(2*x^4-x^2-1)^(1/2))","A"
200,1,22,19,0.229000," ","int((2*x^4-1)/(2*x^4+2*x^2+1)/(2*x^4+3*x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\arctanh \left(\frac{\sqrt{2 x^{4}+3 x^{2}+1}}{x}\right)$&$22$\\ trager&$\frac{\ln \left(-\frac{-2 x^{4}+2 \sqrt{2 x^{4}+3 x^{2}+1}\, x -4 x^{2}-1}{2 x^{4}+2 x^{2}+1}\right)}{2}$&$49$\\ default&$-\frac{i \sqrt{x^{2}+1}\, \sqrt{2 x^{2}+1}\, \EllipticF \left(i x , \sqrt{2}\right)}{\sqrt{2 x^{4}+3 x^{2}+1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(2 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\left(4 \underline{\hspace{1.25 ex}}\alpha^{2}+3\right) \left(\underline{\hspace{1.25 ex}}\alpha^{2}+5 x^{2}+4\right)}{10 \sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{2 x^{4}+3 x^{2}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{4 i \left(-\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{x^{2}+1}\, \sqrt{2 x^{2}+1}\, \EllipticPi \left(i x , 2 \underline{\hspace{1.25 ex}}\alpha^{2}+2, i \sqrt{-2}\right)}{\sqrt{2 x^{4}+3 x^{2}+1}}\right)\right)}{4}$&$170$\\ \hline \end{longtable}"," ",0,"-arctanh((2*x^4+3*x^2+1)^(1/2)/x)","A"
201,1,18,17,0.087000," ","int((-x^5+x^4-1)^(1/4)*(x^5-4)/x^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{4 \left(-x^{5}+x^{4}-1\right)^{\frac{5}{4}}}{5 x^{5}}$&$18$\\ trager&$\frac{4 \left(x^{5}-x^{4}+1\right) \left(-x^{5}+x^{4}-1\right)^{\frac{1}{4}}}{5 x^{5}}$&$28$\\ risch&$-\frac{4 \left(x^{10}-2 x^{9}+x^{8}+2 x^{5}-2 x^{4}+1\right)}{5 \left(-x^{5}+x^{4}-1\right)^{\frac{3}{4}} x^{5}}$&$41$\\ \hline \end{longtable}"," ",0,"-4/5*(-x^5+x^4-1)^(5/4)/x^5","A"
202,1,18,17,0.089000," ","int((x^8+1)*(x^8-2*x^4-1)^(1/2)/x^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{\left(x^{8}-2 x^{4}-1\right)^{\frac{3}{2}}}{6 x^{6}}$&$18$\\ trager&$\frac{\left(x^{8}-2 x^{4}-1\right)^{\frac{3}{2}}}{6 x^{6}}$&$18$\\ risch&$\frac{x^{16}-4 x^{12}+2 x^{8}+4 x^{4}+1}{6 x^{6} \sqrt{x^{8}-2 x^{4}-1}}$&$38$\\ \hline \end{longtable}"," ",0,"1/6*(x^8-2*x^4-1)^(3/2)/x^6","A"
203,1,99,15,0.661000," ","int(x^2*(x^3-2)*(x^3+1)^(1/2)/(4*x^9+13*x^6+12*x^3+4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-4 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{9}+4 \sqrt{x^{3}+1}\, x^{6}-11 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}+4 \sqrt{x^{3}+1}\, x^{3}-12 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-4 \RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(x^{3}+2\right) \left(4 x^{6}+5 x^{3}+2\right)}\right)}{6}$&$99$\\ default&$\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 \textit{\_Z}^{6}+5 \textit{\_Z}^{3}+2\right)}{\sum}\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{3}+1\right) \left(4 \underline{\hspace{1.25 ex}}\alpha^{5}-4 \underline{\hspace{1.25 ex}}\alpha^{4}+4 \underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(3-i \sqrt{3}\right) \sqrt{\frac{1+x}{3-i \sqrt{3}}}\, \sqrt{\frac{-1+2 x -i \sqrt{3}}{-3-i \sqrt{3}}}\, \sqrt{\frac{-1+2 x +i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -6 \underline{\hspace{1.25 ex}}\alpha^{5}+6 \underline{\hspace{1.25 ex}}\alpha^{4}-6 \underline{\hspace{1.25 ex}}\alpha^{3}-\frac{3 \underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{3 \underline{\hspace{1.25 ex}}\alpha }{2}-\frac{3}{2}+2 i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5}-2 i \underline{\hspace{1.25 ex}}\alpha^{4} \sqrt{3}+2 i \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{3}+\frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}}{2}-\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha }{2}+\frac{i \sqrt{3}}{2}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}\right)}{6}+\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+2\right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(3-i \sqrt{3}\right) \sqrt{\frac{1+x}{3-i \sqrt{3}}}\, \sqrt{\frac{-1+2 x -i \sqrt{3}}{-3-i \sqrt{3}}}\, \sqrt{\frac{-1+2 x +i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{3 \underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{3 \underline{\hspace{1.25 ex}}\alpha }{2}-\frac{3}{2}+\frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}}{2}-\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha }{2}+\frac{i \sqrt{3}}{2}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}\right)}{6}$&$417$\\ elliptic&$\text{Expression too large to display}$&$2469$\\ \hline \end{longtable}"," ",0,"1/6*RootOf(_Z^2+1)*ln(-(-4*RootOf(_Z^2+1)*x^9+4*(x^3+1)^(1/2)*x^6-11*RootOf(_Z^2+1)*x^6+4*(x^3+1)^(1/2)*x^3-12*RootOf(_Z^2+1)*x^3-4*RootOf(_Z^2+1))/(x^3+2)/(4*x^6+5*x^3+2))","C"
204,1,13,20,0.082000," ","int(1/(x^2-1)/(x^3-x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{3 x}{2 \left(x^{3}-x \right)^{\frac{1}{3}}}$&$13$\\ risch&$-\frac{3 x}{2 \left(x \left(x^{2}-1\right)\right)^{\frac{1}{3}}}$&$13$\\ trager&$-\frac{3 \left(x^{3}-x \right)^{\frac{2}{3}}}{2 \left(x^{2}-1\right)}$&$19$\\ meijerg&$-\frac{3 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}} x^{\frac{2}{3}}}{2 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}} \left(-x^{2}+1\right)^{\frac{1}{3}}}$&$33$\\ \hline \end{longtable}"," ",0,"-3/2*x/(x^3-x)^(1/3)","A"
205,1,13,20,0.099000," ","int(1/(x^3-1)/(x^4-x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{4 x}{3 \left(x^{4}-x \right)^{\frac{1}{4}}}$&$13$\\ risch&$-\frac{4 x}{3 \left(x \left(x^{3}-1\right)\right)^{\frac{1}{4}}}$&$13$\\ trager&$-\frac{4 \left(x^{4}-x \right)^{\frac{3}{4}}}{3 \left(x^{3}-1\right)}$&$19$\\ meijerg&$-\frac{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}} x^{\frac{3}{4}}}{3 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}} \left(-x^{3}+1\right)^{\frac{1}{4}}}$&$33$\\ \hline \end{longtable}"," ",0,"-4/3*x/(x^4-x)^(1/4)","A"
206,0,0,18,0.023000," ","int((b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2)^(1/2),x)","\[\int \frac{\sqrt{b +\sqrt{a \,x^{2}+b^{2}}}}{\sqrt{a \,x^{2}+b^{2}}}\, dx\]"," ",0,"int((b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2)^(1/2),x)","F"
207,1,59,19,1.332000," ","int(1/x/(x^2+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\Gamma \left(\frac{3}{4}\right) \sqrt{2}\, \left(\frac{\left(-3 \ln \left(2\right)-\frac{\pi}{2}+2 \ln \left(x \right)\right) \pi  \sqrt{2}}{\Gamma \left(\frac{3}{4}\right)}-\frac{\hypergeom \left(\left[1, 1, \frac{5}{4}\right], \left[2, 2\right], -x^{2}\right) \pi  \sqrt{2}\, x^{2}}{4 \Gamma \left(\frac{3}{4}\right)}\right)}{4 \pi}$&$59$\\ trager&$-\frac{\ln \left(-\frac{2 \left(x^{2}+1\right)^{\frac{3}{4}}+2 \sqrt{x^{2}+1}+x^{2}+2 \left(x^{2}+1\right)^{\frac{1}{4}}+2}{x^{2}}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{2}+1}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \left(x^{2}+1\right)^{\frac{3}{4}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(x^{2}+1\right)^{\frac{1}{4}}}{x^{2}}\right)}{2}$&$109$\\ \hline \end{longtable}"," ",0,"1/4*GAMMA(3/4)*2^(1/2)/Pi*((-3*ln(2)-1/2*Pi+2*ln(x))*Pi*2^(1/2)/GAMMA(3/4)-1/4*hypergeom([1,1,5/4],[2,2],-x^2)*Pi*2^(1/2)/GAMMA(3/4)*x^2)","C"
208,1,18,21,0.079000," ","int((-5+2*x)/(x^2-4*x+4)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{2 \left(-2+x \right) \left(-7+2 x \right)}{3 \left(\left(-2+x \right)^{2}\right)^{\frac{1}{4}}}$&$18$\\ gosper&$\frac{2 \left(-2+x \right) \left(-7+2 x \right)}{3 \left(x^{2}-4 x +4\right)^{\frac{1}{4}}}$&$21$\\ meijerg&$\frac{5 \sqrt{2}\, \sqrt{-\mathrm{signum}\left(-2+x \right)}\, \left(-2 \sqrt{\pi}+2 \sqrt{\pi}\, \sqrt{1-\frac{x}{2}}\right)}{\sqrt{\pi}\, \sqrt{\mathrm{signum}\left(-2+x \right)}}+\frac{4 \sqrt{2}\, \sqrt{-\mathrm{signum}\left(-2+x \right)}\, \left(\frac{4 \sqrt{\pi}}{3}-\frac{\sqrt{\pi}\, \left(8+2 x \right) \sqrt{1-\frac{x}{2}}}{6}\right)}{\sqrt{\pi}\, \sqrt{\mathrm{signum}\left(-2+x \right)}}$&$87$\\ \hline \end{longtable}"," ",0,"2/3/((-2+x)^2)^(1/4)*(-2+x)*(-7+2*x)","A"
209,1,17,19,0.065000," ","int(x^5*(x^3+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\hypergeom \left(\left[-\frac{1}{3}, 2\right], \left[3\right], -x^{3}\right) x^{6}}{6}$&$17$\\ risch&$\frac{\left(x^{3}+1\right)^{\frac{1}{3}} \left(4 x^{6}+x^{3}-3\right)}{28}$&$20$\\ trager&$\left(\frac{1}{7} x^{6}+\frac{1}{28} x^{3}-\frac{3}{28}\right) \left(x^{3}+1\right)^{\frac{1}{3}}$&$21$\\ gosper&$\frac{\left(1+x \right) \left(x^{2}-x +1\right) \left(4 x^{3}-3\right) \left(x^{3}+1\right)^{\frac{1}{3}}}{28}$&$28$\\ \hline \end{longtable}"," ",0,"1/6*hypergeom([-1/3,2],[3],-x^3)*x^6","C"
210,1,20,19,0.084000," ","int((3*x^2+1)*(x^3-x)^(1/3)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(x^{2}-1\right) \left(x^{3}-x \right)^{\frac{1}{3}}}{2 x}$&$20$\\ gosper&$\frac{3 \left(-1+x \right) \left(1+x \right) \left(x^{3}-x \right)^{\frac{1}{3}}}{2 x}$&$21$\\ risch&$\frac{3 \left(x \left(x^{2}-1\right)\right)^{\frac{1}{3}} \left(x^{4}-2 x^{2}+1\right)}{2 x \left(x^{2}-1\right)}$&$32$\\ meijerg&$-\frac{3 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{1}{3}, -\frac{1}{3}\right], \left[\frac{2}{3}\right], x^{2}\right)}{2 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}} x^{\frac{2}{3}}}+\frac{9 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], x^{2}\right) x^{\frac{4}{3}}}{4 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}}}$&$66$\\ \hline \end{longtable}"," ",0,"3/2*(x^2-1)*(x^3-x)^(1/3)/x","A"
211,1,13,21,0.075000," ","int(1/(-1+x)/(x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{3 x}{\left(\left(-1+x \right) x^{2}\right)^{\frac{1}{3}}}$&$13$\\ gosper&$-\frac{3 x}{\left(x^{3}-x^{2}\right)^{\frac{1}{3}}}$&$15$\\ trager&$-\frac{3 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}}{\left(-1+x \right) x}$&$22$\\ meijerg&$-\frac{3 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{3}} x^{\frac{1}{3}}}{\mathrm{signum}\left(-1+x \right)^{\frac{1}{3}} \left(1-x \right)^{\frac{1}{3}}}$&$27$\\ \hline \end{longtable}"," ",0,"-3*x/((-1+x)*x^2)^(1/3)","A"
212,1,16,19,0.052000," ","int(1/x^2/(x^3+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{3 \left(1-\frac{3 x}{2}\right) \left(1+x \right)^{\frac{2}{3}}}{5 x^{\frac{5}{3}}}$&$16$\\ trager&$\frac{3 \left(-2+3 x \right) \left(x^{3}+x^{2}\right)^{\frac{2}{3}}}{10 x^{3}}$&$20$\\ gosper&$\frac{3 \left(1+x \right) \left(-2+3 x \right)}{10 x \left(x^{3}+x^{2}\right)^{\frac{1}{3}}}$&$23$\\ risch&$\frac{-\frac{3}{5}+\frac{3}{10} x +\frac{9}{10} x^{2}}{x \left(x^{2} \left(1+x \right)\right)^{\frac{1}{3}}}$&$23$\\ \hline \end{longtable}"," ",0,"-3/5*(1-3/2*x)*(1+x)^(2/3)/x^(5/3)","A"
213,1,17,21,0.115000," ","int((2*x^2+3)*(2*x^3+x)^(1/2)/(2*x^2+1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{x^{2} \sqrt{2}}{\sqrt{\left(x^{2}+\frac{1}{2}\right) x}}$&$17$\\ elliptic&$\frac{x^{2} \sqrt{2}}{\sqrt{\left(x^{2}+\frac{1}{2}\right) x}}$&$17$\\ gosper&$\frac{2 x \sqrt{2 x^{3}+x}}{2 x^{2}+1}$&$22$\\ trager&$\frac{2 x \sqrt{2 x^{3}+x}}{2 x^{2}+1}$&$22$\\ meijerg&$2 \hypergeom \left(\left[\frac{3}{4}, \frac{3}{2}\right], \left[\frac{7}{4}\right], -2 x^{2}\right) x^{\frac{3}{2}}+\frac{4 \hypergeom \left(\left[\frac{3}{2}, \frac{7}{4}\right], \left[\frac{11}{4}\right], -2 x^{2}\right) x^{\frac{7}{2}}}{7}$&$34$\\ \hline \end{longtable}"," ",0,"x^2*2^(1/2)/((x^2+1/2)*x)^(1/2)","A"
214,1,20,19,0.087000," ","int(1/x^6/(x^4-1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{4}-1\right)^{\frac{1}{4}} \left(4 x^{4}+1\right)}{5 x^{5}}$&$20$\\ risch&$\frac{4 x^{8}-3 x^{4}-1}{5 \left(x^{4}-1\right)^{\frac{3}{4}} x^{5}}$&$25$\\ gosper&$\frac{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right) \left(4 x^{4}+1\right)}{5 x^{5} \left(x^{4}-1\right)^{\frac{3}{4}}}$&$31$\\ meijerg&$-\frac{\left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{3}{4}} \left(4 x^{4}+1\right) \left(-x^{4}+1\right)^{\frac{1}{4}}}{5 \mathrm{signum}\left(x^{4}-1\right)^{\frac{3}{4}} x^{5}}$&$40$\\ \hline \end{longtable}"," ",0,"1/5*(x^4-1)^(1/4)*(4*x^4+1)/x^5","A"
215,1,20,19,0.074000," ","int(1/x^4/(x^4+1)^(5/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{4 x^{4}+1}{3 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}}$&$20$\\ trager&$-\frac{4 x^{4}+1}{3 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}}$&$20$\\ meijerg&$-\frac{4 x^{4}+1}{3 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}}$&$20$\\ risch&$-\frac{4 x^{4}+1}{3 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}}$&$20$\\ \hline \end{longtable}"," ",0,"-1/3*(4*x^4+1)/x^3/(x^4+1)^(1/4)","A"
216,1,20,19,0.057000," ","int(1/x^6/(x^4+1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{\left(x^{4}+1\right)^{\frac{1}{4}} \left(4 x^{4}-1\right)}{5 x^{5}}$&$20$\\ trager&$\frac{\left(x^{4}+1\right)^{\frac{1}{4}} \left(4 x^{4}-1\right)}{5 x^{5}}$&$20$\\ meijerg&$-\frac{\left(-4 x^{4}+1\right) \left(x^{4}+1\right)^{\frac{1}{4}}}{5 x^{5}}$&$20$\\ risch&$\frac{4 x^{8}+3 x^{4}-1}{5 \left(x^{4}+1\right)^{\frac{3}{4}} x^{5}}$&$25$\\ \hline \end{longtable}"," ",0,"1/5*(x^4+1)^(1/4)*(4*x^4-1)/x^5","A"
217,1,20,19,0.063000," ","int((x^4-1)/x^6/(x^4+1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{\left(9 x^{4}-1\right) \left(x^{4}+1\right)^{\frac{1}{4}}}{5 x^{5}}$&$20$\\ trager&$-\frac{\left(9 x^{4}-1\right) \left(x^{4}+1\right)^{\frac{1}{4}}}{5 x^{5}}$&$20$\\ risch&$-\frac{9 x^{8}+8 x^{4}-1}{5 \left(x^{4}+1\right)^{\frac{3}{4}} x^{5}}$&$25$\\ meijerg&$-\frac{\left(x^{4}+1\right)^{\frac{1}{4}}}{x}+\frac{\left(-4 x^{4}+1\right) \left(x^{4}+1\right)^{\frac{1}{4}}}{5 x^{5}}$&$33$\\ \hline \end{longtable}"," ",0,"-1/5*(9*x^4-1)*(x^4+1)^(1/4)/x^5","A"
218,1,22,18,0.275000," ","int((x^2+1)/(-x^2+1)/(x^4+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\arctanh \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right) \sqrt{2}}{2}$&$22$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x +\sqrt{x^{4}+1}}{\left(-1+x \right) \left(1+x \right)}\right)}{2}$&$38$\\ default&$-\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}-\frac{2 \left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{\sqrt{x^{4}+1}}$&$112$\\ \hline \end{longtable}"," ",0,"1/2*arctanh(1/2*2^(1/2)/x*(x^4+1)^(1/2))*2^(1/2)","A"
219,1,31,21,0.279000," ","int((2*x^2+2*x-1)/(1+2*x)/(x^4-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(-\frac{-2 x^{2}+2 \sqrt{x^{4}-x}-1}{1+2 x}\right)$&$31$\\ default&$\frac{2 \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+2 \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{3}{2}+\frac{3 i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$774$\\ elliptic&$\frac{2 \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+2 \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{3}{2}+\frac{3 i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$774$\\ \hline \end{longtable}"," ",0,"-ln(-(-2*x^2+2*(x^4-x)^(1/2)-1)/(1+2*x))","A"
220,1,20,19,0.088000," ","int(1/x^5/(x^4+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(2 x^{3}-1\right) \sqrt{x^{4}+x}}{9 x^{5}}$&$20$\\ meijerg&$-\frac{2 \left(-2 x^{3}+1\right) \sqrt{x^{3}+1}}{9 x^{\frac{9}{2}}}$&$20$\\ risch&$\frac{\frac{2}{9} x^{3}-\frac{2}{9}+\frac{4}{9} x^{6}}{x^{4} \sqrt{x \left(x^{3}+1\right)}}$&$25$\\ default&$-\frac{2 \sqrt{x^{4}+x}}{9 x^{5}}+\frac{4 \sqrt{x^{4}+x}}{9 x^{2}}$&$26$\\ elliptic&$-\frac{2 \sqrt{x^{4}+x}}{9 x^{5}}+\frac{4 \sqrt{x^{4}+x}}{9 x^{2}}$&$26$\\ gosper&$\frac{2 \left(x^{2}-x +1\right) \left(1+x \right) \left(2 x^{3}-1\right)}{9 x^{4} \sqrt{x^{4}+x}}$&$31$\\ \hline \end{longtable}"," ",0,"2/9*(2*x^3-1)*(x^4+x)^(1/2)/x^5","A"
221,1,20,19,0.066000," ","int((x^3-1)/x^6/(x^4+x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{4 \left(11 x^{3}-3\right) \left(x^{4}+x \right)^{\frac{3}{4}}}{63 x^{6}}$&$20$\\ risch&$-\frac{4 \left(11 x^{6}+8 x^{3}-3\right)}{63 x^{5} \left(x \left(x^{3}+1\right)\right)^{\frac{1}{4}}}$&$27$\\ gosper&$-\frac{4 \left(11 x^{3}-3\right) \left(1+x \right) \left(x^{2}-x +1\right)}{63 \left(x^{4}+x \right)^{\frac{1}{4}} x^{5}}$&$31$\\ meijerg&$\frac{4 \left(1-\frac{4 x^{3}}{3}\right) \left(x^{3}+1\right)^{\frac{3}{4}}}{21 x^{\frac{21}{4}}}-\frac{4 \left(x^{3}+1\right)^{\frac{3}{4}}}{9 x^{\frac{9}{4}}}$&$33$\\ \hline \end{longtable}"," ",0,"-4/63*(11*x^3-3)*(x^4+x)^(3/4)/x^6","A"
222,1,20,19,0.062000," ","int((2*x^3+1)/x^6/(x^4+x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{4 \left(10 x^{3}+3\right) \left(x^{4}+x \right)^{\frac{3}{4}}}{63 x^{6}}$&$20$\\ risch&$-\frac{4 \left(10 x^{6}+13 x^{3}+3\right)}{63 x^{5} \left(x \left(x^{3}+1\right)\right)^{\frac{1}{4}}}$&$27$\\ gosper&$-\frac{4 \left(x^{2}-x +1\right) \left(1+x \right) \left(10 x^{3}+3\right)}{63 x^{5} \left(x^{4}+x \right)^{\frac{1}{4}}}$&$31$\\ meijerg&$-\frac{4 \left(1-\frac{4 x^{3}}{3}\right) \left(x^{3}+1\right)^{\frac{3}{4}}}{21 x^{\frac{21}{4}}}-\frac{8 \left(x^{3}+1\right)^{\frac{3}{4}}}{9 x^{\frac{9}{4}}}$&$33$\\ \hline \end{longtable}"," ",0,"-4/63*(10*x^3+3)*(x^4+x)^(3/4)/x^6","A"
223,1,13,21,0.074000," ","int((x^2-1)/(x^2+1)/(x^4+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{3 x}{\left(x^{4}+x^{2}\right)^{\frac{1}{3}}}$&$13$\\ risch&$-\frac{3 x}{\left(x^{2} \left(x^{2}+1\right)\right)^{\frac{1}{3}}}$&$15$\\ trager&$-\frac{3 \left(x^{4}+x^{2}\right)^{\frac{2}{3}}}{x \left(x^{2}+1\right)}$&$22$\\ meijerg&$-3 \hypergeom \left(\left[\frac{1}{6}, \frac{4}{3}\right], \left[\frac{7}{6}\right], -x^{2}\right) x^{\frac{1}{3}}+\frac{3 \hypergeom \left(\left[\frac{7}{6}, \frac{4}{3}\right], \left[\frac{13}{6}\right], -x^{2}\right) x^{\frac{7}{3}}}{7}$&$34$\\ \hline \end{longtable}"," ",0,"-3*x/(x^4+x^2)^(1/3)","A"
224,1,13,21,0.065000," ","int(1/(x^2+1)/(x^4+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{2 x}{\left(x^{4}+x^{2}\right)^{\frac{1}{4}}}$&$13$\\ meijerg&$\frac{2 \sqrt{x}}{\left(x^{2}+1\right)^{\frac{1}{4}}}$&$13$\\ risch&$\frac{2 x}{\left(x^{2} \left(x^{2}+1\right)\right)^{\frac{1}{4}}}$&$15$\\ trager&$\frac{2 \left(x^{4}+x^{2}\right)^{\frac{3}{4}}}{x \left(x^{2}+1\right)}$&$22$\\ \hline \end{longtable}"," ",0,"2*x/(x^4+x^2)^(1/4)","A"
225,1,13,21,0.076000," ","int(1/(-1+x)/(x^4-x^3)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{4 x}{\left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}}}$&$13$\\ gosper&$-\frac{4 x}{\left(x^{4}-x^{3}\right)^{\frac{1}{4}}}$&$15$\\ trager&$-\frac{4 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}}{\left(-1+x \right) x^{2}}$&$22$\\ meijerg&$-\frac{4 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{4}} x^{\frac{1}{4}}}{\mathrm{signum}\left(-1+x \right)^{\frac{1}{4}} \left(1-x \right)^{\frac{1}{4}}}$&$27$\\ \hline \end{longtable}"," ",0,"-4*x/(x^3*(-1+x))^(1/4)","A"
226,1,16,19,0.055000," ","int(1/x/(x^4+x^3)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{2 \left(1-2 x \right) \sqrt{1+x}}{3 x^{\frac{3}{2}}}$&$16$\\ gosper&$\frac{2 \left(1+x \right) \left(-1+2 x \right)}{3 \sqrt{x^{4}+x^{3}}}$&$20$\\ trager&$\frac{2 \left(-1+2 x \right) \sqrt{x^{4}+x^{3}}}{3 x^{3}}$&$20$\\ risch&$\frac{-\frac{2}{3}+\frac{2}{3} x +\frac{4}{3} x^{2}}{\sqrt{x^{3} \left(1+x \right)}}$&$20$\\ default&$\frac{2 \sqrt{x \left(1+x \right)}\, \sqrt{x^{2}+x}\, \left(-1+2 x \right)}{3 x \sqrt{x^{4}+x^{3}}}$&$34$\\ \hline \end{longtable}"," ",0,"-2/3*(1-2*x)*(1+x)^(1/2)/x^(3/2)","A"
227,1,16,19,0.050000," ","int(1/x^2/(x^4+x^3)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{4 \left(1-\frac{4 x}{3}\right) \left(1+x \right)^{\frac{3}{4}}}{7 x^{\frac{7}{4}}}$&$16$\\ trager&$\frac{4 \left(-3+4 x \right) \left(x^{4}+x^{3}\right)^{\frac{3}{4}}}{21 x^{4}}$&$20$\\ gosper&$\frac{4 \left(1+x \right) \left(-3+4 x \right)}{21 x \left(x^{4}+x^{3}\right)^{\frac{1}{4}}}$&$23$\\ risch&$\frac{-\frac{4}{7}+\frac{4}{21} x +\frac{16}{21} x^{2}}{x \left(x^{3} \left(1+x \right)\right)^{\frac{1}{4}}}$&$23$\\ \hline \end{longtable}"," ",0,"-4/7*(1-4/3*x)*(1+x)^(3/4)/x^(7/4)","A"
228,1,28,21,0.314000," ","int((1+2*x)/(x^4+2*x^3+x^2+3)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(-x^{2}+\sqrt{x^{4}+2 x^{3}+x^{2}+3}-x \right)$&$28$\\ default&$\frac{i \left(2-i \sqrt{3}\right) \sqrt{-\frac{2 \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(-2+i \sqrt{3}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{2}\, \sqrt{-\frac{i \sqrt{3}\, \left(x +\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{i \sqrt{3}\, \left(x +\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-2+i \sqrt{3}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{3}\, \EllipticF \left(\sqrt{-\frac{2 \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(-2+i \sqrt{3}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \frac{\sqrt{\left(2+i \sqrt{3}\right) \left(2-i \sqrt{3}\right)}}{2}\right)}{6 \sqrt{\left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{i \left(2-i \sqrt{3}\right) \sqrt{-\frac{2 \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(-2+i \sqrt{3}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{2}\, \sqrt{-\frac{i \sqrt{3}\, \left(x +\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{i \sqrt{3}\, \left(x +\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-2+i \sqrt{3}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{3}\, \left(\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticF \left(\sqrt{-\frac{2 \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(-2+i \sqrt{3}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \frac{\sqrt{\left(2+i \sqrt{3}\right) \left(2-i \sqrt{3}\right)}}{2}\right)-i \sqrt{3}\, \EllipticPi \left(\sqrt{-\frac{2 \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(-2+i \sqrt{3}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, 1-\frac{i \sqrt{3}}{2}, \frac{\sqrt{\left(2+i \sqrt{3}\right) \left(2-i \sqrt{3}\right)}}{2}\right)\right)}{3 \sqrt{\left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$528$\\ elliptic&$\frac{i \left(2-i \sqrt{3}\right) \sqrt{-\frac{2 \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(-2+i \sqrt{3}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{2}\, \sqrt{-\frac{i \sqrt{3}\, \left(x +\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{i \sqrt{3}\, \left(x +\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-2+i \sqrt{3}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{3}\, \EllipticF \left(\sqrt{-\frac{2 \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(-2+i \sqrt{3}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \frac{\sqrt{\left(2+i \sqrt{3}\right) \left(2-i \sqrt{3}\right)}}{2}\right)}{6 \sqrt{\left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{i \left(2-i \sqrt{3}\right) \sqrt{-\frac{2 \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(-2+i \sqrt{3}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{2}\, \sqrt{-\frac{i \sqrt{3}\, \left(x +\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{i \sqrt{3}\, \left(x +\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-2+i \sqrt{3}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{3}\, \left(\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticF \left(\sqrt{-\frac{2 \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(-2+i \sqrt{3}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \frac{\sqrt{\left(2+i \sqrt{3}\right) \left(2-i \sqrt{3}\right)}}{2}\right)-i \sqrt{3}\, \EllipticPi \left(\sqrt{-\frac{2 \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(-2+i \sqrt{3}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, 1-\frac{i \sqrt{3}}{2}, \frac{\sqrt{\left(2+i \sqrt{3}\right) \left(2-i \sqrt{3}\right)}}{2}\right)\right)}{3 \sqrt{\left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$528$\\ \hline \end{longtable}"," ",0,"-ln(-x^2+(x^4+2*x^3+x^2+3)^(1/2)-x)","A"
229,1,20,19,0.082000," ","int((2*x^4-1)/x^8/(x^4-1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{4}-1\right)^{\frac{3}{4}} \left(10 x^{4}-3\right)}{21 x^{7}}$&$20$\\ risch&$\frac{10 x^{8}-13 x^{4}+3}{21 x^{7} \left(x^{4}-1\right)^{\frac{1}{4}}}$&$25$\\ gosper&$\frac{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right) \left(10 x^{4}-3\right)}{21 x^{7} \left(x^{4}-1\right)^{\frac{1}{4}}}$&$31$\\ meijerg&$\frac{\left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \left(1+\frac{4 x^{4}}{3}\right) \left(-x^{4}+1\right)^{\frac{3}{4}}}{7 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}} x^{7}}-\frac{2 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \left(-x^{4}+1\right)^{\frac{3}{4}}}{3 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}} x^{3}}$&$73$\\ \hline \end{longtable}"," ",0,"1/21*(x^4-1)^(3/4)*(10*x^4-3)/x^7","A"
230,1,20,19,0.069000," ","int((2*x^4+1)/x^4/(x^4+1)^(5/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{2 x^{4}-1}{3 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}}$&$20$\\ trager&$\frac{2 x^{4}-1}{3 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}}$&$20$\\ risch&$\frac{2 x^{4}-1}{3 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}}$&$20$\\ meijerg&$-\frac{4 x^{4}+1}{3 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}}+\frac{2 x}{\left(x^{4}+1\right)^{\frac{1}{4}}}$&$31$\\ \hline \end{longtable}"," ",0,"1/3*(2*x^4-1)/x^3/(x^4+1)^(1/4)","A"
231,1,19,19,0.149000," ","int((4*x^3+1)*(2*x^4+2*x+1)/(x^4+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\left(\frac{4}{3} x^{4}+\frac{4}{3} x +2\right) \sqrt{x^{4}+x}$&$19$\\ risch&$\frac{2 \left(2 x^{4}+2 x +3\right) x \left(x^{3}+1\right)}{3 \sqrt{x \left(x^{3}+1\right)}}$&$28$\\ gosper&$\frac{2 \left(x^{2}-x +1\right) x \left(1+x \right) \left(2 x^{4}+2 x +3\right)}{3 \sqrt{x^{4}+x}}$&$32$\\ default&$\frac{4 x^{4} \sqrt{x^{4}+x}}{3}+\frac{4 x \sqrt{x^{4}+x}}{3}+2 \sqrt{x^{4}+x}$&$33$\\ elliptic&$\frac{4 x^{4} \sqrt{x^{4}+x}}{3}+\frac{4 x \sqrt{x^{4}+x}}{3}+2 \sqrt{x^{4}+x}$&$33$\\ meijerg&$\frac{-\frac{2 \sqrt{\pi}\, x^{\frac{3}{2}} \left(-10 x^{3}+15\right) \sqrt{x^{3}+1}}{15}+2 \sqrt{\pi}\, \arcsinh \left(x^{\frac{3}{2}}\right)}{\sqrt{\pi}}+\frac{\frac{10 \sqrt{\pi}\, x^{\frac{3}{2}} \sqrt{x^{3}+1}}{3}-\frac{10 \sqrt{\pi}\, \arcsinh \left(x^{\frac{3}{2}}\right)}{3}}{\sqrt{\pi}}+\frac{8 \hypergeom \left(\left[\frac{1}{2}, \frac{7}{6}\right], \left[\frac{13}{6}\right], -x^{3}\right) x^{\frac{7}{2}}}{7}+\frac{4 \arcsinh \left(x^{\frac{3}{2}}\right)}{3}+2 \hypergeom \left(\left[\frac{1}{6}, \frac{1}{2}\right], \left[\frac{7}{6}\right], -x^{3}\right) \sqrt{x}$&$106$\\ \hline \end{longtable}"," ",0,"(4/3*x^4+4/3*x+2)*(x^4+x)^(1/2)","A"
232,1,13,21,0.080000," ","int((x^2-1)/(x^2+1)/(x^5+x^3)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{4 x}{\left(x^{5}+x^{3}\right)^{\frac{1}{4}}}$&$13$\\ risch&$-\frac{4 x}{\left(x^{3} \left(x^{2}+1\right)\right)^{\frac{1}{4}}}$&$15$\\ trager&$-\frac{4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(x^{2}+1\right)}$&$22$\\ meijerg&$-4 \hypergeom \left(\left[\frac{1}{8}, \frac{5}{4}\right], \left[\frac{9}{8}\right], -x^{2}\right) x^{\frac{1}{4}}+\frac{4 \hypergeom \left(\left[\frac{9}{8}, \frac{5}{4}\right], \left[\frac{17}{8}\right], -x^{2}\right) x^{\frac{9}{4}}}{9}$&$34$\\ \hline \end{longtable}"," ",0,"-4*x/(x^5+x^3)^(1/4)","A"
233,1,20,19,0.079000," ","int(1/x^10/(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}-1}\, \left(2 x^{6}+1\right)}{9 x^{9}}$&$20$\\ risch&$\frac{2 x^{12}-x^{6}-1}{9 x^{9} \sqrt{x^{6}-1}}$&$25$\\ gosper&$\frac{\left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right) \left(2 x^{6}+1\right)}{9 x^{9} \sqrt{x^{6}-1}}$&$40$\\ meijerg&$-\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(2 x^{6}+1\right) \sqrt{-x^{6}+1}}{9 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, x^{9}}$&$40$\\ \hline \end{longtable}"," ",0,"1/9*(x^6-1)^(1/2)*(2*x^6+1)/x^9","A"
234,1,20,19,0.077000," ","int((x^6+1)/x^10/(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}-1}\, \left(5 x^{6}+1\right)}{9 x^{9}}$&$20$\\ risch&$\frac{5 x^{12}-4 x^{6}-1}{9 x^{9} \sqrt{x^{6}-1}}$&$25$\\ gosper&$\frac{\left(5 x^{6}+1\right) \left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right)}{9 \sqrt{x^{6}-1}\, x^{9}}$&$40$\\ meijerg&$-\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{-x^{6}+1}}{3 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, x^{3}}-\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(2 x^{6}+1\right) \sqrt{-x^{6}+1}}{9 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, x^{9}}$&$73$\\ \hline \end{longtable}"," ",0,"1/9*(x^6-1)^(1/2)*(5*x^6+1)/x^9","A"
235,1,13,21,0.073000," ","int((3*x^4-1)/(x^4+1)/(x^6+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{3 x}{\left(x^{6}+x^{2}\right)^{\frac{1}{3}}}$&$13$\\ risch&$-\frac{3 x}{\left(x^{2} \left(x^{4}+1\right)\right)^{\frac{1}{3}}}$&$15$\\ trager&$-\frac{3 \left(x^{6}+x^{2}\right)^{\frac{2}{3}}}{x \left(x^{4}+1\right)}$&$22$\\ meijerg&$-3 \hypergeom \left(\left[\frac{1}{12}, \frac{4}{3}\right], \left[\frac{13}{12}\right], -x^{4}\right) x^{\frac{1}{3}}+\frac{9 \hypergeom \left(\left[\frac{13}{12}, \frac{4}{3}\right], \left[\frac{25}{12}\right], -x^{4}\right) x^{\frac{13}{3}}}{13}$&$34$\\ \hline \end{longtable}"," ",0,"-3*x/(x^6+x^2)^(1/3)","A"
236,1,13,21,0.079000," ","int((x^4-1)/(x^4+1)/(x^6+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{2 x}{\left(x^{6}+x^{2}\right)^{\frac{1}{4}}}$&$13$\\ risch&$-\frac{2 x}{\left(x^{2} \left(x^{4}+1\right)\right)^{\frac{1}{4}}}$&$15$\\ trager&$-\frac{2 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{x \left(x^{4}+1\right)}$&$22$\\ meijerg&$-2 \hypergeom \left(\left[\frac{1}{8}, \frac{5}{4}\right], \left[\frac{9}{8}\right], -x^{4}\right) \sqrt{x}+\frac{2 \hypergeom \left(\left[\frac{9}{8}, \frac{5}{4}\right], \left[\frac{17}{8}\right], -x^{4}\right) x^{\frac{9}{2}}}{9}$&$34$\\ \hline \end{longtable}"," ",0,"-2*x/(x^6+x^2)^(1/4)","A"
237,1,22,21,0.098000," ","int(x^2*(2*x^2+3)*(2*x^6+x^2+1)/(x^2+1)^2/(x^6+x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{x^{3} \sqrt{x^{6}+x^{2}+1}}{x^{2}+1}$&$22$\\ trager&$\frac{x^{3} \sqrt{x^{6}+x^{2}+1}}{x^{2}+1}$&$22$\\ risch&$\frac{x^{3} \sqrt{x^{6}+x^{2}+1}}{x^{2}+1}$&$22$\\ \hline \end{longtable}"," ",0,"x^3*(x^6+x^2+1)^(1/2)/(x^2+1)","A"
238,1,33,22,0.097000," ","int(1/(x^3+x^2-5*x+3)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\ln \left(\frac{x^{2}+4 \sqrt{x^{3}+x^{2}-5 x +3}+6 x -7}{\left(-1+x \right)^{2}}\right)}{2}$&$33$\\ default&$-\frac{\left(-1+x \right) \sqrt{3+x}\, \left(\ln \left(\sqrt{3+x}+2\right)-\ln \left(\sqrt{3+x}-2\right)\right)}{2 \sqrt{x^{3}+x^{2}-5 x +3}}$&$43$\\ \hline \end{longtable}"," ",0,"-1/2*ln((x^2+4*(x^3+x^2-5*x+3)^(1/2)+6*x-7)/(-1+x)^2)","A"
239,1,45,22,0.340000," ","int((-1+x)/(1+x)/(x^3+x^2+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)+2 \sqrt{x^{3}+x^{2}+x}}{\left(1+x \right)^{2}}\right)$&$45$\\ default&$\frac{2 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}}-\frac{4 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}\, \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}$&$271$\\ elliptic&$\frac{2 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}}-\frac{4 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}\, \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}$&$271$\\ \hline \end{longtable}"," ",0,"-RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)*x^2+RootOf(_Z^2+1)+2*(x^3+x^2+x)^(1/2))/(1+x)^2)","C"
240,1,32,22,0.180000," ","int((x^2-1)/(x^2+1)/(x^3+x^2+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(\frac{-x^{2}+2 \sqrt{x^{3}+x^{2}+x}-2 x -1}{x^{2}+1}\right)$&$32$\\ default&$\frac{2 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}}+\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{1}{2}-i-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{1}{2}-i-\frac{i \sqrt{3}}{2}\right)}-\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{1}{2}-i-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{\sqrt{x^{3}+x^{2}+x}\, \left(-\frac{1}{2}-i-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{1}{2}+i-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{1}{2}+i-\frac{i \sqrt{3}}{2}\right)}+\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{1}{2}+i-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{\sqrt{x^{3}+x^{2}+x}\, \left(-\frac{1}{2}+i-\frac{i \sqrt{3}}{2}\right)}$&$781$\\ elliptic&$\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}}+\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{\sqrt{x^{3}+x^{2}+x}}+\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{1}{2}-i-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{1}{2}-i-\frac{i \sqrt{3}}{2}\right)}-\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{1}{2}-i-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{\sqrt{x^{3}+x^{2}+x}\, \left(-\frac{1}{2}-i-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{1}{2}+i-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{1}{2}+i-\frac{i \sqrt{3}}{2}\right)}+\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{1}{2}+i-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{\sqrt{x^{3}+x^{2}+x}\, \left(-\frac{1}{2}+i-\frac{i \sqrt{3}}{2}\right)}$&$925$\\ \hline \end{longtable}"," ",0,"ln((-x^2+2*(x^3+x^2+x)^(1/2)-2*x-1)/(x^2+1))","A"
241,1,22,18,0.241000," ","int((x^2-1)/(x^2+1)/(x^4+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\arctan \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right) \sqrt{2}}{2}$&$22$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x -\sqrt{x^{4}+1}}{x^{2}+1}\right)}{2}$&$37$\\ default&$\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{2 \left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{\sqrt{x^{4}+1}}$&$111$\\ \hline \end{longtable}"," ",0,"1/2*arctan(1/2*2^(1/2)/x*(x^4+1)^(1/2))*2^(1/2)","A"
242,1,22,18,0.242000," ","int((x^2+1)/(x^2-1)/(x^4+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\frac{\arctanh \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right) \sqrt{2}}{2}$&$22$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x -\sqrt{x^{4}+1}}{\left(-1+x \right) \left(1+x \right)}\right)}{2}$&$39$\\ default&$\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{2 \left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{\sqrt{x^{4}+1}}$&$111$\\ \hline \end{longtable}"," ",0,"-1/2*arctanh(1/2*2^(1/2)/x*(x^4+1)^(1/2))*2^(1/2)","A"
243,0,0,18,0.021000," ","int((-3*x^5+2)/(x^5+1)^(1/2)/(x^5-a*x^2+1),x)","\[\int \frac{-3 x^{5}+2}{\sqrt{x^{5}+1}\, \left(x^{5}-a \,x^{2}+1\right)}\, dx\]"," ",0,"int((-3*x^5+2)/(x^5+1)^(1/2)/(x^5-a*x^2+1),x)","F"
244,0,0,18,0.036000," ","int((3*x^5+2)/(x^5-1)^(1/2)/(x^5-a*x^2-1),x)","\[\int \frac{3 x^{5}+2}{\sqrt{x^{5}-1}\, \left(x^{5}-a \,x^{2}-1\right)}\, dx\]"," ",0,"int((3*x^5+2)/(x^5-1)^(1/2)/(x^5-a*x^2-1),x)","F"
245,0,0,18,0.031000," ","int((3*x^5+2)/(x^5-1)^(1/2)/(a*x^5-x^2-a),x)","\[\int \frac{3 x^{5}+2}{\sqrt{x^{5}-1}\, \left(a \,x^{5}-x^{2}-a \right)}\, dx\]"," ",0,"int((3*x^5+2)/(x^5-1)^(1/2)/(a*x^5-x^2-a),x)","F"
246,0,0,18,0.020000," ","int((3*x^5-2)/(x^5+1)^(1/2)/(a*x^5-x^2+a),x)","\[\int \frac{3 x^{5}-2}{\sqrt{x^{5}+1}\, \left(a \,x^{5}-x^{2}+a \right)}\, dx\]"," ",0,"int((3*x^5-2)/(x^5+1)^(1/2)/(a*x^5-x^2+a),x)","F"
247,1,16,22,0.052000," ","int((2*x^4-2*x^2-1)/(x^4-x^2+1)/(x^6+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{\left(x^{2}+1\right) x}{\sqrt{x^{6}+1}}$&$16$\\ risch&$-\frac{\left(x^{2}+1\right) x}{\sqrt{x^{6}+1}}$&$16$\\ trager&$-\frac{x \sqrt{x^{6}+1}}{x^{4}-x^{2}+1}$&$23$\\ \hline \end{longtable}"," ",0,"-(x^2+1)*x/(x^6+1)^(1/2)","A"
248,0,0,18,0.022000," ","int((4*x^5-1)/(x^5-a*x+1)/(x^6+x)^(1/2),x)","\[\int \frac{4 x^{5}-1}{\left(x^{5}-a x +1\right) \sqrt{x^{6}+x}}\, dx\]"," ",0,"int((4*x^5-1)/(x^5-a*x+1)/(x^6+x)^(1/2),x)","F"
249,0,0,18,0.019000," ","int((4*x^5-1)/(a*x^5+a-x)/(x^6+x)^(1/2),x)","\[\int \frac{4 x^{5}-1}{\left(a \,x^{5}+a -x \right) \sqrt{x^{6}+x}}\, dx\]"," ",0,"int((4*x^5-1)/(a*x^5+a-x)/(x^6+x)^(1/2),x)","F"
250,1,21,21,0.076000," ","int(x^3*(x^2-1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\left(\frac{3}{16} x^{4}-\frac{3}{40} x^{2}-\frac{9}{80}\right) \left(x^{2}-1\right)^{\frac{2}{3}}$&$21$\\ risch&$\frac{3 \left(x^{2}-1\right)^{\frac{2}{3}} \left(5 x^{4}-2 x^{2}-3\right)}{80}$&$22$\\ gosper&$\frac{3 \left(-1+x \right) \left(1+x \right) \left(5 x^{2}+3\right) \left(x^{2}-1\right)^{\frac{2}{3}}}{80}$&$23$\\ meijerg&$\frac{\mathrm{signum}\left(x^{2}-1\right)^{\frac{2}{3}} \hypergeom \left(\left[-\frac{2}{3}, 2\right], \left[3\right], x^{2}\right) x^{4}}{4 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{2}{3}}}$&$33$\\ \hline \end{longtable}"," ",0,"(3/16*x^4-3/40*x^2-9/80)*(x^2-1)^(2/3)","A"
251,1,21,21,0.079000," ","int(x^3*(x^2-1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\left(\frac{2}{11} x^{4}-\frac{6}{77} x^{2}-\frac{8}{77}\right) \left(x^{2}-1\right)^{\frac{3}{4}}$&$21$\\ risch&$\frac{2 \left(x^{2}-1\right)^{\frac{3}{4}} \left(7 x^{4}-3 x^{2}-4\right)}{77}$&$22$\\ gosper&$\frac{2 \left(-1+x \right) \left(1+x \right) \left(7 x^{2}+4\right) \left(x^{2}-1\right)^{\frac{3}{4}}}{77}$&$23$\\ meijerg&$\frac{\mathrm{signum}\left(x^{2}-1\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{3}{4}, 2\right], \left[3\right], x^{2}\right) x^{4}}{4 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{3}{4}}}$&$33$\\ \hline \end{longtable}"," ",0,"(2/11*x^4-6/77*x^2-8/77)*(x^2-1)^(3/4)","A"
252,1,43,21,1.317000," ","int(1/x/(x^2+1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\left(-3 \ln \left(2\right)+\frac{\pi}{2}+2 \ln \left(x \right)\right) \Gamma \left(\frac{3}{4}\right)-\frac{3 \hypergeom \left(\left[1, 1, \frac{7}{4}\right], \left[2, 2\right], -x^{2}\right) \Gamma \left(\frac{3}{4}\right) x^{2}}{4}}{2 \Gamma \left(\frac{3}{4}\right)}$&$43$\\ trager&$\frac{\ln \left(-\frac{2 \left(x^{2}+1\right)^{\frac{3}{4}}-2 \sqrt{x^{2}+1}-x^{2}+2 \left(x^{2}+1\right)^{\frac{1}{4}}-2}{x^{2}}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{2}+1}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-2 \left(x^{2}+1\right)^{\frac{3}{4}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right)+2 \left(x^{2}+1\right)^{\frac{1}{4}}}{x^{2}}\right)}{2}$&$110$\\ \hline \end{longtable}"," ",0,"1/2/GAMMA(3/4)*((-3*ln(2)+1/2*Pi+2*ln(x))*GAMMA(3/4)-3/4*hypergeom([1,1,7/4],[2,2],-x^2)*GAMMA(3/4)*x^2)","C"
253,1,17,21,0.062000," ","int(x^3*(x^2+1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{2 \left(x^{2}+1\right)^{\frac{7}{4}} \left(7 x^{2}-4\right)}{77}$&$17$\\ meijerg&$\frac{\hypergeom \left(\left[-\frac{3}{4}, 2\right], \left[3\right], -x^{2}\right) x^{4}}{4}$&$17$\\ trager&$\left(\frac{2}{11} x^{4}+\frac{6}{77} x^{2}-\frac{8}{77}\right) \left(x^{2}+1\right)^{\frac{3}{4}}$&$21$\\ risch&$\frac{2 \left(x^{2}+1\right)^{\frac{3}{4}} \left(7 x^{4}+3 x^{2}-4\right)}{77}$&$22$\\ \hline \end{longtable}"," ",0,"2/77*(x^2+1)^(7/4)*(7*x^2-4)","A"
254,1,21,21,0.077000," ","int(x^5*(x^3-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\left(\frac{1}{7} x^{6}-\frac{1}{28} x^{3}-\frac{3}{28}\right) \left(x^{3}-1\right)^{\frac{1}{3}}$&$21$\\ risch&$\frac{\left(x^{3}-1\right)^{\frac{1}{3}} \left(4 x^{6}-x^{3}-3\right)}{28}$&$22$\\ gosper&$\frac{\left(-1+x \right) \left(x^{2}+x +1\right) \left(4 x^{3}+3\right) \left(x^{3}-1\right)^{\frac{1}{3}}}{28}$&$26$\\ meijerg&$\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{1}{3}, 2\right], \left[3\right], x^{3}\right) x^{6}}{6 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}}}$&$33$\\ \hline \end{longtable}"," ",0,"(1/7*x^6-1/28*x^3-3/28)*(x^3-1)^(1/3)","A"
255,1,21,21,0.082000," ","int(x^5*(x^3-1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\left(\frac{4}{33} x^{6}-\frac{4}{77} x^{3}-\frac{16}{231}\right) \left(x^{3}-1\right)^{\frac{3}{4}}$&$21$\\ risch&$\frac{4 \left(x^{3}-1\right)^{\frac{3}{4}} \left(7 x^{6}-3 x^{3}-4\right)}{231}$&$22$\\ gosper&$\frac{4 \left(-1+x \right) \left(x^{2}+x +1\right) \left(7 x^{3}+4\right) \left(x^{3}-1\right)^{\frac{3}{4}}}{231}$&$26$\\ meijerg&$\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{3}{4}, 2\right], \left[3\right], x^{3}\right) x^{6}}{6 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{3}{4}}}$&$33$\\ \hline \end{longtable}"," ",0,"(4/33*x^6-4/77*x^3-16/231)*(x^3-1)^(3/4)","A"
256,1,17,21,0.062000," ","int(x^8/(x^3+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\hypergeom \left(\left[\frac{1}{4}, 3\right], \left[4\right], -x^{3}\right) x^{9}}{9}$&$17$\\ trager&$\left(\frac{4}{33} x^{6}-\frac{32}{231} x^{3}+\frac{128}{693}\right) \left(x^{3}+1\right)^{\frac{3}{4}}$&$21$\\ risch&$\frac{4 \left(x^{3}+1\right)^{\frac{3}{4}} \left(21 x^{6}-24 x^{3}+32\right)}{693}$&$22$\\ gosper&$\frac{4 \left(1+x \right) \left(x^{2}-x +1\right) \left(21 x^{6}-24 x^{3}+32\right)}{693 \left(x^{3}+1\right)^{\frac{1}{4}}}$&$33$\\ \hline \end{longtable}"," ",0,"1/9*hypergeom([1/4,3],[4],-x^3)*x^9","C"
257,1,17,21,0.062000," ","int(x^5*(x^3+1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\hypergeom \left(\left[-\frac{2}{3}, 2\right], \left[3\right], -x^{3}\right) x^{6}}{6}$&$17$\\ trager&$\left(\frac{1}{8} x^{6}+\frac{1}{20} x^{3}-\frac{3}{40}\right) \left(x^{3}+1\right)^{\frac{2}{3}}$&$21$\\ risch&$\frac{\left(x^{3}+1\right)^{\frac{2}{3}} \left(5 x^{6}+2 x^{3}-3\right)}{40}$&$22$\\ gosper&$\frac{\left(1+x \right) \left(x^{2}-x +1\right) \left(5 x^{3}-3\right) \left(x^{3}+1\right)^{\frac{2}{3}}}{40}$&$28$\\ \hline \end{longtable}"," ",0,"1/6*hypergeom([-2/3,2],[3],-x^3)*x^6","C"
258,1,22,21,0.064000," ","int(1/x^2/(x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(2+3 x \right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}}{10 x^{3}}$&$22$\\ gosper&$\frac{3 \left(-1+x \right) \left(2+3 x \right)}{10 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}}$&$25$\\ risch&$\frac{-\frac{3}{5}-\frac{3}{10} x +\frac{9}{10} x^{2}}{x \left(\left(-1+x \right) x^{2}\right)^{\frac{1}{3}}}$&$25$\\ meijerg&$-\frac{3 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{3}} \left(1+\frac{3 x}{2}\right) \left(1-x \right)^{\frac{2}{3}}}{5 \mathrm{signum}\left(-1+x \right)^{\frac{1}{3}} x^{\frac{5}{3}}}$&$32$\\ \hline \end{longtable}"," ",0,"3/10*(2+3*x)*(x^3-x^2)^(2/3)/x^3","A"
259,1,17,21,0.067000," ","int(x^7*(x^4+1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{3 \left(x^{4}+1\right)^{\frac{5}{3}} \left(5 x^{4}-3\right)}{160}$&$17$\\ meijerg&$\frac{\hypergeom \left(\left[-\frac{2}{3}, 2\right], \left[3\right], -x^{4}\right) x^{8}}{8}$&$17$\\ trager&$\left(\frac{3}{32} x^{8}+\frac{3}{80} x^{4}-\frac{9}{160}\right) \left(x^{4}+1\right)^{\frac{2}{3}}$&$21$\\ risch&$\frac{3 \left(x^{4}+1\right)^{\frac{2}{3}} \left(5 x^{8}+2 x^{4}-3\right)}{160}$&$22$\\ \hline \end{longtable}"," ",0,"3/160*(x^4+1)^(5/3)*(5*x^4-3)","A"
260,1,22,21,0.097000," ","int(1/x^5/(x^4-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(2 x^{3}+1\right) \sqrt{x^{4}-x}}{9 x^{5}}$&$22$\\ risch&$\frac{-\frac{2}{9} x^{3}-\frac{2}{9}+\frac{4}{9} x^{6}}{x^{4} \sqrt{x \left(x^{3}-1\right)}}$&$27$\\ default&$\frac{2 \sqrt{x^{4}-x}}{9 x^{5}}+\frac{4 \sqrt{x^{4}-x}}{9 x^{2}}$&$30$\\ elliptic&$\frac{2 \sqrt{x^{4}-x}}{9 x^{5}}+\frac{4 \sqrt{x^{4}-x}}{9 x^{2}}$&$30$\\ gosper&$\frac{2 \left(-1+x \right) \left(x^{2}+x +1\right) \left(2 x^{3}+1\right)}{9 x^{4} \sqrt{x^{4}-x}}$&$31$\\ meijerg&$-\frac{2 \sqrt{-\mathrm{signum}\left(x^{3}-1\right)}\, \left(2 x^{3}+1\right) \sqrt{-x^{3}+1}}{9 \sqrt{\mathrm{signum}\left(x^{3}-1\right)}\, x^{\frac{9}{2}}}$&$40$\\ \hline \end{longtable}"," ",0,"2/9*(2*x^3+1)*(x^4-x)^(1/2)/x^5","A"
261,1,22,21,0.081000," ","int((x^3+1)/x^6/(x^4-x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(11 x^{3}+3\right) \left(x^{4}-x \right)^{\frac{3}{4}}}{63 x^{6}}$&$22$\\ risch&$\frac{\frac{44}{63} x^{6}-\frac{32}{63} x^{3}-\frac{4}{21}}{x^{5} \left(x \left(x^{3}-1\right)\right)^{\frac{1}{4}}}$&$27$\\ gosper&$\frac{4 \left(11 x^{3}+3\right) \left(-1+x \right) \left(x^{2}+x +1\right)}{63 \left(x^{4}-x \right)^{\frac{1}{4}} x^{5}}$&$31$\\ meijerg&$-\frac{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}} \left(1+\frac{4 x^{3}}{3}\right) \left(-x^{3}+1\right)^{\frac{3}{4}}}{21 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}} x^{\frac{21}{4}}}-\frac{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}} \left(-x^{3}+1\right)^{\frac{3}{4}}}{9 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}} x^{\frac{9}{4}}}$&$73$\\ \hline \end{longtable}"," ",0,"4/63*(11*x^3+3)*(x^4-x)^(3/4)/x^6","A"
262,1,15,23,0.096000," ","int((x^2+1)/(x^2-1)/(x^4-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{3 x}{\left(x^{4}-x^{2}\right)^{\frac{1}{3}}}$&$15$\\ risch&$-\frac{3 x}{\left(x^{2} \left(x^{2}-1\right)\right)^{\frac{1}{3}}}$&$15$\\ trager&$-\frac{3 \left(x^{4}-x^{2}\right)^{\frac{2}{3}}}{x \left(x^{2}-1\right)}$&$24$\\ meijerg&$-\frac{3 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}} \hypergeom \left(\left[\frac{1}{6}, \frac{4}{3}\right], \left[\frac{7}{6}\right], x^{2}\right) x^{\frac{1}{3}}}{\mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}}}-\frac{3 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}} \hypergeom \left(\left[\frac{7}{6}, \frac{4}{3}\right], \left[\frac{13}{6}\right], x^{2}\right) x^{\frac{7}{3}}}{7 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}}}$&$66$\\ \hline \end{longtable}"," ",0,"-3*x/(x^4-x^2)^(1/3)","A"
263,1,15,23,0.091000," ","int(1/(x^2-1)/(x^4-x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{2 x}{\left(x^{4}-x^{2}\right)^{\frac{1}{4}}}$&$15$\\ risch&$-\frac{2 x}{\left(x^{2} \left(x^{2}-1\right)\right)^{\frac{1}{4}}}$&$15$\\ trager&$-\frac{2 \left(x^{4}-x^{2}\right)^{\frac{3}{4}}}{x \left(x^{2}-1\right)}$&$24$\\ meijerg&$-\frac{2 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{4}} \sqrt{x}}{\mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{4}} \left(-x^{2}+1\right)^{\frac{1}{4}}}$&$33$\\ \hline \end{longtable}"," ",0,"-2*x/(x^4-x^2)^(1/4)","A"
264,1,20,21,0.061000," ","int(1/x^4/(x^4+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{2 \left(1-\frac{4 x^{2}}{3}\right) \left(x^{2}+1\right)^{\frac{3}{4}}}{7 x^{\frac{7}{2}}}$&$20$\\ trager&$\frac{2 \left(4 x^{2}-3\right) \left(x^{4}+x^{2}\right)^{\frac{3}{4}}}{21 x^{5}}$&$22$\\ gosper&$\frac{2 \left(x^{2}+1\right) \left(4 x^{2}-3\right)}{21 x^{3} \left(x^{4}+x^{2}\right)^{\frac{1}{4}}}$&$27$\\ risch&$\frac{\frac{2}{21} x^{2}-\frac{2}{7}+\frac{8}{21} x^{4}}{x^{3} \left(x^{2} \left(x^{2}+1\right)\right)^{\frac{1}{4}}}$&$27$\\ \hline \end{longtable}"," ",0,"-2/7*(1-4/3*x^2)*(x^2+1)^(3/4)/x^(7/2)","A"
265,1,24,23,0.735000," ","int((-1+2*x)/(x^4-2*x^3+x^2-3)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(-x +x^{2}+\sqrt{x^{4}-2 x^{3}+x^{2}-3}\right)$&$24$\\ default&$-\frac{2 \left(-\frac{\sqrt{1+4 \sqrt{3}}}{2}-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right) \sqrt{\frac{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)^{2} \sqrt{\frac{\sqrt{1+4 \sqrt{3}}\, \left(x -\frac{1}{2}+\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right)}{\left(-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}\, \sqrt{\frac{\sqrt{1+4 \sqrt{3}}\, \left(x -\frac{1}{2}-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}, \sqrt{\frac{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(-\frac{\sqrt{1+4 \sqrt{3}}}{2}-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \sqrt{1+4 \sqrt{3}}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right)}}+\frac{4 \left(-\frac{\sqrt{1+4 \sqrt{3}}}{2}-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right) \sqrt{\frac{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)^{2} \sqrt{\frac{\sqrt{1+4 \sqrt{3}}\, \left(x -\frac{1}{2}+\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right)}{\left(-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}\, \sqrt{\frac{\sqrt{1+4 \sqrt{3}}\, \left(x -\frac{1}{2}-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}\, \left(\left(\frac{1}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \EllipticF \left(\sqrt{\frac{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}, \sqrt{\frac{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(-\frac{\sqrt{1+4 \sqrt{3}}}{2}-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}\right)-\sqrt{1+4 \sqrt{3}}\, \EllipticPi \left(\sqrt{\frac{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}, \frac{\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}}{\frac{i \sqrt{-1+4 \sqrt{3}}}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}}, \sqrt{\frac{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(-\frac{\sqrt{1+4 \sqrt{3}}}{2}-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}\right)\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \sqrt{1+4 \sqrt{3}}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right)}}$&$1358$\\ elliptic&$-\frac{2 \left(-\frac{\sqrt{1+4 \sqrt{3}}}{2}-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right) \sqrt{\frac{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)^{2} \sqrt{\frac{\sqrt{1+4 \sqrt{3}}\, \left(x -\frac{1}{2}+\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right)}{\left(-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}\, \sqrt{\frac{\sqrt{1+4 \sqrt{3}}\, \left(x -\frac{1}{2}-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}, \sqrt{\frac{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(-\frac{\sqrt{1+4 \sqrt{3}}}{2}-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \sqrt{1+4 \sqrt{3}}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right)}}+\frac{4 \left(-\frac{\sqrt{1+4 \sqrt{3}}}{2}-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right) \sqrt{\frac{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)^{2} \sqrt{\frac{\sqrt{1+4 \sqrt{3}}\, \left(x -\frac{1}{2}+\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right)}{\left(-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}\, \sqrt{\frac{\sqrt{1+4 \sqrt{3}}\, \left(x -\frac{1}{2}-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}\, \left(\left(\frac{1}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \EllipticF \left(\sqrt{\frac{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}, \sqrt{\frac{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(-\frac{\sqrt{1+4 \sqrt{3}}}{2}-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}\right)-\sqrt{1+4 \sqrt{3}}\, \EllipticPi \left(\sqrt{\frac{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}, \frac{\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}}{\frac{i \sqrt{-1+4 \sqrt{3}}}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}}, \sqrt{\frac{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(-\frac{\sqrt{1+4 \sqrt{3}}}{2}-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right)}}\right)\right)}{\left(\frac{i \sqrt{-1+4 \sqrt{3}}}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \sqrt{1+4 \sqrt{3}}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{-1+4 \sqrt{3}}}{2}\right)}}$&$1358$\\ \hline \end{longtable}"," ",0,"ln(-x+x^2+(x^4-2*x^3+x^2-3)^(1/2))","A"
266,1,26,23,0.473000," ","int((-1+2*x)/(x^4-2*x^3+x^2+4)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(-x^{2}+\sqrt{x^{4}-2 x^{3}+x^{2}+4}+x \right)$&$26$\\ default&$-\frac{2 \left(-\frac{\sqrt{1+8 i}}{2}-\frac{\sqrt{1-8 i}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{1-8 i}}{2}-\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+8 i}}{2}\right)}{\left(\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right)^{2} \sqrt{\frac{\sqrt{1+8 i}\, \left(x -\frac{1}{2}+\frac{\sqrt{1-8 i}}{2}\right)}{\left(-\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right)}}\, \sqrt{\frac{\sqrt{1+8 i}\, \left(x -\frac{1}{2}-\frac{\sqrt{1-8 i}}{2}\right)}{\left(\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{1-8 i}}{2}-\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+8 i}}{2}\right)}{\left(\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right)}}, \sqrt{-\frac{\left(\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right)^{2}}{\left(\frac{\sqrt{1-8 i}}{2}-\frac{\sqrt{1+8 i}}{2}\right) \left(-\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right)}}\right)}{\left(\frac{\sqrt{1-8 i}}{2}-\frac{\sqrt{1+8 i}}{2}\right) \sqrt{1+8 i}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1-8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1-8 i}}{2}\right)}}+\frac{4 \left(-\frac{\sqrt{1+8 i}}{2}-\frac{\sqrt{1-8 i}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{1-8 i}}{2}-\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+8 i}}{2}\right)}{\left(\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right)^{2} \sqrt{\frac{\sqrt{1+8 i}\, \left(x -\frac{1}{2}+\frac{\sqrt{1-8 i}}{2}\right)}{\left(-\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right)}}\, \sqrt{\frac{\sqrt{1+8 i}\, \left(x -\frac{1}{2}-\frac{\sqrt{1-8 i}}{2}\right)}{\left(\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right)}}\, \left(\left(\frac{1}{2}+\frac{\sqrt{1+8 i}}{2}\right) \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{1-8 i}}{2}-\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+8 i}}{2}\right)}{\left(\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right)}}, \sqrt{-\frac{\left(\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right)^{2}}{\left(\frac{\sqrt{1-8 i}}{2}-\frac{\sqrt{1+8 i}}{2}\right) \left(-\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right)}}\right)-\sqrt{1+8 i}\, \EllipticPi \left(\sqrt{\frac{\left(\frac{\sqrt{1-8 i}}{2}-\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+8 i}}{2}\right)}{\left(\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right)}}, \frac{\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}}{\frac{\sqrt{1-8 i}}{2}-\frac{\sqrt{1+8 i}}{2}}, \sqrt{-\frac{\left(\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right)^{2}}{\left(\frac{\sqrt{1-8 i}}{2}-\frac{\sqrt{1+8 i}}{2}\right) \left(-\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right)}}\right)\right)}{\left(\frac{\sqrt{1-8 i}}{2}-\frac{\sqrt{1+8 i}}{2}\right) \sqrt{1+8 i}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1-8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1-8 i}}{2}\right)}}$&$882$\\ elliptic&$-\frac{2 \left(-\frac{\sqrt{1+8 i}}{2}-\frac{\sqrt{1-8 i}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{1-8 i}}{2}-\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+8 i}}{2}\right)}{\left(\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right)^{2} \sqrt{\frac{\sqrt{1+8 i}\, \left(x -\frac{1}{2}+\frac{\sqrt{1-8 i}}{2}\right)}{\left(-\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right)}}\, \sqrt{\frac{\sqrt{1+8 i}\, \left(x -\frac{1}{2}-\frac{\sqrt{1-8 i}}{2}\right)}{\left(\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{1-8 i}}{2}-\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+8 i}}{2}\right)}{\left(\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right)}}, \sqrt{-\frac{\left(\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right)^{2}}{\left(\frac{\sqrt{1-8 i}}{2}-\frac{\sqrt{1+8 i}}{2}\right) \left(-\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right)}}\right)}{\left(\frac{\sqrt{1-8 i}}{2}-\frac{\sqrt{1+8 i}}{2}\right) \sqrt{1+8 i}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1-8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1-8 i}}{2}\right)}}+\frac{4 \left(-\frac{\sqrt{1+8 i}}{2}-\frac{\sqrt{1-8 i}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{1-8 i}}{2}-\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+8 i}}{2}\right)}{\left(\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right)^{2} \sqrt{\frac{\sqrt{1+8 i}\, \left(x -\frac{1}{2}+\frac{\sqrt{1-8 i}}{2}\right)}{\left(-\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right)}}\, \sqrt{\frac{\sqrt{1+8 i}\, \left(x -\frac{1}{2}-\frac{\sqrt{1-8 i}}{2}\right)}{\left(\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right)}}\, \left(\left(\frac{1}{2}+\frac{\sqrt{1+8 i}}{2}\right) \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{1-8 i}}{2}-\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+8 i}}{2}\right)}{\left(\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right)}}, \sqrt{-\frac{\left(\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right)^{2}}{\left(\frac{\sqrt{1-8 i}}{2}-\frac{\sqrt{1+8 i}}{2}\right) \left(-\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right)}}\right)-\sqrt{1+8 i}\, \EllipticPi \left(\sqrt{\frac{\left(\frac{\sqrt{1-8 i}}{2}-\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+8 i}}{2}\right)}{\left(\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right)}}, \frac{\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}}{\frac{\sqrt{1-8 i}}{2}-\frac{\sqrt{1+8 i}}{2}}, \sqrt{-\frac{\left(\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right)^{2}}{\left(\frac{\sqrt{1-8 i}}{2}-\frac{\sqrt{1+8 i}}{2}\right) \left(-\frac{\sqrt{1-8 i}}{2}+\frac{\sqrt{1+8 i}}{2}\right)}}\right)\right)}{\left(\frac{\sqrt{1-8 i}}{2}-\frac{\sqrt{1+8 i}}{2}\right) \sqrt{1+8 i}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+8 i}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1-8 i}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1-8 i}}{2}\right)}}$&$882$\\ \hline \end{longtable}"," ",0,"-ln(-x^2+(x^4-2*x^3+x^2+4)^(1/2)+x)","A"
267,1,24,23,0.612000," ","int((-1+2*x)/(x^4-2*x^3+x^2+13)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(-x +x^{2}+\sqrt{x^{4}-2 x^{3}+x^{2}+13}\right)$&$24$\\ default&$-\frac{2 \left(-\frac{\sqrt{1+4 i \sqrt{13}}}{2}-\frac{\sqrt{1-4 i \sqrt{13}}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)^{2} \sqrt{\frac{\sqrt{1+4 i \sqrt{13}}\, \left(x -\frac{1}{2}+\frac{\sqrt{1-4 i \sqrt{13}}}{2}\right)}{\left(-\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}\, \sqrt{\frac{\sqrt{1+4 i \sqrt{13}}\, \left(x -\frac{1}{2}-\frac{\sqrt{1-4 i \sqrt{13}}}{2}\right)}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}, \sqrt{-\frac{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)^{2}}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(-\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}\right)}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \sqrt{1+4 i \sqrt{13}}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1-4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1-4 i \sqrt{13}}}{2}\right)}}+\frac{4 \left(-\frac{\sqrt{1+4 i \sqrt{13}}}{2}-\frac{\sqrt{1-4 i \sqrt{13}}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)^{2} \sqrt{\frac{\sqrt{1+4 i \sqrt{13}}\, \left(x -\frac{1}{2}+\frac{\sqrt{1-4 i \sqrt{13}}}{2}\right)}{\left(-\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}\, \sqrt{\frac{\sqrt{1+4 i \sqrt{13}}\, \left(x -\frac{1}{2}-\frac{\sqrt{1-4 i \sqrt{13}}}{2}\right)}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}\, \left(\left(\frac{1}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}, \sqrt{-\frac{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)^{2}}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(-\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}\right)-\sqrt{1+4 i \sqrt{13}}\, \EllipticPi \left(\sqrt{\frac{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}, \frac{\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}}{\frac{\sqrt{1-4 i \sqrt{13}}}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}}, \sqrt{-\frac{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)^{2}}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(-\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}\right)\right)}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \sqrt{1+4 i \sqrt{13}}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1-4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1-4 i \sqrt{13}}}{2}\right)}}$&$1352$\\ elliptic&$-\frac{2 \left(-\frac{\sqrt{1+4 i \sqrt{13}}}{2}-\frac{\sqrt{1-4 i \sqrt{13}}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)^{2} \sqrt{\frac{\sqrt{1+4 i \sqrt{13}}\, \left(x -\frac{1}{2}+\frac{\sqrt{1-4 i \sqrt{13}}}{2}\right)}{\left(-\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}\, \sqrt{\frac{\sqrt{1+4 i \sqrt{13}}\, \left(x -\frac{1}{2}-\frac{\sqrt{1-4 i \sqrt{13}}}{2}\right)}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}, \sqrt{-\frac{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)^{2}}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(-\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}\right)}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \sqrt{1+4 i \sqrt{13}}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1-4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1-4 i \sqrt{13}}}{2}\right)}}+\frac{4 \left(-\frac{\sqrt{1+4 i \sqrt{13}}}{2}-\frac{\sqrt{1-4 i \sqrt{13}}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)^{2} \sqrt{\frac{\sqrt{1+4 i \sqrt{13}}\, \left(x -\frac{1}{2}+\frac{\sqrt{1-4 i \sqrt{13}}}{2}\right)}{\left(-\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}\, \sqrt{\frac{\sqrt{1+4 i \sqrt{13}}\, \left(x -\frac{1}{2}-\frac{\sqrt{1-4 i \sqrt{13}}}{2}\right)}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}\, \left(\left(\frac{1}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}, \sqrt{-\frac{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)^{2}}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(-\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}\right)-\sqrt{1+4 i \sqrt{13}}\, \EllipticPi \left(\sqrt{\frac{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}, \frac{\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}}{\frac{\sqrt{1-4 i \sqrt{13}}}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}}, \sqrt{-\frac{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)^{2}}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(-\frac{\sqrt{1-4 i \sqrt{13}}}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right)}}\right)\right)}{\left(\frac{\sqrt{1-4 i \sqrt{13}}}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \sqrt{1+4 i \sqrt{13}}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1+4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{1-4 i \sqrt{13}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{1-4 i \sqrt{13}}}{2}\right)}}$&$1352$\\ \hline \end{longtable}"," ",0,"ln(-x+x^2+(x^4-2*x^3+x^2+13)^(1/2))","A"
268,1,22,21,0.064000," ","int(1/x^2/(x^4-x^3)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(3+4 x \right) \left(x^{4}-x^{3}\right)^{\frac{3}{4}}}{21 x^{4}}$&$22$\\ gosper&$\frac{4 \left(-1+x \right) \left(3+4 x \right)}{21 x \left(x^{4}-x^{3}\right)^{\frac{1}{4}}}$&$25$\\ risch&$\frac{-\frac{4}{7}-\frac{4}{21} x +\frac{16}{21} x^{2}}{x \left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}}}$&$25$\\ meijerg&$-\frac{4 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{4}} \left(1+\frac{4 x}{3}\right) \left(1-x \right)^{\frac{3}{4}}}{7 \mathrm{signum}\left(-1+x \right)^{\frac{1}{4}} x^{\frac{7}{4}}}$&$32$\\ \hline \end{longtable}"," ",0,"4/21*(3+4*x)*(x^4-x^3)^(3/4)/x^4","A"
269,1,20,21,0.102000," ","int((x^4-1)/x^8/(2*x^4-1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{\left(x^{4}+3\right) \left(2 x^{4}-1\right)^{\frac{3}{4}}}{21 x^{7}}$&$20$\\ trager&$-\frac{\left(x^{4}+3\right) \left(2 x^{4}-1\right)^{\frac{3}{4}}}{21 x^{7}}$&$20$\\ risch&$-\frac{2 x^{8}+5 x^{4}-3}{21 x^{7} \left(2 x^{4}-1\right)^{\frac{1}{4}}}$&$27$\\ meijerg&$\frac{\left(-\mathrm{signum}\left(2 x^{4}-1\right)\right)^{\frac{1}{4}} \left(1+\frac{8 x^{4}}{3}\right) \left(-2 x^{4}+1\right)^{\frac{3}{4}}}{7 \mathrm{signum}\left(2 x^{4}-1\right)^{\frac{1}{4}} x^{7}}-\frac{\left(-\mathrm{signum}\left(2 x^{4}-1\right)\right)^{\frac{1}{4}} \left(-2 x^{4}+1\right)^{\frac{3}{4}}}{3 \mathrm{signum}\left(2 x^{4}-1\right)^{\frac{1}{4}} x^{3}}$&$81$\\ \hline \end{longtable}"," ",0,"-1/21*(x^4+3)*(2*x^4-1)^(3/4)/x^7","A"
270,1,15,23,0.103000," ","int((x^2+1)/(x^2-1)/(x^5-x^3)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{4 x}{\left(x^{5}-x^{3}\right)^{\frac{1}{4}}}$&$15$\\ risch&$-\frac{4 x}{\left(x^{3} \left(x^{2}-1\right)\right)^{\frac{1}{4}}}$&$15$\\ trager&$-\frac{4 \left(x^{5}-x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(x^{2}-1\right)}$&$24$\\ meijerg&$-\frac{4 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[\frac{1}{8}, \frac{5}{4}\right], \left[\frac{9}{8}\right], x^{2}\right) x^{\frac{1}{4}}}{\mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{4}}}-\frac{4 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[\frac{9}{8}, \frac{5}{4}\right], \left[\frac{17}{8}\right], x^{2}\right) x^{\frac{9}{4}}}{9 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{4}}}$&$66$\\ \hline \end{longtable}"," ",0,"-4*x/(x^5-x^3)^(1/4)","A"
271,1,15,23,0.113000," ","int((3*x^4+1)/(x^4-1)/(x^6-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{3 x}{\left(x^{6}-x^{2}\right)^{\frac{1}{3}}}$&$15$\\ risch&$-\frac{3 x}{\left(x^{2} \left(x^{4}-1\right)\right)^{\frac{1}{3}}}$&$15$\\ trager&$-\frac{3 \left(x^{6}-x^{2}\right)^{\frac{2}{3}}}{x \left(x^{4}-1\right)}$&$24$\\ meijerg&$-\frac{3 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{3}} \hypergeom \left(\left[\frac{1}{12}, \frac{4}{3}\right], \left[\frac{13}{12}\right], x^{4}\right) x^{\frac{1}{3}}}{\mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{3}}}-\frac{9 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{3}} \hypergeom \left(\left[\frac{13}{12}, \frac{4}{3}\right], \left[\frac{25}{12}\right], x^{4}\right) x^{\frac{13}{3}}}{13 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{3}}}$&$66$\\ \hline \end{longtable}"," ",0,"-3*x/(x^6-x^2)^(1/3)","A"
272,1,15,23,0.122000," ","int((x^4+1)/(x^4-1)/(x^6-x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{2 x}{\left(x^{6}-x^{2}\right)^{\frac{1}{4}}}$&$15$\\ risch&$-\frac{2 x}{\left(x^{2} \left(x^{4}-1\right)\right)^{\frac{1}{4}}}$&$15$\\ trager&$-\frac{2 \left(x^{6}-x^{2}\right)^{\frac{3}{4}}}{x \left(x^{4}-1\right)}$&$24$\\ meijerg&$-\frac{2 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[\frac{1}{8}, \frac{5}{4}\right], \left[\frac{9}{8}\right], x^{4}\right) \sqrt{x}}{\mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}}}-\frac{2 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[\frac{9}{8}, \frac{5}{4}\right], \left[\frac{17}{8}\right], x^{4}\right) x^{\frac{9}{2}}}{9 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}}}$&$66$\\ \hline \end{longtable}"," ",0,"-2*x/(x^6-x^2)^(1/4)","A"
273,1,20,21,0.062000," ","int(1/x^7/(x^6+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{3 \left(1-\frac{3 x^{4}}{2}\right) \left(x^{4}+1\right)^{\frac{2}{3}}}{20 x^{\frac{20}{3}}}$&$20$\\ trager&$\frac{3 \left(3 x^{4}-2\right) \left(x^{6}+x^{2}\right)^{\frac{2}{3}}}{40 x^{8}}$&$22$\\ gosper&$\frac{3 \left(x^{4}+1\right) \left(3 x^{4}-2\right)}{40 x^{6} \left(x^{6}+x^{2}\right)^{\frac{1}{3}}}$&$27$\\ risch&$\frac{\frac{3}{40} x^{4}-\frac{3}{20}+\frac{9}{40} x^{8}}{x^{6} \left(x^{2} \left(x^{4}+1\right)\right)^{\frac{1}{3}}}$&$27$\\ \hline \end{longtable}"," ",0,"-3/20*(1-3/2*x^4)*(x^4+1)^(2/3)/x^(20/3)","A"
274,1,23,22,0.080000," ","int((x^3-1)^(1/3)/x^8,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{3}-1\right)^{\frac{1}{3}} \left(3 x^{6}+x^{3}-4\right)}{28 x^{7}}$&$23$\\ gosper&$\frac{\left(-1+x \right) \left(x^{2}+x +1\right) \left(3 x^{3}+4\right) \left(x^{3}-1\right)^{\frac{1}{3}}}{28 x^{7}}$&$29$\\ risch&$\frac{3 x^{9}-2 x^{6}-5 x^{3}+4}{28 \left(x^{3}-1\right)^{\frac{2}{3}} x^{7}}$&$30$\\ meijerg&$-\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \left(-\frac{3}{4} x^{6}-\frac{1}{4} x^{3}+1\right) \left(-x^{3}+1\right)^{\frac{1}{3}}}{7 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x^{7}}$&$45$\\ \hline \end{longtable}"," ",0,"1/28*(x^3-1)^(1/3)*(3*x^6+x^3-4)/x^7","A"
275,1,16,24,0.119000," ","int((a*x^2+b)/(a*x^2-b)/(a*x^3-b*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{2 x}{\sqrt{a \,x^{3}-b x}}$&$16$\\ elliptic&$-\frac{2 x}{\sqrt{\left(x^{2}-\frac{b}{a}\right) a x}}$&$19$\\ trager&$-\frac{2 \sqrt{a \,x^{3}-b x}}{a \,x^{2}-b}$&$26$\\ default&$\frac{\sqrt{a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}-b x}}+2 b \left(-\frac{x}{b \sqrt{\left(x^{2}-\frac{b}{a}\right) a x}}-\frac{\sqrt{a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{\sqrt{2}}{2}\right)}{2 b a \sqrt{a \,x^{3}-b x}}\right)$&$231$\\ \hline \end{longtable}"," ",0,"-2*x/(a*x^3-b*x)^(1/2)","A"
276,1,844,20,0.229000," ","int((a*x^3-2*b)/(a*x^3+b)^(1/2)/(a*x^3-c*x^2+b),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{a}}{-\frac{3 \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{3 a \sqrt{a \,x^{3}+b}}+\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}-c \,\textit{\_Z}^{2}+b \right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2} c -3 b \right) \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i a \left(2 x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{a \left(x -\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{-3 \left(-a^{2} b \right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i a \left(2 x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{2 \left(-a^{2} b \right)^{\frac{1}{3}}}}\, \left(-i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a +i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a c -i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, c +\left(-a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+\underline{\hspace{1.25 ex}}\alpha  \left(-a^{2} b \right)^{\frac{2}{3}} a -\left(-a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  a c -\left(-a^{2} b \right)^{\frac{2}{3}} c +2 a^{2} b \right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}}{3}, \frac{-i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a +i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  c +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b -3 \left(-a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a -2 i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, a b -i \sqrt{3}\, a b c +3 \left(-a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  c -3 \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b +3 a b c}{2 a b c}, \sqrt{\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  \left(3 \underline{\hspace{1.25 ex}}\alpha  a -2 c \right) \sqrt{a \,x^{3}+b}}\right)}{a^{2} b c}$&$844$\\ elliptic&$-\frac{2 i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{a}}{-\frac{3 \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{3 a \sqrt{a \,x^{3}+b}}-\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}-c \,\textit{\_Z}^{2}+b \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{2} c +3 b \right) \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i a \left(2 x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{a \left(x -\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{-3 \left(-a^{2} b \right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i a \left(2 x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{2 \left(-a^{2} b \right)^{\frac{1}{3}}}}\, \left(-i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a +i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a c -i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, c +\left(-a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+\underline{\hspace{1.25 ex}}\alpha  \left(-a^{2} b \right)^{\frac{2}{3}} a -\left(-a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  a c -\left(-a^{2} b \right)^{\frac{2}{3}} c +2 a^{2} b \right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}}{3}, \frac{-i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a +i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  c +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b -3 \left(-a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a -2 i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, a b -i \sqrt{3}\, a b c +3 \left(-a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  c -3 \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b +3 a b c}{2 a b c}, \sqrt{\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  \left(3 \underline{\hspace{1.25 ex}}\alpha  a -2 c \right) \sqrt{a \,x^{3}+b}}\right)}{a^{2} b c}$&$845$\\ \hline \end{longtable}"," ",0,"-2/3*I*3^(1/2)/a*(-a^2*b)^(1/3)*(I*(x+1/2/a*(-a^2*b)^(1/3)-1/2*I*3^(1/2)/a*(-a^2*b)^(1/3))*3^(1/2)*a/(-a^2*b)^(1/3))^(1/2)*((x-1/a*(-a^2*b)^(1/3))/(-3/2/a*(-a^2*b)^(1/3)+1/2*I*3^(1/2)/a*(-a^2*b)^(1/3)))^(1/2)*(-I*(x+1/2/a*(-a^2*b)^(1/3)+1/2*I*3^(1/2)/a*(-a^2*b)^(1/3))*3^(1/2)*a/(-a^2*b)^(1/3))^(1/2)/(a*x^3+b)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2/a*(-a^2*b)^(1/3)-1/2*I*3^(1/2)/a*(-a^2*b)^(1/3))*3^(1/2)*a/(-a^2*b)^(1/3))^(1/2),(I*3^(1/2)/a*(-a^2*b)^(1/3)/(-3/2/a*(-a^2*b)^(1/3)+1/2*I*3^(1/2)/a*(-a^2*b)^(1/3)))^(1/2))+I/a^2/b/c*2^(1/2)*sum((_alpha^2*c-3*b)/_alpha/(3*_alpha*a-2*c)*(-a^2*b)^(1/3)*(1/2*I*a*(2*x+1/a*((-a^2*b)^(1/3)-I*3^(1/2)*(-a^2*b)^(1/3)))/(-a^2*b)^(1/3))^(1/2)*(a*(x-1/a*(-a^2*b)^(1/3))/(-3*(-a^2*b)^(1/3)+I*3^(1/2)*(-a^2*b)^(1/3)))^(1/2)*(-1/2*I*a*(2*x+1/a*((-a^2*b)^(1/3)+I*3^(1/2)*(-a^2*b)^(1/3)))/(-a^2*b)^(1/3))^(1/2)/(a*x^3+b)^(1/2)*(-I*(-a^2*b)^(1/3)*3^(1/2)*_alpha^2*a^2+I*(-a^2*b)^(2/3)*3^(1/2)*_alpha*a+I*(-a^2*b)^(1/3)*3^(1/2)*_alpha*a*c-I*(-a^2*b)^(2/3)*3^(1/2)*c+(-a^2*b)^(1/3)*_alpha^2*a^2+_alpha*(-a^2*b)^(2/3)*a-(-a^2*b)^(1/3)*_alpha*a*c-(-a^2*b)^(2/3)*c+2*a^2*b)*EllipticPi(1/3*3^(1/2)*(I*(x+1/2/a*(-a^2*b)^(1/3)-1/2*I*3^(1/2)/a*(-a^2*b)^(1/3))*3^(1/2)*a/(-a^2*b)^(1/3))^(1/2),1/2/a*(-I*(-a^2*b)^(2/3)*3^(1/2)*_alpha^2*a+I*(-a^2*b)^(2/3)*3^(1/2)*_alpha*c+I*3^(1/2)*_alpha*a^2*b-3*(-a^2*b)^(2/3)*_alpha^2*a-2*I*(-a^2*b)^(1/3)*3^(1/2)*a*b-I*3^(1/2)*a*b*c+3*(-a^2*b)^(2/3)*_alpha*c-3*_alpha*a^2*b+3*a*b*c)/b/c,(I*3^(1/2)/a*(-a^2*b)^(1/3)/(-3/2/a*(-a^2*b)^(1/3)+1/2*I*3^(1/2)/a*(-a^2*b)^(1/3)))^(1/2)),_alpha=RootOf(_Z^3*a-_Z^2*c+b))","C"
277,1,841,20,0.204000," ","int((a*x^3-2*b)/(a*x^3+b)^(1/2)/(a*x^3+c*x^2+b),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\frac{2 i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{a}}{-\frac{3 \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{3 a \sqrt{a \,x^{3}+b}}+\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}+c \,\textit{\_Z}^{2}+b \right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2} c +3 b \right) \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i a \left(2 x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{a \left(x -\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{-3 \left(-a^{2} b \right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i a \left(2 x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{2 \left(-a^{2} b \right)^{\frac{1}{3}}}}\, \left(-i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a -i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a c +i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, c +\left(-a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+\underline{\hspace{1.25 ex}}\alpha  \left(-a^{2} b \right)^{\frac{2}{3}} a +\left(-a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  a c +\left(-a^{2} b \right)^{\frac{2}{3}} c +2 a^{2} b \right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}}{3}, -\frac{-i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a -i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  c +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b -3 \left(-a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a -2 i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, a b +i \sqrt{3}\, a b c -3 \left(-a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  c -3 \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b -3 a b c}{2 a b c}, \sqrt{\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  \left(3 \underline{\hspace{1.25 ex}}\alpha  a +2 c \right) \sqrt{a \,x^{3}+b}}\right)}{a^{2} b c}$&$841$\\ default&$-\frac{2 i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{a}}{-\frac{3 \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{3 a \sqrt{a \,x^{3}+b}}-\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}+c \,\textit{\_Z}^{2}+b \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{2} c -3 b \right) \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i a \left(2 x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{a \left(x -\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{-3 \left(-a^{2} b \right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i a \left(2 x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{2 \left(-a^{2} b \right)^{\frac{1}{3}}}}\, \left(-i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a -i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a c +i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, c +\left(-a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+\underline{\hspace{1.25 ex}}\alpha  \left(-a^{2} b \right)^{\frac{2}{3}} a +\left(-a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  a c +\left(-a^{2} b \right)^{\frac{2}{3}} c +2 a^{2} b \right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}}{3}, -\frac{-i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a -i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  c +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b -3 \left(-a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a -2 i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, a b +i \sqrt{3}\, a b c -3 \left(-a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  c -3 \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b -3 a b c}{2 a b c}, \sqrt{\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  \left(3 \underline{\hspace{1.25 ex}}\alpha  a +2 c \right) \sqrt{a \,x^{3}+b}}\right)}{a^{2} b c}$&$842$\\ \hline \end{longtable}"," ",0,"-2/3*I*3^(1/2)/a*(-a^2*b)^(1/3)*(I*(x+1/2/a*(-a^2*b)^(1/3)-1/2*I*3^(1/2)/a*(-a^2*b)^(1/3))*3^(1/2)*a/(-a^2*b)^(1/3))^(1/2)*((x-1/a*(-a^2*b)^(1/3))/(-3/2/a*(-a^2*b)^(1/3)+1/2*I*3^(1/2)/a*(-a^2*b)^(1/3)))^(1/2)*(-I*(x+1/2/a*(-a^2*b)^(1/3)+1/2*I*3^(1/2)/a*(-a^2*b)^(1/3))*3^(1/2)*a/(-a^2*b)^(1/3))^(1/2)/(a*x^3+b)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2/a*(-a^2*b)^(1/3)-1/2*I*3^(1/2)/a*(-a^2*b)^(1/3))*3^(1/2)*a/(-a^2*b)^(1/3))^(1/2),(I*3^(1/2)/a*(-a^2*b)^(1/3)/(-3/2/a*(-a^2*b)^(1/3)+1/2*I*3^(1/2)/a*(-a^2*b)^(1/3)))^(1/2))+I/a^2/b/c*2^(1/2)*sum((_alpha^2*c+3*b)/_alpha/(3*_alpha*a+2*c)*(-a^2*b)^(1/3)*(1/2*I*a*(2*x+1/a*((-a^2*b)^(1/3)-I*3^(1/2)*(-a^2*b)^(1/3)))/(-a^2*b)^(1/3))^(1/2)*(a*(x-1/a*(-a^2*b)^(1/3))/(-3*(-a^2*b)^(1/3)+I*3^(1/2)*(-a^2*b)^(1/3)))^(1/2)*(-1/2*I*a*(2*x+1/a*((-a^2*b)^(1/3)+I*3^(1/2)*(-a^2*b)^(1/3)))/(-a^2*b)^(1/3))^(1/2)/(a*x^3+b)^(1/2)*(-I*(-a^2*b)^(1/3)*3^(1/2)*_alpha^2*a^2+I*(-a^2*b)^(2/3)*3^(1/2)*_alpha*a-I*(-a^2*b)^(1/3)*3^(1/2)*_alpha*a*c+I*(-a^2*b)^(2/3)*3^(1/2)*c+(-a^2*b)^(1/3)*_alpha^2*a^2+_alpha*(-a^2*b)^(2/3)*a+(-a^2*b)^(1/3)*_alpha*a*c+(-a^2*b)^(2/3)*c+2*a^2*b)*EllipticPi(1/3*3^(1/2)*(I*(x+1/2/a*(-a^2*b)^(1/3)-1/2*I*3^(1/2)/a*(-a^2*b)^(1/3))*3^(1/2)*a/(-a^2*b)^(1/3))^(1/2),-1/2/a*(-I*(-a^2*b)^(2/3)*3^(1/2)*_alpha^2*a-I*(-a^2*b)^(2/3)*3^(1/2)*_alpha*c+I*3^(1/2)*_alpha*a^2*b-3*(-a^2*b)^(2/3)*_alpha^2*a-2*I*(-a^2*b)^(1/3)*3^(1/2)*a*b+I*3^(1/2)*a*b*c-3*(-a^2*b)^(2/3)*_alpha*c-3*_alpha*a^2*b-3*a*b*c)/b/c,(I*3^(1/2)/a*(-a^2*b)^(1/3)/(-3/2/a*(-a^2*b)^(1/3)+1/2*I*3^(1/2)/a*(-a^2*b)^(1/3)))^(1/2)),_alpha=RootOf(_Z^3*a+_Z^2*c+b))","C"
278,1,69,19,0.744000," ","int((x^2+1)/(x^2-1)/(x^2+2)/(x^4-3)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x^{6}-3 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{2}-4 \sqrt{x^{4}-3}\, x -2 \RootOf \left(\textit{\_Z}^{2}+2\right)}{\left(x^{2}+2\right) \left(-1+x \right)^{2} \left(1+x \right)^{2}}\right)}{12}$&$69$\\ elliptic&$-\frac{2 \sqrt{1+\frac{\sqrt{3}\, x^{2}}{3}}\, \sqrt{1-\frac{\sqrt{3}\, x^{2}}{3}}\, \EllipticPi \left(\sqrt{-\frac{\sqrt{3}}{3}}\, x , -\sqrt{3}, \frac{3^{\frac{3}{4}}}{3 \sqrt{-\frac{\sqrt{3}}{3}}}\right)}{3 \sqrt{-\frac{\sqrt{3}}{3}}\, \sqrt{x^{4}-3}}-\frac{\EllipticPi \left(\sqrt{-\frac{\sqrt{3}}{3}}\, x , \frac{\sqrt{3}}{2}, i\right) \sqrt{3+\sqrt{3}\, x^{2}}\, \sqrt{3-\sqrt{3}\, x^{2}}}{18 \sqrt{-\frac{\sqrt{3}}{3}}\, \sqrt{x^{4}-3}}$&$125$\\ default&$-\frac{2 \sqrt{1+\frac{\sqrt{3}\, x^{2}}{3}}\, \sqrt{1-\frac{\sqrt{3}\, x^{2}}{3}}\, \EllipticPi \left(\sqrt{-\frac{\sqrt{3}}{3}}\, x , -\sqrt{3}, \frac{3^{\frac{3}{4}}}{3 \sqrt{-\frac{\sqrt{3}}{3}}}\right)}{3 \sqrt{-\frac{\sqrt{3}}{3}}\, \sqrt{x^{4}-3}}+\frac{\sqrt{1+\frac{\sqrt{3}\, x^{2}}{3}}\, \sqrt{1-\frac{\sqrt{3}\, x^{2}}{3}}\, \EllipticPi \left(\sqrt{-\frac{\sqrt{3}}{3}}\, x , \frac{\sqrt{3}}{2}, \frac{3^{\frac{3}{4}}}{3 \sqrt{-\frac{\sqrt{3}}{3}}}\right)}{6 \sqrt{-\frac{\sqrt{3}}{3}}\, \sqrt{x^{4}-3}}$&$136$\\ \hline \end{longtable}"," ",0,"1/12*RootOf(_Z^2+2)*ln(-(RootOf(_Z^2+2)*x^6-3*RootOf(_Z^2+2)*x^2-4*(x^4-3)^(1/2)*x-2*RootOf(_Z^2+2))/(x^2+2)/(-1+x)^2/(1+x)^2)","C"
279,1,20,22,0.081000," ","int((x^4-4)*(x^4+1)^(3/4)/x^12,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{\left(27 x^{4}-28\right) \left(x^{4}+1\right)^{\frac{7}{4}}}{77 x^{11}}$&$20$\\ trager&$-\frac{\left(27 x^{8}-x^{4}-28\right) \left(x^{4}+1\right)^{\frac{3}{4}}}{77 x^{11}}$&$25$\\ risch&$-\frac{27 x^{12}+26 x^{8}-29 x^{4}-28}{77 x^{11} \left(x^{4}+1\right)^{\frac{1}{4}}}$&$30$\\ meijerg&$\frac{4 \left(-\frac{4}{7} x^{8}+\frac{3}{7} x^{4}+1\right) \left(x^{4}+1\right)^{\frac{3}{4}}}{11 x^{11}}-\frac{\left(x^{4}+1\right)^{\frac{7}{4}}}{7 x^{7}}$&$38$\\ \hline \end{longtable}"," ",0,"-1/77*(27*x^4-28)*(x^4+1)^(7/4)/x^11","A"
280,1,38,22,0.535000," ","int((x^4-1)^(1/2)*(x^4+1)/x^2/(x^4+x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\sqrt{x^{4}-1}\, \sqrt{2}}{x}-\sqrt{2}\, \arctan \left(\frac{\sqrt{x^{4}-1}}{x}\right)\right) \sqrt{2}}{2}$&$38$\\ trager&$\frac{\sqrt{x^{4}-1}}{x}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-2 x \sqrt{x^{4}-1}-\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{4}+x^{2}-1}\right)}{2}$&$73$\\ default&$\frac{\sqrt{x^{4}-1}}{x}+\frac{i \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticF \left(i x , i\right)}{\sqrt{x^{4}-1}}-\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+\textit{\_Z}^{2}-1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}-1\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{x^{4}-1}}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{2 i \left(\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticPi \left(i x , -\underline{\hspace{1.25 ex}}\alpha^{2}-1, i\right)}{\sqrt{x^{4}-1}}\right)\right)}{4}$&$146$\\ risch&$\frac{\sqrt{x^{4}-1}}{x}+\frac{i \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticF \left(i x , i\right)}{\sqrt{x^{4}-1}}-\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+\textit{\_Z}^{2}-1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}-1\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{x^{4}-1}}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{2 i \left(\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticPi \left(i x , -\underline{\hspace{1.25 ex}}\alpha^{2}-1, i\right)}{\sqrt{x^{4}-1}}\right)\right)}{4}$&$146$\\ \hline \end{longtable}"," ",0,"1/2*((x^4-1)^(1/2)*2^(1/2)/x-2^(1/2)*arctan((x^4-1)^(1/2)/x))*2^(1/2)","A"
281,1,23,22,0.080000," ","int((x^4-1)*(x^4+x^2+1)/x^4/(x^4+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{\sqrt{x^{4}+1}\, \left(x^{4}+3 x^{2}+1\right)}{3 x^{3}}$&$23$\\ trager&$\frac{\sqrt{x^{4}+1}\, \left(x^{4}+3 x^{2}+1\right)}{3 x^{3}}$&$23$\\ risch&$\frac{x^{8}+3 x^{6}+2 x^{4}+3 x^{2}+1}{3 x^{3} \sqrt{x^{4}+1}}$&$33$\\ default&$\frac{\sqrt{x^{4}+1}\, x}{3}+\frac{\sqrt{x^{4}+1}}{3 x^{3}}+\frac{\sqrt{x^{4}+1}}{x}$&$35$\\ elliptic&$\frac{\left(\frac{\sqrt{2}\, \left(x^{4}+1\right)^{\frac{3}{2}}}{3 x^{3}}+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{x}\right) \sqrt{2}}{2}$&$36$\\ meijerg&$\frac{\hypergeom \left(\left[\frac{1}{2}, \frac{5}{4}\right], \left[\frac{9}{4}\right], -x^{4}\right) x^{5}}{5}+\frac{\hypergeom \left(\left[\frac{1}{2}, \frac{3}{4}\right], \left[\frac{7}{4}\right], -x^{4}\right) x^{3}}{3}+\frac{\hypergeom \left(\left[-\frac{3}{4}, \frac{1}{2}\right], \left[\frac{1}{4}\right], -x^{4}\right)}{3 x^{3}}+\frac{\hypergeom \left(\left[-\frac{1}{4}, \frac{1}{2}\right], \left[\frac{3}{4}\right], -x^{4}\right)}{x}$&$65$\\ \hline \end{longtable}"," ",0,"1/3*(x^4+1)^(1/2)*(x^4+3*x^2+1)/x^3","A"
282,1,23,22,0.106000," ","int((x^3-4)*(x^4+x^3-1)/x^6/(x^3-1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{4 \left(x^{3}-1\right)^{\frac{1}{4}} \left(5 x^{4}+x^{3}-1\right)}{5 x^{5}}$&$23$\\ gosper&$-\frac{4 \left(-1+x \right) \left(x^{2}+x +1\right) \left(5 x^{4}+x^{3}-1\right)}{5 x^{5} \left(x^{3}-1\right)^{\frac{3}{4}}}$&$32$\\ risch&$-\frac{4 \left(5 x^{7}+x^{6}-5 x^{4}-2 x^{3}+1\right)}{5 \left(x^{3}-1\right)^{\frac{3}{4}} x^{5}}$&$33$\\ meijerg&$\frac{\left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[\frac{2}{3}, \frac{3}{4}\right], \left[\frac{5}{3}\right], x^{3}\right) x^{2}}{2 \mathrm{signum}\left(x^{3}-1\right)^{\frac{3}{4}}}+\frac{\left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[\frac{1}{3}, \frac{3}{4}\right], \left[\frac{4}{3}\right], x^{3}\right) x}{\mathrm{signum}\left(x^{3}-1\right)^{\frac{3}{4}}}+\frac{5 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{2}{3}, \frac{3}{4}\right], \left[\frac{1}{3}\right], x^{3}\right)}{2 \mathrm{signum}\left(x^{3}-1\right)^{\frac{3}{4}} x^{2}}-\frac{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{5}{3}, \frac{3}{4}\right], \left[-\frac{2}{3}\right], x^{3}\right)}{5 \mathrm{signum}\left(x^{3}-1\right)^{\frac{3}{4}} x^{5}}+\frac{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{1}{3}, \frac{3}{4}\right], \left[\frac{2}{3}\right], x^{3}\right)}{\mathrm{signum}\left(x^{3}-1\right)^{\frac{3}{4}} x}$&$159$\\ \hline \end{longtable}"," ",0,"-4/5*(x^3-1)^(1/4)*(5*x^4+x^3-1)/x^5","A"
283,0,0,20,0.038000," ","int((3*x^4+1)/(x^4-a*x-1)/(x^5-x)^(1/2),x)","\[\int \frac{3 x^{4}+1}{\left(x^{4}-a x -1\right) \sqrt{x^{5}-x}}\, dx\]"," ",0,"int((3*x^4+1)/(x^4-a*x-1)/(x^5-x)^(1/2),x)","F"
284,0,0,20,0.035000," ","int((3*x^4+1)/(a*x^4-a-x)/(x^5-x)^(1/2),x)","\[\int \frac{3 x^{4}+1}{\left(a \,x^{4}-a -x \right) \sqrt{x^{5}-x}}\, dx\]"," ",0,"int((3*x^4+1)/(a*x^4-a-x)/(x^5-x)^(1/2),x)","F"
285,1,23,22,0.141000," ","int((x^5+4)*(x^5+x^4-1)/x^6/(x^5-1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{5}-1\right)^{\frac{1}{4}} \left(x^{5}+5 x^{4}-1\right)}{5 x^{5}}$&$23$\\ risch&$\frac{-\frac{8}{5} x^{5}+\frac{4}{5}+4 x^{9}-4 x^{4}+\frac{4}{5} x^{10}}{\left(x^{5}-1\right)^{\frac{3}{4}} x^{5}}$&$33$\\ gosper&$\frac{4 \left(x^{4}+x^{3}+x^{2}+x +1\right) \left(-1+x \right) \left(x^{5}+5 x^{4}-1\right)}{5 x^{5} \left(x^{5}-1\right)^{\frac{3}{4}}}$&$38$\\ meijerg&$\frac{\left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[\frac{3}{4}, 1\right], \left[2\right], x^{5}\right) x^{5}}{5 \mathrm{signum}\left(x^{5}-1\right)^{\frac{3}{4}}}+\frac{\left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[\frac{3}{4}, \frac{4}{5}\right], \left[\frac{9}{5}\right], x^{5}\right) x^{4}}{4 \mathrm{signum}\left(x^{5}-1\right)^{\frac{3}{4}}}+\frac{3 \left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{3}{4}} \left(\left(-3 \ln \left(2\right)+\frac{\pi}{2}+5 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{3}{4}\right)+\frac{3 \hypergeom \left(\left[1, 1, \frac{7}{4}\right], \left[2, 2\right], x^{5}\right) \Gamma \left(\frac{3}{4}\right) x^{5}}{4}\right)}{5 \Gamma \left(\frac{3}{4}\right) \mathrm{signum}\left(x^{5}-1\right)^{\frac{3}{4}}}+\frac{4 \left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{3}{4}} \left(\frac{\Gamma \left(\frac{3}{4}\right)}{x^{5}}-\frac{3 \left(\frac{1}{3}-3 \ln \left(2\right)+\frac{\pi}{2}+5 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{3}{4}\right)}{4}-\frac{21 \hypergeom \left(\left[1, 1, \frac{11}{4}\right], \left[2, 3\right], x^{5}\right) \Gamma \left(\frac{3}{4}\right) x^{5}}{32}\right)}{5 \Gamma \left(\frac{3}{4}\right) \mathrm{signum}\left(x^{5}-1\right)^{\frac{3}{4}}}-\frac{4 \left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{1}{5}, \frac{3}{4}\right], \left[\frac{4}{5}\right], x^{5}\right)}{\mathrm{signum}\left(x^{5}-1\right)^{\frac{3}{4}} x}$&$230$\\ \hline \end{longtable}"," ",0,"4/5*(x^5-1)^(1/4)*(x^5+5*x^4-1)/x^5","A"
286,1,23,22,0.122000," ","int((x^5-4)*(x^5+x^4+1)/x^6/(x^5+1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{5}+1\right)^{\frac{1}{4}} \left(x^{5}+5 x^{4}+1\right)}{5 x^{5}}$&$23$\\ risch&$\frac{\frac{8}{5} x^{5}+\frac{4}{5}+4 x^{9}+4 x^{4}+\frac{4}{5} x^{10}}{\left(x^{5}+1\right)^{\frac{3}{4}} x^{5}}$&$33$\\ gosper&$\frac{4 \left(x^{5}+5 x^{4}+1\right) \left(1+x \right) \left(x^{4}-x^{3}+x^{2}-x +1\right)}{5 \left(x^{5}+1\right)^{\frac{3}{4}} x^{5}}$&$42$\\ meijerg&$\frac{\hypergeom \left(\left[\frac{3}{4}, 1\right], \left[2\right], -x^{5}\right) x^{5}}{5}+\frac{\hypergeom \left(\left[\frac{3}{4}, \frac{4}{5}\right], \left[\frac{9}{5}\right], -x^{5}\right) x^{4}}{4}-\frac{3 \left(\left(-3 \ln \left(2\right)+\frac{\pi}{2}+5 \ln \left(x \right)\right) \Gamma \left(\frac{3}{4}\right)-\frac{3 \hypergeom \left(\left[1, 1, \frac{7}{4}\right], \left[2, 2\right], -x^{5}\right) \Gamma \left(\frac{3}{4}\right) x^{5}}{4}\right)}{5 \Gamma \left(\frac{3}{4}\right)}-\frac{4 \left(-\frac{\Gamma \left(\frac{3}{4}\right)}{x^{5}}-\frac{3 \left(\frac{1}{3}-3 \ln \left(2\right)+\frac{\pi}{2}+5 \ln \left(x \right)\right) \Gamma \left(\frac{3}{4}\right)}{4}+\frac{21 \hypergeom \left(\left[1, 1, \frac{11}{4}\right], \left[2, 3\right], -x^{5}\right) \Gamma \left(\frac{3}{4}\right) x^{5}}{32}\right)}{5 \Gamma \left(\frac{3}{4}\right)}+\frac{4 \hypergeom \left(\left[-\frac{1}{5}, \frac{3}{4}\right], \left[\frac{4}{5}\right], -x^{5}\right)}{x}$&$143$\\ \hline \end{longtable}"," ",0,"4/5*(x^5+1)^(1/4)*(x^5+5*x^4+1)/x^5","A"
287,1,23,22,0.094000," ","int((x^6-1)^(1/2)/x^16,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}-1}\, \left(2 x^{12}+x^{6}-3\right)}{45 x^{15}}$&$23$\\ risch&$\frac{2 x^{18}-x^{12}-4 x^{6}+3}{45 x^{15} \sqrt{x^{6}-1}}$&$30$\\ gosper&$\frac{\left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right) \left(2 x^{6}+3\right) \sqrt{x^{6}-1}}{45 x^{15}}$&$40$\\ meijerg&$-\frac{\sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(-\frac{2}{3} x^{12}-\frac{1}{3} x^{6}+1\right) \sqrt{-x^{6}+1}}{15 \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, x^{15}}$&$45$\\ \hline \end{longtable}"," ",0,"1/45*(x^6-1)^(1/2)*(2*x^12+x^6-3)/x^15","A"
288,1,51,24,0.287000," ","int((2*x^4-2*x^2-1)/(2*x^4+1)/(x^6+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-2 \sqrt{x^{6}+1}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right)}{2 x^{4}+1}\right)}{2}$&$51$\\ \hline \end{longtable}"," ",0,"-1/2*RootOf(_Z^2+1)*ln(-(2*RootOf(_Z^2+1)*x^2-2*(x^6+1)^(1/2)*x-RootOf(_Z^2+1))/(2*x^4+1))","C"
289,0,0,20,0.033000," ","int((4*x^5+1)/(x^5-a*x-1)/(x^6-x)^(1/2),x)","\[\int \frac{4 x^{5}+1}{\left(x^{5}-a x -1\right) \sqrt{x^{6}-x}}\, dx\]"," ",0,"int((4*x^5+1)/(x^5-a*x-1)/(x^6-x)^(1/2),x)","F"
290,0,0,20,0.034000," ","int((4*x^5+1)/(a*x^5-a-x)/(x^6-x)^(1/2),x)","\[\int \frac{4 x^{5}+1}{\left(a \,x^{5}-a -x \right) \sqrt{x^{6}-x}}\, dx\]"," ",0,"int((4*x^5+1)/(a*x^5-a-x)/(x^6-x)^(1/2),x)","F"
291,1,23,22,0.118000," ","int((x^6+2)*(x^6-x^4-1)/x^6/(x^6-1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{6}-1\right)^{\frac{1}{4}} \left(x^{6}-5 x^{4}-1\right)}{5 x^{5}}$&$23$\\ risch&$\frac{\frac{2}{5} x^{12}-\frac{4}{5} x^{6}+\frac{2}{5}-2 x^{10}+2 x^{4}}{x^{5} \left(x^{6}-1\right)^{\frac{3}{4}}}$&$33$\\ gosper&$\frac{2 \left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right) \left(x^{6}-5 x^{4}-1\right)}{5 x^{5} \left(x^{6}-1\right)^{\frac{3}{4}}}$&$43$\\ meijerg&$\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[\frac{3}{4}, \frac{7}{6}\right], \left[\frac{13}{6}\right], x^{6}\right) x^{7}}{7 \mathrm{signum}\left(x^{6}-1\right)^{\frac{3}{4}}}-\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[\frac{3}{4}, \frac{5}{6}\right], \left[\frac{11}{6}\right], x^{6}\right) x^{5}}{5 \mathrm{signum}\left(x^{6}-1\right)^{\frac{3}{4}}}+\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[\frac{1}{6}, \frac{3}{4}\right], \left[\frac{7}{6}\right], x^{6}\right) x}{\mathrm{signum}\left(x^{6}-1\right)^{\frac{3}{4}}}+\frac{2 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{5}{6}, \frac{3}{4}\right], \left[\frac{1}{6}\right], x^{6}\right)}{5 \mathrm{signum}\left(x^{6}-1\right)^{\frac{3}{4}} x^{5}}+\frac{2 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{1}{6}, \frac{3}{4}\right], \left[\frac{5}{6}\right], x^{6}\right)}{\mathrm{signum}\left(x^{6}-1\right)^{\frac{3}{4}} x}$&$159$\\ \hline \end{longtable}"," ",0,"2/5*(x^6-1)^(1/4)*(x^6-5*x^4-1)/x^5","A"
292,1,23,22,0.103000," ","int((x^6-2)*(x^6-x^4+1)/x^6/(x^6+1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{6}+1\right)^{\frac{1}{4}} \left(x^{6}-5 x^{4}+1\right)}{5 x^{5}}$&$23$\\ risch&$\frac{\frac{2}{5} x^{12}+\frac{4}{5} x^{6}+\frac{2}{5}-2 x^{10}-2 x^{4}}{\left(x^{6}+1\right)^{\frac{3}{4}} x^{5}}$&$33$\\ gosper&$\frac{2 \left(x^{4}-x^{2}+1\right) \left(x^{2}+1\right) \left(x^{6}-5 x^{4}+1\right)}{5 x^{5} \left(x^{6}+1\right)^{\frac{3}{4}}}$&$38$\\ meijerg&$\frac{\hypergeom \left(\left[\frac{3}{4}, \frac{7}{6}\right], \left[\frac{13}{6}\right], -x^{6}\right) x^{7}}{7}-\frac{\hypergeom \left(\left[\frac{3}{4}, \frac{5}{6}\right], \left[\frac{11}{6}\right], -x^{6}\right) x^{5}}{5}-\hypergeom \left(\left[\frac{1}{6}, \frac{3}{4}\right], \left[\frac{7}{6}\right], -x^{6}\right) x +\frac{2 \hypergeom \left(\left[-\frac{5}{6}, \frac{3}{4}\right], \left[\frac{1}{6}\right], -x^{6}\right)}{5 x^{5}}-\frac{2 \hypergeom \left(\left[-\frac{1}{6}, \frac{3}{4}\right], \left[\frac{5}{6}\right], -x^{6}\right)}{x}$&$80$\\ \hline \end{longtable}"," ",0,"2/5*(x^6+1)^(1/4)*(x^6-5*x^4+1)/x^5","A"
293,1,71,22,0.884000," ","int((x^6-1)^(1/2)*(2*x^6+1)/x^2/(x^6+x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}-1}}{x}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \sqrt{x^{6}-1}\, x +\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{6}+x^{2}-1}\right)}{2}$&$71$\\ risch&$\frac{\sqrt{x^{6}-1}}{x}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \sqrt{x^{6}-1}\, x +\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{6}+x^{2}-1}\right)}{2}$&$72$\\ \hline \end{longtable}"," ",0,"(x^6-1)^(1/2)/x-1/2*RootOf(_Z^2+1)*ln((-RootOf(_Z^2+1)*x^6+RootOf(_Z^2+1)*x^2+2*(x^6-1)^(1/2)*x+RootOf(_Z^2+1))/(x^6+x^2-1))","C"
294,1,23,22,0.117000," ","int((-2*x^7-x^5+x^3-1)^(2/3)*(2*x^7+x^5-x^3+1)*(8*x^7+2*x^5-3)/x^9,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{3 \left(-2 x^{7}-x^{5}+x^{3}-1\right)^{\frac{8}{3}}}{8 x^{8}}$&$23$\\ trager&$\frac{3 \left(4 x^{14}+4 x^{12}-3 x^{10}-2 x^{8}+4 x^{7}+x^{6}+2 x^{5}-2 x^{3}+1\right) \left(-2 x^{7}-x^{5}+x^{3}-1\right)^{\frac{2}{3}}}{8 x^{8}}$&$63$\\ risch&$-\frac{3 \left(8 x^{21}+12 x^{19}-6 x^{17}-11 x^{15}+12 x^{14}+3 x^{13}+12 x^{12}+3 x^{11}-9 x^{10}-x^{9}-6 x^{8}+6 x^{7}+3 x^{6}+3 x^{5}-3 x^{3}+1\right)}{8 x^{8} \left(-2 x^{7}-x^{5}+x^{3}-1\right)^{\frac{1}{3}}}$&$100$\\ \hline \end{longtable}"," ",0,"3/8*(-2*x^7-x^5+x^3-1)^(8/3)/x^8","A"
295,0,0,20,0.020000," ","int(x^4*(4*x^5+9)/(x^6+x)^(1/2)/(x^9-a*x^5-a),x)","\[\int \frac{x^{4} \left(4 x^{5}+9\right)}{\sqrt{x^{6}+x}\, \left(x^{9}-a \,x^{5}-a \right)}\, dx\]"," ",0,"int(x^4*(4*x^5+9)/(x^6+x)^(1/2)/(x^9-a*x^5-a),x)","F"
296,0,0,20,0.015000," ","int(x^4*(5*x^4+9)/(x^5+x)^(1/2)/(a*x^9-x^4-1),x)","\[\int \frac{x^{4} \left(5 x^{4}+9\right)}{\sqrt{x^{5}+x}\, \left(a \,x^{9}-x^{4}-1\right)}\, dx\]"," ",0,"int(x^4*(5*x^4+9)/(x^5+x)^(1/2)/(a*x^9-x^4-1),x)","F"
297,0,0,20,0.019000," ","int(x^4*(4*x^5+9)/(x^6+x)^(1/2)/(a*x^9-x^5-1),x)","\[\int \frac{x^{4} \left(4 x^{5}+9\right)}{\sqrt{x^{6}+x}\, \left(a \,x^{9}-x^{5}-1\right)}\, dx\]"," ",0,"int(x^4*(4*x^5+9)/(x^6+x)^(1/2)/(a*x^9-x^5-1),x)","F"
298,1,19,23,0.132000," ","int(x^5*(-2*x^3+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{\left(3 x^{3}+1\right) \left(-2 x^{3}+1\right)^{\frac{3}{2}}}{45}$&$19$\\ trager&$\left(\frac{2}{15} x^{6}-\frac{1}{45} x^{3}-\frac{1}{45}\right) \sqrt{-2 x^{3}+1}$&$23$\\ risch&$-\frac{\left(6 x^{6}-x^{3}-1\right) \left(2 x^{3}-1\right)}{45 \sqrt{-2 x^{3}+1}}$&$31$\\ meijerg&$-\frac{-\frac{8 \sqrt{\pi}}{15}+\frac{4 \sqrt{\pi}\, \left(-2 x^{3}+1\right)^{\frac{3}{2}} \left(6 x^{3}+2\right)}{15}}{24 \sqrt{\pi}}$&$33$\\ default&$\frac{2 x^{6} \sqrt{-2 x^{3}+1}}{15}-\frac{x^{3} \sqrt{-2 x^{3}+1}}{45}-\frac{\sqrt{-2 x^{3}+1}}{45}$&$41$\\ elliptic&$\frac{2 x^{6} \sqrt{-2 x^{3}+1}}{15}-\frac{x^{3} \sqrt{-2 x^{3}+1}}{45}-\frac{\sqrt{-2 x^{3}+1}}{45}$&$41$\\ \hline \end{longtable}"," ",0,"-1/45*(3*x^3+1)*(-2*x^3+1)^(3/2)","A"
299,1,69,21,0.536000," ","int((2+x)/(-1+x)/(x^3+3*x-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) x^{3}+3 \RootOf \left(\textit{\_Z}^{2}-3\right) x^{2}+3 \RootOf \left(\textit{\_Z}^{2}-3\right) x -6 \sqrt{x^{3}+3 x -1}\, x -\RootOf \left(\textit{\_Z}^{2}-3\right)}{\left(-1+x \right)^{3}}\right)}{3}$&$69$\\ default&$\frac{2 i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right) \sqrt{-\frac{i \left(x +\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}+\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}\right) \sqrt{3}}{\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}}}\, \sqrt{\frac{x -\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}}{-\frac{3 \left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}+\frac{3}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}}}\, \sqrt{\frac{i \left(x +\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}\right) \sqrt{3}}{\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}+\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}\right) \sqrt{3}}{\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{-\frac{3 \left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}+\frac{3}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}}}\right)}{3 \sqrt{x^{3}+3 x -1}}+\frac{2 i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right) \sqrt{-\frac{i \left(x +\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}+\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}\right) \sqrt{3}}{\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}}}\, \sqrt{\frac{x -\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}}{-\frac{3 \left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}+\frac{3}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}}}\, \sqrt{\frac{i \left(x +\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}\right) \sqrt{3}}{\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}+\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}\right) \sqrt{3}}{\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}}}}{3}, -\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{-\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}+\frac{1}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}-1}, \sqrt{-\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{-\frac{3 \left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}+\frac{3}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}}}\right)}{\sqrt{x^{3}+3 x -1}\, \left(-\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}+\frac{1}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}-1\right)}$&$1075$\\ elliptic&$\frac{2 i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right) \sqrt{-\frac{i \left(x +\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}+\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}\right) \sqrt{3}}{\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}}}\, \sqrt{\frac{x -\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}}{-\frac{3 \left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}+\frac{3}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}}}\, \sqrt{\frac{i \left(x +\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}\right) \sqrt{3}}{\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}+\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}\right) \sqrt{3}}{\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{-\frac{3 \left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}+\frac{3}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}}}\right)}{3 \sqrt{x^{3}+3 x -1}}+\frac{2 i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right) \sqrt{-\frac{i \left(x +\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}+\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}\right) \sqrt{3}}{\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}}}\, \sqrt{\frac{x -\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}}{-\frac{3 \left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}+\frac{3}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}}}\, \sqrt{\frac{i \left(x +\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}\right) \sqrt{3}}{\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}+\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}\right) \sqrt{3}}{\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}}}}{3}, -\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{-\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}+\frac{1}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}-1}, \sqrt{-\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{-\frac{3 \left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}+\frac{3}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}}}\right)}{\sqrt{x^{3}+3 x -1}\, \left(-\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{4}+\frac{1}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(4+4 \sqrt{5}\right)^{\frac{1}{3}}}\right)}{2}-1\right)}$&$1075$\\ \hline \end{longtable}"," ",0,"1/3*RootOf(_Z^2-3)*ln(-(RootOf(_Z^2-3)*x^3+3*RootOf(_Z^2-3)*x^2+3*RootOf(_Z^2-3)*x-6*(x^3+3*x-1)^(1/2)*x-RootOf(_Z^2-3))/(-1+x)^3)","C"
300,1,88,25,0.423000," ","int((-1+2*x)/(1+x)/(x^3-x^2-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-5 \RootOf \left(\textit{\_Z}^{2}+1\right) x +4 \sqrt{x^{3}-x^{2}-x}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right)+2 \sqrt{x^{3}-x^{2}-x}}{\left(1+x \right)^{3}}\right)$&$88$\\ default&$\frac{4 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \sqrt{-5 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{5}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}}-\frac{6 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \sqrt{-5 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{5}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)}$&$250$\\ elliptic&$\frac{4 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \sqrt{-5 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{5}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}}-\frac{6 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \sqrt{-5 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{5}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)}$&$250$\\ \hline \end{longtable}"," ",0,"-RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)*x^3-5*RootOf(_Z^2+1)*x^2-5*RootOf(_Z^2+1)*x+4*(x^3-x^2-x)^(1/2)*x-RootOf(_Z^2+1)+2*(x^3-x^2-x)^(1/2))/(1+x)^3)","C"
301,1,24,23,0.063000," ","int(x^5/(a*x^3+b)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{2 \left(a \,x^{3}-2 b \right) \sqrt{a \,x^{3}+b}}{9 a^{2}}$&$24$\\ trager&$\frac{2 \left(a \,x^{3}-2 b \right) \sqrt{a \,x^{3}+b}}{9 a^{2}}$&$24$\\ risch&$\frac{2 \left(a \,x^{3}-2 b \right) \sqrt{a \,x^{3}+b}}{9 a^{2}}$&$24$\\ default&$\frac{2 x^{3} \sqrt{a \,x^{3}+b}}{9 a}-\frac{4 b \sqrt{a \,x^{3}+b}}{9 a^{2}}$&$34$\\ elliptic&$\frac{2 x^{3} \sqrt{a \,x^{3}+b}}{9 a}-\frac{4 b \sqrt{a \,x^{3}+b}}{9 a^{2}}$&$34$\\ \hline \end{longtable}"," ",0,"2/9*(a*x^3-2*b)*(a*x^3+b)^(1/2)/a^2","A"
302,1,24,23,0.077000," ","int(1/x^4/(x^4-x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(4 x^{2}+3\right) \left(x^{4}-x^{2}\right)^{\frac{3}{4}}}{21 x^{5}}$&$24$\\ risch&$\frac{-\frac{2}{21} x^{2}-\frac{2}{7}+\frac{8}{21} x^{4}}{x^{3} \left(x^{2} \left(x^{2}-1\right)\right)^{\frac{1}{4}}}$&$29$\\ gosper&$\frac{2 \left(-1+x \right) \left(1+x \right) \left(4 x^{2}+3\right)}{21 x^{3} \left(x^{4}-x^{2}\right)^{\frac{1}{4}}}$&$30$\\ meijerg&$-\frac{2 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{4}} \left(1+\frac{4 x^{2}}{3}\right) \left(-x^{2}+1\right)^{\frac{3}{4}}}{7 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{4}} x^{\frac{7}{2}}}$&$40$\\ \hline \end{longtable}"," ",0,"2/21*(4*x^2+3)*(x^4-x^2)^(3/4)/x^5","A"
303,1,29,19,0.054000," ","int(1/x/(a*x^4+b)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\ln \left(\frac{2 b +2 \sqrt{b}\, \sqrt{a \,x^{4}+b}}{x^{2}}\right)}{2 \sqrt{b}}$&$29$\\ elliptic&$-\frac{\ln \left(\frac{2 b +2 \sqrt{b}\, \sqrt{a \,x^{4}+b}}{x^{2}}\right)}{2 \sqrt{b}}$&$29$\\ \hline \end{longtable}"," ",0,"-1/2/b^(1/2)*ln((2*b+2*b^(1/2)*(a*x^4+b)^(1/2))/x^2)","A"
304,1,24,23,0.079000," ","int(1/x^7/(x^6-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(3 x^{4}+2\right) \left(x^{6}-x^{2}\right)^{\frac{2}{3}}}{40 x^{8}}$&$24$\\ risch&$\frac{-\frac{3}{40} x^{4}-\frac{3}{20}+\frac{9}{40} x^{8}}{x^{6} \left(x^{2} \left(x^{4}-1\right)\right)^{\frac{1}{3}}}$&$29$\\ gosper&$\frac{3 \left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right) \left(3 x^{4}+2\right)}{40 x^{6} \left(x^{6}-x^{2}\right)^{\frac{1}{3}}}$&$35$\\ meijerg&$-\frac{3 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{3}} \left(1+\frac{3 x^{4}}{2}\right) \left(-x^{4}+1\right)^{\frac{2}{3}}}{20 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{3}} x^{\frac{20}{3}}}$&$40$\\ \hline \end{longtable}"," ",0,"3/40*(3*x^4+2)*(x^6-x^2)^(2/3)/x^8","A"
305,1,21,20,0.366000," ","int((x^3-1)^(1/2)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 \sqrt{x^{3}-1}}{3}-\frac{2 \arctan \left(\sqrt{x^{3}-1}\right)}{3}$&$21$\\ elliptic&$\frac{2 \sqrt{x^{3}-1}}{3}-\frac{2 \arctan \left(\sqrt{x^{3}-1}\right)}{3}$&$21$\\ trager&$\frac{2 \sqrt{x^{3}-1}}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \sqrt{x^{3}-1}-2 \RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{3}}\right)}{3}$&$53$\\ meijerg&$-\frac{\sqrt{\mathrm{signum}\left(x^{3}-1\right)}\, \left(-2 \left(2-2 \ln \left(2\right)+3 \ln \left(x \right)+i \pi \right) \sqrt{\pi}+4 \sqrt{\pi}-4 \sqrt{\pi}\, \sqrt{-x^{3}+1}+4 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{3}+1}}{2}\right)\right)}{6 \sqrt{-\mathrm{signum}\left(x^{3}-1\right)}\, \sqrt{\pi}}$&$82$\\ \hline \end{longtable}"," ",0,"2/3*(x^3-1)^(1/2)-2/3*arctan((x^3-1)^(1/2))","A"
306,1,25,24,0.067000," ","int((x^3-1)*(x^3+1)^(1/3)/x^8,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(5 x^{6}+3 x^{3}-2\right) \left(x^{3}+1\right)^{\frac{1}{3}}}{14 x^{7}}$&$25$\\ risch&$-\frac{5 x^{9}+8 x^{6}+x^{3}-2}{14 \left(x^{3}+1\right)^{\frac{2}{3}} x^{7}}$&$28$\\ gosper&$-\frac{\left(x^{2}-x +1\right) \left(1+x \right) \left(5 x^{3}-2\right) \left(x^{3}+1\right)^{\frac{1}{3}}}{14 x^{7}}$&$31$\\ meijerg&$\frac{\left(-\frac{3}{4} x^{6}+\frac{1}{4} x^{3}+1\right) \left(x^{3}+1\right)^{\frac{1}{3}}}{7 x^{7}}-\frac{\left(x^{3}+1\right)^{\frac{4}{3}}}{4 x^{4}}$&$38$\\ \hline \end{longtable}"," ",0,"-1/14*(5*x^6+3*x^3-2)/x^7*(x^3+1)^(1/3)","A"
307,1,21,20,0.225000," ","int((x^3+1)^(1/2)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 \sqrt{x^{3}+1}}{3}-\frac{2 \arctanh \left(\sqrt{x^{3}+1}\right)}{3}$&$21$\\ elliptic&$\frac{2 \sqrt{x^{3}+1}}{3}-\frac{2 \arctanh \left(\sqrt{x^{3}+1}\right)}{3}$&$21$\\ trager&$\frac{2 \sqrt{x^{3}+1}}{3}+\frac{\ln \left(-\frac{-x^{3}+2 \sqrt{x^{3}+1}-2}{x^{3}}\right)}{3}$&$35$\\ meijerg&$-\frac{-2 \left(2-2 \ln \left(2\right)+3 \ln \left(x \right)\right) \sqrt{\pi}+4 \sqrt{\pi}-4 \sqrt{\pi}\, \sqrt{x^{3}+1}+4 \ln \left(\frac{1}{2}+\frac{\sqrt{x^{3}+1}}{2}\right) \sqrt{\pi}}{6 \sqrt{\pi}}$&$56$\\ \hline \end{longtable}"," ",0,"2/3*(x^3+1)^(1/2)-2/3*arctanh((x^3+1)^(1/2))","A"
308,1,25,24,0.077000," ","int((x^3-1)^(1/3)*(x^3+1)/x^8,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{3}-1\right)^{\frac{1}{3}} \left(5 x^{6}-3 x^{3}-2\right)}{14 x^{7}}$&$25$\\ risch&$\frac{5 x^{9}-8 x^{6}+x^{3}+2}{14 \left(x^{3}-1\right)^{\frac{2}{3}} x^{7}}$&$28$\\ gosper&$\frac{\left(x^{3}-1\right)^{\frac{1}{3}} \left(5 x^{3}+2\right) \left(-1+x \right) \left(x^{2}+x +1\right)}{14 x^{7}}$&$29$\\ meijerg&$-\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \left(-x^{3}+1\right)^{\frac{4}{3}}}{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x^{4}}-\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \left(-\frac{3}{4} x^{6}-\frac{1}{4} x^{3}+1\right) \left(-x^{3}+1\right)^{\frac{1}{3}}}{7 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x^{7}}$&$78$\\ \hline \end{longtable}"," ",0,"1/14*(x^3-1)^(1/3)*(5*x^6-3*x^3-2)/x^7","A"
309,1,25,24,0.081000," ","int((x^3-1)^(2/3)*(x^3+2)/x^9,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{3}-1\right)^{\frac{2}{3}} \left(7 x^{6}-2 x^{3}-5\right)}{20 x^{8}}$&$25$\\ gosper&$\frac{\left(-1+x \right) \left(x^{2}+x +1\right) \left(7 x^{3}+5\right) \left(x^{3}-1\right)^{\frac{2}{3}}}{20 x^{8}}$&$29$\\ risch&$\frac{7 x^{9}-9 x^{6}-3 x^{3}+5}{20 x^{8} \left(x^{3}-1\right)^{\frac{1}{3}}}$&$30$\\ meijerg&$-\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}} \left(-x^{3}+1\right)^{\frac{5}{3}}}{5 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} x^{5}}-\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}} \left(-\frac{3}{5} x^{6}-\frac{2}{5} x^{3}+1\right) \left(-x^{3}+1\right)^{\frac{2}{3}}}{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} x^{8}}$&$78$\\ \hline \end{longtable}"," ",0,"1/20*(x^3-1)^(2/3)*(7*x^6-2*x^3-5)/x^8","A"
310,1,23,24,0.062000," ","int((x^3+1)^(2/3)*(x^3+2)/x^9,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(x^{6}+6 x^{3}+5\right) \left(x^{3}+1\right)^{\frac{2}{3}}}{20 x^{8}}$&$23$\\ risch&$-\frac{x^{9}+7 x^{6}+11 x^{3}+5}{20 x^{8} \left(x^{3}+1\right)^{\frac{1}{3}}}$&$28$\\ gosper&$-\frac{\left(1+x \right) \left(x^{2}-x +1\right) \left(x^{3}+5\right) \left(x^{3}+1\right)^{\frac{2}{3}}}{20 x^{8}}$&$29$\\ meijerg&$-\frac{\left(x^{3}+1\right)^{\frac{5}{3}}}{5 x^{5}}-\frac{\left(-\frac{3}{5} x^{6}+\frac{2}{5} x^{3}+1\right) \left(x^{3}+1\right)^{\frac{2}{3}}}{4 x^{8}}$&$38$\\ \hline \end{longtable}"," ",0,"-1/20*(x^6+6*x^3+5)/x^8*(x^3+1)^(2/3)","A"
311,1,25,24,0.058000," ","int(1/x^6/(x^3+x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{3 \left(x^{3}+x \right)^{\frac{2}{3}} \left(9 x^{4}-6 x^{2}+5\right)}{80 x^{6}}$&$25$\\ meijerg&$-\frac{3 \left(\frac{9}{5} x^{4}-\frac{6}{5} x^{2}+1\right) \left(x^{2}+1\right)^{\frac{2}{3}}}{16 x^{\frac{16}{3}}}$&$25$\\ gosper&$-\frac{3 \left(x^{2}+1\right) \left(9 x^{4}-6 x^{2}+5\right)}{80 x^{5} \left(x^{3}+x \right)^{\frac{1}{3}}}$&$30$\\ risch&$-\frac{3 \left(9 x^{6}+3 x^{4}-x^{2}+5\right)}{80 x^{5} \left(\left(x^{2}+1\right) x \right)^{\frac{1}{3}}}$&$32$\\ \hline \end{longtable}"," ",0,"-3/80*(x^3+x)^(2/3)*(9*x^4-6*x^2+5)/x^6","A"
312,1,17,26,0.105000," ","int((2*x^2-x-2)/(-1+x)/x/(x^3-x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{-4+8 x}{\left(\left(-1+x \right) x^{2}\right)^{\frac{1}{4}}}$&$17$\\ gosper&$\frac{-4+8 x}{\left(x^{3}-x^{2}\right)^{\frac{1}{4}}}$&$19$\\ trager&$\frac{4 \left(-1+2 x \right) \left(x^{3}-x^{2}\right)^{\frac{3}{4}}}{\left(-1+x \right) x^{2}}$&$27$\\ meijerg&$-\frac{4 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{1}{2}, \frac{5}{4}\right], \left[\frac{1}{2}\right], x\right)}{\mathrm{signum}\left(-1+x \right)^{\frac{1}{4}} \sqrt{x}}-\frac{4 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{4}} \hypergeom \left(\left[\frac{5}{4}, \frac{3}{2}\right], \left[\frac{5}{2}\right], x\right) x^{\frac{3}{2}}}{3 \mathrm{signum}\left(-1+x \right)^{\frac{1}{4}}}+\frac{2 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{4}} \hypergeom \left(\left[\frac{1}{2}, \frac{5}{4}\right], \left[\frac{3}{2}\right], x\right) \sqrt{x}}{\mathrm{signum}\left(-1+x \right)^{\frac{1}{4}}}$&$80$\\ \hline \end{longtable}"," ",0,"4*(-1+2*x)/((-1+x)*x^2)^(1/4)","A"
313,1,86,26,0.372000," ","int((2+x)/(-1+x)/(x^3-x^2-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \sqrt{x^{3}-x^{2}-x}\, x +5 \RootOf \left(\textit{\_Z}^{2}+1\right) x -4 \sqrt{x^{3}-x^{2}-x}+\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(-1+x \right)^{3}}\right)$&$86$\\ default&$\frac{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \sqrt{-5 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{5}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}}+\frac{6 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \sqrt{-5 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{5}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{-\frac{1}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(-\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}$&$250$\\ elliptic&$\frac{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \sqrt{-5 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{5}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}}+\frac{6 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \sqrt{-5 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{5}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{-\frac{1}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(-\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}$&$250$\\ \hline \end{longtable}"," ",0,"-RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)*x^3-5*RootOf(_Z^2+1)*x^2+2*(x^3-x^2-x)^(1/2)*x+5*RootOf(_Z^2+1)*x-4*(x^3-x^2-x)^(1/2)+RootOf(_Z^2+1))/(-1+x)^3)","C"
314,1,25,24,0.086000," ","int((x^2+3)*(x^3+x^2+1)/x^6/(x^3+x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{4 \left(x^{3}+x \right)^{\frac{3}{4}} \left(7 x^{3}+3 x^{2}+3\right)}{21 x^{6}}$&$25$\\ gosper&$-\frac{4 \left(x^{2}+1\right) \left(7 x^{3}+3 x^{2}+3\right)}{21 x^{5} \left(x^{3}+x \right)^{\frac{1}{4}}}$&$30$\\ risch&$-\frac{4 \left(7 x^{5}+3 x^{4}+7 x^{3}+6 x^{2}+3\right)}{21 x^{5} \left(\left(x^{2}+1\right) x \right)^{\frac{1}{4}}}$&$37$\\ meijerg&$-\frac{4 \hypergeom \left(\left[-\frac{21}{8}, \frac{1}{4}\right], \left[-\frac{13}{8}\right], -x^{2}\right)}{7 x^{\frac{21}{4}}}-\frac{4 \hypergeom \left(\left[-\frac{9}{8}, \frac{1}{4}\right], \left[-\frac{1}{8}\right], -x^{2}\right)}{3 x^{\frac{9}{4}}}-\frac{16 \hypergeom \left(\left[-\frac{13}{8}, \frac{1}{4}\right], \left[-\frac{5}{8}\right], -x^{2}\right)}{13 x^{\frac{13}{4}}}-\frac{4 \hypergeom \left(\left[-\frac{1}{8}, \frac{1}{4}\right], \left[\frac{7}{8}\right], -x^{2}\right)}{x^{\frac{1}{4}}}-\frac{4 \hypergeom \left(\left[-\frac{5}{8}, \frac{1}{4}\right], \left[\frac{3}{8}\right], -x^{2}\right)}{5 x^{\frac{5}{4}}}$&$82$\\ \hline \end{longtable}"," ",0,"-4/21*(x^3+x)^(3/4)*(7*x^3+3*x^2+3)/x^6","A"
315,1,28,24,0.092000," ","int((x^3-1)^(1/3)*(2*x^3-1)/x^11,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(3 x^{9}+x^{6}-6 x^{3}+2\right) \left(x^{3}-1\right)^{\frac{1}{3}}}{20 x^{10}}$&$28$\\ gosper&$\frac{\left(-1+x \right) \left(x^{2}+x +1\right) \left(3 x^{6}+4 x^{3}-2\right) \left(x^{3}-1\right)^{\frac{1}{3}}}{20 x^{10}}$&$34$\\ risch&$\frac{3 x^{12}-2 x^{9}-7 x^{6}+8 x^{3}-2}{20 \left(x^{3}-1\right)^{\frac{2}{3}} x^{10}}$&$35$\\ meijerg&$-\frac{2 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \left(-\frac{3}{4} x^{6}-\frac{1}{4} x^{3}+1\right) \left(-x^{3}+1\right)^{\frac{1}{3}}}{7 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x^{7}}+\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \left(-\frac{9}{14} x^{9}-\frac{3}{14} x^{6}-\frac{1}{7} x^{3}+1\right) \left(-x^{3}+1\right)^{\frac{1}{3}}}{10 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x^{10}}$&$95$\\ \hline \end{longtable}"," ",0,"1/20*(3*x^9+x^6-6*x^3+2)/x^10*(x^3-1)^(1/3)","A"
316,1,25,24,0.077000," ","int((x^3-1)^(1/3)*(2*x^3-1)/x^8,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{3}-1\right)^{\frac{1}{3}} \left(11 x^{6}-15 x^{3}+4\right)}{28 x^{7}}$&$25$\\ gosper&$\frac{\left(-1+x \right) \left(x^{2}+x +1\right) \left(11 x^{3}-4\right) \left(x^{3}-1\right)^{\frac{1}{3}}}{28 x^{7}}$&$29$\\ risch&$\frac{11 x^{9}-26 x^{6}+19 x^{3}-4}{28 \left(x^{3}-1\right)^{\frac{2}{3}} x^{7}}$&$30$\\ meijerg&$-\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \left(-x^{3}+1\right)^{\frac{4}{3}}}{2 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x^{4}}+\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \left(-\frac{3}{4} x^{6}-\frac{1}{4} x^{3}+1\right) \left(-x^{3}+1\right)^{\frac{1}{3}}}{7 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x^{7}}$&$78$\\ \hline \end{longtable}"," ",0,"1/28*(x^3-1)^(1/3)*(11*x^6-15*x^3+4)/x^7","A"
317,1,25,24,0.067000," ","int((x^2+3)*(2*x^3-x^2-1)/x^6/(x^3+x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{4 \left(x^{3}+x \right)^{\frac{3}{4}} \left(14 x^{3}-3 x^{2}-3\right)}{21 x^{6}}$&$25$\\ gosper&$-\frac{4 \left(14 x^{3}-3 x^{2}-3\right) \left(x^{2}+1\right)}{21 x^{5} \left(x^{3}+x \right)^{\frac{1}{4}}}$&$30$\\ risch&$-\frac{4 \left(14 x^{5}-3 x^{4}+14 x^{3}-6 x^{2}-3\right)}{21 x^{5} \left(\left(x^{2}+1\right) x \right)^{\frac{1}{4}}}$&$37$\\ meijerg&$\frac{4 \hypergeom \left(\left[-\frac{21}{8}, \frac{1}{4}\right], \left[-\frac{13}{8}\right], -x^{2}\right)}{7 x^{\frac{21}{4}}}-\frac{8 \hypergeom \left(\left[-\frac{9}{8}, \frac{1}{4}\right], \left[-\frac{1}{8}\right], -x^{2}\right)}{3 x^{\frac{9}{4}}}+\frac{16 \hypergeom \left(\left[-\frac{13}{8}, \frac{1}{4}\right], \left[-\frac{5}{8}\right], -x^{2}\right)}{13 x^{\frac{13}{4}}}-\frac{8 \hypergeom \left(\left[-\frac{1}{8}, \frac{1}{4}\right], \left[\frac{7}{8}\right], -x^{2}\right)}{x^{\frac{1}{4}}}+\frac{4 \hypergeom \left(\left[-\frac{5}{8}, \frac{1}{4}\right], \left[\frac{3}{8}\right], -x^{2}\right)}{5 x^{\frac{5}{4}}}$&$82$\\ \hline \end{longtable}"," ",0,"-4/21*(x^3+x)^(3/4)*(14*x^3-3*x^2-3)/x^6","A"
318,1,786,26,0.216000," ","int((a*x^3+2*b)/(a*x^3-b)^(1/2)/(a*x^3+x^2-b),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{a}}{-\frac{3 \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}}}\, \sqrt{\frac{i \left(x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(a^{2} b \right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{3 a \sqrt{a \,x^{3}-b}}-\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}+\textit{\_Z}^{2}-b \right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2}-3 b \right) \left(a^{2} b \right)^{\frac{1}{3}} \sqrt{-\frac{i a \left(2 x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}+i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{2 \left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{a \left(x -\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{-3 \left(a^{2} b \right)^{\frac{1}{3}}-i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{2}\, \sqrt{\frac{i a \left(2 x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}-i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \left(-i \left(a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+i \left(a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a -i \left(a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a -\left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+i \left(a^{2} b \right)^{\frac{2}{3}} \sqrt{3}-\underline{\hspace{1.25 ex}}\alpha  \left(a^{2} b \right)^{\frac{2}{3}} a -\left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  a +2 a^{2} b -\left(a^{2} b \right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(a^{2} b \right)^{\frac{1}{3}}}}}{3}, \frac{i \left(a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b +i \left(a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  -3 \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a -2 i \left(a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, a b +i \sqrt{3}\, a b +3 \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b -3 \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +3 a b}{2 a b}, \sqrt{-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  \left(3 \underline{\hspace{1.25 ex}}\alpha  a +2\right) \sqrt{a \,x^{3}-b}}\right)}{a^{2} b}$&$786$\\ elliptic&$\frac{2 i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{a}}{-\frac{3 \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}}}\, \sqrt{\frac{i \left(x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(a^{2} b \right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{3 a \sqrt{a \,x^{3}-b}}-\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}+\textit{\_Z}^{2}-b \right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2}-3 b \right) \left(a^{2} b \right)^{\frac{1}{3}} \sqrt{-\frac{i a \left(2 x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}+i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{2 \left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{a \left(x -\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{-3 \left(a^{2} b \right)^{\frac{1}{3}}-i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{2}\, \sqrt{\frac{i a \left(2 x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}-i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \left(-i \left(a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+i \left(a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a -i \left(a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a -\left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+i \left(a^{2} b \right)^{\frac{2}{3}} \sqrt{3}-\underline{\hspace{1.25 ex}}\alpha  \left(a^{2} b \right)^{\frac{2}{3}} a -\left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  a +2 a^{2} b -\left(a^{2} b \right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(a^{2} b \right)^{\frac{1}{3}}}}}{3}, \frac{i \left(a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b +i \left(a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  -3 \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a -2 i \left(a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, a b +i \sqrt{3}\, a b +3 \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b -3 \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +3 a b}{2 a b}, \sqrt{-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  \left(3 \underline{\hspace{1.25 ex}}\alpha  a +2\right) \sqrt{a \,x^{3}-b}}\right)}{a^{2} b}$&$786$\\ \hline \end{longtable}"," ",0,"2/3*I*3^(1/2)/a*(a^2*b)^(1/3)*(-I*(x+1/2/a*(a^2*b)^(1/3)+1/2*I*3^(1/2)/a*(a^2*b)^(1/3))*3^(1/2)*a/(a^2*b)^(1/3))^(1/2)*((x-1/a*(a^2*b)^(1/3))/(-3/2/a*(a^2*b)^(1/3)-1/2*I*3^(1/2)/a*(a^2*b)^(1/3)))^(1/2)*(I*(x+1/2/a*(a^2*b)^(1/3)-1/2*I*3^(1/2)/a*(a^2*b)^(1/3))*3^(1/2)*a/(a^2*b)^(1/3))^(1/2)/(a*x^3-b)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2/a*(a^2*b)^(1/3)+1/2*I*3^(1/2)/a*(a^2*b)^(1/3))*3^(1/2)*a/(a^2*b)^(1/3))^(1/2),(-I*3^(1/2)/a*(a^2*b)^(1/3)/(-3/2/a*(a^2*b)^(1/3)-1/2*I*3^(1/2)/a*(a^2*b)^(1/3)))^(1/2))-I/a^2/b*2^(1/2)*sum((_alpha^2-3*b)/_alpha/(3*_alpha*a+2)*(a^2*b)^(1/3)*(-1/2*I*a*(2*x+1/a*((a^2*b)^(1/3)+I*3^(1/2)*(a^2*b)^(1/3)))/(a^2*b)^(1/3))^(1/2)*(a*(x-1/a*(a^2*b)^(1/3))/(-3*(a^2*b)^(1/3)-I*3^(1/2)*(a^2*b)^(1/3)))^(1/2)*(1/2*I*a*(2*x+1/a*((a^2*b)^(1/3)-I*3^(1/2)*(a^2*b)^(1/3)))/(a^2*b)^(1/3))^(1/2)/(a*x^3-b)^(1/2)*(-I*(a^2*b)^(1/3)*3^(1/2)*_alpha^2*a^2+I*(a^2*b)^(2/3)*3^(1/2)*_alpha*a-I*(a^2*b)^(1/3)*3^(1/2)*_alpha*a-(a^2*b)^(1/3)*_alpha^2*a^2+I*(a^2*b)^(2/3)*3^(1/2)-_alpha*(a^2*b)^(2/3)*a-(a^2*b)^(1/3)*_alpha*a+2*a^2*b-(a^2*b)^(2/3))*EllipticPi(1/3*3^(1/2)*(-I*(x+1/2/a*(a^2*b)^(1/3)+1/2*I*3^(1/2)/a*(a^2*b)^(1/3))*3^(1/2)*a/(a^2*b)^(1/3))^(1/2),1/2/a*(I*(a^2*b)^(2/3)*3^(1/2)*_alpha^2*a+I*3^(1/2)*_alpha*a^2*b+I*(a^2*b)^(2/3)*3^(1/2)*_alpha-3*(a^2*b)^(2/3)*_alpha^2*a-2*I*(a^2*b)^(1/3)*3^(1/2)*a*b+I*3^(1/2)*a*b+3*_alpha*a^2*b-3*(a^2*b)^(2/3)*_alpha+3*a*b)/b,(-I*3^(1/2)/a*(a^2*b)^(1/3)/(-3/2/a*(a^2*b)^(1/3)-1/2*I*3^(1/2)/a*(a^2*b)^(1/3)))^(1/2)),_alpha=RootOf(_Z^3*a+_Z^2-b))","C"
319,1,25,24,0.100000," ","int((x^4-4)*(x^4-1)^(3/4)/x^12,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(5 x^{8}+23 x^{4}-28\right) \left(x^{4}-1\right)^{\frac{3}{4}}}{77 x^{11}}$&$25$\\ risch&$-\frac{5 x^{12}+18 x^{8}-51 x^{4}+28}{77 x^{11} \left(x^{4}-1\right)^{\frac{1}{4}}}$&$30$\\ gosper&$-\frac{\left(x^{2}+1\right) \left(1+x \right) \left(-1+x \right) \left(5 x^{4}+28\right) \left(x^{4}-1\right)^{\frac{3}{4}}}{77 x^{11}}$&$31$\\ meijerg&$\frac{4 \mathrm{signum}\left(x^{4}-1\right)^{\frac{3}{4}} \left(-\frac{4}{7} x^{8}-\frac{3}{7} x^{4}+1\right) \left(-x^{4}+1\right)^{\frac{3}{4}}}{11 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{3}{4}} x^{11}}-\frac{\mathrm{signum}\left(x^{4}-1\right)^{\frac{3}{4}} \left(-x^{4}+1\right)^{\frac{7}{4}}}{7 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{3}{4}} x^{7}}$&$78$\\ \hline \end{longtable}"," ",0,"-1/77*(5*x^8+23*x^4-28)/x^11*(x^4-1)^(3/4)","A"
320,1,21,20,0.182000," ","int((x^4+1)^(1/2)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{x^{4}+1}}{2}-\frac{\arctanh \left(\frac{1}{\sqrt{x^{4}+1}}\right)}{2}$&$21$\\ elliptic&$\frac{\sqrt{x^{4}+1}}{2}-\frac{\arctanh \left(\frac{1}{\sqrt{x^{4}+1}}\right)}{2}$&$21$\\ trager&$\frac{\sqrt{x^{4}+1}}{2}+\frac{\ln \left(\frac{-1+\sqrt{x^{4}+1}}{x^{2}}\right)}{2}$&$27$\\ meijerg&$-\frac{-2 \left(2-2 \ln \left(2\right)+4 \ln \left(x \right)\right) \sqrt{\pi}+4 \sqrt{\pi}-4 \sqrt{\pi}\, \sqrt{x^{4}+1}+4 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{x^{4}+1}}{2}\right)}{8 \sqrt{\pi}}$&$56$\\ \hline \end{longtable}"," ",0,"1/2*(x^4+1)^(1/2)-1/2*arctanh(1/(x^4+1)^(1/2))","A"
321,1,25,24,0.087000," ","int((x^4-x)^(1/4)/x^8,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{4}-x \right)^{\frac{1}{4}} \left(4 x^{6}+x^{3}-5\right)}{135 x^{7}}$&$25$\\ gosper&$\frac{4 \left(-1+x \right) \left(x^{2}+x +1\right) \left(4 x^{3}+5\right) \left(x^{4}-x \right)^{\frac{1}{4}}}{135 x^{7}}$&$31$\\ risch&$\frac{4 \left(x \left(x^{3}-1\right)\right)^{\frac{1}{4}} \left(4 x^{9}-3 x^{6}-6 x^{3}+5\right)}{135 x^{7} \left(x^{3}-1\right)}$&$39$\\ meijerg&$-\frac{4 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}} \left(-\frac{4}{5} x^{6}-\frac{1}{5} x^{3}+1\right) \left(-x^{3}+1\right)^{\frac{1}{4}}}{27 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}} x^{\frac{27}{4}}}$&$45$\\ \hline \end{longtable}"," ",0,"4/135*(x^4-x)^(1/4)*(4*x^6+x^3-5)/x^7","A"
322,1,25,24,0.073000," ","int((x^4+x)^(1/4)/x^8,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{4}+x \right)^{\frac{1}{4}} \left(4 x^{6}-x^{3}-5\right)}{135 x^{7}}$&$25$\\ meijerg&$-\frac{4 \left(-\frac{4}{5} x^{6}+\frac{1}{5} x^{3}+1\right) \left(x^{3}+1\right)^{\frac{1}{4}}}{27 x^{\frac{27}{4}}}$&$25$\\ gosper&$\frac{4 \left(1+x \right) \left(x^{2}-x +1\right) \left(4 x^{3}-5\right) \left(x^{4}+x \right)^{\frac{1}{4}}}{135 x^{7}}$&$31$\\ risch&$\frac{4 \left(x \left(x^{3}+1\right)\right)^{\frac{1}{4}} \left(4 x^{9}+3 x^{6}-6 x^{3}-5\right)}{135 x^{7} \left(x^{3}+1\right)}$&$39$\\ \hline \end{longtable}"," ",0,"4/135*(x^4+x)^(1/4)*(4*x^6-x^3-5)/x^7","A"
323,1,92,26,0.385000," ","int((x^2+2)/(x^2-1)/(x^4-x^2-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}-5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-2 \sqrt{x^{4}-x^{2}-1}\, x^{3}+5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+4 x \sqrt{x^{4}-x^{2}-1}+\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(-1+x \right)^{3} \left(1+x \right)^{3}}\right)}{2}$&$92$\\ default&$\frac{2 \sqrt{1-\left(-\frac{1}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{-2-2 \sqrt{5}}}{2}, \frac{i \sqrt{5}}{2}-\frac{i}{2}\right)}{\sqrt{-2-2 \sqrt{5}}\, \sqrt{x^{4}-x^{2}-1}}-\frac{3 \sqrt{1-\left(-\frac{1}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}-\frac{\sqrt{5}}{2}}\, x , \frac{1}{-\frac{1}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}}}{\sqrt{-\frac{1}{2}-\frac{\sqrt{5}}{2}}}\right)}{\sqrt{-\frac{1}{2}-\frac{\sqrt{5}}{2}}\, \sqrt{x^{4}-x^{2}-1}}$&$174$\\ elliptic&$\frac{2 \sqrt{1+\frac{x^{2}}{2}+\frac{\sqrt{5}\, x^{2}}{2}}\, \sqrt{1-\frac{\sqrt{5}\, x^{2}}{2}+\frac{x^{2}}{2}}\, \EllipticF \left(\frac{x \sqrt{-2-2 \sqrt{5}}}{2}, \frac{i \sqrt{5}}{2}-\frac{i}{2}\right)}{\sqrt{-2-2 \sqrt{5}}\, \sqrt{x^{4}-x^{2}-1}}-\frac{3 \sqrt{1+\frac{x^{2}}{2}+\frac{\sqrt{5}\, x^{2}}{2}}\, \sqrt{1-\frac{\sqrt{5}\, x^{2}}{2}+\frac{x^{2}}{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}-\frac{\sqrt{5}}{2}}\, x , \frac{1}{-\frac{1}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}}}{\sqrt{-\frac{1}{2}-\frac{\sqrt{5}}{2}}}\right)}{\sqrt{-\frac{1}{2}-\frac{\sqrt{5}}{2}}\, \sqrt{x^{4}-x^{2}-1}}$&$178$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)*x^6-5*RootOf(_Z^2+1)*x^4-2*(x^4-x^2-1)^(1/2)*x^3+5*RootOf(_Z^2+1)*x^2+4*x*(x^4-x^2-1)^(1/2)+RootOf(_Z^2+1))/(-1+x)^3/(1+x)^3)","C"
324,1,25,24,0.083000," ","int((x^3+4)*(x^4-x^3-1)/x^6/(x^3+1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{4 \left(x^{3}+1\right)^{\frac{1}{4}} \left(5 x^{4}-x^{3}-1\right)}{5 x^{5}}$&$25$\\ risch&$-\frac{4 \left(5 x^{7}-x^{6}+5 x^{4}-2 x^{3}-1\right)}{5 \left(x^{3}+1\right)^{\frac{3}{4}} x^{5}}$&$35$\\ gosper&$-\frac{4 \left(1+x \right) \left(x^{2}-x +1\right) \left(5 x^{4}-x^{3}-1\right)}{5 x^{5} \left(x^{3}+1\right)^{\frac{3}{4}}}$&$36$\\ meijerg&$\frac{\hypergeom \left(\left[\frac{2}{3}, \frac{3}{4}\right], \left[\frac{5}{3}\right], -x^{3}\right) x^{2}}{2}-\hypergeom \left(\left[\frac{1}{3}, \frac{3}{4}\right], \left[\frac{4}{3}\right], -x^{3}\right) x +\frac{5 \hypergeom \left(\left[-\frac{2}{3}, \frac{3}{4}\right], \left[\frac{1}{3}\right], -x^{3}\right)}{2 x^{2}}+\frac{4 \hypergeom \left(\left[-\frac{5}{3}, \frac{3}{4}\right], \left[-\frac{2}{3}\right], -x^{3}\right)}{5 x^{5}}-\frac{4 \hypergeom \left(\left[-\frac{1}{3}, \frac{3}{4}\right], \left[\frac{2}{3}\right], -x^{3}\right)}{x}$&$80$\\ \hline \end{longtable}"," ",0,"-4/5*(x^3+1)^(1/4)*(5*x^4-x^3-1)/x^5","A"
325,1,25,24,0.092000," ","int((x^3+4)*(x^4-x^3-1)/x^8/(x^3+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{4 \left(x^{3}+1\right)^{\frac{3}{4}} \left(7 x^{4}-3 x^{3}-3\right)}{21 x^{7}}$&$25$\\ risch&$-\frac{4 \left(7 x^{7}-3 x^{6}+7 x^{4}-6 x^{3}-3\right)}{21 x^{7} \left(x^{3}+1\right)^{\frac{1}{4}}}$&$35$\\ gosper&$-\frac{4 \left(1+x \right) \left(x^{2}-x +1\right) \left(7 x^{4}-3 x^{3}-3\right)}{21 x^{7} \left(x^{3}+1\right)^{\frac{1}{4}}}$&$36$\\ meijerg&$\frac{4 \hypergeom \left(\left[-\frac{7}{3}, \frac{1}{4}\right], \left[-\frac{4}{3}\right], -x^{3}\right)}{7 x^{7}}+\frac{2 \sqrt{2}\, \Gamma \left(\frac{3}{4}\right) \left(-\frac{\pi  \sqrt{2}}{\Gamma \left(\frac{3}{4}\right) x^{3}}-\frac{\left(3-3 \ln \left(2\right)-\frac{\pi}{2}+3 \ln \left(x \right)\right) \pi  \sqrt{2}}{4 \Gamma \left(\frac{3}{4}\right)}+\frac{5 \hypergeom \left(\left[1, 1, \frac{9}{4}\right], \left[2, 3\right], -x^{3}\right) \pi  \sqrt{2}\, x^{3}}{32 \Gamma \left(\frac{3}{4}\right)}\right)}{3 \pi}+\frac{5 \hypergeom \left(\left[-\frac{4}{3}, \frac{1}{4}\right], \left[-\frac{1}{3}\right], -x^{3}\right)}{4 x^{4}}+\frac{\sqrt{2}\, \Gamma \left(\frac{3}{4}\right) \left(\frac{\left(-3 \ln \left(2\right)-\frac{\pi}{2}+3 \ln \left(x \right)\right) \pi  \sqrt{2}}{\Gamma \left(\frac{3}{4}\right)}-\frac{\hypergeom \left(\left[1, 1, \frac{5}{4}\right], \left[2, 2\right], -x^{3}\right) \pi  \sqrt{2}\, x^{3}}{4 \Gamma \left(\frac{3}{4}\right)}\right)}{6 \pi}+\frac{\hypergeom \left(\left[-\frac{1}{3}, \frac{1}{4}\right], \left[\frac{2}{3}\right], -x^{3}\right)}{x}$&$180$\\ \hline \end{longtable}"," ",0,"-4/21*(x^3+1)^(3/4)*(7*x^4-3*x^3-3)/x^7","A"
326,1,25,24,0.116000," ","int((x^3-4)*(x^4-x^3+1)/x^8/(x^3-1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{4 \left(x^{3}-1\right)^{\frac{3}{4}} \left(7 x^{4}-3 x^{3}+3\right)}{21 x^{7}}$&$25$\\ gosper&$-\frac{4 \left(-1+x \right) \left(x^{2}+x +1\right) \left(7 x^{4}-3 x^{3}+3\right)}{21 x^{7} \left(x^{3}-1\right)^{\frac{1}{4}}}$&$34$\\ risch&$-\frac{4 \left(7 x^{7}-3 x^{6}-7 x^{4}+6 x^{3}-3\right)}{21 x^{7} \left(x^{3}-1\right)^{\frac{1}{4}}}$&$35$\\ meijerg&$\frac{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{7}{3}, \frac{1}{4}\right], \left[-\frac{4}{3}\right], x^{3}\right)}{7 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}} x^{7}}+\frac{2 \sqrt{2}\, \Gamma \left(\frac{3}{4}\right) \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}} \left(\frac{\pi  \sqrt{2}}{\Gamma \left(\frac{3}{4}\right) x^{3}}-\frac{\left(3-3 \ln \left(2\right)-\frac{\pi}{2}+3 \ln \left(x \right)+i \pi \right) \pi  \sqrt{2}}{4 \Gamma \left(\frac{3}{4}\right)}-\frac{5 \hypergeom \left(\left[1, 1, \frac{9}{4}\right], \left[2, 3\right], x^{3}\right) \pi  \sqrt{2}\, x^{3}}{32 \Gamma \left(\frac{3}{4}\right)}\right)}{3 \pi  \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}}}-\frac{5 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{4}{3}, \frac{1}{4}\right], \left[-\frac{1}{3}\right], x^{3}\right)}{4 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}} x^{4}}+\frac{\sqrt{2}\, \Gamma \left(\frac{3}{4}\right) \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}} \left(\frac{\left(-3 \ln \left(2\right)-\frac{\pi}{2}+3 \ln \left(x \right)+i \pi \right) \pi  \sqrt{2}}{\Gamma \left(\frac{3}{4}\right)}+\frac{\hypergeom \left(\left[1, 1, \frac{5}{4}\right], \left[2, 2\right], x^{3}\right) \pi  \sqrt{2}\, x^{3}}{4 \Gamma \left(\frac{3}{4}\right)}\right)}{6 \pi  \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}}}+\frac{\left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{1}{3}, \frac{1}{4}\right], \left[\frac{2}{3}\right], x^{3}\right)}{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}} x}$&$267$\\ \hline \end{longtable}"," ",0,"-4/21*(x^3-1)^(3/4)*(7*x^4-3*x^3+3)/x^7","A"
327,1,7,26,0.085000," ","int(x/(x^4+x^3)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$2 \arcsinh \left(\sqrt{x}\right)$&$7$\\ trager&$\ln \left(\frac{2 x^{2}+2 \sqrt{x^{4}+x^{3}}+x}{x}\right)$&$24$\\ default&$\frac{x \sqrt{x \left(1+x \right)}\, \ln \left(x +\frac{1}{2}+\sqrt{x^{2}+x}\right)}{\sqrt{x^{4}+x^{3}}}$&$30$\\ \hline \end{longtable}"," ",0,"2*arcsinh(x^(1/2))","A"
328,1,16,24,0.068000," ","int(1/x/(1+x)/(x^4+x^3)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{4 \left(1+4 x \right)}{3 \left(1+x \right)^{\frac{1}{4}} x^{\frac{3}{4}}}$&$16$\\ gosper&$-\frac{4 \left(1+4 x \right)}{3 \left(x^{4}+x^{3}\right)^{\frac{1}{4}}}$&$17$\\ risch&$-\frac{4 \left(1+4 x \right)}{3 \left(x^{3} \left(1+x \right)\right)^{\frac{1}{4}}}$&$17$\\ trager&$-\frac{4 \left(1+4 x \right) \left(x^{4}+x^{3}\right)^{\frac{3}{4}}}{3 x^{3} \left(1+x \right)}$&$25$\\ \hline \end{longtable}"," ",0,"-4/3*(1+4*x)/(1+x)^(1/4)/x^(3/4)","A"
329,1,25,24,0.068000," ","int((x^3+4)*(2*x^4-x^3-1)/x^6/(x^3+1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{4 \left(x^{3}+1\right)^{\frac{1}{4}} \left(10 x^{4}-x^{3}-1\right)}{5 x^{5}}$&$25$\\ risch&$-\frac{4 \left(10 x^{7}-x^{6}+10 x^{4}-2 x^{3}-1\right)}{5 \left(x^{3}+1\right)^{\frac{3}{4}} x^{5}}$&$35$\\ gosper&$-\frac{4 \left(10 x^{4}-x^{3}-1\right) \left(1+x \right) \left(x^{2}-x +1\right)}{5 \left(x^{3}+1\right)^{\frac{3}{4}} x^{5}}$&$36$\\ meijerg&$\hypergeom \left(\left[\frac{2}{3}, \frac{3}{4}\right], \left[\frac{5}{3}\right], -x^{3}\right) x^{2}-\hypergeom \left(\left[\frac{1}{3}, \frac{3}{4}\right], \left[\frac{4}{3}\right], -x^{3}\right) x +\frac{5 \hypergeom \left(\left[-\frac{2}{3}, \frac{3}{4}\right], \left[\frac{1}{3}\right], -x^{3}\right)}{2 x^{2}}+\frac{4 \hypergeom \left(\left[-\frac{5}{3}, \frac{3}{4}\right], \left[-\frac{2}{3}\right], -x^{3}\right)}{5 x^{5}}-\frac{8 \hypergeom \left(\left[-\frac{1}{3}, \frac{3}{4}\right], \left[\frac{2}{3}\right], -x^{3}\right)}{x}$&$79$\\ \hline \end{longtable}"," ",0,"-4/5*(x^3+1)^(1/4)*(10*x^4-x^3-1)/x^5","A"
330,1,25,24,0.095000," ","int((x^4-3)*(x^4-x^3+1)/x^6/(x^5+x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(3 x^{4}-7 x^{3}+3\right) \left(x^{5}+x \right)^{\frac{3}{4}}}{21 x^{6}}$&$25$\\ gosper&$\frac{4 \left(x^{4}+1\right) \left(3 x^{4}-7 x^{3}+3\right)}{21 x^{5} \left(x^{5}+x \right)^{\frac{1}{4}}}$&$30$\\ risch&$\frac{-\frac{4}{3} x^{7}-\frac{4}{3} x^{3}+\frac{4}{7} x^{8}+\frac{8}{7} x^{4}+\frac{4}{7}}{x^{5} \left(x \left(x^{4}+1\right)\right)^{\frac{1}{4}}}$&$37$\\ meijerg&$\frac{4 \hypergeom \left(\left[-\frac{21}{16}, \frac{1}{4}\right], \left[-\frac{5}{16}\right], -x^{4}\right)}{7 x^{\frac{21}{4}}}+\frac{8 \hypergeom \left(\left[-\frac{5}{16}, \frac{1}{4}\right], \left[\frac{11}{16}\right], -x^{4}\right)}{5 x^{\frac{5}{4}}}-\frac{4 \hypergeom \left(\left[-\frac{9}{16}, \frac{1}{4}\right], \left[\frac{7}{16}\right], -x^{4}\right)}{3 x^{\frac{9}{4}}}+\frac{4 \hypergeom \left(\left[\frac{1}{4}, \frac{11}{16}\right], \left[\frac{27}{16}\right], -x^{4}\right) x^{\frac{11}{4}}}{11}-\frac{4 \hypergeom \left(\left[\frac{1}{4}, \frac{7}{16}\right], \left[\frac{23}{16}\right], -x^{4}\right) x^{\frac{7}{4}}}{7}$&$82$\\ \hline \end{longtable}"," ",0,"4/21*(3*x^4-7*x^3+3)*(x^5+x)^(3/4)/x^6","A"
331,1,40,20,0.346000," ","int((x^6-1)^(1/2)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}-1}}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{3}$&$40$\\ meijerg&$-\frac{\sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(-2 \left(2-2 \ln \left(2\right)+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}+4 \sqrt{\pi}-4 \sqrt{\pi}\, \sqrt{-x^{6}+1}+4 \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right) \sqrt{\pi}\right)}{12 \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$82$\\ \hline \end{longtable}"," ",0,"1/3*(x^6-1)^(1/2)+1/3*RootOf(_Z^2+1)*ln((-RootOf(_Z^2+1)+(x^6-1)^(1/2))/x^3)","C"
332,1,27,20,0.221000," ","int((x^6-1)/x/(x^6+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}+1}}{3}+\frac{\ln \left(\frac{\sqrt{x^{6}+1}+1}{x^{3}}\right)}{3}$&$27$\\ default&$\frac{\sqrt{x^{6}+1}}{3}-\frac{\ln \left(\frac{\sqrt{x^{6}+1}-1}{\sqrt{x^{6}}}\right)}{3}$&$29$\\ meijerg&$\frac{-2 \sqrt{\pi}+2 \sqrt{\pi}\, \sqrt{x^{6}+1}}{6 \sqrt{\pi}}-\frac{\left(-2 \ln \left(2\right)+6 \ln \left(x \right)\right) \sqrt{\pi}-2 \ln \left(\frac{1}{2}+\frac{\sqrt{x^{6}+1}}{2}\right) \sqrt{\pi}}{6 \sqrt{\pi}}$&$61$\\ \hline \end{longtable}"," ",0,"1/3*(x^6+1)^(1/2)+1/3*ln(((x^6+1)^(1/2)+1)/x^3)","A"
333,1,27,20,0.214000," ","int((x^6+1)^(1/2)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}+1}}{3}-\frac{\ln \left(\frac{\sqrt{x^{6}+1}+1}{x^{3}}\right)}{3}$&$27$\\ meijerg&$-\frac{-2 \left(2-2 \ln \left(2\right)+6 \ln \left(x \right)\right) \sqrt{\pi}+4 \sqrt{\pi}-4 \sqrt{\pi}\, \sqrt{x^{6}+1}+4 \ln \left(\frac{1}{2}+\frac{\sqrt{x^{6}+1}}{2}\right) \sqrt{\pi}}{12 \sqrt{\pi}}$&$56$\\ \hline \end{longtable}"," ",0,"1/3*(x^6+1)^(1/2)-1/3*ln(((x^6+1)^(1/2)+1)/x^3)","A"
334,1,25,24,0.101000," ","int((x^6-1)^(1/3)*(x^6+1)/x^15,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{6}-1\right)^{\frac{1}{3}} \left(5 x^{12}-3 x^{6}-2\right)}{28 x^{14}}$&$25$\\ risch&$\frac{5 x^{18}-8 x^{12}+x^{6}+2}{28 \left(x^{6}-1\right)^{\frac{2}{3}} x^{14}}$&$28$\\ gosper&$\frac{\left(x^{6}-1\right)^{\frac{1}{3}} \left(5 x^{6}+2\right) \left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right)}{28 x^{14}}$&$40$\\ meijerg&$-\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}} \left(-x^{6}+1\right)^{\frac{4}{3}}}{8 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} x^{8}}-\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}} \left(-\frac{3}{4} x^{12}-\frac{1}{4} x^{6}+1\right) \left(-x^{6}+1\right)^{\frac{1}{3}}}{14 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} x^{14}}$&$78$\\ \hline \end{longtable}"," ",0,"1/28*(x^6-1)^(1/3)*(5*x^12-3*x^6-2)/x^14","A"
335,1,25,24,0.106000," ","int((x^5-x^3+1)*(2*x^5-3)/x^6/(x^6+x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(3 x^{5}-7 x^{3}+3\right) \left(x^{6}+x \right)^{\frac{3}{4}}}{21 x^{6}}$&$25$\\ risch&$\frac{\frac{4}{7} x^{10}+\frac{8}{7} x^{5}-\frac{4}{3} x^{8}-\frac{4}{3} x^{3}+\frac{4}{7}}{x^{5} \left(x \left(x^{5}+1\right)\right)^{\frac{1}{4}}}$&$37$\\ gosper&$\frac{4 \left(x^{4}-x^{3}+x^{2}-x +1\right) \left(1+x \right) \left(3 x^{5}-7 x^{3}+3\right)}{21 x^{5} \left(x^{6}+x \right)^{\frac{1}{4}}}$&$44$\\ meijerg&$\frac{4 \hypergeom \left(\left[-\frac{21}{20}, \frac{1}{4}\right], \left[-\frac{1}{20}\right], -x^{5}\right)}{7 x^{\frac{21}{4}}}+\frac{4 \hypergeom \left(\left[-\frac{1}{20}, \frac{1}{4}\right], \left[\frac{19}{20}\right], -x^{5}\right)}{x^{\frac{1}{4}}}+\frac{8 \hypergeom \left(\left[\frac{1}{4}, \frac{19}{20}\right], \left[\frac{39}{20}\right], -x^{5}\right) x^{\frac{19}{4}}}{19}-\frac{8 \hypergeom \left(\left[\frac{1}{4}, \frac{11}{20}\right], \left[\frac{31}{20}\right], -x^{5}\right) x^{\frac{11}{4}}}{11}-\frac{4 \hypergeom \left(\left[-\frac{9}{20}, \frac{1}{4}\right], \left[\frac{11}{20}\right], -x^{5}\right)}{3 x^{\frac{9}{4}}}$&$82$\\ \hline \end{longtable}"," ",0,"4/21*(3*x^5-7*x^3+3)*(x^6+x)^(3/4)/x^6","A"
336,1,25,24,0.102000," ","int((x^6-2)*(x^6-x^4+1)/x^8/(x^6+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{6}+1\right)^{\frac{3}{4}} \left(3 x^{6}-7 x^{4}+3\right)}{21 x^{7}}$&$25$\\ risch&$\frac{\frac{2}{7} x^{12}+\frac{4}{7} x^{6}-\frac{2}{3} x^{10}-\frac{2}{3} x^{4}+\frac{2}{7}}{x^{7} \left(x^{6}+1\right)^{\frac{1}{4}}}$&$35$\\ gosper&$\frac{2 \left(x^{2}+1\right) \left(x^{4}-x^{2}+1\right) \left(3 x^{6}-7 x^{4}+3\right)}{21 x^{7} \left(x^{6}+1\right)^{\frac{1}{4}}}$&$40$\\ meijerg&$\frac{2 \hypergeom \left(\left[-\frac{7}{6}, \frac{1}{4}\right], \left[-\frac{1}{6}\right], -x^{6}\right)}{7 x^{7}}+\frac{\hypergeom \left(\left[-\frac{1}{6}, \frac{1}{4}\right], \left[\frac{5}{6}\right], -x^{6}\right)}{x}-\frac{2 \hypergeom \left(\left[-\frac{1}{2}, \frac{1}{4}\right], \left[\frac{1}{2}\right], -x^{6}\right)}{3 x^{3}}+\frac{\hypergeom \left(\left[\frac{1}{4}, \frac{5}{6}\right], \left[\frac{11}{6}\right], -x^{6}\right) x^{5}}{5}-\frac{\hypergeom \left(\left[\frac{1}{4}, \frac{1}{2}\right], \left[\frac{3}{2}\right], -x^{6}\right) x^{3}}{3}$&$81$\\ \hline \end{longtable}"," ",0,"2/21*(x^6+1)^(3/4)*(3*x^6-7*x^4+3)/x^7","A"
337,1,25,24,0.095000," ","int((x^6-1)^(1/3)*(2*x^6-1)/x^15,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{6}-1\right)^{\frac{1}{3}} \left(11 x^{12}-15 x^{6}+4\right)}{56 x^{14}}$&$25$\\ risch&$\frac{11 x^{18}-26 x^{12}+19 x^{6}-4}{56 \left(x^{6}-1\right)^{\frac{2}{3}} x^{14}}$&$30$\\ gosper&$\frac{\left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right) \left(11 x^{6}-4\right) \left(x^{6}-1\right)^{\frac{1}{3}}}{56 x^{14}}$&$40$\\ meijerg&$-\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}} \left(-x^{6}+1\right)^{\frac{4}{3}}}{4 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} x^{8}}+\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}} \left(-\frac{3}{4} x^{12}-\frac{1}{4} x^{6}+1\right) \left(-x^{6}+1\right)^{\frac{1}{3}}}{14 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} x^{14}}$&$78$\\ \hline \end{longtable}"," ",0,"1/56*(x^6-1)^(1/3)*(11*x^12-15*x^6+4)/x^14","A"
338,1,87,21,0.380000," ","int(x^2*(x^3-2)*(x^3+1)^(1/2)/(x^9+3*x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) x^{9}+6 \RootOf \left(\textit{\_Z}^{2}-3\right) x^{6}-6 \sqrt{x^{3}+1}\, x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-3\right) x^{3}-6 \sqrt{x^{3}+1}\, x^{3}+\RootOf \left(\textit{\_Z}^{2}-3\right)}{x^{9}+3 x^{3}+1}\right)}{9}$&$87$\\ default&$\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{9}+3 \textit{\_Z}^{3}+1\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{6}+\underline{\hspace{1.25 ex}}\alpha^{3}-1\right) \left(-\underline{\hspace{1.25 ex}}\alpha^{8}+\underline{\hspace{1.25 ex}}\alpha^{7}-\underline{\hspace{1.25 ex}}\alpha^{6}+\underline{\hspace{1.25 ex}}\alpha^{5}-\underline{\hspace{1.25 ex}}\alpha^{4}+\underline{\hspace{1.25 ex}}\alpha^{3}-4 \underline{\hspace{1.25 ex}}\alpha^{2}+4 \underline{\hspace{1.25 ex}}\alpha  -4\right) \left(3-i \sqrt{3}\right) \sqrt{\frac{1+x}{3-i \sqrt{3}}}\, \sqrt{\frac{-1+2 x -i \sqrt{3}}{-3-i \sqrt{3}}}\, \sqrt{\frac{-1+2 x +i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{8}}{2}-\frac{\underline{\hspace{1.25 ex}}\alpha^{7}}{2}+\frac{\underline{\hspace{1.25 ex}}\alpha^{6}}{2}-\frac{\underline{\hspace{1.25 ex}}\alpha^{5}}{2}+\frac{\underline{\hspace{1.25 ex}}\alpha^{4}}{2}-\frac{\underline{\hspace{1.25 ex}}\alpha^{3}}{2}+2 \underline{\hspace{1.25 ex}}\alpha^{2}-2 \underline{\hspace{1.25 ex}}\alpha  +2+\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{7}}{6}-\frac{i \underline{\hspace{1.25 ex}}\alpha^{4} \sqrt{3}}{6}-\frac{2 i \sqrt{3}}{3}+\frac{i \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{3}}{6}-\frac{2 i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}}{3}-\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{6}}{6}-\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{8}}{6}+\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5}}{6}+\frac{2 i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha }{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}\right)}{27}$&$298$\\ elliptic&$\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{9}+3 \textit{\_Z}^{3}+1\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{6}+\underline{\hspace{1.25 ex}}\alpha^{3}-1\right) \left(-\underline{\hspace{1.25 ex}}\alpha^{8}+\underline{\hspace{1.25 ex}}\alpha^{7}-\underline{\hspace{1.25 ex}}\alpha^{6}+\underline{\hspace{1.25 ex}}\alpha^{5}-\underline{\hspace{1.25 ex}}\alpha^{4}+\underline{\hspace{1.25 ex}}\alpha^{3}-4 \underline{\hspace{1.25 ex}}\alpha^{2}+4 \underline{\hspace{1.25 ex}}\alpha  -4\right) \left(3-i \sqrt{3}\right) \sqrt{\frac{1+x}{3-i \sqrt{3}}}\, \sqrt{\frac{-1+2 x -i \sqrt{3}}{-3-i \sqrt{3}}}\, \sqrt{\frac{-1+2 x +i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{8}}{2}-\frac{\underline{\hspace{1.25 ex}}\alpha^{7}}{2}+\frac{\underline{\hspace{1.25 ex}}\alpha^{6}}{2}-\frac{\underline{\hspace{1.25 ex}}\alpha^{5}}{2}+\frac{\underline{\hspace{1.25 ex}}\alpha^{4}}{2}-\frac{\underline{\hspace{1.25 ex}}\alpha^{3}}{2}+2 \underline{\hspace{1.25 ex}}\alpha^{2}-2 \underline{\hspace{1.25 ex}}\alpha  +2+\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{7}}{6}-\frac{i \underline{\hspace{1.25 ex}}\alpha^{4} \sqrt{3}}{6}-\frac{2 i \sqrt{3}}{3}+\frac{i \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{3}}{6}-\frac{2 i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}}{3}-\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{6}}{6}-\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{8}}{6}+\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5}}{6}+\frac{2 i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha }{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}\right)}{27}$&$298$\\ \hline \end{longtable}"," ",0,"1/9*RootOf(_Z^2-3)*ln(-(RootOf(_Z^2-3)*x^9+6*RootOf(_Z^2-3)*x^6-6*(x^3+1)^(1/2)*x^6+3*RootOf(_Z^2-3)*x^3-6*(x^3+1)^(1/2)*x^3+RootOf(_Z^2-3))/(x^9+3*x^3+1))","C"
339,0,0,22,0.036000," ","int(x^4*(4*x^5-9)/(x^6-x)^(1/2)/(x^9-a*x^5+a),x)","\[\int \frac{x^{4} \left(4 x^{5}-9\right)}{\sqrt{x^{6}-x}\, \left(x^{9}-a \,x^{5}+a \right)}\, dx\]"," ",0,"int(x^4*(4*x^5-9)/(x^6-x)^(1/2)/(x^9-a*x^5+a),x)","F"
340,0,0,22,0.032000," ","int(x^4*(5*x^4-9)/(x^5-x)^(1/2)/(a*x^9-x^4+1),x)","\[\int \frac{x^{4} \left(5 x^{4}-9\right)}{\sqrt{x^{5}-x}\, \left(a \,x^{9}-x^{4}+1\right)}\, dx\]"," ",0,"int(x^4*(5*x^4-9)/(x^5-x)^(1/2)/(a*x^9-x^4+1),x)","F"
341,0,0,22,0.037000," ","int(x^4*(4*x^5-9)/(x^6-x)^(1/2)/(a*x^9-x^5+1),x)","\[\int \frac{x^{4} \left(4 x^{5}-9\right)}{\sqrt{x^{6}-x}\, \left(a \,x^{9}-x^{5}+1\right)}\, dx\]"," ",0,"int(x^4*(4*x^5-9)/(x^6-x)^(1/2)/(a*x^9-x^5+1),x)","F"
342,1,25,24,0.102000," ","int((x^12+1)/x^16/(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}-1}\, \left(23 x^{12}+4 x^{6}+3\right)}{45 x^{15}}$&$25$\\ risch&$\frac{23 x^{18}-19 x^{12}-x^{6}-3}{45 x^{15} \sqrt{x^{6}-1}}$&$30$\\ gosper&$\frac{\left(23 x^{12}+4 x^{6}+3\right) \left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right)}{45 \sqrt{x^{6}-1}\, x^{15}}$&$45$\\ meijerg&$-\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{-x^{6}+1}}{3 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, x^{3}}-\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(\frac{8}{3} x^{12}+\frac{4}{3} x^{6}+1\right) \sqrt{-x^{6}+1}}{15 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, x^{15}}$&$78$\\ \hline \end{longtable}"," ",0,"1/45*(x^6-1)^(1/2)*(23*x^12+4*x^6+3)/x^15","A"
343,1,149,25,1.395000," ","int((-1+x)/(-3+x)/(1+x)/(x^2-2*x-2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{2}-2 x -2}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \left(x^{2}-2 x -2\right)^{\frac{3}{4}}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) x +\RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(x^{2}-2 x -2\right)^{\frac{1}{4}}}{\left(1+x \right) \left(-3+x \right)}\right)}{2}-\frac{\ln \left(\frac{2 \left(x^{2}-2 x -2\right)^{\frac{3}{4}}+2 \sqrt{x^{2}-2 x -2}+x^{2}+2 \left(x^{2}-2 x -2\right)^{\frac{1}{4}}-2 x -1}{\left(1+x \right) \left(-3+x \right)}\right)}{2}$&$149$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^2+1)*ln((2*RootOf(_Z^2+1)*(x^2-2*x-2)^(1/2)-RootOf(_Z^2+1)*x^2+2*(x^2-2*x-2)^(3/4)+2*RootOf(_Z^2+1)*x+RootOf(_Z^2+1)-2*(x^2-2*x-2)^(1/4))/(1+x)/(-3+x))-1/2*ln((2*(x^2-2*x-2)^(3/4)+2*(x^2-2*x-2)^(1/2)+x^2+2*(x^2-2*x-2)^(1/4)-2*x-1)/(1+x)/(-3+x))","C"
344,1,145,25,1.257000," ","int(1/(-1+x)/(x^2-2*x+2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{2}-2 x +2}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \left(x^{2}-2 x +2\right)^{\frac{3}{4}}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) x -3 \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(x^{2}-2 x +2\right)^{\frac{1}{4}}}{\left(-1+x \right)^{2}}\right)}{2}+\frac{\ln \left(-\frac{2 \left(x^{2}-2 x +2\right)^{\frac{3}{4}}-2 \sqrt{x^{2}-2 x +2}-x^{2}+2 \left(x^{2}-2 x +2\right)^{\frac{1}{4}}+2 x -3}{\left(-1+x \right)^{2}}\right)}{2}$&$145$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^2+1)*ln(-(2*RootOf(_Z^2+1)*(x^2-2*x+2)^(1/2)-RootOf(_Z^2+1)*x^2+2*(x^2-2*x+2)^(3/4)+2*RootOf(_Z^2+1)*x-3*RootOf(_Z^2+1)-2*(x^2-2*x+2)^(1/4))/(-1+x)^2)+1/2*ln(-(2*(x^2-2*x+2)^(3/4)-2*(x^2-2*x+2)^(1/2)-x^2+2*(x^2-2*x+2)^(1/4)+2*x-3)/(-1+x)^2)","C"
345,1,143,25,1.153000," ","int(1/(1+x)/(x^2+2*x+2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\ln \left(-\frac{2 \left(x^{2}+2 x +2\right)^{\frac{3}{4}}+2 \sqrt{x^{2}+2 x +2}+x^{2}+2 \left(x^{2}+2 x +2\right)^{\frac{1}{4}}+2 x +3}{\left(1+x \right)^{2}}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{2}+2 x +2}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \left(x^{2}+2 x +2\right)^{\frac{3}{4}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x -3 \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(x^{2}+2 x +2\right)^{\frac{1}{4}}}{\left(1+x \right)^{2}}\right)}{2}$&$143$\\ \hline \end{longtable}"," ",0,"-1/2*ln(-(2*(x^2+2*x+2)^(3/4)+2*(x^2+2*x+2)^(1/2)+x^2+2*(x^2+2*x+2)^(1/4)+2*x+3)/(1+x)^2)+1/2*RootOf(_Z^2+1)*ln(-(2*RootOf(_Z^2+1)*(x^2+2*x+2)^(1/2)-RootOf(_Z^2+1)*x^2+2*(x^2+2*x+2)^(3/4)-2*RootOf(_Z^2+1)*x-3*RootOf(_Z^2+1)-2*(x^2+2*x+2)^(1/4))/(1+x)^2)","C"
346,1,59,21,1.954000," ","int(1/x/(x^3+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\sqrt{2}\, \Gamma \left(\frac{3}{4}\right) \left(\frac{\left(-3 \ln \left(2\right)-\frac{\pi}{2}+3 \ln \left(x \right)\right) \pi  \sqrt{2}}{\Gamma \left(\frac{3}{4}\right)}-\frac{\hypergeom \left(\left[1, 1, \frac{5}{4}\right], \left[2, 2\right], -x^{3}\right) \pi  \sqrt{2}\, x^{3}}{4 \Gamma \left(\frac{3}{4}\right)}\right)}{6 \pi}$&$59$\\ trager&$-\frac{\ln \left(\frac{2 \left(x^{3}+1\right)^{\frac{3}{4}}+x^{3}+2 \sqrt{x^{3}+1}+2 \left(x^{3}+1\right)^{\frac{1}{4}}+2}{x^{3}}\right)}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{3}+1}+2 \left(x^{3}+1\right)^{\frac{3}{4}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(x^{3}+1\right)^{\frac{1}{4}}}{x^{3}}\right)}{3}$&$107$\\ \hline \end{longtable}"," ",0,"1/6/Pi*2^(1/2)*GAMMA(3/4)*((-3*ln(2)-1/2*Pi+3*ln(x))*Pi*2^(1/2)/GAMMA(3/4)-1/4*hypergeom([1,1,5/4],[2,2],-x^3)*Pi*2^(1/2)/GAMMA(3/4)*x^3)","C"
347,1,26,21,0.059000," ","int(1/x/(a*x^3-b)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 \arctanh \left(\frac{\sqrt{a \,x^{3}-b}}{\sqrt{-b}}\right)}{3 \sqrt{-b}}$&$26$\\ elliptic&$-\frac{2 \arctanh \left(\frac{\sqrt{a \,x^{3}-b}}{\sqrt{-b}}\right)}{3 \sqrt{-b}}$&$26$\\ \hline \end{longtable}"," ",0,"-2/3*arctanh((a*x^3-b)^(1/2)/(-b)^(1/2))/(-b)^(1/2)","A"
348,1,26,25,0.059000," ","int(x^5/(a*x^3-b)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{2 \sqrt{a \,x^{3}-b}\, \left(a \,x^{3}+2 b \right)}{9 a^{2}}$&$26$\\ trager&$\frac{2 \sqrt{a \,x^{3}-b}\, \left(a \,x^{3}+2 b \right)}{9 a^{2}}$&$26$\\ risch&$\frac{2 \sqrt{a \,x^{3}-b}\, \left(a \,x^{3}+2 b \right)}{9 a^{2}}$&$26$\\ default&$\frac{2 x^{3} \sqrt{a \,x^{3}-b}}{9 a}+\frac{4 b \sqrt{a \,x^{3}-b}}{9 a^{2}}$&$38$\\ elliptic&$\frac{2 x^{3} \sqrt{a \,x^{3}-b}}{9 a}+\frac{4 b \sqrt{a \,x^{3}-b}}{9 a^{2}}$&$38$\\ \hline \end{longtable}"," ",0,"2/9*(a*x^3-b)^(1/2)*(a*x^3+2*b)/a^2","A"
349,1,31,27,0.326000," ","int((1+x)/(-1+x)/(x^4-x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(-\frac{-2 x^{2}+\sqrt{x^{4}-x^{2}+1}+3 x -2}{\left(-1+x \right)^{2}}\right)$&$31$\\ elliptic&$-\arctanh \left(\frac{x^{2}+1}{2 \sqrt{\left(x^{2}-1\right)^{2}+x^{2}}}\right)-\arctanh \left(\frac{\sqrt{x^{4}-x^{2}+1}}{x}\right)$&$44$\\ default&$\frac{2 \sqrt{1-\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}}\, \sqrt{1-\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{2+2 i \sqrt{3}}}{2}, \frac{\sqrt{-2-2 i \sqrt{3}}}{2}\right)}{\sqrt{2+2 i \sqrt{3}}\, \sqrt{x^{4}-x^{2}+1}}-\arctanh \left(\frac{x^{2}+1}{2 \sqrt{x^{4}-x^{2}+1}}\right)-\frac{2 \sqrt{1-\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}}\, \sqrt{1-\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , \frac{1}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \frac{\sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}-x^{2}+1}}$&$210$\\ \hline \end{longtable}"," ",0,"ln(-(-2*x^2+(x^4-x^2+1)^(1/2)+3*x-2)/(-1+x)^2)","A"
350,1,26,25,0.093000," ","int((x^4-1)*(x^4+1)/(x^4+x^2+1)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{x \left(3 x^{4}+2 x^{2}+3\right)}{3 \left(x^{4}+x^{2}+1\right)^{\frac{3}{2}}}$&$26$\\ risch&$-\frac{x \left(3 x^{4}+2 x^{2}+3\right)}{3 \left(x^{4}+x^{2}+1\right)^{\frac{3}{2}}}$&$26$\\ gosper&$-\frac{\left(3 x^{4}+2 x^{2}+3\right) x \left(x^{2}+x +1\right) \left(x^{2}-x +1\right)}{3 \left(x^{4}+x^{2}+1\right)^{\frac{5}{2}}}$&$40$\\ elliptic&$\frac{\left(\frac{\sqrt{2}\, x^{3}}{3 \left(x^{4}+x^{2}+1\right)^{\frac{3}{2}}}-\frac{\sqrt{2}\, x}{\sqrt{x^{4}+x^{2}+1}}\right) \sqrt{2}}{2}$&$41$\\ default&$\frac{\frac{2}{9} x^{3}+\frac{1}{9} x}{\left(x^{4}+x^{2}+1\right)^{\frac{3}{2}}}-\frac{2 \left(\frac{7}{27} x^{3}+\frac{11}{27} x \right)}{\sqrt{x^{4}+x^{2}+1}}-\frac{\frac{1}{9} x -\frac{1}{9} x^{3}}{\left(x^{4}+x^{2}+1\right)^{\frac{3}{2}}}+\frac{\frac{14}{27} x^{3}-\frac{5}{27} x}{\sqrt{x^{4}+x^{2}+1}}$&$85$\\ \hline \end{longtable}"," ",0,"-1/3*x*(3*x^4+2*x^2+3)/(x^4+x^2+1)^(3/2)","A"
351,1,153,25,0.866000," ","int(x^2*(x^3-4)/(x^3-1)^(3/4)/(x^4-x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(\frac{2 \left(x^{3}-1\right)^{\frac{3}{4}} x -2 x^{2} \sqrt{x^{3}-1}+2 \left(x^{3}-1\right)^{\frac{1}{4}} x^{3}-x^{4}-x^{3}+1}{x^{4}-x^{3}+1}\right)+\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{3}-1}\, x^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-2 \left(x^{3}-1\right)^{\frac{3}{4}} x +2 \left(x^{3}-1\right)^{\frac{1}{4}} x^{3}+\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{4}-x^{3}+1}\right)$&$153$\\ \hline \end{longtable}"," ",0,"ln((2*(x^3-1)^(3/4)*x-2*x^2*(x^3-1)^(1/2)+2*(x^3-1)^(1/4)*x^3-x^4-x^3+1)/(x^4-x^3+1))+RootOf(_Z^2+1)*ln(-(2*RootOf(_Z^2+1)*(x^3-1)^(1/2)*x^2-RootOf(_Z^2+1)*x^4-RootOf(_Z^2+1)*x^3-2*(x^3-1)^(3/4)*x+2*(x^3-1)^(1/4)*x^3+RootOf(_Z^2+1))/(x^4-x^3+1))","C"
352,1,34,27,0.728000," ","int((1+2*x)/(x^4+2*x^3-3*x^2-4*x-4)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(-x^{2}+\sqrt{x^{4}+2 x^{3}-3 x^{2}-4 x -4}-x +2\right)$&$34$\\ default&$-\frac{2 i \left(-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}-\frac{\sqrt{9+8 \sqrt{2}}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}\, \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)^{2} \sqrt{\frac{i \sqrt{-9+8 \sqrt{2}}\, \left(x +\frac{1}{2}+\frac{\sqrt{9+8 \sqrt{2}}}{2}\right)}{\left(-\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}\, \sqrt{\frac{i \sqrt{-9+8 \sqrt{2}}\, \left(x +\frac{1}{2}-\frac{\sqrt{9+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}, \sqrt{\frac{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}-\frac{\sqrt{9+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(-\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \sqrt{-9+8 \sqrt{2}}\, \sqrt{\left(x +\frac{1}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}+\frac{\sqrt{9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{\sqrt{9+8 \sqrt{2}}}{2}\right)}}-\frac{4 i \left(-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}-\frac{\sqrt{9+8 \sqrt{2}}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}\, \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)^{2} \sqrt{\frac{i \sqrt{-9+8 \sqrt{2}}\, \left(x +\frac{1}{2}+\frac{\sqrt{9+8 \sqrt{2}}}{2}\right)}{\left(-\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}\, \sqrt{\frac{i \sqrt{-9+8 \sqrt{2}}\, \left(x +\frac{1}{2}-\frac{\sqrt{9+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}\, \left(\left(-\frac{1}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}, \sqrt{\frac{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}-\frac{\sqrt{9+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(-\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}\right)-i \sqrt{-9+8 \sqrt{2}}\, \EllipticPi \left(\sqrt{\frac{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}, \frac{\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}}{\frac{\sqrt{9+8 \sqrt{2}}}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}}, \sqrt{\frac{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}-\frac{\sqrt{9+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(-\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}\right)\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \sqrt{-9+8 \sqrt{2}}\, \sqrt{\left(x +\frac{1}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}+\frac{\sqrt{9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{\sqrt{9+8 \sqrt{2}}}{2}\right)}}$&$1382$\\ elliptic&$-\frac{2 i \left(-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}-\frac{\sqrt{9+8 \sqrt{2}}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}\, \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)^{2} \sqrt{\frac{i \sqrt{-9+8 \sqrt{2}}\, \left(x +\frac{1}{2}+\frac{\sqrt{9+8 \sqrt{2}}}{2}\right)}{\left(-\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}\, \sqrt{\frac{i \sqrt{-9+8 \sqrt{2}}\, \left(x +\frac{1}{2}-\frac{\sqrt{9+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}, \sqrt{\frac{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}-\frac{\sqrt{9+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(-\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \sqrt{-9+8 \sqrt{2}}\, \sqrt{\left(x +\frac{1}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}+\frac{\sqrt{9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{\sqrt{9+8 \sqrt{2}}}{2}\right)}}-\frac{4 i \left(-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}-\frac{\sqrt{9+8 \sqrt{2}}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}\, \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)^{2} \sqrt{\frac{i \sqrt{-9+8 \sqrt{2}}\, \left(x +\frac{1}{2}+\frac{\sqrt{9+8 \sqrt{2}}}{2}\right)}{\left(-\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}\, \sqrt{\frac{i \sqrt{-9+8 \sqrt{2}}\, \left(x +\frac{1}{2}-\frac{\sqrt{9+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}\, \left(\left(-\frac{1}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}, \sqrt{\frac{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}-\frac{\sqrt{9+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(-\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}\right)-i \sqrt{-9+8 \sqrt{2}}\, \EllipticPi \left(\sqrt{\frac{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}, \frac{\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}}{\frac{\sqrt{9+8 \sqrt{2}}}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}}, \sqrt{\frac{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}-\frac{\sqrt{9+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(-\frac{\sqrt{9+8 \sqrt{2}}}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right)}}\right)\right)}{\left(\frac{\sqrt{9+8 \sqrt{2}}}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \sqrt{-9+8 \sqrt{2}}\, \sqrt{\left(x +\frac{1}{2}+\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{-9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}+\frac{\sqrt{9+8 \sqrt{2}}}{2}\right) \left(x +\frac{1}{2}-\frac{\sqrt{9+8 \sqrt{2}}}{2}\right)}}$&$1382$\\ \hline \end{longtable}"," ",0,"-ln(-x^2+(x^4+2*x^3-3*x^2-4*x-4)^(1/2)-x+2)","A"
353,1,35,21,0.058000," ","int(1/x/(a*x^4-b)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\ln \left(\frac{-2 b +2 \sqrt{-b}\, \sqrt{a \,x^{4}-b}}{x^{2}}\right)}{2 \sqrt{-b}}$&$35$\\ elliptic&$-\frac{\ln \left(\frac{-2 b +2 \sqrt{-b}\, \sqrt{a \,x^{4}-b}}{x^{2}}\right)}{2 \sqrt{-b}}$&$35$\\ \hline \end{longtable}"," ",0,"-1/2/(-b)^(1/2)*ln((-2*b+2*(-b)^(1/2)*(a*x^4-b)^(1/2))/x^2)","A"
354,1,74,23,0.268000," ","int((2*x^6-1)/(x^6+1)/(x^6-2*x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x^{6}-4 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{2}+4 \sqrt{x^{6}-2 x^{2}+1}\, x +\RootOf \left(\textit{\_Z}^{2}+2\right)}{\left(x^{2}+1\right) \left(x^{4}-x^{2}+1\right)}\right)}{4}$&$74$\\ \hline \end{longtable}"," ",0,"-1/4*RootOf(_Z^2+2)*ln(-(RootOf(_Z^2+2)*x^6-4*RootOf(_Z^2+2)*x^2+4*(x^6-2*x^2+1)^(1/2)*x+RootOf(_Z^2+2))/(x^2+1)/(x^4-x^2+1))","C"
355,1,84,23,0.299000," ","int((2*x^6+1)/(x^6-1)/(x^6-2*x^2-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x^{6}-4 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{2}-4 \sqrt{x^{6}-2 x^{2}-1}\, x -\RootOf \left(\textit{\_Z}^{2}+2\right)}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right)}\right)}{4}$&$84$\\ \hline \end{longtable}"," ",0,"1/4*RootOf(_Z^2+2)*ln((RootOf(_Z^2+2)*x^6-4*RootOf(_Z^2+2)*x^2-4*(x^6-2*x^2-1)^(1/2)*x-RootOf(_Z^2+2))/(-1+x)/(1+x)/(x^2+x+1)/(x^2-x+1))","C"
356,1,26,26,0.080000," ","int(x^8*(x^3-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\left(\frac{1}{10} x^{9}-\frac{1}{70} x^{6}-\frac{3}{140} x^{3}-\frac{9}{140}\right) \left(x^{3}-1\right)^{\frac{1}{3}}$&$26$\\ risch&$\frac{\left(x^{3}-1\right)^{\frac{1}{3}} \left(14 x^{9}-2 x^{6}-3 x^{3}-9\right)}{140}$&$27$\\ gosper&$\frac{\left(-1+x \right) \left(x^{2}+x +1\right) \left(14 x^{6}+12 x^{3}+9\right) \left(x^{3}-1\right)^{\frac{1}{3}}}{140}$&$31$\\ meijerg&$\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{1}{3}, 3\right], \left[4\right], x^{3}\right) x^{9}}{9 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}}}$&$33$\\ \hline \end{longtable}"," ",0,"(1/10*x^9-1/70*x^6-3/140*x^3-9/140)*(x^3-1)^(1/3)","A"
357,1,17,26,0.072000," ","int(x^8*(x^3+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\hypergeom \left(\left[-\frac{1}{4}, 3\right], \left[4\right], -x^{3}\right) x^{9}}{9}$&$17$\\ trager&$\left(\frac{4}{39} x^{9}+\frac{4}{351} x^{6}-\frac{32}{1755} x^{3}+\frac{128}{1755}\right) \left(x^{3}+1\right)^{\frac{1}{4}}$&$26$\\ risch&$\frac{4 \left(x^{3}+1\right)^{\frac{1}{4}} \left(45 x^{9}+5 x^{6}-8 x^{3}+32\right)}{1755}$&$27$\\ gosper&$\frac{4 \left(1+x \right) \left(x^{2}-x +1\right) \left(45 x^{6}-40 x^{3}+32\right) \left(x^{3}+1\right)^{\frac{1}{4}}}{1755}$&$33$\\ \hline \end{longtable}"," ",0,"1/9*hypergeom([-1/4,3],[4],-x^3)*x^9","C"
358,1,27,26,0.076000," ","int(1/x^6/(x^3-x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(x^{3}-x \right)^{\frac{2}{3}} \left(9 x^{4}+6 x^{2}+5\right)}{80 x^{6}}$&$27$\\ risch&$\frac{-\frac{3}{80} x^{2}-\frac{3}{16}-\frac{9}{80} x^{4}+\frac{27}{80} x^{6}}{x^{5} \left(x \left(x^{2}-1\right)\right)^{\frac{1}{3}}}$&$32$\\ gosper&$\frac{3 \left(-1+x \right) \left(1+x \right) \left(9 x^{4}+6 x^{2}+5\right)}{80 x^{5} \left(x^{3}-x \right)^{\frac{1}{3}}}$&$33$\\ meijerg&$-\frac{3 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}} \left(\frac{9}{5} x^{4}+\frac{6}{5} x^{2}+1\right) \left(-x^{2}+1\right)^{\frac{2}{3}}}{16 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}} x^{\frac{16}{3}}}$&$45$\\ \hline \end{longtable}"," ",0,"3/80*(x^3-x)^(2/3)*(9*x^4+6*x^2+5)/x^6","A"
359,1,27,26,0.072000," ","int(1/x^3/(x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(9 x^{2}+6 x +5\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}}{40 x^{4}}$&$27$\\ gosper&$\frac{3 \left(-1+x \right) \left(9 x^{2}+6 x +5\right)}{40 x^{2} \left(x^{3}-x^{2}\right)^{\frac{1}{3}}}$&$30$\\ risch&$\frac{-\frac{3}{8}-\frac{3}{40} x -\frac{9}{40} x^{2}+\frac{27}{40} x^{3}}{x^{2} \left(\left(-1+x \right) x^{2}\right)^{\frac{1}{3}}}$&$30$\\ meijerg&$-\frac{3 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{3}} \left(\frac{9}{5} x^{2}+\frac{6}{5} x +1\right) \left(1-x \right)^{\frac{2}{3}}}{8 \mathrm{signum}\left(-1+x \right)^{\frac{1}{3}} x^{\frac{8}{3}}}$&$37$\\ \hline \end{longtable}"," ",0,"3/40*(9*x^2+6*x+5)*(x^3-x^2)^(2/3)/x^4","A"
360,1,27,26,0.123000," ","int((x^2-3)*(x^3-x^2+1)/x^6/(x^3-x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{4 \left(x^{3}-x \right)^{\frac{3}{4}} \left(7 x^{3}-3 x^{2}+3\right)}{21 x^{6}}$&$27$\\ gosper&$-\frac{4 \left(-1+x \right) \left(1+x \right) \left(7 x^{3}-3 x^{2}+3\right)}{21 x^{5} \left(x^{3}-x \right)^{\frac{1}{4}}}$&$33$\\ risch&$-\frac{4 \left(7 x^{5}-3 x^{4}-7 x^{3}+6 x^{2}-3\right)}{21 x^{5} \left(x \left(x^{2}-1\right)\right)^{\frac{1}{4}}}$&$37$\\ meijerg&$\frac{4 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{21}{8}, \frac{1}{4}\right], \left[-\frac{13}{8}\right], x^{2}\right)}{7 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{4}} x^{\frac{21}{4}}}+\frac{4 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{9}{8}, \frac{1}{4}\right], \left[-\frac{1}{8}\right], x^{2}\right)}{3 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{4}} x^{\frac{9}{4}}}-\frac{16 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{13}{8}, \frac{1}{4}\right], \left[-\frac{5}{8}\right], x^{2}\right)}{13 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{4}} x^{\frac{13}{4}}}-\frac{4 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{1}{8}, \frac{1}{4}\right], \left[\frac{7}{8}\right], x^{2}\right)}{\mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{4}} x^{\frac{1}{4}}}+\frac{4 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{5}{8}, \frac{1}{4}\right], \left[\frac{3}{8}\right], x^{2}\right)}{5 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{4}} x^{\frac{5}{4}}}$&$162$\\ \hline \end{longtable}"," ",0,"-4/21*(x^3-x)^(3/4)*(7*x^3-3*x^2+3)/x^6","A"
361,1,63,28,0.339000," ","int((x^2+1)/(x^2-1)/(x^3-x^2-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) x +2 \sqrt{x^{3}-x^{2}-x}+\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(-1+x \right) \left(1+x \right)}\right)$&$63$\\ default&$\frac{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \sqrt{-5 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{5}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}}-\frac{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \sqrt{-5 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{5}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)}+\frac{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \sqrt{-5 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{5}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{-\frac{1}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(-\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}$&$387$\\ elliptic&$\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{5 \sqrt{x^{3}-x^{2}-x}}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)}+\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)}+\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{-\frac{1}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{5 \sqrt{x^{3}-x^{2}-x}\, \left(-\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{-\frac{1}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(-\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}$&$853$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2+1)*ln((-RootOf(_Z^2+1)*x^2+2*RootOf(_Z^2+1)*x+2*(x^3-x^2-x)^(1/2)+RootOf(_Z^2+1))/(-1+x)/(1+x))","C"
362,1,20,26,0.090000," ","int((x^3-1)/x^3/(x^3+1)/(x^4+x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{\frac{28 x^{3}}{9}+\frac{4}{9}}{\left(x^{4}+x \right)^{\frac{1}{4}} x^{2}}$&$20$\\ risch&$\frac{\frac{28 x^{3}}{9}+\frac{4}{9}}{x^{2} \left(x \left(x^{3}+1\right)\right)^{\frac{1}{4}}}$&$22$\\ trager&$\frac{4 \left(7 x^{3}+1\right) \left(x^{4}+x \right)^{\frac{3}{4}}}{9 x^{3} \left(x^{3}+1\right)}$&$27$\\ meijerg&$\frac{\frac{16 x^{3}}{9}+\frac{4}{9}}{\left(x^{3}+1\right)^{\frac{1}{4}} x^{\frac{9}{4}}}+\frac{4 x^{\frac{3}{4}}}{3 \left(x^{3}+1\right)^{\frac{1}{4}}}$&$33$\\ \hline \end{longtable}"," ",0,"4/9*(7*x^3+1)/(x^4+x)^(1/4)/x^2","A"
363,1,27,26,0.077000," ","int((x^4-x^2)^(1/4)/x^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{4}-x^{2}\right)^{\frac{1}{4}} \left(4 x^{4}+x^{2}-5\right)}{45 x^{5}}$&$27$\\ gosper&$\frac{2 \left(-1+x \right) \left(1+x \right) \left(4 x^{2}+5\right) \left(x^{4}-x^{2}\right)^{\frac{1}{4}}}{45 x^{5}}$&$30$\\ risch&$\frac{2 \left(x^{2} \left(x^{2}-1\right)\right)^{\frac{1}{4}} \left(4 x^{6}-3 x^{4}-6 x^{2}+5\right)}{45 x^{5} \left(x^{2}-1\right)}$&$41$\\ meijerg&$-\frac{2 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{4}} \left(-\frac{4}{5} x^{4}-\frac{1}{5} x^{2}+1\right) \left(-x^{2}+1\right)^{\frac{1}{4}}}{9 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{4}} x^{\frac{9}{2}}}$&$45$\\ \hline \end{longtable}"," ",0,"2/45*(x^4-x^2)^(1/4)*(4*x^4+x^2-5)/x^5","A"
364,1,29,28,0.610000," ","int((-1+2*x)/(x^4-2*x^3+x+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(1+2 x -2 x^{2}+2 \sqrt{x^{4}-2 x^{3}+x +1}\right)$&$29$\\ default&$-\frac{2 \left(-\frac{\sqrt{3-2 i \sqrt{3}}}{2}-\frac{\sqrt{3+2 i \sqrt{3}}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)^{2} \sqrt{\frac{\sqrt{3-2 i \sqrt{3}}\, \left(x -\frac{1}{2}+\frac{\sqrt{3+2 i \sqrt{3}}}{2}\right)}{\left(-\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}\, \sqrt{\frac{\sqrt{3-2 i \sqrt{3}}\, \left(x -\frac{1}{2}-\frac{\sqrt{3+2 i \sqrt{3}}}{2}\right)}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}, \sqrt{-\frac{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)^{2}}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(-\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}\right)}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \sqrt{3-2 i \sqrt{3}}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{3+2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3+2 i \sqrt{3}}}{2}\right)}}+\frac{4 \left(-\frac{\sqrt{3-2 i \sqrt{3}}}{2}-\frac{\sqrt{3+2 i \sqrt{3}}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)^{2} \sqrt{\frac{\sqrt{3-2 i \sqrt{3}}\, \left(x -\frac{1}{2}+\frac{\sqrt{3+2 i \sqrt{3}}}{2}\right)}{\left(-\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}\, \sqrt{\frac{\sqrt{3-2 i \sqrt{3}}\, \left(x -\frac{1}{2}-\frac{\sqrt{3+2 i \sqrt{3}}}{2}\right)}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}\, \left(\left(\frac{1}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}, \sqrt{-\frac{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)^{2}}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(-\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}\right)-\sqrt{3-2 i \sqrt{3}}\, \EllipticPi \left(\sqrt{\frac{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}, \frac{\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}}{\frac{\sqrt{3+2 i \sqrt{3}}}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}}, \sqrt{-\frac{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)^{2}}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(-\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}\right)\right)}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \sqrt{3-2 i \sqrt{3}}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{3+2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3+2 i \sqrt{3}}}{2}\right)}}$&$1352$\\ elliptic&$-\frac{2 \left(-\frac{\sqrt{3-2 i \sqrt{3}}}{2}-\frac{\sqrt{3+2 i \sqrt{3}}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)^{2} \sqrt{\frac{\sqrt{3-2 i \sqrt{3}}\, \left(x -\frac{1}{2}+\frac{\sqrt{3+2 i \sqrt{3}}}{2}\right)}{\left(-\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}\, \sqrt{\frac{\sqrt{3-2 i \sqrt{3}}\, \left(x -\frac{1}{2}-\frac{\sqrt{3+2 i \sqrt{3}}}{2}\right)}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}, \sqrt{-\frac{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)^{2}}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(-\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}\right)}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \sqrt{3-2 i \sqrt{3}}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{3+2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3+2 i \sqrt{3}}}{2}\right)}}+\frac{4 \left(-\frac{\sqrt{3-2 i \sqrt{3}}}{2}-\frac{\sqrt{3+2 i \sqrt{3}}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)^{2} \sqrt{\frac{\sqrt{3-2 i \sqrt{3}}\, \left(x -\frac{1}{2}+\frac{\sqrt{3+2 i \sqrt{3}}}{2}\right)}{\left(-\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}\, \sqrt{\frac{\sqrt{3-2 i \sqrt{3}}\, \left(x -\frac{1}{2}-\frac{\sqrt{3+2 i \sqrt{3}}}{2}\right)}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}\, \left(\left(\frac{1}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}, \sqrt{-\frac{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)^{2}}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(-\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}\right)-\sqrt{3-2 i \sqrt{3}}\, \EllipticPi \left(\sqrt{\frac{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}, \frac{\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}}{\frac{\sqrt{3+2 i \sqrt{3}}}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}}, \sqrt{-\frac{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)^{2}}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(-\frac{\sqrt{3+2 i \sqrt{3}}}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right)}}\right)\right)}{\left(\frac{\sqrt{3+2 i \sqrt{3}}}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \sqrt{3-2 i \sqrt{3}}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3-2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{3+2 i \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{3+2 i \sqrt{3}}}{2}\right)}}$&$1352$\\ \hline \end{longtable}"," ",0,"-ln(1+2*x-2*x^2+2*(x^4-2*x^3+x+1)^(1/2))","A"
365,1,17,26,0.097000," ","int((1+x)/(-1+x)/x/(x^4-x^3)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{4 \left(-1+7 x \right)}{3 \left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}}}$&$17$\\ gosper&$-\frac{4 \left(-1+7 x \right)}{3 \left(x^{4}-x^{3}\right)^{\frac{1}{4}}}$&$19$\\ trager&$-\frac{4 \left(-1+7 x \right) \left(x^{4}-x^{3}\right)^{\frac{3}{4}}}{3 \left(-1+x \right) x^{3}}$&$27$\\ meijerg&$\frac{4 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{4}} \left(1-4 x \right)}{3 \mathrm{signum}\left(-1+x \right)^{\frac{1}{4}} \left(1-x \right)^{\frac{1}{4}} x^{\frac{3}{4}}}-\frac{4 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{4}} x^{\frac{1}{4}}}{\mathrm{signum}\left(-1+x \right)^{\frac{1}{4}} \left(1-x \right)^{\frac{1}{4}}}$&$59$\\ \hline \end{longtable}"," ",0,"-4/3*(-1+7*x)/(x^3*(-1+x))^(1/4)","A"
366,1,27,26,0.108000," ","int((x^4+3)*(x^4-x^3-1)/x^6/(x^5-x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(3 x^{4}-7 x^{3}-3\right) \left(x^{5}-x \right)^{\frac{3}{4}}}{21 x^{6}}$&$27$\\ risch&$\frac{-\frac{4}{3} x^{7}+\frac{4}{3} x^{3}+\frac{4}{7} x^{8}-\frac{8}{7} x^{4}+\frac{4}{7}}{x^{5} \left(x \left(x^{4}-1\right)\right)^{\frac{1}{4}}}$&$37$\\ gosper&$\frac{4 \left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right) \left(3 x^{4}-7 x^{3}-3\right)}{21 x^{5} \left(x^{5}-x \right)^{\frac{1}{4}}}$&$38$\\ meijerg&$\frac{4 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{21}{16}, \frac{1}{4}\right], \left[-\frac{5}{16}\right], x^{4}\right)}{7 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}} x^{\frac{21}{4}}}-\frac{8 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{5}{16}, \frac{1}{4}\right], \left[\frac{11}{16}\right], x^{4}\right)}{5 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}} x^{\frac{5}{4}}}+\frac{4 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{9}{16}, \frac{1}{4}\right], \left[\frac{7}{16}\right], x^{4}\right)}{3 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}} x^{\frac{9}{4}}}+\frac{4 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[\frac{1}{4}, \frac{11}{16}\right], \left[\frac{27}{16}\right], x^{4}\right) x^{\frac{11}{4}}}{11 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}}}-\frac{4 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[\frac{1}{4}, \frac{7}{16}\right], \left[\frac{23}{16}\right], x^{4}\right) x^{\frac{7}{4}}}{7 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}}}$&$162$\\ \hline \end{longtable}"," ",0,"4/21*(3*x^4-7*x^3-3)*(x^5-x)^(3/4)/x^6","A"
367,1,27,26,0.094000," ","int((x^4+3)*(x^4+x^3-1)/x^6/(x^5-x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(3 x^{4}+7 x^{3}-3\right) \left(x^{5}-x \right)^{\frac{3}{4}}}{21 x^{6}}$&$27$\\ risch&$\frac{\frac{4}{3} x^{7}-\frac{4}{3} x^{3}+\frac{4}{7} x^{8}-\frac{8}{7} x^{4}+\frac{4}{7}}{x^{5} \left(x \left(x^{4}-1\right)\right)^{\frac{1}{4}}}$&$37$\\ gosper&$\frac{4 \left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right) \left(3 x^{4}+7 x^{3}-3\right)}{21 x^{5} \left(x^{5}-x \right)^{\frac{1}{4}}}$&$38$\\ meijerg&$\frac{4 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{21}{16}, \frac{1}{4}\right], \left[-\frac{5}{16}\right], x^{4}\right)}{7 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}} x^{\frac{21}{4}}}-\frac{8 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{5}{16}, \frac{1}{4}\right], \left[\frac{11}{16}\right], x^{4}\right)}{5 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}} x^{\frac{5}{4}}}-\frac{4 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{9}{16}, \frac{1}{4}\right], \left[\frac{7}{16}\right], x^{4}\right)}{3 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}} x^{\frac{9}{4}}}+\frac{4 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[\frac{1}{4}, \frac{11}{16}\right], \left[\frac{27}{16}\right], x^{4}\right) x^{\frac{11}{4}}}{11 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}}}+\frac{4 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[\frac{1}{4}, \frac{7}{16}\right], \left[\frac{23}{16}\right], x^{4}\right) x^{\frac{7}{4}}}{7 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}}}$&$162$\\ \hline \end{longtable}"," ",0,"4/21*(3*x^4+7*x^3-3)*(x^5-x)^(3/4)/x^6","A"
368,0,0,24,0.018000," ","int((3*x^4-1)/(x^4-a*x+1)/(x^5+x)^(1/2),x)","\[\int \frac{3 x^{4}-1}{\left(x^{4}-a x +1\right) \sqrt{x^{5}+x}}\, dx\]"," ",0,"int((3*x^4-1)/(x^4-a*x+1)/(x^5+x)^(1/2),x)","F"
369,0,0,24,0.018000," ","int((3*x^4-1)/(a*x^4+a-x)/(x^5+x)^(1/2),x)","\[\int \frac{3 x^{4}-1}{\left(a \,x^{4}+a -x \right) \sqrt{x^{5}+x}}\, dx\]"," ",0,"int((3*x^4-1)/(a*x^4+a-x)/(x^5+x)^(1/2),x)","F"
370,1,53,26,0.405000," ","int((x^6-1)^(1/2)*(x^6+2)/x^3/(x^6-x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}-1}}{x^{2}}+\frac{\ln \left(\frac{-x^{6}-x^{4}+2 x^{2} \sqrt{x^{6}-1}+1}{x^{6}-x^{4}-1}\right)}{2}$&$53$\\ risch&$\frac{\sqrt{x^{6}-1}}{x^{2}}+\frac{\ln \left(-\frac{-x^{6}-x^{4}+2 x^{2} \sqrt{x^{6}-1}+1}{x^{6}-x^{4}-1}\right)}{2}$&$54$\\ \hline \end{longtable}"," ",0,"(x^6-1)^(1/2)/x^2+1/2*ln((-x^6-x^4+2*x^2*(x^6-1)^(1/2)+1)/(x^6-x^4-1))","A"
371,1,78,26,0.900000," ","int((-x^6+1)^(1/2)*(2*x^6+1)/x^2/(x^6-x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{-x^{6}+1}}{x}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \sqrt{-x^{6}+1}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{6}-x^{2}-1}\right)}{2}$&$78$\\ risch&$-\frac{x^{6}-1}{x \sqrt{-x^{6}+1}}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-2 \sqrt{-x^{6}+1}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{6}-x^{2}-1}\right)}{2}$&$84$\\ \hline \end{longtable}"," ",0,"(-x^6+1)^(1/2)/x-1/2*RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)*x^6+RootOf(_Z^2+1)*x^2+2*(-x^6+1)^(1/2)*x-RootOf(_Z^2+1))/(x^6-x^2-1))","C"
372,1,24,23,0.374000," ","int(1/x^4/(x^3-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{x^{3}-1}}{3 x^{3}}+\frac{\arctan \left(\sqrt{x^{3}-1}\right)}{3}$&$24$\\ risch&$\frac{\sqrt{x^{3}-1}}{3 x^{3}}+\frac{\arctan \left(\sqrt{x^{3}-1}\right)}{3}$&$24$\\ elliptic&$\frac{\sqrt{x^{3}-1}}{3 x^{3}}+\frac{\arctan \left(\sqrt{x^{3}-1}\right)}{3}$&$24$\\ trager&$\frac{\sqrt{x^{3}-1}}{3 x^{3}}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \sqrt{x^{3}-1}+2 \RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{3}}\right)}{6}$&$57$\\ meijerg&$-\frac{\sqrt{-\mathrm{signum}\left(x^{3}-1\right)}\, \left(\frac{\sqrt{\pi}}{x^{3}}-\frac{\left(1-2 \ln \left(2\right)+3 \ln \left(x \right)+i \pi \right) \sqrt{\pi}}{2}-\frac{\sqrt{\pi}\, \left(-4 x^{3}+8\right)}{8 x^{3}}+\frac{\sqrt{\pi}\, \sqrt{-x^{3}+1}}{x^{3}}+\sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{3}+1}}{2}\right)\right)}{3 \sqrt{\mathrm{signum}\left(x^{3}-1\right)}\, \sqrt{\pi}}$&$100$\\ \hline \end{longtable}"," ",0,"1/3*(x^3-1)^(1/2)/x^3+1/3*arctan((x^3-1)^(1/2))","A"
373,1,58,25,0.523000," ","int((x^2-2*x-2)/(x^2-x+3)/(x^3-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}+3 \RootOf \left(\textit{\_Z}^{2}-2\right) x -\RootOf \left(\textit{\_Z}^{2}-2\right)+4 \sqrt{x^{3}-1}}{x^{2}-x +3}\right)}{2}$&$58$\\ default&$\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{2 \left(\frac{1}{2}-\frac{i \sqrt{11}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(\frac{1}{2}+\frac{i \sqrt{11}}{2}\right) \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{1}{4}+\frac{i \sqrt{11}}{4}+\frac{i \left(\frac{1}{2}+\frac{i \sqrt{11}}{2}\right) \sqrt{3}}{6}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}-1}}-\frac{2 \left(\frac{1}{2}+\frac{i \sqrt{11}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(\frac{1}{2}-\frac{i \sqrt{11}}{2}\right) \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{1}{4}-\frac{i \sqrt{11}}{4}+\frac{i \left(\frac{1}{2}-\frac{i \sqrt{11}}{2}\right) \sqrt{3}}{6}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}-1}}$&$423$\\ elliptic&$\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{2 \left(-\frac{1}{2}+\frac{i \sqrt{11}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(\frac{1}{2}+\frac{i \sqrt{11}}{2}\right) \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{1}{4}+\frac{i \sqrt{11}}{4}+\frac{i \left(\frac{1}{2}+\frac{i \sqrt{11}}{2}\right) \sqrt{3}}{6}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}-1}}+\frac{2 \left(-\frac{1}{2}-\frac{i \sqrt{11}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(\frac{1}{2}-\frac{i \sqrt{11}}{2}\right) \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{1}{4}-\frac{i \sqrt{11}}{4}+\frac{i \left(\frac{1}{2}-\frac{i \sqrt{11}}{2}\right) \sqrt{3}}{6}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}-1}}$&$423$\\ \hline \end{longtable}"," ",0,"-1/2*RootOf(_Z^2-2)*ln((RootOf(_Z^2-2)*x^2+3*RootOf(_Z^2-2)*x-RootOf(_Z^2-2)+4*(x^3-1)^(1/2))/(x^2-x+3))","C"
374,1,59,25,0.427000," ","int((x^2-2*x-2)/(x^2+3*x-1)/(x^3-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}+2\right) x +3 \RootOf \left(\textit{\_Z}^{2}+2\right)-4 \sqrt{x^{3}-1}}{x^{2}+3 x -1}\right)}{2}$&$59$\\ default&$\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{3 \sqrt{13}\, \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{5}{2}-\frac{\sqrt{13}}{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}-1}\, \left(\frac{5}{2}-\frac{\sqrt{13}}{2}\right)}-\frac{i \sqrt{13}\, \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{5}{2}-\frac{\sqrt{13}}{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}-1}\, \left(\frac{5}{2}-\frac{\sqrt{13}}{2}\right)}+\frac{15 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{5}{2}-\frac{\sqrt{13}}{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}-1}\, \left(\frac{5}{2}-\frac{\sqrt{13}}{2}\right)}+\frac{5 i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{5}{2}-\frac{\sqrt{13}}{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}-1}\, \left(\frac{5}{2}-\frac{\sqrt{13}}{2}\right)}+\frac{3 \sqrt{13}\, \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{5}{2}+\frac{\sqrt{13}}{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}-1}\, \left(\frac{5}{2}+\frac{\sqrt{13}}{2}\right)}+\frac{i \sqrt{13}\, \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{5}{2}+\frac{\sqrt{13}}{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}-1}\, \left(\frac{5}{2}+\frac{\sqrt{13}}{2}\right)}+\frac{15 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{5}{2}+\frac{\sqrt{13}}{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}-1}\, \left(\frac{5}{2}+\frac{\sqrt{13}}{2}\right)}+\frac{5 i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{5}{2}+\frac{\sqrt{13}}{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}-1}\, \left(\frac{5}{2}+\frac{\sqrt{13}}{2}\right)}$&$1641$\\ elliptic&$-\frac{3 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}-\frac{3 \sqrt{13}\, \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{5}{2}-\frac{\sqrt{13}}{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}-1}\, \left(\frac{5}{2}-\frac{\sqrt{13}}{2}\right)}-\frac{i \sqrt{13}\, \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{5}{2}-\frac{\sqrt{13}}{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}-1}\, \left(\frac{5}{2}-\frac{\sqrt{13}}{2}\right)}+\frac{15 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{5}{2}-\frac{\sqrt{13}}{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}-1}\, \left(\frac{5}{2}-\frac{\sqrt{13}}{2}\right)}+\frac{5 i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{5}{2}-\frac{\sqrt{13}}{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}-1}\, \left(\frac{5}{2}-\frac{\sqrt{13}}{2}\right)}+\frac{3 \sqrt{13}\, \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{5}{2}+\frac{\sqrt{13}}{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}-1}\, \left(\frac{5}{2}+\frac{\sqrt{13}}{2}\right)}+\frac{i \sqrt{13}\, \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{5}{2}+\frac{\sqrt{13}}{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}-1}\, \left(\frac{5}{2}+\frac{\sqrt{13}}{2}\right)}+\frac{15 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{5}{2}+\frac{\sqrt{13}}{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}-1}\, \left(\frac{5}{2}+\frac{\sqrt{13}}{2}\right)}+\frac{5 i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{5}{2}+\frac{\sqrt{13}}{2}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}-1}\, \left(\frac{5}{2}+\frac{\sqrt{13}}{2}\right)}$&$1850$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^2+2)*ln(-(RootOf(_Z^2+2)*x^2-RootOf(_Z^2+2)*x+3*RootOf(_Z^2+2)-4*(x^3-1)^(1/2))/(x^2+3*x-1))","C"
375,1,24,23,0.327000," ","int((x^3-1)^(1/2)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{x^{3}-1}}{3 x^{3}}+\frac{\arctan \left(\sqrt{x^{3}-1}\right)}{3}$&$24$\\ risch&$-\frac{\sqrt{x^{3}-1}}{3 x^{3}}+\frac{\arctan \left(\sqrt{x^{3}-1}\right)}{3}$&$24$\\ elliptic&$-\frac{\sqrt{x^{3}-1}}{3 x^{3}}+\frac{\arctan \left(\sqrt{x^{3}-1}\right)}{3}$&$24$\\ trager&$-\frac{\sqrt{x^{3}-1}}{3 x^{3}}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \sqrt{x^{3}-1}+2 \RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{3}}\right)}{6}$&$57$\\ meijerg&$\frac{\sqrt{\mathrm{signum}\left(x^{3}-1\right)}\, \left(-\frac{2 \sqrt{\pi}}{x^{3}}-\left(-2 \ln \left(2\right)-1+3 \ln \left(x \right)+i \pi \right) \sqrt{\pi}+\frac{\sqrt{\pi}\, \left(-4 x^{3}+8\right)}{4 x^{3}}-\frac{2 \sqrt{\pi}\, \sqrt{-x^{3}+1}}{x^{3}}+2 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{3}+1}}{2}\right)\right)}{6 \sqrt{-\mathrm{signum}\left(x^{3}-1\right)}\, \sqrt{\pi}}$&$103$\\ \hline \end{longtable}"," ",0,"-1/3*(x^3-1)^(1/2)/x^3+1/3*arctan((x^3-1)^(1/2))","A"
376,1,24,23,0.230000," ","int(1/x^4/(x^3+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{x^{3}+1}}{3 x^{3}}+\frac{\arctanh \left(\sqrt{x^{3}+1}\right)}{3}$&$24$\\ risch&$-\frac{\sqrt{x^{3}+1}}{3 x^{3}}+\frac{\arctanh \left(\sqrt{x^{3}+1}\right)}{3}$&$24$\\ elliptic&$-\frac{\sqrt{x^{3}+1}}{3 x^{3}}+\frac{\arctanh \left(\sqrt{x^{3}+1}\right)}{3}$&$24$\\ trager&$-\frac{\sqrt{x^{3}+1}}{3 x^{3}}-\frac{\ln \left(-\frac{-x^{3}+2 \sqrt{x^{3}+1}-2}{x^{3}}\right)}{6}$&$38$\\ meijerg&$\frac{-\frac{\sqrt{\pi}}{x^{3}}-\frac{\left(1-2 \ln \left(2\right)+3 \ln \left(x \right)\right) \sqrt{\pi}}{2}+\frac{\sqrt{\pi}\, \left(4 x^{3}+8\right)}{8 x^{3}}-\frac{\sqrt{\pi}\, \sqrt{x^{3}+1}}{x^{3}}+\ln \left(\frac{1}{2}+\frac{\sqrt{x^{3}+1}}{2}\right) \sqrt{\pi}}{3 \sqrt{\pi}}$&$76$\\ \hline \end{longtable}"," ",0,"-1/3*(x^3+1)^(1/2)/x^3+1/3*arctanh((x^3+1)^(1/2))","A"
377,1,44,21,0.238000," ","int((1+x)/(-2+x)/(x^3+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(\frac{-x^{3}+6 x \sqrt{x^{3}+1}-12 x^{2}+6 \sqrt{x^{3}+1}+6 x -10}{\left(-2+x \right)^{3}}\right)}{3}$&$44$\\ default&$\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{1}{2}-\frac{i \sqrt{3}}{6}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}$&$240$\\ elliptic&$\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{1}{2}-\frac{i \sqrt{3}}{6}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}$&$240$\\ \hline \end{longtable}"," ",0,"1/3*ln((-x^3+6*x*(x^3+1)^(1/2)-12*x^2+6*(x^3+1)^(1/2)+6*x-10)/(-2+x)^3)","B"
378,1,24,23,0.211000," ","int((x^3+1)^(1/2)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{x^{3}+1}}{3 x^{3}}-\frac{\arctanh \left(\sqrt{x^{3}+1}\right)}{3}$&$24$\\ risch&$-\frac{\sqrt{x^{3}+1}}{3 x^{3}}-\frac{\arctanh \left(\sqrt{x^{3}+1}\right)}{3}$&$24$\\ elliptic&$-\frac{\sqrt{x^{3}+1}}{3 x^{3}}-\frac{\arctanh \left(\sqrt{x^{3}+1}\right)}{3}$&$24$\\ trager&$-\frac{\sqrt{x^{3}+1}}{3 x^{3}}+\frac{\ln \left(-\frac{-x^{3}+2 \sqrt{x^{3}+1}-2}{x^{3}}\right)}{6}$&$38$\\ meijerg&$-\frac{\frac{2 \sqrt{\pi}}{x^{3}}-\left(-2 \ln \left(2\right)-1+3 \ln \left(x \right)\right) \sqrt{\pi}-\frac{\sqrt{\pi}\, \left(4 x^{3}+8\right)}{4 x^{3}}+\frac{2 \sqrt{\pi}\, \sqrt{x^{3}+1}}{x^{3}}+2 \ln \left(\frac{1}{2}+\frac{\sqrt{x^{3}+1}}{2}\right) \sqrt{\pi}}{6 \sqrt{\pi}}$&$77$\\ \hline \end{longtable}"," ",0,"-1/3*(x^3+1)^(1/2)/x^3-1/3*arctanh((x^3+1)^(1/2))","A"
379,1,46,21,0.262000," ","int((1+x)/(-1+2*x)/(x^4+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(\frac{-10 x^{3}+6 x \sqrt{x^{4}+x}+6 x^{2}+6 \sqrt{x^{4}+x}-12 x -1}{\left(-1+2 x \right)^{3}}\right)}{3}$&$46$\\ default&$-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+2 \EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{3}{2}+\frac{3 i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$491$\\ elliptic&$-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+2 \EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{3}{2}+\frac{3 i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$491$\\ \hline \end{longtable}"," ",0,"1/3*ln((-10*x^3+6*x*(x^4+x)^(1/2)+6*x^2+6*(x^4+x)^(1/2)-12*x-1)/(-1+2*x)^3)","B"
380,1,30,27,0.578000," ","int((-1+x)/(x^4-4*x^3+4*x^2-5)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\ln \left(-x^{2}+\sqrt{x^{4}-4 x^{3}+4 x^{2}-5}+2 x \right)}{2}$&$30$\\ default&$-\frac{2 \left(-\sqrt{\sqrt{5}+1}-i \sqrt{\sqrt{5}-1}\right) \sqrt{\frac{\left(i \sqrt{\sqrt{5}-1}-\sqrt{\sqrt{5}+1}\right) \left(x -1+\sqrt{\sqrt{5}+1}\right)}{\left(i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(x -1-\sqrt{\sqrt{5}+1}\right)}}\, \left(x -1-\sqrt{\sqrt{5}+1}\right)^{2} \sqrt{\frac{\sqrt{\sqrt{5}+1}\, \left(x -1+i \sqrt{\sqrt{5}-1}\right)}{\left(-i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(x -1-\sqrt{\sqrt{5}+1}\right)}}\, \sqrt{\frac{\sqrt{\sqrt{5}+1}\, \left(x -1-i \sqrt{\sqrt{5}-1}\right)}{\left(i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(x -1-\sqrt{\sqrt{5}+1}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(i \sqrt{\sqrt{5}-1}-\sqrt{\sqrt{5}+1}\right) \left(x -1+\sqrt{\sqrt{5}+1}\right)}{\left(i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(x -1-\sqrt{\sqrt{5}+1}\right)}}, \sqrt{\frac{\left(i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(-\sqrt{\sqrt{5}+1}-i \sqrt{\sqrt{5}-1}\right)}{\left(i \sqrt{\sqrt{5}-1}-\sqrt{\sqrt{5}+1}\right) \left(-i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right)}}\right)}{\left(i \sqrt{\sqrt{5}-1}-\sqrt{\sqrt{5}+1}\right) \sqrt{\sqrt{5}+1}\, \sqrt{\left(x -1+\sqrt{\sqrt{5}+1}\right) \left(x -1-\sqrt{\sqrt{5}+1}\right) \left(x -1+i \sqrt{\sqrt{5}-1}\right) \left(x -1-i \sqrt{\sqrt{5}-1}\right)}}+\frac{2 \left(-\sqrt{\sqrt{5}+1}-i \sqrt{\sqrt{5}-1}\right) \sqrt{\frac{\left(i \sqrt{\sqrt{5}-1}-\sqrt{\sqrt{5}+1}\right) \left(x -1+\sqrt{\sqrt{5}+1}\right)}{\left(i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(x -1-\sqrt{\sqrt{5}+1}\right)}}\, \left(x -1-\sqrt{\sqrt{5}+1}\right)^{2} \sqrt{\frac{\sqrt{\sqrt{5}+1}\, \left(x -1+i \sqrt{\sqrt{5}-1}\right)}{\left(-i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(x -1-\sqrt{\sqrt{5}+1}\right)}}\, \sqrt{\frac{\sqrt{\sqrt{5}+1}\, \left(x -1-i \sqrt{\sqrt{5}-1}\right)}{\left(i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(x -1-\sqrt{\sqrt{5}+1}\right)}}\, \left(\left(1+\sqrt{\sqrt{5}+1}\right) \EllipticF \left(\sqrt{\frac{\left(i \sqrt{\sqrt{5}-1}-\sqrt{\sqrt{5}+1}\right) \left(x -1+\sqrt{\sqrt{5}+1}\right)}{\left(i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(x -1-\sqrt{\sqrt{5}+1}\right)}}, \sqrt{\frac{\left(i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(-\sqrt{\sqrt{5}+1}-i \sqrt{\sqrt{5}-1}\right)}{\left(i \sqrt{\sqrt{5}-1}-\sqrt{\sqrt{5}+1}\right) \left(-i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right)}}\right)-2 \sqrt{\sqrt{5}+1}\, \EllipticPi \left(\sqrt{\frac{\left(i \sqrt{\sqrt{5}-1}-\sqrt{\sqrt{5}+1}\right) \left(x -1+\sqrt{\sqrt{5}+1}\right)}{\left(i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(x -1-\sqrt{\sqrt{5}+1}\right)}}, \frac{i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}}{i \sqrt{\sqrt{5}-1}-\sqrt{\sqrt{5}+1}}, \sqrt{\frac{\left(i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(-\sqrt{\sqrt{5}+1}-i \sqrt{\sqrt{5}-1}\right)}{\left(i \sqrt{\sqrt{5}-1}-\sqrt{\sqrt{5}+1}\right) \left(-i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right)}}\right)\right)}{\left(i \sqrt{\sqrt{5}-1}-\sqrt{\sqrt{5}+1}\right) \sqrt{\sqrt{5}+1}\, \sqrt{\left(x -1+\sqrt{\sqrt{5}+1}\right) \left(x -1-\sqrt{\sqrt{5}+1}\right) \left(x -1+i \sqrt{\sqrt{5}-1}\right) \left(x -1-i \sqrt{\sqrt{5}-1}\right)}}$&$1110$\\ elliptic&$-\frac{2 \left(-\sqrt{\sqrt{5}+1}-i \sqrt{\sqrt{5}-1}\right) \sqrt{\frac{\left(i \sqrt{\sqrt{5}-1}-\sqrt{\sqrt{5}+1}\right) \left(x -1+\sqrt{\sqrt{5}+1}\right)}{\left(i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(x -1-\sqrt{\sqrt{5}+1}\right)}}\, \left(x -1-\sqrt{\sqrt{5}+1}\right)^{2} \sqrt{\frac{\sqrt{\sqrt{5}+1}\, \left(x -1+i \sqrt{\sqrt{5}-1}\right)}{\left(-i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(x -1-\sqrt{\sqrt{5}+1}\right)}}\, \sqrt{\frac{\sqrt{\sqrt{5}+1}\, \left(x -1-i \sqrt{\sqrt{5}-1}\right)}{\left(i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(x -1-\sqrt{\sqrt{5}+1}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(i \sqrt{\sqrt{5}-1}-\sqrt{\sqrt{5}+1}\right) \left(x -1+\sqrt{\sqrt{5}+1}\right)}{\left(i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(x -1-\sqrt{\sqrt{5}+1}\right)}}, \sqrt{\frac{\left(i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(-\sqrt{\sqrt{5}+1}-i \sqrt{\sqrt{5}-1}\right)}{\left(i \sqrt{\sqrt{5}-1}-\sqrt{\sqrt{5}+1}\right) \left(-i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right)}}\right)}{\left(i \sqrt{\sqrt{5}-1}-\sqrt{\sqrt{5}+1}\right) \sqrt{\sqrt{5}+1}\, \sqrt{\left(x -1+\sqrt{\sqrt{5}+1}\right) \left(x -1-\sqrt{\sqrt{5}+1}\right) \left(x -1+i \sqrt{\sqrt{5}-1}\right) \left(x -1-i \sqrt{\sqrt{5}-1}\right)}}+\frac{2 \left(-\sqrt{\sqrt{5}+1}-i \sqrt{\sqrt{5}-1}\right) \sqrt{\frac{\left(i \sqrt{\sqrt{5}-1}-\sqrt{\sqrt{5}+1}\right) \left(x -1+\sqrt{\sqrt{5}+1}\right)}{\left(i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(x -1-\sqrt{\sqrt{5}+1}\right)}}\, \left(x -1-\sqrt{\sqrt{5}+1}\right)^{2} \sqrt{\frac{\sqrt{\sqrt{5}+1}\, \left(x -1+i \sqrt{\sqrt{5}-1}\right)}{\left(-i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(x -1-\sqrt{\sqrt{5}+1}\right)}}\, \sqrt{\frac{\sqrt{\sqrt{5}+1}\, \left(x -1-i \sqrt{\sqrt{5}-1}\right)}{\left(i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(x -1-\sqrt{\sqrt{5}+1}\right)}}\, \left(\left(1+\sqrt{\sqrt{5}+1}\right) \EllipticF \left(\sqrt{\frac{\left(i \sqrt{\sqrt{5}-1}-\sqrt{\sqrt{5}+1}\right) \left(x -1+\sqrt{\sqrt{5}+1}\right)}{\left(i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(x -1-\sqrt{\sqrt{5}+1}\right)}}, \sqrt{\frac{\left(i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(-\sqrt{\sqrt{5}+1}-i \sqrt{\sqrt{5}-1}\right)}{\left(i \sqrt{\sqrt{5}-1}-\sqrt{\sqrt{5}+1}\right) \left(-i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right)}}\right)-2 \sqrt{\sqrt{5}+1}\, \EllipticPi \left(\sqrt{\frac{\left(i \sqrt{\sqrt{5}-1}-\sqrt{\sqrt{5}+1}\right) \left(x -1+\sqrt{\sqrt{5}+1}\right)}{\left(i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(x -1-\sqrt{\sqrt{5}+1}\right)}}, \frac{i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}}{i \sqrt{\sqrt{5}-1}-\sqrt{\sqrt{5}+1}}, \sqrt{\frac{\left(i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right) \left(-\sqrt{\sqrt{5}+1}-i \sqrt{\sqrt{5}-1}\right)}{\left(i \sqrt{\sqrt{5}-1}-\sqrt{\sqrt{5}+1}\right) \left(-i \sqrt{\sqrt{5}-1}+\sqrt{\sqrt{5}+1}\right)}}\right)\right)}{\left(i \sqrt{\sqrt{5}-1}-\sqrt{\sqrt{5}+1}\right) \sqrt{\sqrt{5}+1}\, \sqrt{\left(x -1+\sqrt{\sqrt{5}+1}\right) \left(x -1-\sqrt{\sqrt{5}+1}\right) \left(x -1+i \sqrt{\sqrt{5}-1}\right) \left(x -1-i \sqrt{\sqrt{5}-1}\right)}}$&$1110$\\ \hline \end{longtable}"," ",0,"-1/2*ln(-x^2+(x^4-4*x^3+4*x^2-5)^(1/2)+2*x)","A"
381,1,30,27,0.595000," ","int((2+x)/(x^4+8*x^3+16*x^2+13)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\ln \left(-x^{2}+\sqrt{x^{4}+8 x^{3}+16 x^{2}+13}-4 x \right)}{2}$&$30$\\ default&$\frac{4 \left(-\sqrt{4+i \sqrt{13}}-\sqrt{4-i \sqrt{13}}\right) \sqrt{\frac{\left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) \left(x +2+\sqrt{4+i \sqrt{13}}\right)}{\left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) \left(x +2-\sqrt{4+i \sqrt{13}}\right)}}\, \left(x +2-\sqrt{4+i \sqrt{13}}\right)^{2} \sqrt{\frac{\sqrt{4+i \sqrt{13}}\, \left(x +2+\sqrt{4-i \sqrt{13}}\right)}{\left(-\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) \left(x +2-\sqrt{4+i \sqrt{13}}\right)}}\, \sqrt{\frac{\sqrt{4+i \sqrt{13}}\, \left(x +2-\sqrt{4-i \sqrt{13}}\right)}{\left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) \left(x +2-\sqrt{4+i \sqrt{13}}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) \left(x +2+\sqrt{4+i \sqrt{13}}\right)}{\left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) \left(x +2-\sqrt{4+i \sqrt{13}}\right)}}, \sqrt{-\frac{\left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right)^{2}}{\left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) \left(-\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right)}}\right)}{\left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) \sqrt{4+i \sqrt{13}}\, \sqrt{\left(x +2+\sqrt{4+i \sqrt{13}}\right) \left(x +2-\sqrt{4+i \sqrt{13}}\right) \left(x +2+\sqrt{4-i \sqrt{13}}\right) \left(x +2-\sqrt{4-i \sqrt{13}}\right)}}+\frac{2 \left(-\sqrt{4+i \sqrt{13}}-\sqrt{4-i \sqrt{13}}\right) \sqrt{\frac{\left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) \left(x +2+\sqrt{4+i \sqrt{13}}\right)}{\left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) \left(x +2-\sqrt{4+i \sqrt{13}}\right)}}\, \left(x +2-\sqrt{4+i \sqrt{13}}\right)^{2} \sqrt{\frac{\sqrt{4+i \sqrt{13}}\, \left(x +2+\sqrt{4-i \sqrt{13}}\right)}{\left(-\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) \left(x +2-\sqrt{4+i \sqrt{13}}\right)}}\, \sqrt{\frac{\sqrt{4+i \sqrt{13}}\, \left(x +2-\sqrt{4-i \sqrt{13}}\right)}{\left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) \left(x +2-\sqrt{4+i \sqrt{13}}\right)}}\, \left(\left(-2+\sqrt{4+i \sqrt{13}}\right) \EllipticF \left(\sqrt{\frac{\left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) \left(x +2+\sqrt{4+i \sqrt{13}}\right)}{\left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) \left(x +2-\sqrt{4+i \sqrt{13}}\right)}}, \sqrt{-\frac{\left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right)^{2}}{\left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) \left(-\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right)}}\right)-2 \sqrt{4+i \sqrt{13}}\, \EllipticPi \left(\sqrt{\frac{\left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) \left(x +2+\sqrt{4+i \sqrt{13}}\right)}{\left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) \left(x +2-\sqrt{4+i \sqrt{13}}\right)}}, \frac{\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}}{\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}}, \sqrt{-\frac{\left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right)^{2}}{\left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) \left(-\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right)}}\right)\right)}{\left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) \sqrt{4+i \sqrt{13}}\, \sqrt{\left(x +2+\sqrt{4+i \sqrt{13}}\right) \left(x +2-\sqrt{4+i \sqrt{13}}\right) \left(x +2+\sqrt{4-i \sqrt{13}}\right) \left(x +2-\sqrt{4-i \sqrt{13}}\right)}}$&$1252$\\ elliptic&$\frac{4 \left(-\sqrt{4+i \sqrt{13}}-\sqrt{4-i \sqrt{13}}\right) \sqrt{\frac{\left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) \left(x +2+\sqrt{4+i \sqrt{13}}\right)}{\left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) \left(x +2-\sqrt{4+i \sqrt{13}}\right)}}\, \left(x +2-\sqrt{4+i \sqrt{13}}\right)^{2} \sqrt{\frac{\sqrt{4+i \sqrt{13}}\, \left(x +2+\sqrt{4-i \sqrt{13}}\right)}{\left(-\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) \left(x +2-\sqrt{4+i \sqrt{13}}\right)}}\, \sqrt{\frac{\sqrt{4+i \sqrt{13}}\, \left(x +2-\sqrt{4-i \sqrt{13}}\right)}{\left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) \left(x +2-\sqrt{4+i \sqrt{13}}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) \left(x +2+\sqrt{4+i \sqrt{13}}\right)}{\left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) \left(x +2-\sqrt{4+i \sqrt{13}}\right)}}, \sqrt{-\frac{\left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right)^{2}}{\left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) \left(-\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right)}}\right)}{\left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) \sqrt{4+i \sqrt{13}}\, \sqrt{\left(x +2+\sqrt{4+i \sqrt{13}}\right) \left(x +2-\sqrt{4+i \sqrt{13}}\right) \left(x +2+\sqrt{4-i \sqrt{13}}\right) \left(x +2-\sqrt{4-i \sqrt{13}}\right)}}+\frac{2 \left(-\sqrt{4+i \sqrt{13}}-\sqrt{4-i \sqrt{13}}\right) \sqrt{\frac{\left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) \left(x +2+\sqrt{4+i \sqrt{13}}\right)}{\left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) \left(x +2-\sqrt{4+i \sqrt{13}}\right)}}\, \left(x +2-\sqrt{4+i \sqrt{13}}\right)^{2} \sqrt{\frac{\sqrt{4+i \sqrt{13}}\, \left(x +2+\sqrt{4-i \sqrt{13}}\right)}{\left(-\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) \left(x +2-\sqrt{4+i \sqrt{13}}\right)}}\, \sqrt{\frac{\sqrt{4+i \sqrt{13}}\, \left(x +2-\sqrt{4-i \sqrt{13}}\right)}{\left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) \left(x +2-\sqrt{4+i \sqrt{13}}\right)}}\, \left(\left(-2+\sqrt{4+i \sqrt{13}}\right) \EllipticF \left(\sqrt{\frac{\left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) \left(x +2+\sqrt{4+i \sqrt{13}}\right)}{\left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) \left(x +2-\sqrt{4+i \sqrt{13}}\right)}}, \sqrt{-\frac{\left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right)^{2}}{\left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) \left(-\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right)}}\right)-2 \sqrt{4+i \sqrt{13}}\, \EllipticPi \left(\sqrt{\frac{\left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) \left(x +2+\sqrt{4+i \sqrt{13}}\right)}{\left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right) \left(x +2-\sqrt{4+i \sqrt{13}}\right)}}, \frac{\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}}{\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}}, \sqrt{-\frac{\left(\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right)^{2}}{\left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) \left(-\sqrt{4-i \sqrt{13}}+\sqrt{4+i \sqrt{13}}\right)}}\right)\right)}{\left(\sqrt{4-i \sqrt{13}}-\sqrt{4+i \sqrt{13}}\right) \sqrt{4+i \sqrt{13}}\, \sqrt{\left(x +2+\sqrt{4+i \sqrt{13}}\right) \left(x +2-\sqrt{4+i \sqrt{13}}\right) \left(x +2+\sqrt{4-i \sqrt{13}}\right) \left(x +2-\sqrt{4-i \sqrt{13}}\right)}}$&$1252$\\ \hline \end{longtable}"," ",0,"-1/2*ln(-x^2+(x^4+8*x^3+16*x^2+13)^(1/2)-4*x)","A"
382,1,24,23,0.048000," ","int(x/(a*x^4+b)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(\sqrt{a}\, x^{2}+\sqrt{a \,x^{4}+b}\right)}{2 \sqrt{a}}$&$24$\\ elliptic&$\frac{\ln \left(\sqrt{a}\, x^{2}+\sqrt{a \,x^{4}+b}\right)}{2 \sqrt{a}}$&$24$\\ \hline \end{longtable}"," ",0,"1/2*ln(a^(1/2)*x^2+(a*x^4+b)^(1/2))/a^(1/2)","A"
383,1,20,23,0.366000," ","int(1/x^7/(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\sqrt{x^{6}-1}}{6 x^{6}}-\frac{\arcsin \left(\frac{1}{x^{3}}\right)}{6}$&$20$\\ trager&$\frac{\sqrt{x^{6}-1}}{6 x^{6}}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)-\sqrt{x^{6}-1}}{x^{3}}\right)}{6}$&$44$\\ meijerg&$-\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(\frac{\sqrt{\pi}}{x^{6}}-\frac{\left(1-2 \ln \left(2\right)+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}}{2}-\frac{\sqrt{\pi}\, \left(-4 x^{6}+8\right)}{8 x^{6}}+\frac{\sqrt{\pi}\, \sqrt{-x^{6}+1}}{x^{6}}+\ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right) \sqrt{\pi}\right)}{6 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$100$\\ \hline \end{longtable}"," ",0,"1/6*(x^6-1)^(1/2)/x^6-1/6*arcsin(1/x^3)","A"
384,1,20,23,0.338000," ","int((x^6-1)^(1/2)/x^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{\sqrt{x^{6}-1}}{6 x^{6}}-\frac{\arcsin \left(\frac{1}{x^{3}}\right)}{6}$&$20$\\ trager&$-\frac{\sqrt{x^{6}-1}}{6 x^{6}}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{6}$&$41$\\ meijerg&$\frac{\sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(-\frac{2 \sqrt{\pi}}{x^{6}}-\left(-2 \ln \left(2\right)-1+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}+\frac{\sqrt{\pi}\, \left(-4 x^{6}+8\right)}{4 x^{6}}-\frac{2 \sqrt{\pi}\, \sqrt{-x^{6}+1}}{x^{6}}+2 \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right) \sqrt{\pi}\right)}{12 \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$103$\\ \hline \end{longtable}"," ",0,"-1/6*(x^6-1)^(1/2)/x^6-1/6*arcsin(1/x^3)","A"
385,1,30,23,0.244000," ","int((x^6-1)/x^7/(x^6+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}+1}}{6 x^{6}}-\frac{\ln \left(\frac{\sqrt{x^{6}+1}+1}{x^{3}}\right)}{2}$&$30$\\ risch&$\frac{\sqrt{x^{6}+1}}{6 x^{6}}+\frac{\ln \left(\frac{\sqrt{x^{6}+1}-1}{\sqrt{x^{6}}}\right)}{2}$&$32$\\ meijerg&$\frac{\left(-2 \ln \left(2\right)+6 \ln \left(x \right)\right) \sqrt{\pi}-2 \ln \left(\frac{1}{2}+\frac{\sqrt{x^{6}+1}}{2}\right) \sqrt{\pi}}{6 \sqrt{\pi}}-\frac{-\frac{\sqrt{\pi}}{x^{6}}-\frac{\left(1-2 \ln \left(2\right)+6 \ln \left(x \right)\right) \sqrt{\pi}}{2}+\frac{\sqrt{\pi}\, \left(4 x^{6}+8\right)}{8 x^{6}}-\frac{\sqrt{\pi}\, \sqrt{x^{6}+1}}{x^{6}}+\ln \left(\frac{1}{2}+\frac{\sqrt{x^{6}+1}}{2}\right) \sqrt{\pi}}{6 \sqrt{\pi}}$&$113$\\ \hline \end{longtable}"," ",0,"1/6*(x^6+1)^(1/2)/x^6-1/2*ln(((x^6+1)^(1/2)+1)/x^3)","A"
386,1,30,23,0.222000," ","int((x^6+1)^(1/2)/x^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\sqrt{x^{6}+1}}{6 x^{6}}+\frac{\ln \left(\frac{\sqrt{x^{6}+1}-1}{x^{3}}\right)}{6}$&$30$\\ risch&$-\frac{\sqrt{x^{6}+1}}{6 x^{6}}+\frac{\ln \left(\frac{\sqrt{x^{6}+1}-1}{\sqrt{x^{6}}}\right)}{6}$&$32$\\ meijerg&$-\frac{\frac{2 \sqrt{\pi}}{x^{6}}-\left(-2 \ln \left(2\right)-1+6 \ln \left(x \right)\right) \sqrt{\pi}-\frac{\sqrt{\pi}\, \left(4 x^{6}+8\right)}{4 x^{6}}+\frac{2 \sqrt{\pi}\, \sqrt{x^{6}+1}}{x^{6}}+2 \ln \left(\frac{1}{2}+\frac{\sqrt{x^{6}+1}}{2}\right) \sqrt{\pi}}{12 \sqrt{\pi}}$&$77$\\ \hline \end{longtable}"," ",0,"-1/6*(x^6+1)^(1/2)/x^6+1/6*ln(((x^6+1)^(1/2)-1)/x^3)","A"
387,1,28,27,0.145000," ","int((x^6+2)*(x^12+x^8-2*x^6+1)/x^10/(x^6-1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{6}-1\right)^{\frac{1}{4}} \left(x^{12}+9 x^{8}-2 x^{6}+1\right)}{9 x^{9}}$&$28$\\ risch&$\frac{\frac{2}{9} x^{18}-\frac{2}{3} x^{12}+2 x^{14}-2 x^{8}+\frac{2}{3} x^{6}-\frac{2}{9}}{\left(x^{6}-1\right)^{\frac{3}{4}} x^{9}}$&$38$\\ gosper&$\frac{2 \left(-1+x \right) \left(x^{2}+x +1\right) \left(1+x \right) \left(x^{2}-x +1\right) \left(x^{12}+9 x^{8}-2 x^{6}+1\right)}{9 x^{9} \left(x^{6}-1\right)^{\frac{3}{4}}}$&$48$\\ meijerg&$\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[\frac{3}{4}, \frac{3}{2}\right], \left[\frac{5}{2}\right], x^{6}\right) x^{9}}{9 \mathrm{signum}\left(x^{6}-1\right)^{\frac{3}{4}}}+\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[\frac{3}{4}, \frac{5}{6}\right], \left[\frac{11}{6}\right], x^{6}\right) x^{5}}{5 \mathrm{signum}\left(x^{6}-1\right)^{\frac{3}{4}}}+\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{1}{2}, \frac{3}{4}\right], \left[\frac{1}{2}\right], x^{6}\right)}{\mathrm{signum}\left(x^{6}-1\right)^{\frac{3}{4}} x^{3}}-\frac{2 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{3}{2}, \frac{3}{4}\right], \left[-\frac{1}{2}\right], x^{6}\right)}{9 \mathrm{signum}\left(x^{6}-1\right)^{\frac{3}{4}} x^{9}}-\frac{2 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{1}{6}, \frac{3}{4}\right], \left[\frac{5}{6}\right], x^{6}\right)}{\mathrm{signum}\left(x^{6}-1\right)^{\frac{3}{4}} x}$&$161$\\ \hline \end{longtable}"," ",0,"2/9*(x^6-1)^(1/4)*(x^12+9*x^8-2*x^6+1)/x^9","A"
388,1,62,26,0.523000," ","int((2*x^2+2*x-1)/(3*x^2-x+1)/(x^4-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+2\right) x +4 \sqrt{x^{4}-x}-\RootOf \left(\textit{\_Z}^{2}+2\right)}{3 x^{2}-x +1}\right)}{2}$&$62$\\ default&$\frac{4 \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{3 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{2 \left(\frac{4}{3}+\frac{i \sqrt{11}}{3}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\frac{5}{6}+\frac{i \sqrt{11}}{6}\right) \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\left(\frac{1}{2}-\frac{i \sqrt{11}}{2}\right) \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, -\frac{i \sqrt{3}\, \left(\frac{1}{6}+\frac{i \sqrt{11}}{6}\right)}{2}+\frac{1}{4}+\frac{i \sqrt{11}}{4}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{3 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{2 \left(\frac{4}{3}-\frac{i \sqrt{11}}{3}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\frac{5}{6}-\frac{i \sqrt{11}}{6}\right) \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\left(\frac{1}{2}+\frac{i \sqrt{11}}{2}\right) \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, -\frac{i \sqrt{3}\, \left(\frac{1}{6}-\frac{i \sqrt{11}}{6}\right)}{2}+\frac{1}{4}-\frac{i \sqrt{11}}{4}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{3 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$828$\\ elliptic&$\frac{4 \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{3 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{2 \left(\frac{4}{9}+\frac{i \sqrt{11}}{9}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\frac{5}{6}+\frac{i \sqrt{11}}{6}\right) \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\left(\frac{1}{2}-\frac{i \sqrt{11}}{2}\right) \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, -\frac{i \sqrt{3}\, \left(\frac{1}{6}+\frac{i \sqrt{11}}{6}\right)}{2}+\frac{1}{4}+\frac{i \sqrt{11}}{4}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{2 \left(\frac{4}{9}-\frac{i \sqrt{11}}{9}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\frac{5}{6}-\frac{i \sqrt{11}}{6}\right) \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\left(\frac{1}{2}+\frac{i \sqrt{11}}{2}\right) \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, -\frac{i \sqrt{3}\, \left(\frac{1}{6}-\frac{i \sqrt{11}}{6}\right)}{2}+\frac{1}{4}-\frac{i \sqrt{11}}{4}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$828$\\ \hline \end{longtable}"," ",0,"-1/2*RootOf(_Z^2+2)*ln((RootOf(_Z^2+2)*x^2-3*RootOf(_Z^2+2)*x+4*(x^4-x)^(1/2)-RootOf(_Z^2+2))/(3*x^2-x+1))","C"
389,1,22,28,0.115000," ","int((x^3+1)/x^3/(x^3-1)/(x^4-x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{4 \left(7 x^{3}-1\right)}{9 \left(x^{4}-x \right)^{\frac{1}{4}} x^{2}}$&$22$\\ risch&$-\frac{4 \left(7 x^{3}-1\right)}{9 x^{2} \left(x \left(x^{3}-1\right)\right)^{\frac{1}{4}}}$&$22$\\ trager&$-\frac{4 \left(7 x^{3}-1\right) \left(x^{4}-x \right)^{\frac{3}{4}}}{9 x^{3} \left(x^{3}-1\right)}$&$29$\\ meijerg&$\frac{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}} \left(-4 x^{3}+1\right)}{9 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}} \left(-x^{3}+1\right)^{\frac{1}{4}} x^{\frac{9}{4}}}-\frac{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}} x^{\frac{3}{4}}}{3 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}} \left(-x^{3}+1\right)^{\frac{1}{4}}}$&$73$\\ \hline \end{longtable}"," ",0,"-4/9*(7*x^3-1)/(x^4-x)^(1/4)/x^2","A"
390,1,56,26,0.388000," ","int((2*x^2-2*x-1)/(x^2+3*x-1)/(x^4+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{3 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}-2\right) x +\RootOf \left(\textit{\_Z}^{2}-2\right)+4 \sqrt{x^{4}+x}}{x^{2}+3 x -1}\right)}{2}$&$56$\\ default&$\text{Expression too large to display}$&$13798$\\ elliptic&$\text{Expression too large to display}$&$15100$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^2-2)*ln((3*RootOf(_Z^2-2)*x^2+RootOf(_Z^2-2)*x+RootOf(_Z^2-2)+4*(x^4+x)^(1/2))/(x^2+3*x-1))","C"
391,1,22,28,0.086000," ","int((x^2-1)/x^2/(x^2+1)/(x^4+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{\frac{14 x^{2}}{3}+\frac{2}{3}}{x \left(x^{4}+x^{2}\right)^{\frac{1}{4}}}$&$22$\\ risch&$\frac{\frac{14 x^{2}}{3}+\frac{2}{3}}{x \left(x^{2} \left(x^{2}+1\right)\right)^{\frac{1}{4}}}$&$24$\\ trager&$\frac{2 \left(7 x^{2}+1\right) \left(x^{4}+x^{2}\right)^{\frac{3}{4}}}{3 x^{3} \left(x^{2}+1\right)}$&$29$\\ meijerg&$\frac{\frac{8 x^{2}}{3}+\frac{2}{3}}{\left(x^{2}+1\right)^{\frac{1}{4}} x^{\frac{3}{2}}}+\frac{2 \sqrt{x}}{\left(x^{2}+1\right)^{\frac{1}{4}}}$&$33$\\ \hline \end{longtable}"," ",0,"2/3*(7*x^2+1)/(x^4+x^2)^(1/4)/x","A"
392,1,33,30,0.350000," ","int((-1+2*x)/(x^4-2*x^3+9*x^2-8*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(x^{2}-\sqrt{x^{4}-2 x^{3}+9 x^{2}-8 x}-x +4\right)$&$33$\\ default&$-\frac{2 \left(-\frac{1}{2}-\frac{i \sqrt{31}}{2}\right) \sqrt{\frac{\left(-\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{31}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{31}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{31}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(-1+x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(-\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{31}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{31}}{2}\right)}}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \sqrt{x \left(-1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{31}}{2}\right)}}+\frac{4 \left(-\frac{1}{2}-\frac{i \sqrt{31}}{2}\right) \sqrt{\frac{\left(-\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{31}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{31}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{31}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{31}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{31}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(-1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{31}}{2}}{-\frac{1}{2}+\frac{i \sqrt{31}}{2}}, \sqrt{\frac{\left(\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{31}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{31}}{2}\right)}}\right)\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \sqrt{x \left(-1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{31}}{2}\right)}}$&$487$\\ elliptic&$-\frac{2 \left(-\frac{1}{2}-\frac{i \sqrt{31}}{2}\right) \sqrt{\frac{\left(-\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{31}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{31}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{31}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(-1+x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(-\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{31}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{31}}{2}\right)}}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \sqrt{x \left(-1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{31}}{2}\right)}}+\frac{4 \left(-\frac{1}{2}-\frac{i \sqrt{31}}{2}\right) \sqrt{\frac{\left(-\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{31}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{31}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{31}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{31}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{31}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(-1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{31}}{2}}{-\frac{1}{2}+\frac{i \sqrt{31}}{2}}, \sqrt{\frac{\left(\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{31}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{31}}{2}\right)}}\right)\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \sqrt{x \left(-1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{31}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{31}}{2}\right)}}$&$487$\\ \hline \end{longtable}"," ",0,"-ln(x^2-(x^4-2*x^3+9*x^2-8*x)^(1/2)-x+4)","A"
393,0,0,29,0.121000," ","int((-a+2*x)/(-a*x+x^2+b-1)/(-a*x+x^2+b)^(1/4),x)","\[\int \frac{-a +2 x}{\left(-a x +x^{2}+b -1\right) \left(-a x +x^{2}+b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((-a+2*x)/(-a*x+x^2+b-1)/(-a*x+x^2+b)^(1/4),x)","F"
394,1,30,29,0.096000," ","int((x^3-4)*(x^3-1)^(2/3)/x^12,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(39 x^{9}+26 x^{6}+95 x^{3}-160\right) \left(x^{3}-1\right)^{\frac{2}{3}}}{440 x^{11}}$&$30$\\ gosper&$-\frac{\left(x^{2}+x +1\right) \left(-1+x \right) \left(39 x^{6}+65 x^{3}+160\right) \left(x^{3}-1\right)^{\frac{2}{3}}}{440 x^{11}}$&$34$\\ risch&$-\frac{39 x^{12}-13 x^{9}+69 x^{6}-255 x^{3}+160}{440 x^{11} \left(x^{3}-1\right)^{\frac{1}{3}}}$&$35$\\ meijerg&$\frac{4 \mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}} \left(-\frac{9}{20} x^{9}-\frac{3}{10} x^{6}-\frac{1}{4} x^{3}+1\right) \left(-x^{3}+1\right)^{\frac{2}{3}}}{11 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} x^{11}}-\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}} \left(-\frac{3}{5} x^{6}-\frac{2}{5} x^{3}+1\right) \left(-x^{3}+1\right)^{\frac{2}{3}}}{8 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} x^{8}}$&$95$\\ \hline \end{longtable}"," ",0,"-1/440*(39*x^9+26*x^6+95*x^3-160)/x^11*(x^3-1)^(2/3)","A"
395,1,57,27,0.378000," ","int((x^2+2*x-2)/(x^2-3*x-1)/(x^3+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}-2\right) x +3 \RootOf \left(\textit{\_Z}^{2}-2\right)+4 \sqrt{x^{3}+1}}{x^{2}-3 x -1}\right)}{2}$&$57$\\ default&$\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{3 \sqrt{13}\, \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{5}{2}-\frac{\sqrt{13}}{2}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}\, \left(-\frac{5}{2}-\frac{\sqrt{13}}{2}\right)}-\frac{i \sqrt{13}\, \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{5}{2}-\frac{\sqrt{13}}{2}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}\, \left(-\frac{5}{2}-\frac{\sqrt{13}}{2}\right)}+\frac{15 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{5}{2}-\frac{\sqrt{13}}{2}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}\, \left(-\frac{5}{2}-\frac{\sqrt{13}}{2}\right)}-\frac{5 i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{5}{2}-\frac{\sqrt{13}}{2}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}\, \left(-\frac{5}{2}-\frac{\sqrt{13}}{2}\right)}-\frac{3 \sqrt{13}\, \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{5}{2}+\frac{\sqrt{13}}{2}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}\, \left(-\frac{5}{2}+\frac{\sqrt{13}}{2}\right)}+\frac{i \sqrt{13}\, \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{5}{2}+\frac{\sqrt{13}}{2}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}\, \left(-\frac{5}{2}+\frac{\sqrt{13}}{2}\right)}+\frac{15 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{5}{2}+\frac{\sqrt{13}}{2}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}\, \left(-\frac{5}{2}+\frac{\sqrt{13}}{2}\right)}-\frac{5 i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{5}{2}+\frac{\sqrt{13}}{2}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}\, \left(-\frac{5}{2}+\frac{\sqrt{13}}{2}\right)}$&$1625$\\ elliptic&$\frac{3 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}+\frac{3 \sqrt{13}\, \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{5}{2}-\frac{\sqrt{13}}{2}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}\, \left(-\frac{5}{2}-\frac{\sqrt{13}}{2}\right)}-\frac{i \sqrt{13}\, \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{5}{2}-\frac{\sqrt{13}}{2}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}\, \left(-\frac{5}{2}-\frac{\sqrt{13}}{2}\right)}+\frac{15 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{5}{2}-\frac{\sqrt{13}}{2}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}\, \left(-\frac{5}{2}-\frac{\sqrt{13}}{2}\right)}-\frac{5 i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{5}{2}-\frac{\sqrt{13}}{2}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}\, \left(-\frac{5}{2}-\frac{\sqrt{13}}{2}\right)}-\frac{3 \sqrt{13}\, \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{5}{2}+\frac{\sqrt{13}}{2}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}\, \left(-\frac{5}{2}+\frac{\sqrt{13}}{2}\right)}+\frac{i \sqrt{13}\, \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{5}{2}+\frac{\sqrt{13}}{2}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}\, \left(-\frac{5}{2}+\frac{\sqrt{13}}{2}\right)}+\frac{15 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{5}{2}+\frac{\sqrt{13}}{2}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}\, \left(-\frac{5}{2}+\frac{\sqrt{13}}{2}\right)}-\frac{5 i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{5}{2}+\frac{\sqrt{13}}{2}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}\, \left(-\frac{5}{2}+\frac{\sqrt{13}}{2}\right)}$&$1830$\\ \hline \end{longtable}"," ",0,"-1/2*RootOf(_Z^2-2)*ln((RootOf(_Z^2-2)*x^2+RootOf(_Z^2-2)*x+3*RootOf(_Z^2-2)+4*(x^3+1)^(1/2))/(x^2-3*x-1))","C"
396,1,62,28,0.556000," ","int((x^2+2*x-2)/(2*x^2-x+3)/(x^3+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{2}+3 \RootOf \left(\textit{\_Z}^{2}+2\right) x +4 \sqrt{x^{3}+1}-\RootOf \left(\textit{\_Z}^{2}+2\right)}{2 x^{2}-x +3}\right)}{2}$&$62$\\ default&$\frac{\left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{\left(\frac{5}{4}+\frac{i \sqrt{23}}{4}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(-\frac{5}{12}+\frac{i \sqrt{23}}{12}\right) \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{5}{8}-\frac{i \sqrt{23}}{8}-\frac{i \sqrt{3}}{4}+\frac{i \left(\frac{1}{4}+\frac{i \sqrt{23}}{4}\right) \sqrt{3}}{6}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{\left(\frac{5}{4}-\frac{i \sqrt{23}}{4}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(-\frac{5}{12}-\frac{i \sqrt{23}}{12}\right) \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{5}{8}+\frac{i \sqrt{23}}{8}-\frac{i \sqrt{3}}{4}+\frac{i \left(\frac{1}{4}-\frac{i \sqrt{23}}{4}\right) \sqrt{3}}{6}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}$&$432$\\ elliptic&$\frac{\left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{2 \left(\frac{5}{8}+\frac{i \sqrt{23}}{8}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(-\frac{5}{12}+\frac{i \sqrt{23}}{12}\right) \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{5}{8}-\frac{i \sqrt{23}}{8}-\frac{i \sqrt{3}}{4}+\frac{i \left(\frac{1}{4}+\frac{i \sqrt{23}}{4}\right) \sqrt{3}}{6}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{2 \left(\frac{5}{8}-\frac{i \sqrt{23}}{8}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(-\frac{5}{12}-\frac{i \sqrt{23}}{12}\right) \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{5}{8}+\frac{i \sqrt{23}}{8}-\frac{i \sqrt{3}}{4}+\frac{i \left(\frac{1}{4}-\frac{i \sqrt{23}}{4}\right) \sqrt{3}}{6}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}$&$434$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^2+2)*ln(-(-2*RootOf(_Z^2+2)*x^2+3*RootOf(_Z^2+2)*x+4*(x^3+1)^(1/2)-RootOf(_Z^2+2))/(2*x^2-x+3))","C"
397,1,61,28,0.596000," ","int((x^2+2*x-2)/(3*x^2-4*x+2)/(x^3+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(\frac{3 \RootOf \left(\textit{\_Z}^{2}-3\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{2}-3\right) x +4 \RootOf \left(\textit{\_Z}^{2}-3\right)-6 \sqrt{x^{3}+1}}{3 x^{2}-4 x +2}\right)}{3}$&$61$\\ default&$\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}+1}}+\frac{4 \left(\frac{5}{6}+\frac{i \sqrt{2}}{6}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(-\frac{5}{9}+\frac{i \sqrt{2}}{9}\right) \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{5}{6}-\frac{i \sqrt{2}}{6}-\frac{7 i \sqrt{3}}{18}+\frac{i \left(\frac{2}{3}+\frac{i \sqrt{2}}{3}\right) \sqrt{3}}{6}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}+1}}+\frac{4 \left(\frac{5}{6}-\frac{i \sqrt{2}}{6}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(-\frac{5}{9}-\frac{i \sqrt{2}}{9}\right) \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{5}{6}+\frac{i \sqrt{2}}{6}-\frac{7 i \sqrt{3}}{18}+\frac{i \left(\frac{2}{3}-\frac{i \sqrt{2}}{3}\right) \sqrt{3}}{6}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}+1}}$&$435$\\ elliptic&$\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}+1}}+\frac{2 \left(\frac{5}{9}+\frac{i \sqrt{2}}{9}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(-\frac{5}{9}+\frac{i \sqrt{2}}{9}\right) \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{5}{6}-\frac{i \sqrt{2}}{6}-\frac{7 i \sqrt{3}}{18}+\frac{i \left(\frac{2}{3}+\frac{i \sqrt{2}}{3}\right) \sqrt{3}}{6}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{2 \left(\frac{5}{9}-\frac{i \sqrt{2}}{9}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(-\frac{5}{9}-\frac{i \sqrt{2}}{9}\right) \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{5}{6}+\frac{i \sqrt{2}}{6}-\frac{7 i \sqrt{3}}{18}+\frac{i \left(\frac{2}{3}-\frac{i \sqrt{2}}{3}\right) \sqrt{3}}{6}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}$&$435$\\ \hline \end{longtable}"," ",0,"1/3*RootOf(_Z^2-3)*ln((3*RootOf(_Z^2-3)*x^2-2*RootOf(_Z^2-3)*x+4*RootOf(_Z^2-3)-6*(x^3+1)^(1/2))/(3*x^2-4*x+2))","C"
398,1,30,29,0.076000," ","int((x^3-1)*(x^3+1)^(1/3)/x^11,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{3}+1\right)^{\frac{1}{3}} \left(12 x^{9}-4 x^{6}-9 x^{3}+7\right)}{70 x^{10}}$&$30$\\ risch&$\frac{12 x^{12}+8 x^{9}-13 x^{6}-2 x^{3}+7}{70 \left(x^{3}+1\right)^{\frac{2}{3}} x^{10}}$&$35$\\ gosper&$\frac{\left(x^{2}-x +1\right) \left(1+x \right) \left(12 x^{6}-16 x^{3}+7\right) \left(x^{3}+1\right)^{\frac{1}{3}}}{70 x^{10}}$&$36$\\ meijerg&$\frac{\left(\frac{9}{14} x^{9}-\frac{3}{14} x^{6}+\frac{1}{7} x^{3}+1\right) \left(x^{3}+1\right)^{\frac{1}{3}}}{10 x^{10}}-\frac{\left(-\frac{3}{4} x^{6}+\frac{1}{4} x^{3}+1\right) \left(x^{3}+1\right)^{\frac{1}{3}}}{7 x^{7}}$&$55$\\ \hline \end{longtable}"," ",0,"1/70*(x^3+1)^(1/3)*(12*x^9-4*x^6-9*x^3+7)/x^10","A"
399,1,30,29,0.085000," ","int((x^3-1)^(1/3)*(x^3+1)/x^11,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{3}-1\right)^{\frac{1}{3}} \left(12 x^{9}+4 x^{6}-9 x^{3}-7\right)}{70 x^{10}}$&$30$\\ gosper&$\frac{\left(x^{3}-1\right)^{\frac{1}{3}} \left(12 x^{6}+16 x^{3}+7\right) \left(-1+x \right) \left(x^{2}+x +1\right)}{70 x^{10}}$&$34$\\ risch&$\frac{12 x^{12}-8 x^{9}-13 x^{6}+2 x^{3}+7}{70 \left(x^{3}-1\right)^{\frac{2}{3}} x^{10}}$&$35$\\ meijerg&$-\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \left(-\frac{3}{4} x^{6}-\frac{1}{4} x^{3}+1\right) \left(-x^{3}+1\right)^{\frac{1}{3}}}{7 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x^{7}}-\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \left(-\frac{9}{14} x^{9}-\frac{3}{14} x^{6}-\frac{1}{7} x^{3}+1\right) \left(-x^{3}+1\right)^{\frac{1}{3}}}{10 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x^{10}}$&$95$\\ \hline \end{longtable}"," ",0,"1/70*(x^3-1)^(1/3)*(12*x^9+4*x^6-9*x^3-7)/x^10","A"
400,1,28,29,0.058000," ","int((3*x^3+x^2-2*x-1)/(x^3-3*x^2+3*x-1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{4 \left(-1+x \right) \left(135 x^{3}+245 x^{2}+158 x +47\right)}{585 \left(\left(-1+x \right)^{3}\right)^{\frac{1}{4}}}$&$28$\\ gosper&$\frac{4 \left(-1+x \right) \left(135 x^{3}+245 x^{2}+158 x +47\right)}{585 \left(x^{3}-3 x^{2}+3 x -1\right)^{\frac{1}{4}}}$&$36$\\ trager&$\frac{4 \left(135 x^{3}+245 x^{2}+158 x +47\right) \left(x^{3}-3 x^{2}+3 x -1\right)^{\frac{3}{4}}}{585 \left(-1+x \right)^{2}}$&$38$\\ \hline \end{longtable}"," ",0,"4/585*(-1+x)*(135*x^3+245*x^2+158*x+47)/((-1+x)^3)^(1/4)","A"
401,1,30,29,0.039000," ","int((x^3-3*x^2+3*x-1)^(1/4)*(3*x^3+x^2-2*x-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{4 \left(\left(-1+x \right)^{3}\right)^{\frac{1}{4}} \left(693 x^{4}+154 x^{3}-1029 x^{2}-549 x +731\right)}{4389}$&$30$\\ gosper&$\frac{4 \left(-1+x \right) \left(693 x^{3}+847 x^{2}-182 x -731\right) \left(x^{3}-3 x^{2}+3 x -1\right)^{\frac{1}{4}}}{4389}$&$36$\\ trager&$\left(\frac{12}{19} x^{4}+\frac{8}{57} x^{3}-\frac{196}{209} x^{2}-\frac{732}{1463} x +\frac{2924}{4389}\right) \left(x^{3}-3 x^{2}+3 x -1\right)^{\frac{1}{4}}$&$37$\\ \hline \end{longtable}"," ",0,"4/4389*((-1+x)^3)^(1/4)*(693*x^4+154*x^3-1029*x^2-549*x+731)","A"
402,1,841,29,0.480000," ","int((a*x^3-2*b)*(a*x^3+b)^(1/2)/x^2/(a*x^3-x^2+b),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{a}}{-\frac{3 \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{3 a \sqrt{a \,x^{3}+b}}-\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}-\textit{\_Z}^{2}+b \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{2}+3 b \right) \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i a \left(2 x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{a \left(x -\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{-3 \left(-a^{2} b \right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i a \left(2 x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{2 \left(-a^{2} b \right)^{\frac{1}{3}}}}\, \left(-i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a +i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a +\left(-a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}+\underline{\hspace{1.25 ex}}\alpha  \left(-a^{2} b \right)^{\frac{2}{3}} a -\left(-a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  a +2 a^{2} b -\left(-a^{2} b \right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}}{3}, \frac{-i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b +i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  -3 \left(-a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a -2 i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, a b -i \sqrt{3}\, a b -3 \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b +3 \left(-a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +3 a b}{2 a b}, \sqrt{\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  \left(3 \underline{\hspace{1.25 ex}}\alpha  a -2\right) \sqrt{a \,x^{3}+b}}\right)}{a^{2} b}+\frac{2 \sqrt{a \,x^{3}+b}}{x}$&$841$\\ risch&$-\frac{2 i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{a}}{-\frac{3 \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{3 a \sqrt{a \,x^{3}+b}}-\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}-\textit{\_Z}^{2}+b \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{2}+3 b \right) \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i a \left(2 x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{a \left(x -\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{-3 \left(-a^{2} b \right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i a \left(2 x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{2 \left(-a^{2} b \right)^{\frac{1}{3}}}}\, \left(-i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a +i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a +\left(-a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}+\underline{\hspace{1.25 ex}}\alpha  \left(-a^{2} b \right)^{\frac{2}{3}} a -\left(-a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  a +2 a^{2} b -\left(-a^{2} b \right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}}{3}, \frac{-i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b +i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  -3 \left(-a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a -2 i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, a b -i \sqrt{3}\, a b -3 \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b +3 \left(-a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +3 a b}{2 a b}, \sqrt{\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  \left(3 \underline{\hspace{1.25 ex}}\alpha  a -2\right) \sqrt{a \,x^{3}+b}}\right)}{a^{2} b}+\frac{2 \sqrt{a \,x^{3}+b}}{x}$&$841$\\ elliptic&$-\frac{2 i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{a}}{-\frac{3 \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{3 a \sqrt{a \,x^{3}+b}}-\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}-\textit{\_Z}^{2}+b \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{2}+3 b \right) \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i a \left(2 x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{a \left(x -\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{-3 \left(-a^{2} b \right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i a \left(2 x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{2 \left(-a^{2} b \right)^{\frac{1}{3}}}}\, \left(-i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a +i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a +\left(-a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}+\underline{\hspace{1.25 ex}}\alpha  \left(-a^{2} b \right)^{\frac{2}{3}} a -\left(-a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  a +2 a^{2} b -\left(-a^{2} b \right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}}{3}, \frac{-i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b +i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  -3 \left(-a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a -2 i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, a b -i \sqrt{3}\, a b -3 \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b +3 \left(-a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +3 a b}{2 a b}, \sqrt{\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  \left(3 \underline{\hspace{1.25 ex}}\alpha  a -2\right) \sqrt{a \,x^{3}+b}}\right)}{a^{2} b}+\frac{2 \sqrt{a \,x^{3}+b}}{x}$&$841$\\ \hline \end{longtable}"," ",0,"-2/3*I*3^(1/2)/a*(-a^2*b)^(1/3)*(I*(x+1/2/a*(-a^2*b)^(1/3)-1/2*I*3^(1/2)/a*(-a^2*b)^(1/3))*3^(1/2)*a/(-a^2*b)^(1/3))^(1/2)*((x-1/a*(-a^2*b)^(1/3))/(-3/2/a*(-a^2*b)^(1/3)+1/2*I*3^(1/2)/a*(-a^2*b)^(1/3)))^(1/2)*(-I*(x+1/2/a*(-a^2*b)^(1/3)+1/2*I*3^(1/2)/a*(-a^2*b)^(1/3))*3^(1/2)*a/(-a^2*b)^(1/3))^(1/2)/(a*x^3+b)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2/a*(-a^2*b)^(1/3)-1/2*I*3^(1/2)/a*(-a^2*b)^(1/3))*3^(1/2)*a/(-a^2*b)^(1/3))^(1/2),(I*3^(1/2)/a*(-a^2*b)^(1/3)/(-3/2/a*(-a^2*b)^(1/3)+1/2*I*3^(1/2)/a*(-a^2*b)^(1/3)))^(1/2))-I/a^2/b*2^(1/2)*sum((-_alpha^2+3*b)/_alpha/(3*_alpha*a-2)*(-a^2*b)^(1/3)*(1/2*I*a*(2*x+1/a*((-a^2*b)^(1/3)-I*3^(1/2)*(-a^2*b)^(1/3)))/(-a^2*b)^(1/3))^(1/2)*(a*(x-1/a*(-a^2*b)^(1/3))/(-3*(-a^2*b)^(1/3)+I*3^(1/2)*(-a^2*b)^(1/3)))^(1/2)*(-1/2*I*a*(2*x+1/a*((-a^2*b)^(1/3)+I*3^(1/2)*(-a^2*b)^(1/3)))/(-a^2*b)^(1/3))^(1/2)/(a*x^3+b)^(1/2)*(-I*(-a^2*b)^(1/3)*3^(1/2)*_alpha^2*a^2+I*(-a^2*b)^(2/3)*3^(1/2)*_alpha*a+I*(-a^2*b)^(1/3)*3^(1/2)*_alpha*a+(-a^2*b)^(1/3)*_alpha^2*a^2-I*(-a^2*b)^(2/3)*3^(1/2)+_alpha*(-a^2*b)^(2/3)*a-(-a^2*b)^(1/3)*_alpha*a+2*a^2*b-(-a^2*b)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2/a*(-a^2*b)^(1/3)-1/2*I*3^(1/2)/a*(-a^2*b)^(1/3))*3^(1/2)*a/(-a^2*b)^(1/3))^(1/2),1/2/a*(-I*(-a^2*b)^(2/3)*3^(1/2)*_alpha^2*a+I*3^(1/2)*_alpha*a^2*b+I*(-a^2*b)^(2/3)*3^(1/2)*_alpha-3*(-a^2*b)^(2/3)*_alpha^2*a-2*I*(-a^2*b)^(1/3)*3^(1/2)*a*b-I*3^(1/2)*a*b-3*_alpha*a^2*b+3*(-a^2*b)^(2/3)*_alpha+3*a*b)/b,(I*3^(1/2)/a*(-a^2*b)^(1/3)/(-3/2/a*(-a^2*b)^(1/3)+1/2*I*3^(1/2)/a*(-a^2*b)^(1/3)))^(1/2)),_alpha=RootOf(_Z^3*a-_Z^2+b))+2*(a*x^3+b)^(1/2)/x","C"
403,1,14,25,2.250000," ","int(1/(x^4+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\hypergeom \left(\left[\frac{1}{4}, \frac{1}{4}\right], \left[\frac{5}{4}\right], -x^{4}\right) x$&$14$\\ trager&$-\frac{\ln \left(2 \left(x^{4}+1\right)^{\frac{3}{4}} x -2 x^{2} \sqrt{x^{4}+1}+2 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}-2 x^{4}-1\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}\, x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \left(x^{4}+1\right)^{\frac{3}{4}} x -2 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{4}$&$113$\\ \hline \end{longtable}"," ",0,"hypergeom([1/4,1/4],[5/4],-x^4)*x","C"
404,1,62,27,0.551000," ","int((2*x^2-2*x-1)/(4*x^2+2*x+1)/(x^4+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{2}+4 \RootOf \left(\textit{\_Z}^{2}+3\right) x -\RootOf \left(\textit{\_Z}^{2}+3\right)-6 \sqrt{x^{4}+x}}{4 x^{2}+2 x +1}\right)}{3}$&$62$\\ default&$-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{3 \left(\frac{1}{4}-\frac{i \sqrt{3}}{12}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-1+\frac{i \sqrt{3}}{3}\right) \left(\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\left(-1-i \sqrt{3}\right) \EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, -\frac{2 i \left(-\frac{1}{4}+\frac{i \sqrt{3}}{4}\right) \sqrt{3}}{3}-\frac{2 i \sqrt{3}}{3}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{3 \left(\frac{1}{4}+\frac{i \sqrt{3}}{12}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-1-\frac{i \sqrt{3}}{3}\right) \left(\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\left(i \sqrt{3}-1\right) \EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, -\frac{2 i \left(-\frac{1}{4}-\frac{i \sqrt{3}}{4}\right) \sqrt{3}}{3}+\frac{i \sqrt{3}}{3}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$830$\\ elliptic&$-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}-\frac{2 \left(-\frac{3}{8}+\frac{i \sqrt{3}}{8}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-1+\frac{i \sqrt{3}}{3}\right) \left(\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\left(-1-i \sqrt{3}\right) \EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, -\frac{2 i \left(-\frac{1}{4}+\frac{i \sqrt{3}}{4}\right) \sqrt{3}}{3}-\frac{2 i \sqrt{3}}{3}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}-\frac{2 \left(-\frac{3}{8}-\frac{i \sqrt{3}}{8}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-1-\frac{i \sqrt{3}}{3}\right) \left(\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\left(i \sqrt{3}-1\right) \EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, -\frac{2 i \left(-\frac{1}{4}-\frac{i \sqrt{3}}{4}\right) \sqrt{3}}{3}+\frac{i \sqrt{3}}{3}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$830$\\ \hline \end{longtable}"," ",0,"-1/3*RootOf(_Z^2+3)*ln(-(2*RootOf(_Z^2+3)*x^2+4*RootOf(_Z^2+3)*x-RootOf(_Z^2+3)-6*(x^4+x)^(1/2))/(4*x^2+2*x+1))","C"
405,1,31,25,0.275000," ","int((x^4+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{-2 \sqrt{\pi}\, x^{\frac{3}{2}} \sqrt{x^{3}+1}-2 \sqrt{\pi}\, \arcsinh \left(x^{\frac{3}{2}}\right)}{6 \sqrt{\pi}}$&$31$\\ trager&$\frac{x \sqrt{x^{4}+x}}{3}-\frac{\ln \left(2 x^{3}-2 x \sqrt{x^{4}+x}+1\right)}{6}$&$32$\\ default&$\frac{x \sqrt{x^{4}+x}}{3}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$301$\\ elliptic&$\frac{x \sqrt{x^{4}+x}}{3}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$301$\\ risch&$\frac{x^{2} \left(x^{3}+1\right)}{3 \sqrt{x \left(x^{3}+1\right)}}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$310$\\ \hline \end{longtable}"," ",0,"-1/6/Pi^(1/2)*(-2*Pi^(1/2)*x^(3/2)*(x^3+1)^(1/2)-2*Pi^(1/2)*arcsinh(x^(3/2)))","A"
406,1,33,29,1.300000," ","int(1/(x^4-x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{2 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{4}} \hypergeom \left(\left[\frac{1}{4}, \frac{1}{4}\right], \left[\frac{5}{4}\right], x^{2}\right) \sqrt{x}}{\mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{4}}}$&$33$\\ trager&$\frac{\ln \left(\frac{2 \left(x^{4}-x^{2}\right)^{\frac{3}{4}}+2 \sqrt{x^{4}-x^{2}}\, x +2 x^{2} \left(x^{4}-x^{2}\right)^{\frac{1}{4}}+2 x^{3}-x}{x}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}-x^{2}}\, x +2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{4}-x^{2}\right)^{\frac{3}{4}}-2 x^{2} \left(x^{4}-x^{2}\right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right) x}{x}\right)}{2}$&$144$\\ \hline \end{longtable}"," ",0,"2/signum(x^2-1)^(1/4)*(-signum(x^2-1))^(1/4)*hypergeom([1/4,1/4],[5/4],x^2)*x^(1/2)","C"
407,0,0,29,0.018000," ","int((a*x^2+2*b)/(a*x^2+b)^(1/4)/(x^4-a*x^2-b),x)","\[\int \frac{a \,x^{2}+2 b}{\left(a \,x^{2}+b \right)^{\frac{1}{4}} \left(x^{4}-a \,x^{2}-b \right)}\, dx\]"," ",0,"int((a*x^2+2*b)/(a*x^2+b)^(1/4)/(x^4-a*x^2-b),x)","F"
408,1,34,31,0.756000," ","int((-1+2*x)/(x^4-2*x^3+3*x^2-2*x-2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(x^{2}-\sqrt{x^{4}-2 x^{3}+3 x^{2}-2 x -2}-x +1\right)$&$34$\\ default&$-\frac{2 \left(-\frac{\sqrt{-3+4 \sqrt{3}}}{2}-\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right) \sqrt{\frac{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)^{2} \sqrt{\frac{\sqrt{-3+4 \sqrt{3}}\, \left(x -\frac{1}{2}+\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right)}{\left(-\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}\, \sqrt{\frac{\sqrt{-3+4 \sqrt{3}}\, \left(x -\frac{1}{2}-\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}, \sqrt{\frac{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(-\frac{\sqrt{-3+4 \sqrt{3}}}{2}-\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(-\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \sqrt{-3+4 \sqrt{3}}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right)}}+\frac{4 \left(-\frac{\sqrt{-3+4 \sqrt{3}}}{2}-\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right) \sqrt{\frac{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)^{2} \sqrt{\frac{\sqrt{-3+4 \sqrt{3}}\, \left(x -\frac{1}{2}+\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right)}{\left(-\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}\, \sqrt{\frac{\sqrt{-3+4 \sqrt{3}}\, \left(x -\frac{1}{2}-\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}\, \left(\left(\frac{1}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \EllipticF \left(\sqrt{\frac{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}, \sqrt{\frac{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(-\frac{\sqrt{-3+4 \sqrt{3}}}{2}-\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(-\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}\right)-\sqrt{-3+4 \sqrt{3}}\, \EllipticPi \left(\sqrt{\frac{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}, \frac{\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}}{\frac{i \sqrt{3+4 \sqrt{3}}}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}}, \sqrt{\frac{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(-\frac{\sqrt{-3+4 \sqrt{3}}}{2}-\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(-\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}\right)\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \sqrt{-3+4 \sqrt{3}}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right)}}$&$1358$\\ elliptic&$-\frac{2 \left(-\frac{\sqrt{-3+4 \sqrt{3}}}{2}-\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right) \sqrt{\frac{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)^{2} \sqrt{\frac{\sqrt{-3+4 \sqrt{3}}\, \left(x -\frac{1}{2}+\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right)}{\left(-\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}\, \sqrt{\frac{\sqrt{-3+4 \sqrt{3}}\, \left(x -\frac{1}{2}-\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}, \sqrt{\frac{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(-\frac{\sqrt{-3+4 \sqrt{3}}}{2}-\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(-\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \sqrt{-3+4 \sqrt{3}}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right)}}+\frac{4 \left(-\frac{\sqrt{-3+4 \sqrt{3}}}{2}-\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right) \sqrt{\frac{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)^{2} \sqrt{\frac{\sqrt{-3+4 \sqrt{3}}\, \left(x -\frac{1}{2}+\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right)}{\left(-\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}\, \sqrt{\frac{\sqrt{-3+4 \sqrt{3}}\, \left(x -\frac{1}{2}-\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}\, \left(\left(\frac{1}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \EllipticF \left(\sqrt{\frac{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}, \sqrt{\frac{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(-\frac{\sqrt{-3+4 \sqrt{3}}}{2}-\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(-\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}\right)-\sqrt{-3+4 \sqrt{3}}\, \EllipticPi \left(\sqrt{\frac{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}, \frac{\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}}{\frac{i \sqrt{3+4 \sqrt{3}}}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}}, \sqrt{\frac{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(-\frac{\sqrt{-3+4 \sqrt{3}}}{2}-\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(-\frac{i \sqrt{3+4 \sqrt{3}}}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right)}}\right)\right)}{\left(\frac{i \sqrt{3+4 \sqrt{3}}}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \sqrt{-3+4 \sqrt{3}}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3+4 \sqrt{3}}}{2}\right)}}$&$1358$\\ \hline \end{longtable}"," ",0,"-ln(x^2-(x^4-2*x^3+3*x^2-2*x-2)^(1/2)-x+1)","A"
409,1,32,31,0.760000," ","int((-1+2*x)/(x^4-2*x^3+5*x^2-4*x-4)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(-2+x -x^{2}+\sqrt{x^{4}-2 x^{3}+5 x^{2}-4 x -4}\right)$&$32$\\ default&$\frac{2 i \left(-\frac{i \sqrt{7+8 \sqrt{2}}}{2}-\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)^{2} \sqrt{\frac{i \sqrt{7+8 \sqrt{2}}\, \left(x -\frac{1}{2}+\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right)}{\left(-\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}\, \sqrt{\frac{i \sqrt{7+8 \sqrt{2}}\, \left(x -\frac{1}{2}-\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}, \sqrt{\frac{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(-\frac{i \sqrt{7+8 \sqrt{2}}}{2}-\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(-\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \sqrt{7+8 \sqrt{2}}\, \sqrt{\left(x -\frac{1}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right)}}-\frac{4 i \left(-\frac{i \sqrt{7+8 \sqrt{2}}}{2}-\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)^{2} \sqrt{\frac{i \sqrt{7+8 \sqrt{2}}\, \left(x -\frac{1}{2}+\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right)}{\left(-\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}\, \sqrt{\frac{i \sqrt{7+8 \sqrt{2}}\, \left(x -\frac{1}{2}-\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}\, \left(\left(\frac{1}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}, \sqrt{\frac{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(-\frac{i \sqrt{7+8 \sqrt{2}}}{2}-\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(-\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}\right)-i \sqrt{7+8 \sqrt{2}}\, \EllipticPi \left(\sqrt{\frac{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}, \frac{\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}}{\frac{\sqrt{-7+8 \sqrt{2}}}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}}, \sqrt{\frac{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(-\frac{i \sqrt{7+8 \sqrt{2}}}{2}-\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(-\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}\right)\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \sqrt{7+8 \sqrt{2}}\, \sqrt{\left(x -\frac{1}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right)}}$&$1382$\\ elliptic&$\frac{2 i \left(-\frac{i \sqrt{7+8 \sqrt{2}}}{2}-\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)^{2} \sqrt{\frac{i \sqrt{7+8 \sqrt{2}}\, \left(x -\frac{1}{2}+\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right)}{\left(-\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}\, \sqrt{\frac{i \sqrt{7+8 \sqrt{2}}\, \left(x -\frac{1}{2}-\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}, \sqrt{\frac{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(-\frac{i \sqrt{7+8 \sqrt{2}}}{2}-\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(-\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \sqrt{7+8 \sqrt{2}}\, \sqrt{\left(x -\frac{1}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right)}}-\frac{4 i \left(-\frac{i \sqrt{7+8 \sqrt{2}}}{2}-\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)^{2} \sqrt{\frac{i \sqrt{7+8 \sqrt{2}}\, \left(x -\frac{1}{2}+\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right)}{\left(-\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}\, \sqrt{\frac{i \sqrt{7+8 \sqrt{2}}\, \left(x -\frac{1}{2}-\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}\, \left(\left(\frac{1}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}, \sqrt{\frac{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(-\frac{i \sqrt{7+8 \sqrt{2}}}{2}-\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(-\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}\right)-i \sqrt{7+8 \sqrt{2}}\, \EllipticPi \left(\sqrt{\frac{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}, \frac{\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}}{\frac{\sqrt{-7+8 \sqrt{2}}}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}}, \sqrt{\frac{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(-\frac{i \sqrt{7+8 \sqrt{2}}}{2}-\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(-\frac{\sqrt{-7+8 \sqrt{2}}}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right)}}\right)\right)}{\left(\frac{\sqrt{-7+8 \sqrt{2}}}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \sqrt{7+8 \sqrt{2}}\, \sqrt{\left(x -\frac{1}{2}+\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{-7+8 \sqrt{2}}}{2}\right)}}$&$1382$\\ \hline \end{longtable}"," ",0,"-ln(-2+x-x^2+(x^4-2*x^3+5*x^2-4*x-4)^(1/2))","A"
410,1,26,29,0.065000," ","int(1/x^4/(x^4+x^3)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{4 \left(-\frac{128}{77} x^{3}+\frac{96}{77} x^{2}-\frac{12}{11} x +1\right) \left(1+x \right)^{\frac{3}{4}}}{15 x^{\frac{15}{4}}}$&$26$\\ trager&$\frac{4 \left(128 x^{3}-96 x^{2}+84 x -77\right) \left(x^{4}+x^{3}\right)^{\frac{3}{4}}}{1155 x^{6}}$&$30$\\ gosper&$\frac{4 \left(1+x \right) \left(128 x^{3}-96 x^{2}+84 x -77\right)}{1155 x^{3} \left(x^{4}+x^{3}\right)^{\frac{1}{4}}}$&$33$\\ risch&$\frac{-\frac{4}{15}+\frac{4}{165} x -\frac{16}{385} x^{2}+\frac{128}{1155} x^{3}+\frac{512}{1155} x^{4}}{x^{3} \left(x^{3} \left(1+x \right)\right)^{\frac{1}{4}}}$&$35$\\ \hline \end{longtable}"," ",0,"-4/15*(-128/77*x^3+96/77*x^2-12/11*x+1)*(1+x)^(3/4)/x^(15/4)","A"
411,1,26,25,0.052000," ","int(x/(a*x^4-b)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(\sqrt{a}\, x^{2}+\sqrt{a \,x^{4}-b}\right)}{2 \sqrt{a}}$&$26$\\ elliptic&$\frac{\ln \left(\sqrt{a}\, x^{2}+\sqrt{a \,x^{4}-b}\right)}{2 \sqrt{a}}$&$26$\\ \hline \end{longtable}"," ",0,"1/2*ln(a^(1/2)*x^2+(a*x^4-b)^(1/2))/a^(1/2)","A"
412,1,30,29,0.072000," ","int((x^3+1)^(2/3)*(2*x^6-x^3+1)/x^12,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(227 x^{9}+142 x^{6}-45 x^{3}+40\right) \left(x^{3}+1\right)^{\frac{2}{3}}}{440 x^{11}}$&$30$\\ risch&$-\frac{227 x^{12}+369 x^{9}+97 x^{6}-5 x^{3}+40}{440 x^{11} \left(x^{3}+1\right)^{\frac{1}{3}}}$&$35$\\ gosper&$-\frac{\left(x^{2}-x +1\right) \left(1+x \right) \left(227 x^{6}-85 x^{3}+40\right) \left(x^{3}+1\right)^{\frac{2}{3}}}{440 x^{11}}$&$36$\\ meijerg&$-\frac{2 \left(x^{3}+1\right)^{\frac{5}{3}}}{5 x^{5}}+\frac{\left(-\frac{3}{5} x^{6}+\frac{2}{5} x^{3}+1\right) \left(x^{3}+1\right)^{\frac{2}{3}}}{8 x^{8}}-\frac{\left(\frac{9}{20} x^{9}-\frac{3}{10} x^{6}+\frac{1}{4} x^{3}+1\right) \left(x^{3}+1\right)^{\frac{2}{3}}}{11 x^{11}}$&$67$\\ \hline \end{longtable}"," ",0,"-1/440*(227*x^9+142*x^6-45*x^3+40)/x^11*(x^3+1)^(2/3)","A"
413,1,101,29,0.635000," ","int((x^4+3)*(-x^5+x)^(1/2)/(x^8-x^6-2*x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \sqrt{-x^{5}+x}\, x +\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{4}-x^{3}-1}\right)}{2}-\frac{\ln \left(\frac{x^{4}-x^{3}+2 \sqrt{-x^{5}+x}\, x -1}{x^{4}+x^{3}-1}\right)}{2}$&$101$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^2+1)*ln((-RootOf(_Z^2+1)*x^4-RootOf(_Z^2+1)*x^3+2*(-x^5+x)^(1/2)*x+RootOf(_Z^2+1))/(x^4-x^3-1))-1/2*ln((x^4-x^3+2*(-x^5+x)^(1/2)*x-1)/(x^4+x^3-1))","C"
414,1,30,29,0.128000," ","int((x^16-1)/x^8/(x^4-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{4}-1}\, \left(3 x^{12}+5 x^{8}-5 x^{4}-3\right)}{21 x^{7}}$&$30$\\ risch&$\frac{3 x^{16}+2 x^{12}-10 x^{8}+2 x^{4}+3}{21 x^{7} \sqrt{x^{4}-1}}$&$35$\\ gosper&$\frac{\left(x^{2}+1\right) \left(1+x \right) \left(-1+x \right) \left(3 x^{8}+8 x^{4}+3\right) \sqrt{x^{4}-1}}{21 x^{7}}$&$36$\\ elliptic&$\frac{\left(\frac{\left(x^{4}-1\right)^{\frac{7}{2}} \sqrt{2}}{7 x^{7}}+\frac{2 \left(x^{4}-1\right)^{\frac{3}{2}} \sqrt{2}}{3 x^{3}}\right) \sqrt{2}}{2}$&$37$\\ default&$\frac{x^{5} \sqrt{x^{4}-1}}{7}+\frac{5 x \sqrt{x^{4}-1}}{21}-\frac{\sqrt{x^{4}-1}}{7 x^{7}}-\frac{5 \sqrt{x^{4}-1}}{21 x^{3}}$&$48$\\ meijerg&$\frac{\sqrt{-\mathrm{signum}\left(x^{4}-1\right)}\, \hypergeom \left(\left[\frac{1}{2}, \frac{9}{4}\right], \left[\frac{13}{4}\right], x^{4}\right) x^{9}}{9 \sqrt{\mathrm{signum}\left(x^{4}-1\right)}}+\frac{\sqrt{-\mathrm{signum}\left(x^{4}-1\right)}\, \hypergeom \left(\left[-\frac{7}{4}, \frac{1}{2}\right], \left[-\frac{3}{4}\right], x^{4}\right)}{7 \sqrt{\mathrm{signum}\left(x^{4}-1\right)}\, x^{7}}$&$66$\\ \hline \end{longtable}"," ",0,"1/21*(x^4-1)^(1/2)*(3*x^12+5*x^8-5*x^4-3)/x^7","A"
415,1,16,29,0.090000," ","int(((-1+x)^(3/2)+(1+x)^(3/2))/(-1+x)^(3/2)/(1+x)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2}{\sqrt{1+x}}-\frac{2}{\sqrt{-1+x}}$&$16$\\ meijerg&$\frac{2 \sqrt{\pi}-\frac{2 \sqrt{\pi}}{\sqrt{1+x}}}{\sqrt{\pi}}-\frac{2 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{3}{2}} \left(\sqrt{\pi}-\frac{\sqrt{\pi}}{\sqrt{1-x}}\right)}{\sqrt{\pi}\, \mathrm{signum}\left(-1+x \right)^{\frac{3}{2}}}$&$56$\\ \hline \end{longtable}"," ",0,"-2/(1+x)^(1/2)-2/(-1+x)^(1/2)","A"
416,1,54,28,0.316000," ","int((1+x)/(-1+x)/(x^3+x^2+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) x^{2}+4 \RootOf \left(\textit{\_Z}^{2}-3\right) x +\RootOf \left(\textit{\_Z}^{2}-3\right)+6 \sqrt{x^{3}+x^{2}+x}}{\left(-1+x \right)^{2}}\right)}{3}$&$54$\\ default&$\frac{2 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}}+\frac{4 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}$&$271$\\ elliptic&$\frac{2 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}}+\frac{4 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}$&$271$\\ \hline \end{longtable}"," ",0,"-1/3*RootOf(_Z^2-3)*ln((RootOf(_Z^2-3)*x^2+4*RootOf(_Z^2-3)*x+RootOf(_Z^2-3)+6*(x^3+x^2+x)^(1/2))/(-1+x)^2)","C"
417,1,59,28,0.382000," ","int((x^2-1)/(x^2-x+1)/(x^3+x^2+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}+3 \RootOf \left(\textit{\_Z}^{2}-2\right) x +\RootOf \left(\textit{\_Z}^{2}-2\right)+4 \sqrt{x^{3}+x^{2}+x}}{x^{2}-x +1}\right)}{2}$&$59$\\ default&$\frac{2 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}}+\frac{2 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \left(-\frac{i \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{4}-\frac{5}{8}+\frac{3 i \sqrt{3}}{8}\right) \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}}+\frac{2 \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \left(-\frac{i \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{4}-\frac{5}{8}+\frac{i \sqrt{3}}{8}\right) \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}+\frac{i \sqrt{3}}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}}$&$425$\\ elliptic&$\frac{2 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}}+\frac{2 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \left(-\frac{i \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{4}-\frac{5}{8}+\frac{3 i \sqrt{3}}{8}\right) \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}}+\frac{2 \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \left(-\frac{i \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{4}-\frac{5}{8}+\frac{i \sqrt{3}}{8}\right) \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}+\frac{i \sqrt{3}}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}}$&$425$\\ \hline \end{longtable}"," ",0,"-1/2*RootOf(_Z^2-2)*ln((RootOf(_Z^2-2)*x^2+3*RootOf(_Z^2-2)*x+RootOf(_Z^2-2)+4*(x^3+x^2+x)^(1/2))/(x^2-x+1))","C"
418,1,49,28,0.247000," ","int((-1+x)/(1+x)/(x^4+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}-2\right) x +\sqrt{x^{4}+1}+\RootOf \left(\textit{\_Z}^{2}-2\right)}{\left(1+x \right)^{2}}\right)}{2}$&$49$\\ elliptic&$\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4 \sqrt{\left(x^{2}-1\right)^{2}+2 x^{2}}}\right)}{2}-\frac{\arctanh \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right) \sqrt{2}}{2}$&$56$\\ default&$\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4 \sqrt{x^{4}+1}}\right)}{2}+\frac{2 \left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{\sqrt{x^{4}+1}}$&$136$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^2-2)*ln(-(RootOf(_Z^2-2)*x^2+RootOf(_Z^2-2)*x+(x^4+1)^(1/2)+RootOf(_Z^2-2))/(1+x)^2)","C"
419,1,52,28,0.228000," ","int((1+x)/(-1+x)/(x^4+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}-2\right) x +\sqrt{x^{4}+1}-\RootOf \left(\textit{\_Z}^{2}-2\right)}{\left(-1+x \right)^{2}}\right)}{2}$&$52$\\ elliptic&$-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4 \sqrt{\left(x^{2}-1\right)^{2}+2 x^{2}}}\right)}{2}-\frac{\arctanh \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right) \sqrt{2}}{2}$&$56$\\ default&$\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4 \sqrt{x^{4}+1}}\right)}{2}+\frac{2 \left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{\sqrt{x^{4}+1}}$&$136$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^2-2)*ln(-(-RootOf(_Z^2-2)*x^2+RootOf(_Z^2-2)*x+(x^4+1)^(1/2)-RootOf(_Z^2-2))/(-1+x)^2)","C"
420,1,58,28,0.299000," ","int((1+x)/(-1+x)/(x^4+x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}-3\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}-3\right) x +2 \RootOf \left(\textit{\_Z}^{2}-3\right)+3 \sqrt{x^{4}+x^{2}+1}}{\left(-1+x \right)^{2}}\right)}{3}$&$58$\\ elliptic&$-\frac{\sqrt{3}\, \arctanh \left(\frac{\left(3 x^{2}+3\right) \sqrt{3}}{6 \sqrt{\left(x^{2}-1\right)^{2}+3 x^{2}}}\right)}{3}-\frac{\sqrt{6}\, \arctanh \left(\frac{\sqrt{6}\, \sqrt{x^{4}+x^{2}+1}\, \sqrt{2}}{6 x}\right) \sqrt{2}}{6}$&$65$\\ default&$\frac{2 \sqrt{1-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{-2+2 i \sqrt{3}}}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}-\frac{\sqrt{3}\, \arctanh \left(\frac{\left(3 x^{2}+3\right) \sqrt{3}}{6 \sqrt{x^{4}+x^{2}+1}}\right)}{3}-\frac{2 \sqrt{1-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , \frac{1}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+x^{2}+1}}$&$212$\\ \hline \end{longtable}"," ",0,"-1/3*RootOf(_Z^2-3)*ln(-(2*RootOf(_Z^2-3)*x^2-RootOf(_Z^2-3)*x+2*RootOf(_Z^2-3)+3*(x^4+x^2+1)^(1/2))/(-1+x)^2)","C"
421,1,44,32,1.156000," ","int((x^2+1)/(x^2-1)/(x^4+x^3-x^2-x+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(-\frac{x^{2}+2 \sqrt{x^{4}+x^{3}-x^{2}-x +1}+2 x -1}{\left(-1+x \right) \left(1+x \right)}\right)$&$44$\\ default&$\text{Expression too large to display}$&$4112$\\ elliptic&$\text{Expression too large to display}$&$105548$\\ \hline \end{longtable}"," ",0,"-ln(-(x^2+2*(x^4+x^3-x^2-x+1)^(1/2)+2*x-1)/(-1+x)/(1+x))","A"
422,1,61,30,1.345000," ","int(x/(x^4+2*x^3-3*x^2-11*x+11)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(2 x^{3}+2 x \sqrt{x^{4}+2 x^{3}-3 x^{2}-11 x +11}+6 x^{2}+4 \sqrt{x^{4}+2 x^{3}-3 x^{2}-11 x +11}-15\right)}{3}$&$61$\\ default&$\frac{2 \left(2+\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \sqrt{\frac{\left(-\frac{3 \left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}-\frac{3}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(-1+x \right)}{\left(-\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-2-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(x -\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+1\right)}}\, \left(x -\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+1\right)^{2} \sqrt{\frac{\left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-2\right) \left(x +\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+1-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right)}{\left(-\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-2+\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(x -\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+1\right)}}\, \sqrt{\frac{\left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-2\right) \left(x +\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+1+\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right)}{\left(-\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-2-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(x -\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+1\right)}}\, \left(\left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-1\right) \EllipticF \left(\sqrt{\frac{\left(-\frac{3 \left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}-\frac{3}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(-1+x \right)}{\left(-\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-2-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(x -\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+1\right)}}, \sqrt{\frac{\left(\frac{3 \left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{3}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(2+\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right)}{\left(2+\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(\frac{3 \left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{3}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right)}}\right)+\left(2-\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right) \EllipticPi \left(\sqrt{\frac{\left(-\frac{3 \left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}-\frac{3}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(-1+x \right)}{\left(-\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-2-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(x -\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+1\right)}}, \frac{-\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-2-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}}{-\frac{3 \left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}-\frac{3}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}}, \sqrt{\frac{\left(\frac{3 \left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{3}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(2+\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right)}{\left(2+\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(\frac{3 \left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{3}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right)}}\right)\right)}{\left(-\frac{3 \left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}-\frac{3}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-2\right) \sqrt{\left(-1+x \right) \left(x -\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+1\right) \left(x +\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+1-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(x +\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+1+\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right)}}$&$1625$\\ elliptic&$\frac{2 \left(2+\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \sqrt{\frac{\left(-\frac{3 \left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}-\frac{3}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(-1+x \right)}{\left(-\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-2-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(x -\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+1\right)}}\, \left(x -\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+1\right)^{2} \sqrt{\frac{\left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-2\right) \left(x +\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+1-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right)}{\left(-\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-2+\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(x -\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+1\right)}}\, \sqrt{\frac{\left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-2\right) \left(x +\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+1+\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right)}{\left(-\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-2-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(x -\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+1\right)}}\, \left(\left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-1\right) \EllipticF \left(\sqrt{\frac{\left(-\frac{3 \left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}-\frac{3}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(-1+x \right)}{\left(-\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-2-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(x -\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+1\right)}}, \sqrt{\frac{\left(\frac{3 \left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{3}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(2+\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right)}{\left(2+\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(\frac{3 \left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{3}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right)}}\right)+\left(2-\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right) \EllipticPi \left(\sqrt{\frac{\left(-\frac{3 \left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}-\frac{3}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(-1+x \right)}{\left(-\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-2-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(x -\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+1\right)}}, \frac{-\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}-\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-2-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}}{-\frac{3 \left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}-\frac{3}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}}, \sqrt{\frac{\left(\frac{3 \left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{3}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(2+\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right)}{\left(2+\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(\frac{3 \left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{3}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right)}}\right)\right)}{\left(-\frac{3 \left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}-\frac{3}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}+\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}-2\right) \sqrt{\left(-1+x \right) \left(x -\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+1\right) \left(x +\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+1-\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right) \left(x +\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{4}+\frac{1}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}+1+\frac{i \sqrt{3}\, \left(\frac{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}{2}-\frac{2}{\left(36+4 \sqrt{77}\right)^{\frac{1}{3}}}\right)}{2}\right)}}$&$1625$\\ \hline \end{longtable}"," ",0,"1/3*ln(2*x^3+2*x*(x^4+2*x^3-3*x^2-11*x+11)^(1/2)+6*x^2+4*(x^4+2*x^3-3*x^2-11*x+11)^(1/2)-15)","A"
423,1,59,30,1.119000," ","int((1+x)/(x^4+2*x^3-3*x^2-5*x+2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\ln \left(-2 x^{3}+2 \sqrt{x^{4}+2 x^{3}-3 x^{2}-5 x +2}\, x -2 \sqrt{x^{4}+2 x^{3}-3 x^{2}-5 x +2}+6 x -3\right)}{3}$&$59$\\ default&$\text{Expression too large to display}$&$2934$\\ elliptic&$\text{Expression too large to display}$&$2934$\\ \hline \end{longtable}"," ",0,"-1/3*ln(-2*x^3+2*(x^4+2*x^3-3*x^2-5*x+2)^(1/2)*x-2*(x^4+2*x^3-3*x^2-5*x+2)^(1/2)+6*x-3)","A"
424,1,61,30,1.389000," ","int(x/(x^4+2*x^3-3*x^2+3*x-3)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(2 x^{3}+2 x \sqrt{x^{4}+2 x^{3}-3 x^{2}+3 x -3}+6 x^{2}+4 \sqrt{x^{4}+2 x^{3}-3 x^{2}+3 x -3}-1\right)}{3}$&$61$\\ default&$\text{Expression too large to display}$&$1633$\\ elliptic&$\text{Expression too large to display}$&$1633$\\ \hline \end{longtable}"," ",0,"1/3*ln(2*x^3+2*x*(x^4+2*x^3-3*x^2+3*x-3)^(1/2)+6*x^2+4*(x^4+2*x^3-3*x^2+3*x-3)^(1/2)-1)","A"
425,1,53,30,0.567000," ","int((-x^6+1)^(1/2)*(x^6+2)/x^3/(x^6+x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{-x^{6}+1}}{x^{2}}-\frac{\ln \left(\frac{-x^{6}+x^{4}+2 \sqrt{-x^{6}+1}\, x^{2}+1}{x^{6}+x^{4}-1}\right)}{2}$&$53$\\ risch&$-\frac{x^{6}-1}{x^{2} \sqrt{-x^{6}+1}}-\frac{\ln \left(-\frac{-x^{6}+x^{4}+2 \sqrt{-x^{6}+1}\, x^{2}+1}{x^{6}+x^{4}-1}\right)}{2}$&$60$\\ \hline \end{longtable}"," ",0,"(-x^6+1)^(1/2)/x^2-1/2*ln((-x^6+x^4+2*(-x^6+1)^(1/2)*x^2+1)/(x^6+x^4-1))","A"
426,1,42,27,0.093000," ","int(x^(1/2)/(x^2-2)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\left(-\mathrm{signum}\left(-1+\frac{x^{2}}{2}\right)\right)^{\frac{3}{4}} 2^{\frac{1}{4}} \hypergeom \left(\left[\frac{3}{4}, \frac{3}{4}\right], \left[\frac{7}{4}\right], \frac{x^{2}}{2}\right) x^{\frac{3}{2}}}{3 \mathrm{signum}\left(-1+\frac{x^{2}}{2}\right)^{\frac{3}{4}}}$&$42$\\ \hline \end{longtable}"," ",0,"1/3*(-signum(-1+1/2*x^2))^(3/4)/signum(-1+1/2*x^2)^(3/4)*2^(1/4)*hypergeom([3/4,3/4],[7/4],1/2*x^2)*x^(3/2)","C"
427,0,0,31,0.112000," ","int((a+x)/(2*a*x+x^2+2*b-1)/(2*a*x+x^2+2*b)^(1/4),x)","\[\int \frac{a +x}{\left(2 a x +x^{2}+2 b -1\right) \left(2 a x +x^{2}+2 b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a+x)/(2*a*x+x^2+2*b-1)/(2*a*x+x^2+2*b)^(1/4),x)","F"
428,1,30,29,0.191000," ","int(1/(a*x^2+b*x+c)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(\frac{\frac{b}{2}+a x}{\sqrt{a}}+\sqrt{a \,x^{2}+b x +c}\right)}{\sqrt{a}}$&$30$\\ \hline \end{longtable}"," ",0,"ln((1/2*b+a*x)/a^(1/2)+(a*x^2+b*x+c)^(1/2))/a^(1/2)","A"
429,1,31,31,0.090000," ","int(x^11*(x^3-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\left(\frac{1}{13} x^{12}-\frac{1}{130} x^{9}-\frac{9}{910} x^{6}-\frac{27}{1820} x^{3}-\frac{81}{1820}\right) \left(x^{3}-1\right)^{\frac{1}{3}}$&$31$\\ risch&$\frac{\left(x^{3}-1\right)^{\frac{1}{3}} \left(140 x^{12}-14 x^{9}-18 x^{6}-27 x^{3}-81\right)}{1820}$&$32$\\ meijerg&$\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{1}{3}, 4\right], \left[5\right], x^{3}\right) x^{12}}{12 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}}}$&$33$\\ gosper&$\frac{\left(-1+x \right) \left(x^{2}+x +1\right) \left(140 x^{9}+126 x^{6}+108 x^{3}+81\right) \left(x^{3}-1\right)^{\frac{1}{3}}}{1820}$&$36$\\ \hline \end{longtable}"," ",0,"(1/13*x^12-1/130*x^9-9/910*x^6-27/1820*x^3-81/1820)*(x^3-1)^(1/3)","A"
430,1,61,28,0.570000," ","int((x^2-2*x-1)/(3*x^2+2*x+1)/(x^3-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(\frac{-3 \RootOf \left(\textit{\_Z}^{2}-3\right) x^{2}-4 \RootOf \left(\textit{\_Z}^{2}-3\right) x +6 \sqrt{x^{3}-x}+\RootOf \left(\textit{\_Z}^{2}-3\right)}{3 x^{2}+2 x +1}\right)}{3}$&$61$\\ elliptic&$\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticF \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}\right)}{3 \sqrt{x^{3}-x}}+\frac{\left(-\frac{4}{9}+\frac{i \sqrt{2}}{9}\right) \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \left(-1+\frac{i \sqrt{2}}{2}\right) \EllipticPi \left(\sqrt{1+x}, 1-\frac{i \sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}}+\frac{\left(-\frac{4}{9}-\frac{i \sqrt{2}}{9}\right) \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \left(-1-\frac{i \sqrt{2}}{2}\right) \EllipticPi \left(\sqrt{1+x}, 1+\frac{i \sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}}$&$165$\\ default&$\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticF \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}\right)}{3 \sqrt{x^{3}-x}}-\frac{4 \left(\frac{1}{3}-\frac{i \sqrt{2}}{12}\right) \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \left(-1+\frac{i \sqrt{2}}{2}\right) \EllipticPi \left(\sqrt{1+x}, 1-\frac{i \sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)}{3 \sqrt{x^{3}-x}}-\frac{4 \left(\frac{1}{3}+\frac{i \sqrt{2}}{12}\right) \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \left(-1-\frac{i \sqrt{2}}{2}\right) \EllipticPi \left(\sqrt{1+x}, 1+\frac{i \sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)}{3 \sqrt{x^{3}-x}}$&$167$\\ \hline \end{longtable}"," ",0,"1/3*RootOf(_Z^2-3)*ln((-3*RootOf(_Z^2-3)*x^2-4*RootOf(_Z^2-3)*x+6*(x^3-x)^(1/2)+RootOf(_Z^2-3))/(3*x^2+2*x+1))","C"
431,1,31,33,0.480000," ","int((x^2-1)*(-x^4-4*x^3-5*x^2-4*x-1)^(1/2)/(x^2+x+1)/(x^2+3*x+1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{x^{2}+x +1}{\sqrt{-x^{4}-4 x^{3}-5 x^{2}-4 x -1}}$&$31$\\ default&$\frac{-x^{2}-x -1}{\sqrt{\left(x^{2}+3 x +1\right) \left(-x^{2}-x -1\right)}}$&$33$\\ elliptic&$\frac{-x^{2}-x -1}{\sqrt{\left(x^{2}+3 x +1\right) \left(-x^{2}-x -1\right)}}$&$33$\\ gosper&$\frac{\sqrt{-x^{4}-4 x^{3}-5 x^{2}-4 x -1}}{x^{2}+3 x +1}$&$34$\\ trager&$\frac{\sqrt{-x^{4}-4 x^{3}-5 x^{2}-4 x -1}}{x^{2}+3 x +1}$&$34$\\ \hline \end{longtable}"," ",0,"-(x^2+x+1)/(-x^4-4*x^3-5*x^2-4*x-1)^(1/2)","A"
432,1,20,27,0.184000," ","int((x^4-1)/x^3/(x^4+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arcsinh \left(x^{2}\right)}{2}+\frac{\sqrt{x^{4}+1}}{2 x^{2}}$&$20$\\ meijerg&$\frac{\arcsinh \left(x^{2}\right)}{2}+\frac{\sqrt{x^{4}+1}}{2 x^{2}}$&$20$\\ risch&$\frac{\arcsinh \left(x^{2}\right)}{2}+\frac{\sqrt{x^{4}+1}}{2 x^{2}}$&$20$\\ elliptic&$\frac{\arcsinh \left(x^{2}\right)}{2}+\frac{\sqrt{x^{4}+1}}{2 x^{2}}$&$20$\\ trager&$\frac{\sqrt{x^{4}+1}}{2 x^{2}}-\frac{\ln \left(x^{2}-\sqrt{x^{4}+1}\right)}{2}$&$30$\\ \hline \end{longtable}"," ",0,"1/2*arcsinh(x^2)+1/2*(x^4+1)^(1/2)/x^2","A"
433,1,25,31,0.096000," ","int((x^3-1)/x^6/(x^3+1)/(x^4+x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{4 \left(20 x^{6}+5 x^{3}-1\right)}{21 \left(x^{4}+x \right)^{\frac{1}{4}} x^{5}}$&$25$\\ risch&$-\frac{4 \left(20 x^{6}+5 x^{3}-1\right)}{21 x^{5} \left(x \left(x^{3}+1\right)\right)^{\frac{1}{4}}}$&$27$\\ trager&$-\frac{4 \left(x^{4}+x \right)^{\frac{3}{4}} \left(20 x^{6}+5 x^{3}-1\right)}{21 x^{6} \left(x^{3}+1\right)}$&$32$\\ meijerg&$\frac{4 \left(-32 x^{6}-8 x^{3}+3\right) \left(x^{3}+1\right)^{\frac{3}{4}}}{21 \left(3 x^{3}+3\right) x^{\frac{21}{4}}}-\frac{4 \left(4 x^{3}+1\right)}{9 \left(x^{3}+1\right)^{\frac{1}{4}} x^{\frac{9}{4}}}$&$54$\\ \hline \end{longtable}"," ",0,"-4/21*(20*x^6+5*x^3-1)/(x^4+x)^(1/4)/x^5","A"
434,1,31,27,0.251000," ","int((x^4+x)^(1/2)/x^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\frac{4 \sqrt{\pi}\, \sqrt{x^{3}+1}}{x^{\frac{3}{2}}}-4 \sqrt{\pi}\, \arcsinh \left(x^{\frac{3}{2}}\right)}{6 \sqrt{\pi}}$&$31$\\ trager&$-\frac{2 \sqrt{x^{4}+x}}{3 x^{2}}-\frac{\ln \left(2 x^{3}-2 x \sqrt{x^{4}+x}+1\right)}{3}$&$34$\\ default&$-\frac{2 \sqrt{x^{4}+x}}{3 x^{2}}+\frac{2 \sqrt{-\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \left(\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \EllipticF \left(\sqrt{-\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \sqrt{-\frac{i \sqrt{3}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticPi \left(\sqrt{-\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, -\frac{1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{-\frac{i \sqrt{3}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$300$\\ elliptic&$-\frac{2 \sqrt{x^{4}+x}}{3 x^{2}}+\frac{2 \sqrt{-\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \left(\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \EllipticF \left(\sqrt{-\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \sqrt{-\frac{i \sqrt{3}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticPi \left(\sqrt{-\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, -\frac{1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{-\frac{i \sqrt{3}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$300$\\ risch&$-\frac{2 \left(x^{3}+1\right)}{3 x \sqrt{x \left(x^{3}+1\right)}}-\frac{2 \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$310$\\ \hline \end{longtable}"," ",0,"-1/6/Pi^(1/2)*(4*Pi^(1/2)/x^(3/2)*(x^3+1)^(1/2)-4*Pi^(1/2)*arcsinh(x^(3/2)))","A"
435,1,30,31,0.070000," ","int(1/x^8/(x^4+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{2 \left(-\frac{128}{77} x^{6}+\frac{96}{77} x^{4}-\frac{12}{11} x^{2}+1\right) \left(x^{2}+1\right)^{\frac{3}{4}}}{15 x^{\frac{15}{2}}}$&$30$\\ trager&$\frac{2 \left(x^{4}+x^{2}\right)^{\frac{3}{4}} \left(128 x^{6}-96 x^{4}+84 x^{2}-77\right)}{1155 x^{9}}$&$32$\\ gosper&$\frac{2 \left(x^{2}+1\right) \left(128 x^{6}-96 x^{4}+84 x^{2}-77\right)}{1155 x^{7} \left(x^{4}+x^{2}\right)^{\frac{1}{4}}}$&$37$\\ risch&$\frac{\frac{2}{165} x^{2}-\frac{2}{15}-\frac{8}{385} x^{4}+\frac{64}{1155} x^{6}+\frac{256}{1155} x^{8}}{x^{7} \left(x^{2} \left(x^{2}+1\right)\right)^{\frac{1}{4}}}$&$39$\\ \hline \end{longtable}"," ",0,"-2/15*(-128/77*x^6+96/77*x^4-12/11*x^2+1)*(x^2+1)^(3/4)/x^(15/2)","A"
436,1,36,33,0.490000," ","int((1-2*x)/(x^4-2*x^3-4*x^2+5*x+5)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(2 x^{2}+2 \sqrt{x^{4}-2 x^{3}-4 x^{2}+5 x +5}-2 x -5\right)$&$36$\\ default&$\frac{2 \left(-\frac{\sqrt{11-2 \sqrt{5}}}{2}-\frac{\sqrt{11+2 \sqrt{5}}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)^{2} \sqrt{-\frac{\left(x -\frac{1}{2}+\frac{\sqrt{11+2 \sqrt{5}}}{2}\right) \sqrt{11-2 \sqrt{5}}}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}}\, \sqrt{\frac{\sqrt{11-2 \sqrt{5}}\, \left(x -\frac{1}{2}-\frac{\sqrt{11+2 \sqrt{5}}}{2}\right)}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}}, \sqrt{\frac{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)^{2}}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)^{2}}}\right)}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \sqrt{11-2 \sqrt{5}}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{11+2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11+2 \sqrt{5}}}{2}\right)}}-\frac{4 \left(-\frac{\sqrt{11-2 \sqrt{5}}}{2}-\frac{\sqrt{11+2 \sqrt{5}}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)^{2} \sqrt{-\frac{\left(x -\frac{1}{2}+\frac{\sqrt{11+2 \sqrt{5}}}{2}\right) \sqrt{11-2 \sqrt{5}}}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}}\, \sqrt{\frac{\sqrt{11-2 \sqrt{5}}\, \left(x -\frac{1}{2}-\frac{\sqrt{11+2 \sqrt{5}}}{2}\right)}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}}\, \left(\left(\frac{1}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}}, \sqrt{\frac{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)^{2}}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)^{2}}}\right)-\sqrt{11-2 \sqrt{5}}\, \EllipticPi \left(\sqrt{\frac{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}}, \frac{\frac{\sqrt{11+2 \sqrt{5}}}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}}{\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}}, \sqrt{\frac{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)^{2}}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)^{2}}}\right)\right)}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \sqrt{11-2 \sqrt{5}}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{11+2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11+2 \sqrt{5}}}{2}\right)}}$&$1182$\\ elliptic&$\frac{2 \left(-\frac{\sqrt{11-2 \sqrt{5}}}{2}-\frac{\sqrt{11+2 \sqrt{5}}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)^{2} \sqrt{-\frac{\left(x -\frac{1}{2}+\frac{\sqrt{11+2 \sqrt{5}}}{2}\right) \sqrt{11-2 \sqrt{5}}}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}}\, \sqrt{\frac{\sqrt{11-2 \sqrt{5}}\, \left(x -\frac{1}{2}-\frac{\sqrt{11+2 \sqrt{5}}}{2}\right)}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}}, \sqrt{\frac{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)^{2}}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)^{2}}}\right)}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \sqrt{11-2 \sqrt{5}}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{11+2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11+2 \sqrt{5}}}{2}\right)}}-\frac{4 \left(-\frac{\sqrt{11-2 \sqrt{5}}}{2}-\frac{\sqrt{11+2 \sqrt{5}}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)^{2} \sqrt{-\frac{\left(x -\frac{1}{2}+\frac{\sqrt{11+2 \sqrt{5}}}{2}\right) \sqrt{11-2 \sqrt{5}}}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}}\, \sqrt{\frac{\sqrt{11-2 \sqrt{5}}\, \left(x -\frac{1}{2}-\frac{\sqrt{11+2 \sqrt{5}}}{2}\right)}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}}\, \left(\left(\frac{1}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}}, \sqrt{\frac{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)^{2}}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)^{2}}}\right)-\sqrt{11-2 \sqrt{5}}\, \EllipticPi \left(\sqrt{\frac{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)}}, \frac{\frac{\sqrt{11+2 \sqrt{5}}}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}}{\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}}, \sqrt{\frac{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)^{2}}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right)^{2}}}\right)\right)}{\left(\frac{\sqrt{11+2 \sqrt{5}}}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \sqrt{11-2 \sqrt{5}}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11-2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{11+2 \sqrt{5}}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{11+2 \sqrt{5}}}{2}\right)}}$&$1182$\\ \hline \end{longtable}"," ",0,"-ln(2*x^2+2*(x^4-2*x^3-4*x^2+5*x+5)^(1/2)-2*x-5)","A"
437,1,32,31,0.077000," ","int(1/x^4/(x^4-x^3)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(128 x^{3}+96 x^{2}+84 x +77\right) \left(x^{4}-x^{3}\right)^{\frac{3}{4}}}{1155 x^{6}}$&$32$\\ gosper&$\frac{4 \left(-1+x \right) \left(128 x^{3}+96 x^{2}+84 x +77\right)}{1155 x^{3} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}}$&$35$\\ risch&$\frac{-\frac{4}{15}-\frac{4}{165} x -\frac{16}{385} x^{2}-\frac{128}{1155} x^{3}+\frac{512}{1155} x^{4}}{x^{3} \left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}}}$&$35$\\ meijerg&$-\frac{4 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{4}} \left(\frac{128}{77} x^{3}+\frac{96}{77} x^{2}+\frac{12}{11} x +1\right) \left(1-x \right)^{\frac{3}{4}}}{15 \mathrm{signum}\left(-1+x \right)^{\frac{1}{4}} x^{\frac{15}{4}}}$&$42$\\ \hline \end{longtable}"," ",0,"4/1155*(128*x^3+96*x^2+84*x+77)*(x^4-x^3)^(3/4)/x^6","A"
438,1,36,33,0.408000," ","int((1+2*x)/(x^4+2*x^3-2*x^2-3*x-4)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(-2 x^{2}+2 \sqrt{x^{4}+2 x^{3}-2 x^{2}-3 x -4}-2 x +3\right)$&$36$\\ default&$-\frac{2 i \left(-\frac{i \sqrt{3}}{2}-\frac{\sqrt{17}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{17}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{\frac{i \sqrt{3}\, \left(x +\frac{1}{2}+\frac{\sqrt{17}}{2}\right)}{\left(-\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{i \sqrt{3}\, \left(x +\frac{1}{2}-\frac{\sqrt{17}}{2}\right)}{\left(\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{3}\, \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{17}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \sqrt{\frac{\left(\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{i \sqrt{3}}{2}-\frac{\sqrt{17}}{2}\right)}{\left(\frac{\sqrt{17}}{2}-\frac{i \sqrt{3}}{2}\right) \left(-\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right)}}\right)}{3 \left(\frac{\sqrt{17}}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{\sqrt{17}}{2}\right) \left(x +\frac{1}{2}-\frac{\sqrt{17}}{2}\right)}}-\frac{4 i \left(-\frac{i \sqrt{3}}{2}-\frac{\sqrt{17}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{17}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{\frac{i \sqrt{3}\, \left(x +\frac{1}{2}+\frac{\sqrt{17}}{2}\right)}{\left(-\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{i \sqrt{3}\, \left(x +\frac{1}{2}-\frac{\sqrt{17}}{2}\right)}{\left(\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{3}\, \left(\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{17}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \sqrt{\frac{\left(\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{i \sqrt{3}}{2}-\frac{\sqrt{17}}{2}\right)}{\left(\frac{\sqrt{17}}{2}-\frac{i \sqrt{3}}{2}\right) \left(-\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right)}}\right)-i \sqrt{3}\, \EllipticPi \left(\sqrt{\frac{\left(\frac{\sqrt{17}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \frac{\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}}{\frac{\sqrt{17}}{2}-\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{i \sqrt{3}}{2}-\frac{\sqrt{17}}{2}\right)}{\left(\frac{\sqrt{17}}{2}-\frac{i \sqrt{3}}{2}\right) \left(-\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{3 \left(\frac{\sqrt{17}}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{\sqrt{17}}{2}\right) \left(x +\frac{1}{2}-\frac{\sqrt{17}}{2}\right)}}$&$782$\\ elliptic&$-\frac{2 i \left(-\frac{i \sqrt{3}}{2}-\frac{\sqrt{17}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{17}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{\frac{i \sqrt{3}\, \left(x +\frac{1}{2}+\frac{\sqrt{17}}{2}\right)}{\left(-\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{i \sqrt{3}\, \left(x +\frac{1}{2}-\frac{\sqrt{17}}{2}\right)}{\left(\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{3}\, \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{17}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \sqrt{\frac{\left(\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{i \sqrt{3}}{2}-\frac{\sqrt{17}}{2}\right)}{\left(\frac{\sqrt{17}}{2}-\frac{i \sqrt{3}}{2}\right) \left(-\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right)}}\right)}{3 \left(\frac{\sqrt{17}}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{\sqrt{17}}{2}\right) \left(x +\frac{1}{2}-\frac{\sqrt{17}}{2}\right)}}-\frac{4 i \left(-\frac{i \sqrt{3}}{2}-\frac{\sqrt{17}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{17}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{\frac{i \sqrt{3}\, \left(x +\frac{1}{2}+\frac{\sqrt{17}}{2}\right)}{\left(-\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{i \sqrt{3}\, \left(x +\frac{1}{2}-\frac{\sqrt{17}}{2}\right)}{\left(\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{3}\, \left(\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{17}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \sqrt{\frac{\left(\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{i \sqrt{3}}{2}-\frac{\sqrt{17}}{2}\right)}{\left(\frac{\sqrt{17}}{2}-\frac{i \sqrt{3}}{2}\right) \left(-\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right)}}\right)-i \sqrt{3}\, \EllipticPi \left(\sqrt{\frac{\left(\frac{\sqrt{17}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \frac{\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}}{\frac{\sqrt{17}}{2}-\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{i \sqrt{3}}{2}-\frac{\sqrt{17}}{2}\right)}{\left(\frac{\sqrt{17}}{2}-\frac{i \sqrt{3}}{2}\right) \left(-\frac{\sqrt{17}}{2}+\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{3 \left(\frac{\sqrt{17}}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{\sqrt{17}}{2}\right) \left(x +\frac{1}{2}-\frac{\sqrt{17}}{2}\right)}}$&$782$\\ \hline \end{longtable}"," ",0,"-ln(-2*x^2+2*(x^4+2*x^3-2*x^2-3*x-4)^(1/2)-2*x+3)","A"
439,0,0,31,0.019000," ","int((a*x^3+4*b)/(a*x^3+b)^(1/4)/(-a*x^3+x^4-b),x)","\[\int \frac{a \,x^{3}+4 b}{\left(a \,x^{3}+b \right)^{\frac{1}{4}} \left(-a \,x^{3}+x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^3+4*b)/(a*x^3+b)^(1/4)/(-a*x^3+x^4-b),x)","F"
440,1,28,27,0.188000," ","int(x^8/(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{x^{3} \sqrt{x^{6}-1}}{6}+\frac{\ln \left(x^{3}+\sqrt{x^{6}-1}\right)}{6}$&$28$\\ risch&$\frac{x^{3} \sqrt{x^{6}-1}}{6}+\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \arcsin \left(x^{3}\right)}{6 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}$&$38$\\ meijerg&$\frac{i \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(i \sqrt{\pi}\, x^{3} \sqrt{-x^{6}+1}-i \sqrt{\pi}\, \arcsin \left(x^{3}\right)\right)}{6 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$54$\\ \hline \end{longtable}"," ",0,"1/6*x^3*(x^6-1)^(1/2)+1/6*ln(x^3+(x^6-1)^(1/2))","A"
441,1,30,27,0.236000," ","int((x^6-1)^(1/2)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\sqrt{x^{6}-1}}{3 x^{3}}-\frac{\ln \left(-x^{3}+\sqrt{x^{6}-1}\right)}{3}$&$30$\\ risch&$-\frac{\sqrt{x^{6}-1}}{3 x^{3}}+\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \arcsin \left(x^{3}\right)}{3 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}$&$38$\\ meijerg&$-\frac{i \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(-\frac{4 i \sqrt{\pi}\, \sqrt{-x^{6}+1}}{x^{3}}-4 i \sqrt{\pi}\, \arcsin \left(x^{3}\right)\right)}{12 \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$54$\\ \hline \end{longtable}"," ",0,"-1/3*(x^6-1)^(1/2)/x^3-1/3*ln(-x^3+(x^6-1)^(1/2))","A"
442,1,30,27,0.183000," ","int(x^2*(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{x^{3} \sqrt{x^{6}-1}}{6}+\frac{\ln \left(x^{3}-\sqrt{x^{6}-1}\right)}{6}$&$30$\\ risch&$\frac{x^{3} \sqrt{x^{6}-1}}{6}-\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \arcsin \left(x^{3}\right)}{6 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}$&$38$\\ meijerg&$\frac{i \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(-2 i \sqrt{\pi}\, x^{3} \sqrt{-x^{6}+1}-2 i \sqrt{\pi}\, \arcsin \left(x^{3}\right)\right)}{12 \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$54$\\ \hline \end{longtable}"," ",0,"1/6*x^3*(x^6-1)^(1/2)+1/6*ln(x^3-(x^6-1)^(1/2))","A"
443,1,20,27,0.164000," ","int(x^8/(x^6+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x^{3} \sqrt{x^{6}+1}}{6}-\frac{\arcsinh \left(x^{3}\right)}{6}$&$20$\\ trager&$\frac{x^{3} \sqrt{x^{6}+1}}{6}+\frac{\ln \left(x^{3}-\sqrt{x^{6}+1}\right)}{6}$&$30$\\ meijerg&$\frac{\sqrt{\pi}\, x^{3} \sqrt{x^{6}+1}-\sqrt{\pi}\, \arcsinh \left(x^{3}\right)}{6 \sqrt{\pi}}$&$30$\\ \hline \end{longtable}"," ",0,"1/6*x^3*(x^6+1)^(1/2)-1/6*arcsinh(x^3)","A"
444,1,20,27,0.201000," ","int((x^6+1)^(1/2)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{\sqrt{x^{6}+1}}{3 x^{3}}+\frac{\arcsinh \left(x^{3}\right)}{3}$&$20$\\ trager&$-\frac{\sqrt{x^{6}+1}}{3 x^{3}}-\frac{\ln \left(-x^{3}+\sqrt{x^{6}+1}\right)}{3}$&$30$\\ meijerg&$-\frac{\frac{4 \sqrt{\pi}\, \sqrt{x^{6}+1}}{x^{3}}-4 \sqrt{\pi}\, \arcsinh \left(x^{3}\right)}{12 \sqrt{\pi}}$&$31$\\ \hline \end{longtable}"," ",0,"-1/3*(x^6+1)^(1/2)/x^3+1/3*arcsinh(x^3)","A"
445,1,25,31,0.089000," ","int((x^6+1)/x^6/(x^3+1)/(x^4+x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{\frac{212}{63} x^{6}+\frac{32}{63} x^{3}-\frac{4}{21}}{\left(x^{4}+x \right)^{\frac{1}{4}} x^{5}}$&$25$\\ risch&$\frac{\frac{212}{63} x^{6}+\frac{32}{63} x^{3}-\frac{4}{21}}{x^{5} \left(x \left(x^{3}+1\right)\right)^{\frac{1}{4}}}$&$27$\\ trager&$\frac{4 \left(x^{4}+x \right)^{\frac{3}{4}} \left(53 x^{6}+8 x^{3}-3\right)}{63 x^{6} \left(x^{3}+1\right)}$&$32$\\ meijerg&$-\frac{4 \left(-32 x^{6}-8 x^{3}+3\right) \left(x^{3}+1\right)^{\frac{3}{4}}}{21 \left(3 x^{3}+3\right) x^{\frac{21}{4}}}+\frac{4 x^{\frac{3}{4}}}{3 \left(x^{3}+1\right)^{\frac{1}{4}}}$&$47$\\ \hline \end{longtable}"," ",0,"4/63*(53*x^6+8*x^3-3)/(x^4+x)^(1/4)/x^5","A"
446,1,27,27,0.278000," ","int(x*(x^6+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x^{3} \left(x^{5}+1\right)}{5 \sqrt{x \left(x^{5}+1\right)}}+\frac{\arcsinh \left(x^{\frac{5}{2}}\right)}{5}$&$27$\\ meijerg&$-\frac{-2 \sqrt{\pi}\, x^{\frac{5}{2}} \sqrt{x^{5}+1}-2 \sqrt{\pi}\, \arcsinh \left(x^{\frac{5}{2}}\right)}{10 \sqrt{\pi}}$&$31$\\ trager&$\frac{x^{2} \sqrt{x^{6}+x}}{5}+\frac{\ln \left(2 x^{5}+2 x^{2} \sqrt{x^{6}+x}+1\right)}{10}$&$36$\\ \hline \end{longtable}"," ",0,"1/5*x^3*(x^5+1)/(x*(x^5+1))^(1/2)+1/5*arcsinh(x^(5/2))","A"
447,0,0,31,0.023000," ","int((a*c*x^6-2*b*c)/(a*x^6+b)^(1/4)/(-c^4*x^4+a*x^6+b),x)","\[\int \frac{a c \,x^{6}-2 b c}{\left(a \,x^{6}+b \right)^{\frac{1}{4}} \left(-c^{4} x^{4}+a \,x^{6}+b \right)}\, dx\]"," ",0,"int((a*c*x^6-2*b*c)/(a*x^6+b)^(1/4)/(-c^4*x^4+a*x^6+b),x)","F"
448,1,62,25,0.044000," ","int(1/(x+(x^2+1)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{-\frac{32 \sqrt{\pi}\, \sqrt{2}\, \cosh \left(\frac{3 \arcsinh \left(\frac{1}{x}\right)}{2}\right)}{3 x^{\frac{3}{2}}}-\frac{8 \sqrt{\pi}\, \sqrt{2}\, x^{\frac{3}{2}} \left(-\frac{4}{3 x^{4}}-\frac{2}{3 x^{2}}+\frac{2}{3}\right) \sinh \left(\frac{3 \arcsinh \left(\frac{1}{x}\right)}{2}\right)}{\sqrt{1+\frac{1}{x^{2}}}}}{8 \sqrt{\pi}}$&$62$\\ \hline \end{longtable}"," ",0,"-1/8/Pi^(1/2)*(-32/3*Pi^(1/2)*2^(1/2)/x^(3/2)*cosh(3/2*arcsinh(1/x))-8*Pi^(1/2)*2^(1/2)*x^(3/2)*(-4/3/x^4-2/3/x^2+2/3)*sinh(3/2*arcsinh(1/x))/(1+1/x^2)^(1/2))","C"
449,1,45,30,1.173000," ","int((x^2+1)^(1/4)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{-4 \left(4-3 \ln \left(2\right)+\frac{\pi}{2}+2 \ln \left(x \right)\right) \Gamma \left(\frac{3}{4}\right)-\hypergeom \left(\left[\frac{3}{4}, 1, 1\right], \left[2, 2\right], -x^{2}\right) \Gamma \left(\frac{3}{4}\right) x^{2}}{8 \Gamma \left(\frac{3}{4}\right)}$&$45$\\ trager&$2 \left(x^{2}+1\right)^{\frac{1}{4}}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{2}+1}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \left(x^{2}+1\right)^{\frac{3}{4}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(x^{2}+1\right)^{\frac{1}{4}}}{x^{2}}\right)}{2}-\frac{\ln \left(-\frac{2 \left(x^{2}+1\right)^{\frac{3}{4}}+2 \sqrt{x^{2}+1}+x^{2}+2 \left(x^{2}+1\right)^{\frac{1}{4}}+2}{x^{2}}\right)}{2}$&$118$\\ \hline \end{longtable}"," ",0,"-1/8/GAMMA(3/4)*(-4*(4-3*ln(2)+1/2*Pi+2*ln(x))*GAMMA(3/4)-hypergeom([3/4,1,1],[2,2],-x^2)*GAMMA(3/4)*x^2)","C"
450,1,34,28,0.370000," ","int((x^3-1)^(1/2)/x^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x^{6}-3 x^{3}+2}{12 x^{6} \sqrt{x^{3}-1}}+\frac{\arctan \left(\sqrt{x^{3}-1}\right)}{12}$&$34$\\ default&$-\frac{\sqrt{x^{3}-1}}{6 x^{6}}+\frac{\sqrt{x^{3}-1}}{12 x^{3}}+\frac{\arctan \left(\sqrt{x^{3}-1}\right)}{12}$&$36$\\ elliptic&$-\frac{\sqrt{x^{3}-1}}{6 x^{6}}+\frac{\sqrt{x^{3}-1}}{12 x^{3}}+\frac{\arctan \left(\sqrt{x^{3}-1}\right)}{12}$&$36$\\ trager&$\frac{\left(x^{3}-2\right) \sqrt{x^{3}-1}}{12 x^{6}}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \sqrt{x^{3}-1}-2 \RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{3}}\right)}{24}$&$61$\\ meijerg&$-\frac{\sqrt{\mathrm{signum}\left(x^{3}-1\right)}\, \left(\frac{\sqrt{\pi}}{x^{6}}-\frac{\sqrt{\pi}}{x^{3}}+\frac{\left(\frac{1}{2}-2 \ln \left(2\right)+3 \ln \left(x \right)+i \pi \right) \sqrt{\pi}}{4}-\frac{\sqrt{\pi}\, \left(x^{6}-8 x^{3}+8\right)}{8 x^{6}}+\frac{\sqrt{\pi}\, \left(-4 x^{3}+8\right) \sqrt{-x^{3}+1}}{8 x^{6}}-\frac{\sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{3}+1}}{2}\right)}{2}\right)}{6 \sqrt{-\mathrm{signum}\left(x^{3}-1\right)}\, \sqrt{\pi}}$&$120$\\ \hline \end{longtable}"," ",0,"1/12*(x^6-3*x^3+2)/x^6/(x^3-1)^(1/2)+1/12*arctan((x^3-1)^(1/2))","A"
451,1,1142,30,0.275000," ","int((a*x^2-b)/(a*x^2+c*x+b)/(a*x^3+b*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}+b x}}+\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{-c +\sqrt{-4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) c^{2}}{2 \sqrt{-4 a b +c^{2}}\, a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{c}{2 a}-\frac{\sqrt{-4 a b +c^{2}}}{2 a}\right)}-\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{-c +\sqrt{-4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) c}{2 a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{c}{2 a}-\frac{\sqrt{-4 a b +c^{2}}}{2 a}\right)}-\frac{2 \sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{-c +\sqrt{-4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) b}{\sqrt{-4 a b +c^{2}}\, a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{c}{2 a}-\frac{\sqrt{-4 a b +c^{2}}}{2 a}\right)}-\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{c +\sqrt{-4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) c^{2}}{2 \sqrt{-4 a b +c^{2}}\, a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{c}{2 a}+\frac{\sqrt{-4 a b +c^{2}}}{2 a}\right)}-\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{c +\sqrt{-4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) c}{2 a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{c}{2 a}+\frac{\sqrt{-4 a b +c^{2}}}{2 a}\right)}+\frac{2 \sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{c +\sqrt{-4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) b}{\sqrt{-4 a b +c^{2}}\, a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{c}{2 a}+\frac{\sqrt{-4 a b +c^{2}}}{2 a}\right)}$&$1142$\\ default&$\frac{\sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}+b x}}+\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{-c +\sqrt{-4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) c^{2}}{2 \sqrt{-4 a b +c^{2}}\, a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{c}{2 a}-\frac{\sqrt{-4 a b +c^{2}}}{2 a}\right)}-\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{-c +\sqrt{-4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) c}{2 a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{c}{2 a}-\frac{\sqrt{-4 a b +c^{2}}}{2 a}\right)}-\frac{2 \sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{-c +\sqrt{-4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) b}{\sqrt{-4 a b +c^{2}}\, a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{c}{2 a}-\frac{\sqrt{-4 a b +c^{2}}}{2 a}\right)}-\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{c +\sqrt{-4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) c^{2}}{2 \sqrt{-4 a b +c^{2}}\, a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{c}{2 a}+\frac{\sqrt{-4 a b +c^{2}}}{2 a}\right)}-\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{c +\sqrt{-4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) c}{2 a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{c}{2 a}+\frac{\sqrt{-4 a b +c^{2}}}{2 a}\right)}+\frac{2 \sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{c +\sqrt{-4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) b}{\sqrt{-4 a b +c^{2}}\, a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{c}{2 a}+\frac{\sqrt{-4 a b +c^{2}}}{2 a}\right)}$&$1161$\\ \hline \end{longtable}"," ",0,"1/a*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)*EllipticF(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))+1/2/(-4*a*b+c^2)^(1/2)/a^2*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)+1/2*c/a-1/2/a*(-4*a*b+c^2)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)-1/2/a*(-c+(-4*a*b+c^2)^(1/2))),1/2*2^(1/2))*c^2-1/2/a^2*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)+1/2*c/a-1/2/a*(-4*a*b+c^2)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)-1/2/a*(-c+(-4*a*b+c^2)^(1/2))),1/2*2^(1/2))*c-2/(-4*a*b+c^2)^(1/2)/a*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)+1/2*c/a-1/2/a*(-4*a*b+c^2)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)-1/2/a*(-c+(-4*a*b+c^2)^(1/2))),1/2*2^(1/2))*b-1/2/(-4*a*b+c^2)^(1/2)/a^2*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)+1/2*c/a+1/2/a*(-4*a*b+c^2)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)+1/2*(c+(-4*a*b+c^2)^(1/2))/a),1/2*2^(1/2))*c^2-1/2/a^2*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)+1/2*c/a+1/2/a*(-4*a*b+c^2)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)+1/2*(c+(-4*a*b+c^2)^(1/2))/a),1/2*2^(1/2))*c+2/(-4*a*b+c^2)^(1/2)/a*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)+1/2*c/a+1/2/a*(-4*a*b+c^2)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)+1/2*(c+(-4*a*b+c^2)^(1/2))/a),1/2*2^(1/2))*b","C"
452,1,64,32,0.455000," ","int((-1+x)/(x^4-4*x^3+6*x^2-x-2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\ln \left(-2 x^{3}+2 \sqrt{x^{4}-4 x^{3}+6 x^{2}-x -2}\, x +6 x^{2}-2 \sqrt{x^{4}-4 x^{3}+6 x^{2}-x -2}-6 x -1\right)}{3}$&$64$\\ default&$\frac{2 \left(-\frac{3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}\right) \sqrt{\frac{\left(\frac{3 \,3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(-1+x \right)}{\left(\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(x +3^{\frac{1}{3}}-1\right)}}\, \left(x +3^{\frac{1}{3}}-1\right)^{2} \sqrt{-\frac{3^{\frac{1}{3}} \left(x -\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}-1\right)}{\left(\frac{3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}\right) \left(x +3^{\frac{1}{3}}-1\right)}}\, \sqrt{-\frac{3^{\frac{1}{3}} \left(x -\frac{3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}-1\right)}{\left(\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(x +3^{\frac{1}{3}}-1\right)}}\, 3^{\frac{2}{3}} \EllipticF \left(\sqrt{\frac{\left(\frac{3 \,3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(-1+x \right)}{\left(\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(x +3^{\frac{1}{3}}-1\right)}}, \sqrt{\frac{\left(-\frac{3 \,3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(-\frac{3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}\right)}{\left(-\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(-\frac{3 \,3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}\right)}}\right)}{3 \left(\frac{3 \,3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \sqrt{\left(-1+x \right) \left(x +3^{\frac{1}{3}}-1\right) \left(x -\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}-1\right) \left(x -\frac{3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}-1\right)}}-\frac{2 \left(-\frac{3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}\right) \sqrt{\frac{\left(\frac{3 \,3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(-1+x \right)}{\left(\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(x +3^{\frac{1}{3}}-1\right)}}\, \left(x +3^{\frac{1}{3}}-1\right)^{2} \sqrt{-\frac{3^{\frac{1}{3}} \left(x -\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}-1\right)}{\left(\frac{3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}\right) \left(x +3^{\frac{1}{3}}-1\right)}}\, \sqrt{-\frac{3^{\frac{1}{3}} \left(x -\frac{3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}-1\right)}{\left(\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(x +3^{\frac{1}{3}}-1\right)}}\, 3^{\frac{2}{3}} \left(\left(-3^{\frac{1}{3}}+1\right) \EllipticF \left(\sqrt{\frac{\left(\frac{3 \,3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(-1+x \right)}{\left(\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(x +3^{\frac{1}{3}}-1\right)}}, \sqrt{\frac{\left(-\frac{3 \,3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(-\frac{3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}\right)}{\left(-\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(-\frac{3 \,3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}\right)}}\right)+3^{\frac{1}{3}} \EllipticPi \left(\sqrt{\frac{\left(\frac{3 \,3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(-1+x \right)}{\left(\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(x +3^{\frac{1}{3}}-1\right)}}, \frac{\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}}{\frac{3 \,3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}}, \sqrt{\frac{\left(-\frac{3 \,3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(-\frac{3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}\right)}{\left(-\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(-\frac{3 \,3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}\right)}}\right)\right)}{3 \left(\frac{3 \,3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \sqrt{\left(-1+x \right) \left(x +3^{\frac{1}{3}}-1\right) \left(x -\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}-1\right) \left(x -\frac{3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}-1\right)}}$&$740$\\ elliptic&$\frac{2 \left(-\frac{3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}\right) \sqrt{\frac{\left(\frac{3 \,3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(-1+x \right)}{\left(\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(x +3^{\frac{1}{3}}-1\right)}}\, \left(x +3^{\frac{1}{3}}-1\right)^{2} \sqrt{-\frac{3^{\frac{1}{3}} \left(x -\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}-1\right)}{\left(\frac{3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}\right) \left(x +3^{\frac{1}{3}}-1\right)}}\, \sqrt{-\frac{3^{\frac{1}{3}} \left(x -\frac{3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}-1\right)}{\left(\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(x +3^{\frac{1}{3}}-1\right)}}\, 3^{\frac{2}{3}} \EllipticF \left(\sqrt{\frac{\left(\frac{3 \,3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(-1+x \right)}{\left(\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(x +3^{\frac{1}{3}}-1\right)}}, \sqrt{\frac{\left(-\frac{3 \,3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(-\frac{3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}\right)}{\left(-\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(-\frac{3 \,3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}\right)}}\right)}{3 \left(\frac{3 \,3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \sqrt{\left(-1+x \right) \left(x +3^{\frac{1}{3}}-1\right) \left(x -\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}-1\right) \left(x -\frac{3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}-1\right)}}-\frac{2 \left(-\frac{3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}\right) \sqrt{\frac{\left(\frac{3 \,3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(-1+x \right)}{\left(\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(x +3^{\frac{1}{3}}-1\right)}}\, \left(x +3^{\frac{1}{3}}-1\right)^{2} \sqrt{-\frac{3^{\frac{1}{3}} \left(x -\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}-1\right)}{\left(\frac{3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}\right) \left(x +3^{\frac{1}{3}}-1\right)}}\, \sqrt{-\frac{3^{\frac{1}{3}} \left(x -\frac{3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}-1\right)}{\left(\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(x +3^{\frac{1}{3}}-1\right)}}\, 3^{\frac{2}{3}} \left(\left(-3^{\frac{1}{3}}+1\right) \EllipticF \left(\sqrt{\frac{\left(\frac{3 \,3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(-1+x \right)}{\left(\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(x +3^{\frac{1}{3}}-1\right)}}, \sqrt{\frac{\left(-\frac{3 \,3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(-\frac{3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}\right)}{\left(-\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(-\frac{3 \,3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}\right)}}\right)+3^{\frac{1}{3}} \EllipticPi \left(\sqrt{\frac{\left(\frac{3 \,3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(-1+x \right)}{\left(\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(x +3^{\frac{1}{3}}-1\right)}}, \frac{\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}}{\frac{3 \,3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}}, \sqrt{\frac{\left(-\frac{3 \,3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(-\frac{3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}\right)}{\left(-\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \left(-\frac{3 \,3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}\right)}}\right)\right)}{3 \left(\frac{3 \,3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}\right) \sqrt{\left(-1+x \right) \left(x +3^{\frac{1}{3}}-1\right) \left(x -\frac{3^{\frac{1}{3}}}{2}+\frac{i 3^{\frac{5}{6}}}{2}-1\right) \left(x -\frac{3^{\frac{1}{3}}}{2}-\frac{i 3^{\frac{5}{6}}}{2}-1\right)}}$&$740$\\ \hline \end{longtable}"," ",0,"-1/3*ln(-2*x^3+2*(x^4-4*x^3+6*x^2-x-2)^(1/2)*x+6*x^2-2*(x^4-4*x^3+6*x^2-x-2)^(1/2)-6*x-1)","A"
453,1,30,28,0.356000," ","int((x^6-1)^(1/2)/x^13,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x^{12}-3 x^{6}+2}{24 x^{12} \sqrt{x^{6}-1}}-\frac{\arcsin \left(\frac{1}{x^{3}}\right)}{24}$&$30$\\ trager&$\frac{\left(x^{6}-2\right) \sqrt{x^{6}-1}}{24 x^{12}}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{24}$&$46$\\ meijerg&$-\frac{\sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(\frac{\sqrt{\pi}}{x^{12}}-\frac{\sqrt{\pi}}{x^{6}}+\frac{\left(\frac{1}{2}-2 \ln \left(2\right)+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}}{4}-\frac{\sqrt{\pi}\, \left(x^{12}-8 x^{6}+8\right)}{8 x^{12}}+\frac{\sqrt{\pi}\, \left(-4 x^{6}+8\right) \sqrt{-x^{6}+1}}{8 x^{12}}-\frac{\ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right) \sqrt{\pi}}{2}\right)}{12 \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$120$\\ \hline \end{longtable}"," ",0,"1/24*(x^12-3*x^6+2)/x^12/(x^6-1)^(1/2)-1/24*arcsin(1/x^3)","A"
454,1,69,31,0.297000," ","int((2*x^4-2*x^2-1)/(x^4-3*x^2+2)/(x^6+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{3 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{4}-\RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}-4 \sqrt{x^{6}+1}\, x +2 \RootOf \left(\textit{\_Z}^{2}-2\right)}{\left(x^{2}-2\right) \left(-1+x \right) \left(1+x \right)}\right)}{4}$&$69$\\ \hline \end{longtable}"," ",0,"1/4*RootOf(_Z^2-2)*ln((3*RootOf(_Z^2-2)*x^4-RootOf(_Z^2-2)*x^2-4*(x^6+1)^(1/2)*x+2*RootOf(_Z^2-2))/(x^2-2)/(-1+x)/(1+x))","C"
455,1,206,35,0.108000," ","int((k*x-1)/(k*x+1)/((1-x)*x*(-k^2*x+1))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{4 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{3} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}$&$206$\\ elliptic&$-\frac{2 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{4 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{3} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}$&$206$\\ \hline \end{longtable}"," ",0,"-2/k^2*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticF((-(x-1/k^2)*k^2)^(1/2),(1/k^2/(1/k^2-1))^(1/2))+4/k^3*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/k)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+1/k),(1/k^2/(1/k^2-1))^(1/2))","C"
456,1,210,35,0.068000," ","int((k*x+1)/(k*x-1)/((1-x)*x*(-k^2*x+1))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}-\frac{4 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{3} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}$&$210$\\ elliptic&$-\frac{2 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}-\frac{4 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{3} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}$&$210$\\ \hline \end{longtable}"," ",0,"-2/k^2*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticF((-(x-1/k^2)*k^2)^(1/2),(1/k^2/(1/k^2-1))^(1/2))-4/k^3*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-1/k)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-1/k),(1/k^2/(1/k^2-1))^(1/2))","C"
457,1,39,29,0.332000," ","int((x^2-1)*(x^4+1)^(1/2)/x^2/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{x}-2 \arctan \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)\right) \sqrt{2}}{2}$&$39$\\ trager&$\frac{\sqrt{x^{4}+1}}{x}-\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x +\sqrt{x^{4}+1}}{x^{2}+1}\right)$&$46$\\ risch&$\frac{\sqrt{x^{4}+1}}{x}-\frac{2 \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}-\frac{4 \left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{\sqrt{x^{4}+1}}$&$123$\\ default&$\frac{\sqrt{x^{4}+1}}{x}-\frac{2 i \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \left(\EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)-\EllipticE \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}-\frac{2 \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{2 i \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}-\frac{2 i \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticE \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}-\frac{4 \left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{\sqrt{x^{4}+1}}$&$326$\\ \hline \end{longtable}"," ",0,"1/2*(2^(1/2)/x*(x^4+1)^(1/2)-2*arctan(1/2*2^(1/2)/x*(x^4+1)^(1/2)))*2^(1/2)","A"
458,1,27,33,0.122000," ","int((x^3+1)/x^6/(x^3-1)/(x^4-x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{4 \left(20 x^{6}-5 x^{3}-1\right)}{21 \left(x^{4}-x \right)^{\frac{1}{4}} x^{5}}$&$27$\\ risch&$-\frac{4 \left(20 x^{6}-5 x^{3}-1\right)}{21 x^{5} \left(x \left(x^{3}-1\right)\right)^{\frac{1}{4}}}$&$27$\\ trager&$-\frac{4 \left(x^{4}-x \right)^{\frac{3}{4}} \left(20 x^{6}-5 x^{3}-1\right)}{21 x^{6} \left(x^{3}-1\right)}$&$34$\\ meijerg&$\frac{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}} \left(-32 x^{6}+8 x^{3}+3\right) \left(-x^{3}+1\right)^{\frac{3}{4}}}{21 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}} \left(-3 x^{3}+3\right) x^{\frac{21}{4}}}+\frac{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}} \left(-4 x^{3}+1\right)}{9 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}} \left(-x^{3}+1\right)^{\frac{1}{4}} x^{\frac{9}{4}}}$&$94$\\ \hline \end{longtable}"," ",0,"-4/21*(20*x^6-5*x^3-1)/(x^4-x)^(1/4)/x^5","A"
459,1,36,29,0.316000," ","int((x^4-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{x \sqrt{x^{4}-x}}{3}-\frac{\ln \left(-2 x^{3}-2 x \sqrt{x^{4}-x}+1\right)}{6}$&$36$\\ meijerg&$\frac{i \sqrt{\mathrm{signum}\left(x^{3}-1\right)}\, \left(-2 i \sqrt{\pi}\, x^{\frac{3}{2}} \sqrt{-x^{3}+1}-2 i \sqrt{\pi}\, \arcsin \left(x^{\frac{3}{2}}\right)\right)}{6 \sqrt{\pi}\, \sqrt{-\mathrm{signum}\left(x^{3}-1\right)}}$&$54$\\ default&$\frac{x \sqrt{x^{4}-x}}{3}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$301$\\ elliptic&$\frac{x \sqrt{x^{4}-x}}{3}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$301$\\ risch&$\frac{x^{2} \left(x^{3}-1\right)}{3 \sqrt{x \left(x^{3}-1\right)}}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$308$\\ \hline \end{longtable}"," ",0,"1/3*x*(x^4-x)^(1/2)-1/6*ln(-2*x^3-2*x*(x^4-x)^(1/2)+1)","A"
460,1,34,33,0.086000," ","int(1/x^8/(x^4-x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{4}-x^{2}\right)^{\frac{3}{4}} \left(128 x^{6}+96 x^{4}+84 x^{2}+77\right)}{1155 x^{9}}$&$34$\\ risch&$\frac{-\frac{2}{165} x^{2}-\frac{2}{15}-\frac{8}{385} x^{4}-\frac{64}{1155} x^{6}+\frac{256}{1155} x^{8}}{x^{7} \left(x^{2} \left(x^{2}-1\right)\right)^{\frac{1}{4}}}$&$39$\\ gosper&$\frac{2 \left(-1+x \right) \left(1+x \right) \left(128 x^{6}+96 x^{4}+84 x^{2}+77\right)}{1155 x^{7} \left(x^{4}-x^{2}\right)^{\frac{1}{4}}}$&$40$\\ meijerg&$-\frac{2 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{4}} \left(\frac{128}{77} x^{6}+\frac{96}{77} x^{4}+\frac{12}{11} x^{2}+1\right) \left(-x^{2}+1\right)^{\frac{3}{4}}}{15 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{4}} x^{\frac{15}{2}}}$&$50$\\ \hline \end{longtable}"," ",0,"2/1155*(x^4-x^2)^(3/4)*(128*x^6+96*x^4+84*x^2+77)/x^9","A"
461,1,34,33,0.398000," ","int((-1+x)/(x^4-4*x^3+2*x^2+4*x-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\ln \left(1+2 x -x^{2}+\sqrt{x^{4}-4 x^{3}+2 x^{2}+4 x -1}\right)}{2}$&$34$\\ default&$-\frac{2 \left(-\sqrt{2-\sqrt{2}}-\sqrt{2+\sqrt{2}}\right) \sqrt{\frac{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right) \left(x -1+\sqrt{2-\sqrt{2}}\right)}{\left(\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}\right) \left(x -1-\sqrt{2-\sqrt{2}}\right)}}\, \left(x -1-\sqrt{2-\sqrt{2}}\right)^{2} \sqrt{-\frac{\left(x -1+\sqrt{2+\sqrt{2}}\right) \sqrt{2-\sqrt{2}}}{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right) \left(x -1-\sqrt{2-\sqrt{2}}\right)}}\, \sqrt{\frac{\sqrt{2-\sqrt{2}}\, \left(x -1-\sqrt{2+\sqrt{2}}\right)}{\left(\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}\right) \left(x -1-\sqrt{2-\sqrt{2}}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right) \left(x -1+\sqrt{2-\sqrt{2}}\right)}{\left(\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}\right) \left(x -1-\sqrt{2-\sqrt{2}}\right)}}, \sqrt{\frac{\left(\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}\right)^{2}}{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right)^{2}}}\right)}{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right) \sqrt{2-\sqrt{2}}\, \sqrt{\left(x -1+\sqrt{2-\sqrt{2}}\right) \left(x -1-\sqrt{2-\sqrt{2}}\right) \left(x -1+\sqrt{2+\sqrt{2}}\right) \left(x -1-\sqrt{2+\sqrt{2}}\right)}}+\frac{2 \left(-\sqrt{2-\sqrt{2}}-\sqrt{2+\sqrt{2}}\right) \sqrt{\frac{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right) \left(x -1+\sqrt{2-\sqrt{2}}\right)}{\left(\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}\right) \left(x -1-\sqrt{2-\sqrt{2}}\right)}}\, \left(x -1-\sqrt{2-\sqrt{2}}\right)^{2} \sqrt{-\frac{\left(x -1+\sqrt{2+\sqrt{2}}\right) \sqrt{2-\sqrt{2}}}{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right) \left(x -1-\sqrt{2-\sqrt{2}}\right)}}\, \sqrt{\frac{\sqrt{2-\sqrt{2}}\, \left(x -1-\sqrt{2+\sqrt{2}}\right)}{\left(\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}\right) \left(x -1-\sqrt{2-\sqrt{2}}\right)}}\, \left(\left(1+\sqrt{2-\sqrt{2}}\right) \EllipticF \left(\sqrt{\frac{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right) \left(x -1+\sqrt{2-\sqrt{2}}\right)}{\left(\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}\right) \left(x -1-\sqrt{2-\sqrt{2}}\right)}}, \sqrt{\frac{\left(\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}\right)^{2}}{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right)^{2}}}\right)-2 \sqrt{2-\sqrt{2}}\, \EllipticPi \left(\sqrt{\frac{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right) \left(x -1+\sqrt{2-\sqrt{2}}\right)}{\left(\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}\right) \left(x -1-\sqrt{2-\sqrt{2}}\right)}}, \frac{\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}}, \sqrt{\frac{\left(\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}\right)^{2}}{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right)^{2}}}\right)\right)}{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right) \sqrt{2-\sqrt{2}}\, \sqrt{\left(x -1+\sqrt{2-\sqrt{2}}\right) \left(x -1-\sqrt{2-\sqrt{2}}\right) \left(x -1+\sqrt{2+\sqrt{2}}\right) \left(x -1-\sqrt{2+\sqrt{2}}\right)}}$&$1020$\\ elliptic&$-\frac{2 \left(-\sqrt{2-\sqrt{2}}-\sqrt{2+\sqrt{2}}\right) \sqrt{\frac{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right) \left(x -1+\sqrt{2-\sqrt{2}}\right)}{\left(\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}\right) \left(x -1-\sqrt{2-\sqrt{2}}\right)}}\, \left(x -1-\sqrt{2-\sqrt{2}}\right)^{2} \sqrt{-\frac{\left(x -1+\sqrt{2+\sqrt{2}}\right) \sqrt{2-\sqrt{2}}}{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right) \left(x -1-\sqrt{2-\sqrt{2}}\right)}}\, \sqrt{\frac{\sqrt{2-\sqrt{2}}\, \left(x -1-\sqrt{2+\sqrt{2}}\right)}{\left(\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}\right) \left(x -1-\sqrt{2-\sqrt{2}}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right) \left(x -1+\sqrt{2-\sqrt{2}}\right)}{\left(\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}\right) \left(x -1-\sqrt{2-\sqrt{2}}\right)}}, \sqrt{\frac{\left(\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}\right)^{2}}{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right)^{2}}}\right)}{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right) \sqrt{2-\sqrt{2}}\, \sqrt{\left(x -1+\sqrt{2-\sqrt{2}}\right) \left(x -1-\sqrt{2-\sqrt{2}}\right) \left(x -1+\sqrt{2+\sqrt{2}}\right) \left(x -1-\sqrt{2+\sqrt{2}}\right)}}+\frac{2 \left(-\sqrt{2-\sqrt{2}}-\sqrt{2+\sqrt{2}}\right) \sqrt{\frac{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right) \left(x -1+\sqrt{2-\sqrt{2}}\right)}{\left(\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}\right) \left(x -1-\sqrt{2-\sqrt{2}}\right)}}\, \left(x -1-\sqrt{2-\sqrt{2}}\right)^{2} \sqrt{-\frac{\left(x -1+\sqrt{2+\sqrt{2}}\right) \sqrt{2-\sqrt{2}}}{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right) \left(x -1-\sqrt{2-\sqrt{2}}\right)}}\, \sqrt{\frac{\sqrt{2-\sqrt{2}}\, \left(x -1-\sqrt{2+\sqrt{2}}\right)}{\left(\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}\right) \left(x -1-\sqrt{2-\sqrt{2}}\right)}}\, \left(\left(1+\sqrt{2-\sqrt{2}}\right) \EllipticF \left(\sqrt{\frac{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right) \left(x -1+\sqrt{2-\sqrt{2}}\right)}{\left(\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}\right) \left(x -1-\sqrt{2-\sqrt{2}}\right)}}, \sqrt{\frac{\left(\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}\right)^{2}}{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right)^{2}}}\right)-2 \sqrt{2-\sqrt{2}}\, \EllipticPi \left(\sqrt{\frac{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right) \left(x -1+\sqrt{2-\sqrt{2}}\right)}{\left(\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}\right) \left(x -1-\sqrt{2-\sqrt{2}}\right)}}, \frac{\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}}, \sqrt{\frac{\left(\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}\right)^{2}}{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right)^{2}}}\right)\right)}{\left(\sqrt{2+\sqrt{2}}-\sqrt{2-\sqrt{2}}\right) \sqrt{2-\sqrt{2}}\, \sqrt{\left(x -1+\sqrt{2-\sqrt{2}}\right) \left(x -1-\sqrt{2-\sqrt{2}}\right) \left(x -1+\sqrt{2+\sqrt{2}}\right) \left(x -1-\sqrt{2+\sqrt{2}}\right)}}$&$1020$\\ \hline \end{longtable}"," ",0,"-1/2*ln(1+2*x-x^2+(x^4-4*x^3+2*x^2+4*x-1)^(1/2))","A"
462,1,27,33,0.378000," ","int((x^4-x^3)^(1/4)/(-1+x)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{4 \mathrm{signum}\left(-1+x \right)^{\frac{1}{4}} \hypergeom \left(\left[\frac{3}{4}, \frac{3}{4}\right], \left[\frac{7}{4}\right], x\right) x^{\frac{3}{4}}}{3 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{4}}}$&$27$\\ trager&$\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \sqrt{x^{4}-x^{3}}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}-2 x^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}}{x^{2}}\right)+\ln \left(\frac{2 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}+2 \sqrt{x^{4}-x^{3}}\, x +2 x^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}+2 x^{3}-x^{2}}{x^{2}}\right)$&$144$\\ \hline \end{longtable}"," ",0,"-4/3/(-signum(-1+x))^(1/4)*signum(-1+x)^(1/4)*hypergeom([3/4,3/4],[7/4],x)*x^(3/4)","C"
463,1,43,29,0.460000," ","int((x^3-2)/x/(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(x^{3}+\sqrt{x^{6}-1}\right)}{3}-\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{3}$&$43$\\ meijerg&$\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \arcsin \left(x^{3}\right)}{3 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}-\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(\left(-2 \ln \left(2\right)+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}-2 \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right) \sqrt{\pi}\right)}{3 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$86$\\ \hline \end{longtable}"," ",0,"1/3*ln(x^3+(x^6-1)^(1/2))-2/3*RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)+(x^6-1)^(1/2))/x^3)","C"
464,1,43,29,0.406000," ","int((x^3+1)/x/(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(x^{3}+\sqrt{x^{6}-1}\right)}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{3}$&$43$\\ meijerg&$\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \arcsin \left(x^{3}\right)}{3 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}+\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(\left(-2 \ln \left(2\right)+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}-2 \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right) \sqrt{\pi}\right)}{6 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$86$\\ \hline \end{longtable}"," ",0,"1/3*ln(x^3+(x^6-1)^(1/2))+1/3*RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)+(x^6-1)^(1/2))/x^3)","C"
465,1,46,29,0.426000," ","int((2*x^3-1)/x/(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \ln \left(x^{3}+\sqrt{x^{6}-1}\right)}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)-\sqrt{x^{6}-1}}{x^{3}}\right)}{3}$&$46$\\ meijerg&$\frac{2 \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \arcsin \left(x^{3}\right)}{3 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}-\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(\left(-2 \ln \left(2\right)+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}-2 \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right) \sqrt{\pi}\right)}{6 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$86$\\ \hline \end{longtable}"," ",0,"2/3*ln(x^3+(x^6-1)^(1/2))+1/3*RootOf(_Z^2+1)*ln(-(RootOf(_Z^2+1)-(x^6-1)^(1/2))/x^3)","C"
466,1,43,29,0.439000," ","int((2*x^3+1)/x/(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{3}+\frac{2 \ln \left(x^{3}+\sqrt{x^{6}-1}\right)}{3}$&$43$\\ meijerg&$\frac{2 \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \arcsin \left(x^{3}\right)}{3 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}+\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(\left(-2 \ln \left(2\right)+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}-2 \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right) \sqrt{\pi}\right)}{6 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$86$\\ \hline \end{longtable}"," ",0,"1/3*RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)+(x^6-1)^(1/2))/x^3)+2/3*ln(x^3+(x^6-1)^(1/2))","C"
467,1,43,29,0.433000," ","int((4*x^3+1)/x/(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{3}+\frac{4 \ln \left(x^{3}+\sqrt{x^{6}-1}\right)}{3}$&$43$\\ meijerg&$\frac{4 \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \arcsin \left(x^{3}\right)}{3 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}+\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(\left(-2 \ln \left(2\right)+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}-2 \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right) \sqrt{\pi}\right)}{6 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$86$\\ \hline \end{longtable}"," ",0,"1/3*RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)+(x^6-1)^(1/2))/x^3)+4/3*ln(x^3+(x^6-1)^(1/2))","C"
468,1,27,33,0.111000," ","int((x^6+1)/x^6/(x^3-1)/(x^4-x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{4 \left(53 x^{6}-8 x^{3}-3\right)}{63 \left(x^{4}-x \right)^{\frac{1}{4}} x^{5}}$&$27$\\ risch&$-\frac{4 \left(53 x^{6}-8 x^{3}-3\right)}{63 x^{5} \left(x \left(x^{3}-1\right)\right)^{\frac{1}{4}}}$&$27$\\ trager&$-\frac{4 \left(x^{4}-x \right)^{\frac{3}{4}} \left(53 x^{6}-8 x^{3}-3\right)}{63 x^{6} \left(x^{3}-1\right)}$&$34$\\ meijerg&$\frac{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}} \left(-32 x^{6}+8 x^{3}+3\right) \left(-x^{3}+1\right)^{\frac{3}{4}}}{21 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}} \left(-3 x^{3}+3\right) x^{\frac{21}{4}}}-\frac{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}} x^{\frac{3}{4}}}{3 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}} \left(-x^{3}+1\right)^{\frac{1}{4}}}$&$87$\\ \hline \end{longtable}"," ",0,"-4/63*(53*x^6-8*x^3-3)/(x^4-x)^(1/4)/x^5","A"
469,0,0,33,0.019000," ","int(x*(5*a*x^3+8*b)/(a*x^3+b)^(1/4)/(x^8-a*x^3-b),x)","\[\int \frac{x \left(5 a \,x^{3}+8 b \right)}{\left(a \,x^{3}+b \right)^{\frac{1}{4}} \left(x^{8}-a \,x^{3}-b \right)}\, dx\]"," ",0,"int(x*(5*a*x^3+8*b)/(a*x^3+b)^(1/4)/(x^8-a*x^3-b),x)","F"
470,1,57,27,0.018000," ","int((x+(x^2+1)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\frac{16 \sqrt{\pi}\, \sqrt{2}\, x^{\frac{3}{2}} \left(1-\frac{1}{x^{2}}\right) \cosh \left(\frac{\arcsinh \left(\frac{1}{x}\right)}{2}\right)}{3}+\frac{16 \sqrt{\pi}\, \sqrt{2}\, \sqrt{x}\, \sqrt{1+\frac{1}{x^{2}}}\, \sinh \left(\frac{\arcsinh \left(\frac{1}{x}\right)}{2}\right)}{3}}{8 \sqrt{\pi}}$&$57$\\ \hline \end{longtable}"," ",0,"1/8/Pi^(1/2)*(16/3*Pi^(1/2)*2^(1/2)*x^(3/2)*(1-1/x^2)*cosh(1/2*arcsinh(1/x))+16/3*Pi^(1/2)*2^(1/2)*x^(1/2)*(1+1/x^2)^(1/2)*sinh(1/2*arcsinh(1/x)))","C"
471,1,3392,32,0.293000," ","int((a*b-x^2)/(x*(-a+x)*(-b+x))^(1/2)/(a*b-(a+b+d)*x+x^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$3392$\\ elliptic&$\text{Expression too large to display}$&$3397$\\ \hline \end{longtable}"," ",0,"2*a*(-(-a+x)/a)^(1/2)*((-b+x)/(a-b))^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)*EllipticF((-(-a+x)/a)^(1/2),(a/(a-b))^(1/2))+1/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a^3*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))-2/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a^2*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*b+2/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a^2*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*d+a^2*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))+1/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*b^2+2/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*b*d+a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*b+1/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*d^2+a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*d-1/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a^3*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))+2/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a^2*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*b-2/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a^2*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*d+a^2*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))-1/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*b^2-2/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*b*d+a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*b-1/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*d^2+a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*d","C"
472,1,4000,32,0.316000," ","int((a*b-x^2)/(x*(-a+x)*(-b+x))^(1/2)/(a*b*d-(a*d+b*d+1)*x+d*x^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$4000$\\ elliptic&$\text{Expression too large to display}$&$4018$\\ \hline \end{longtable}"," ",0,"2/d*a*(-(-a+x)/a)^(1/2)*((-b+x)/(a-b))^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)*EllipticF((-(-a+x)/a)^(1/2),(a/(a-b))^(1/2))+1/d*(1/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*a^3*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2/d-1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2/d*(a*d+b*d+1+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))),(a/(a-b))^(1/2))*d-2/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*a^2*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2/d-1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2/d*(a*d+b*d+1+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))),(a/(a-b))^(1/2))*b*d+2/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*a^2*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2/d-1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2/d*(a*d+b*d+1+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))),(a/(a-b))^(1/2))+1/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2/d-1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2/d*(a*d+b*d+1+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))),(a/(a-b))^(1/2))*b^2*d+2/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2/d-1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2/d*(a*d+b*d+1+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))),(a/(a-b))^(1/2))*b+1/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2/d-1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2/d*(a*d+b*d+1+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))),(a/(a-b))^(1/2))/d+a^2*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2/d-1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2/d*(a*d+b*d+1+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))),(a/(a-b))^(1/2))+a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2/d-1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2/d*(a*d+b*d+1+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))),(a/(a-b))^(1/2))*b+a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2/d-1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2/d*(a*d+b*d+1+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))),(a/(a-b))^(1/2))/d-1/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*a^3*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b+1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-a+x)/a)^(1/2),a/(a+1/2*(-a*d-b*d+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1)/d),(a/(a-b))^(1/2))*d+2/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*a^2*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b+1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-a+x)/a)^(1/2),a/(a+1/2*(-a*d-b*d+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1)/d),(a/(a-b))^(1/2))*b*d-2/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*a^2*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b+1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-a+x)/a)^(1/2),a/(a+1/2*(-a*d-b*d+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1)/d),(a/(a-b))^(1/2))-1/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b+1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-a+x)/a)^(1/2),a/(a+1/2*(-a*d-b*d+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1)/d),(a/(a-b))^(1/2))*b^2*d-2/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b+1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-a+x)/a)^(1/2),a/(a+1/2*(-a*d-b*d+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1)/d),(a/(a-b))^(1/2))*b+a^2*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b+1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-a+x)/a)^(1/2),a/(a+1/2*(-a*d-b*d+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1)/d),(a/(a-b))^(1/2))+a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b+1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-a+x)/a)^(1/2),a/(a+1/2*(-a*d-b*d+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1)/d),(a/(a-b))^(1/2))*b+a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b+1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-a+x)/a)^(1/2),a/(a+1/2*(-a*d-b*d+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1)/d),(a/(a-b))^(1/2))/d-1/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b+1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-a+x)/a)^(1/2),a/(a+1/2*(-a*d-b*d+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1)/d),(a/(a-b))^(1/2))/d)","C"
473,1,37,36,0.125000," ","int((k*x^2-1)/(k*x^2+1)/((-x^2+1)*(-k^2*x^2+1))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\arctan \left(\frac{\sqrt{\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)}}{x \left(1+k \right)}\right)}{1+k}$&$37$\\ default&$\frac{\sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticF \left(x , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}-\frac{2 \sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticPi \left(x , -k , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}$&$104$\\ \hline \end{longtable}"," ",0,"1/(1+k)*arctan(((-x^2+1)*(-k^2*x^2+1))^(1/2)/x/(1+k))","A"
474,1,37,36,0.089000," ","int((k*x^2+1)/(k*x^2-1)/((-x^2+1)*(-k^2*x^2+1))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\arctan \left(\frac{\sqrt{\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)}}{x \left(-1+k \right)}\right)}{-1+k}$&$37$\\ default&$\frac{\sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticF \left(x , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}-\frac{2 \sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticPi \left(x , k , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}$&$102$\\ \hline \end{longtable}"," ",0,"1/(-1+k)*arctan(((-x^2+1)*(-k^2*x^2+1))^(1/2)/x/(-1+k))","A"
475,1,20,36,0.129000," ","int((k^2*x^2-2*k^2*x+1)/x/((1-x)*x*(-k^2*x+1))^(1/2)/(k^2*x-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{2 \left(-1+x \right)}{\sqrt{\left(-1+x \right) x \left(k^{2} x -1\right)}}$&$20$\\ trager&$-\frac{2 \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}{\left(k^{2} x -1\right) x}$&$39$\\ risch&$\frac{2 \left(-1+x \right) \left(k^{2} x -1\right)}{\sqrt{\left(-1+x \right) x \left(k^{2} x -1\right)}}-\frac{2 x \left(-1+x \right) k^{2}}{\sqrt{\left(-1+x \right) x \left(k^{2} x -1\right)}}$&$51$\\ elliptic&$-\frac{2 \left(k^{2} x^{2}-k^{2} x \right)}{\sqrt{\left(x -\frac{1}{k^{2}}\right) \left(k^{2} x^{2}-k^{2} x \right)}}+\frac{2 k^{2} x^{2}-2 k^{2} x -2 x +2}{\sqrt{x \left(k^{2} x^{2}-k^{2} x -x +1\right)}}$&$84$\\ default&$-\frac{2 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\left(-k^{2}+1\right) \left(\frac{2 k^{2} x^{2}-2 k^{2} x}{\left(k^{2}-1\right) \sqrt{\left(x -\frac{1}{k^{2}}\right) \left(k^{2} x^{2}-k^{2} x \right)}}-\frac{2 \left(-1+\frac{k^{2}}{k^{2}-1}\right) \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{2 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \left(\left(\frac{1}{k^{2}}-1\right) \EllipticE \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)+\EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)\right)}{\left(k^{2}-1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}\right)+\frac{2 k^{2} x^{2}-2 k^{2} x -2 x +2}{\sqrt{x \left(k^{2} x^{2}-k^{2} x -x +1\right)}}+\frac{2 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \left(\left(\frac{1}{k^{2}}-1\right) \EllipticE \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)+\EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)\right)}{\sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}$&$548$\\ \hline \end{longtable}"," ",0,"-2*(-1+x)/((-1+x)*x*(k^2*x-1))^(1/2)","A"
476,1,36,30,0.335000," ","int(1/x^7/(x^3-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{x^{3}-1}}{6 x^{6}}+\frac{\sqrt{x^{3}-1}}{4 x^{3}}+\frac{\arctan \left(\sqrt{x^{3}-1}\right)}{4}$&$36$\\ risch&$\frac{3 x^{6}-x^{3}-2}{12 x^{6} \sqrt{x^{3}-1}}+\frac{\arctan \left(\sqrt{x^{3}-1}\right)}{4}$&$36$\\ elliptic&$\frac{\sqrt{x^{3}-1}}{6 x^{6}}+\frac{\sqrt{x^{3}-1}}{4 x^{3}}+\frac{\arctan \left(\sqrt{x^{3}-1}\right)}{4}$&$36$\\ trager&$\frac{\sqrt{x^{3}-1}\, \left(3 x^{3}+2\right)}{12 x^{6}}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-2 \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \sqrt{x^{3}-1}}{x^{3}}\right)}{8}$&$62$\\ meijerg&$\frac{\sqrt{-\mathrm{signum}\left(x^{3}-1\right)}\, \left(-\frac{\sqrt{\pi}}{2 x^{6}}-\frac{\sqrt{\pi}}{2 x^{3}}+\frac{3 \left(\frac{7}{6}-2 \ln \left(2\right)+3 \ln \left(x \right)+i \pi \right) \sqrt{\pi}}{8}+\frac{\sqrt{\pi}\, \left(-7 x^{6}+8 x^{3}+8\right)}{16 x^{6}}-\frac{\sqrt{\pi}\, \left(12 x^{3}+8\right) \sqrt{-x^{3}+1}}{16 x^{6}}-\frac{3 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{3}+1}}{2}\right)}{4}\right)}{3 \sqrt{\mathrm{signum}\left(x^{3}-1\right)}\, \sqrt{\pi}}$&$123$\\ \hline \end{longtable}"," ",0,"1/6*(x^3-1)^(1/2)/x^6+1/4*(x^3-1)^(1/2)/x^3+1/4*arctan((x^3-1)^(1/2))","A"
477,1,34,30,0.230000," ","int(1/x^7/(x^3+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 x^{6}+x^{3}-2}{12 x^{6} \sqrt{x^{3}+1}}-\frac{\arctanh \left(\sqrt{x^{3}+1}\right)}{4}$&$34$\\ default&$-\frac{\sqrt{x^{3}+1}}{6 x^{6}}+\frac{\sqrt{x^{3}+1}}{4 x^{3}}-\frac{\arctanh \left(\sqrt{x^{3}+1}\right)}{4}$&$36$\\ elliptic&$-\frac{\sqrt{x^{3}+1}}{6 x^{6}}+\frac{\sqrt{x^{3}+1}}{4 x^{3}}-\frac{\arctanh \left(\sqrt{x^{3}+1}\right)}{4}$&$36$\\ trager&$\frac{\sqrt{x^{3}+1}\, \left(3 x^{3}-2\right)}{12 x^{6}}+\frac{\ln \left(-\frac{-x^{3}+2 \sqrt{x^{3}+1}-2}{x^{3}}\right)}{8}$&$45$\\ meijerg&$\frac{-\frac{\sqrt{\pi}}{2 x^{6}}+\frac{\sqrt{\pi}}{2 x^{3}}+\frac{3 \left(\frac{7}{6}-2 \ln \left(2\right)+3 \ln \left(x \right)\right) \sqrt{\pi}}{8}+\frac{\sqrt{\pi}\, \left(-7 x^{6}-8 x^{3}+8\right)}{16 x^{6}}-\frac{\sqrt{\pi}\, \left(-12 x^{3}+8\right) \sqrt{x^{3}+1}}{16 x^{6}}-\frac{3 \ln \left(\frac{1}{2}+\frac{\sqrt{x^{3}+1}}{2}\right) \sqrt{\pi}}{4}}{3 \sqrt{\pi}}$&$97$\\ \hline \end{longtable}"," ",0,"1/12*(3*x^6+x^3-2)/x^6/(x^3+1)^(1/2)-1/4*arctanh((x^3+1)^(1/2))","A"
478,1,34,30,0.207000," ","int((x^3+1)^(1/2)/x^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{x^{6}+3 x^{3}+2}{12 x^{6} \sqrt{x^{3}+1}}+\frac{\arctanh \left(\sqrt{x^{3}+1}\right)}{12}$&$34$\\ default&$-\frac{\sqrt{x^{3}+1}}{6 x^{6}}-\frac{\sqrt{x^{3}+1}}{12 x^{3}}+\frac{\arctanh \left(\sqrt{x^{3}+1}\right)}{12}$&$36$\\ elliptic&$-\frac{\sqrt{x^{3}+1}}{6 x^{6}}-\frac{\sqrt{x^{3}+1}}{12 x^{3}}+\frac{\arctanh \left(\sqrt{x^{3}+1}\right)}{12}$&$36$\\ trager&$-\frac{\left(x^{3}+2\right) \sqrt{x^{3}+1}}{12 x^{6}}+\frac{\ln \left(-\frac{x^{3}+2 \sqrt{x^{3}+1}+2}{x^{3}}\right)}{24}$&$41$\\ meijerg&$-\frac{\frac{\sqrt{\pi}}{x^{6}}+\frac{\sqrt{\pi}}{x^{3}}+\frac{\left(\frac{1}{2}-2 \ln \left(2\right)+3 \ln \left(x \right)\right) \sqrt{\pi}}{4}-\frac{\sqrt{\pi}\, \left(x^{6}+8 x^{3}+8\right)}{8 x^{6}}+\frac{\sqrt{\pi}\, \left(4 x^{3}+8\right) \sqrt{x^{3}+1}}{8 x^{6}}-\frac{\ln \left(\frac{1}{2}+\frac{\sqrt{x^{3}+1}}{2}\right) \sqrt{\pi}}{2}}{6 \sqrt{\pi}}$&$93$\\ \hline \end{longtable}"," ",0,"-1/12*(x^6+3*x^3+2)/x^6/(x^3+1)^(1/2)+1/12*arctanh((x^3+1)^(1/2))","A"
479,1,36,30,0.339000," ","int((x^3+1)/x^7/(x^3-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{x^{3}-1}}{6 x^{6}}+\frac{7 \sqrt{x^{3}-1}}{12 x^{3}}+\frac{7 \arctan \left(\sqrt{x^{3}-1}\right)}{12}$&$36$\\ risch&$\frac{7 x^{6}-5 x^{3}-2}{12 x^{6} \sqrt{x^{3}-1}}+\frac{7 \arctan \left(\sqrt{x^{3}-1}\right)}{12}$&$36$\\ elliptic&$\frac{\sqrt{x^{3}-1}}{6 x^{6}}+\frac{7 \sqrt{x^{3}-1}}{12 x^{3}}+\frac{7 \arctan \left(\sqrt{x^{3}-1}\right)}{12}$&$36$\\ trager&$\frac{\sqrt{x^{3}-1}\, \left(7 x^{3}+2\right)}{12 x^{6}}-\frac{7 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \sqrt{x^{3}-1}-2 \RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{3}}\right)}{24}$&$63$\\ meijerg&$-\frac{\sqrt{-\mathrm{signum}\left(x^{3}-1\right)}\, \left(\frac{\sqrt{\pi}}{x^{3}}-\frac{\left(1-2 \ln \left(2\right)+3 \ln \left(x \right)+i \pi \right) \sqrt{\pi}}{2}-\frac{\sqrt{\pi}\, \left(-4 x^{3}+8\right)}{8 x^{3}}+\frac{\sqrt{\pi}\, \sqrt{-x^{3}+1}}{x^{3}}+\sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{3}+1}}{2}\right)\right)}{3 \sqrt{\mathrm{signum}\left(x^{3}-1\right)}\, \sqrt{\pi}}+\frac{\sqrt{-\mathrm{signum}\left(x^{3}-1\right)}\, \left(-\frac{\sqrt{\pi}}{2 x^{6}}-\frac{\sqrt{\pi}}{2 x^{3}}+\frac{3 \left(\frac{7}{6}-2 \ln \left(2\right)+3 \ln \left(x \right)+i \pi \right) \sqrt{\pi}}{8}+\frac{\sqrt{\pi}\, \left(-7 x^{6}+8 x^{3}+8\right)}{16 x^{6}}-\frac{\sqrt{\pi}\, \left(12 x^{3}+8\right) \sqrt{-x^{3}+1}}{16 x^{6}}-\frac{3 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{3}+1}}{2}\right)}{4}\right)}{3 \sqrt{\mathrm{signum}\left(x^{3}-1\right)}\, \sqrt{\pi}}$&$223$\\ \hline \end{longtable}"," ",0,"1/6*(x^3-1)^(1/2)/x^6+7/12*(x^3-1)^(1/2)/x^3+7/12*arctan((x^3-1)^(1/2))","A"
480,1,75,30,0.517000," ","int((x^3-1)^(1/2)*(x^3+2)/x^2/(2*x^3-4*x^2-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{3}-1}}{x}+\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}-2\right) x^{3}-2 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}+4 \sqrt{x^{3}-1}\, x +\RootOf \left(\textit{\_Z}^{2}-2\right)}{x^{3}-2 x^{2}-1}\right)}{2}$&$75$\\ default&$\frac{\sqrt{x^{3}-1}}{x}+\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}-2 \textit{\_Z}^{2}-1\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(-\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(-3-i \sqrt{3}\right) \sqrt{\frac{-1+x}{-3-i \sqrt{3}}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{3-i \sqrt{3}}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{3 \underline{\hspace{1.25 ex}}\alpha^{2}}{4}+\frac{3 \underline{\hspace{1.25 ex}}\alpha }{4}+\frac{3}{4}-\frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}}{4}+\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha }{4}+\frac{i \sqrt{3}}{4}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}\right)}{2}$&$306$\\ risch&$\frac{\sqrt{x^{3}-1}}{x}+\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}-2 \textit{\_Z}^{2}-1\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(-\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(-3-i \sqrt{3}\right) \sqrt{\frac{-1+x}{-3-i \sqrt{3}}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{3-i \sqrt{3}}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{3 \underline{\hspace{1.25 ex}}\alpha^{2}}{4}+\frac{3 \underline{\hspace{1.25 ex}}\alpha }{4}+\frac{3}{4}-\frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}}{4}+\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha }{4}+\frac{i \sqrt{3}}{4}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}\right)}{2}$&$306$\\ elliptic&$\frac{\sqrt{x^{3}-1}}{x}+\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}-2 \textit{\_Z}^{2}-1\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(-\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(-3-i \sqrt{3}\right) \sqrt{\frac{-1+x}{-3-i \sqrt{3}}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{3-i \sqrt{3}}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{3 \underline{\hspace{1.25 ex}}\alpha^{2}}{4}+\frac{3 \underline{\hspace{1.25 ex}}\alpha }{4}+\frac{3}{4}-\frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}}{4}+\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha }{4}+\frac{i \sqrt{3}}{4}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}\right)}{2}$&$306$\\ \hline \end{longtable}"," ",0,"(x^3-1)^(1/2)/x+1/2*RootOf(_Z^2-2)*ln(-(-RootOf(_Z^2-2)*x^3-2*RootOf(_Z^2-2)*x^2+4*(x^3-1)^(1/2)*x+RootOf(_Z^2-2))/(x^3-2*x^2-1))","C"
481,1,25,34,0.076000," ","int(x^5*(a*x^3+b)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{2 \left(a \,x^{3}+b \right)^{\frac{3}{2}} \left(3 a \,x^{3}-2 b \right)}{45 a^{2}}$&$25$\\ trager&$\frac{2 \sqrt{a \,x^{3}+b}\, \left(3 a^{2} x^{6}+a b \,x^{3}-2 b^{2}\right)}{45 a^{2}}$&$35$\\ risch&$\frac{2 \sqrt{a \,x^{3}+b}\, \left(3 a^{2} x^{6}+a b \,x^{3}-2 b^{2}\right)}{45 a^{2}}$&$35$\\ default&$\frac{2 x^{6} \sqrt{a \,x^{3}+b}}{15}+\frac{2 b \,x^{3} \sqrt{a \,x^{3}+b}}{45 a}-\frac{4 b^{2} \sqrt{a \,x^{3}+b}}{45 a^{2}}$&$51$\\ elliptic&$\frac{2 x^{6} \sqrt{a \,x^{3}+b}}{15}+\frac{2 b \,x^{3} \sqrt{a \,x^{3}+b}}{45 a}-\frac{4 b^{2} \sqrt{a \,x^{3}+b}}{45 a^{2}}$&$51$\\ \hline \end{longtable}"," ",0,"2/45*(a*x^3+b)^(3/2)*(3*a*x^3-2*b)/a^2","A"
482,1,25,34,0.125000," ","int((x^4-3)*(x^4+1)^(1/3)*(x^4+x^3+1)/x^8,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{3 \left(x^{4}+1\right)^{\frac{4}{3}} \left(4 x^{4}+7 x^{3}+4\right)}{28 x^{7}}$&$25$\\ trager&$\frac{3 \left(x^{4}+1\right)^{\frac{1}{3}} \left(4 x^{8}+7 x^{7}+8 x^{4}+7 x^{3}+4\right)}{28 x^{7}}$&$35$\\ risch&$\frac{\frac{9}{7} x^{8}+\frac{9}{7} x^{4}+\frac{3}{7}+\frac{3}{2} x^{7}+\frac{3}{4} x^{3}+\frac{3}{7} x^{12}+\frac{3}{4} x^{11}}{x^{7} \left(x^{4}+1\right)^{\frac{2}{3}}}$&$45$\\ meijerg&$\frac{2 \hypergeom \left(\left[-\frac{3}{4}, -\frac{1}{3}\right], \left[\frac{1}{4}\right], -x^{4}\right)}{3 x^{3}}+\frac{\frac{3 \Gamma \left(\frac{2}{3}\right)}{x^{4}}-\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+4 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)+\frac{\hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 3\right], -x^{4}\right) \Gamma \left(\frac{2}{3}\right) x^{4}}{3}}{4 \Gamma \left(\frac{2}{3}\right)}+\frac{3 \hypergeom \left(\left[-\frac{7}{4}, -\frac{1}{3}\right], \left[-\frac{3}{4}\right], -x^{4}\right)}{7 x^{7}}+\hypergeom \left(\left[-\frac{1}{3}, \frac{1}{4}\right], \left[\frac{5}{4}\right], -x^{4}\right) x -\frac{-3 \left(3+\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)-\hypergeom \left(\left[\frac{2}{3}, 1, 1\right], \left[2, 2\right], -x^{4}\right) \Gamma \left(\frac{2}{3}\right) x^{4}}{12 \Gamma \left(\frac{2}{3}\right)}$&$148$\\ \hline \end{longtable}"," ",0,"3/28*(x^4+1)^(4/3)*(4*x^4+7*x^3+4)/x^7","A"
483,1,25,34,0.126000," ","int((x^4-3)*(x^4+1)^(2/3)*(x^4+x^3+1)/x^9,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{3 \left(x^{4}+1\right)^{\frac{5}{3}} \left(5 x^{4}+8 x^{3}+5\right)}{40 x^{8}}$&$25$\\ trager&$\frac{3 \left(x^{4}+1\right)^{\frac{2}{3}} \left(5 x^{8}+8 x^{7}+10 x^{4}+8 x^{3}+5\right)}{40 x^{8}}$&$35$\\ risch&$\frac{\frac{3}{5} x^{11}+\frac{6}{5} x^{7}+\frac{3}{5} x^{3}+\frac{9}{8} x^{8}+\frac{9}{8} x^{4}+\frac{3}{8}+\frac{3}{8} x^{12}}{x^{8} \left(x^{4}+1\right)^{\frac{1}{3}}}$&$45$\\ meijerg&$\frac{\Gamma \left(\frac{2}{3}\right) \sqrt{3}\, \left(\frac{\pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right) x^{4}}-\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+4 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}+\frac{\hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 3\right], -x^{4}\right) \pi  \sqrt{3}\, x^{4}}{9 \Gamma \left(\frac{2}{3}\right)}\right)}{6 \pi}+\frac{3 \hypergeom \left(\left[-\frac{5}{4}, -\frac{2}{3}\right], \left[-\frac{1}{4}\right], -x^{4}\right)}{5 x^{5}}+\frac{\Gamma \left(\frac{2}{3}\right) \sqrt{3}\, \left(\frac{\pi  \sqrt{3}}{2 \Gamma \left(\frac{2}{3}\right) x^{8}}+\frac{2 \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right) x^{4}}+\frac{\left(\frac{3}{2}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)\right) \pi  \sqrt{3}}{9 \Gamma \left(\frac{2}{3}\right)}-\frac{4 \hypergeom \left(\left[1, 1, \frac{7}{3}\right], \left[2, 4\right], -x^{4}\right) \pi  \sqrt{3}\, x^{4}}{81 \Gamma \left(\frac{2}{3}\right)}\right)}{4 \pi}-\frac{\Gamma \left(\frac{2}{3}\right) \sqrt{3}\, \left(-\frac{\left(\frac{3}{2}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)\right) \pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right)}-\frac{2 \hypergeom \left(\left[\frac{1}{3}, 1, 1\right], \left[2, 2\right], -x^{4}\right) \pi  \sqrt{3}\, x^{4}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{12 \pi}-\frac{\hypergeom \left(\left[-\frac{2}{3}, -\frac{1}{4}\right], \left[\frac{3}{4}\right], -x^{4}\right)}{x}$&$261$\\ \hline \end{longtable}"," ",0,"3/40*(x^4+1)^(5/3)*(5*x^4+8*x^3+5)/x^8","A"
484,1,35,34,0.142000," ","int((x^4-1)^(2/3)*(x^4+3)*(2*x^4-x^3-2)/x^9,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(x^{4}-1\right)^{\frac{2}{3}} \left(5 x^{8}-4 x^{7}-10 x^{4}+4 x^{3}+5\right)}{20 x^{8}}$&$35$\\ gosper&$\frac{3 \left(x^{2}+1\right) \left(-1+x \right) \left(1+x \right) \left(5 x^{4}-4 x^{3}-5\right) \left(x^{4}-1\right)^{\frac{2}{3}}}{20 x^{8}}$&$36$\\ risch&$\frac{-\frac{3}{5} x^{11}+\frac{6}{5} x^{7}-\frac{3}{5} x^{3}-\frac{9}{4} x^{8}+\frac{9}{4} x^{4}-\frac{3}{4}+\frac{3}{4} x^{12}}{x^{8} \left(x^{4}-1\right)^{\frac{1}{3}}}$&$45$\\ meijerg&$-\frac{\mathrm{signum}\left(x^{4}-1\right)^{\frac{2}{3}} \Gamma \left(\frac{2}{3}\right) \sqrt{3}\, \left(-\frac{\left(\frac{3}{2}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right)}+\frac{2 \hypergeom \left(\left[\frac{1}{3}, 1, 1\right], \left[2, 2\right], x^{4}\right) \pi  \sqrt{3}\, x^{4}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{6 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{2}{3}} \pi}+\frac{\mathrm{signum}\left(x^{4}-1\right)^{\frac{2}{3}} \hypergeom \left(\left[-\frac{2}{3}, -\frac{1}{4}\right], \left[\frac{3}{4}\right], x^{4}\right)}{\left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{2}{3}} x}+\frac{\mathrm{signum}\left(x^{4}-1\right)^{\frac{2}{3}} \Gamma \left(\frac{2}{3}\right) \sqrt{3}\, \left(-\frac{\pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right) x^{4}}-\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+4 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}-\frac{\hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 3\right], x^{4}\right) \pi  \sqrt{3}\, x^{4}}{9 \Gamma \left(\frac{2}{3}\right)}\right)}{3 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{2}{3}} \pi}+\frac{3 \mathrm{signum}\left(x^{4}-1\right)^{\frac{2}{3}} \hypergeom \left(\left[-\frac{5}{4}, -\frac{2}{3}\right], \left[-\frac{1}{4}\right], x^{4}\right)}{5 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{2}{3}} x^{5}}+\frac{\mathrm{signum}\left(x^{4}-1\right)^{\frac{2}{3}} \Gamma \left(\frac{2}{3}\right) \sqrt{3}\, \left(\frac{\pi  \sqrt{3}}{2 \Gamma \left(\frac{2}{3}\right) x^{8}}-\frac{2 \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right) x^{4}}+\frac{\left(\frac{3}{2}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{4 \hypergeom \left(\left[1, 1, \frac{7}{3}\right], \left[2, 4\right], x^{4}\right) \pi  \sqrt{3}\, x^{4}}{81 \Gamma \left(\frac{2}{3}\right)}\right)}{2 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{2}{3}} \pi}$&$353$\\ \hline \end{longtable}"," ",0,"3/20*(x^4-1)^(2/3)*(5*x^8-4*x^7-10*x^4+4*x^3+5)/x^8","A"
485,1,35,34,0.147000," ","int((x^5-1)^(3/4)*(x^5+4)*(x^5-x^4-1)/x^12,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{5}-1\right)^{\frac{3}{4}} \left(7 x^{10}-11 x^{9}-14 x^{5}+11 x^{4}+7\right)}{77 x^{11}}$&$35$\\ gosper&$\frac{4 \left(x^{5}-1\right)^{\frac{3}{4}} \left(7 x^{5}-11 x^{4}-7\right) \left(-1+x \right) \left(x^{4}+x^{3}+x^{2}+x +1\right)}{77 x^{11}}$&$40$\\ risch&$\frac{-\frac{4}{7} x^{14}+\frac{8}{7} x^{9}+\frac{4}{11} x^{15}-\frac{12}{11} x^{10}+\frac{12}{11} x^{5}-\frac{4}{11}-\frac{4}{7} x^{4}}{x^{11} \left(x^{5}-1\right)^{\frac{1}{4}}}$&$45$\\ meijerg&$-\frac{\mathrm{signum}\left(x^{5}-1\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{3}{4}, -\frac{1}{5}\right], \left[\frac{4}{5}\right], x^{5}\right)}{\left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{3}{4}} x}+\frac{\mathrm{signum}\left(x^{5}-1\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{3}{4}, -\frac{2}{5}\right], \left[\frac{3}{5}\right], x^{5}\right)}{2 \left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{3}{4}} x^{2}}-\frac{\mathrm{signum}\left(x^{5}-1\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{6}{5}, -\frac{3}{4}\right], \left[-\frac{1}{5}\right], x^{5}\right)}{2 \left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{3}{4}} x^{6}}+\frac{4 \mathrm{signum}\left(x^{5}-1\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{7}{5}, -\frac{3}{4}\right], \left[-\frac{2}{5}\right], x^{5}\right)}{7 \left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{3}{4}} x^{7}}+\frac{4 \mathrm{signum}\left(x^{5}-1\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{11}{5}, -\frac{3}{4}\right], \left[-\frac{6}{5}\right], x^{5}\right)}{11 \left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{3}{4}} x^{11}}$&$162$\\ \hline \end{longtable}"," ",0,"4/77*(x^5-1)^(3/4)*(7*x^10-11*x^9-14*x^5+11*x^4+7)/x^11","A"
486,1,35,34,0.138000," ","int((x^5+1)^(2/3)*(x^5+x^3+1)*(2*x^5-3)/x^9,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(x^{5}+1\right)^{\frac{2}{3}} \left(5 x^{10}+8 x^{8}+10 x^{5}+8 x^{3}+5\right)}{40 x^{8}}$&$35$\\ gosper&$\frac{3 \left(x^{4}-x^{3}+x^{2}-x +1\right) \left(1+x \right) \left(5 x^{5}+8 x^{3}+5\right) \left(x^{5}+1\right)^{\frac{2}{3}}}{40 x^{8}}$&$44$\\ risch&$\frac{\frac{6}{5} x^{8}+\frac{3}{5} x^{3}+\frac{9}{8} x^{10}+\frac{9}{8} x^{5}+\frac{3}{8}+\frac{3}{8} x^{15}+\frac{3}{5} x^{13}}{x^{8} \left(x^{5}+1\right)^{\frac{1}{3}}}$&$45$\\ meijerg&$\hypergeom \left(\left[-\frac{2}{3}, \frac{2}{5}\right], \left[\frac{7}{5}\right], -x^{5}\right) x^{2}+\frac{\hypergeom \left(\left[-\frac{2}{3}, -\frac{3}{5}\right], \left[\frac{2}{5}\right], -x^{5}\right)}{3 x^{3}}-\frac{2 \Gamma \left(\frac{2}{3}\right) \sqrt{3}\, \left(-\frac{\left(\frac{3}{2}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+5 \ln \left(x \right)\right) \pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right)}-\frac{2 \hypergeom \left(\left[\frac{1}{3}, 1, 1\right], \left[2, 2\right], -x^{5}\right) \pi  \sqrt{3}\, x^{5}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{15 \pi}+\frac{\Gamma \left(\frac{2}{3}\right) \sqrt{3}\, \left(\frac{\pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right) x^{5}}-\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+5 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}+\frac{\hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 3\right], -x^{5}\right) \pi  \sqrt{3}\, x^{5}}{9 \Gamma \left(\frac{2}{3}\right)}\right)}{5 \pi}+\frac{3 \hypergeom \left(\left[-\frac{8}{5}, -\frac{2}{3}\right], \left[-\frac{3}{5}\right], -x^{5}\right)}{8 x^{8}}$&$187$\\ \hline \end{longtable}"," ",0,"3/40*(x^5+1)^(2/3)*(5*x^10+8*x^8+10*x^5+8*x^3+5)/x^8","A"
487,1,35,34,0.151000," ","int((x^5-1)^(2/3)*(x^5+x^3-1)*(2*x^5+3)/x^9,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(x^{5}-1\right)^{\frac{2}{3}} \left(5 x^{10}+8 x^{8}-10 x^{5}-8 x^{3}+5\right)}{40 x^{8}}$&$35$\\ gosper&$\frac{3 \left(x^{4}+x^{3}+x^{2}+x +1\right) \left(-1+x \right) \left(5 x^{5}+8 x^{3}-5\right) \left(x^{5}-1\right)^{\frac{2}{3}}}{40 x^{8}}$&$40$\\ risch&$\frac{-\frac{6}{5} x^{8}+\frac{3}{5} x^{3}-\frac{9}{8} x^{10}+\frac{9}{8} x^{5}-\frac{3}{8}+\frac{3}{8} x^{15}+\frac{3}{5} x^{13}}{x^{8} \left(x^{5}-1\right)^{\frac{1}{3}}}$&$45$\\ meijerg&$\frac{\mathrm{signum}\left(x^{5}-1\right)^{\frac{2}{3}} \hypergeom \left(\left[-\frac{2}{3}, \frac{2}{5}\right], \left[\frac{7}{5}\right], x^{5}\right) x^{2}}{\left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{2}{3}}}-\frac{\mathrm{signum}\left(x^{5}-1\right)^{\frac{2}{3}} \hypergeom \left(\left[-\frac{2}{3}, -\frac{3}{5}\right], \left[\frac{2}{5}\right], x^{5}\right)}{3 \left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{2}{3}} x^{3}}-\frac{2 \mathrm{signum}\left(x^{5}-1\right)^{\frac{2}{3}} \Gamma \left(\frac{2}{3}\right) \sqrt{3}\, \left(-\frac{\left(\frac{3}{2}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+5 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right)}+\frac{2 \hypergeom \left(\left[\frac{1}{3}, 1, 1\right], \left[2, 2\right], x^{5}\right) \pi  \sqrt{3}\, x^{5}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{15 \left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{2}{3}} \pi}+\frac{\mathrm{signum}\left(x^{5}-1\right)^{\frac{2}{3}} \Gamma \left(\frac{2}{3}\right) \sqrt{3}\, \left(-\frac{\pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right) x^{5}}-\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+5 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}-\frac{\hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 3\right], x^{5}\right) \pi  \sqrt{3}\, x^{5}}{9 \Gamma \left(\frac{2}{3}\right)}\right)}{5 \left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{2}{3}} \pi}+\frac{3 \mathrm{signum}\left(x^{5}-1\right)^{\frac{2}{3}} \hypergeom \left(\left[-\frac{8}{5}, -\frac{2}{3}\right], \left[-\frac{3}{5}\right], x^{5}\right)}{8 \left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{2}{3}} x^{8}}$&$276$\\ \hline \end{longtable}"," ",0,"3/40*(x^5-1)^(2/3)*(5*x^10+8*x^8-10*x^5-8*x^3+5)/x^8","A"
488,1,35,34,0.125000," ","int((x^5-4)*(x^5+1)^(3/4)*(2*x^5-x^4+2)/x^12,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{5}+1\right)^{\frac{3}{4}} \left(14 x^{10}-11 x^{9}+28 x^{5}-11 x^{4}+14\right)}{77 x^{11}}$&$35$\\ gosper&$\frac{4 \left(x^{4}-x^{3}+x^{2}-x +1\right) \left(1+x \right) \left(14 x^{5}-11 x^{4}+14\right) \left(x^{5}+1\right)^{\frac{3}{4}}}{77 x^{11}}$&$44$\\ risch&$\frac{-\frac{4}{7} x^{14}-\frac{8}{7} x^{9}+\frac{8}{11} x^{15}+\frac{24}{11} x^{10}+\frac{24}{11} x^{5}+\frac{8}{11}-\frac{4}{7} x^{4}}{x^{11} \left(x^{5}+1\right)^{\frac{1}{4}}}$&$45$\\ meijerg&$\frac{\hypergeom \left(\left[-\frac{6}{5}, -\frac{3}{4}\right], \left[-\frac{1}{5}\right], -x^{5}\right)}{x^{6}}-\frac{4 \hypergeom \left(\left[-\frac{7}{5}, -\frac{3}{4}\right], \left[-\frac{2}{5}\right], -x^{5}\right)}{7 x^{7}}+\frac{8 \hypergeom \left(\left[-\frac{11}{5}, -\frac{3}{4}\right], \left[-\frac{6}{5}\right], -x^{5}\right)}{11 x^{11}}-\frac{2 \hypergeom \left(\left[-\frac{3}{4}, -\frac{1}{5}\right], \left[\frac{4}{5}\right], -x^{5}\right)}{x}+\frac{\hypergeom \left(\left[-\frac{3}{4}, -\frac{2}{5}\right], \left[\frac{3}{5}\right], -x^{5}\right)}{2 x^{2}}$&$81$\\ \hline \end{longtable}"," ",0,"4/77*(x^5+1)^(3/4)*(14*x^10-11*x^9+28*x^5-11*x^4+14)/x^11","A"
489,1,35,34,0.098000," ","int((x^5+1)^(2/3)*(2*x^5-3)*(4*x^5+3*x^3+4)/x^9,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(x^{5}+1\right)^{\frac{2}{3}} \left(5 x^{10}+6 x^{8}+10 x^{5}+6 x^{3}+5\right)}{10 x^{8}}$&$35$\\ gosper&$\frac{3 \left(x^{4}-x^{3}+x^{2}-x +1\right) \left(1+x \right) \left(5 x^{5}+6 x^{3}+5\right) \left(x^{5}+1\right)^{\frac{2}{3}}}{10 x^{8}}$&$44$\\ risch&$\frac{\frac{18}{5} x^{8}+\frac{9}{5} x^{3}+\frac{9}{2} x^{10}+\frac{9}{2} x^{5}+\frac{3}{2}+\frac{3}{2} x^{15}+\frac{9}{5} x^{13}}{x^{8} \left(x^{5}+1\right)^{\frac{1}{3}}}$&$45$\\ meijerg&$4 \hypergeom \left(\left[-\frac{2}{3}, \frac{2}{5}\right], \left[\frac{7}{5}\right], -x^{5}\right) x^{2}-\frac{2 \Gamma \left(\frac{2}{3}\right) \sqrt{3}\, \left(-\frac{\left(\frac{3}{2}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+5 \ln \left(x \right)\right) \pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right)}-\frac{2 \hypergeom \left(\left[\frac{1}{3}, 1, 1\right], \left[2, 2\right], -x^{5}\right) \pi  \sqrt{3}\, x^{5}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{5 \pi}+\frac{4 \hypergeom \left(\left[-\frac{2}{3}, -\frac{3}{5}\right], \left[\frac{2}{5}\right], -x^{5}\right)}{3 x^{3}}+\frac{3 \Gamma \left(\frac{2}{3}\right) \sqrt{3}\, \left(\frac{\pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right) x^{5}}-\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+5 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}+\frac{\hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 3\right], -x^{5}\right) \pi  \sqrt{3}\, x^{5}}{9 \Gamma \left(\frac{2}{3}\right)}\right)}{5 \pi}+\frac{3 \hypergeom \left(\left[-\frac{8}{5}, -\frac{2}{3}\right], \left[-\frac{3}{5}\right], -x^{5}\right)}{2 x^{8}}$&$188$\\ \hline \end{longtable}"," ",0,"3/10*(x^5+1)^(2/3)*(5*x^10+6*x^8+10*x^5+6*x^3+5)/x^8","A"
490,1,32,30,0.359000," ","int(1/x^13/(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 x^{12}-x^{6}-2}{24 x^{12} \sqrt{x^{6}-1}}-\frac{\arcsin \left(\frac{1}{x^{3}}\right)}{8}$&$32$\\ trager&$\frac{\sqrt{x^{6}-1}\, \left(3 x^{6}+2\right)}{24 x^{12}}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{8}$&$48$\\ meijerg&$\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(-\frac{\sqrt{\pi}}{2 x^{12}}-\frac{\sqrt{\pi}}{2 x^{6}}+\frac{3 \left(\frac{7}{6}-2 \ln \left(2\right)+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}}{8}+\frac{\sqrt{\pi}\, \left(-7 x^{12}+8 x^{6}+8\right)}{16 x^{12}}-\frac{\sqrt{\pi}\, \left(12 x^{6}+8\right) \sqrt{-x^{6}+1}}{16 x^{12}}-\frac{3 \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right) \sqrt{\pi}}{4}\right)}{6 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$123$\\ \hline \end{longtable}"," ",0,"1/24*(3*x^12-x^6-2)/x^12/(x^6-1)^(1/2)-1/8*arcsin(1/x^3)","A"
491,1,37,30,0.244000," ","int((x^6-1)/x^13/(x^6+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(7 x^{6}-2\right) \sqrt{x^{6}+1}}{24 x^{12}}-\frac{7 \ln \left(\frac{\sqrt{x^{6}+1}-1}{x^{3}}\right)}{24}$&$37$\\ risch&$-\frac{7 x^{12}+5 x^{6}-2}{24 x^{12} \sqrt{x^{6}+1}}-\frac{7 \ln \left(\frac{\sqrt{x^{6}+1}-1}{\sqrt{x^{6}}}\right)}{24}$&$44$\\ meijerg&$\frac{-\frac{\sqrt{\pi}}{x^{6}}-\frac{\left(1-2 \ln \left(2\right)+6 \ln \left(x \right)\right) \sqrt{\pi}}{2}+\frac{\sqrt{\pi}\, \left(4 x^{6}+8\right)}{8 x^{6}}-\frac{\sqrt{\pi}\, \sqrt{x^{6}+1}}{x^{6}}+\ln \left(\frac{1}{2}+\frac{\sqrt{x^{6}+1}}{2}\right) \sqrt{\pi}}{6 \sqrt{\pi}}-\frac{-\frac{\sqrt{\pi}}{2 x^{12}}+\frac{\sqrt{\pi}}{2 x^{6}}+\frac{3 \left(\frac{7}{6}-2 \ln \left(2\right)+6 \ln \left(x \right)\right) \sqrt{\pi}}{8}+\frac{\sqrt{\pi}\, \left(-7 x^{12}-8 x^{6}+8\right)}{16 x^{12}}-\frac{\sqrt{\pi}\, \left(-12 x^{6}+8\right) \sqrt{x^{6}+1}}{16 x^{12}}-\frac{3 \ln \left(\frac{1}{2}+\frac{\sqrt{x^{6}+1}}{2}\right) \sqrt{\pi}}{4}}{6 \sqrt{\pi}}$&$173$\\ \hline \end{longtable}"," ",0,"-1/24*(7*x^6-2)/x^12*(x^6+1)^(1/2)-7/24*ln(((x^6+1)^(1/2)-1)/x^3)","A"
492,1,35,30,0.230000," ","int((x^6+1)^(1/2)/x^13,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(x^{6}+2\right) \sqrt{x^{6}+1}}{24 x^{12}}+\frac{\ln \left(\frac{\sqrt{x^{6}+1}+1}{x^{3}}\right)}{24}$&$35$\\ risch&$-\frac{x^{12}+3 x^{6}+2}{24 x^{12} \sqrt{x^{6}+1}}-\frac{\ln \left(\frac{\sqrt{x^{6}+1}-1}{\sqrt{x^{6}}}\right)}{24}$&$42$\\ meijerg&$-\frac{\frac{\sqrt{\pi}}{x^{12}}+\frac{\sqrt{\pi}}{x^{6}}+\frac{\left(\frac{1}{2}-2 \ln \left(2\right)+6 \ln \left(x \right)\right) \sqrt{\pi}}{4}-\frac{\sqrt{\pi}\, \left(x^{12}+8 x^{6}+8\right)}{8 x^{12}}+\frac{\sqrt{\pi}\, \left(4 x^{6}+8\right) \sqrt{x^{6}+1}}{8 x^{12}}-\frac{\ln \left(\frac{1}{2}+\frac{\sqrt{x^{6}+1}}{2}\right) \sqrt{\pi}}{2}}{12 \sqrt{\pi}}$&$93$\\ \hline \end{longtable}"," ",0,"-1/24*(x^6+2)/x^12*(x^6+1)^(1/2)+1/24*ln(((x^6+1)^(1/2)+1)/x^3)","A"
493,1,32,30,0.377000," ","int((x^6+1)/x^13/(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{7 x^{12}-5 x^{6}-2}{24 x^{12} \sqrt{x^{6}-1}}-\frac{7 \arcsin \left(\frac{1}{x^{3}}\right)}{24}$&$32$\\ trager&$\frac{\sqrt{x^{6}-1}\, \left(7 x^{6}+2\right)}{24 x^{12}}-\frac{7 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{24}$&$50$\\ meijerg&$-\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(\frac{\sqrt{\pi}}{x^{6}}-\frac{\left(1-2 \ln \left(2\right)+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}}{2}-\frac{\sqrt{\pi}\, \left(-4 x^{6}+8\right)}{8 x^{6}}+\frac{\sqrt{\pi}\, \sqrt{-x^{6}+1}}{x^{6}}+\ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right) \sqrt{\pi}\right)}{6 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}+\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(-\frac{\sqrt{\pi}}{2 x^{12}}-\frac{\sqrt{\pi}}{2 x^{6}}+\frac{3 \left(\frac{7}{6}-2 \ln \left(2\right)+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}}{8}+\frac{\sqrt{\pi}\, \left(-7 x^{12}+8 x^{6}+8\right)}{16 x^{12}}-\frac{\sqrt{\pi}\, \left(12 x^{6}+8\right) \sqrt{-x^{6}+1}}{16 x^{12}}-\frac{3 \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right) \sqrt{\pi}}{4}\right)}{6 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$223$\\ \hline \end{longtable}"," ",0,"1/24*(7*x^12-5*x^6-2)/x^12/(x^6-1)^(1/2)-7/24*arcsin(1/x^3)","A"
494,1,35,34,0.164000," ","int((x^6-1)^(1/3)*(x^6+1)*(x^6+x^3-1)/x^8,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{6}-1\right)^{\frac{1}{3}} \left(4 x^{12}+7 x^{9}-8 x^{6}-7 x^{3}+4\right)}{28 x^{7}}$&$35$\\ gosper&$\frac{\left(x^{6}-1\right)^{\frac{1}{3}} \left(4 x^{6}+7 x^{3}-4\right) \left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right)}{28 x^{7}}$&$45$\\ risch&$\frac{4 x^{18}+7 x^{15}-12 x^{12}-14 x^{9}+12 x^{6}+7 x^{3}-4}{28 \left(x^{6}-1\right)^{\frac{2}{3}} x^{7}}$&$45$\\ meijerg&$\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{5}{6}\right], \left[\frac{11}{6}\right], x^{6}\right) x^{5}}{5 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}}}+\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{6}\right) x^{2}}{2 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}}}-\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{2}{3}, -\frac{1}{3}\right], \left[\frac{1}{3}\right], x^{6}\right)}{4 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} x^{4}}+\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{7}{6}, -\frac{1}{3}\right], \left[-\frac{1}{6}\right], x^{6}\right)}{7 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} x^{7}}$&$130$\\ \hline \end{longtable}"," ",0,"1/28*(x^6-1)^(1/3)*(4*x^12+7*x^9-8*x^6-7*x^3+4)/x^7","A"
495,1,35,34,0.150000," ","int((x^6-1)^(3/4)*(x^6+2)*(x^6-x^4-1)/x^12,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{6}-1\right)^{\frac{3}{4}} \left(7 x^{12}-11 x^{10}-14 x^{6}+11 x^{4}+7\right)}{77 x^{11}}$&$35$\\ gosper&$\frac{2 \left(-1+x \right) \left(x^{2}+x +1\right) \left(1+x \right) \left(x^{2}-x +1\right) \left(7 x^{6}-11 x^{4}-7\right) \left(x^{6}-1\right)^{\frac{3}{4}}}{77 x^{11}}$&$45$\\ risch&$\frac{\frac{2}{11} x^{18}-\frac{6}{11} x^{12}+\frac{6}{11} x^{6}-\frac{2}{11}-\frac{2}{7} x^{16}+\frac{4}{7} x^{10}-\frac{2}{7} x^{4}}{x^{11} \left(x^{6}-1\right)^{\frac{1}{4}}}$&$45$\\ meijerg&$\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{3}{4}, \frac{1}{6}\right], \left[\frac{7}{6}\right], x^{6}\right) x}{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{3}{4}}}+\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{3}{4}, -\frac{1}{6}\right], \left[\frac{5}{6}\right], x^{6}\right)}{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{3}{4}} x}-\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{5}{6}, -\frac{3}{4}\right], \left[\frac{1}{6}\right], x^{6}\right)}{5 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{3}{4}} x^{5}}+\frac{2 \mathrm{signum}\left(x^{6}-1\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{7}{6}, -\frac{3}{4}\right], \left[-\frac{1}{6}\right], x^{6}\right)}{7 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{3}{4}} x^{7}}+\frac{2 \mathrm{signum}\left(x^{6}-1\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{11}{6}, -\frac{3}{4}\right], \left[-\frac{5}{6}\right], x^{6}\right)}{11 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{3}{4}} x^{11}}$&$158$\\ \hline \end{longtable}"," ",0,"2/77*(x^6-1)^(3/4)*(7*x^12-11*x^10-14*x^6+11*x^4+7)/x^11","A"
496,1,35,34,0.135000," ","int((x^6-2)*(x^6+1)^(3/4)*(x^6-x^4+1)/x^12,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{6}+1\right)^{\frac{3}{4}} \left(7 x^{12}-11 x^{10}+14 x^{6}-11 x^{4}+7\right)}{77 x^{11}}$&$35$\\ gosper&$\frac{2 \left(x^{2}+1\right) \left(x^{4}-x^{2}+1\right) \left(7 x^{6}-11 x^{4}+7\right) \left(x^{6}+1\right)^{\frac{3}{4}}}{77 x^{11}}$&$40$\\ risch&$\frac{\frac{2}{11} x^{18}+\frac{6}{11} x^{12}+\frac{6}{11} x^{6}+\frac{2}{11}-\frac{2}{7} x^{16}-\frac{4}{7} x^{10}-\frac{2}{7} x^{4}}{x^{11} \left(x^{6}+1\right)^{\frac{1}{4}}}$&$45$\\ meijerg&$\frac{\hypergeom \left(\left[-\frac{5}{6}, -\frac{3}{4}\right], \left[\frac{1}{6}\right], -x^{6}\right)}{5 x^{5}}-\frac{2 \hypergeom \left(\left[-\frac{7}{6}, -\frac{3}{4}\right], \left[-\frac{1}{6}\right], -x^{6}\right)}{7 x^{7}}+\frac{2 \hypergeom \left(\left[-\frac{11}{6}, -\frac{3}{4}\right], \left[-\frac{5}{6}\right], -x^{6}\right)}{11 x^{11}}+\hypergeom \left(\left[-\frac{3}{4}, \frac{1}{6}\right], \left[\frac{7}{6}\right], -x^{6}\right) x +\frac{\hypergeom \left(\left[-\frac{3}{4}, -\frac{1}{6}\right], \left[\frac{5}{6}\right], -x^{6}\right)}{x}$&$78$\\ \hline \end{longtable}"," ",0,"2/77*(x^6+1)^(3/4)*(7*x^12-11*x^10+14*x^6-11*x^4+7)/x^11","A"
497,1,37,36,0.184000," ","int((3*x^2-2*x)/(x^6-2*x^5+x^4+4*x^3-4*x^2+5)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(2-x^{2}+x^{3}+\sqrt{x^{6}-2 x^{5}+x^{4}+4 x^{3}-4 x^{2}+5}\right)$&$37$\\ \hline \end{longtable}"," ",0,"ln(2-x^2+x^3+(x^6-2*x^5+x^4+4*x^3-4*x^2+5)^(1/2))","A"
498,1,76,29,0.863000," ","int((5*x^6-2)/x/(x^6-1)^(1/2)/(x^6+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{3}-\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) x^{6}-4 \RootOf \left(\textit{\_Z}^{2}+3\right)+6 \sqrt{x^{6}-1}}{x^{6}+2}\right)}{3}$&$76$\\ \hline \end{longtable}"," ",0,"1/3*RootOf(_Z^2+1)*ln((-RootOf(_Z^2+1)+(x^6-1)^(1/2))/x^3)-1/3*RootOf(_Z^2+3)*ln((RootOf(_Z^2+3)*x^6-4*RootOf(_Z^2+3)+6*(x^6-1)^(1/2))/(x^6+2))","C"
499,1,87,29,0.916000," ","int((10*x^6-1)/x/(x^6-1)^(1/2)/(4*x^6-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{6}-7 \RootOf \left(\textit{\_Z}^{2}+3\right)-12 \sqrt{x^{6}-1}}{\left(2 x^{3}-1\right) \left(2 x^{3}+1\right)}\right)}{6}$&$87$\\ \hline \end{longtable}"," ",0,"1/3*RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)+(x^6-1)^(1/2))/x^3)+1/6*RootOf(_Z^2+3)*ln(-(4*RootOf(_Z^2+3)*x^6-7*RootOf(_Z^2+3)-12*(x^6-1)^(1/2))/(2*x^3-1)/(2*x^3+1))","C"
500,1,56,33,1.181000," ","int((x^2+x+2)/x^2/(x^2+1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{2 \left(x^{2}+1\right)^{\frac{1}{4}}}{x}+\frac{\left(-3 \ln \left(2\right)+\frac{\pi}{2}+2 \ln \left(x \right)\right) \Gamma \left(\frac{3}{4}\right)-\frac{3 \hypergeom \left(\left[1, 1, \frac{7}{4}\right], \left[2, 2\right], -x^{2}\right) \Gamma \left(\frac{3}{4}\right) x^{2}}{4}}{2 \Gamma \left(\frac{3}{4}\right)}$&$56$\\ meijerg&$\hypergeom \left(\left[\frac{1}{2}, \frac{3}{4}\right], \left[\frac{3}{2}\right], -x^{2}\right) x +\frac{\left(-3 \ln \left(2\right)+\frac{\pi}{2}+2 \ln \left(x \right)\right) \Gamma \left(\frac{3}{4}\right)-\frac{3 \hypergeom \left(\left[1, 1, \frac{7}{4}\right], \left[2, 2\right], -x^{2}\right) \Gamma \left(\frac{3}{4}\right) x^{2}}{4}}{2 \Gamma \left(\frac{3}{4}\right)}-\frac{2 \hypergeom \left(\left[-\frac{1}{2}, \frac{3}{4}\right], \left[\frac{1}{2}\right], -x^{2}\right)}{x}$&$73$\\ trager&$-\frac{2 \left(x^{2}+1\right)^{\frac{1}{4}}}{x}-\frac{\ln \left(-\frac{2 \left(x^{2}+1\right)^{\frac{3}{4}}+2 \sqrt{x^{2}+1}+x^{2}+2 \left(x^{2}+1\right)^{\frac{1}{4}}+2}{x^{2}}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{2}+1}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-2 \left(x^{2}+1\right)^{\frac{3}{4}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right)+2 \left(x^{2}+1\right)^{\frac{1}{4}}}{x^{2}}\right)}{2}$&$120$\\ \hline \end{longtable}"," ",0,"-2*(x^2+1)^(1/4)/x+1/2/GAMMA(3/4)*((-3*ln(2)+1/2*Pi+2*ln(x))*GAMMA(3/4)-3/4*hypergeom([1,1,7/4],[2,2],-x^2)*GAMMA(3/4)*x^2)","C"
501,1,150,35,1.804000," ","int((-3+2*x)/(x^2-x)^(1/4)/(x^3-x+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(-\frac{2 \left(x^{2}-x \right)^{\frac{3}{4}}+2 x \sqrt{x^{2}-x}+2 \left(x^{2}-x \right)^{\frac{1}{4}} x^{2}+x^{3}+x -1}{x^{3}-x +1}\right)+\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{2}-x}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{2}-x \right)^{\frac{3}{4}}-2 \left(x^{2}-x \right)^{\frac{1}{4}} x^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right) x +\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{3}-x +1}\right)$&$150$\\ \hline \end{longtable}"," ",0,"-ln(-(2*(x^2-x)^(3/4)+2*x*(x^2-x)^(1/2)+2*(x^2-x)^(1/4)*x^2+x^3+x-1)/(x^3-x+1))+RootOf(_Z^2+1)*ln(-(2*RootOf(_Z^2+1)*(x^2-x)^(1/2)*x-RootOf(_Z^2+1)*x^3+2*(x^2-x)^(3/4)-2*(x^2-x)^(1/4)*x^2-RootOf(_Z^2+1)*x+RootOf(_Z^2+1))/(x^3-x+1))","C"
502,1,71,35,0.411000," ","int((x^2-1)*(x^3+x)^(1/2)/(x^2+1)/(x^2+x+1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{3}+x}}{x^{2}+x +1}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right) x +\RootOf \left(\textit{\_Z}^{2}+1\right)+2 \sqrt{x^{3}+x}}{x^{2}+x +1}\right)}{2}$&$71$\\ elliptic&$\frac{\sqrt{x^{3}+x}}{x^{2}+x +1}+\frac{i \sqrt{-i \left(i+x \right)}\, \sqrt{2}\, \sqrt{i \left(-i+x \right)}\, \sqrt{i x}\, \EllipticF \left(\sqrt{-i \left(i+x \right)}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{3}+x}}+\frac{i \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{-i \left(i+x \right)}\, \sqrt{2}\, \sqrt{i \left(-i+x \right)}\, \sqrt{i x}\, \left(i \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)+1+i\right) \EllipticPi \left(\sqrt{-i \left(i+x \right)}, \frac{1}{2}-i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{3}+x}}+\frac{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-i \left(i+x \right)}\, \sqrt{2}\, \sqrt{i \left(-i+x \right)}\, \sqrt{i x}\, \left(i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)+1+i\right) \EllipticPi \left(\sqrt{-i \left(i+x \right)}, \frac{1}{2}-i-\frac{i \sqrt{3}}{2}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{3}+x}}$&$240$\\ risch&$\frac{\left(x^{2}+1\right) x}{\left(x^{2}+x +1\right) \sqrt{\left(x^{2}+1\right) x}}+\frac{i \sqrt{-i \left(i+x \right)}\, \sqrt{2}\, \sqrt{i \left(-i+x \right)}\, \sqrt{i x}\, \EllipticF \left(\sqrt{-i \left(i+x \right)}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{3}+x}}+\frac{i \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{-i \left(i+x \right)}\, \sqrt{2}\, \sqrt{i \left(-i+x \right)}\, \sqrt{i x}\, \left(i \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)+1+i\right) \EllipticPi \left(\sqrt{-i \left(i+x \right)}, \frac{1}{2}-i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{3}+x}}+\frac{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-i \left(i+x \right)}\, \sqrt{2}\, \sqrt{i \left(-i+x \right)}\, \sqrt{i x}\, \left(i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)+1+i\right) \EllipticPi \left(\sqrt{-i \left(i+x \right)}, \frac{1}{2}-i-\frac{i \sqrt{3}}{2}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{3}+x}}$&$248$\\ default&$\frac{i \sqrt{-i \left(i+x \right)}\, \sqrt{2}\, \sqrt{i \left(-i+x \right)}\, \sqrt{i x}\, \EllipticF \left(\sqrt{-i \left(i+x \right)}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{3}+x}}-\frac{2 i \left(\frac{1}{2}-\frac{i \sqrt{3}}{6}\right) \sqrt{-i \left(i+x \right)}\, \sqrt{2}\, \sqrt{i \left(-i+x \right)}\, \sqrt{i x}\, \left(i \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)+1+i\right) \EllipticPi \left(\sqrt{-i \left(i+x \right)}, \frac{1}{2}-i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}+x}}-\frac{2 i \left(\frac{i \sqrt{3}}{6}+\frac{1}{2}\right) \sqrt{-i \left(i+x \right)}\, \sqrt{2}\, \sqrt{i \left(-i+x \right)}\, \sqrt{i x}\, \left(i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)+1+i\right) \EllipticPi \left(\sqrt{-i \left(i+x \right)}, \frac{1}{2}-i-\frac{i \sqrt{3}}{2}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}+x}}+\frac{\sqrt{x^{3}+x}}{x^{2}+x +1}-\frac{i \left(-\frac{3}{4}+\frac{i \sqrt{3}}{12}\right) \sqrt{-i \left(i+x \right)}\, \sqrt{2}\, \sqrt{i \left(-i+x \right)}\, \sqrt{i x}\, \left(i \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)+1+i\right) \EllipticPi \left(\sqrt{-i \left(i+x \right)}, \frac{1}{2}-i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}+x}}-\frac{i \left(-\frac{3}{4}-\frac{i \sqrt{3}}{12}\right) \sqrt{-i \left(i+x \right)}\, \sqrt{2}\, \sqrt{i \left(-i+x \right)}\, \sqrt{i x}\, \left(i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)+1+i\right) \EllipticPi \left(\sqrt{-i \left(i+x \right)}, \frac{1}{2}-i-\frac{i \sqrt{3}}{2}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}+x}}$&$410$\\ \hline \end{longtable}"," ",0,"(x^3+x)^(1/2)/(x^2+x+1)-1/2*RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)*x^2-RootOf(_Z^2+1)*x+RootOf(_Z^2+1)+2*(x^3+x)^(1/2))/(x^2+x+1))","C"
503,1,98,35,4.174000," ","int((x^3-2)*(2*x^3+x^2+2)^(1/2)/(x^3+1)/(x^3+x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(-\frac{x^{3}+\sqrt{2 x^{3}+x^{2}+2}\, x +x^{2}+1}{\left(1+x \right) \left(x^{2}-x +1\right)}\right)+\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+\sqrt{2 x^{3}+x^{2}+2}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{3}+x^{2}+1}\right)$&$98$\\ default&$\text{Expression too large to display}$&$4717$\\ elliptic&$\text{Expression too large to display}$&$73157$\\ \hline \end{longtable}"," ",0,"-ln(-(x^3+(2*x^3+x^2+2)^(1/2)*x+x^2+1)/(1+x)/(x^2-x+1))+RootOf(_Z^2+1)*ln(-(-RootOf(_Z^2+1)*x^3+(2*x^3+x^2+2)^(1/2)*x-RootOf(_Z^2+1))/(x^3+x^2+1))","C"
504,1,1089,33,0.250000," ","int((a*x^2+b)/(a*x^2+c*x-b)/(a*x^3-b*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}-b x}}+\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}-\frac{-c +\sqrt{4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) c^{2}}{2 \sqrt{4 a b +c^{2}}\, a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{c}{2 a}-\frac{\sqrt{4 a b +c^{2}}}{2 a}\right)}-\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}-\frac{-c +\sqrt{4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) c}{2 a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{c}{2 a}-\frac{\sqrt{4 a b +c^{2}}}{2 a}\right)}+\frac{2 \sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}-\frac{-c +\sqrt{4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) b}{\sqrt{4 a b +c^{2}}\, a \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{c}{2 a}-\frac{\sqrt{4 a b +c^{2}}}{2 a}\right)}-\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}+\frac{c +\sqrt{4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) c^{2}}{2 \sqrt{4 a b +c^{2}}\, a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{c}{2 a}+\frac{\sqrt{4 a b +c^{2}}}{2 a}\right)}-\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}+\frac{c +\sqrt{4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) c}{2 a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{c}{2 a}+\frac{\sqrt{4 a b +c^{2}}}{2 a}\right)}-\frac{2 \sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}+\frac{c +\sqrt{4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) b}{\sqrt{4 a b +c^{2}}\, a \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{c}{2 a}+\frac{\sqrt{4 a b +c^{2}}}{2 a}\right)}$&$1089$\\ default&$\frac{\sqrt{a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}-b x}}+\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}-\frac{-c +\sqrt{4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) c^{2}}{2 \sqrt{4 a b +c^{2}}\, a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{c}{2 a}-\frac{\sqrt{4 a b +c^{2}}}{2 a}\right)}-\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}-\frac{-c +\sqrt{4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) c}{2 a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{c}{2 a}-\frac{\sqrt{4 a b +c^{2}}}{2 a}\right)}+\frac{2 \sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}-\frac{-c +\sqrt{4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) b}{\sqrt{4 a b +c^{2}}\, a \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{c}{2 a}-\frac{\sqrt{4 a b +c^{2}}}{2 a}\right)}-\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}+\frac{c +\sqrt{4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) c^{2}}{2 \sqrt{4 a b +c^{2}}\, a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{c}{2 a}+\frac{\sqrt{4 a b +c^{2}}}{2 a}\right)}-\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}+\frac{c +\sqrt{4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) c}{2 a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{c}{2 a}+\frac{\sqrt{4 a b +c^{2}}}{2 a}\right)}-\frac{2 \sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}+\frac{c +\sqrt{4 a b +c^{2}}}{2 a}\right)}, \frac{\sqrt{2}}{2}\right) b}{\sqrt{4 a b +c^{2}}\, a \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{c}{2 a}+\frac{\sqrt{4 a b +c^{2}}}{2 a}\right)}$&$1106$\\ \hline \end{longtable}"," ",0,"1/a*(a*b)^(1/2)*(x*a/(a*b)^(1/2)+1)^(1/2)*(-2*x*a/(a*b)^(1/2)+2)^(1/2)*(-x*a/(a*b)^(1/2))^(1/2)/(a*x^3-b*x)^(1/2)*EllipticF(((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2),1/2*2^(1/2))+1/2/(4*a*b+c^2)^(1/2)/a^2*(a*b)^(1/2)*(x*a/(a*b)^(1/2)+1)^(1/2)*(-2*x*a/(a*b)^(1/2)+2)^(1/2)*(-x*a/(a*b)^(1/2))^(1/2)/(a*x^3-b*x)^(1/2)/(-1/a*(a*b)^(1/2)+1/2*c/a-1/2/a*(4*a*b+c^2)^(1/2))*EllipticPi(((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2),-1/a*(a*b)^(1/2)/(-1/a*(a*b)^(1/2)-1/2/a*(-c+(4*a*b+c^2)^(1/2))),1/2*2^(1/2))*c^2-1/2/a^2*(a*b)^(1/2)*(x*a/(a*b)^(1/2)+1)^(1/2)*(-2*x*a/(a*b)^(1/2)+2)^(1/2)*(-x*a/(a*b)^(1/2))^(1/2)/(a*x^3-b*x)^(1/2)/(-1/a*(a*b)^(1/2)+1/2*c/a-1/2/a*(4*a*b+c^2)^(1/2))*EllipticPi(((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2),-1/a*(a*b)^(1/2)/(-1/a*(a*b)^(1/2)-1/2/a*(-c+(4*a*b+c^2)^(1/2))),1/2*2^(1/2))*c+2/(4*a*b+c^2)^(1/2)/a*(a*b)^(1/2)*(x*a/(a*b)^(1/2)+1)^(1/2)*(-2*x*a/(a*b)^(1/2)+2)^(1/2)*(-x*a/(a*b)^(1/2))^(1/2)/(a*x^3-b*x)^(1/2)/(-1/a*(a*b)^(1/2)+1/2*c/a-1/2/a*(4*a*b+c^2)^(1/2))*EllipticPi(((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2),-1/a*(a*b)^(1/2)/(-1/a*(a*b)^(1/2)-1/2/a*(-c+(4*a*b+c^2)^(1/2))),1/2*2^(1/2))*b-1/2/(4*a*b+c^2)^(1/2)/a^2*(a*b)^(1/2)*(x*a/(a*b)^(1/2)+1)^(1/2)*(-2*x*a/(a*b)^(1/2)+2)^(1/2)*(-x*a/(a*b)^(1/2))^(1/2)/(a*x^3-b*x)^(1/2)/(-1/a*(a*b)^(1/2)+1/2*c/a+1/2/a*(4*a*b+c^2)^(1/2))*EllipticPi(((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2),-1/a*(a*b)^(1/2)/(-1/a*(a*b)^(1/2)+1/2*(c+(4*a*b+c^2)^(1/2))/a),1/2*2^(1/2))*c^2-1/2/a^2*(a*b)^(1/2)*(x*a/(a*b)^(1/2)+1)^(1/2)*(-2*x*a/(a*b)^(1/2)+2)^(1/2)*(-x*a/(a*b)^(1/2))^(1/2)/(a*x^3-b*x)^(1/2)/(-1/a*(a*b)^(1/2)+1/2*c/a+1/2/a*(4*a*b+c^2)^(1/2))*EllipticPi(((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2),-1/a*(a*b)^(1/2)/(-1/a*(a*b)^(1/2)+1/2*(c+(4*a*b+c^2)^(1/2))/a),1/2*2^(1/2))*c-2/(4*a*b+c^2)^(1/2)/a*(a*b)^(1/2)*(x*a/(a*b)^(1/2)+1)^(1/2)*(-2*x*a/(a*b)^(1/2)+2)^(1/2)*(-x*a/(a*b)^(1/2))^(1/2)/(a*x^3-b*x)^(1/2)/(-1/a*(a*b)^(1/2)+1/2*c/a+1/2/a*(4*a*b+c^2)^(1/2))*EllipticPi(((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2),-1/a*(a*b)^(1/2)/(-1/a*(a*b)^(1/2)+1/2*(c+(4*a*b+c^2)^(1/2))/a),1/2*2^(1/2))*b","C"
505,1,28,31,0.149000," ","int(x*(x^4-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{x^{2} \sqrt{x^{4}-1}}{4}-\frac{\ln \left(x^{2}+\sqrt{x^{4}-1}\right)}{4}$&$28$\\ risch&$\frac{x^{2} \sqrt{x^{4}-1}}{4}-\frac{\ln \left(x^{2}+\sqrt{x^{4}-1}\right)}{4}$&$28$\\ elliptic&$\frac{x^{2} \sqrt{x^{4}-1}}{4}-\frac{\ln \left(x^{2}+\sqrt{x^{4}-1}\right)}{4}$&$28$\\ trager&$\frac{x^{2} \sqrt{x^{4}-1}}{4}+\frac{\ln \left(x^{2}-\sqrt{x^{4}-1}\right)}{4}$&$30$\\ meijerg&$\frac{i \sqrt{\mathrm{signum}\left(x^{4}-1\right)}\, \left(-2 i \sqrt{\pi}\, x^{2} \sqrt{-x^{4}+1}-2 i \sqrt{\pi}\, \arcsin \left(x^{2}\right)\right)}{8 \sqrt{-\mathrm{signum}\left(x^{4}-1\right)}\, \sqrt{\pi}}$&$54$\\ \hline \end{longtable}"," ",0,"1/4*x^2*(x^4-1)^(1/2)-1/4*ln(x^2+(x^4-1)^(1/2))","A"
506,1,38,31,0.243000," ","int((x^4-x)^(1/2)/x^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{2 \sqrt{x^{4}-x}}{3 x^{2}}+\frac{\ln \left(-2 x^{3}-2 x \sqrt{x^{4}-x}+1\right)}{3}$&$38$\\ meijerg&$-\frac{i \sqrt{\mathrm{signum}\left(x^{3}-1\right)}\, \left(-\frac{4 i \sqrt{\pi}\, \sqrt{-x^{3}+1}}{x^{\frac{3}{2}}}-4 i \sqrt{\pi}\, \arcsin \left(x^{\frac{3}{2}}\right)\right)}{6 \sqrt{-\mathrm{signum}\left(x^{3}-1\right)}\, \sqrt{\pi}}$&$54$\\ default&$-\frac{2 \sqrt{x^{4}-x}}{3 x^{2}}+\frac{2 \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$303$\\ elliptic&$-\frac{2 \sqrt{x^{4}-x}}{3 x^{2}}+\frac{2 \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$303$\\ risch&$-\frac{2 \left(x^{3}-1\right)}{3 x \sqrt{x \left(x^{3}-1\right)}}+\frac{2 \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$308$\\ \hline \end{longtable}"," ",0,"-2/3*(x^4-x)^(1/2)/x^2+1/3*ln(-2*x^3-2*x*(x^4-x)^(1/2)+1)","A"
507,1,38,31,0.224000," ","int(x^3*(x^4+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{-\frac{\sqrt{\pi}\, x^{\frac{3}{2}} \left(6 x^{3}+3\right) \sqrt{x^{3}+1}}{6}+\frac{\sqrt{\pi}\, \arcsinh \left(x^{\frac{3}{2}}\right)}{2}}{6 \sqrt{\pi}}$&$38$\\ trager&$\frac{x \left(2 x^{3}+1\right) \sqrt{x^{4}+x}}{12}+\frac{\ln \left(2 x^{3}-2 x \sqrt{x^{4}+x}+1\right)}{24}$&$39$\\ default&$\frac{x^{4} \sqrt{x^{4}+x}}{6}+\frac{x \sqrt{x^{4}+x}}{12}+\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{4 \left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$313$\\ elliptic&$\frac{x^{4} \sqrt{x^{4}+x}}{6}+\frac{x \sqrt{x^{4}+x}}{12}+\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{4 \left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$313$\\ risch&$\frac{x^{2} \left(2 x^{3}+1\right) \left(x^{3}+1\right)}{12 \sqrt{x \left(x^{3}+1\right)}}+\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{4 \left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$317$\\ \hline \end{longtable}"," ",0,"-1/6/Pi^(1/2)*(-1/6*Pi^(1/2)*x^(3/2)*(6*x^3+3)*(x^3+1)^(1/2)+1/2*Pi^(1/2)*arcsinh(x^(3/2)))","A"
508,1,36,35,0.725000," ","int((1+x)/(x^4+4*x^3+13*x^2+18*x+16)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\ln \left(-2 x^{2}+2 \sqrt{x^{4}+4 x^{3}+13 x^{2}+18 x +16}-4 x -9\right)}{2}$&$36$\\ default&$-\frac{2 i \left(-\frac{i \sqrt{14+2 \sqrt{17}}}{2}-\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right) \sqrt{\frac{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}\, \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)^{2} \sqrt{\frac{i \sqrt{14+2 \sqrt{17}}\, \left(x +1+\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right)}{\left(-\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}\, \sqrt{\frac{i \sqrt{14+2 \sqrt{17}}\, \left(x +1-\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}, \sqrt{\frac{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(-\frac{i \sqrt{14+2 \sqrt{17}}}{2}-\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(-\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \sqrt{14+2 \sqrt{17}}\, \sqrt{\left(x +1+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1+\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right)}}-\frac{2 i \left(-\frac{i \sqrt{14+2 \sqrt{17}}}{2}-\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right) \sqrt{\frac{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}\, \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)^{2} \sqrt{\frac{i \sqrt{14+2 \sqrt{17}}\, \left(x +1+\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right)}{\left(-\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}\, \sqrt{\frac{i \sqrt{14+2 \sqrt{17}}\, \left(x +1-\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}\, \left(\left(-1+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \EllipticF \left(\sqrt{\frac{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}, \sqrt{\frac{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(-\frac{i \sqrt{14+2 \sqrt{17}}}{2}-\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(-\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}\right)-i \sqrt{14+2 \sqrt{17}}\, \EllipticPi \left(\sqrt{\frac{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}, \frac{\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}}{\frac{i \sqrt{14-2 \sqrt{17}}}{2}-\frac{i \sqrt{14+2 \sqrt{17}}}{2}}, \sqrt{\frac{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(-\frac{i \sqrt{14+2 \sqrt{17}}}{2}-\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(-\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}\right)\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \sqrt{14+2 \sqrt{17}}\, \sqrt{\left(x +1+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1+\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right)}}$&$1422$\\ elliptic&$-\frac{2 i \left(-\frac{i \sqrt{14+2 \sqrt{17}}}{2}-\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right) \sqrt{\frac{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}\, \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)^{2} \sqrt{\frac{i \sqrt{14+2 \sqrt{17}}\, \left(x +1+\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right)}{\left(-\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}\, \sqrt{\frac{i \sqrt{14+2 \sqrt{17}}\, \left(x +1-\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}, \sqrt{\frac{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(-\frac{i \sqrt{14+2 \sqrt{17}}}{2}-\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(-\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \sqrt{14+2 \sqrt{17}}\, \sqrt{\left(x +1+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1+\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right)}}-\frac{2 i \left(-\frac{i \sqrt{14+2 \sqrt{17}}}{2}-\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right) \sqrt{\frac{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}\, \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)^{2} \sqrt{\frac{i \sqrt{14+2 \sqrt{17}}\, \left(x +1+\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right)}{\left(-\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}\, \sqrt{\frac{i \sqrt{14+2 \sqrt{17}}\, \left(x +1-\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}\, \left(\left(-1+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \EllipticF \left(\sqrt{\frac{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}, \sqrt{\frac{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(-\frac{i \sqrt{14+2 \sqrt{17}}}{2}-\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(-\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}\right)-i \sqrt{14+2 \sqrt{17}}\, \EllipticPi \left(\sqrt{\frac{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}, \frac{\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}}{\frac{i \sqrt{14-2 \sqrt{17}}}{2}-\frac{i \sqrt{14+2 \sqrt{17}}}{2}}, \sqrt{\frac{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(-\frac{i \sqrt{14+2 \sqrt{17}}}{2}-\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(-\frac{i \sqrt{14-2 \sqrt{17}}}{2}+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right)}}\right)\right)}{\left(\frac{i \sqrt{14-2 \sqrt{17}}}{2}-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \sqrt{14+2 \sqrt{17}}\, \sqrt{\left(x +1+\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14+2 \sqrt{17}}}{2}\right) \left(x +1+\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right) \left(x +1-\frac{i \sqrt{14-2 \sqrt{17}}}{2}\right)}}$&$1422$\\ \hline \end{longtable}"," ",0,"-1/2*ln(-2*x^2+2*(x^4+4*x^3+13*x^2+18*x+16)^(1/2)-4*x-9)","A"
509,0,0,31,0.013000," ","int((x^5-1)^(1/2)*(3*x^5+2)/x^2/(x^5-a*x^2-1),x)","\[\int \frac{\sqrt{x^{5}-1}\, \left(3 x^{5}+2\right)}{x^{2} \left(x^{5}-a \,x^{2}-1\right)}\, dx\]"," ",0,"int((x^5-1)^(1/2)*(3*x^5+2)/x^2/(x^5-a*x^2-1),x)","F"
510,1,40,31,0.320000," ","int(x*(x^6-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{x^{2} \sqrt{x^{6}-x}}{5}-\frac{\ln \left(2 x^{5}+2 x^{2} \sqrt{x^{6}-x}-1\right)}{10}$&$40$\\ risch&$\frac{x^{3} \left(x^{5}-1\right)}{5 \sqrt{x \left(x^{5}-1\right)}}-\frac{\sqrt{-\mathrm{signum}\left(x^{5}-1\right)}\, \arcsin \left(x^{\frac{5}{2}}\right)}{5 \sqrt{\mathrm{signum}\left(x^{5}-1\right)}}$&$45$\\ meijerg&$\frac{i \sqrt{\mathrm{signum}\left(x^{5}-1\right)}\, \left(-2 i \sqrt{\pi}\, x^{\frac{5}{2}} \sqrt{-x^{5}+1}-2 i \sqrt{\pi}\, \arcsin \left(x^{\frac{5}{2}}\right)\right)}{10 \sqrt{-\mathrm{signum}\left(x^{5}-1\right)}\, \sqrt{\pi}}$&$54$\\ \hline \end{longtable}"," ",0,"1/5*x^2*(x^6-x)^(1/2)-1/10*ln(2*x^5+2*x^2*(x^6-x)^(1/2)-1)","A"
511,0,0,31,0.023000," ","int((x^5+1)*(4*x^5-1)/x/(x^5-a*x+1)/(x^6+x)^(1/2),x)","\[\int \frac{\left(x^{5}+1\right) \left(4 x^{5}-1\right)}{x \left(x^{5}-a x +1\right) \sqrt{x^{6}+x}}\, dx\]"," ",0,"int((x^5+1)*(4*x^5-1)/x/(x^5-a*x+1)/(x^6+x)^(1/2),x)","F"
512,0,0,29,0.015000," ","int(1/(x-(x^2-1)^(1/2))^(1/2),x)","\[\int \frac{1}{\sqrt{x -\sqrt{x^{2}-1}}}\, dx\]"," ",0,"int(1/(x-(x^2-1)^(1/2))^(1/2),x)","F"
513,1,66,34,0.346000," ","int((x^2+1)/(x^2+2*x-1)/(x^3-x^2-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) x^{2}-4 \RootOf \left(\textit{\_Z}^{2}+3\right) x -\RootOf \left(\textit{\_Z}^{2}+3\right)-6 \sqrt{x^{3}-x^{2}-x}}{x^{2}+2 x -1}\right)}{3}$&$66$\\ default&$\frac{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \sqrt{-5 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{5}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}}+\frac{\sqrt{2}\, \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}-\frac{\sqrt{5}}{2}-\sqrt{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}-\frac{\sqrt{5}}{2}-\sqrt{2}\right)}-\frac{\sqrt{2}\, \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}-\frac{\sqrt{5}}{2}-\sqrt{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}-\frac{\sqrt{5}}{2}-\sqrt{2}\right)}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}-\frac{\sqrt{5}}{2}-\sqrt{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}-\frac{\sqrt{5}}{2}-\sqrt{2}\right)}+\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}-\frac{\sqrt{5}}{2}-\sqrt{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}-\frac{\sqrt{5}}{2}-\sqrt{2}\right)}-\frac{\sqrt{2}\, \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}+\sqrt{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}+\sqrt{2}-\frac{\sqrt{5}}{2}\right)}+\frac{\sqrt{2}\, \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}+\sqrt{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}+\sqrt{2}-\frac{\sqrt{5}}{2}\right)}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}+\sqrt{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}+\sqrt{2}-\frac{\sqrt{5}}{2}\right)}+\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}+\sqrt{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}+\sqrt{2}-\frac{\sqrt{5}}{2}\right)}$&$1393$\\ elliptic&$\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{5 \sqrt{x^{3}-x^{2}-x}}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}}+\frac{\sqrt{2}\, \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}-\frac{\sqrt{5}}{2}-\sqrt{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}-\frac{\sqrt{5}}{2}-\sqrt{2}\right)}-\frac{\sqrt{2}\, \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}-\frac{\sqrt{5}}{2}-\sqrt{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}-\frac{\sqrt{5}}{2}-\sqrt{2}\right)}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}-\frac{\sqrt{5}}{2}-\sqrt{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}-\frac{\sqrt{5}}{2}-\sqrt{2}\right)}+\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}-\frac{\sqrt{5}}{2}-\sqrt{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}-\frac{\sqrt{5}}{2}-\sqrt{2}\right)}-\frac{\sqrt{2}\, \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}+\sqrt{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}+\sqrt{2}-\frac{\sqrt{5}}{2}\right)}+\frac{\sqrt{2}\, \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}+\sqrt{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}+\sqrt{2}-\frac{\sqrt{5}}{2}\right)}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}+\sqrt{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}+\sqrt{2}-\frac{\sqrt{5}}{2}\right)}+\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}+\sqrt{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}+\sqrt{2}-\frac{\sqrt{5}}{2}\right)}$&$1531$\\ \hline \end{longtable}"," ",0,"1/3*RootOf(_Z^2+3)*ln(-(RootOf(_Z^2+3)*x^2-4*RootOf(_Z^2+3)*x-RootOf(_Z^2+3)-6*(x^3-x^2-x)^(1/2))/(x^2+2*x-1))","C"
514,1,65,36,1.574000," ","int((x^3+2)*(x^3+x^2-1)^(1/2)/(x^3-1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{x \sqrt{x^{3}+x^{2}-1}}{x^{3}-1}+\frac{\ln \left(-\frac{-x^{3}+2 \sqrt{x^{3}+x^{2}-1}\, x -2 x^{2}+1}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right)}{2}$&$65$\\ risch&$\text{Expression too large to display}$&$3389$\\ default&$\text{Expression too large to display}$&$5693$\\ elliptic&$\text{Expression too large to display}$&$51070$\\ \hline \end{longtable}"," ",0,"-x*(x^3+x^2-1)^(1/2)/(x^3-1)+1/2*ln(-(-x^3+2*(x^3+x^2-1)^(1/2)*x-2*x^2+1)/(-1+x)/(x^2+x+1))","A"
515,1,63,34,0.371000," ","int((x^2+2)/(x^2-2)/(x^3+2*x^2-2*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}+4 \RootOf \left(\textit{\_Z}^{2}-2\right) x -2 \RootOf \left(\textit{\_Z}^{2}-2\right)-4 \sqrt{x^{3}+2 x^{2}-2 x}}{x^{2}-2}\right)}{2}$&$63$\\ default&$\frac{\left(1+\sqrt{3}\right) \sqrt{\frac{x +1+\sqrt{3}}{1+\sqrt{3}}}\, \sqrt{-6 \left(x -\sqrt{3}+1\right) \sqrt{3}}\, \sqrt{-\frac{x}{1+\sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{x +1+\sqrt{3}}{1+\sqrt{3}}}, \frac{\sqrt{6}\, \sqrt{\left(1+\sqrt{3}\right) \sqrt{3}}}{6}\right)}{3 \sqrt{x^{3}+2 x^{2}-2 x}}+\frac{\sqrt{2}\, \sqrt{\frac{x}{1+\sqrt{3}}+\frac{1}{1+\sqrt{3}}+\frac{\sqrt{3}}{1+\sqrt{3}}}\, \sqrt{-6 x \sqrt{3}+18-6 \sqrt{3}}\, \sqrt{-\frac{x}{1+\sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{x +1+\sqrt{3}}{1+\sqrt{3}}}, \frac{-1-\sqrt{3}}{-1-\sqrt{3}-\sqrt{2}}, \frac{\sqrt{6}\, \sqrt{\left(1+\sqrt{3}\right) \sqrt{3}}}{6}\right)}{3 \sqrt{x^{3}+2 x^{2}-2 x}\, \left(-1-\sqrt{3}-\sqrt{2}\right)}+\frac{\sqrt{2}\, \sqrt{\frac{x}{1+\sqrt{3}}+\frac{1}{1+\sqrt{3}}+\frac{\sqrt{3}}{1+\sqrt{3}}}\, \sqrt{-6 x \sqrt{3}+18-6 \sqrt{3}}\, \sqrt{-\frac{x}{1+\sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{x +1+\sqrt{3}}{1+\sqrt{3}}}, \frac{-1-\sqrt{3}}{-1-\sqrt{3}-\sqrt{2}}, \frac{\sqrt{6}\, \sqrt{\left(1+\sqrt{3}\right) \sqrt{3}}}{6}\right) \sqrt{3}}{3 \sqrt{x^{3}+2 x^{2}-2 x}\, \left(-1-\sqrt{3}-\sqrt{2}\right)}-\frac{\sqrt{2}\, \sqrt{\frac{x}{1+\sqrt{3}}+\frac{1}{1+\sqrt{3}}+\frac{\sqrt{3}}{1+\sqrt{3}}}\, \sqrt{-6 x \sqrt{3}+18-6 \sqrt{3}}\, \sqrt{-\frac{x}{1+\sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{x +1+\sqrt{3}}{1+\sqrt{3}}}, \frac{-1-\sqrt{3}}{-1-\sqrt{3}+\sqrt{2}}, \frac{\sqrt{6}\, \sqrt{\left(1+\sqrt{3}\right) \sqrt{3}}}{6}\right)}{3 \sqrt{x^{3}+2 x^{2}-2 x}\, \left(-1-\sqrt{3}+\sqrt{2}\right)}-\frac{\sqrt{2}\, \sqrt{\frac{x}{1+\sqrt{3}}+\frac{1}{1+\sqrt{3}}+\frac{\sqrt{3}}{1+\sqrt{3}}}\, \sqrt{-6 x \sqrt{3}+18-6 \sqrt{3}}\, \sqrt{-\frac{x}{1+\sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{x +1+\sqrt{3}}{1+\sqrt{3}}}, \frac{-1-\sqrt{3}}{-1-\sqrt{3}+\sqrt{2}}, \frac{\sqrt{6}\, \sqrt{\left(1+\sqrt{3}\right) \sqrt{3}}}{6}\right) \sqrt{3}}{3 \sqrt{x^{3}+2 x^{2}-2 x}\, \left(-1-\sqrt{3}+\sqrt{2}\right)}$&$677$\\ elliptic&$\frac{\sqrt{\frac{x}{1+\sqrt{3}}+\frac{1}{1+\sqrt{3}}+\frac{\sqrt{3}}{1+\sqrt{3}}}\, \sqrt{-6 x \sqrt{3}+18-6 \sqrt{3}}\, \sqrt{-\frac{x}{1+\sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{x +1+\sqrt{3}}{1+\sqrt{3}}}, \frac{\sqrt{6}\, \sqrt{\left(1+\sqrt{3}\right) \sqrt{3}}}{6}\right)}{3 \sqrt{x^{3}+2 x^{2}-2 x}}+\frac{\sqrt{\frac{x}{1+\sqrt{3}}+\frac{1}{1+\sqrt{3}}+\frac{\sqrt{3}}{1+\sqrt{3}}}\, \sqrt{-6 x \sqrt{3}+18-6 \sqrt{3}}\, \sqrt{-\frac{x}{1+\sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{x +1+\sqrt{3}}{1+\sqrt{3}}}, \frac{\sqrt{6}\, \sqrt{\left(1+\sqrt{3}\right) \sqrt{3}}}{6}\right) \sqrt{3}}{3 \sqrt{x^{3}+2 x^{2}-2 x}}+\frac{\sqrt{2}\, \sqrt{\frac{x}{1+\sqrt{3}}+\frac{1}{1+\sqrt{3}}+\frac{\sqrt{3}}{1+\sqrt{3}}}\, \sqrt{-6 x \sqrt{3}+18-6 \sqrt{3}}\, \sqrt{-\frac{x}{1+\sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{x +1+\sqrt{3}}{1+\sqrt{3}}}, \frac{-1-\sqrt{3}}{-1-\sqrt{3}-\sqrt{2}}, \frac{\sqrt{6}\, \sqrt{\left(1+\sqrt{3}\right) \sqrt{3}}}{6}\right)}{3 \sqrt{x^{3}+2 x^{2}-2 x}\, \left(-1-\sqrt{3}-\sqrt{2}\right)}+\frac{\sqrt{2}\, \sqrt{\frac{x}{1+\sqrt{3}}+\frac{1}{1+\sqrt{3}}+\frac{\sqrt{3}}{1+\sqrt{3}}}\, \sqrt{-6 x \sqrt{3}+18-6 \sqrt{3}}\, \sqrt{-\frac{x}{1+\sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{x +1+\sqrt{3}}{1+\sqrt{3}}}, \frac{-1-\sqrt{3}}{-1-\sqrt{3}-\sqrt{2}}, \frac{\sqrt{6}\, \sqrt{\left(1+\sqrt{3}\right) \sqrt{3}}}{6}\right) \sqrt{3}}{3 \sqrt{x^{3}+2 x^{2}-2 x}\, \left(-1-\sqrt{3}-\sqrt{2}\right)}-\frac{\sqrt{2}\, \sqrt{\frac{x}{1+\sqrt{3}}+\frac{1}{1+\sqrt{3}}+\frac{\sqrt{3}}{1+\sqrt{3}}}\, \sqrt{-6 x \sqrt{3}+18-6 \sqrt{3}}\, \sqrt{-\frac{x}{1+\sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{x +1+\sqrt{3}}{1+\sqrt{3}}}, \frac{-1-\sqrt{3}}{-1-\sqrt{3}+\sqrt{2}}, \frac{\sqrt{6}\, \sqrt{\left(1+\sqrt{3}\right) \sqrt{3}}}{6}\right)}{3 \sqrt{x^{3}+2 x^{2}-2 x}\, \left(-1-\sqrt{3}+\sqrt{2}\right)}-\frac{\sqrt{2}\, \sqrt{\frac{x}{1+\sqrt{3}}+\frac{1}{1+\sqrt{3}}+\frac{\sqrt{3}}{1+\sqrt{3}}}\, \sqrt{-6 x \sqrt{3}+18-6 \sqrt{3}}\, \sqrt{-\frac{x}{1+\sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{x +1+\sqrt{3}}{1+\sqrt{3}}}, \frac{-1-\sqrt{3}}{-1-\sqrt{3}+\sqrt{2}}, \frac{\sqrt{6}\, \sqrt{\left(1+\sqrt{3}\right) \sqrt{3}}}{6}\right) \sqrt{3}}{3 \sqrt{x^{3}+2 x^{2}-2 x}\, \left(-1-\sqrt{3}+\sqrt{2}\right)}$&$795$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^2-2)*ln(-(RootOf(_Z^2-2)*x^2+4*RootOf(_Z^2-2)*x-2*RootOf(_Z^2-2)-4*(x^3+2*x^2-2*x)^(1/2))/(x^2-2))","C"
516,1,3006,34,0.730000," ","int((2+x)/(-1+x)/(a*x^2+x^3+3*x-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$3006$\\ elliptic&$\text{Expression too large to display}$&$3006$\\ \hline \end{longtable}"," ",0,"2/3*I*3^(1/2)*(1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3))*(-I*(x+1/12*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+1/3*a+1/2*I*3^(1/2)*(1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))^(1/2)*((x-1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+1/3*a)/(-1/4*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+9*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-1/2*I*3^(1/2)*(1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3))))^(1/2)*(I*(x+1/12*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+1/3*a-1/2*I*3^(1/2)*(1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))^(1/2)/(a*x^2+x^3+3*x-1)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/12*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+1/3*a+1/2*I*3^(1/2)*(1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))^(1/2),(-I*3^(1/2)*(1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3))/(-1/4*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+9*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-1/2*I*3^(1/2)*(1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3))))^(1/2))+2*I*3^(1/2)*(1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3))*(-I*(x+1/12*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+1/3*a+1/2*I*3^(1/2)*(1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))^(1/2)*((x-1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+1/3*a)/(-1/4*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+9*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-1/2*I*3^(1/2)*(1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3))))^(1/2)*(I*(x+1/12*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+1/3*a-1/2*I*3^(1/2)*(1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))^(1/2)/(a*x^2+x^3+3*x-1)^(1/2)/(-1/12*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+3*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-1/3*a-1/2*I*3^(1/2)*(1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3))-1)*EllipticPi(1/3*3^(1/2)*(-I*(x+1/12*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+1/3*a+1/2*I*3^(1/2)*(1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))^(1/2),-I*3^(1/2)*(1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3))/(-1/12*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+3*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-1/3*a-1/2*I*3^(1/2)*(1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3))-1),(-I*3^(1/2)*(1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3))/(-1/4*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+9*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-1/2*I*3^(1/2)*(1/6*(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a+108-8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3))))^(1/2))","C"
517,1,3006,34,0.699000," ","int((-2+x)/(1+x)/(a*x^2+x^3+3*x+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$3006$\\ elliptic&$\text{Expression too large to display}$&$3006$\\ \hline \end{longtable}"," ",0,"2/3*I*3^(1/2)*(1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3))*(-I*(x+1/12*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+1/3*a+1/2*I*3^(1/2)*(1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))^(1/2)*((x-1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+1/3*a)/(-1/4*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+9*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-1/2*I*3^(1/2)*(1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3))))^(1/2)*(I*(x+1/12*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+1/3*a-1/2*I*3^(1/2)*(1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))^(1/2)/(a*x^2+x^3+3*x+1)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/12*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+1/3*a+1/2*I*3^(1/2)*(1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))^(1/2),(-I*3^(1/2)*(1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3))/(-1/4*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+9*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-1/2*I*3^(1/2)*(1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3))))^(1/2))-2*I*3^(1/2)*(1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3))*(-I*(x+1/12*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+1/3*a+1/2*I*3^(1/2)*(1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))^(1/2)*((x-1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+1/3*a)/(-1/4*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+9*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-1/2*I*3^(1/2)*(1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3))))^(1/2)*(I*(x+1/12*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+1/3*a-1/2*I*3^(1/2)*(1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))^(1/2)/(a*x^2+x^3+3*x+1)^(1/2)/(-1/12*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+3*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-1/3*a-1/2*I*3^(1/2)*(1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3))+1)*EllipticPi(1/3*3^(1/2)*(-I*(x+1/12*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+1/3*a+1/2*I*3^(1/2)*(1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))^(1/2),-I*3^(1/2)*(1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3))/(-1/12*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+3*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-1/3*a-1/2*I*3^(1/2)*(1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3))+1),(-I*3^(1/2)*(1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3))/(-1/4*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+9*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-1/2*I*3^(1/2)*(1/6*(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(108*a-108-8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3))))^(1/2))","C"
518,1,291,34,0.097000," ","int(x*(3*a*b-2*(a+b)*x+x^2)/(x*(-a+x)*(-b+x))^(1/2)/(-a*b*d+(a+b)*d*x-d*x^2+x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 a \sqrt{-\frac{-a +x}{a}}\, \sqrt{\frac{-b +x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticF \left(\sqrt{-\frac{-a +x}{a}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}+\frac{2 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}-d \,\textit{\_Z}^{2}+\left(a d +b d \right) \textit{\_Z} -a b d \right)}{\sum}\frac{\left(-2 \underline{\hspace{1.25 ex}}\alpha^{2} a -2 \underline{\hspace{1.25 ex}}\alpha^{2} b +\underline{\hspace{1.25 ex}}\alpha^{2} d +3 \underline{\hspace{1.25 ex}}\alpha  a b -\underline{\hspace{1.25 ex}}\alpha  a d -\underline{\hspace{1.25 ex}}\alpha  b d +a b d \right) \left(\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  d +a^{2}+b d \right) \sqrt{-\frac{-a +x}{a}}\, \sqrt{\frac{-b +x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  d +a^{2}+b d}{a^{2}}, \sqrt{\frac{a}{a -b}}\right)}{\left(-3 \underline{\hspace{1.25 ex}}\alpha^{2}+2 \underline{\hspace{1.25 ex}}\alpha  d -a d -b d \right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}\right)}{a^{2}}$&$291$\\ elliptic&$-\frac{2 a \sqrt{-\frac{-a +x}{a}}\, \sqrt{\frac{-b +x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticF \left(\sqrt{-\frac{-a +x}{a}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}-\frac{2 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}-d \,\textit{\_Z}^{2}+\left(a d +b d \right) \textit{\_Z} -a b d \right)}{\sum}\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2} a +2 \underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha^{2} d -3 \underline{\hspace{1.25 ex}}\alpha  a b +\underline{\hspace{1.25 ex}}\alpha  a d +\underline{\hspace{1.25 ex}}\alpha  b d -a b d \right) \left(\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  d +a^{2}+b d \right) \sqrt{-\frac{-a +x}{a}}\, \sqrt{\frac{-b +x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  d +a^{2}+b d}{a^{2}}, \sqrt{\frac{a}{a -b}}\right)}{\left(-3 \underline{\hspace{1.25 ex}}\alpha^{2}+2 \underline{\hspace{1.25 ex}}\alpha  d -a d -b d \right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}\right)}{a^{2}}$&$291$\\ \hline \end{longtable}"," ",0,"-2*a*(-(-a+x)/a)^(1/2)*((-b+x)/(a-b))^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)*EllipticF((-(-a+x)/a)^(1/2),(a/(a-b))^(1/2))+2/a^2*sum((-2*_alpha^2*a-2*_alpha^2*b+_alpha^2*d+3*_alpha*a*b-_alpha*a*d-_alpha*b*d+a*b*d)/(-3*_alpha^2+2*_alpha*d-a*d-b*d)*(_alpha^2+_alpha*a-_alpha*d+a^2+b*d)*(-(-a+x)/a)^(1/2)*((-b+x)/(a-b))^(1/2)*(1/a*x)^(1/2)/(x*(a*b-a*x-b*x+x^2))^(1/2)*EllipticPi((-(-a+x)/a)^(1/2),(_alpha^2+_alpha*a-_alpha*d+a^2+b*d)/a^2,(a/(a-b))^(1/2)),_alpha=RootOf(_Z^3-d*_Z^2+(a*d+b*d)*_Z-a*b*d))","C"
519,1,293,34,0.091000," ","int((3*a*b*x-2*(a+b)*x^2+x^3)/(x*(-a+x)*(-b+x))^(1/2)/(-a*b+(a+b)*x-x^2+d*x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\frac{2 a \sqrt{-\frac{-a +x}{a}}\, \sqrt{\frac{-b +x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticF \left(\sqrt{-\frac{-a +x}{a}}, \sqrt{\frac{a}{a -b}}\right)}{d \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}+\frac{2 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(d \,\textit{\_Z}^{3}-\textit{\_Z}^{2}+\left(a +b \right) \textit{\_Z} -a b \right)}{\sum}\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2} a d +2 \underline{\hspace{1.25 ex}}\alpha^{2} b d -3 \underline{\hspace{1.25 ex}}\alpha  a b d -\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  a +\underline{\hspace{1.25 ex}}\alpha  b -a b \right) \left(\underline{\hspace{1.25 ex}}\alpha^{2} d +\underline{\hspace{1.25 ex}}\alpha  a d +a^{2} d -\underline{\hspace{1.25 ex}}\alpha  +b \right) \sqrt{-\frac{-a +x}{a}}\, \sqrt{\frac{-b +x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2} d +\underline{\hspace{1.25 ex}}\alpha  a d +a^{2} d -\underline{\hspace{1.25 ex}}\alpha  +b}{a^{2} d}, \sqrt{\frac{a}{a -b}}\right)}{\left(3 \underline{\hspace{1.25 ex}}\alpha^{2} d -2 \underline{\hspace{1.25 ex}}\alpha  +a +b \right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}\right)}{d^{2} a^{2}}$&$293$\\ default&$-\frac{2 a \sqrt{-\frac{-a +x}{a}}\, \sqrt{\frac{-b +x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticF \left(\sqrt{-\frac{-a +x}{a}}, \sqrt{\frac{a}{a -b}}\right)}{d \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}+\frac{2 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(d \,\textit{\_Z}^{3}-\textit{\_Z}^{2}+\left(a +b \right) \textit{\_Z} -a b \right)}{\sum}\frac{\left(-2 \underline{\hspace{1.25 ex}}\alpha^{2} a d -2 \underline{\hspace{1.25 ex}}\alpha^{2} b d +3 \underline{\hspace{1.25 ex}}\alpha  a b d +\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  b +a b \right) \left(\underline{\hspace{1.25 ex}}\alpha^{2} d +\underline{\hspace{1.25 ex}}\alpha  a d +a^{2} d -\underline{\hspace{1.25 ex}}\alpha  +b \right) \sqrt{-\frac{-a +x}{a}}\, \sqrt{\frac{-b +x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2} d +\underline{\hspace{1.25 ex}}\alpha  a d +a^{2} d -\underline{\hspace{1.25 ex}}\alpha  +b}{a^{2} d}, \sqrt{\frac{a}{a -b}}\right)}{\left(-3 \underline{\hspace{1.25 ex}}\alpha^{2} d +2 \underline{\hspace{1.25 ex}}\alpha  -a -b \right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}\right)}{d^{2} a^{2}}$&$296$\\ \hline \end{longtable}"," ",0,"-2/d*a*(-(-a+x)/a)^(1/2)*((-b+x)/(a-b))^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)*EllipticF((-(-a+x)/a)^(1/2),(a/(a-b))^(1/2))+2/d^2/a^2*sum((2*_alpha^2*a*d+2*_alpha^2*b*d-3*_alpha*a*b*d-_alpha^2+_alpha*a+_alpha*b-a*b)/(3*_alpha^2*d-2*_alpha+a+b)*(_alpha^2*d+_alpha*a*d+a^2*d-_alpha+b)*(-(-a+x)/a)^(1/2)*((-b+x)/(a-b))^(1/2)*(1/a*x)^(1/2)/(x*(a*b-a*x-b*x+x^2))^(1/2)*EllipticPi((-(-a+x)/a)^(1/2),(_alpha^2*d+_alpha*a*d+a^2*d-_alpha+b)/a^2/d,(a/(a-b))^(1/2)),_alpha=RootOf(d*_Z^3-_Z^2+(a+b)*_Z-a*b))","C"
520,1,67,34,0.065000," ","int((x^2-1)*((x^2+1)^2)^(1/2)/(x^2+1)/(x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\sqrt{\left(x^{2}+1\right)^{2}}\, \sqrt{2}\, \ln \left(x^{2}-\sqrt{2}\, x +1\right)}{4 x^{2}+4}-\frac{\sqrt{\left(x^{2}+1\right)^{2}}\, \sqrt{2}\, \ln \left(x^{2}+\sqrt{2}\, x +1\right)}{4 \left(x^{2}+1\right)}$&$67$\\ default&$-\frac{\sqrt{\left(x^{2}+1\right)^{2}}\, \sqrt{2}\, \left(\ln \left(-\frac{x^{2}+\sqrt{2}\, x +1}{\sqrt{2}\, x -x^{2}-1}\right)-\ln \left(-\frac{\sqrt{2}\, x -x^{2}-1}{x^{2}+\sqrt{2}\, x +1}\right)\right)}{8 \left(x^{2}+1\right)}$&$79$\\ \hline \end{longtable}"," ",0,"1/4*((x^2+1)^2)^(1/2)/(x^2+1)*2^(1/2)*ln(x^2-2^(1/2)*x+1)-1/4*((x^2+1)^2)^(1/2)/(x^2+1)*2^(1/2)*ln(x^2+2^(1/2)*x+1)","A"
521,1,41,38,0.091000," ","int((-1+x)/(x^4-12*x^3+14*x^2+4*x-7)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(-\frac{-5+6 x -x^{2}+\sqrt{x^{4}-12 x^{3}+14 x^{2}+4 x -7}}{-1+x}\right)$&$41$\\ default&$\frac{\left(-1+x \right) \sqrt{x^{2}-10 x -7}\, \ln \left(-5+x +\sqrt{x^{2}-10 x -7}\right)}{\sqrt{x^{4}-12 x^{3}+14 x^{2}+4 x -7}}$&$49$\\ \hline \end{longtable}"," ",0,"-ln(-(-5+6*x-x^2+(x^4-12*x^3+14*x^2+4*x-7)^(1/2))/(-1+x))","A"
522,1,29,38,0.161000," ","int((k^2*x^4-2*k^2*x^2+1)/x^2/((-x^2+1)*(-k^2*x^2+1))^(1/2)/(k^2*x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{\left(-1+x \right) \left(1+x \right)}{\sqrt{\left(x^{2}-1\right) \left(k^{2} x^{2}-1\right)}\, x}$&$29$\\ elliptic&$\frac{-x^{2}+1}{x \sqrt{\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)}\, k^{2}}$&$35$\\ trager&$-\frac{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}{x \left(k^{2} x^{2}-1\right)}$&$41$\\ risch&$\frac{\left(x^{2}-1\right) \left(k^{2} x^{2}-1\right)}{x \sqrt{\left(x^{2}-1\right) \left(k^{2} x^{2}-1\right)}}-\frac{\left(1+x \right) \left(-1+x \right) k^{2} x}{\sqrt{\left(x^{2}-1\right) \left(k^{2} x^{2}-1\right)}}$&$66$\\ default&$\frac{\sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticF \left(x , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}+\left(\frac{k^{2}}{2}-\frac{1}{2}\right) \left(-\frac{k^{2} x^{3}-k^{2} x -k \,x^{2}+k}{\left(k^{2}-1\right) \sqrt{\left(x +\frac{1}{k}\right) \left(k^{2} x^{3}-k^{2} x -k \,x^{2}+k \right)}}+\frac{\left(\frac{k^{2}-2}{2 k^{2}-2}-\frac{k^{2}}{2 \left(k^{2}-1\right)}\right) \sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticF \left(x , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}+\frac{\sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \left(\EllipticF \left(x , k\right)-\EllipticE \left(x , k\right)\right)}{\left(k^{2}-1\right) \sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}\right)+\frac{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}{x}-\frac{\sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \left(\EllipticF \left(x , k\right)-\EllipticE \left(x , k\right)\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}+\left(-\frac{k^{2}}{2}+\frac{1}{2}\right) \left(\frac{k^{2} x^{3}-k^{2} x +k \,x^{2}-k}{\left(k^{2}-1\right) \sqrt{\left(x -\frac{1}{k}\right) \left(k^{2} x^{3}-k^{2} x +k \,x^{2}-k \right)}}+\frac{\left(-\frac{k^{2}-2}{2 \left(k^{2}-1\right)}+\frac{k^{2}}{2 k^{2}-2}\right) \sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticF \left(x , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}-\frac{\sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \left(\EllipticF \left(x , k\right)-\EllipticE \left(x , k\right)\right)}{\left(k^{2}-1\right) \sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}\right)$&$551$\\ \hline \end{longtable}"," ",0,"-(-1+x)*(1+x)/((x^2-1)*(k^2*x^2-1))^(1/2)/x","A"
523,1,77,29,0.859000," ","int((x^6-2)/x/(x^6-1)^(1/2)/(x^6+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+3\right) x^{6}+6 \sqrt{x^{6}-1}+4 \RootOf \left(\textit{\_Z}^{2}+3\right)}{x^{6}+2}\right)}{9}$&$77$\\ \hline \end{longtable}"," ",0,"1/3*RootOf(_Z^2+1)*ln((-RootOf(_Z^2+1)+(x^6-1)^(1/2))/x^3)+1/9*RootOf(_Z^2+3)*ln((-RootOf(_Z^2+3)*x^6+6*(x^6-1)^(1/2)+4*RootOf(_Z^2+3))/(x^6+2))","C"
524,1,45,32,0.249000," ","int((x^3+2)*(x^6+x^3+1)/x/(x^3+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 \sqrt{x^{3}+1}\, x^{6}}{15}+\frac{22 \sqrt{x^{3}+1}\, x^{3}}{45}+\frac{46 \sqrt{x^{3}+1}}{45}-\frac{4 \arctanh \left(\sqrt{x^{3}+1}\right)}{3}$&$45$\\ elliptic&$\frac{2 \sqrt{x^{3}+1}\, x^{6}}{15}+\frac{22 \sqrt{x^{3}+1}\, x^{3}}{45}+\frac{46 \sqrt{x^{3}+1}}{45}-\frac{4 \arctanh \left(\sqrt{x^{3}+1}\right)}{3}$&$45$\\ trager&$\left(\frac{2}{15} x^{6}+\frac{22}{45} x^{3}+\frac{46}{45}\right) \sqrt{x^{3}+1}+\frac{2 \ln \left(-\frac{-x^{3}+2 \sqrt{x^{3}+1}-2}{x^{3}}\right)}{3}$&$46$\\ meijerg&$\frac{-\frac{16 \sqrt{\pi}}{15}+\frac{\sqrt{\pi}\, \left(6 x^{6}-8 x^{3}+16\right) \sqrt{x^{3}+1}}{15}}{3 \sqrt{\pi}}+\frac{\frac{4 \sqrt{\pi}}{3}-\frac{\sqrt{\pi}\, \left(-4 x^{3}+8\right) \sqrt{x^{3}+1}}{6}}{\sqrt{\pi}}+\frac{-2 \sqrt{\pi}+2 \sqrt{\pi}\, \sqrt{x^{3}+1}}{\sqrt{\pi}}+\frac{\frac{2 \left(-2 \ln \left(2\right)+3 \ln \left(x \right)\right) \sqrt{\pi}}{3}-\frac{4 \ln \left(\frac{1}{2}+\frac{\sqrt{x^{3}+1}}{2}\right) \sqrt{\pi}}{3}}{\sqrt{\pi}}$&$124$\\ \hline \end{longtable}"," ",0,"2/15*(x^3+1)^(1/2)*x^6+22/45*(x^3+1)^(1/2)*x^3+46/45*(x^3+1)^(1/2)-4/3*arctanh((x^3+1)^(1/2))","A"
525,1,39,38,0.194000," ","int((3*x^2+4*x)/(x^6+4*x^5+4*x^4+2*x^3+4*x^2-5)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(1+2 x^{2}+x^{3}+\sqrt{x^{6}+4 x^{5}+4 x^{4}+2 x^{3}+4 x^{2}-5}\right)$&$39$\\ \hline \end{longtable}"," ",0,"ln(1+2*x^2+x^3+(x^6+4*x^5+4*x^4+2*x^3+4*x^2-5)^(1/2))","A"
526,0,0,28,0.024000," ","int(x^2*(p*x^5+q)^(1/2)*(3*p*x^5-2*q)/(b*x^6+a*(p*x^5+q)^3),x)","\[\int \frac{x^{2} \sqrt{p \,x^{5}+q}\, \left(3 p \,x^{5}-2 q \right)}{b \,x^{6}+a \left(p \,x^{5}+q \right)^{3}}\, dx\]"," ",0,"int(x^2*(p*x^5+q)^(1/2)*(3*p*x^5-2*q)/(b*x^6+a*(p*x^5+q)^3),x)","F"
527,1,38,37,0.077000," ","int(x^8/(a*x^3-b)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{2 \sqrt{a \,x^{3}-b}\, \left(3 a^{2} x^{6}+4 a b \,x^{3}+8 b^{2}\right)}{45 a^{3}}$&$38$\\ trager&$\frac{2 \sqrt{a \,x^{3}-b}\, \left(3 a^{2} x^{6}+4 a b \,x^{3}+8 b^{2}\right)}{45 a^{3}}$&$38$\\ risch&$\frac{2 \sqrt{a \,x^{3}-b}\, \left(3 a^{2} x^{6}+4 a b \,x^{3}+8 b^{2}\right)}{45 a^{3}}$&$38$\\ default&$\frac{2 x^{6} \sqrt{a \,x^{3}-b}}{15 a}+\frac{8 b \,x^{3} \sqrt{a \,x^{3}-b}}{45 a^{2}}+\frac{16 b^{2} \sqrt{a \,x^{3}-b}}{45 a^{3}}$&$60$\\ elliptic&$\frac{2 x^{6} \sqrt{a \,x^{3}-b}}{15 a}+\frac{8 b \,x^{3} \sqrt{a \,x^{3}-b}}{45 a^{2}}+\frac{16 b^{2} \sqrt{a \,x^{3}-b}}{45 a^{3}}$&$60$\\ \hline \end{longtable}"," ",0,"2/45*(a*x^3-b)^(1/2)*(3*a^2*x^6+4*a*b*x^3+8*b^2)/a^3","A"
528,1,27,37,0.058000," ","int(x^5*(a*x^3-b)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{2 \left(a \,x^{3}-b \right)^{\frac{3}{2}} \left(3 a \,x^{3}+2 b \right)}{45 a^{2}}$&$27$\\ trager&$\frac{2 \sqrt{a \,x^{3}-b}\, \left(3 a^{2} x^{6}-a b \,x^{3}-2 b^{2}\right)}{45 a^{2}}$&$38$\\ risch&$\frac{2 \sqrt{a \,x^{3}-b}\, \left(3 a^{2} x^{6}-a b \,x^{3}-2 b^{2}\right)}{45 a^{2}}$&$38$\\ default&$\frac{2 x^{6} \sqrt{a \,x^{3}-b}}{15}-\frac{2 b \,x^{3} \sqrt{a \,x^{3}-b}}{45 a}-\frac{4 b^{2} \sqrt{a \,x^{3}-b}}{45 a^{2}}$&$57$\\ elliptic&$\frac{2 x^{6} \sqrt{a \,x^{3}-b}}{15}-\frac{2 b \,x^{3} \sqrt{a \,x^{3}-b}}{45 a}-\frac{4 b^{2} \sqrt{a \,x^{3}-b}}{45 a^{2}}$&$57$\\ \hline \end{longtable}"," ",0,"2/45*(a*x^3-b)^(3/2)*(3*a*x^3+2*b)/a^2","A"
529,1,790,33,0.199000," ","int((a*x^3+2*b)/(a*x^3-b)^(1/2)/(2*a*x^3-3*x^2-2*b),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{a}}{-\frac{3 \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}}}\, \sqrt{\frac{i \left(x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(a^{2} b \right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{3 a \sqrt{a \,x^{3}-b}}+\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(2 a \,\textit{\_Z}^{3}-3 \textit{\_Z}^{2}-2 b \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{2}-2 b \right) \left(a^{2} b \right)^{\frac{1}{3}} \sqrt{-\frac{i a \left(2 x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}+i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{2 \left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{a \left(x -\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{-3 \left(a^{2} b \right)^{\frac{1}{3}}-i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{2}\, \sqrt{\frac{i a \left(2 x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}-i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \left(-2 i \left(a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+2 i \left(a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a +3 i \left(a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a -2 \left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-3 i \left(a^{2} b \right)^{\frac{2}{3}} \sqrt{3}-2 \underline{\hspace{1.25 ex}}\alpha  \left(a^{2} b \right)^{\frac{2}{3}} a +3 \left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  a +4 a^{2} b +3 \left(a^{2} b \right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(a^{2} b \right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a +2 i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b -3 i \left(a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  -6 \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a -4 i \left(a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, a b -3 i \sqrt{3}\, a b +6 \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b +9 \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  -9 a b}{6 a b}, \sqrt{-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha  a -1\right) \sqrt{a \,x^{3}-b}}\right)}{12 a^{2} b}$&$790$\\ elliptic&$\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{a}}{-\frac{3 \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}}}\, \sqrt{\frac{i \left(x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(a^{2} b \right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{3 a \sqrt{a \,x^{3}-b}}+\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(2 a \,\textit{\_Z}^{3}-3 \textit{\_Z}^{2}-2 b \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{2}-2 b \right) \left(a^{2} b \right)^{\frac{1}{3}} \sqrt{-\frac{i a \left(2 x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}+i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{2 \left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{a \left(x -\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{-3 \left(a^{2} b \right)^{\frac{1}{3}}-i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{2}\, \sqrt{\frac{i a \left(2 x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}-i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \left(-2 i \left(a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+2 i \left(a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a +3 i \left(a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a -2 \left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-3 i \left(a^{2} b \right)^{\frac{2}{3}} \sqrt{3}-2 \underline{\hspace{1.25 ex}}\alpha  \left(a^{2} b \right)^{\frac{2}{3}} a +3 \left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  a +4 a^{2} b +3 \left(a^{2} b \right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(a^{2} b \right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a +2 i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b -3 i \left(a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  -6 \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a -4 i \left(a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, a b -3 i \sqrt{3}\, a b +6 \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b +9 \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  -9 a b}{6 a b}, \sqrt{-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha  a -1\right) \sqrt{a \,x^{3}-b}}\right)}{12 a^{2} b}$&$790$\\ \hline \end{longtable}"," ",0,"1/3*I*3^(1/2)/a*(a^2*b)^(1/3)*(-I*(x+1/2/a*(a^2*b)^(1/3)+1/2*I*3^(1/2)/a*(a^2*b)^(1/3))*3^(1/2)*a/(a^2*b)^(1/3))^(1/2)*((x-1/a*(a^2*b)^(1/3))/(-3/2/a*(a^2*b)^(1/3)-1/2*I*3^(1/2)/a*(a^2*b)^(1/3)))^(1/2)*(I*(x+1/2/a*(a^2*b)^(1/3)-1/2*I*3^(1/2)/a*(a^2*b)^(1/3))*3^(1/2)*a/(a^2*b)^(1/3))^(1/2)/(a*x^3-b)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2/a*(a^2*b)^(1/3)+1/2*I*3^(1/2)/a*(a^2*b)^(1/3))*3^(1/2)*a/(a^2*b)^(1/3))^(1/2),(-I*3^(1/2)/a*(a^2*b)^(1/3)/(-3/2/a*(a^2*b)^(1/3)-1/2*I*3^(1/2)/a*(a^2*b)^(1/3)))^(1/2))+1/12*I/a^2/b*2^(1/2)*sum((-_alpha^2-2*b)/_alpha/(_alpha*a-1)*(a^2*b)^(1/3)*(-1/2*I*a*(2*x+1/a*((a^2*b)^(1/3)+I*3^(1/2)*(a^2*b)^(1/3)))/(a^2*b)^(1/3))^(1/2)*(a*(x-1/a*(a^2*b)^(1/3))/(-3*(a^2*b)^(1/3)-I*3^(1/2)*(a^2*b)^(1/3)))^(1/2)*(1/2*I*a*(2*x+1/a*((a^2*b)^(1/3)-I*3^(1/2)*(a^2*b)^(1/3)))/(a^2*b)^(1/3))^(1/2)/(a*x^3-b)^(1/2)*(-2*I*(a^2*b)^(1/3)*3^(1/2)*_alpha^2*a^2+2*I*(a^2*b)^(2/3)*3^(1/2)*_alpha*a+3*I*(a^2*b)^(1/3)*3^(1/2)*_alpha*a-2*(a^2*b)^(1/3)*_alpha^2*a^2-3*I*(a^2*b)^(2/3)*3^(1/2)-2*_alpha*(a^2*b)^(2/3)*a+3*(a^2*b)^(1/3)*_alpha*a+4*a^2*b+3*(a^2*b)^(2/3))*EllipticPi(1/3*3^(1/2)*(-I*(x+1/2/a*(a^2*b)^(1/3)+1/2*I*3^(1/2)/a*(a^2*b)^(1/3))*3^(1/2)*a/(a^2*b)^(1/3))^(1/2),-1/6/a*(2*I*(a^2*b)^(2/3)*3^(1/2)*_alpha^2*a+2*I*3^(1/2)*_alpha*a^2*b-3*I*(a^2*b)^(2/3)*3^(1/2)*_alpha-6*(a^2*b)^(2/3)*_alpha^2*a-4*I*(a^2*b)^(1/3)*3^(1/2)*a*b-3*I*3^(1/2)*a*b+6*_alpha*a^2*b+9*(a^2*b)^(2/3)*_alpha-9*a*b)/b,(-I*3^(1/2)/a*(a^2*b)^(1/3)/(-3/2/a*(a^2*b)^(1/3)-1/2*I*3^(1/2)/a*(a^2*b)^(1/3)))^(1/2)),_alpha=RootOf(2*_Z^3*a-3*_Z^2-2*b))","C"
530,1,54,35,0.325000," ","int((x^4-1)*(x^4+1)^(1/2)*(x^4+x^2+1)/x^4/(x^4-x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\sqrt{2}\, \left(x^{4}+1\right)^{\frac{3}{2}}}{3 x^{3}}+\frac{2 \sqrt{2}\, \sqrt{x^{4}+1}}{x}-2 \sqrt{2}\, \arctanh \left(\frac{\sqrt{x^{4}+1}}{x}\right)\right) \sqrt{2}}{2}$&$54$\\ trager&$\frac{\sqrt{x^{4}+1}\, \left(x^{4}+6 x^{2}+1\right)}{3 x^{3}}-\ln \left(\frac{x^{4}+2 \sqrt{x^{4}+1}\, x +x^{2}+1}{x^{4}-x^{2}+1}\right)$&$58$\\ risch&$\frac{x^{8}+6 x^{6}+2 x^{4}+6 x^{2}+1}{3 x^{3} \sqrt{x^{4}+1}}+\frac{2 \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}-\textit{\_Z}^{2}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}+1\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{x^{4}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{2 \left(-1\right)^{\frac{3}{4}} \left(-\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \underline{\hspace{1.25 ex}}\alpha^{2}-i, i\right)}{\sqrt{x^{4}+1}}\right)\right)}{2}$&$203$\\ default&$\frac{\sqrt{x^{4}+1}\, x}{3}+\frac{2 \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\sqrt{x^{4}+1}}{3 x^{3}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}-\textit{\_Z}^{2}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}+1\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{x^{4}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{2 \left(-1\right)^{\frac{3}{4}} \left(-\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \underline{\hspace{1.25 ex}}\alpha^{2}-i, i\right)}{\sqrt{x^{4}+1}}\right)\right)}{2}+\frac{2 \sqrt{x^{4}+1}}{x}$&$205$\\ \hline \end{longtable}"," ",0,"1/2*(1/3*2^(1/2)/x^3*(x^4+1)^(3/2)+2*2^(1/2)/x*(x^4+1)^(1/2)-2*2^(1/2)*arctanh((x^4+1)^(1/2)/x))*2^(1/2)","A"
531,0,0,37,0.080000," ","int((2*a*x^2+3*b*x+4*c)/(a*x^2+b*x+c)^(1/4)/(x^4-a*x^2-b*x-c),x)","\[\int \frac{2 a \,x^{2}+3 b x +4 c}{\left(a \,x^{2}+b x +c \right)^{\frac{1}{4}} \left(x^{4}-a \,x^{2}-b x -c \right)}\, dx\]"," ",0,"int((2*a*x^2+3*b*x+4*c)/(a*x^2+b*x+c)^(1/4)/(x^4-a*x^2-b*x-c),x)","F"
532,1,45,33,0.250000," ","int((x^3+2)*(x^6+x^3+1)/x^4/(x^3+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 \sqrt{x^{3}+1}\, x^{3}}{9}+\frac{14 \sqrt{x^{3}+1}}{9}-\frac{4 \arctanh \left(\sqrt{x^{3}+1}\right)}{3}-\frac{2 \sqrt{x^{3}+1}}{3 x^{3}}$&$45$\\ risch&$\frac{2 \sqrt{x^{3}+1}\, x^{3}}{9}+\frac{14 \sqrt{x^{3}+1}}{9}-\frac{4 \arctanh \left(\sqrt{x^{3}+1}\right)}{3}-\frac{2 \sqrt{x^{3}+1}}{3 x^{3}}$&$45$\\ elliptic&$\frac{2 \sqrt{x^{3}+1}\, x^{3}}{9}+\frac{14 \sqrt{x^{3}+1}}{9}-\frac{4 \arctanh \left(\sqrt{x^{3}+1}\right)}{3}-\frac{2 \sqrt{x^{3}+1}}{3 x^{3}}$&$45$\\ trager&$\frac{2 \sqrt{x^{3}+1}\, \left(x^{6}+7 x^{3}-3\right)}{9 x^{3}}-\frac{2 \ln \left(-\frac{x^{3}+2 \sqrt{x^{3}+1}+2}{x^{3}}\right)}{3}$&$46$\\ meijerg&$\frac{\frac{4 \sqrt{\pi}}{3}-\frac{\sqrt{\pi}\, \left(-4 x^{3}+8\right) \sqrt{x^{3}+1}}{6}}{3 \sqrt{\pi}}+\frac{-2 \sqrt{\pi}+2 \sqrt{\pi}\, \sqrt{x^{3}+1}}{\sqrt{\pi}}+\frac{\left(-2 \ln \left(2\right)+3 \ln \left(x \right)\right) \sqrt{\pi}-2 \ln \left(\frac{1}{2}+\frac{\sqrt{x^{3}+1}}{2}\right) \sqrt{\pi}}{\sqrt{\pi}}+\frac{-\frac{2 \sqrt{\pi}}{3 x^{3}}-\frac{\left(1-2 \ln \left(2\right)+3 \ln \left(x \right)\right) \sqrt{\pi}}{3}+\frac{\sqrt{\pi}\, \left(4 x^{3}+8\right)}{12 x^{3}}-\frac{2 \sqrt{\pi}\, \sqrt{x^{3}+1}}{3 x^{3}}+\frac{2 \ln \left(\frac{1}{2}+\frac{\sqrt{x^{3}+1}}{2}\right) \sqrt{\pi}}{3}}{\sqrt{\pi}}$&$164$\\ \hline \end{longtable}"," ",0,"2/9*(x^3+1)^(1/2)*x^3+14/9*(x^3+1)^(1/2)-4/3*arctanh((x^3+1)^(1/2))-2/3*(x^3+1)^(1/2)/x^3","A"
533,1,41,33,0.400000," ","int((x^3-1)^(1/2)*(2*x^6+x^3-2)/x^10,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{2 \left(3 x^{9}-2 x^{6}-2 x^{3}+1\right)}{9 x^{9} \sqrt{x^{3}-1}}+\frac{2 \arctan \left(\sqrt{x^{3}-1}\right)}{3}$&$41$\\ default&$\frac{2 \sqrt{x^{3}-1}}{9 x^{9}}-\frac{2 \sqrt{x^{3}-1}}{9 x^{6}}-\frac{2 \sqrt{x^{3}-1}}{3 x^{3}}+\frac{2 \arctan \left(\sqrt{x^{3}-1}\right)}{3}$&$48$\\ elliptic&$\frac{2 \sqrt{x^{3}-1}}{9 x^{9}}-\frac{2 \sqrt{x^{3}-1}}{9 x^{6}}-\frac{2 \sqrt{x^{3}-1}}{3 x^{3}}+\frac{2 \arctan \left(\sqrt{x^{3}-1}\right)}{3}$&$48$\\ trager&$-\frac{2 \sqrt{x^{3}-1}\, \left(3 x^{6}+x^{3}-1\right)}{9 x^{9}}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-2 \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \sqrt{x^{3}-1}}{x^{3}}\right)}{3}$&$65$\\ meijerg&$\frac{\sqrt{\mathrm{signum}\left(x^{3}-1\right)}\, \left(-\frac{2 \sqrt{\pi}}{x^{3}}-\left(-2 \ln \left(2\right)-1+3 \ln \left(x \right)+i \pi \right) \sqrt{\pi}+\frac{\sqrt{\pi}\, \left(-4 x^{3}+8\right)}{4 x^{3}}-\frac{2 \sqrt{\pi}\, \sqrt{-x^{3}+1}}{x^{3}}+2 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{3}+1}}{2}\right)\right)}{3 \sqrt{-\mathrm{signum}\left(x^{3}-1\right)}\, \sqrt{\pi}}-\frac{\sqrt{\mathrm{signum}\left(x^{3}-1\right)}\, \left(\frac{\sqrt{\pi}}{x^{6}}-\frac{\sqrt{\pi}}{x^{3}}+\frac{\left(\frac{1}{2}-2 \ln \left(2\right)+3 \ln \left(x \right)+i \pi \right) \sqrt{\pi}}{4}-\frac{\sqrt{\pi}\, \left(x^{6}-8 x^{3}+8\right)}{8 x^{6}}+\frac{\sqrt{\pi}\, \left(-4 x^{3}+8\right) \sqrt{-x^{3}+1}}{8 x^{6}}-\frac{\sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{3}+1}}{2}\right)}{2}\right)}{6 \sqrt{-\mathrm{signum}\left(x^{3}-1\right)}\, \sqrt{\pi}}-\frac{\sqrt{\mathrm{signum}\left(x^{3}-1\right)}\, \left(-\frac{2 \sqrt{\pi}}{3 x^{9}}+\frac{\sqrt{\pi}}{2 x^{6}}+\frac{\sqrt{\pi}}{4 x^{3}}-\frac{\left(\frac{5}{6}-2 \ln \left(2\right)+3 \ln \left(x \right)+i \pi \right) \sqrt{\pi}}{8}+\frac{\sqrt{\pi}\, \left(20 x^{9}-48 x^{6}-96 x^{3}+128\right)}{192 x^{9}}-\frac{\sqrt{\pi}\, \left(-48 x^{6}-32 x^{3}+128\right) \sqrt{-x^{3}+1}}{192 x^{9}}+\frac{\sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{3}+1}}{2}\right)}{4}\right)}{3 \sqrt{-\mathrm{signum}\left(x^{3}-1\right)}\, \sqrt{\pi}}$&$363$\\ \hline \end{longtable}"," ",0,"-2/9*(3*x^9-2*x^6-2*x^3+1)/x^9/(x^3-1)^(1/2)+2/3*arctan((x^3-1)^(1/2))","A"
534,1,87,29,0.877000," ","int((13*x^6-4)/x/(x^6-1)^(1/2)/(4*x^6-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{3}-\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{6}-7 \RootOf \left(\textit{\_Z}^{2}+3\right)-12 \sqrt{x^{6}-1}}{\left(2 x^{3}-1\right) \left(2 x^{3}+1\right)}\right)}{12}$&$87$\\ \hline \end{longtable}"," ",0,"4/3*RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)+(x^6-1)^(1/2))/x^3)-1/12*RootOf(_Z^2+3)*ln(-(4*RootOf(_Z^2+3)*x^6-7*RootOf(_Z^2+3)-12*(x^6-1)^(1/2))/(2*x^3-1)/(2*x^3+1))","C"
535,0,0,37,0.022000," ","int((2*a*x^3-b)/(a*x^3+b-x)/(a*x^6+b*x^3)^(1/4),x)","\[\int \frac{2 a \,x^{3}-b}{\left(a \,x^{3}+b -x \right) \left(a \,x^{6}+b \,x^{3}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((2*a*x^3-b)/(a*x^3+b-x)/(a*x^6+b*x^3)^(1/4),x)","F"
536,0,0,33,0.020000," ","int(x^3*(2*a*x^5+b)/(a*x^6+b*x)^(1/4)/(a*x^10+b*x^5-1),x)","\[\int \frac{x^{3} \left(2 a \,x^{5}+b \right)}{\left(a \,x^{6}+b x \right)^{\frac{1}{4}} \left(a \,x^{10}+b \,x^{5}-1\right)}\, dx\]"," ",0,"int(x^3*(2*a*x^5+b)/(a*x^6+b*x)^(1/4)/(a*x^10+b*x^5-1),x)","F"
537,1,45,30,1.565000," ","int((x^3+1)^(1/4)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{-4 \left(4-3 \ln \left(2\right)+\frac{\pi}{2}+3 \ln \left(x \right)\right) \Gamma \left(\frac{3}{4}\right)-\hypergeom \left(\left[\frac{3}{4}, 1, 1\right], \left[2, 2\right], -x^{3}\right) \Gamma \left(\frac{3}{4}\right) x^{3}}{12 \Gamma \left(\frac{3}{4}\right)}$&$45$\\ trager&$\frac{4 \left(x^{3}+1\right)^{\frac{1}{4}}}{3}+\frac{\ln \left(\frac{2 \left(x^{3}+1\right)^{\frac{3}{4}}-x^{3}-2 \sqrt{x^{3}+1}+2 \left(x^{3}+1\right)^{\frac{1}{4}}-2}{x^{3}}\right)}{3}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{3}+1}+2 \left(x^{3}+1\right)^{\frac{3}{4}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(x^{3}+1\right)^{\frac{1}{4}}}{x^{3}}\right)}{3}$&$118$\\ \hline \end{longtable}"," ",0,"-1/12/GAMMA(3/4)*(-4*(4-3*ln(2)+1/2*Pi+3*ln(x))*GAMMA(3/4)-hypergeom([3/4,1,1],[2,2],-x^3)*GAMMA(3/4)*x^3)","C"
538,1,2262,32,0.771000," ","int((a*p*x^3+3*b*p*x^2-2*a*q)/(p*x^3+q)^(1/2)/(a^2*c*x^2+d*p*x^3+2*a*b*c*x+b^2*c+d*q),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\text{Expression too large to display}$&$2262$\\ default&$\text{Expression too large to display}$&$2264$\\ \hline \end{longtable}"," ",0,"-2/3*I*a/d*3^(1/2)/p*(-q*p^2)^(1/3)*(I*(x+1/2/p*(-q*p^2)^(1/3)-1/2*I*3^(1/2)/p*(-q*p^2)^(1/3))*3^(1/2)*p/(-q*p^2)^(1/3))^(1/2)*((x-1/p*(-q*p^2)^(1/3))/(-3/2/p*(-q*p^2)^(1/3)+1/2*I*3^(1/2)/p*(-q*p^2)^(1/3)))^(1/2)*(-I*(x+1/2/p*(-q*p^2)^(1/3)+1/2*I*3^(1/2)/p*(-q*p^2)^(1/3))*3^(1/2)*p/(-q*p^2)^(1/3))^(1/2)/(p*x^3+q)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2/p*(-q*p^2)^(1/3)-1/2*I*3^(1/2)/p*(-q*p^2)^(1/3))*3^(1/2)*p/(-q*p^2)^(1/3))^(1/2),(I*3^(1/2)/p*(-q*p^2)^(1/3)/(-3/2/p*(-q*p^2)^(1/3)+1/2*I*3^(1/2)/p*(-q*p^2)^(1/3)))^(1/2))-I/d/p^2/c*2^(1/2)*sum((_alpha^2*a^3*c-3*_alpha^2*b*d*p+2*_alpha*a^2*b*c+a*b^2*c+3*a*d*q)/(3*_alpha^2*d*p+2*_alpha*a^2*c+2*a*b*c)/(a^6*q^2-2*a^3*b^3*p*q+b^6*p^2)*(-q*p^2)^(1/3)*(1/2*I*p*(2*x+1/p*(-I*3^(1/2)*(-q*p^2)^(1/3)+(-q*p^2)^(1/3)))/(-q*p^2)^(1/3))^(1/2)*(p*(x-1/p*(-q*p^2)^(1/3))/(-3*(-q*p^2)^(1/3)+I*3^(1/2)*(-q*p^2)^(1/3)))^(1/2)*(-1/2*I*p*(2*x+1/p*(I*3^(1/2)*(-q*p^2)^(1/3)+(-q*p^2)^(1/3)))/(-q*p^2)^(1/3))^(1/2)/(p*x^3+q)^(1/2)*(-(-q*p^2)^(2/3)*a^6*c*q+(-q*p^2)^(2/3)*b^4*d*p^2+4*(-q*p^2)^(2/3)*a^3*b^3*c*p-3*(-q*p^2)^(1/3)*a^2*b^4*c*p^2+4*I*(-q*p^2)^(2/3)*3^(1/2)*a^3*b^3*p*c+3*I*(-q*p^2)^(1/3)*3^(1/2)*a^2*b^4*p^2*c+2*p^2*(-2*_alpha^2*a^3*b*d*p*q-_alpha^2*b^4*d*p^2-2*_alpha*a^5*b*c*q-_alpha*a^2*b^4*c*p+3*_alpha*a^2*b^2*d*p*q-a^4*b^2*c*q-2*a*b^5*c*p-a^4*d*q^2-2*a*b^3*d*p*q)+2*I*(-q*p^2)^(2/3)*3^(1/2)*a^3*b*d*q*p+3*I*(-q*p^2)^(1/3)*3^(1/2)*a^2*b^2*d*q*p^2+2*(-q*p^2)^(1/3)*_alpha*a^3*b*d*p^2*q-I*(-q*p^2)^(1/3)*p^3*3^(1/2)*_alpha*b^4*d+2*(-q*p^2)^(2/3)*a^3*b*d*p*q-3*(-q*p^2)^(1/3)*a^2*b^2*d*p^2*q+I*(-q*p^2)^(2/3)*3^(1/2)*b^4*d*p^2-I*(-q*p^2)^(2/3)*3^(1/2)*a^6*q*c+(-q*p^2)^(1/3)*_alpha*b^4*d*p^3+3*(-q*p^2)^(2/3)*_alpha^2*a^2*b^2*d*p^2+3*(-q*p^2)^(2/3)*_alpha*a^4*b^2*c*p-(-q*p^2)^(1/3)*_alpha^2*a^4*d*p^2*q-2*(-q*p^2)^(1/3)*_alpha^2*a*b^3*d*p^3-(-q*p^2)^(1/3)*_alpha*a^6*c*p*q-2*(-q*p^2)^(1/3)*_alpha*a^3*b^3*c*p^2-(-q*p^2)^(2/3)*_alpha*a^4*d*p*q-2*(-q*p^2)^(2/3)*_alpha*a*b^3*d*p^2+3*I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^2*a^2*b^2*d*p^2+3*I*(-q*p^2)^(2/3)*3^(1/2)*_alpha*a^4*b^2*p*c+2*I*(-q*p^2)^(1/3)*p^3*3^(1/2)*_alpha^2*a*b^3*d+2*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha*a^3*b^3*p^2*c-I*(-q*p^2)^(2/3)*3^(1/2)*_alpha*a^4*d*q*p-2*I*(-q*p^2)^(2/3)*3^(1/2)*_alpha*a*b^3*d*p^2+I*(-q*p^2)^(1/3)*3^(1/2)*_alpha^2*a^4*d*q*p^2+I*(-q*p^2)^(1/3)*3^(1/2)*_alpha*a^6*q*p*c-2*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha*a^3*b*d*q*p^2)*EllipticPi(1/3*3^(1/2)*(I*(x+1/2/p*(-q*p^2)^(1/3)-1/2*I*3^(1/2)/p*(-q*p^2)^(1/3))*3^(1/2)*p/(-q*p^2)^(1/3))^(1/2),-1/2/p*(-2*I*3^(1/2)*a^3*b*d*p^2*q^2-3*I*(-q*p^2)^(2/3)*3^(1/2)*a^2*b^4*c*p-4*I*(-q*p^2)^(1/3)*3^(1/2)*a*b^5*c*p^2-4*I*3^(1/2)*a^3*b^3*c*p^2*q-2*I*(-q*p^2)^(1/3)*3^(1/2)*a^4*d*p*q^2+3*p^3*b^4*d*q-3*a^6*q^2*p*c-4*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha*a^5*b*c*p*q+2*I*(-q*p^2)^(2/3)*3^(1/2)*_alpha*a^3*b*d*p*q+6*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha*a^2*b^2*d*p^2*q+12*a^3*b^3*p^2*q*c+I*(-q*p^2)^(2/3)*3^(1/2)*_alpha*b^4*d*p^2+I*3^(1/2)*_alpha*a^4*d*p^2*q^2-I*(-q*p^2)^(2/3)*3^(1/2)*_alpha*a^6*c*q-2*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha^2*b^4*d*p^3+6*(-q*p^2)^(2/3)*_alpha*a^3*b*d*p*q+6*a^3*b*d*q^2*p^2+9*p^3*_alpha^2*a^2*b^2*d*q+9*_alpha*a^4*b^2*p^2*q*c-6*p^3*_alpha*a*b^3*d*q-3*(-q*p^2)^(2/3)*a^4*d*_alpha^2*p*q-6*(-q*p^2)^(2/3)*a*d*_alpha^2*b^3*p^2-6*(-q*p^2)^(2/3)*_alpha*a^3*b^3*p*c-9*(-q*p^2)^(2/3)*a^2*b^4*p*c-3*_alpha*a^4*d*q^2*p^2-3*(-q*p^2)^(2/3)*_alpha*a^6*q*c+3*(-q*p^2)^(2/3)*_alpha*b^4*d*p^2-9*(-q*p^2)^(2/3)*a^2*b^2*d*p*q+I*3^(1/2)*a^6*c*p*q^2-I*3^(1/2)*b^4*d*p^3*q-2*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha*a^2*b^4*c*p^2-3*I*3^(1/2)*_alpha^2*a^2*b^2*d*p^3*q-3*I*3^(1/2)*_alpha*a^4*b^2*c*p^2*q+2*I*3^(1/2)*_alpha*a*b^3*d*p^3*q-I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^2*a^4*d*p*q-2*I*(-q*p^2)^(1/3)*3^(1/2)*a^4*b^2*c*p*q-3*I*(-q*p^2)^(2/3)*3^(1/2)*a^2*b^2*d*p*q-4*I*(-q*p^2)^(1/3)*3^(1/2)*a*b^3*d*p^2*q-2*I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^2*a*b^3*d*p^2-2*I*(-q*p^2)^(2/3)*3^(1/2)*_alpha*a^3*b^3*c*p-4*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha^2*a^3*b*d*p^2*q)/(a^6*q^2-2*a^3*b^3*p*q+b^6*p^2)/c,(I*3^(1/2)/p*(-q*p^2)^(1/3)/(-3/2/p*(-q*p^2)^(1/3)+1/2*I*3^(1/2)/p*(-q*p^2)^(1/3)))^(1/2)),_alpha=RootOf(_Z^3*d*p+_Z^2*a^2*c+2*_Z*a*b*c+b^2*c+d*q))","C"
539,1,37,36,0.351000," ","int((x^3-1)*(x^6-1)^(1/2)/x^7/(x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{4 x^{9}-x^{6}-4 x^{3}+1}{6 x^{6} \sqrt{x^{6}-1}}-\frac{\arcsin \left(\frac{1}{x^{3}}\right)}{2}$&$37$\\ trager&$-\frac{\left(4 x^{3}-1\right) \sqrt{x^{6}-1}}{6 x^{6}}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{2}$&$50$\\ \hline \end{longtable}"," ",0,"-1/6*(4*x^9-x^6-4*x^3+1)/x^6/(x^6-1)^(1/2)-1/2*arcsin(1/x^3)","A"
540,1,35,36,0.330000," ","int((x^3+1)*(x^6-1)^(1/2)/x^7/(x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{4 x^{9}+x^{6}-4 x^{3}-1}{6 x^{6} \sqrt{x^{6}-1}}-\frac{\arcsin \left(\frac{1}{x^{3}}\right)}{2}$&$35$\\ trager&$\frac{\left(4 x^{3}+1\right) \sqrt{x^{6}-1}}{6 x^{6}}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{2}$&$50$\\ \hline \end{longtable}"," ",0,"1/6*(4*x^9+x^6-4*x^3-1)/x^6/(x^6-1)^(1/2)-1/2*arcsin(1/x^3)","A"
541,1,45,30,4.947000," ","int((x^6+1)^(1/4)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{-4 \left(4-3 \ln \left(2\right)+\frac{\pi}{2}+6 \ln \left(x \right)\right) \Gamma \left(\frac{3}{4}\right)-\hypergeom \left(\left[\frac{3}{4}, 1, 1\right], \left[2, 2\right], -x^{6}\right) \Gamma \left(\frac{3}{4}\right) x^{6}}{24 \Gamma \left(\frac{3}{4}\right)}$&$45$\\ trager&$\frac{2 \left(x^{6}+1\right)^{\frac{1}{4}}}{3}-\frac{\ln \left(\frac{x^{6}+2 \left(x^{6}+1\right)^{\frac{3}{4}}+2 \sqrt{x^{6}+1}+2 \left(x^{6}+1\right)^{\frac{1}{4}}+2}{x^{6}}\right)}{6}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}+2 \sqrt{x^{6}+1}\, \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(x^{6}+1\right)^{\frac{3}{4}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right)+2 \left(x^{6}+1\right)^{\frac{1}{4}}}{x^{6}}\right)}{6}$&$117$\\ \hline \end{longtable}"," ",0,"-1/24/GAMMA(3/4)*(-4*(4-3*ln(2)+1/2*Pi+6*ln(x))*GAMMA(3/4)-hypergeom([3/4,1,1],[2,2],-x^6)*GAMMA(3/4)*x^6)","C"
542,1,33,34,0.229000," ","int((x^12+1)/x^4/(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}-1}\, \left(x^{6}+2\right)}{6 x^{3}}+\frac{\ln \left(x^{3}+\sqrt{x^{6}-1}\right)}{6}$&$33$\\ risch&$\frac{x^{12}+x^{6}-2}{6 x^{3} \sqrt{x^{6}-1}}+\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \arcsin \left(x^{3}\right)}{6 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}$&$46$\\ meijerg&$\frac{i \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(i \sqrt{\pi}\, x^{3} \sqrt{-x^{6}+1}-i \sqrt{\pi}\, \arcsin \left(x^{3}\right)\right)}{6 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}-\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{-x^{6}+1}}{3 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, x^{3}}$&$87$\\ \hline \end{longtable}"," ",0,"1/6*(x^6-1)^(1/2)*(x^6+2)/x^3+1/6*ln(x^3+(x^6-1)^(1/2))","A"
543,1,41,35,0.230000," ","int(1/x^10/(x^3+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{15 x^{9}+5 x^{6}-2 x^{3}+8}{72 x^{9} \sqrt{x^{3}+1}}+\frac{5 \arctanh \left(\sqrt{x^{3}+1}\right)}{24}$&$41$\\ default&$-\frac{\sqrt{x^{3}+1}}{9 x^{9}}+\frac{5 \sqrt{x^{3}+1}}{36 x^{6}}-\frac{5 \sqrt{x^{3}+1}}{24 x^{3}}+\frac{5 \arctanh \left(\sqrt{x^{3}+1}\right)}{24}$&$48$\\ elliptic&$-\frac{\sqrt{x^{3}+1}}{9 x^{9}}+\frac{5 \sqrt{x^{3}+1}}{36 x^{6}}-\frac{5 \sqrt{x^{3}+1}}{24 x^{3}}+\frac{5 \arctanh \left(\sqrt{x^{3}+1}\right)}{24}$&$48$\\ trager&$-\frac{\left(15 x^{6}-10 x^{3}+8\right) \sqrt{x^{3}+1}}{72 x^{9}}-\frac{5 \ln \left(-\frac{-x^{3}+2 \sqrt{x^{3}+1}-2}{x^{3}}\right)}{48}$&$50$\\ meijerg&$\frac{-\frac{\sqrt{\pi}}{3 x^{9}}+\frac{\sqrt{\pi}}{4 x^{6}}-\frac{3 \sqrt{\pi}}{8 x^{3}}-\frac{5 \left(\frac{37}{30}-2 \ln \left(2\right)+3 \ln \left(x \right)\right) \sqrt{\pi}}{16}+\frac{\sqrt{\pi}\, \left(148 x^{9}+144 x^{6}-96 x^{3}+128\right)}{384 x^{9}}-\frac{\sqrt{\pi}\, \left(240 x^{6}-160 x^{3}+128\right) \sqrt{x^{3}+1}}{384 x^{9}}+\frac{5 \ln \left(\frac{1}{2}+\frac{\sqrt{x^{3}+1}}{2}\right) \sqrt{\pi}}{8}}{3 \sqrt{\pi}}$&$115$\\ \hline \end{longtable}"," ",0,"-1/72*(15*x^9+5*x^6-2*x^3+8)/x^9/(x^3+1)^(1/2)+5/24*arctanh((x^3+1)^(1/2))","A"
544,1,36,39,0.069000," ","int((x^3-1)/x^6/(x^3+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 \hypergeom \left(\left[-\frac{17}{3}, \frac{1}{3}\right], \left[-\frac{14}{3}\right], -x \right)}{17 x^{\frac{17}{3}}}-\frac{3 \left(\frac{9}{5} x^{2}-\frac{6}{5} x +1\right) \left(1+x \right)^{\frac{2}{3}}}{8 x^{\frac{8}{3}}}$&$36$\\ trager&$-\frac{3 \left(x^{3}+x^{2}\right)^{\frac{2}{3}} \left(19071 x^{5}-12714 x^{4}+10595 x^{3}-3600 x^{2}+3300 x -3080\right)}{52360 x^{7}}$&$40$\\ gosper&$-\frac{3 \left(19071 x^{5}-12714 x^{4}+10595 x^{3}-3600 x^{2}+3300 x -3080\right) \left(1+x \right)}{52360 \left(x^{3}+x^{2}\right)^{\frac{1}{3}} x^{5}}$&$43$\\ risch&$-\frac{3 \left(19071 x^{6}+6357 x^{5}-2119 x^{4}+6995 x^{3}-300 x^{2}+220 x -3080\right)}{52360 x^{5} \left(x^{2} \left(1+x \right)\right)^{\frac{1}{3}}}$&$45$\\ \hline \end{longtable}"," ",0,"3/17*hypergeom([-17/3,1/3],[-14/3],-x)/x^(17/3)-3/8*(9/5*x^2-6/5*x+1)*(1+x)^(2/3)/x^(8/3)","C"
545,1,84,37,0.461000," ","int((x^3-2)*(x^3+1)^(1/2)*(2*x^3+x^2+2)/x^4/(x^3+x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \sqrt{x^{3}+1}\, \left(2 x^{3}-3 x^{2}+2\right)}{3 x^{3}}-\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 x \sqrt{x^{3}+1}+\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{3}+x^{2}+1}\right)$&$84$\\ default&$\frac{4 \sqrt{x^{3}+1}}{3}+\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+\textit{\_Z}^{2}+1\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha^{3} \left(3-i \sqrt{3}\right) \sqrt{\frac{1+x}{3-i \sqrt{3}}}\, \sqrt{\frac{-1+2 x -i \sqrt{3}}{-3-i \sqrt{3}}}\, \sqrt{\frac{-1+2 x +i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{3 \underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}}{2}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}\right)+\frac{4 \sqrt{x^{3}+1}}{3 x^{3}}-\frac{2 \sqrt{x^{3}+1}}{x}$&$302$\\ elliptic&$\frac{4 \sqrt{x^{3}+1}}{3}+\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+\textit{\_Z}^{2}+1\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha^{3} \left(3-i \sqrt{3}\right) \sqrt{\frac{1+x}{3-i \sqrt{3}}}\, \sqrt{\frac{-1+2 x -i \sqrt{3}}{-3-i \sqrt{3}}}\, \sqrt{\frac{-1+2 x +i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{3 \underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}}{2}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}\right)+\frac{4 \sqrt{x^{3}+1}}{3 x^{3}}-\frac{2 \sqrt{x^{3}+1}}{x}$&$302$\\ risch&$\frac{-2 x^{5}-2 x^{2}+\frac{8}{3} x^{3}+\frac{4}{3}+\frac{4}{3} x^{6}}{\sqrt{x^{3}+1}\, x^{3}}+\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+\textit{\_Z}^{2}+1\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha^{3} \left(3-i \sqrt{3}\right) \sqrt{\frac{1+x}{3-i \sqrt{3}}}\, \sqrt{\frac{-1+2 x -i \sqrt{3}}{-3-i \sqrt{3}}}\, \sqrt{\frac{-1+2 x +i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{3 \underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}}{2}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}\right)$&$303$\\ \hline \end{longtable}"," ",0,"2/3*(x^3+1)^(1/2)*(2*x^3-3*x^2+2)/x^3-RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)*x^3-RootOf(_Z^2+1)*x^2+2*x*(x^3+1)^(1/2)+RootOf(_Z^2+1))/(x^3+x^2+1))","C"
546,1,70,35,0.500000," ","int((x^4-1)*(x^4+x^2+1)^(1/2)/(x^4+1)/(x^4-x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(-\ln \left(1+\frac{\sqrt{x^{4}+x^{2}+1}\, \sqrt{2}}{2 x}\right)+\sqrt{2}\, \arctanh \left(\frac{\sqrt{x^{4}+x^{2}+1}}{x}\right)+\ln \left(-1+\frac{\sqrt{x^{4}+x^{2}+1}\, \sqrt{2}}{2 x}\right)\right) \sqrt{2}}{2}$&$70$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x^{4}+3 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}+4 \sqrt{x^{4}+x^{2}+1}\, x +\RootOf \left(\textit{\_Z}^{2}-2\right)}{x^{4}-x^{2}+1}\right)}{2}-\frac{\ln \left(-\frac{-x^{4}+2 \sqrt{x^{4}+x^{2}+1}\, x -2 x^{2}-1}{x^{4}+1}\right)}{2}$&$103$\\ default&$\frac{2 \sqrt{1-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{-2+2 i \sqrt{3}}}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}+\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}-\textit{\_Z}^{2}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2}+1\right) \left(-3 \underline{\hspace{1.25 ex}}\alpha^{2}+7 x^{2}+8\right) \sqrt{2}}{28 \sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{x^{4}+x^{2}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}}-\frac{2 \left(-\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{x^{2}+2-i \sqrt{3}\, x^{2}}\, \sqrt{x^{2}+2+i \sqrt{3}\, x^{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , \frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}}{2}+\frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{2}-\frac{1}{2}-\frac{i \sqrt{3}}{2}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{i \sqrt{3}-1}\, \sqrt{x^{4}+x^{2}+1}}\right)\right)}{4}-\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2}+1\right) \left(-3 \underline{\hspace{1.25 ex}}\alpha^{2}+5 x^{2}+4\right)}{10 \sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{x^{4}+x^{2}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{\sqrt{2}\, \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{x^{2}+2-i \sqrt{3}\, x^{2}}\, \sqrt{x^{2}+2+i \sqrt{3}\, x^{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , \frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}}{2}+\frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{2}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{i \sqrt{3}-1}\, \sqrt{x^{4}+x^{2}+1}}\right)\right)}{4}$&$436$\\ \hline \end{longtable}"," ",0,"1/2*(-ln(1+1/2*(x^4+x^2+1)^(1/2)*2^(1/2)/x)+2^(1/2)*arctanh(1/x*(x^4+x^2+1)^(1/2))+ln(-1+1/2*(x^4+x^2+1)^(1/2)*2^(1/2)/x))*2^(1/2)","A"
547,1,66,39,1.244000," ","int((x^4+x^2+x+1)^(1/2)*(2*x^4-x-2)/(x^4+x+1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{x \sqrt{x^{4}+x^{2}+x +1}}{x^{4}+x +1}+\frac{\ln \left(-\frac{-x^{4}+2 \sqrt{x^{4}+x^{2}+x +1}\, x -2 x^{2}-x -1}{x^{4}+x +1}\right)}{2}$&$66$\\ risch&$\text{Expression too large to display}$&$4900$\\ elliptic&$\text{Expression too large to display}$&$4900$\\ default&$\text{Expression too large to display}$&$9105$\\ \hline \end{longtable}"," ",0,"-x*(x^4+x^2+x+1)^(1/2)/(x^4+x+1)+1/2*ln(-(-x^4+2*(x^4+x^2+x+1)^(1/2)*x-2*x^2-x-1)/(x^4+x+1))","A"
548,0,0,35,0.023000," ","int((x^4-1)*(3*x^4+1)/x/(x^4-a*x-1)/(x^5-x)^(1/2),x)","\[\int \frac{\left(x^{4}-1\right) \left(3 x^{4}+1\right)}{x \left(x^{4}-a x -1\right) \sqrt{x^{5}-x}}\, dx\]"," ",0,"int((x^4-1)*(3*x^4+1)/x/(x^4-a*x-1)/(x^5-x)^(1/2),x)","F"
549,1,37,35,0.371000," ","int(1/x^19/(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{15 x^{18}-5 x^{12}-2 x^{6}-8}{144 x^{18} \sqrt{x^{6}-1}}-\frac{5 \arcsin \left(\frac{1}{x^{3}}\right)}{48}$&$37$\\ trager&$\frac{\sqrt{x^{6}-1}\, \left(15 x^{12}+10 x^{6}+8\right)}{144 x^{18}}+\frac{5 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{48}$&$53$\\ meijerg&$-\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(\frac{\sqrt{\pi}}{3 x^{18}}+\frac{\sqrt{\pi}}{4 x^{12}}+\frac{3 \sqrt{\pi}}{8 x^{6}}-\frac{5 \left(\frac{37}{30}-2 \ln \left(2\right)+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}}{16}-\frac{\sqrt{\pi}\, \left(-148 x^{18}+144 x^{12}+96 x^{6}+128\right)}{384 x^{18}}+\frac{\sqrt{\pi}\, \left(240 x^{12}+160 x^{6}+128\right) \sqrt{-x^{6}+1}}{384 x^{18}}+\frac{5 \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right) \sqrt{\pi}}{8}\right)}{6 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$141$\\ \hline \end{longtable}"," ",0,"1/144*(15*x^18-5*x^12-2*x^6-8)/x^18/(x^6-1)^(1/2)-5/48*arcsin(1/x^3)","A"
550,1,37,35,0.194000," ","int(x^14/(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{x^{3} \left(2 x^{6}+3\right) \sqrt{x^{6}-1}}{24}-\frac{\ln \left(x^{3}-\sqrt{x^{6}-1}\right)}{8}$&$37$\\ risch&$\frac{x^{3} \left(2 x^{6}+3\right) \sqrt{x^{6}-1}}{24}+\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \arcsin \left(x^{3}\right)}{8 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}$&$45$\\ meijerg&$-\frac{i \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(-\frac{i \sqrt{\pi}\, x^{3} \left(10 x^{6}+15\right) \sqrt{-x^{6}+1}}{20}+\frac{3 i \sqrt{\pi}\, \arcsin \left(x^{3}\right)}{4}\right)}{6 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$61$\\ \hline \end{longtable}"," ",0,"1/24*x^3*(2*x^6+3)*(x^6-1)^(1/2)-1/8*ln(x^3-(x^6-1)^(1/2))","A"
551,1,37,35,0.374000," ","int((x^6-1)^(1/2)/x^19,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 x^{18}-x^{12}-10 x^{6}+8}{144 x^{18} \sqrt{x^{6}-1}}-\frac{\arcsin \left(\frac{1}{x^{3}}\right)}{48}$&$37$\\ trager&$\frac{\sqrt{x^{6}-1}\, \left(3 x^{12}+2 x^{6}-8\right)}{144 x^{18}}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{48}$&$55$\\ meijerg&$\frac{\sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(-\frac{2 \sqrt{\pi}}{3 x^{18}}+\frac{\sqrt{\pi}}{2 x^{12}}+\frac{\sqrt{\pi}}{4 x^{6}}-\frac{\left(\frac{5}{6}-2 \ln \left(2\right)+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}}{8}+\frac{\sqrt{\pi}\, \left(20 x^{18}-48 x^{12}-96 x^{6}+128\right)}{192 x^{18}}-\frac{\sqrt{\pi}\, \left(-48 x^{12}-32 x^{6}+128\right) \sqrt{-x^{6}+1}}{192 x^{18}}+\frac{\ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right) \sqrt{\pi}}{4}\right)}{12 \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$141$\\ \hline \end{longtable}"," ",0,"1/144*(3*x^18-x^12-10*x^6+8)/x^18/(x^6-1)^(1/2)-1/48*arcsin(1/x^3)","A"
552,1,37,35,0.184000," ","int(x^8*(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{x^{3} \left(2 x^{6}-1\right) \sqrt{x^{6}-1}}{24}+\frac{\ln \left(x^{3}-\sqrt{x^{6}-1}\right)}{24}$&$37$\\ risch&$\frac{x^{3} \left(2 x^{6}-1\right) \sqrt{x^{6}-1}}{24}-\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \arcsin \left(x^{3}\right)}{24 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}$&$45$\\ meijerg&$-\frac{i \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(-\frac{i \sqrt{\pi}\, x^{3} \left(-6 x^{6}+3\right) \sqrt{-x^{6}+1}}{6}+\frac{i \sqrt{\pi}\, \arcsin \left(x^{3}\right)}{2}\right)}{12 \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$61$\\ \hline \end{longtable}"," ",0,"1/24*x^3*(2*x^6-1)*(x^6-1)^(1/2)+1/24*ln(x^3-(x^6-1)^(1/2))","A"
553,1,42,31,0.342000," ","int((x^6-1)/(x^4+1)^(1/2)/(x^6+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\arctan \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{3}-\frac{2 \sqrt{2}\, \arctanh \left(\frac{\sqrt{x^{4}+1}}{x}\right)}{3}\right) \sqrt{2}}{2}$&$42$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x +\sqrt{x^{4}+1}}{x^{2}+1}\right)}{6}+\frac{\ln \left(-\frac{-x^{4}+2 \sqrt{x^{4}+1}\, x -x^{2}-1}{x^{4}-x^{2}+1}\right)}{3}$&$74$\\ default&$\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}-\textit{\_Z}^{2}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}+1\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{x^{4}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{2 \left(-1\right)^{\frac{3}{4}} \left(-\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \underline{\hspace{1.25 ex}}\alpha^{2}-i, i\right)}{\sqrt{x^{4}+1}}\right)\right)}{6}+\frac{2 \left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{3 \sqrt{x^{4}+1}}$&$220$\\ \hline \end{longtable}"," ",0,"1/2*(1/3*arctan(1/2*2^(1/2)/x*(x^4+1)^(1/2))-2/3*2^(1/2)*arctanh((x^4+1)^(1/2)/x))*2^(1/2)","A"
554,1,27,35,0.161000," ","int(x^14/(x^6+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x^{3} \left(2 x^{6}-3\right) \sqrt{x^{6}+1}}{24}+\frac{\arcsinh \left(x^{3}\right)}{8}$&$27$\\ trager&$\frac{x^{3} \left(2 x^{6}-3\right) \sqrt{x^{6}+1}}{24}-\frac{\ln \left(x^{3}-\sqrt{x^{6}+1}\right)}{8}$&$37$\\ meijerg&$\frac{-\frac{\sqrt{\pi}\, x^{3} \left(-10 x^{6}+15\right) \sqrt{x^{6}+1}}{20}+\frac{3 \sqrt{\pi}\, \arcsinh \left(x^{3}\right)}{4}}{6 \sqrt{\pi}}$&$38$\\ \hline \end{longtable}"," ",0,"1/24*x^3*(2*x^6-3)*(x^6+1)^(1/2)+1/8*arcsinh(x^3)","A"
555,1,42,35,0.255000," ","int((x^6-1)/x^19/(x^6+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}+1}\, \left(33 x^{12}-22 x^{6}+8\right)}{144 x^{18}}+\frac{11 \ln \left(\frac{\sqrt{x^{6}+1}-1}{x^{3}}\right)}{48}$&$42$\\ risch&$\frac{33 x^{18}+11 x^{12}-14 x^{6}+8}{144 x^{18} \sqrt{x^{6}+1}}+\frac{11 \ln \left(\frac{\sqrt{x^{6}+1}-1}{\sqrt{x^{6}}}\right)}{48}$&$49$\\ meijerg&$\frac{-\frac{\sqrt{\pi}}{2 x^{12}}+\frac{\sqrt{\pi}}{2 x^{6}}+\frac{3 \left(\frac{7}{6}-2 \ln \left(2\right)+6 \ln \left(x \right)\right) \sqrt{\pi}}{8}+\frac{\sqrt{\pi}\, \left(-7 x^{12}-8 x^{6}+8\right)}{16 x^{12}}-\frac{\sqrt{\pi}\, \left(-12 x^{6}+8\right) \sqrt{x^{6}+1}}{16 x^{12}}-\frac{3 \ln \left(\frac{1}{2}+\frac{\sqrt{x^{6}+1}}{2}\right) \sqrt{\pi}}{4}}{6 \sqrt{\pi}}-\frac{-\frac{\sqrt{\pi}}{3 x^{18}}+\frac{\sqrt{\pi}}{4 x^{12}}-\frac{3 \sqrt{\pi}}{8 x^{6}}-\frac{5 \left(\frac{37}{30}-2 \ln \left(2\right)+6 \ln \left(x \right)\right) \sqrt{\pi}}{16}+\frac{\sqrt{\pi}\, \left(148 x^{18}+144 x^{12}-96 x^{6}+128\right)}{384 x^{18}}-\frac{\sqrt{\pi}\, \left(240 x^{12}-160 x^{6}+128\right) \sqrt{x^{6}+1}}{384 x^{18}}+\frac{5 \ln \left(\frac{1}{2}+\frac{\sqrt{x^{6}+1}}{2}\right) \sqrt{\pi}}{8}}{6 \sqrt{\pi}}$&$212$\\ \hline \end{longtable}"," ",0,"1/144*(x^6+1)^(1/2)*(33*x^12-22*x^6+8)/x^18+11/48*ln(((x^6+1)^(1/2)-1)/x^3)","A"
556,1,64,31,0.415000," ","int((x^6+1)/(x^4+1)^(1/2)/(-x^6+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\ln \left(1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{6}-\frac{2 \sqrt{2}\, \arctan \left(\frac{\sqrt{x^{4}+1}}{x}\right)}{3}-\frac{\ln \left(-1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{6}\right) \sqrt{2}}{2}$&$64$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x +\sqrt{x^{4}+1}}{\left(-1+x \right) \left(1+x \right)}\right)}{6}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \sqrt{x^{4}+1}\, x +\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(x^{2}+x +1\right) \left(x^{2}-x +1\right)}\right)}{3}$&$106$\\ default&$-\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}-\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{\arctanh \left(\frac{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \left(x^{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{3}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(\frac{\arctanh \left(\frac{\sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}\, \left(x^{2}-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{3}-\frac{2 \left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{3 \sqrt{x^{4}+1}}-\frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{\arctanh \left(\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x^{2}-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{3}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-\frac{\arctanh \left(\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x^{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{3}$&$572$\\ \hline \end{longtable}"," ",0,"1/2*(1/6*ln(1+1/2*2^(1/2)/x*(x^4+1)^(1/2))-2/3*2^(1/2)*arctan((x^4+1)^(1/2)/x)-1/6*ln(-1+1/2*2^(1/2)/x*(x^4+1)^(1/2)))*2^(1/2)","B"
557,1,64,31,0.349000," ","int((x^6+1)/(x^4+1)^(1/2)/(x^6-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(-\frac{\ln \left(1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{6}+\frac{2 \sqrt{2}\, \arctan \left(\frac{\sqrt{x^{4}+1}}{x}\right)}{3}+\frac{\ln \left(-1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{6}\right) \sqrt{2}}{2}$&$64$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x +\sqrt{x^{4}+1}}{\left(-1+x \right) \left(1+x \right)}\right)}{6}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \sqrt{x^{4}+1}\, x +\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(x^{2}+x +1\right) \left(x^{2}-x +1\right)}\right)}{3}$&$106$\\ default&$\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{\arctanh \left(\frac{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \left(x^{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{3}+\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(\frac{\arctanh \left(\frac{\sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}\, \left(x^{2}-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{3}+\frac{2 \left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{3 \sqrt{x^{4}+1}}+\frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{\arctanh \left(\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x^{2}-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{3}+\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-\frac{\arctanh \left(\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x^{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{3}$&$571$\\ \hline \end{longtable}"," ",0,"1/2*(-1/6*ln(1+1/2*2^(1/2)/x*(x^4+1)^(1/2))+2/3*2^(1/2)*arctan((x^4+1)^(1/2)/x)+1/6*ln(-1+1/2*2^(1/2)/x*(x^4+1)^(1/2)))*2^(1/2)","B"
558,0,0,35,0.024000," ","int((x^5-1)*(4*x^5+1)/x/(x^5-a*x-1)/(x^6-x)^(1/2),x)","\[\int \frac{\left(x^{5}-1\right) \left(4 x^{5}+1\right)}{x \left(x^{5}-a x -1\right) \sqrt{x^{6}-x}}\, dx\]"," ",0,"int((x^5-1)*(4*x^5+1)/x/(x^5-a*x-1)/(x^6-x)^(1/2),x)","F"
559,1,45,35,0.250000," ","int((x^3+2)*(x^6+x^3+1)/x^7/(x^3+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 \sqrt{x^{3}+1}}{3}-\frac{3 \arctanh \left(\sqrt{x^{3}+1}\right)}{2}-\frac{\sqrt{x^{3}+1}}{3 x^{6}}-\frac{\sqrt{x^{3}+1}}{2 x^{3}}$&$45$\\ risch&$-\frac{3 x^{6}+5 x^{3}+2}{6 x^{6} \sqrt{x^{3}+1}}+\frac{2 \sqrt{x^{3}+1}}{3}-\frac{3 \arctanh \left(\sqrt{x^{3}+1}\right)}{2}$&$45$\\ elliptic&$\frac{2 \sqrt{x^{3}+1}}{3}-\frac{3 \arctanh \left(\sqrt{x^{3}+1}\right)}{2}-\frac{\sqrt{x^{3}+1}}{3 x^{6}}-\frac{\sqrt{x^{3}+1}}{2 x^{3}}$&$45$\\ trager&$\frac{\sqrt{x^{3}+1}\, \left(4 x^{6}-3 x^{3}-2\right)}{6 x^{6}}-\frac{3 \ln \left(-\frac{x^{3}+2 \sqrt{x^{3}+1}+2}{x^{3}}\right)}{4}$&$48$\\ meijerg&$\frac{-2 \sqrt{\pi}+2 \sqrt{\pi}\, \sqrt{x^{3}+1}}{3 \sqrt{\pi}}+\frac{\left(-2 \ln \left(2\right)+3 \ln \left(x \right)\right) \sqrt{\pi}-2 \ln \left(\frac{1}{2}+\frac{\sqrt{x^{3}+1}}{2}\right) \sqrt{\pi}}{\sqrt{\pi}}+\frac{-\frac{\sqrt{\pi}}{x^{3}}-\frac{\left(1-2 \ln \left(2\right)+3 \ln \left(x \right)\right) \sqrt{\pi}}{2}+\frac{\sqrt{\pi}\, \left(4 x^{3}+8\right)}{8 x^{3}}-\frac{\sqrt{\pi}\, \sqrt{x^{3}+1}}{x^{3}}+\ln \left(\frac{1}{2}+\frac{\sqrt{x^{3}+1}}{2}\right) \sqrt{\pi}}{\sqrt{\pi}}+\frac{-\frac{\sqrt{\pi}}{3 x^{6}}+\frac{\sqrt{\pi}}{3 x^{3}}+\frac{\left(\frac{7}{6}-2 \ln \left(2\right)+3 \ln \left(x \right)\right) \sqrt{\pi}}{4}+\frac{\sqrt{\pi}\, \left(-7 x^{6}-8 x^{3}+8\right)}{24 x^{6}}-\frac{\sqrt{\pi}\, \left(-12 x^{3}+8\right) \sqrt{x^{3}+1}}{24 x^{6}}-\frac{\ln \left(\frac{1}{2}+\frac{\sqrt{x^{3}+1}}{2}\right) \sqrt{\pi}}{2}}{\sqrt{\pi}}$&$230$\\ \hline \end{longtable}"," ",0,"2/3*(x^3+1)^(1/2)-3/2*arctanh((x^3+1)^(1/2))-1/3/x^6*(x^3+1)^(1/2)-1/2*(x^3+1)^(1/2)/x^3","A"
560,0,0,35,0.028000," ","int((4*x^6-x)/(x^5+1)/(a*x^5+a-x)/(x^6+x)^(1/2),x)","\[\int \frac{4 x^{6}-x}{\left(x^{5}+1\right) \left(a \,x^{5}+a -x \right) \sqrt{x^{6}+x}}\, dx\]"," ",0,"int((4*x^6-x)/(x^5+1)/(a*x^5+a-x)/(x^6+x)^(1/2),x)","F"
561,1,347,35,122.003000," ","int((x^6+x^3+2)/x/(x^6+1)^(1/4)/(x^9-4*x^6+5*x^3-4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\ln \left(-\frac{x^{12}+2 \left(x^{6}+1\right)^{\frac{1}{4}} x^{9}-4 x^{9}+2 \sqrt{x^{6}+1}\, x^{6}-6 \left(x^{6}+1\right)^{\frac{1}{4}} x^{6}+2 \left(x^{6}+1\right)^{\frac{3}{4}} x^{3}+7 x^{6}-4 x^{3} \sqrt{x^{6}+1}+6 \left(x^{6}+1\right)^{\frac{1}{4}} x^{3}-2 \left(x^{6}+1\right)^{\frac{3}{4}}-4 x^{3}+2 \sqrt{x^{6}+1}-2 \left(x^{6}+1\right)^{\frac{1}{4}}+2}{x^{3} \left(x^{9}-4 x^{6}+5 x^{3}-4\right)}\right)}{6}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{12}+4 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{9}-2 \left(x^{6}+1\right)^{\frac{1}{4}} x^{9}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{6}+1}\, x^{6}-7 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}+6 \left(x^{6}+1\right)^{\frac{1}{4}} x^{6}-4 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{6}+1}\, x^{3}+2 \left(x^{6}+1\right)^{\frac{3}{4}} x^{3}+4 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-6 \left(x^{6}+1\right)^{\frac{1}{4}} x^{3}+2 \sqrt{x^{6}+1}\, \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(x^{6}+1\right)^{\frac{3}{4}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right)+2 \left(x^{6}+1\right)^{\frac{1}{4}}}{x^{3} \left(x^{9}-4 x^{6}+5 x^{3}-4\right)}\right)}{6}$&$347$\\ \hline \end{longtable}"," ",0,"-1/6*ln(-(x^12+2*(x^6+1)^(1/4)*x^9-4*x^9+2*(x^6+1)^(1/2)*x^6-6*(x^6+1)^(1/4)*x^6+2*(x^6+1)^(3/4)*x^3+7*x^6-4*x^3*(x^6+1)^(1/2)+6*(x^6+1)^(1/4)*x^3-2*(x^6+1)^(3/4)-4*x^3+2*(x^6+1)^(1/2)-2*(x^6+1)^(1/4)+2)/x^3/(x^9-4*x^6+5*x^3-4))+1/6*RootOf(_Z^2+1)*ln(-(-RootOf(_Z^2+1)*x^12+4*RootOf(_Z^2+1)*x^9-2*(x^6+1)^(1/4)*x^9+2*RootOf(_Z^2+1)*(x^6+1)^(1/2)*x^6-7*RootOf(_Z^2+1)*x^6+6*(x^6+1)^(1/4)*x^6-4*RootOf(_Z^2+1)*(x^6+1)^(1/2)*x^3+2*(x^6+1)^(3/4)*x^3+4*RootOf(_Z^2+1)*x^3-6*(x^6+1)^(1/4)*x^3+2*(x^6+1)^(1/2)*RootOf(_Z^2+1)-2*(x^6+1)^(3/4)-2*RootOf(_Z^2+1)+2*(x^6+1)^(1/4))/x^3/(x^9-4*x^6+5*x^3-4))","C"
562,1,78,38,0.172000," ","int((1024*x^10-16640*x^9+112000*x^8-401440*x^7+820340*x^6-954733*x^5+615255*x^4-225810*x^3+47250*x^2-5265*x+243)^(1/5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{x \left(8 x^{2}-39 x +18\right) \left(1024 x^{10}-16640 x^{9}+112000 x^{8}-401440 x^{7}+820340 x^{6}-954733 x^{5}+615255 x^{4}-225810 x^{3}+47250 x^{2}-5265 x +243\right)^{\frac{1}{5}}}{6 \left(-1+4 x \right) \left(-3+x \right)}$&$78$\\ risch&$\frac{4 \left(\left(4 x^{2}-13 x +3\right)^{5}\right)^{\frac{1}{5}} x^{3}}{3 \left(4 x^{2}-13 x +3\right)}-\frac{13 \left(\left(4 x^{2}-13 x +3\right)^{5}\right)^{\frac{1}{5}} x^{2}}{2 \left(4 x^{2}-13 x +3\right)}+\frac{3 \left(\left(4 x^{2}-13 x +3\right)^{5}\right)^{\frac{1}{5}} x}{4 x^{2}-13 x +3}$&$93$\\ \hline \end{longtable}"," ",0,"1/6*x*(8*x^2-39*x+18)*(1024*x^10-16640*x^9+112000*x^8-401440*x^7+820340*x^6-954733*x^5+615255*x^4-225810*x^3+47250*x^2-5265*x+243)^(1/5)/(-1+4*x)/(-3+x)","B"
563,0,0,35,0.020000," ","int((2*a*x^8-b*x^3)/(a*x^6-b*x)^(1/4)/(a*x^10-b*x^5-1),x)","\[\int \frac{2 a \,x^{8}-b \,x^{3}}{\left(a \,x^{6}-b x \right)^{\frac{1}{4}} \left(a \,x^{10}-b \,x^{5}-1\right)}\, dx\]"," ",0,"int((2*a*x^8-b*x^3)/(a*x^6-b*x)^(1/4)/(a*x^10-b*x^5-1),x)","F"
564,0,0,39,0.021000," ","int(x^5*(10*a*x^3-7*b)/(a*x^6-b*x^3)^(1/4)/(a*x^10-b*x^7-1),x)","\[\int \frac{x^{5} \left(10 a \,x^{3}-7 b \right)}{\left(a \,x^{6}-b \,x^{3}\right)^{\frac{1}{4}} \left(a \,x^{10}-b \,x^{7}-1\right)}\, dx\]"," ",0,"int(x^5*(10*a*x^3-7*b)/(a*x^6-b*x^3)^(1/4)/(a*x^10-b*x^7-1),x)","F"
565,0,0,39,0.035000," ","int(1/x/(-a/b^2+a^2*x^2/b^2)^(1/2)/(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2),x)","\[\int \frac{1}{x \sqrt{-\frac{a}{b^{2}}+\frac{a^{2} x^{2}}{b^{2}}}\, \sqrt{a \,x^{2}+b x \sqrt{-\frac{a}{b^{2}}+\frac{a^{2} x^{2}}{b^{2}}}}}\, dx\]"," ",0,"int(1/x/(-a/b^2+a^2*x^2/b^2)^(1/2)/(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2),x)","F"
566,1,2321,38,0.241000," ","int((a*b-2*a*x+x^2)/(x*(-a+x)*(-b+x))^(1/2)/(a*d-(b+d)*x+x^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 a \sqrt{-\frac{-a +x}{a}}\, \sqrt{\frac{-b +x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticF \left(\sqrt{-\frac{-a +x}{a}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}+\frac{4 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) d}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}+\frac{2 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) b^{2}}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{2 a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) b d}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) b}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) d^{2}}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) d}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{4 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) d}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}+\frac{2 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}+\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) b^{2}}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}+\frac{2 a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) b d}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) b}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}+\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) d^{2}}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) d}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}$&$2321$\\ elliptic&$-\frac{2 a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticF \left(\sqrt{-\frac{-a +x}{a}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}+\frac{4 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) d}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}+\frac{2 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) b^{2}}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{2 a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) b d}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) b}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) d^{2}}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) d}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{4 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) d}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}+\frac{2 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}+\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) b^{2}}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}+\frac{2 a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) b d}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) b}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}+\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) d^{2}}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{a}{a -b}}\right) d}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}$&$2326$\\ \hline \end{longtable}"," ",0,"-2*a*(-(-a+x)/a)^(1/2)*((-b+x)/(a-b))^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)*EllipticF((-(-a+x)/a)^(1/2),(a/(a-b))^(1/2))+4/(-4*a*d+b^2+2*b*d+d^2)^(1/2)*a^2*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*d+2*a^2*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))-1/(-4*a*d+b^2+2*b*d+d^2)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*b^2-2/(-4*a*d+b^2+2*b*d+d^2)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*b*d-a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*b-1/(-4*a*d+b^2+2*b*d+d^2)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*d^2-a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*d-4/(-4*a*d+b^2+2*b*d+d^2)^(1/2)*a^2*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*d+2*a^2*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))+1/(-4*a*d+b^2+2*b*d+d^2)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*b^2+2/(-4*a*d+b^2+2*b*d+d^2)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*b*d-a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*b+1/(-4*a*d+b^2+2*b*d+d^2)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*d^2-a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*d","C"
567,1,2508,38,0.273000," ","int((a*b-2*a*x+x^2)/(x*(-a+x)*(-b+x))^(1/2)/(a-(b*d+1)*x+d*x^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 a \sqrt{-\frac{-a +x}{a}}\, \sqrt{\frac{-b +x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticF \left(\sqrt{-\frac{-a +x}{a}}, \sqrt{\frac{a}{a -b}}\right)}{d \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}+\frac{-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b^{2} d}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}-\frac{2 a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}+\frac{4 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right) d}+\frac{2 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right) d}+\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b^{2} d}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}+\frac{2 a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}+\frac{2 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right) d}-\frac{4 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}+\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right) d}}{d}$&$2508$\\ elliptic&$-\frac{2 a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticF \left(\sqrt{-\frac{-a +x}{a}}, \sqrt{\frac{a}{a -b}}\right)}{d \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b^{2}}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}-\frac{2 a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right) d}+\frac{4 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right) d}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right) d^{2}}+\frac{2 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right) d}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right) d}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right) d^{2}}+\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b^{2}}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}+\frac{2 a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right) d}+\frac{2 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right) d}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right) d}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right) d^{2}}-\frac{4 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right) d}+\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right) d^{2}}$&$2530$\\ \hline \end{longtable}"," ",0,"-2/d*a*(-(-a+x)/a)^(1/2)*((-b+x)/(a-b))^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)*EllipticF((-(-a+x)/a)^(1/2),(a/(a-b))^(1/2))+1/d*(-1/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b-1/2/d-1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2/d*(b*d+1+(b^2*d^2-4*a*d+2*b*d+1)^(1/2))),(a/(a-b))^(1/2))*b^2*d-2/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b-1/2/d-1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2/d*(b*d+1+(b^2*d^2-4*a*d+2*b*d+1)^(1/2))),(a/(a-b))^(1/2))*b+4/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*a^2*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b-1/2/d-1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2/d*(b*d+1+(b^2*d^2-4*a*d+2*b*d+1)^(1/2))),(a/(a-b))^(1/2))-1/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b-1/2/d-1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2/d*(b*d+1+(b^2*d^2-4*a*d+2*b*d+1)^(1/2))),(a/(a-b))^(1/2))/d+2*a^2*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b-1/2/d-1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2/d*(b*d+1+(b^2*d^2-4*a*d+2*b*d+1)^(1/2))),(a/(a-b))^(1/2))-a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b-1/2/d-1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2/d*(b*d+1+(b^2*d^2-4*a*d+2*b*d+1)^(1/2))),(a/(a-b))^(1/2))*b-a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b-1/2/d-1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(a-1/2/d*(b*d+1+(b^2*d^2-4*a*d+2*b*d+1)^(1/2))),(a/(a-b))^(1/2))/d+1/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b+1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-a+x)/a)^(1/2),a/(a+1/2*(-b*d+(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1)/d),(a/(a-b))^(1/2))*b^2*d+2/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b+1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-a+x)/a)^(1/2),a/(a+1/2*(-b*d+(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1)/d),(a/(a-b))^(1/2))*b+2*a^2*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b+1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-a+x)/a)^(1/2),a/(a+1/2*(-b*d+(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1)/d),(a/(a-b))^(1/2))-a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b+1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-a+x)/a)^(1/2),a/(a+1/2*(-b*d+(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1)/d),(a/(a-b))^(1/2))*b-a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b+1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-a+x)/a)^(1/2),a/(a+1/2*(-b*d+(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1)/d),(a/(a-b))^(1/2))/d-4/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*a^2*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b+1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-a+x)/a)^(1/2),a/(a+1/2*(-b*d+(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1)/d),(a/(a-b))^(1/2))+1/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*a*(1-1/a*x)^(1/2)*(-1/(a-b)*b+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(a-1/2*b+1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-a+x)/a)^(1/2),a/(a+1/2*(-b*d+(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1)/d),(a/(a-b))^(1/2))/d)","C"
568,1,96,40,0.967000," ","int((x^3-2)*(x^3-x^2+1)^(1/2)/(x^3+1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{x \sqrt{x^{3}-x^{2}+1}}{x^{3}+1}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \sqrt{x^{3}-x^{2}+1}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(1+x \right) \left(x^{2}-x +1\right)}\right)}{2}$&$96$\\ risch&$\text{Expression too large to display}$&$3383$\\ default&$\text{Expression too large to display}$&$5687$\\ elliptic&$\text{Expression too large to display}$&$50736$\\ \hline \end{longtable}"," ",0,"-x*(x^3-x^2+1)^(1/2)/(x^3+1)+1/2*RootOf(_Z^2+1)*ln(-(-RootOf(_Z^2+1)*x^3+2*RootOf(_Z^2+1)*x^2+2*(x^3-x^2+1)^(1/2)*x-RootOf(_Z^2+1))/(1+x)/(x^2-x+1))","C"
569,1,370,38,0.107000," ","int((a^2*b-a*(2*a-b)*x-(-a+2*b)*x^2+x^3)/(x*(-a+x)*(-b+x))^(1/2)/(-a^3+(3*a^2+b*d)*x-(3*a+d)*x^2+x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 a \sqrt{-\frac{-a +x}{a}}\, \sqrt{\frac{-b +x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticF \left(\sqrt{-\frac{-a +x}{a}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}-2 b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+\left(-3 a -d \right) \textit{\_Z}^{2}+\left(3 a^{2}+b d \right) \textit{\_Z} -a^{3}\right)}{\sum}\frac{\left(4 \underline{\hspace{1.25 ex}}\alpha^{2} a -2 \underline{\hspace{1.25 ex}}\alpha^{2} b +\underline{\hspace{1.25 ex}}\alpha^{2} d -5 \underline{\hspace{1.25 ex}}\alpha  \,a^{2}+\underline{\hspace{1.25 ex}}\alpha  a b -\underline{\hspace{1.25 ex}}\alpha  b d +a^{3}+a^{2} b \right) \left(\underline{\hspace{1.25 ex}}\alpha^{2}-3 \underline{\hspace{1.25 ex}}\alpha  a +\underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  d +3 a^{2}-3 a b +b^{2}\right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, -\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2}-3 \underline{\hspace{1.25 ex}}\alpha  a +\underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  d +3 a^{2}-3 a b +b^{2}\right) b}{a^{3}-3 a^{2} b +3 a \,b^{2}-b^{3}}, \sqrt{\frac{b}{-a +b}}\right)}{\left(-3 \underline{\hspace{1.25 ex}}\alpha^{2}+6 \underline{\hspace{1.25 ex}}\alpha  a +2 \underline{\hspace{1.25 ex}}\alpha  d -3 a^{2}-b d \right) \left(a^{3}-3 a^{2} b +3 a \,b^{2}-b^{3}\right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}\right)$&$370$\\ elliptic&$-\frac{2 b \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}+2 b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+\left(-3 a -d \right) \textit{\_Z}^{2}+\left(3 a^{2}+b d \right) \textit{\_Z} -a^{3}\right)}{\sum}\frac{\left(-4 \underline{\hspace{1.25 ex}}\alpha^{2} a +2 \underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha^{2} d +5 \underline{\hspace{1.25 ex}}\alpha  \,a^{2}-\underline{\hspace{1.25 ex}}\alpha  a b +\underline{\hspace{1.25 ex}}\alpha  b d -a^{3}-a^{2} b \right) \left(\underline{\hspace{1.25 ex}}\alpha^{2}-3 \underline{\hspace{1.25 ex}}\alpha  a +\underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  d +3 a^{2}-3 a b +b^{2}\right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, -\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2}-3 \underline{\hspace{1.25 ex}}\alpha  a +\underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  d +3 a^{2}-3 a b +b^{2}\right) b}{a^{3}-3 a^{2} b +3 a \,b^{2}-b^{3}}, \sqrt{\frac{b}{-a +b}}\right)}{\left(-3 \underline{\hspace{1.25 ex}}\alpha^{2}+6 \underline{\hspace{1.25 ex}}\alpha  a +2 \underline{\hspace{1.25 ex}}\alpha  d -3 a^{2}-b d \right) \left(a^{3}-3 a^{2} b +3 a \,b^{2}-b^{3}\right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}\right)$&$374$\\ \hline \end{longtable}"," ",0,"-2*a*(-(-a+x)/a)^(1/2)*((-b+x)/(a-b))^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)*EllipticF((-(-a+x)/a)^(1/2),(a/(a-b))^(1/2))-2*b*sum((4*_alpha^2*a-2*_alpha^2*b+_alpha^2*d-5*_alpha*a^2+_alpha*a*b-_alpha*b*d+a^3+a^2*b)/(-3*_alpha^2+6*_alpha*a+2*_alpha*d-3*a^2-b*d)*(_alpha^2-3*_alpha*a+_alpha*b-_alpha*d+3*a^2-3*a*b+b^2)/(a^3-3*a^2*b+3*a*b^2-b^3)*(-(-b+x)/b)^(1/2)*((-a+x)/(-a+b))^(1/2)*(x/b)^(1/2)/(x*(a*b-a*x-b*x+x^2))^(1/2)*EllipticPi((-(-b+x)/b)^(1/2),-(_alpha^2-3*_alpha*a+_alpha*b-_alpha*d+3*a^2-3*a*b+b^2)*b/(a^3-3*a^2*b+3*a*b^2-b^3),(b/(-a+b))^(1/2)),_alpha=RootOf(_Z^3+(-3*a-d)*_Z^2+(3*a^2+b*d)*_Z-a^3))","C"
570,1,399,38,0.108000," ","int((a^2*b-a*(2*a-b)*x-(-a+2*b)*x^2+x^3)/(x*(-a+x)*(-b+x))^(1/2)/(-a^3*d+(3*a^2*d+b)*x-(3*a*d+1)*x^2+d*x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 a \sqrt{-\frac{-a +x}{a}}\, \sqrt{\frac{-b +x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticF \left(\sqrt{-\frac{-a +x}{a}}, \sqrt{\frac{a}{a -b}}\right)}{d \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}-\frac{2 b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(d \,\textit{\_Z}^{3}+\left(-3 a d -1\right) \textit{\_Z}^{2}+\left(3 a^{2} d +b \right) \textit{\_Z} -a^{3} d \right)}{\sum}\frac{\left(4 \underline{\hspace{1.25 ex}}\alpha^{2} a d -2 \underline{\hspace{1.25 ex}}\alpha^{2} b d -5 \underline{\hspace{1.25 ex}}\alpha  \,a^{2} d +\underline{\hspace{1.25 ex}}\alpha  a b d +a^{3} d +a^{2} b d +\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  b \right) \left(\underline{\hspace{1.25 ex}}\alpha^{2} d -3 \underline{\hspace{1.25 ex}}\alpha  a d +\underline{\hspace{1.25 ex}}\alpha  b d +3 a^{2} d -3 a b d +b^{2} d -\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, -\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2} d -3 \underline{\hspace{1.25 ex}}\alpha  a d +\underline{\hspace{1.25 ex}}\alpha  b d +3 a^{2} d -3 a b d +b^{2} d -\underline{\hspace{1.25 ex}}\alpha  \right) b}{d \left(a^{3}-3 a^{2} b +3 a \,b^{2}-b^{3}\right)}, \sqrt{\frac{b}{-a +b}}\right)}{\left(-3 \underline{\hspace{1.25 ex}}\alpha^{2} d +6 \underline{\hspace{1.25 ex}}\alpha  a d -3 a^{2} d +2 \underline{\hspace{1.25 ex}}\alpha  -b \right) \left(a^{3}-3 a^{2} b +3 a \,b^{2}-b^{3}\right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}\right)}{d^{2}}$&$399$\\ elliptic&$-\frac{2 b \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)}{d \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}-\frac{2 b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(d \,\textit{\_Z}^{3}+\left(-3 a d -1\right) \textit{\_Z}^{2}+\left(3 a^{2} d +b \right) \textit{\_Z} -a^{3} d \right)}{\sum}\frac{\left(-4 \underline{\hspace{1.25 ex}}\alpha^{2} a d +2 \underline{\hspace{1.25 ex}}\alpha^{2} b d +5 \underline{\hspace{1.25 ex}}\alpha  \,a^{2} d -\underline{\hspace{1.25 ex}}\alpha  a b d -a^{3} d -a^{2} b d -\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  b \right) \left(\underline{\hspace{1.25 ex}}\alpha^{2} d -3 \underline{\hspace{1.25 ex}}\alpha  a d +\underline{\hspace{1.25 ex}}\alpha  b d +3 a^{2} d -3 a b d +b^{2} d -\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, -\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2} d -3 \underline{\hspace{1.25 ex}}\alpha  a d +\underline{\hspace{1.25 ex}}\alpha  b d +3 a^{2} d -3 a b d +b^{2} d -\underline{\hspace{1.25 ex}}\alpha  \right) b}{d \left(a^{3}-3 a^{2} b +3 a \,b^{2}-b^{3}\right)}, \sqrt{\frac{b}{-a +b}}\right)}{\left(3 \underline{\hspace{1.25 ex}}\alpha^{2} d -6 \underline{\hspace{1.25 ex}}\alpha  a d +3 a^{2} d -2 \underline{\hspace{1.25 ex}}\alpha  +b \right) \left(a^{3}-3 a^{2} b +3 a \,b^{2}-b^{3}\right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}\right)}{d^{2}}$&$401$\\ \hline \end{longtable}"," ",0,"-2/d*a*(-(-a+x)/a)^(1/2)*((-b+x)/(a-b))^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)*EllipticF((-(-a+x)/a)^(1/2),(a/(a-b))^(1/2))-2/d^2*b*sum((4*_alpha^2*a*d-2*_alpha^2*b*d-5*_alpha*a^2*d+_alpha*a*b*d+a^3*d+a^2*b*d+_alpha^2-_alpha*b)/(-3*_alpha^2*d+6*_alpha*a*d-3*a^2*d+2*_alpha-b)*(_alpha^2*d-3*_alpha*a*d+_alpha*b*d+3*a^2*d-3*a*b*d+b^2*d-_alpha)/(a^3-3*a^2*b+3*a*b^2-b^3)*(-(-b+x)/b)^(1/2)*((-a+x)/(-a+b))^(1/2)*(x/b)^(1/2)/(x*(a*b-a*x-b*x+x^2))^(1/2)*EllipticPi((-(-b+x)/b)^(1/2),-(_alpha^2*d-3*_alpha*a*d+_alpha*b*d+3*a^2*d-3*a*b*d+b^2*d-_alpha)*b/d/(a^3-3*a^2*b+3*a*b^2-b^3),(b/(-a+b))^(1/2)),_alpha=RootOf(d*_Z^3+(-3*a*d-1)*_Z^2+(3*a^2*d+b)*_Z-a^3*d))","C"
571,1,69,39,1.554000," ","int((2*x^2-3*x)/(x^3+2*x-2)/(3*x^4+2*x^2-2*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{5 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{3}+2 \RootOf \left(\textit{\_Z}^{2}-2\right) x -4 x \sqrt{3 x^{4}+2 x^{2}-2 x}-2 \RootOf \left(\textit{\_Z}^{2}-2\right)}{x^{3}+2 x -2}\right)}{4}$&$69$\\ default&$\text{Expression too large to display}$&$1659$\\ elliptic&$\text{Expression too large to display}$&$1659$\\ \hline \end{longtable}"," ",0,"-1/4*RootOf(_Z^2-2)*ln((5*RootOf(_Z^2-2)*x^3+2*RootOf(_Z^2-2)*x-4*x*(3*x^4+2*x^2-2*x)^(1/2)-2*RootOf(_Z^2-2))/(x^3+2*x-2))","C"
572,1,3170,34,0.803000," ","int((a*p*x^4-3*b*p*x^2+4*a*q*x)/(p*x^3+q)^(1/2)/(a^2*c*x^4+2*a*b*c*x^2+d*p*x^3+b^2*c+d*q),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$3170$\\ elliptic&$\text{Expression too large to display}$&$3170$\\ \hline \end{longtable}"," ",0,"-2/3*I/a/c*3^(1/2)*(-q*p^2)^(1/3)*(I*(x+1/2/p*(-q*p^2)^(1/3)-1/2*I*3^(1/2)/p*(-q*p^2)^(1/3))*3^(1/2)*p/(-q*p^2)^(1/3))^(1/2)*((x-1/p*(-q*p^2)^(1/3))/(-3/2/p*(-q*p^2)^(1/3)+1/2*I*3^(1/2)/p*(-q*p^2)^(1/3)))^(1/2)*(-I*(x+1/2/p*(-q*p^2)^(1/3)+1/2*I*3^(1/2)/p*(-q*p^2)^(1/3))*3^(1/2)*p/(-q*p^2)^(1/3))^(1/2)/(p*x^3+q)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2/p*(-q*p^2)^(1/3)-1/2*I*3^(1/2)/p*(-q*p^2)^(1/3))*3^(1/2)*p/(-q*p^2)^(1/3))^(1/2),(I*3^(1/2)/p*(-q*p^2)^(1/3)/(-3/2/p*(-q*p^2)^(1/3)+1/2*I*3^(1/2)/p*(-q*p^2)^(1/3)))^(1/2))-I/a/c^2/p^2*2^(1/2)*sum((_alpha^3*d*p^2+5*_alpha^2*a*b*c*p-4*_alpha*a^2*c*q+b^2*c*p+d*p*q)/_alpha/(4*_alpha^2*a^2*c+3*_alpha*d*p+4*a*b*c)/(a^6*q^4+2*a^3*b^3*p^2*q^2+b^6*p^4)*(-q*p^2)^(1/3)*(1/2*I*p*(2*x+1/p*(-I*3^(1/2)*(-q*p^2)^(1/3)+(-q*p^2)^(1/3)))/(-q*p^2)^(1/3))^(1/2)*(p*(x-1/p*(-q*p^2)^(1/3))/(-3*(-q*p^2)^(1/3)+I*3^(1/2)*(-q*p^2)^(1/3)))^(1/2)*(-1/2*I*p*(2*x+1/p*(I*3^(1/2)*(-q*p^2)^(1/3)+(-q*p^2)^(1/3)))/(-q*p^2)^(1/3))^(1/2)/(p*x^3+q)^(1/2)*(-(-q*p^2)^(2/3)*a^6*c*q^3+(-q*p^2)^(2/3)*b^4*d*p^4+2*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha^2*a^5*b*q^2*p^2*c+3*I*(-q*p^2)^(1/3)*p^4*3^(1/2)*_alpha^2*a^2*b^2*d*q+4*I*(-q*p^2)^(1/3)*p^3*3^(1/2)*_alpha*a^3*b^3*q*c+2*p^2*(2*_alpha^3*a^5*b*c*p*q^2-_alpha^3*a^2*b^4*c*p^3+_alpha^2*a^6*c*q^3-2*_alpha^2*a^3*b^3*c*p^2*q+2*_alpha^2*a^3*b*d*p^2*q^2-_alpha^2*b^4*d*p^4+_alpha*a^4*b^2*c*p*q^2-2*_alpha*a*b^5*c*p^3+_alpha*a^4*d*p*q^3-2*_alpha*a*b^3*d*p^3*q-3*a^2*b^4*c*p^2*q-3*a^2*b^2*d*p^2*q^2)+I*(-q*p^2)^(1/3)*3^(1/2)*a^4*b^2*q^2*p^2*c-3*(-q*p^2)^(1/3)*_alpha^3*a^4*b^2*c*p^3*q-3*(-q*p^2)^(2/3)*_alpha^2*a^4*b^2*c*p^2*q-2*(-q*p^2)^(1/3)*_alpha^2*a^5*b*c*p^2*q^2-3*(-q*p^2)^(1/3)*_alpha^2*a^2*b^2*d*p^4*q-4*(-q*p^2)^(1/3)*_alpha*a^3*b^3*c*p^3*q-3*(-q*p^2)^(2/3)*_alpha*a^2*b^2*d*p^3*q-2*(-q*p^2)^(1/3)*_alpha*a^3*b*d*p^3*q^2-I*(-q*p^2)^(1/3)*p^5*3^(1/2)*_alpha*b^4*d+(-q*p^2)^(2/3)*_alpha^3*a^6*c*p*q^2+I*(-q*p^2)^(1/3)*3^(1/2)*_alpha*a^6*q^3*p*c+I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^3*a^6*q^2*p*c+I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^2*a^4*d*q^2*p^2-2*I*(-q*p^2)^(2/3)*p^4*3^(1/2)*_alpha^2*a*b^3*d-3*I*(-q*p^2)^(2/3)*p^3*3^(1/2)*_alpha*a^2*b^4*c-2*I*(-q*p^2)^(2/3)*p^3*3^(1/2)*_alpha^3*a^3*b^3*c-I*(-q*p^2)^(1/3)*p^4*3^(1/2)*_alpha^2*a^2*b^4*c+(-q*p^2)^(1/3)*_alpha*b^4*d*p^5+2*(-q*p^2)^(1/3)*a*b^5*c*p^4-(-q*p^2)^(1/3)*a^4*d*p^2*q^3+I*(-q*p^2)^(1/3)*3^(1/2)*a^4*d*q^3*p^2-2*I*(-q*p^2)^(1/3)*p^4*3^(1/2)*a*b^5*c-4*(-q*p^2)^(2/3)*a^3*b^3*c*p^2*q-(-q*p^2)^(1/3)*a^4*b^2*c*p^2*q^2-2*(-q*p^2)^(2/3)*a^3*b*d*p^2*q^2+2*(-q*p^2)^(1/3)*a*b^3*d*p^4*q+I*(-q*p^2)^(2/3)*p^4*3^(1/2)*b^4*d-I*(-q*p^2)^(2/3)*3^(1/2)*a^6*q^3*c-4*I*(-q*p^2)^(2/3)*3^(1/2)*a^3*b^3*q*p^2*c-2*I*(-q*p^2)^(2/3)*3^(1/2)*a^3*b*d*q^2*p^2-2*I*(-q*p^2)^(1/3)*p^4*3^(1/2)*a*b^3*d*q-3*I*(-q*p^2)^(2/3)*p^3*3^(1/2)*_alpha*a^2*b^2*d*q+2*I*(-q*p^2)^(1/3)*p^3*3^(1/2)*_alpha*a^3*b*d*q^2+3*I*(-q*p^2)^(1/3)*p^3*3^(1/2)*_alpha^3*a^4*b^2*q*c-3*I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^2*a^4*b^2*q*p^2*c-2*(-q*p^2)^(2/3)*_alpha^3*a^3*b^3*c*p^3+(-q*p^2)^(1/3)*_alpha^2*a^2*b^4*c*p^4+(-q*p^2)^(2/3)*_alpha^2*a^4*d*p^2*q^2-2*(-q*p^2)^(2/3)*_alpha^2*a*b^3*d*p^4-3*(-q*p^2)^(2/3)*_alpha*a^2*b^4*c*p^3-(-q*p^2)^(1/3)*_alpha*a^6*c*p*q^3)*EllipticPi(1/3*3^(1/2)*(I*(x+1/2/p*(-q*p^2)^(1/3)-1/2*I*3^(1/2)/p*(-q*p^2)^(1/3))*3^(1/2)*p/(-q*p^2)^(1/3))^(1/2),1/2/p*(12*p^3*a^3*b^3*q^2*c-3*p^5*b^4*d*q+3*a^6*q^4*p*c+I*(-q*p^2)^(2/3)*3^(1/2)*a^4*d*p*q^3-2*I*(-q*p^2)^(2/3)*3^(1/2)*a*b^5*c*p^3-4*I*3^(1/2)*a^3*b^3*c*p^3*q^2-2*I*3^(1/2)*a^3*b*d*p^3*q^3+I*(-q*p^2)^(2/3)*3^(1/2)*a^4*b^2*c*p*q^2-6*p^3*(-q*p^2)^(2/3)*a*b^5*c+3*q^3*(-q*p^2)^(2/3)*a^4*d*p+3*q^2*(-q*p^2)^(2/3)*a^4*b^2*p*c-6*p^3*(-q*p^2)^(2/3)*a*b^3*d*q+I*3^(1/2)*b^4*d*p^5*q-I*3^(1/2)*a^6*c*p*q^4+4*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha*a*b^5*c*p^4-2*I*3^(1/2)*_alpha^2*a*b^3*d*p^5*q-3*I*3^(1/2)*_alpha*a^2*b^4*c*p^4*q-2*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha*a^4*d*p^2*q^3-3*I*3^(1/2)*_alpha*a^2*b^2*d*p^4*q^2+6*p^3*a^3*b*d*q^3-3*_alpha^3*a^6*q^3*p^2*c-3*p^3*_alpha^2*a^4*d*q^3+3*q^3*(-q*p^2)^(2/3)*_alpha*a^6*c-3*p^4*(-q*p^2)^(2/3)*_alpha*b^4*d+2*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha^3*a^2*b^4*c*p^4-2*I*3^(1/2)*_alpha^3*a^3*b^3*c*p^4*q-I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^2*a^2*b^4*c*p^3-2*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha^2*a^6*c*p*q^3-3*I*3^(1/2)*_alpha^2*a^4*b^2*c*p^3*q^2+9*(-q*p^2)^(2/3)*_alpha^3*a^4*b^2*p^2*q*c+6*q^2*(-q*p^2)^(2/3)*_alpha^2*a^5*b*p*c+9*p^3*(-q*p^2)^(2/3)*_alpha^2*a^2*b^2*d*q+12*(-q*p^2)^(2/3)*_alpha*a^3*b^3*p^2*q*c+6*q^2*(-q*p^2)^(2/3)*_alpha*a^3*b*d*p^2+I*3^(1/2)*_alpha^3*a^6*c*p^2*q^3+I*(-q*p^2)^(2/3)*3^(1/2)*_alpha*a^6*c*q^3+I*3^(1/2)*_alpha^2*a^4*d*p^3*q^3+2*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha^2*b^4*d*p^5-I*(-q*p^2)^(2/3)*3^(1/2)*_alpha*b^4*d*p^4+3*I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^3*a^4*b^2*c*p^2*q-4*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha^3*a^5*b*c*p^2*q^2+2*I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^2*a^5*b*c*p*q^2+4*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha^2*a^3*b^3*c*p^3*q+3*I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^2*a^2*b^2*d*p^3*q+4*I*(-q*p^2)^(2/3)*3^(1/2)*_alpha*a^3*b^3*c*p^2*q-4*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha^2*a^3*b*d*p^3*q^2-2*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha*a^4*b^2*c*p^2*q^2+2*I*(-q*p^2)^(2/3)*3^(1/2)*_alpha*a^3*b*d*p^2*q^2+4*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha*a*b^3*d*p^4*q+6*I*(-q*p^2)^(1/3)*3^(1/2)*a^2*b^4*c*p^3*q-2*I*(-q*p^2)^(2/3)*3^(1/2)*a*b^3*d*p^3*q+6*I*(-q*p^2)^(1/3)*3^(1/2)*a^2*b^2*d*p^3*q^2+6*p^5*_alpha^2*a*b^3*d*q+9*p^4*_alpha*a^2*b^4*q*c+9*p^4*_alpha*a^2*b^2*d*q^2-3*p^3*(-q*p^2)^(2/3)*_alpha^2*a^2*b^4*c+6*p^4*_alpha^3*a^3*b^3*q*c+9*p^3*_alpha^2*a^4*b^2*q^2*c)/c/(a^6*q^4+2*a^3*b^3*p^2*q^2+b^6*p^4),(I*3^(1/2)/p*(-q*p^2)^(1/3)/(-3/2/p*(-q*p^2)^(1/3)+1/2*I*3^(1/2)/p*(-q*p^2)^(1/3)))^(1/2)),_alpha=RootOf(_Z^4*a^2*c+_Z^3*d*p+2*_Z^2*a*b*c+b^2*c+d*q))","C"
573,1,37,36,0.271000," ","int((x^12+1)/x^10/(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}-1}\, \left(2 x^{6}+1\right)}{9 x^{9}}-\frac{\ln \left(-x^{3}+\sqrt{x^{6}-1}\right)}{3}$&$37$\\ risch&$\frac{2 x^{12}-x^{6}-1}{9 x^{9} \sqrt{x^{6}-1}}+\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \arcsin \left(x^{3}\right)}{3 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}$&$50$\\ meijerg&$\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \arcsin \left(x^{3}\right)}{3 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}-\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(2 x^{6}+1\right) \sqrt{-x^{6}+1}}{9 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, x^{9}}$&$65$\\ \hline \end{longtable}"," ",0,"1/9*(x^6-1)^(1/2)*(2*x^6+1)/x^9-1/3*ln(-x^3+(x^6-1)^(1/2))","A"
574,0,0,34,0.017000," ","int((x^2-1)/(x^2+1)/(x^20+5*x^16+10*x^12+10*x^8+5*x^4+1)^(1/10),x)","\[\int \frac{x^{2}-1}{\left(x^{2}+1\right) \left(x^{20}+5 x^{16}+10 x^{12}+10 x^{8}+5 x^{4}+1\right)^{\frac{1}{10}}}\, dx\]"," ",0,"int((x^2-1)/(x^2+1)/(x^20+5*x^16+10*x^12+10*x^8+5*x^4+1)^(1/10),x)","F"
575,0,0,32,0.017000," ","int((b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2),x)","\[\int \frac{\sqrt{b +\sqrt{a \,x^{2}+b^{2}}}}{a \,x^{2}+b^{2}}\, dx\]"," ",0,"int((b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2),x)","F"
576,0,0,35,0.018000," ","int((x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2),x)","\[\int \frac{\sqrt{x^{2}+\sqrt{x^{4}+1}}}{\sqrt{x^{4}+1}}\, dx\]"," ",0,"int((x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2),x)","F"
577,1,52,33,1.215000," ","int(1/x^3/(x^2+1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{-\frac{\Gamma \left(\frac{3}{4}\right)}{x^{2}}-\frac{3 \left(\frac{1}{3}-3 \ln \left(2\right)+\frac{\pi}{2}+2 \ln \left(x \right)\right) \Gamma \left(\frac{3}{4}\right)}{4}+\frac{21 \hypergeom \left(\left[1, 1, \frac{11}{4}\right], \left[2, 3\right], -x^{2}\right) \Gamma \left(\frac{3}{4}\right) x^{2}}{32}}{2 \Gamma \left(\frac{3}{4}\right)}$&$52$\\ risch&$-\frac{\left(x^{2}+1\right)^{\frac{1}{4}}}{2 x^{2}}-\frac{3 \left(\left(-3 \ln \left(2\right)+\frac{\pi}{2}+2 \ln \left(x \right)\right) \Gamma \left(\frac{3}{4}\right)-\frac{3 \hypergeom \left(\left[1, 1, \frac{7}{4}\right], \left[2, 2\right], -x^{2}\right) \Gamma \left(\frac{3}{4}\right) x^{2}}{4}\right)}{8 \Gamma \left(\frac{3}{4}\right)}$&$56$\\ trager&$-\frac{\left(x^{2}+1\right)^{\frac{1}{4}}}{2 x^{2}}+\frac{3 \ln \left(-\frac{2 \left(x^{2}+1\right)^{\frac{3}{4}}+2 \sqrt{x^{2}+1}+x^{2}+2 \left(x^{2}+1\right)^{\frac{1}{4}}+2}{x^{2}}\right)}{8}+\frac{3 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{2}+1}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \left(x^{2}+1\right)^{\frac{3}{4}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(x^{2}+1\right)^{\frac{1}{4}}}{x^{2}}\right)}{8}$&$121$\\ \hline \end{longtable}"," ",0,"1/2/GAMMA(3/4)*(-GAMMA(3/4)/x^2-3/4*(1/3-3*ln(2)+1/2*Pi+2*ln(x))*GAMMA(3/4)+21/32*hypergeom([1,1,11/4],[2,3],-x^2)*GAMMA(3/4)*x^2)","C"
578,1,72,33,1.833000," ","int(1/x^4/(x^3+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{\left(x^{3}+1\right)^{\frac{3}{4}}}{3 x^{3}}-\frac{\sqrt{2}\, \Gamma \left(\frac{3}{4}\right) \left(\frac{\left(-3 \ln \left(2\right)-\frac{\pi}{2}+3 \ln \left(x \right)\right) \pi  \sqrt{2}}{\Gamma \left(\frac{3}{4}\right)}-\frac{\hypergeom \left(\left[1, 1, \frac{5}{4}\right], \left[2, 2\right], -x^{3}\right) \pi  \sqrt{2}\, x^{3}}{4 \Gamma \left(\frac{3}{4}\right)}\right)}{24 \pi}$&$72$\\ meijerg&$\frac{\sqrt{2}\, \Gamma \left(\frac{3}{4}\right) \left(-\frac{\pi  \sqrt{2}}{\Gamma \left(\frac{3}{4}\right) x^{3}}-\frac{\left(3-3 \ln \left(2\right)-\frac{\pi}{2}+3 \ln \left(x \right)\right) \pi  \sqrt{2}}{4 \Gamma \left(\frac{3}{4}\right)}+\frac{5 \hypergeom \left(\left[1, 1, \frac{9}{4}\right], \left[2, 3\right], -x^{3}\right) \pi  \sqrt{2}\, x^{3}}{32 \Gamma \left(\frac{3}{4}\right)}\right)}{6 \pi}$&$74$\\ trager&$-\frac{\left(x^{3}+1\right)^{\frac{3}{4}}}{3 x^{3}}+\frac{\ln \left(\frac{2 \left(x^{3}+1\right)^{\frac{3}{4}}+x^{3}+2 \sqrt{x^{3}+1}+2 \left(x^{3}+1\right)^{\frac{1}{4}}+2}{x^{3}}\right)}{12}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{3}+1}-2 \left(x^{3}+1\right)^{\frac{3}{4}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right)+2 \left(x^{3}+1\right)^{\frac{1}{4}}}{x^{3}}\right)}{12}$&$120$\\ \hline \end{longtable}"," ",0,"-1/3*(x^3+1)^(3/4)/x^3-1/24/Pi*2^(1/2)*GAMMA(3/4)*((-3*ln(2)-1/2*Pi+3*ln(x))*Pi*2^(1/2)/GAMMA(3/4)-1/4*hypergeom([1,1,5/4],[2,2],-x^3)*Pi*2^(1/2)/GAMMA(3/4)*x^3)","C"
579,1,52,33,1.588000," ","int((x^3+1)^(1/4)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\frac{4 \Gamma \left(\frac{3}{4}\right)}{x^{3}}-\left(-3 \ln \left(2\right)+\frac{\pi}{2}-1+3 \ln \left(x \right)\right) \Gamma \left(\frac{3}{4}\right)+\frac{3 \hypergeom \left(\left[1, 1, \frac{7}{4}\right], \left[2, 3\right], -x^{3}\right) \Gamma \left(\frac{3}{4}\right) x^{3}}{8}}{12 \Gamma \left(\frac{3}{4}\right)}$&$52$\\ risch&$-\frac{\left(x^{3}+1\right)^{\frac{1}{4}}}{3 x^{3}}+\frac{\left(-3 \ln \left(2\right)+\frac{\pi}{2}+3 \ln \left(x \right)\right) \Gamma \left(\frac{3}{4}\right)-\frac{3 \hypergeom \left(\left[1, 1, \frac{7}{4}\right], \left[2, 2\right], -x^{3}\right) \Gamma \left(\frac{3}{4}\right) x^{3}}{4}}{12 \Gamma \left(\frac{3}{4}\right)}$&$56$\\ trager&$-\frac{\left(x^{3}+1\right)^{\frac{1}{4}}}{3 x^{3}}-\frac{\ln \left(\frac{2 \left(x^{3}+1\right)^{\frac{3}{4}}+x^{3}+2 \sqrt{x^{3}+1}+2 \left(x^{3}+1\right)^{\frac{1}{4}}+2}{x^{3}}\right)}{12}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{3}+1}+2 \left(x^{3}+1\right)^{\frac{3}{4}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(x^{3}+1\right)^{\frac{1}{4}}}{x^{3}}\right)}{12}$&$119$\\ \hline \end{longtable}"," ",0,"-1/12/GAMMA(3/4)*(4*GAMMA(3/4)/x^3-(-3*ln(2)+1/2*Pi-1+3*ln(x))*GAMMA(3/4)+3/8*hypergeom([1,1,7/4],[2,3],-x^3)*GAMMA(3/4)*x^3)","C"
580,1,43,37,0.290000," ","int(x^3*(x^4-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{x \left(2 x^{3}-1\right) \sqrt{x^{4}-x}}{12}+\frac{\ln \left(2 x^{3}-2 x \sqrt{x^{4}-x}-1\right)}{24}$&$43$\\ meijerg&$-\frac{i \sqrt{\mathrm{signum}\left(x^{3}-1\right)}\, \left(-\frac{i \sqrt{\pi}\, x^{\frac{3}{2}} \left(-6 x^{3}+3\right) \sqrt{-x^{3}+1}}{6}+\frac{i \sqrt{\pi}\, \arcsin \left(x^{\frac{3}{2}}\right)}{2}\right)}{6 \sqrt{-\mathrm{signum}\left(x^{3}-1\right)}\, \sqrt{\pi}}$&$61$\\ default&$\frac{x^{4} \sqrt{x^{4}-x}}{6}-\frac{x \sqrt{x^{4}-x}}{12}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{4 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$315$\\ risch&$\frac{x^{2} \left(2 x^{3}-1\right) \left(x^{3}-1\right)}{12 \sqrt{x \left(x^{3}-1\right)}}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{4 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$315$\\ elliptic&$\frac{x^{4} \sqrt{x^{4}-x}}{6}-\frac{x \sqrt{x^{4}-x}}{12}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{4 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$315$\\ \hline \end{longtable}"," ",0,"1/12*x*(2*x^3-1)*(x^4-x)^(1/2)+1/24*ln(2*x^3-2*x*(x^4-x)^(1/2)-1)","A"
581,0,0,37,0.021000," ","int((x^4+1)*(3*x^4-1)/x/(x^4-a*x+1)/(x^5+x)^(1/2),x)","\[\int \frac{\left(x^{4}+1\right) \left(3 x^{4}-1\right)}{x \left(x^{4}-a x +1\right) \sqrt{x^{5}+x}}\, dx\]"," ",0,"int((x^4+1)*(3*x^4-1)/x/(x^4-a*x+1)/(x^5+x)^(1/2),x)","F"
582,1,113,37,0.435000," ","int((x^5+x^2+1)^(1/2)*(3*x^5-2)/(x^5+1)/(x^5-x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x^{5}+3 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}-4 \sqrt{x^{5}+x^{2}+1}\, x +\RootOf \left(\textit{\_Z}^{2}-2\right)}{x^{5}-x^{2}+1}\right)+\ln \left(-\frac{x^{5}+2 \sqrt{x^{5}+x^{2}+1}\, x +2 x^{2}+1}{\left(1+x \right) \left(x^{4}-x^{3}+x^{2}-x +1\right)}\right)$&$113$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2-2)*ln((RootOf(_Z^2-2)*x^5+3*RootOf(_Z^2-2)*x^2-4*(x^5+x^2+1)^(1/2)*x+RootOf(_Z^2-2))/(x^5-x^2+1))+ln(-(x^5+2*(x^5+x^2+1)^(1/2)*x+2*x^2+1)/(1+x)/(x^4-x^3+x^2-x+1))","C"
583,1,52,33,4.980000," ","int((x^6+1)^(1/4)/x^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\frac{4 \Gamma \left(\frac{3}{4}\right)}{x^{6}}-\left(-3 \ln \left(2\right)+\frac{\pi}{2}-1+6 \ln \left(x \right)\right) \Gamma \left(\frac{3}{4}\right)+\frac{3 \hypergeom \left(\left[1, 1, \frac{7}{4}\right], \left[2, 3\right], -x^{6}\right) \Gamma \left(\frac{3}{4}\right) x^{6}}{8}}{24 \Gamma \left(\frac{3}{4}\right)}$&$52$\\ risch&$-\frac{\left(x^{6}+1\right)^{\frac{1}{4}}}{6 x^{6}}+\frac{\left(-3 \ln \left(2\right)+\frac{\pi}{2}+6 \ln \left(x \right)\right) \Gamma \left(\frac{3}{4}\right)-\frac{3 \hypergeom \left(\left[1, 1, \frac{7}{4}\right], \left[2, 2\right], -x^{6}\right) \Gamma \left(\frac{3}{4}\right) x^{6}}{4}}{24 \Gamma \left(\frac{3}{4}\right)}$&$56$\\ trager&$-\frac{\left(x^{6}+1\right)^{\frac{1}{4}}}{6 x^{6}}+\frac{\ln \left(\frac{-x^{6}+2 \left(x^{6}+1\right)^{\frac{3}{4}}-2 \sqrt{x^{6}+1}+2 \left(x^{6}+1\right)^{\frac{1}{4}}-2}{x^{6}}\right)}{24}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}+2 \sqrt{x^{6}+1}\, \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(x^{6}+1\right)^{\frac{3}{4}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right)+2 \left(x^{6}+1\right)^{\frac{1}{4}}}{x^{6}}\right)}{24}$&$122$\\ \hline \end{longtable}"," ",0,"-1/24/GAMMA(3/4)*(4*GAMMA(3/4)/x^6-(-3*ln(2)+1/2*Pi-1+6*ln(x))*GAMMA(3/4)+3/8*hypergeom([1,1,7/4],[2,3],-x^6)*GAMMA(3/4)*x^6)","C"
584,1,807,41,4.747000," ","int((-1+x)^2*(5*x^3+5*x^2-8*x-10)/((1+x)/(x^2-2))^(3/4)/(x^2-2)/(x^6-4*x^5+4*x^4+4*x^3-11*x^2+7*x-3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(-\frac{2 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{3}{4}} x^{3}+2 \sqrt{-\frac{-1-x}{x^{2}-2}}\, x^{4}+2 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x^{5}+x^{6}-2 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{3}{4}} x^{2}-4 \sqrt{-\frac{-1-x}{x^{2}-2}}\, x^{3}-6 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x^{4}-4 x^{5}-4 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{3}{4}} x -2 \sqrt{-\frac{-1-x}{x^{2}-2}}\, x^{2}+2 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x^{3}+4 x^{4}+4 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{3}{4}}+8 \sqrt{-\frac{-1-x}{x^{2}-2}}\, x +10 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x^{2}+4 x^{3}-4 \sqrt{-\frac{-1-x}{x^{2}-2}}-12 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x -11 x^{2}+4 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}}+9 x -1}{x^{6}-4 x^{5}+4 x^{4}+4 x^{3}-11 x^{2}+7 x -3}\right)-\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{-\frac{-1-x}{x^{2}-2}}\, x^{4}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}+2 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{3}{4}} x^{3}-4 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{-\frac{-1-x}{x^{2}-2}}\, x^{3}-2 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x^{5}+4 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{5}-2 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{3}{4}} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{-\frac{-1-x}{x^{2}-2}}\, x^{2}+6 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x^{4}-4 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-4 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{3}{4}} x +8 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{-\frac{-1-x}{x^{2}-2}}\, x -2 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x^{3}-4 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+4 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{3}{4}}-4 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{-\frac{-1-x}{x^{2}-2}}-10 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x^{2}+11 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+12 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x -9 \RootOf \left(\textit{\_Z}^{2}+1\right) x -4 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{6}-4 x^{5}+4 x^{4}+4 x^{3}-11 x^{2}+7 x -3}\right)$&$807$\\ \hline \end{longtable}"," ",0,"-ln(-(2*(-(-1-x)/(x^2-2))^(3/4)*x^3+2*(-(-1-x)/(x^2-2))^(1/2)*x^4+2*(-(-1-x)/(x^2-2))^(1/4)*x^5+x^6-2*(-(-1-x)/(x^2-2))^(3/4)*x^2-4*(-(-1-x)/(x^2-2))^(1/2)*x^3-6*(-(-1-x)/(x^2-2))^(1/4)*x^4-4*x^5-4*(-(-1-x)/(x^2-2))^(3/4)*x-2*(-(-1-x)/(x^2-2))^(1/2)*x^2+2*(-(-1-x)/(x^2-2))^(1/4)*x^3+4*x^4+4*(-(-1-x)/(x^2-2))^(3/4)+8*(-(-1-x)/(x^2-2))^(1/2)*x+10*(-(-1-x)/(x^2-2))^(1/4)*x^2+4*x^3-4*(-(-1-x)/(x^2-2))^(1/2)-12*(-(-1-x)/(x^2-2))^(1/4)*x-11*x^2+4*(-(-1-x)/(x^2-2))^(1/4)+9*x-1)/(x^6-4*x^5+4*x^4+4*x^3-11*x^2+7*x-3))-RootOf(_Z^2+1)*ln(-(2*RootOf(_Z^2+1)*(-(-1-x)/(x^2-2))^(1/2)*x^4-RootOf(_Z^2+1)*x^6+2*(-(-1-x)/(x^2-2))^(3/4)*x^3-4*RootOf(_Z^2+1)*(-(-1-x)/(x^2-2))^(1/2)*x^3-2*(-(-1-x)/(x^2-2))^(1/4)*x^5+4*RootOf(_Z^2+1)*x^5-2*(-(-1-x)/(x^2-2))^(3/4)*x^2-2*RootOf(_Z^2+1)*(-(-1-x)/(x^2-2))^(1/2)*x^2+6*(-(-1-x)/(x^2-2))^(1/4)*x^4-4*RootOf(_Z^2+1)*x^4-4*(-(-1-x)/(x^2-2))^(3/4)*x+8*RootOf(_Z^2+1)*(-(-1-x)/(x^2-2))^(1/2)*x-2*(-(-1-x)/(x^2-2))^(1/4)*x^3-4*RootOf(_Z^2+1)*x^3+4*(-(-1-x)/(x^2-2))^(3/4)-4*RootOf(_Z^2+1)*(-(-1-x)/(x^2-2))^(1/2)-10*(-(-1-x)/(x^2-2))^(1/4)*x^2+11*RootOf(_Z^2+1)*x^2+12*(-(-1-x)/(x^2-2))^(1/4)*x-9*RootOf(_Z^2+1)*x-4*(-(-1-x)/(x^2-2))^(1/4)+RootOf(_Z^2+1))/(x^6-4*x^5+4*x^4+4*x^3-11*x^2+7*x-3))","C"
585,0,0,41,0.021000," ","int(x^2*(9*a*x+10*b)/(a*x^3+b*x^2)^(1/4)/(x^10-a*x-b),x)","\[\int \frac{x^{2} \left(9 a x +10 b \right)}{\left(a \,x^{3}+b \,x^{2}\right)^{\frac{1}{4}} \left(x^{10}-a x -b \right)}\, dx\]"," ",0,"int(x^2*(9*a*x+10*b)/(a*x^3+b*x^2)^(1/4)/(x^10-a*x-b),x)","F"
586,1,67,11,11.915000," ","int((x^16-1)/(x^4+1)^(1/2)/(x^16+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\munderset{\textit{\_R} =\RootOf \left(8 \textit{\_Z}^{8}-8 \textit{\_Z}^{4}+1\right)}{\sum}\frac{\left(2 \textit{\_R}^{6}-\textit{\_R}^{2}\right) \ln \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}-\textit{\_R} \right)}{2 \textit{\_R}^{7}-\textit{\_R}^{3}}\right) \sqrt{2}}{16}$&$67$\\ default&$\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{16}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{14}+x^{2}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}+1}\, \sqrt{x^{4}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}+1}}-\frac{2 \left(-1\right)^{\frac{3}{4}} \underline{\hspace{1.25 ex}}\alpha^{15} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \underline{\hspace{1.25 ex}}\alpha^{14}, i\right)}{\sqrt{x^{4}+1}}\right)\right)}{16}$&$161$\\ trager&$\text{Expression too large to display}$&$2481$\\ \hline \end{longtable}"," ",0,"1/16*sum((2*_R^6-_R^2)/(2*_R^7-_R^3)*ln(1/2*2^(1/2)/x*(x^4+1)^(1/2)-_R),_R=RootOf(8*_Z^8-8*_Z^4+1))*2^(1/2)","B"
587,1,63,11,6.629000," ","int((x^16-1)/(x^4-1)^(1/2)/(x^16-x^8+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\munderset{\textit{\_R} =\RootOf \left(16 \textit{\_Z}^{8}+16 \textit{\_Z}^{4}+1\right)}{\sum}\frac{\left(2 \textit{\_R}^{6}+\textit{\_R}^{2}\right) \ln \left(\frac{\sqrt{x^{4}-1}\, \sqrt{2}}{2 x}-\textit{\_R} \right)}{2 \textit{\_R}^{7}+\textit{\_R}^{3}}\right) \sqrt{2}}{16}$&$63$\\ default&$-\frac{i \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticF \left(i x , i\right)}{\sqrt{x^{4}-1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{16}-\textit{\_Z}^{8}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{14}-\underline{\hspace{1.25 ex}}\alpha^{6}+x^{2}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}-1}\, \sqrt{x^{4}-1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}-1}}+\frac{2 i \left(-\underline{\hspace{1.25 ex}}\alpha^{15}+\underline{\hspace{1.25 ex}}\alpha^{7}\right) \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticPi \left(i x , \underline{\hspace{1.25 ex}}\alpha^{14}-\underline{\hspace{1.25 ex}}\alpha^{6}, i\right)}{\sqrt{x^{4}-1}}\right)\right)}{16}$&$145$\\ trager&$-262144 \ln \left(\frac{-64 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{2} x^{2}-x^{4}+16 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right) \sqrt{x^{4}-1}\, x +1}{64 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{2} x^{2}-x^{4}+1}\right) \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{7}-256 \ln \left(\frac{-64 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{2} x^{2}-x^{4}+16 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right) \sqrt{x^{4}-1}\, x +1}{64 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{2} x^{2}-x^{4}+1}\right) \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{3}+64 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{2} \RootOf \left(-4096 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{6}-4 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{2}+\textit{\_Z}^{2}\right) \ln \left(-\frac{-67108864 \RootOf \left(-4096 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{6}-4 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{2}+\textit{\_Z}^{2}\right) \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{8} x^{2}-65536 \RootOf \left(-4096 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{6}-4 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{2}+\textit{\_Z}^{2}\right) \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{4} x^{2}-256 \RootOf \left(-4096 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{6}-4 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{2}+\textit{\_Z}^{2}\right) \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{2} x^{4}+256 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{2} \RootOf \left(-4096 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{6}-4 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{2}+\textit{\_Z}^{2}\right)+x \sqrt{x^{4}-1}}{262144 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{6} x^{2}+256 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{2} x^{2}-x^{4}+1}\right)+\RootOf \left(-4096 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{6}-4 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{2}+\textit{\_Z}^{2}\right) \ln \left(\frac{256 \RootOf \left(-4096 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{6}-4 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{2}+\textit{\_Z}^{2}\right) \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{2} x^{2}-4 \RootOf \left(-4096 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{6}-4 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{2}+\textit{\_Z}^{2}\right) x^{4}+x \sqrt{x^{4}-1}+4 \RootOf \left(-4096 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{6}-4 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{2}+\textit{\_Z}^{2}\right)}{64 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{2} x^{2}+x^{4}-1}\right)+\RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right) \ln \left(-\frac{1048576 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{7} x^{2}+1024 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{3} x^{2}-4 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right) x^{4}+x \sqrt{x^{4}-1}+4 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)}{262144 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{6} x^{2}+256 \RootOf \left(16777216 \textit{\_Z}^{8}+16384 \textit{\_Z}^{4}+1\right)^{2} x^{2}+x^{4}-1}\right)$&$919$\\ \hline \end{longtable}"," ",0,"1/16*sum((2*_R^6+_R^2)/(2*_R^7+_R^3)*ln(1/2*(x^4-1)^(1/2)*2^(1/2)/x-_R),_R=RootOf(16*_Z^8+16*_Z^4+1))*2^(1/2)","B"
588,0,0,35,0.035000," ","int((x^2+x*(x^2-1)^(1/2))^(1/2)/x/(x^2-1)^(1/2),x)","\[\int \frac{\sqrt{x^{2}+x \sqrt{x^{2}-1}}}{x \sqrt{x^{2}-1}}\, dx\]"," ",0,"int((x^2+x*(x^2-1)^(1/2))^(1/2)/x/(x^2-1)^(1/2),x)","F"
589,1,43,38,0.286000," ","int(x^6*(x^4+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\frac{\sqrt{\pi}\, x^{\frac{3}{2}} \left(-40 x^{6}-10 x^{3}+15\right) \sqrt{x^{3}+1}}{60}-\frac{\sqrt{\pi}\, \arcsinh \left(x^{\frac{3}{2}}\right)}{4}}{6 \sqrt{\pi}}$&$43$\\ trager&$\frac{x \left(8 x^{6}+2 x^{3}-3\right) \sqrt{x^{4}+x}}{72}-\frac{\ln \left(2 x^{3}-2 x \sqrt{x^{4}+x}+1\right)}{48}$&$44$\\ risch&$\frac{x^{2} \left(8 x^{6}+2 x^{3}-3\right) \left(x^{3}+1\right)}{72 \sqrt{x \left(x^{3}+1\right)}}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{8 \left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$322$\\ default&$\frac{x^{7} \sqrt{x^{4}+x}}{9}+\frac{x^{4} \sqrt{x^{4}+x}}{36}-\frac{x \sqrt{x^{4}+x}}{24}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{8 \left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$325$\\ elliptic&$\frac{x^{7} \sqrt{x^{4}+x}}{9}+\frac{x^{4} \sqrt{x^{4}+x}}{36}-\frac{x \sqrt{x^{4}+x}}{24}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{8 \left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$325$\\ \hline \end{longtable}"," ",0,"-1/6/Pi^(1/2)*(1/60*Pi^(1/2)*x^(3/2)*(-40*x^6-10*x^3+15)*(x^3+1)^(1/2)-1/4*Pi^(1/2)*arcsinh(x^(3/2)))","A"
590,1,36,42,0.345000," ","int((-1+x)*(1+x)^3/(x^2+1)^2/(x^4+x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{2 \sqrt{x^{4}+x^{2}+1}}{x^{2}+1}+\arctan \left(\frac{\sqrt{x^{4}+x^{2}+1}}{x}\right)$&$36$\\ trager&$\frac{2 \sqrt{x^{4}+x^{2}+1}}{x^{2}+1}+\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x +\sqrt{x^{4}+x^{2}+1}}{x^{2}+1}\right)$&$56$\\ risch&$\frac{2 \sqrt{x^{4}+x^{2}+1}}{x^{2}+1}+\frac{2 \sqrt{1-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{-2+2 i \sqrt{3}}}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}-\frac{2 \sqrt{1+\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}}\, \sqrt{1+\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , -\frac{1}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+x^{2}+1}}$&$207$\\ default&$\frac{2 \sqrt{1-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{-2+2 i \sqrt{3}}}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}+\arctanh \left(\frac{x^{2}}{2 \sqrt{x^{4}+x^{2}+1}}-\frac{1}{2 \sqrt{x^{4}+x^{2}+1}}\right)-\frac{2 \sqrt{1+\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}}\, \sqrt{1+\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , -\frac{1}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+x^{2}+1}}+\frac{2 \sqrt{\left(x^{2}+1\right)^{2}-x^{2}}}{x^{2}+1}+\arctanh \left(\frac{-x^{2}+1}{2 \sqrt{\left(x^{2}+1\right)^{2}-x^{2}}}\right)$&$266$\\ \hline \end{longtable}"," ",0,"2*(x^4+x^2+1)^(1/2)/(x^2+1)+arctan(1/x*(x^4+x^2+1)^(1/2))","A"
591,1,67,40,1.171000," ","int((x^2-1)/(x^2+1)/(x^4-x^3-x^2-x+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) x^{2}+6 \RootOf \left(\textit{\_Z}^{2}+3\right) x +6 \sqrt{x^{4}-x^{3}-x^{2}-x +1}+\RootOf \left(\textit{\_Z}^{2}+3\right)}{x^{2}+1}\right)}{3}$&$67$\\ default&$\text{Expression too large to display}$&$100440$\\ elliptic&$\text{Expression too large to display}$&$114996$\\ \hline \end{longtable}"," ",0,"1/3*RootOf(_Z^2+3)*ln(-(RootOf(_Z^2+3)*x^2+6*RootOf(_Z^2+3)*x+6*(x^4-x^3-x^2-x+1)^(1/2)+RootOf(_Z^2+3))/(x^2+1))","C"
592,1,45,44,0.202000," ","int((3*x^2-2*x-1)/(x^6-2*x^5-x^4+4*x^3-x^2-2*x-3)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(-x^{3}+x^{2}-\sqrt{x^{6}-2 x^{5}-x^{4}+4 x^{3}-x^{2}-2 x -3}+x -1\right)$&$45$\\ \hline \end{longtable}"," ",0,"ln(-x^3+x^2-(x^6-2*x^5-x^4+4*x^3-x^2-2*x-3)^(1/2)+x-1)","A"
593,1,53,42,0.495000," ","int((x^2-x)/(x^6-2*x^5+x^4-2*x^3+4*x^2-2*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(-\frac{x^{4}-x^{3}+x \sqrt{x^{6}-2 x^{5}+x^{4}-2 x^{3}+4 x^{2}-2 x}-x +1}{-1+x}\right)}{3}$&$53$\\ default&$-\frac{4 \left(-1+x \right) \sqrt{x \left(x^{3}-2\right)}\, \left(1+i \sqrt{3}\right) \sqrt{-\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(-x +2^{\frac{1}{3}}\right)}}\, \left(-x +2^{\frac{1}{3}}\right)^{2} \sqrt{\frac{i \sqrt{3}\, 2^{\frac{1}{3}}-2^{\frac{1}{3}}-2 x}{\left(i \sqrt{3}-1\right) \left(-x +2^{\frac{1}{3}}\right)}}\, \sqrt{\frac{i \sqrt{3}\, 2^{\frac{1}{3}}+2^{\frac{1}{3}}+2 x}{\left(1+i \sqrt{3}\right) \left(-x +2^{\frac{1}{3}}\right)}}\, \left(\EllipticF \left(\sqrt{-\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(-x +2^{\frac{1}{3}}\right)}}, \sqrt{\frac{\left(-3+i \sqrt{3}\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(3+i \sqrt{3}\right)}}\right)-\EllipticPi \left(\sqrt{-\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(-x +2^{\frac{1}{3}}\right)}}, \frac{1+i \sqrt{3}}{3+i \sqrt{3}}, \sqrt{\frac{\left(-3+i \sqrt{3}\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(3+i \sqrt{3}\right)}}\right)\right)}{\sqrt{x^{6}-2 x^{5}+x^{4}-2 x^{3}+4 x^{2}-2 x}\, \left(3+i \sqrt{3}\right) \sqrt{x \left(-x +2^{\frac{1}{3}}\right) \left(i \sqrt{3}\, 2^{\frac{1}{3}}-2^{\frac{1}{3}}-2 x \right) \left(i \sqrt{3}\, 2^{\frac{1}{3}}+2^{\frac{1}{3}}+2 x \right)}}$&$390$\\ \hline \end{longtable}"," ",0,"1/3*ln(-(x^4-x^3+x*(x^6-2*x^5+x^4-2*x^3+4*x^2-2*x)^(1/2)-x+1)/(-1+x))","A"
594,1,33,37,2.398000," ","int((x^4-1)^(1/4)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{1}{4}, -\frac{1}{4}\right], \left[\frac{3}{4}\right], x^{4}\right)}{\left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} x}$&$33$\\ risch&$-\frac{\left(x^{4}-1\right)^{\frac{1}{4}}}{x}+\frac{\left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[\frac{3}{4}, \frac{3}{4}\right], \left[\frac{7}{4}\right], x^{4}\right) x^{3}}{3 \mathrm{signum}\left(x^{4}-1\right)^{\frac{3}{4}}}$&$46$\\ trager&$-\frac{\left(x^{4}-1\right)^{\frac{1}{4}}}{x}+\frac{\ln \left(2 \left(x^{4}-1\right)^{\frac{3}{4}} x +2 x^{2} \sqrt{x^{4}-1}+2 x^{3} \left(x^{4}-1\right)^{\frac{1}{4}}+2 x^{4}-1\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}-1}\, x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \left(x^{4}-1\right)^{\frac{3}{4}} x -2 x^{3} \left(x^{4}-1\right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{4}$&$125$\\ \hline \end{longtable}"," ",0,"-1/(-signum(x^4-1))^(1/4)*signum(x^4-1)^(1/4)*hypergeom([-1/4,-1/4],[3/4],x^4)/x","C"
595,1,62,35,4.358000," ","int((x^4-1)*(x^4+1)^(1/4)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{-4 \left(4-3 \ln \left(2\right)+\frac{\pi}{2}+4 \ln \left(x \right)\right) \Gamma \left(\frac{3}{4}\right)-\hypergeom \left(\left[\frac{3}{4}, 1, 1\right], \left[2, 2\right], -x^{4}\right) \Gamma \left(\frac{3}{4}\right) x^{4}}{16 \Gamma \left(\frac{3}{4}\right)}+\frac{\hypergeom \left(\left[-\frac{1}{4}, 1\right], \left[2\right], -x^{4}\right) x^{4}}{4}$&$62$\\ trager&$\left(\frac{x^{4}}{5}-\frac{4}{5}\right) \left(x^{4}+1\right)^{\frac{1}{4}}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}+2 \left(x^{4}+1\right)^{\frac{3}{4}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(x^{4}+1\right)^{\frac{1}{4}}}{x^{4}}\right)}{4}-\frac{\ln \left(\frac{-x^{4}+2 \left(x^{4}+1\right)^{\frac{3}{4}}-2 \sqrt{x^{4}+1}+2 \left(x^{4}+1\right)^{\frac{1}{4}}-2}{x^{4}}\right)}{4}$&$124$\\ \hline \end{longtable}"," ",0,"1/16/GAMMA(3/4)*(-4*(4-3*ln(2)+1/2*Pi+4*ln(x))*GAMMA(3/4)-hypergeom([3/4,1,1],[2,2],-x^4)*GAMMA(3/4)*x^4)+1/4*hypergeom([-1/4,1],[2],-x^4)*x^4","C"
596,1,48,38,0.160000," ","int(1/(x^4+4*x+3)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(1+x \right) \sqrt{x^{2}-2 x +3}\, \sqrt{6}\, \arctanh \left(\frac{\left(-2+x \right) \sqrt{6}}{3 \sqrt{x^{2}-2 x +3}}\right)}{6 \sqrt{x^{4}+4 x +3}}$&$48$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-6\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-6\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}-6\right) x +3 \sqrt{x^{4}+4 x +3}-2 \RootOf \left(\textit{\_Z}^{2}-6\right)}{\left(1+x \right)^{2}}\right)}{6}$&$56$\\ \hline \end{longtable}"," ",0,"1/6/(x^4+4*x+3)^(1/2)*(1+x)*(x^2-2*x+3)^(1/2)*6^(1/2)*arctanh(1/3*(-2+x)*6^(1/2)/(x^2-2*x+3)^(1/2))","A"
597,1,76,39,0.551000," ","int((x^4+1)*(x^4+2*x^2-1)^(1/2)/(x^4-1)/(x^4+x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(-\ln \left(1+\frac{\sqrt{x^{4}+2 x^{2}-1}\, \sqrt{2}}{2 x}\right)+\sqrt{2}\, \arctanh \left(\frac{\sqrt{x^{4}+2 x^{2}-1}}{x}\right)+\ln \left(-1+\frac{\sqrt{x^{4}+2 x^{2}-1}\, \sqrt{2}}{2 x}\right)\right) \sqrt{2}}{2}$&$76$\\ trager&$\frac{\ln \left(-\frac{x^{4}+2 \sqrt{x^{4}+2 x^{2}-1}\, x +3 x^{2}-1}{x^{4}+x^{2}-1}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}-2\right) x^{4}-4 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}+4 \sqrt{x^{4}+2 x^{2}-1}\, x +\RootOf \left(\textit{\_Z}^{2}-2\right)}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)}{2}$&$114$\\ default&$-\frac{2 \sqrt{1-\left(1-\sqrt{2}\right) x^{2}}\, \sqrt{1-\left(1+\sqrt{2}\right) x^{2}}\, \left(\EllipticF \left(x \sqrt{1-\sqrt{2}}, i+i \sqrt{2}\right)-\EllipticE \left(x \sqrt{1-\sqrt{2}}, i+i \sqrt{2}\right)\right)}{\sqrt{1-\sqrt{2}}\, \sqrt{x^{4}+2 x^{2}-1}\, \left(2+2 \sqrt{2}\right)}-\frac{2 \sqrt{1-\left(1-\sqrt{2}\right) x^{2}}\, \sqrt{1-\left(1+\sqrt{2}\right) x^{2}}\, \EllipticPi \left(x \sqrt{1-\sqrt{2}}, \frac{1}{1-\sqrt{2}}, \frac{\sqrt{1+\sqrt{2}}}{\sqrt{1-\sqrt{2}}}\right)}{\sqrt{1-\sqrt{2}}\, \sqrt{x^{4}+2 x^{2}-1}}+\frac{\sqrt{\sqrt{2}\, x^{2}-x^{2}+1}\, \sqrt{-\sqrt{2}\, x^{2}-x^{2}+1}\, \EllipticF \left(x \sqrt{1-\sqrt{2}}, i+i \sqrt{2}\right)}{\sqrt{1-\sqrt{2}}\, \sqrt{x^{4}+2 x^{2}-1}}+\frac{2 \sqrt{\sqrt{2}\, x^{2}-x^{2}+1}\, \sqrt{-\sqrt{2}\, x^{2}-x^{2}+1}\, \EllipticF \left(x \sqrt{1-\sqrt{2}}, i+i \sqrt{2}\right)}{\sqrt{1-\sqrt{2}}\, \sqrt{x^{4}+2 x^{2}-1}\, \left(2+2 \sqrt{2}\right)}-\frac{2 \sqrt{\sqrt{2}\, x^{2}-x^{2}+1}\, \sqrt{-\sqrt{2}\, x^{2}-x^{2}+1}\, \EllipticE \left(x \sqrt{1-\sqrt{2}}, i+i \sqrt{2}\right)}{\sqrt{1-\sqrt{2}}\, \sqrt{x^{4}+2 x^{2}-1}\, \left(2+2 \sqrt{2}\right)}-\frac{2 \sqrt{\sqrt{2}\, x^{2}-x^{2}+1}\, \sqrt{-\sqrt{2}\, x^{2}-x^{2}+1}\, \EllipticPi \left(x \sqrt{1-\sqrt{2}}, -\frac{1}{1-\sqrt{2}}, \frac{\sqrt{1+\sqrt{2}}}{\sqrt{1-\sqrt{2}}}\right)}{\sqrt{1-\sqrt{2}}\, \sqrt{x^{4}+2 x^{2}-1}}-\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+\textit{\_Z}^{2}-1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2}+1\right) \left(-2 \underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}+1\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{x^{4}+2 x^{2}-1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}}-\frac{2 \left(\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{\sqrt{2}\, x^{2}-x^{2}+1}\, \sqrt{-\sqrt{2}\, x^{2}-x^{2}+1}\, \EllipticPi \left(x \sqrt{1-\sqrt{2}}, -\underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{2}-\underline{\hspace{1.25 ex}}\alpha^{2}-\sqrt{2}-1, \frac{\sqrt{1+\sqrt{2}}}{\sqrt{1-\sqrt{2}}}\right)}{\sqrt{1-\sqrt{2}}\, \sqrt{x^{4}+2 x^{2}-1}}\right)\right)}{4}$&$712$\\ \hline \end{longtable}"," ",0,"1/2*(-ln(1+1/2*(x^4+2*x^2-1)^(1/2)*2^(1/2)/x)+2^(1/2)*arctanh((x^4+2*x^2-1)^(1/2)/x)+ln(-1+1/2*(x^4+2*x^2-1)^(1/2)*2^(1/2)/x))*2^(1/2)","A"
598,1,99,43,12.643000," ","int((x^4-x^2+x-1)^(1/2)*(2*x^4-x+2)/(x^4+x-1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{x \sqrt{x^{4}-x^{2}+x -1}}{x^{4}+x -1}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \sqrt{x^{4}-x^{2}+x -1}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{4}+x -1}\right)}{2}$&$99$\\ risch&$\text{Expression too large to display}$&$3619$\\ elliptic&$\text{Expression too large to display}$&$3619$\\ default&$\text{Expression too large to display}$&$6119$\\ \hline \end{longtable}"," ",0,"-x*(x^4-x^2+x-1)^(1/2)/(x^4+x-1)+1/2*RootOf(_Z^2+1)*ln(-(RootOf(_Z^2+1)*x^4-2*RootOf(_Z^2+1)*x^2+RootOf(_Z^2+1)*x-2*(x^4-x^2+x-1)^(1/2)*x-RootOf(_Z^2+1))/(x^4+x-1))","C"
599,0,0,39,0.027000," ","int((3*x^5+x)/(x^4-1)/(a*x^4-a-x)/(x^5-x)^(1/2),x)","\[\int \frac{3 x^{5}+x}{\left(x^{4}-1\right) \left(a \,x^{4}-a -x \right) \sqrt{x^{5}-x}}\, dx\]"," ",0,"int((3*x^5+x)/(x^4-1)/(a*x^4-a-x)/(x^5-x)^(1/2),x)","F"
600,1,117,36,0.368000," ","int((x^6+x^2+1)^(1/2)*(2*x^6-1)/(x^6+1)/(2*x^6-x^2+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-6\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}-6\right) x^{6}+5 \RootOf \left(\textit{\_Z}^{2}-6\right) x^{2}-12 \sqrt{x^{6}+x^{2}+1}\, x +2 \RootOf \left(\textit{\_Z}^{2}-6\right)}{2 x^{6}-x^{2}+2}\right)}{4}+\frac{\ln \left(-\frac{x^{6}+2 \sqrt{x^{6}+x^{2}+1}\, x +2 x^{2}+1}{\left(x^{2}+1\right) \left(x^{4}-x^{2}+1\right)}\right)}{2}$&$117$\\ \hline \end{longtable}"," ",0,"1/4*RootOf(_Z^2-6)*ln((2*RootOf(_Z^2-6)*x^6+5*RootOf(_Z^2-6)*x^2-12*(x^6+x^2+1)^(1/2)*x+2*RootOf(_Z^2-6))/(2*x^6-x^2+2))+1/2*ln(-(x^6+2*(x^6+x^2+1)^(1/2)*x+2*x^2+1)/(x^2+1)/(x^4-x^2+1))","C"
601,0,0,39,0.026000," ","int((4*x^6+x)/(x^5-1)/(a*x^5-a-x)/(x^6-x)^(1/2),x)","\[\int \frac{4 x^{6}+x}{\left(x^{5}-1\right) \left(a \,x^{5}-a -x \right) \sqrt{x^{6}-x}}\, dx\]"," ",0,"int((4*x^6+x)/(x^5-1)/(a*x^5-a-x)/(x^6-x)^(1/2),x)","F"
602,1,100,43,0.666000," ","int((6*x^4-1)*(2*x^5+x)^(1/2)/(2*x^4+1)/(4*x^8+4*x^4-x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(-\frac{-2 x^{4}+2 \sqrt{2 x^{5}+x}-x -1}{2 x^{4}-x +1}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+\RootOf \left(\textit{\_Z}^{2}+1\right) x +2 \sqrt{2 x^{5}+x}-\RootOf \left(\textit{\_Z}^{2}+1\right)}{2 x^{4}+x +1}\right)}{2}$&$100$\\ \hline \end{longtable}"," ",0,"1/2*ln(-(-2*x^4+2*(2*x^5+x)^(1/2)-x-1)/(2*x^4-x+1))-1/2*RootOf(_Z^2+1)*ln(-(-2*RootOf(_Z^2+1)*x^4+RootOf(_Z^2+1)*x+2*(2*x^5+x)^(1/2)-RootOf(_Z^2+1))/(2*x^4+x+1))","C"
603,1,17,33,0.073000," ","int((1+(1+x)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\hypergeom \left(\left[-\frac{1}{4}, \frac{1}{4}, 1\right], \left[\frac{1}{2}, 2\right], -x \right) \sqrt{2}\, x$&$17$\\ derivativedivides&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{5}{2}}}{5}-\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}$&$24$\\ default&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{5}{2}}}{5}-\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}$&$24$\\ \hline \end{longtable}"," ",0,"hypergeom([-1/4,1/4,1],[1/2,2],-x)*2^(1/2)*x","C"
604,1,51,36,0.052000," ","int((1+(x^2+1)^(1/2))^(1/2)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{-4 \left(-4 \ln \left(2\right)+4+2 \ln \left(x \right)\right) \sqrt{\pi}\, \sqrt{2}-\frac{\hypergeom \left(\left[\frac{3}{4}, 1, 1, \frac{5}{4}\right], \left[\frac{3}{2}, 2, 2\right], -x^{2}\right) \sqrt{\pi}\, \sqrt{2}\, x^{2}}{2}}{8 \sqrt{\pi}}$&$51$\\ \hline \end{longtable}"," ",0,"-1/8/Pi^(1/2)*(-4*(-4*ln(2)+4+2*ln(x))*Pi^(1/2)*2^(1/2)-1/2*hypergeom([3/4,1,1,5/4],[3/2,2,2],-x^2)*Pi^(1/2)*2^(1/2)*x^2)","C"
605,0,0,41,0.018000," ","int(1/(1+(x^2-6*x+9)^(1/4)),x)","\[\int \frac{1}{1+\left(x^{2}-6 x +9\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(1+(x^2-6*x+9)^(1/4)),x)","F"
606,1,121,39,1.459000," ","int(x^2/(x^2-2)/(x^2-1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(-\frac{\left(x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+2\right)-x \sqrt{x^{2}-1}-\RootOf \left(\textit{\_Z}^{2}+2\right) \left(x^{2}-1\right)^{\frac{1}{4}}+x}{x^{2}-2}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{\left(x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}-2\right)-x \sqrt{x^{2}-1}+\RootOf \left(\textit{\_Z}^{2}-2\right) \left(x^{2}-1\right)^{\frac{1}{4}}-x}{x^{2}-2}\right)}{2}$&$121$\\ \hline \end{longtable}"," ",0,"-1/2*RootOf(_Z^2+2)*ln(-((x^2-1)^(3/4)*RootOf(_Z^2+2)-x*(x^2-1)^(1/2)-RootOf(_Z^2+2)*(x^2-1)^(1/4)+x)/(x^2-2))+1/2*RootOf(_Z^2-2)*ln(-((x^2-1)^(3/4)*RootOf(_Z^2-2)-x*(x^2-1)^(1/2)+RootOf(_Z^2-2)*(x^2-1)^(1/4)-x)/(x^2-2))","C"
607,1,53,36,0.271000," ","int((x^2-1)*(x^4+1)^(1/2)/(x^2+1)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{x \sqrt{x^{4}+1}}{2 \left(x^{2}+1\right)^{2}}-\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+2\right) x +\sqrt{x^{4}+1}}{x^{2}+1}\right)}{4}$&$53$\\ elliptic&$\frac{\left(-\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{4 \left(\frac{x^{4}+1}{2 x^{2}}+1\right) x}+\frac{\arctan \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{2}\right) \sqrt{2}}{2}$&$54$\\ risch&$-\frac{x \sqrt{x^{4}+1}}{2 \left(x^{2}+1\right)^{2}}+\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{2 \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{\sqrt{x^{4}+1}}$&$128$\\ default&$\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{2 \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}-\frac{i \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \left(\EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)-\EllipticE \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)\right)}{2 \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}-\frac{x \sqrt{x^{4}+1}}{2 \left(x^{2}+1\right)^{2}}+\frac{i \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{2 \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}-\frac{i \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticE \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{2 \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{\sqrt{x^{4}+1}}$&$331$\\ \hline \end{longtable}"," ",0,"-1/2*x*(x^4+1)^(1/2)/(x^2+1)^2-1/4*RootOf(_Z^2+2)*ln((-RootOf(_Z^2+2)*x+(x^4+1)^(1/2))/(x^2+1))","C"
608,1,75,43,0.472000," ","int((5*x^2-46*x+77)/(-23*x^2+82*x-23)/(x^4-3*x^3-21*x^2+83*x-60)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+42\right) \ln \left(-\frac{19 \RootOf \left(\textit{\_Z}^{2}+42\right) x^{2}-86 \RootOf \left(\textit{\_Z}^{2}+42\right) x +103 \RootOf \left(\textit{\_Z}^{2}+42\right)+84 \sqrt{x^{4}-3 x^{3}-21 x^{2}+83 x -60}}{23 x^{2}-82 x +23}\right)}{42}$&$75$\\ default&$\text{Expression too large to display}$&$3042$\\ elliptic&$\text{Expression too large to display}$&$3260$\\ \hline \end{longtable}"," ",0,"1/42*RootOf(_Z^2+42)*ln(-(19*RootOf(_Z^2+42)*x^2-86*RootOf(_Z^2+42)*x+103*RootOf(_Z^2+42)+84*(x^4-3*x^3-21*x^2+83*x-60)^(1/2))/(23*x^2-82*x+23))","C"
609,1,30,38,0.762000," ","int((-1+x)*(x^4+x^3)^(1/4)/x/(1+x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{4 \hypergeom \left(\left[\frac{3}{4}, \frac{3}{4}\right], \left[\frac{7}{4}\right], -x \right) x^{\frac{3}{4}}}{3}+\frac{4 \hypergeom \left(\left[\frac{3}{4}, \frac{7}{4}\right], \left[\frac{11}{4}\right], -x \right) x^{\frac{7}{4}}}{7}$&$30$\\ trager&$\left(x^{4}+x^{3}\right)^{\frac{1}{4}}+\frac{7 \ln \left(\frac{2 \left(x^{4}+x^{3}\right)^{\frac{3}{4}}-2 \sqrt{x^{4}+x^{3}}\, x +2 \left(x^{4}+x^{3}\right)^{\frac{1}{4}} x^{2}-2 x^{3}-x^{2}}{x^{2}}\right)}{4}-\frac{7 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \sqrt{x^{4}+x^{3}}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{4}+x^{3}\right)^{\frac{3}{4}}-2 \left(x^{4}+x^{3}\right)^{\frac{1}{4}} x^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}}{x^{2}}\right)}{4}$&$145$\\ risch&$\left(x^{3} \left(1+x \right)\right)^{\frac{1}{4}}+\frac{\left(-\frac{7 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, \RootOf \left(\textit{\_Z}^{2}+1\right)-5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{3}{4}}+2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x^{2}-4 \RootOf \left(\textit{\_Z}^{2}+1\right) x +4 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x -\RootOf \left(\textit{\_Z}^{2}+1\right)+2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}}}{\left(1+x \right)^{2}}\right)}{4}-\frac{7 \ln \left(\frac{2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{3}{4}}+2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, x +2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x^{2}+2 x^{3}+2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}+4 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x +5 x^{2}+2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}}+4 x +1}{\left(1+x \right)^{2}}\right)}{4}\right) \left(x^{3} \left(1+x \right)\right)^{\frac{1}{4}} \left(\left(1+x \right)^{3} x \right)^{\frac{1}{4}}}{x \left(1+x \right)}$&$369$\\ \hline \end{longtable}"," ",0,"-4/3*hypergeom([3/4,3/4],[7/4],-x)*x^(3/4)+4/7*hypergeom([3/4,7/4],[11/4],-x)*x^(7/4)","C"
610,1,36,44,0.090000," ","int((x^4-1)*(x^4+x^3)^(1/4)/x^8,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{4 \hypergeom \left(\left[-\frac{25}{4}, -\frac{1}{4}\right], \left[-\frac{21}{4}\right], -x \right)}{25 x^{\frac{25}{4}}}-\frac{4 \left(-\frac{4}{5} x^{2}+\frac{1}{5} x +1\right) \left(1+x \right)^{\frac{1}{4}}}{9 x^{\frac{9}{4}}}$&$36$\\ gosper&$\frac{4 \left(1+x \right)^{2} \left(22748 x^{4}-51183 x^{3}+39663 x^{2}-27183 x +13923\right) \left(x^{4}+x^{3}\right)^{\frac{1}{4}}}{348075 x^{7}}$&$40$\\ trager&$\frac{4 \left(x^{4}+x^{3}\right)^{\frac{1}{4}} \left(22748 x^{6}-5687 x^{5}-39955 x^{4}+960 x^{3}-780 x^{2}+663 x +13923\right)}{348075 x^{7}}$&$45$\\ risch&$\frac{4 \left(x^{3} \left(1+x \right)\right)^{\frac{1}{4}} \left(22748 x^{7}+17061 x^{6}-45642 x^{5}-38995 x^{4}+180 x^{3}-117 x^{2}+14586 x +13923\right)}{348075 x^{7} \left(1+x \right)}$&$55$\\ \hline \end{longtable}"," ",0,"4/25*hypergeom([-25/4,-1/4],[-21/4],-x)/x^(25/4)-4/9*(-4/5*x^2+1/5*x+1)*(1+x)^(1/4)/x^(9/4)","C"
611,1,168,38,0.457000," ","int((4*x^4-4*x^2+4*x-1)/((-2*x^2+1)/(2*x^2+1))^(1/2)/(2*x^2+1)/(4*x^4-8*x^3+12*x^2-4*x-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}-6\right) \ln \left(\frac{4 \RootOf \left(\textit{\_Z}^{2}-6\right) x^{4}-8 \RootOf \left(\textit{\_Z}^{2}-6\right) x^{3}-24 \sqrt{-\frac{2 x^{2}-1}{2 x^{2}+1}}\, x^{3}+24 \sqrt{-\frac{2 x^{2}-1}{2 x^{2}+1}}\, x^{2}-4 \RootOf \left(\textit{\_Z}^{2}-6\right) x -12 x \sqrt{-\frac{2 x^{2}-1}{2 x^{2}+1}}+5 \RootOf \left(\textit{\_Z}^{2}-6\right)+12 \sqrt{-\frac{2 x^{2}-1}{2 x^{2}+1}}}{4 x^{4}-8 x^{3}+12 x^{2}-4 x -1}\right)}{12}$&$168$\\ default&$-\frac{\left(2 x^{2}-1\right) \left(24 \sqrt{2}\, \sqrt{-2 x^{2}+1}\, \sqrt{2 x^{2}+1}\, \EllipticF \left(\sqrt{2}\, x , i\right)+\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 \textit{\_Z}^{4}-8 \textit{\_Z}^{3}+12 \textit{\_Z}^{2}-4 \textit{\_Z} -1\right)}{\sum}\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{3}-2 \underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  -1\right) \left(16 \sqrt{2}\, \sqrt{-2 \underline{\hspace{1.25 ex}}\alpha^{3}+3 \underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha }\, \sqrt{-2 x^{2}+1}\, \sqrt{2 x^{2}+1}\, \EllipticPi \left(\sqrt{2}\, x , -8 \underline{\hspace{1.25 ex}}\alpha^{3}+18 \underline{\hspace{1.25 ex}}\alpha^{2}-28 \underline{\hspace{1.25 ex}}\alpha  +14, \frac{\sqrt{-2}\, \sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha^{3}-32 \sqrt{2}\, \sqrt{-2 \underline{\hspace{1.25 ex}}\alpha^{3}+3 \underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha }\, \sqrt{-2 x^{2}+1}\, \sqrt{2 x^{2}+1}\, \EllipticPi \left(\sqrt{2}\, x , -8 \underline{\hspace{1.25 ex}}\alpha^{3}+18 \underline{\hspace{1.25 ex}}\alpha^{2}-28 \underline{\hspace{1.25 ex}}\alpha  +14, \frac{\sqrt{-2}\, \sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha^{2}+48 \sqrt{2}\, \sqrt{-2 \underline{\hspace{1.25 ex}}\alpha^{3}+3 \underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha }\, \sqrt{-2 x^{2}+1}\, \sqrt{2 x^{2}+1}\, \EllipticPi \left(\sqrt{2}\, x , -8 \underline{\hspace{1.25 ex}}\alpha^{3}+18 \underline{\hspace{1.25 ex}}\alpha^{2}-28 \underline{\hspace{1.25 ex}}\alpha  +14, \frac{\sqrt{-2}\, \sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha  -16 \sqrt{2}\, \sqrt{-2 x^{2}+1}\, \sqrt{2 x^{2}+1}\, \EllipticPi \left(\sqrt{2}\, x , -8 \underline{\hspace{1.25 ex}}\alpha^{3}+18 \underline{\hspace{1.25 ex}}\alpha^{2}-28 \underline{\hspace{1.25 ex}}\alpha  +14, \frac{\sqrt{-2}\, \sqrt{2}}{2}\right) \sqrt{-2 \underline{\hspace{1.25 ex}}\alpha^{3}+3 \underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha }-\sqrt{4}\, \arctanh \left(\frac{2 \underline{\hspace{1.25 ex}}\alpha^{2} \left(4 \underline{\hspace{1.25 ex}}\alpha^{3}-9 \underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}+14 \underline{\hspace{1.25 ex}}\alpha  -7\right)}{\sqrt{-2 \underline{\hspace{1.25 ex}}\alpha^{3}+3 \underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha }\, \sqrt{-4 x^{4}+1}}\right) \sqrt{-4 x^{4}+1}\right)}{\sqrt{-2 \underline{\hspace{1.25 ex}}\alpha^{3}+3 \underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha }\, \sqrt{-4 x^{4}+1}}\right) \sqrt{-4 x^{4}+1}\right)}{48 \sqrt{-\frac{2 x^{2}-1}{2 x^{2}+1}}\, \sqrt{-\left(2 x^{2}+1\right) \left(2 x^{2}-1\right)}\, \sqrt{-4 x^{4}+1}}$&$505$\\ \hline \end{longtable}"," ",0,"-1/12*RootOf(_Z^2-6)*ln((4*RootOf(_Z^2-6)*x^4-8*RootOf(_Z^2-6)*x^3-24*(-(2*x^2-1)/(2*x^2+1))^(1/2)*x^3+24*(-(2*x^2-1)/(2*x^2+1))^(1/2)*x^2-4*RootOf(_Z^2-6)*x-12*x*(-(2*x^2-1)/(2*x^2+1))^(1/2)+5*RootOf(_Z^2-6)+12*(-(2*x^2-1)/(2*x^2+1))^(1/2))/(4*x^4-8*x^3+12*x^2-4*x-1))","C"
612,1,38,44,0.148000," ","int((x^4-3)*(x^4-2*x^3+1)*(x^4-x^3+1)/x^6/(x^4+1)/(x^5+x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{-8 x^{6}-4 x^{7}-4 x^{3}+\frac{4}{7} x^{8}+\frac{8}{7} x^{4}+\frac{4}{7}}{\left(x^{5}+x \right)^{\frac{1}{4}} x^{5}}$&$38$\\ risch&$\frac{-8 x^{6}-4 x^{7}-4 x^{3}+\frac{4}{7} x^{8}+\frac{8}{7} x^{4}+\frac{4}{7}}{x^{5} \left(x \left(x^{4}+1\right)\right)^{\frac{1}{4}}}$&$40$\\ trager&$\frac{4 \left(x^{5}+x \right)^{\frac{3}{4}} \left(x^{8}-7 x^{7}-14 x^{6}+2 x^{4}-7 x^{3}+1\right)}{7 x^{6} \left(x^{4}+1\right)}$&$45$\\ meijerg&$\frac{4 \hypergeom \left(\left[-\frac{21}{16}, \frac{5}{4}\right], \left[-\frac{5}{16}\right], -x^{4}\right)}{7 x^{\frac{21}{4}}}+\frac{4 \hypergeom \left(\left[-\frac{5}{16}, \frac{5}{4}\right], \left[\frac{11}{16}\right], -x^{4}\right)}{x^{\frac{5}{4}}}-\frac{4 \hypergeom \left(\left[-\frac{9}{16}, \frac{5}{4}\right], \left[\frac{7}{16}\right], -x^{4}\right)}{x^{\frac{9}{4}}}-\frac{4 \hypergeom \left(\left[\frac{11}{16}, \frac{5}{4}\right], \left[\frac{27}{16}\right], -x^{4}\right) x^{\frac{11}{4}}}{11}+\frac{24 \hypergeom \left(\left[\frac{7}{16}, \frac{5}{4}\right], \left[\frac{23}{16}\right], -x^{4}\right) x^{\frac{7}{4}}}{7}-8 \hypergeom \left(\left[\frac{3}{16}, \frac{5}{4}\right], \left[\frac{19}{16}\right], -x^{4}\right) x^{\frac{3}{4}}+\frac{4 \hypergeom \left(\left[\frac{5}{4}, \frac{27}{16}\right], \left[\frac{43}{16}\right], -x^{4}\right) x^{\frac{27}{4}}}{27}-\frac{12 \hypergeom \left(\left[\frac{5}{4}, \frac{23}{16}\right], \left[\frac{39}{16}\right], -x^{4}\right) x^{\frac{23}{4}}}{23}+\frac{8 \hypergeom \left(\left[\frac{19}{16}, \frac{5}{4}\right], \left[\frac{35}{16}\right], -x^{4}\right) x^{\frac{19}{4}}}{19}$&$146$\\ \hline \end{longtable}"," ",0,"4/7*(x^8-7*x^7-14*x^6+2*x^4-7*x^3+1)/(x^5+x)^(1/4)/x^5","A"
613,1,40,40,0.211000," ","int(x^20/(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{x^{3} \left(8 x^{12}+10 x^{6}+15\right) \sqrt{x^{6}-1}}{144}+\frac{5 \ln \left(x^{3}+\sqrt{x^{6}-1}\right)}{48}$&$40$\\ risch&$\frac{x^{3} \left(8 x^{12}+10 x^{6}+15\right) \sqrt{x^{6}-1}}{144}+\frac{5 \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \arcsin \left(x^{3}\right)}{48 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}$&$50$\\ meijerg&$\frac{i \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(\frac{i \sqrt{\pi}\, x^{3} \left(56 x^{12}+70 x^{6}+105\right) \sqrt{-x^{6}+1}}{168}-\frac{5 i \sqrt{\pi}\, \arcsin \left(x^{3}\right)}{8}\right)}{6 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$66$\\ \hline \end{longtable}"," ",0,"1/144*x^3*(8*x^12+10*x^6+15)*(x^6-1)^(1/2)+5/48*ln(x^3+(x^6-1)^(1/2))","A"
614,1,40,40,0.205000," ","int(x^14*(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{x^{3} \left(8 x^{12}-2 x^{6}-3\right) \sqrt{x^{6}-1}}{144}-\frac{\ln \left(x^{3}+\sqrt{x^{6}-1}\right)}{48}$&$40$\\ risch&$\frac{x^{3} \left(8 x^{12}-2 x^{6}-3\right) \sqrt{x^{6}-1}}{144}-\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \arcsin \left(x^{3}\right)}{48 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}$&$50$\\ meijerg&$\frac{i \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(\frac{i \sqrt{\pi}\, x^{3} \left(-40 x^{12}+10 x^{6}+15\right) \sqrt{-x^{6}+1}}{60}-\frac{i \sqrt{\pi}\, \arcsin \left(x^{3}\right)}{4}\right)}{12 \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$66$\\ \hline \end{longtable}"," ",0,"1/144*x^3*(8*x^12-2*x^6-3)*(x^6-1)^(1/2)-1/48*ln(x^3+(x^6-1)^(1/2))","A"
615,1,32,40,0.176000," ","int(x^20/(x^6+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x^{3} \left(8 x^{12}-10 x^{6}+15\right) \sqrt{x^{6}+1}}{144}-\frac{5 \arcsinh \left(x^{3}\right)}{48}$&$32$\\ trager&$\frac{x^{3} \left(8 x^{12}-10 x^{6}+15\right) \sqrt{x^{6}+1}}{144}-\frac{5 \ln \left(x^{3}+\sqrt{x^{6}+1}\right)}{48}$&$40$\\ meijerg&$\frac{\frac{\sqrt{\pi}\, x^{3} \left(56 x^{12}-70 x^{6}+105\right) \sqrt{x^{6}+1}}{168}-\frac{5 \sqrt{\pi}\, \arcsinh \left(x^{3}\right)}{8}}{6 \sqrt{\pi}}$&$43$\\ \hline \end{longtable}"," ",0,"1/144*x^3*(8*x^12-10*x^6+15)*(x^6+1)^(1/2)-5/48*arcsinh(x^3)","A"
616,0,0,36,0.018000," ","int((-4*x^6+x)/(x^6+x)^(1/2)/(x^10+2*x^5-a*x^2+1),x)","\[\int \frac{-4 x^{6}+x}{\sqrt{x^{6}+x}\, \left(x^{10}+2 x^{5}-a \,x^{2}+1\right)}\, dx\]"," ",0,"int((-4*x^6+x)/(x^6+x)^(1/2)/(x^10+2*x^5-a*x^2+1),x)","F"
617,0,0,36,0.018000," ","int((4*x^6-x)/(x^6+x)^(1/2)/(a*x^10+2*a*x^5-x^2+a),x)","\[\int \frac{4 x^{6}-x}{\sqrt{x^{6}+x}\, \left(a \,x^{10}+2 a \,x^{5}-x^{2}+a \right)}\, dx\]"," ",0,"int((4*x^6-x)/(x^6+x)^(1/2)/(a*x^10+2*a*x^5-x^2+a),x)","F"
618,0,0,36,0.021000," ","int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(1/2),x)","\[\int \frac{\sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\sqrt{x^{2}+1}}\, dx\]"," ",0,"int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(1/2),x)","F"
619,0,0,45,0.019000," ","int((2*a*x-3*b)/(a*x^2-b*x)^(1/4)/(x^3-a*x+b),x)","\[\int \frac{2 a x -3 b}{\left(a \,x^{2}-b x \right)^{\frac{1}{4}} \left(x^{3}-a x +b \right)}\, dx\]"," ",0,"int((2*a*x-3*b)/(a*x^2-b*x)^(1/4)/(x^3-a*x+b),x)","F"
620,1,128,41,0.642000," ","int((x^3-4)*(x^3-x^2+2)^(1/2)/(x^3+2)/(x^3+x^2+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{2}-4 x \sqrt{x^{3}-x^{2}+2}+2 \RootOf \left(\textit{\_Z}^{2}+2\right)}{x^{3}+x^{2}+2}\right)+\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 x \sqrt{x^{3}-x^{2}+2}+2 \RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{3}+2}\right)$&$128$\\ default&$\frac{\left(4-2 i\right) \sqrt{\left(\frac{2}{5}+\frac{i}{5}\right) \left(1+x \right)}\, \sqrt{\left(-\frac{2}{5}+\frac{i}{5}\right) \left(x -1-i\right)}\, \sqrt{\left(-\frac{2}{5}-\frac{i}{5}\right) \left(x -1+i\right)}\, \EllipticF \left(\sqrt{\left(\frac{2}{5}+\frac{i}{5}\right) \left(1+x \right)}, \frac{2 \sqrt{5}}{5}-\frac{i \sqrt{5}}{5}\right)}{\sqrt{x^{3}-x^{2}+2}}+\left(-4+2 i\right) \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+2\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +1\right) \sqrt{\left(\frac{2}{5}+\frac{i}{5}\right) \left(1+x \right)}\, \sqrt{\left(-\frac{2}{5}+\frac{i}{5}\right) \left(x -1-i\right)}\, \sqrt{\left(-\frac{2}{5}-\frac{i}{5}\right) \left(x -1+i\right)}\, \EllipticPi \left(\sqrt{\left(\frac{2}{5}+\frac{i}{5}\right) \left(1+x \right)}, i \underline{\hspace{1.25 ex}}\alpha^{2}-2 \underline{\hspace{1.25 ex}}\alpha^{2}-i \underline{\hspace{1.25 ex}}\alpha  +2 \underline{\hspace{1.25 ex}}\alpha  +i-2, \frac{2 \sqrt{5}}{5}-\frac{i \sqrt{5}}{5}\right)}{\sqrt{x^{3}-x^{2}+2}}\right)+\left(4-2 i\right) \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+\textit{\_Z}^{2}+2\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{\left(\frac{2}{5}+\frac{i}{5}\right) \left(1+x \right)}\, \sqrt{\left(-\frac{2}{5}+\frac{i}{5}\right) \left(x -1-i\right)}\, \sqrt{\left(-\frac{2}{5}-\frac{i}{5}\right) \left(x -1+i\right)}\, \EllipticPi \left(\sqrt{\left(\frac{2}{5}+\frac{i}{5}\right) \left(1+x \right)}, \frac{1}{2} i \underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha^{2}, \frac{2 \sqrt{5}}{5}-\frac{i \sqrt{5}}{5}\right)}{\sqrt{x^{3}-x^{2}+2}}\right)$&$278$\\ elliptic&$\frac{4 \sqrt{\frac{2}{5}+\frac{1}{5} i+\frac{2}{5} x +\frac{1}{5} i x}\, \sqrt{-\frac{2}{5} x +\frac{1}{5} i x +\frac{3}{5}+\frac{1}{5} i}\, \sqrt{-\frac{2}{5} x -\frac{1}{5} i x +\frac{3}{5}-\frac{1}{5} i}\, \EllipticF \left(\sqrt{\left(\frac{2}{5}+\frac{i}{5}\right) \left(1+x \right)}, \frac{2 \sqrt{5}}{5}-\frac{i \sqrt{5}}{5}\right)}{\sqrt{x^{3}-x^{2}+2}}-\frac{2 i \sqrt{\frac{2}{5}+\frac{1}{5} i+\frac{2}{5} x +\frac{1}{5} i x}\, \sqrt{-\frac{2}{5} x +\frac{1}{5} i x +\frac{3}{5}+\frac{1}{5} i}\, \sqrt{-\frac{2}{5} x -\frac{1}{5} i x +\frac{3}{5}-\frac{1}{5} i}\, \EllipticF \left(\sqrt{\left(\frac{2}{5}+\frac{i}{5}\right) \left(1+x \right)}, \frac{2 \sqrt{5}}{5}-\frac{i \sqrt{5}}{5}\right)}{\sqrt{x^{3}-x^{2}+2}}+\frac{4 \sqrt{\frac{2}{5}+\frac{1}{5} i+\frac{2}{5} x +\frac{1}{5} i x}\, \sqrt{-\frac{2}{5} x +\frac{1}{5} i x +\frac{3}{5}+\frac{1}{5} i}\, \sqrt{-\frac{2}{5} x -\frac{1}{5} i x +\frac{3}{5}-\frac{1}{5} i}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+2\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha^{3} \EllipticPi \left(\sqrt{\left(\frac{2}{5}+\frac{i}{5}\right) \left(1+x \right)}, i \underline{\hspace{1.25 ex}}\alpha^{2}-2 \underline{\hspace{1.25 ex}}\alpha^{2}-i \underline{\hspace{1.25 ex}}\alpha  +2 \underline{\hspace{1.25 ex}}\alpha  +i-2, \frac{2 \sqrt{5}}{5}-\frac{i \sqrt{5}}{5}\right)\right)}{\sqrt{x^{3}-x^{2}+2}}-\frac{2 i \sqrt{\frac{2}{5}+\frac{1}{5} i+\frac{2}{5} x +\frac{1}{5} i x}\, \sqrt{-\frac{2}{5} x +\frac{1}{5} i x +\frac{3}{5}+\frac{1}{5} i}\, \sqrt{-\frac{2}{5} x -\frac{1}{5} i x +\frac{3}{5}-\frac{1}{5} i}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+2\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha^{3} \EllipticPi \left(\sqrt{\left(\frac{2}{5}+\frac{i}{5}\right) \left(1+x \right)}, i \underline{\hspace{1.25 ex}}\alpha^{2}-2 \underline{\hspace{1.25 ex}}\alpha^{2}-i \underline{\hspace{1.25 ex}}\alpha  +2 \underline{\hspace{1.25 ex}}\alpha  +i-2, \frac{2 \sqrt{5}}{5}-\frac{i \sqrt{5}}{5}\right)\right)}{\sqrt{x^{3}-x^{2}+2}}-\frac{4 \sqrt{\frac{2}{5}+\frac{1}{5} i+\frac{2}{5} x +\frac{1}{5} i x}\, \sqrt{-\frac{2}{5} x +\frac{1}{5} i x +\frac{3}{5}+\frac{1}{5} i}\, \sqrt{-\frac{2}{5} x -\frac{1}{5} i x +\frac{3}{5}-\frac{1}{5} i}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+2\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha^{2} \EllipticPi \left(\sqrt{\left(\frac{2}{5}+\frac{i}{5}\right) \left(1+x \right)}, i \underline{\hspace{1.25 ex}}\alpha^{2}-2 \underline{\hspace{1.25 ex}}\alpha^{2}-i \underline{\hspace{1.25 ex}}\alpha  +2 \underline{\hspace{1.25 ex}}\alpha  +i-2, \frac{2 \sqrt{5}}{5}-\frac{i \sqrt{5}}{5}\right)\right)}{\sqrt{x^{3}-x^{2}+2}}+\frac{2 i \sqrt{\frac{2}{5}+\frac{1}{5} i+\frac{2}{5} x +\frac{1}{5} i x}\, \sqrt{-\frac{2}{5} x +\frac{1}{5} i x +\frac{3}{5}+\frac{1}{5} i}\, \sqrt{-\frac{2}{5} x -\frac{1}{5} i x +\frac{3}{5}-\frac{1}{5} i}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+2\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha^{2} \EllipticPi \left(\sqrt{\left(\frac{2}{5}+\frac{i}{5}\right) \left(1+x \right)}, i \underline{\hspace{1.25 ex}}\alpha^{2}-2 \underline{\hspace{1.25 ex}}\alpha^{2}-i \underline{\hspace{1.25 ex}}\alpha  +2 \underline{\hspace{1.25 ex}}\alpha  +i-2, \frac{2 \sqrt{5}}{5}-\frac{i \sqrt{5}}{5}\right)\right)}{\sqrt{x^{3}-x^{2}+2}}+\frac{4 \sqrt{\frac{2}{5}+\frac{1}{5} i+\frac{2}{5} x +\frac{1}{5} i x}\, \sqrt{-\frac{2}{5} x +\frac{1}{5} i x +\frac{3}{5}+\frac{1}{5} i}\, \sqrt{-\frac{2}{5} x -\frac{1}{5} i x +\frac{3}{5}-\frac{1}{5} i}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+2\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \EllipticPi \left(\sqrt{\left(\frac{2}{5}+\frac{i}{5}\right) \left(1+x \right)}, i \underline{\hspace{1.25 ex}}\alpha^{2}-2 \underline{\hspace{1.25 ex}}\alpha^{2}-i \underline{\hspace{1.25 ex}}\alpha  +2 \underline{\hspace{1.25 ex}}\alpha  +i-2, \frac{2 \sqrt{5}}{5}-\frac{i \sqrt{5}}{5}\right)\right)}{\sqrt{x^{3}-x^{2}+2}}-\frac{2 i \sqrt{\frac{2}{5}+\frac{1}{5} i+\frac{2}{5} x +\frac{1}{5} i x}\, \sqrt{-\frac{2}{5} x +\frac{1}{5} i x +\frac{3}{5}+\frac{1}{5} i}\, \sqrt{-\frac{2}{5} x -\frac{1}{5} i x +\frac{3}{5}-\frac{1}{5} i}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+2\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \EllipticPi \left(\sqrt{\left(\frac{2}{5}+\frac{i}{5}\right) \left(1+x \right)}, i \underline{\hspace{1.25 ex}}\alpha^{2}-2 \underline{\hspace{1.25 ex}}\alpha^{2}-i \underline{\hspace{1.25 ex}}\alpha  +2 \underline{\hspace{1.25 ex}}\alpha  +i-2, \frac{2 \sqrt{5}}{5}-\frac{i \sqrt{5}}{5}\right)\right)}{\sqrt{x^{3}-x^{2}+2}}-\frac{4 \sqrt{\frac{2}{5}+\frac{1}{5} i+\frac{2}{5} x +\frac{1}{5} i x}\, \sqrt{-\frac{2}{5} x +\frac{1}{5} i x +\frac{3}{5}+\frac{1}{5} i}\, \sqrt{-\frac{2}{5} x -\frac{1}{5} i x +\frac{3}{5}-\frac{1}{5} i}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+\textit{\_Z}^{2}+2\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha^{3} \EllipticPi \left(\sqrt{\left(\frac{2}{5}+\frac{i}{5}\right) \left(1+x \right)}, \frac{1}{2} i \underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha^{2}, \frac{2 \sqrt{5}}{5}-\frac{i \sqrt{5}}{5}\right)\right)}{\sqrt{x^{3}-x^{2}+2}}+\frac{2 i \sqrt{\frac{2}{5}+\frac{1}{5} i+\frac{2}{5} x +\frac{1}{5} i x}\, \sqrt{-\frac{2}{5} x +\frac{1}{5} i x +\frac{3}{5}+\frac{1}{5} i}\, \sqrt{-\frac{2}{5} x -\frac{1}{5} i x +\frac{3}{5}-\frac{1}{5} i}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+\textit{\_Z}^{2}+2\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha^{3} \EllipticPi \left(\sqrt{\left(\frac{2}{5}+\frac{i}{5}\right) \left(1+x \right)}, \frac{1}{2} i \underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha^{2}, \frac{2 \sqrt{5}}{5}-\frac{i \sqrt{5}}{5}\right)\right)}{\sqrt{x^{3}-x^{2}+2}}$&$1019$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2+2)*ln((RootOf(_Z^2+2)*x^3-3*RootOf(_Z^2+2)*x^2-4*x*(x^3-x^2+2)^(1/2)+2*RootOf(_Z^2+2))/(x^3+x^2+2))+RootOf(_Z^2+1)*ln(-(RootOf(_Z^2+1)*x^3-2*RootOf(_Z^2+1)*x^2+2*x*(x^3-x^2+2)^(1/2)+2*RootOf(_Z^2+1))/(x^3+2))","C"
621,1,33,37,1.891000," ","int(x^2*(x^4-1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{1}{4}, \frac{3}{4}\right], \left[\frac{7}{4}\right], x^{4}\right) x^{3}}{3 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}}}$&$33$\\ risch&$\frac{x^{3} \left(x^{4}-1\right)^{\frac{1}{4}}}{4}-\frac{\left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[\frac{3}{4}, \frac{3}{4}\right], \left[\frac{7}{4}\right], x^{4}\right) x^{3}}{12 \mathrm{signum}\left(x^{4}-1\right)^{\frac{3}{4}}}$&$46$\\ trager&$\frac{x^{3} \left(x^{4}-1\right)^{\frac{1}{4}}}{4}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{4}-1\right)^{\frac{3}{4}} x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{4}-1\right)^{\frac{1}{4}} x^{3}+2 x^{2} \sqrt{x^{4}-1}-2 x^{4}+1\right)}{16}-\frac{\ln \left(2 \left(x^{4}-1\right)^{\frac{3}{4}} x +2 x^{2} \sqrt{x^{4}-1}+2 x^{3} \left(x^{4}-1\right)^{\frac{1}{4}}+2 x^{4}-1\right)}{16}$&$120$\\ \hline \end{longtable}"," ",0,"1/3/(-signum(x^4-1))^(1/4)*signum(x^4-1)^(1/4)*hypergeom([-1/4,3/4],[7/4],x^4)*x^3","C"
622,1,17,37,1.785000," ","int(x^2*(x^4+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\hypergeom \left(\left[-\frac{1}{4}, \frac{3}{4}\right], \left[\frac{7}{4}\right], -x^{4}\right) x^{3}}{3}$&$17$\\ risch&$\frac{x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}}{4}+\frac{\hypergeom \left(\left[\frac{3}{4}, \frac{3}{4}\right], \left[\frac{7}{4}\right], -x^{4}\right) x^{3}}{12}$&$30$\\ trager&$\frac{x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}}{4}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}\, x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \left(x^{4}+1\right)^{\frac{3}{4}} x -2 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{16}-\frac{\ln \left(2 \left(x^{4}+1\right)^{\frac{3}{4}} x -2 x^{2} \sqrt{x^{4}+1}+2 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}-2 x^{4}-1\right)}{16}$&$127$\\ \hline \end{longtable}"," ",0,"1/3*hypergeom([-1/4,3/4],[7/4],-x^4)*x^3","C"
623,1,48,41,0.292000," ","int((a*x^3-b)*(x^4+x)^(1/2)/x^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(a \,x^{3}+2 b \right) \sqrt{x^{4}+x}}{3 x^{2}}+\frac{\left(a -2 b \right) \ln \left(-2 x^{3}-2 x \sqrt{x^{4}+x}-1\right)}{6}$&$48$\\ meijerg&$-\frac{a \left(-2 \sqrt{\pi}\, x^{\frac{3}{2}} \sqrt{x^{3}+1}-2 \sqrt{\pi}\, \arcsinh \left(x^{\frac{3}{2}}\right)\right)}{6 \sqrt{\pi}}+\frac{b \left(\frac{4 \sqrt{\pi}\, \sqrt{x^{3}+1}}{x^{\frac{3}{2}}}-4 \sqrt{\pi}\, \arcsinh \left(x^{\frac{3}{2}}\right)\right)}{6 \sqrt{\pi}}$&$64$\\ elliptic&$\frac{2 b \sqrt{x^{4}+x}}{3 x^{2}}+\frac{a x \sqrt{x^{4}+x}}{3}-\frac{2 \left(\frac{a}{2}-b \right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$322$\\ risch&$\frac{\left(x^{3}+1\right) \left(a \,x^{3}+2 b \right)}{3 x \sqrt{x \left(x^{3}+1\right)}}-\frac{2 \left(\frac{a}{2}-b \right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$326$\\ default&$a \left(\frac{x \sqrt{x^{4}+x}}{3}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-b \left(-\frac{2 \sqrt{x^{4}+x}}{3 x^{2}}+\frac{2 \sqrt{-\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \left(\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \EllipticF \left(\sqrt{-\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \sqrt{-\frac{i \sqrt{3}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticPi \left(\sqrt{-\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, -\frac{1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{-\frac{i \sqrt{3}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)$&$606$\\ \hline \end{longtable}"," ",0,"1/3*(a*x^3+2*b)*(x^4+x)^(1/2)/x^2+1/6*(a-2*b)*ln(-2*x^3-2*x*(x^4+x)^(1/2)-1)","A"
624,1,3669,11,68.381000," ","int(1/(x^4-2)/(x^4+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$3669$\\ \hline \end{longtable}"," ",0,"-8388608*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*ln(-(5360119185408*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^11*x^3-5360119185408*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^11*x-21474836480*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^7*x^3+187695104*RootOf(8388608*_Z^8-8192*_Z^4+1)^5*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*(x^4+x^2)^(1/2)*x-771751936*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^7*x-56492032*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-8192*_Z^4+1)^6*x^2+14163968*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^3*x^3+516096*(x^4+x^2)^(3/4)*RootOf(8388608*_Z^8-8192*_Z^4+1)^4-156160*RootOf(8388608*_Z^8-8192*_Z^4+1)*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*(x^4+x^2)^(1/2)*x+4358144*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^3*x+47104*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-8192*_Z^4+1)^2*x^2-431*(x^4+x^2)^(3/4))/(4096*x^2*RootOf(8388608*_Z^8-8192*_Z^4+1)^4-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^4-3*x^2+4)/x)*RootOf(8388608*_Z^8-8192*_Z^4+1)^7*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)+4096*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*ln(-(5360119185408*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^11*x^3-5360119185408*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^11*x-21474836480*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^7*x^3+187695104*RootOf(8388608*_Z^8-8192*_Z^4+1)^5*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*(x^4+x^2)^(1/2)*x-771751936*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^7*x-56492032*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-8192*_Z^4+1)^6*x^2+14163968*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^3*x^3+516096*(x^4+x^2)^(3/4)*RootOf(8388608*_Z^8-8192*_Z^4+1)^4-156160*RootOf(8388608*_Z^8-8192*_Z^4+1)*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*(x^4+x^2)^(1/2)*x+4358144*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^3*x+47104*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-8192*_Z^4+1)^2*x^2-431*(x^4+x^2)^(3/4))/(4096*x^2*RootOf(8388608*_Z^8-8192*_Z^4+1)^4-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^4-3*x^2+4)/x)*RootOf(8388608*_Z^8-8192*_Z^4+1)^3*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)-RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*ln(-(-1845493760*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^8*x^3+187695104*(x^4+x^2)^(1/2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^6*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*x+1845493760*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^8*x+23461888*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-8192*_Z^4+1)^6*x^2-3792896*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^4*x^3-516096*(x^4+x^2)^(3/4)*RootOf(8388608*_Z^8-8192*_Z^4+1)^4-27136*(x^4+x^2)^(1/2)*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^2*x-3866624*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^4*x-3392*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-8192*_Z^4+1)^2*x^2+576*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*x^3+73*(x^4+x^2)^(3/4)+512*RootOf(4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6-3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*x)/(4096*x^2*RootOf(8388608*_Z^8-8192*_Z^4+1)^4-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^4-x^2)/x)-RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*ln((1845493760*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^8*x^3+187695104*(x^4+x^2)^(1/2)*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^6*x-1845493760*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^8*x+23461888*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-8192*_Z^4+1)^6*x^2+3792896*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^4*x^3+516096*(x^4+x^2)^(3/4)*RootOf(8388608*_Z^8-8192*_Z^4+1)^4-27136*(x^4+x^2)^(1/2)*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^2*x+3866624*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^4*x-3392*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-8192*_Z^4+1)^2*x^2-576*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*x^3-73*(x^4+x^2)^(3/4)-512*RootOf(-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^6+3*RootOf(8388608*_Z^8-8192*_Z^4+1)^2+_Z^2)*x)/(4096*x^2*RootOf(8388608*_Z^8-8192*_Z^4+1)^4-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^4-x^2)/x)+RootOf(8388608*_Z^8-8192*_Z^4+1)*ln(-(1845493760*RootOf(8388608*_Z^8-8192*_Z^4+1)^9*x^3-451936256*(x^4+x^2)^(1/2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^7*x-1845493760*RootOf(8388608*_Z^8-8192*_Z^4+1)^9*x+56492032*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-8192*_Z^4+1)^6*x^2-7397376*RootOf(8388608*_Z^8-8192*_Z^4+1)^5*x^3+516096*(x^4+x^2)^(3/4)*RootOf(8388608*_Z^8-8192*_Z^4+1)^4+376832*(x^4+x^2)^(1/2)*RootOf(8388608*_Z^8-8192*_Z^4+1)^3*x-262144*RootOf(8388608*_Z^8-8192*_Z^4+1)^5*x-47104*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-8192*_Z^4+1)^2*x^2+4888*RootOf(8388608*_Z^8-8192*_Z^4+1)*x^3-431*(x^4+x^2)^(3/4)+1504*RootOf(8388608*_Z^8-8192*_Z^4+1)*x)/(4096*x^2*RootOf(8388608*_Z^8-8192*_Z^4+1)^4-4096*RootOf(8388608*_Z^8-8192*_Z^4+1)^4-3*x^2+4)/x)","B"
625,0,0,45,0.022000," ","int((a*x^3-4*b)/(a*x^3-b)^(1/4)/(-a*x^3+x^4+b),x)","\[\int \frac{a \,x^{3}-4 b}{\left(a \,x^{3}-b \right)^{\frac{1}{4}} \left(-a \,x^{3}+x^{4}+b \right)}\, dx\]"," ",0,"int((a*x^3-4*b)/(a*x^3-b)^(1/4)/(-a*x^3+x^4+b),x)","F"
626,0,0,41,0.016000," ","int((3*x^5-x)/(x^4+1)/(a*x^4+a-x)/(x^5+x)^(1/2),x)","\[\int \frac{3 x^{5}-x}{\left(x^{4}+1\right) \left(a \,x^{4}+a -x \right) \sqrt{x^{5}+x}}\, dx\]"," ",0,"int((3*x^5-x)/(x^4+1)/(a*x^4+a-x)/(x^5+x)^(1/2),x)","F"
627,1,42,41,0.464000," ","int((x^3-1)*(x^6-1)^(1/2)/x^10,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{2 x^{12}+3 x^{9}-4 x^{6}-3 x^{3}+2}{18 x^{9} \sqrt{x^{6}-1}}-\frac{\arcsin \left(\frac{1}{x^{3}}\right)}{6}$&$42$\\ trager&$-\frac{\left(2 x^{6}+3 x^{3}-2\right) \sqrt{x^{6}-1}}{18 x^{9}}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)-\sqrt{x^{6}-1}}{x^{3}}\right)}{6}$&$56$\\ meijerg&$\frac{\sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(-x^{6}+1\right)^{\frac{3}{2}}}{9 \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, x^{9}}+\frac{\sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(-\frac{2 \sqrt{\pi}}{x^{6}}-\left(-2 \ln \left(2\right)-1+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}+\frac{\sqrt{\pi}\, \left(-4 x^{6}+8\right)}{4 x^{6}}-\frac{2 \sqrt{\pi}\, \sqrt{-x^{6}+1}}{x^{6}}+2 \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right) \sqrt{\pi}\right)}{12 \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \sqrt{\pi}}$&$136$\\ \hline \end{longtable}"," ",0,"-1/18*(2*x^12+3*x^9-4*x^6-3*x^3+2)/x^9/(x^6-1)^(1/2)-1/6*arcsin(1/x^3)","A"
628,0,0,11,180.000000," ","int((x^6+1)/(x^5-x^3)^(1/4)/(-x^6+x^3+1),x)","\[\int \frac{x^{6}+1}{\left(x^{5}-x^{3}\right)^{\frac{1}{4}} \left(-x^{6}+x^{3}+1\right)}\, dx\]"," ",0,"int((x^6+1)/(x^5-x^3)^(1/4)/(-x^6+x^3+1),x)","F"
629,-1,0,11,180.000000," ","int((x^6+1)/(x^5-x^3)^(1/4)/(-x^6+x^3+1),x,method=_RETURNVERBOSE)","\text{hanged}"," ",0,"int((x^6+1)/(x^5-x^3)^(1/4)/(-x^6+x^3+1),x,method=_RETURNVERBOSE)","F"
630,0,0,45,0.030000," ","int(x*(5*a*x+6*b)/(a*x^3+b*x^2)^(1/4)/(x^6-a*x-b),x)","\[\int \frac{x \left(5 a x +6 b \right)}{\left(a \,x^{3}+b \,x^{2}\right)^{\frac{1}{4}} \left(x^{6}-a x -b \right)}\, dx\]"," ",0,"int(x*(5*a*x+6*b)/(a*x^3+b*x^2)^(1/4)/(x^6-a*x-b),x)","F"
631,0,0,37,0.031000," ","int((x^5-1)^(1/2)*(3*x^5+2)/(x^10-a*x^4-2*x^5+1),x)","\[\int \frac{\sqrt{x^{5}-1}\, \left(3 x^{5}+2\right)}{x^{10}-a \,x^{4}-2 x^{5}+1}\, dx\]"," ",0,"int((x^5-1)^(1/2)*(3*x^5+2)/(x^10-a*x^4-2*x^5+1),x)","F"
632,0,0,37,0.028000," ","int((x^5-1)^(1/2)*(3*x^5+2)/(a*x^10-2*a*x^5-x^4+a),x)","\[\int \frac{\sqrt{x^{5}-1}\, \left(3 x^{5}+2\right)}{a \,x^{10}-2 a \,x^{5}-x^{4}+a}\, dx\]"," ",0,"int((x^5-1)^(1/2)*(3*x^5+2)/(a*x^10-2*a*x^5-x^4+a),x)","F"
633,0,0,37,0.013000," ","int((x^5+1)^(1/2)*(3*x^5-2)/(a*x^10+2*a*x^5-x^4+a),x)","\[\int \frac{\sqrt{x^{5}+1}\, \left(3 x^{5}-2\right)}{a \,x^{10}+2 a \,x^{5}-x^{4}+a}\, dx\]"," ",0,"int((x^5+1)^(1/2)*(3*x^5-2)/(a*x^10+2*a*x^5-x^4+a),x)","F"
634,1,20,38,0.097000," ","int(1/(1+(x^2+1)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\sqrt{2}\, x \hypergeom \left(\left[\frac{1}{4}, \frac{1}{2}, \frac{3}{4}\right], \left[\frac{3}{2}, \frac{3}{2}\right], -x^{2}\right)}{2}$&$20$\\ \hline \end{longtable}"," ",0,"1/2*2^(1/2)*x*hypergeom([1/4,1/2,3/4],[3/2,3/2],-x^2)","C"
635,1,48,42,0.611000," ","int(x^6*(x^4-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{x \left(8 x^{6}-2 x^{3}-3\right) \sqrt{x^{4}-x}}{72}+\frac{\ln \left(2 x^{3}-2 x \sqrt{x^{4}-x}-1\right)}{48}$&$48$\\ meijerg&$\frac{i \sqrt{\mathrm{signum}\left(x^{3}-1\right)}\, \left(\frac{i \sqrt{\pi}\, x^{\frac{3}{2}} \left(-40 x^{6}+10 x^{3}+15\right) \sqrt{-x^{3}+1}}{60}-\frac{i \sqrt{\pi}\, \arcsin \left(x^{\frac{3}{2}}\right)}{4}\right)}{6 \sqrt{\pi}\, \sqrt{-\mathrm{signum}\left(x^{3}-1\right)}}$&$66$\\ risch&$\frac{x^{2} \left(8 x^{6}-2 x^{3}-3\right) \left(x^{3}-1\right)}{72 \sqrt{x \left(x^{3}-1\right)}}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{8 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$320$\\ default&$\frac{x^{7} \sqrt{x^{4}-x}}{9}-\frac{x^{4} \sqrt{x^{4}-x}}{36}-\frac{x \sqrt{x^{4}-x}}{24}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{8 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$329$\\ elliptic&$\frac{x^{7} \sqrt{x^{4}-x}}{9}-\frac{x^{4} \sqrt{x^{4}-x}}{36}-\frac{x \sqrt{x^{4}-x}}{24}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{8 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$329$\\ \hline \end{longtable}"," ",0,"1/72*x*(8*x^6-2*x^3-3)*(x^4-x)^(1/2)+1/48*ln(2*x^3-2*x*(x^4-x)^(1/2)-1)","A"
636,1,42,46,0.122000," ","int((x^2-1)*(x^4-x^3)^(1/4)/x^8,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{4 \left(x^{4}-x^{3}\right)^{\frac{1}{4}} \left(-1+x \right)^{2} \left(5248 x^{4}+11808 x^{3}+19188 x^{2}+27183 x +13923\right)}{348075 x^{7}}$&$42$\\ trager&$\frac{4 \left(x^{4}-x^{3}\right)^{\frac{1}{4}} \left(5248 x^{6}+1312 x^{5}+820 x^{4}+615 x^{3}-21255 x^{2}-663 x +13923\right)}{348075 x^{7}}$&$47$\\ risch&$\frac{4 \left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}} \left(5248 x^{7}-3936 x^{6}-492 x^{5}-205 x^{4}-21870 x^{3}+20592 x^{2}+14586 x -13923\right)}{348075 x^{7} \left(-1+x \right)}$&$55$\\ meijerg&$\frac{4 \mathrm{signum}\left(-1+x \right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{25}{4}, -\frac{1}{4}\right], \left[-\frac{21}{4}\right], x\right)}{25 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{4}} x^{\frac{25}{4}}}-\frac{4 \mathrm{signum}\left(-1+x \right)^{\frac{1}{4}} \left(-\frac{128}{195} x^{4}-\frac{32}{195} x^{3}-\frac{4}{39} x^{2}-\frac{1}{13} x +1\right) \left(1-x \right)^{\frac{1}{4}}}{17 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{4}} x^{\frac{17}{4}}}$&$74$\\ \hline \end{longtable}"," ",0,"4/348075*(x^4-x^3)^(1/4)*(-1+x)^2*(5248*x^4+11808*x^3+19188*x^2+27183*x+13923)/x^7","A"
637,1,55,38,0.523000," ","int((x^3-1)*(x^6-1)^(1/2)/x/(x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}-1}}{3}-\frac{2 \ln \left(x^{3}+\sqrt{x^{6}-1}\right)}{3}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)-\sqrt{x^{6}-1}}{x^{3}}\right)}{3}$&$55$\\ \hline \end{longtable}"," ",0,"1/3*(x^6-1)^(1/2)-2/3*ln(x^3+(x^6-1)^(1/2))-1/3*RootOf(_Z^2+1)*ln(-(RootOf(_Z^2+1)-(x^6-1)^(1/2))/x^3)","C"
638,1,52,38,0.561000," ","int((x^3+1)*(x^6-1)^(1/2)/x/(x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}-1}}{3}+\frac{2 \ln \left(x^{3}+\sqrt{x^{6}-1}\right)}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{3}$&$52$\\ \hline \end{longtable}"," ",0,"1/3*(x^6-1)^(1/2)+2/3*ln(x^3+(x^6-1)^(1/2))+1/3*RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)+(x^6-1)^(1/2))/x^3)","C"
639,0,0,11,0.019000," ","int((a*x^4+2*b)/(a*x^4+b)^(1/4)/(x^8-2*a*x^4-2*b),x)","\[\int \frac{a \,x^{4}+2 b}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(x^{8}-2 a \,x^{4}-2 b \right)}\, dx\]"," ",0,"int((a*x^4+2*b)/(a*x^4+b)^(1/4)/(x^8-2*a*x^4-2*b),x)","F"
640,0,0,11,0.000000," ","int((a*x^4+2*b)/(a*x^4+b)^(1/4)/(x^8-2*a*x^4-2*b),x)","\[\int \frac{a \,x^{4}+2 b}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(x^{8}-2 a \,x^{4}-2 b \right)}\, dx\]"," ",0,"int((a*x^4+2*b)/(a*x^4+b)^(1/4)/(x^8-2*a*x^4-2*b),x)","F"
641,0,0,11,180.000000," ","int((x^6-1)*(x^6+1)/(x^7-x^4+x)^(1/4)/(x^12+3*x^6+1),x)","\[\int \frac{\left(x^{6}-1\right) \left(x^{6}+1\right)}{\left(x^{7}-x^{4}+x \right)^{\frac{1}{4}} \left(x^{12}+3 x^{6}+1\right)}\, dx\]"," ",0,"int((x^6-1)*(x^6+1)/(x^7-x^4+x)^(1/4)/(x^12+3*x^6+1),x)","F"
642,1,55,36,0.028000," ","int((1+(x^2+1)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{-\frac{32 \sqrt{\pi}\, \sqrt{2}\, x^{3} \cosh \left(\frac{3 \arcsinh \left(x \right)}{2}\right)}{3}-\frac{8 \sqrt{\pi}\, \sqrt{2}\, \left(-\frac{4}{3} x^{4}-\frac{2}{3} x^{2}+\frac{2}{3}\right) \sinh \left(\frac{3 \arcsinh \left(x \right)}{2}\right)}{\sqrt{x^{2}+1}}}{8 \sqrt{\pi}}$&$55$\\ \hline \end{longtable}"," ",0,"-1/8/Pi^(1/2)*(-32/3*Pi^(1/2)*2^(1/2)*x^3*cosh(3/2*arcsinh(x))-8*Pi^(1/2)*2^(1/2)*(-4/3*x^4-2/3*x^2+2/3)*sinh(3/2*arcsinh(x))/(x^2+1)^(1/2))","C"
643,1,22,40,0.032000," ","int((1+(x^2+1)^(1/2))^(1/2)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{2}\, \hypergeom \left(\left[-\frac{1}{2}, -\frac{1}{4}, \frac{1}{4}\right], \left[\frac{1}{2}, \frac{1}{2}\right], -x^{2}\right)}{x}$&$22$\\ \hline \end{longtable}"," ",0,"-2^(1/2)/x*hypergeom([-1/2,-1/4,1/4],[1/2,1/2],-x^2)","C"
644,0,0,39,0.014000," ","int(1/x/(a*x^2+b)^(3/4),x)","\[\int \frac{1}{x \left(a \,x^{2}+b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x/(a*x^2+b)^(3/4),x)","F"
645,1,70,43,0.361000," ","int((-7+x)/(-11+5*x)/(x^4-3*x^3-21*x^2+83*x-60)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-6\right) \ln \left(-\frac{-29 \RootOf \left(\textit{\_Z}^{2}-6\right) x^{2}+106 \RootOf \left(\textit{\_Z}^{2}-6\right) x +36 \sqrt{x^{4}-3 x^{3}-21 x^{2}+83 x -60}-41 \RootOf \left(\textit{\_Z}^{2}-6\right)}{\left(-11+5 x \right)^{2}}\right)}{18}$&$70$\\ default&$-\frac{\sqrt{\frac{5+x}{-1+x}}\, \left(-1+x \right)^{2} \sqrt{\frac{-3+x}{-1+x}}\, \sqrt{6}\, \sqrt{\frac{x -4}{-1+x}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{5+x}{-1+x}}}{3}, \frac{\sqrt{3}}{2}\right)}{30 \sqrt{\left(5+x \right) \left(-1+x \right) \left(-3+x \right) \left(x -4\right)}}-\frac{2 \sqrt{\frac{5+x}{-1+x}}\, \left(-1+x \right)^{2} \sqrt{\frac{-3+x}{-1+x}}\, \sqrt{6}\, \sqrt{\frac{x -4}{-1+x}}\, \left(\EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{5+x}{-1+x}}}{3}, \frac{\sqrt{3}}{2}\right)-\frac{5 \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{5+x}{-1+x}}}{3}, \frac{1}{2}, \frac{\sqrt{3}}{2}\right)}{6}\right)}{15 \sqrt{\left(5+x \right) \left(-1+x \right) \left(-3+x \right) \left(x -4\right)}}$&$188$\\ elliptic&$-\frac{\sqrt{\frac{5+x}{-1+x}}\, \left(-1+x \right)^{2} \sqrt{\frac{-3+x}{-1+x}}\, \sqrt{6}\, \sqrt{\frac{x -4}{-1+x}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{5+x}{-1+x}}}{3}, \frac{\sqrt{3}}{2}\right)}{30 \sqrt{\left(5+x \right) \left(-1+x \right) \left(-3+x \right) \left(x -4\right)}}-\frac{2 \sqrt{\frac{5+x}{-1+x}}\, \left(-1+x \right)^{2} \sqrt{\frac{-3+x}{-1+x}}\, \sqrt{6}\, \sqrt{\frac{x -4}{-1+x}}\, \left(\EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{5+x}{-1+x}}}{3}, \frac{\sqrt{3}}{2}\right)-\frac{5 \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{5+x}{-1+x}}}{3}, \frac{1}{2}, \frac{\sqrt{3}}{2}\right)}{6}\right)}{15 \sqrt{\left(5+x \right) \left(-1+x \right) \left(-3+x \right) \left(x -4\right)}}$&$188$\\ \hline \end{longtable}"," ",0,"1/18*RootOf(_Z^2-6)*ln(-(-29*RootOf(_Z^2-6)*x^2+106*RootOf(_Z^2-6)*x+36*(x^4-3*x^3-21*x^2+83*x-60)^(1/2)-41*RootOf(_Z^2-6))/(-11+5*x)^2)","C"
646,1,83,38,0.857000," ","int((x^6-2)*(x^6-1)^(1/2)/x/(x^6+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}-1}}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) x^{6}+6 \sqrt{x^{6}-1}-4 \RootOf \left(\textit{\_Z}^{2}+3\right)}{x^{6}+2}\right)}{3}$&$83$\\ \hline \end{longtable}"," ",0,"1/3*(x^6-1)^(1/2)+1/3*RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)+(x^6-1)^(1/2))/x^3)+1/3*RootOf(_Z^2+3)*ln((RootOf(_Z^2+3)*x^6+6*(x^6-1)^(1/2)-4*RootOf(_Z^2+3))/(x^6+2))","C"
647,1,154,40,0.544000," ","int((x^6-x^2-1)^(1/2)*(2*x^6+1)/(x^6-1)/(2*x^6+x^2-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+6\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+6\right) x^{6}-5 \RootOf \left(\textit{\_Z}^{2}+6\right) x^{2}+12 \sqrt{x^{6}-x^{2}-1}\, x -2 \RootOf \left(\textit{\_Z}^{2}+6\right)}{2 x^{6}+x^{2}-2}\right)}{4}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-2 \sqrt{x^{6}-x^{2}-1}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right)}\right)}{2}$&$154$\\ \hline \end{longtable}"," ",0,"-1/4*RootOf(_Z^2+6)*ln(-(2*RootOf(_Z^2+6)*x^6-5*RootOf(_Z^2+6)*x^2+12*(x^6-x^2-1)^(1/2)*x-2*RootOf(_Z^2+6))/(2*x^6+x^2-2))-1/2*RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)*x^6-2*RootOf(_Z^2+1)*x^2-2*(x^6-x^2-1)^(1/2)*x-RootOf(_Z^2+1))/(-1+x)/(1+x)/(x^2+x+1)/(x^2-x+1))","C"
648,0,0,47,0.019000," ","int(x*(5*a*x^3-8*b)/(a*x^3-b)^(1/4)/(x^8-a*x^3+b),x)","\[\int \frac{x \left(5 a \,x^{3}-8 b \right)}{\left(a \,x^{3}-b \right)^{\frac{1}{4}} \left(x^{8}-a \,x^{3}+b \right)}\, dx\]"," ",0,"int(x*(5*a*x^3-8*b)/(a*x^3-b)^(1/4)/(x^8-a*x^3+b),x)","F"
649,1,1012,47,13.177000," ","int((-9*x^3-x^2+16*x+2)/((1+x)/(x^2-2))^(1/4)/(x^2-2)/(x^9-x^8-5*x^7+5*x^6+9*x^5-9*x^4-7*x^3+7*x^2+2*x-3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(-\frac{-1+2 x +x^{9}-5 x^{7}+9 x^{5}+5 x^{6}+7 x^{2}-7 x^{3}-x^{8}-9 x^{4}+4 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}}-4 \sqrt{-\frac{-1-x}{x^{2}-2}}+4 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{3}{4}}+2 \sqrt{-\frac{-1-x}{x^{2}-2}}\, x^{5}-2 \sqrt{-\frac{-1-x}{x^{2}-2}}\, x^{4}-6 \sqrt{-\frac{-1-x}{x^{2}-2}}\, x^{3}+6 \sqrt{-\frac{-1-x}{x^{2}-2}}\, x^{2}+4 \sqrt{-\frac{-1-x}{x^{2}-2}}\, x +2 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x^{7}-2 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x^{6}+2 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{3}{4}} x^{3}-8 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x^{5}-2 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{3}{4}} x^{2}+8 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x^{4}-4 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{3}{4}} x +10 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x^{3}-10 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x^{2}-4 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x}{x^{9}-x^{8}-5 x^{7}+5 x^{6}+9 x^{5}-9 x^{4}-7 x^{3}+7 x^{2}+2 x -3}\right)+\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)+4 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}}-4 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{3}{4}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x -\RootOf \left(\textit{\_Z}^{2}+1\right) x^{9}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{8}+5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{7}-9 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{5}+9 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+7 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-4 \sqrt{-\frac{-1-x}{x^{2}-2}}\, \RootOf \left(\textit{\_Z}^{2}+1\right)-5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}-7 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-6 \sqrt{-\frac{-1-x}{x^{2}-2}}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+6 \sqrt{-\frac{-1-x}{x^{2}-2}}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+4 \sqrt{-\frac{-1-x}{x^{2}-2}}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x +2 \sqrt{-\frac{-1-x}{x^{2}-2}}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x^{5}-2 \sqrt{-\frac{-1-x}{x^{2}-2}}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x^{7}-2 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x^{6}-2 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{3}{4}} x^{3}-8 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x^{5}+2 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{3}{4}} x^{2}+8 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x^{4}+4 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{3}{4}} x +10 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x^{3}-10 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x^{2}-4 \left(-\frac{-1-x}{x^{2}-2}\right)^{\frac{1}{4}} x}{x^{9}-x^{8}-5 x^{7}+5 x^{6}+9 x^{5}-9 x^{4}-7 x^{3}+7 x^{2}+2 x -3}\right)$&$1012$\\ \hline \end{longtable}"," ",0,"ln(-(-1+2*x+x^9-5*x^7+9*x^5+5*x^6+7*x^2-7*x^3-x^8-9*x^4+4*(-(-1-x)/(x^2-2))^(1/4)-4*(-(-1-x)/(x^2-2))^(1/2)+4*(-(-1-x)/(x^2-2))^(3/4)+2*(-(-1-x)/(x^2-2))^(1/2)*x^5-2*(-(-1-x)/(x^2-2))^(1/2)*x^4-6*(-(-1-x)/(x^2-2))^(1/2)*x^3+6*(-(-1-x)/(x^2-2))^(1/2)*x^2+4*(-(-1-x)/(x^2-2))^(1/2)*x+2*(-(-1-x)/(x^2-2))^(1/4)*x^7-2*(-(-1-x)/(x^2-2))^(1/4)*x^6+2*(-(-1-x)/(x^2-2))^(3/4)*x^3-8*(-(-1-x)/(x^2-2))^(1/4)*x^5-2*(-(-1-x)/(x^2-2))^(3/4)*x^2+8*(-(-1-x)/(x^2-2))^(1/4)*x^4-4*(-(-1-x)/(x^2-2))^(3/4)*x+10*(-(-1-x)/(x^2-2))^(1/4)*x^3-10*(-(-1-x)/(x^2-2))^(1/4)*x^2-4*(-(-1-x)/(x^2-2))^(1/4)*x)/(x^9-x^8-5*x^7+5*x^6+9*x^5-9*x^4-7*x^3+7*x^2+2*x-3))+RootOf(_Z^2+1)*ln((-2*RootOf(_Z^2+1)*x-7*RootOf(_Z^2+1)*x^2-RootOf(_Z^2+1)*x^9+RootOf(_Z^2+1)*x^8+5*RootOf(_Z^2+1)*x^7-5*RootOf(_Z^2+1)*x^6-9*RootOf(_Z^2+1)*x^5+9*RootOf(_Z^2+1)*x^4+7*RootOf(_Z^2+1)*x^3-4*(-(-1-x)/(x^2-2))^(1/2)*RootOf(_Z^2+1)+RootOf(_Z^2+1)+4*(-(-1-x)/(x^2-2))^(1/4)-4*(-(-1-x)/(x^2-2))^(3/4)-6*(-(-1-x)/(x^2-2))^(1/2)*RootOf(_Z^2+1)*x^3+6*(-(-1-x)/(x^2-2))^(1/2)*RootOf(_Z^2+1)*x^2+4*(-(-1-x)/(x^2-2))^(1/2)*RootOf(_Z^2+1)*x+2*(-(-1-x)/(x^2-2))^(1/2)*RootOf(_Z^2+1)*x^5-2*(-(-1-x)/(x^2-2))^(1/2)*RootOf(_Z^2+1)*x^4+2*(-(-1-x)/(x^2-2))^(1/4)*x^7-2*(-(-1-x)/(x^2-2))^(1/4)*x^6-2*(-(-1-x)/(x^2-2))^(3/4)*x^3-8*(-(-1-x)/(x^2-2))^(1/4)*x^5+2*(-(-1-x)/(x^2-2))^(3/4)*x^2+8*(-(-1-x)/(x^2-2))^(1/4)*x^4+4*(-(-1-x)/(x^2-2))^(3/4)*x+10*(-(-1-x)/(x^2-2))^(1/4)*x^3-10*(-(-1-x)/(x^2-2))^(1/4)*x^2-4*(-(-1-x)/(x^2-2))^(1/4)*x)/(x^9-x^8-5*x^7+5*x^6+9*x^5-9*x^4-7*x^3+7*x^2+2*x-3))","C"
650,1,46,45,0.229000," ","int((7*x^8-1)/(x^8+1)/(3*x^16-x^9+6*x^8+x^2-x+3)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(-\frac{x^{8}+2 \sqrt{3 x^{16}-x^{9}+6 x^{8}+x^{2}-x +3}-2 x +1}{x^{8}+1}\right)$&$46$\\ \hline \end{longtable}"," ",0,"ln(-(x^8+2*(3*x^16-x^9+6*x^8+x^2-x+3)^(1/2)-2*x+1)/(x^8+1))","A"
651,0,0,40,0.015000," ","int((1+(x^2+1)^(1/2))^(1/2)/x^2/(x^2+1)^(1/2),x)","\[\int \frac{\sqrt{1+\sqrt{x^{2}+1}}}{x^{2} \sqrt{x^{2}+1}}\, dx\]"," ",0,"int((1+(x^2+1)^(1/2))^(1/2)/x^2/(x^2+1)^(1/2),x)","F"
652,1,54,39,0.054000," ","int(x/(x+(1+(1+x)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\left(1+\sqrt{1+x}\right)^{2}-2-2 \sqrt{1+x}-4 \sqrt{1+\sqrt{1+x}}+\frac{8 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}+1\right) \sqrt{5}}{5}\right)}{5}$&$54$\\ default&$\left(1+\sqrt{1+x}\right)^{2}-2-2 \sqrt{1+x}-4 \sqrt{1+\sqrt{1+x}}+\frac{8 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}+1\right) \sqrt{5}}{5}\right)}{5}$&$54$\\ \hline \end{longtable}"," ",0,"(1+(1+x)^(1/2))^2-2-2*(1+x)^(1/2)-4*(1+(1+x)^(1/2))^(1/2)+8/5*5^(1/2)*arctanh(1/5*(2*(1+(1+x)^(1/2))^(1/2)+1)*5^(1/2))","A"
653,0,0,40,0.107000," ","int((a+2*x)/(a*x+x^2+b)^(1/4)/(2*a*x+2*x^2+2*b-1),x)","\[\int \frac{a +2 x}{\left(a x +x^{2}+b \right)^{\frac{1}{4}} \left(2 a x +2 x^{2}+2 b -1\right)}\, dx\]"," ",0,"int((a+2*x)/(a*x+x^2+b)^(1/4)/(2*a*x+2*x^2+2*b-1),x)","F"
654,1,82,40,1.895000," ","int(1/x^7/(x^3+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{5 x^{6}+x^{3}-4}{24 x^{6} \left(x^{3}+1\right)^{\frac{1}{4}}}+\frac{5 \sqrt{2}\, \Gamma \left(\frac{3}{4}\right) \left(-\frac{\pi  \sqrt{2}\, x^{3} \hypergeom \left(\left[1, 1, \frac{5}{4}\right], \left[2, 2\right], -x^{3}\right)}{4 \Gamma \left(\frac{3}{4}\right)}+\frac{\left(-3 \ln \left(2\right)-\frac{\pi}{2}+3 \ln \left(x \right)\right) \pi  \sqrt{2}}{\Gamma \left(\frac{3}{4}\right)}\right)}{192 \pi}$&$82$\\ meijerg&$\frac{\sqrt{2}\, \Gamma \left(\frac{3}{4}\right) \left(-\frac{15 \pi  \sqrt{2}\, x^{3} \hypergeom \left(\left[1, 1, \frac{13}{4}\right], \left[2, 4\right], -x^{3}\right)}{128 \Gamma \left(\frac{3}{4}\right)}+\frac{5 \left(\frac{33}{10}-3 \ln \left(2\right)-\frac{\pi}{2}+3 \ln \left(x \right)\right) \pi  \sqrt{2}}{32 \Gamma \left(\frac{3}{4}\right)}-\frac{\pi  \sqrt{2}}{2 \Gamma \left(\frac{3}{4}\right) x^{6}}+\frac{\pi  \sqrt{2}}{4 \Gamma \left(\frac{3}{4}\right) x^{3}}\right)}{6 \pi}$&$87$\\ trager&$\frac{\left(x^{3}+1\right)^{\frac{3}{4}} \left(5 x^{3}-4\right)}{24 x^{6}}-\frac{5 \ln \left(\frac{2 \left(x^{3}+1\right)^{\frac{3}{4}}+x^{3}+2 \sqrt{x^{3}+1}+2 \left(x^{3}+1\right)^{\frac{1}{4}}+2}{x^{3}}\right)}{96}-\frac{5 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{3}+1\right)^{\frac{3}{4}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{3}+1}-2 \left(x^{3}+1\right)^{\frac{1}{4}}+2 \RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{3}}\right)}{96}$&$125$\\ \hline \end{longtable}"," ",0,"1/24*(5*x^6+x^3-4)/x^6/(x^3+1)^(1/4)+5/192/Pi*2^(1/2)*GAMMA(3/4)*(-1/4*Pi*2^(1/2)/GAMMA(3/4)*x^3*hypergeom([1,1,5/4],[2,2],-x^3)+(-3*ln(2)-1/2*Pi+3*ln(x))*Pi*2^(1/2)/GAMMA(3/4))","C"
655,1,58,40,1.683000," ","int((x^3+1)^(1/4)/x^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{-\frac{7 \Gamma \left(\frac{3}{4}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{11}{4}\right], \left[2, 4\right], -x^{3}\right)}{32}+\frac{3 \left(-\frac{1}{6}-3 \ln \left(2\right)+\frac{\pi}{2}+3 \ln \left(x \right)\right) \Gamma \left(\frac{3}{4}\right)}{8}+\frac{2 \Gamma \left(\frac{3}{4}\right)}{x^{6}}+\frac{\Gamma \left(\frac{3}{4}\right)}{x^{3}}}{12 \Gamma \left(\frac{3}{4}\right)}$&$58$\\ risch&$-\frac{x^{6}+5 x^{3}+4}{24 x^{6} \left(x^{3}+1\right)^{\frac{3}{4}}}-\frac{-\frac{3 \Gamma \left(\frac{3}{4}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{7}{4}\right], \left[2, 2\right], -x^{3}\right)}{4}+\left(-3 \ln \left(2\right)+\frac{\pi}{2}+3 \ln \left(x \right)\right) \Gamma \left(\frac{3}{4}\right)}{32 \Gamma \left(\frac{3}{4}\right)}$&$66$\\ trager&$-\frac{\left(x^{3}+4\right) \left(x^{3}+1\right)^{\frac{1}{4}}}{24 x^{6}}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{3}+1}+2 \left(x^{3}+1\right)^{\frac{3}{4}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(x^{3}+1\right)^{\frac{1}{4}}}{x^{3}}\right)}{32}-\frac{\ln \left(\frac{2 \left(x^{3}+1\right)^{\frac{3}{4}}-x^{3}-2 \sqrt{x^{3}+1}+2 \left(x^{3}+1\right)^{\frac{1}{4}}-2}{x^{3}}\right)}{32}$&$126$\\ \hline \end{longtable}"," ",0,"-1/12/GAMMA(3/4)*(-7/32*GAMMA(3/4)*x^3*hypergeom([1,1,11/4],[2,4],-x^3)+3/8*(-1/6-3*ln(2)+1/2*Pi+3*ln(x))*GAMMA(3/4)+2*GAMMA(3/4)/x^6+GAMMA(3/4)/x^3)","C"
656,1,47,40,0.294000," ","int((a*x^3+b)^(1/2)*(a*x^3+2*b)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 \left(a \,x^{3}+b \right)^{\frac{3}{2}}}{9}+2 b \left(\frac{2 \sqrt{a \,x^{3}+b}}{3}-\frac{2 \sqrt{b}\, \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{3}\right)$&$47$\\ elliptic&$\frac{2 a \,x^{3} \sqrt{a \,x^{3}+b}}{9}+\frac{14 b \sqrt{a \,x^{3}+b}}{9}-\frac{4 b^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{3}$&$48$\\ \hline \end{longtable}"," ",0,"2/9*(a*x^3+b)^(3/2)+2*b*(2/3*(a*x^3+b)^(1/2)-2/3*b^(1/2)*arctanh((a*x^3+b)^(1/2)/b^(1/2)))","A"
657,1,47,44,0.386000," ","int((x^3+1)*(x^6-1)^(1/2)/x^13/(x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{32 x^{15}+21 x^{12}-16 x^{9}-15 x^{6}-16 x^{3}-6}{72 x^{12} \sqrt{x^{6}-1}}-\frac{7 \arcsin \left(\frac{1}{x^{3}}\right)}{24}$&$47$\\ trager&$\frac{\sqrt{x^{6}-1}\, \left(32 x^{9}+21 x^{6}+16 x^{3}+6\right)}{72 x^{12}}+\frac{7 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{24}$&$58$\\ \hline \end{longtable}"," ",0,"1/72*(32*x^15+21*x^12-16*x^9-15*x^6-16*x^3-6)/x^12/(x^6-1)^(1/2)-7/24*arcsin(1/x^3)","A"
658,1,46,44,0.487000," ","int((x^4+x)^(1/2)*(a*x^6-b)/x^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{a \left(-2 \sqrt{\pi}\, x^{\frac{3}{2}} \sqrt{x^{3}+1}-2 \sqrt{\pi}\, \arcsinh \left(x^{\frac{3}{2}}\right)\right)}{6 \sqrt{\pi}}+\frac{2 b \left(x^{3}+1\right)^{\frac{3}{2}}}{9 x^{\frac{9}{2}}}$&$46$\\ trager&$\frac{\sqrt{x^{4}+x}\, \left(3 a \,x^{6}+2 b \,x^{3}+2 b \right)}{9 x^{5}}+\frac{a \ln \left(-2 x^{3}-2 x \sqrt{x^{4}+x}-1\right)}{6}$&$51$\\ risch&$\frac{\left(x^{3}+1\right) \left(3 a \,x^{6}+2 b \,x^{3}+2 b \right)}{9 x^{4} \sqrt{x \left(x^{3}+1\right)}}-\frac{a \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$327$\\ elliptic&$\frac{2 b \sqrt{x^{4}+x}}{9 x^{5}}+\frac{2 b \sqrt{x^{4}+x}}{9 x^{2}}+\frac{a x \sqrt{x^{4}+x}}{3}-\frac{a \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$329$\\ default&$a \left(\frac{x \sqrt{x^{4}+x}}{3}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-b \left(-\frac{2 \sqrt{x^{4}+x}}{9 x^{5}}-\frac{2 \sqrt{x^{4}+x}}{9 x^{2}}\right)$&$332$\\ \hline \end{longtable}"," ",0,"-1/6/Pi^(1/2)*a*(-2*Pi^(1/2)*x^(3/2)*(x^3+1)^(1/2)-2*Pi^(1/2)*arcsinh(x^(3/2)))+2/9*b/x^(9/2)*(x^3+1)^(3/2)","A"
659,0,0,48,0.019000," ","int((5*a*x^3-7*b*x)/(a*x^3-b*x)^(1/4)/(x^7-a*x^2+b),x)","\[\int \frac{5 a \,x^{3}-7 b x}{\left(a \,x^{3}-b x \right)^{\frac{1}{4}} \left(x^{7}-a \,x^{2}+b \right)}\, dx\]"," ",0,"int((5*a*x^3-7*b*x)/(a*x^3-b*x)^(1/4)/(x^7-a*x^2+b),x)","F"
660,0,0,40,0.031000," ","int((3*x^5+x)/(x^5-x)^(1/2)/(x^8-2*x^4-a*x^2+1),x)","\[\int \frac{3 x^{5}+x}{\sqrt{x^{5}-x}\, \left(x^{8}-2 x^{4}-a \,x^{2}+1\right)}\, dx\]"," ",0,"int((3*x^5+x)/(x^5-x)^(1/2)/(x^8-2*x^4-a*x^2+1),x)","F"
661,0,0,40,0.030000," ","int((3*x^5+x)/(x^5-x)^(1/2)/(a*x^8-2*a*x^4-x^2+a),x)","\[\int \frac{3 x^{5}+x}{\sqrt{x^{5}-x}\, \left(a \,x^{8}-2 a \,x^{4}-x^{2}+a \right)}\, dx\]"," ",0,"int((3*x^5+x)/(x^5-x)^(1/2)/(a*x^8-2*a*x^4-x^2+a),x)","F"
662,0,0,40,0.030000," ","int((4*x^6+x)/(x^6-x)^(1/2)/(x^10-2*x^5-a*x^2+1),x)","\[\int \frac{4 x^{6}+x}{\sqrt{x^{6}-x}\, \left(x^{10}-2 x^{5}-a \,x^{2}+1\right)}\, dx\]"," ",0,"int((4*x^6+x)/(x^6-x)^(1/2)/(x^10-2*x^5-a*x^2+1),x)","F"
663,0,0,40,0.029000," ","int((4*x^6+x)/(x^6-x)^(1/2)/(a*x^10-2*a*x^5-x^2+a),x)","\[\int \frac{4 x^{6}+x}{\sqrt{x^{6}-x}\, \left(a \,x^{10}-2 a \,x^{5}-x^{2}+a \right)}\, dx\]"," ",0,"int((4*x^6+x)/(x^6-x)^(1/2)/(a*x^10-2*a*x^5-x^2+a),x)","F"
664,1,48,42,0.103000," ","int(1/(-5+2*x)^2/(x^2-4*x+4)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{-2+x}{\left(-5+2 x \right) \left(\left(-2+x \right)^{2}\right)^{\frac{1}{4}}}+\frac{\arctanh \left(\sqrt{2}\, \sqrt{-2+x}\right) \sqrt{2}\, \sqrt{-2+x}}{2 \left(\left(-2+x \right)^{2}\right)^{\frac{1}{4}}}$&$48$\\ \hline \end{longtable}"," ",0,"-(-2+x)/(-5+2*x)/((-2+x)^2)^(1/4)+1/2*arctanh(2^(1/2)*(-2+x)^(1/2))*2^(1/2)/((-2+x)^2)^(1/4)*(-2+x)^(1/2)","A"
665,1,87,43,0.642000," ","int((x^3-2)*(x^3+1)^(1/2)*(2*x^3-x^2+2)/x^4/(x^3-3*x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \sqrt{x^{3}+1}\, \left(2 x^{3}+15 x^{2}+2\right)}{3 x^{3}}-5 \RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) x^{3}+3 \RootOf \left(\textit{\_Z}^{2}-3\right) x^{2}+6 x \sqrt{x^{3}+1}+\RootOf \left(\textit{\_Z}^{2}-3\right)}{x^{3}-3 x^{2}+1}\right)$&$87$\\ default&$\frac{4 \sqrt{x^{3}+1}}{3 x^{3}}+\frac{10 \sqrt{x^{3}+1}}{x}+\frac{4 \sqrt{x^{3}+1}}{3}+\frac{30 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+5 \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}-3 \textit{\_Z}^{2}+1\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(-\underline{\hspace{1.25 ex}}\alpha^{2}+4 \underline{\hspace{1.25 ex}}\alpha  -4\right) \left(3-i \sqrt{3}\right) \sqrt{\frac{1+x}{3-i \sqrt{3}}}\, \sqrt{\frac{-1+2 x -i \sqrt{3}}{-3-i \sqrt{3}}}\, \sqrt{\frac{i \sqrt{3}+2 x -1}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{2}-2 \underline{\hspace{1.25 ex}}\alpha  +2-\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{6}+\frac{2 i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha }{3}-\frac{2 i \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}\right)$&$330$\\ elliptic&$\frac{4 \sqrt{x^{3}+1}}{3 x^{3}}+\frac{10 \sqrt{x^{3}+1}}{x}+\frac{4 \sqrt{x^{3}+1}}{3}+\frac{30 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+5 \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}-3 \textit{\_Z}^{2}+1\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(-\underline{\hspace{1.25 ex}}\alpha^{2}+4 \underline{\hspace{1.25 ex}}\alpha  -4\right) \left(3-i \sqrt{3}\right) \sqrt{\frac{1+x}{3-i \sqrt{3}}}\, \sqrt{\frac{-1+2 x -i \sqrt{3}}{-3-i \sqrt{3}}}\, \sqrt{\frac{i \sqrt{3}+2 x -1}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{2}-2 \underline{\hspace{1.25 ex}}\alpha  +2-\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{6}+\frac{2 i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha }{3}-\frac{2 i \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}\right)$&$330$\\ risch&$\frac{10 x^{5}+10 x^{2}+\frac{8}{3} x^{3}+\frac{4}{3}+\frac{4}{3} x^{6}}{x^{3} \sqrt{x^{3}+1}}+\frac{30 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+5 \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}-3 \textit{\_Z}^{2}+1\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(-\underline{\hspace{1.25 ex}}\alpha^{2}+4 \underline{\hspace{1.25 ex}}\alpha  -4\right) \left(3-i \sqrt{3}\right) \sqrt{\frac{1+x}{3-i \sqrt{3}}}\, \sqrt{\frac{-1+2 x -i \sqrt{3}}{-3-i \sqrt{3}}}\, \sqrt{\frac{i \sqrt{3}+2 x -1}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{2}-2 \underline{\hspace{1.25 ex}}\alpha  +2-\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{6}+\frac{2 i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha }{3}-\frac{2 i \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}\right)$&$331$\\ \hline \end{longtable}"," ",0,"2/3*(x^3+1)^(1/2)*(2*x^3+15*x^2+2)/x^3-5*RootOf(_Z^2-3)*ln(-(RootOf(_Z^2-3)*x^3+3*RootOf(_Z^2-3)*x^2+6*x*(x^3+1)^(1/2)+RootOf(_Z^2-3))/(x^3-3*x^2+1))","C"
666,1,47,41,0.086000," ","int((a*x^3-b)*(a*x^3+b)^(1/2)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 \left(a \,x^{3}+b \right)^{\frac{3}{2}}}{9}-b \left(\frac{2 \sqrt{a \,x^{3}+b}}{3}-\frac{2 \sqrt{b}\, \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{3}\right)$&$47$\\ elliptic&$\frac{2 a \,x^{3} \sqrt{a \,x^{3}+b}}{9}-\frac{4 b \sqrt{a \,x^{3}+b}}{9}+\frac{2 b^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{3}$&$48$\\ \hline \end{longtable}"," ",0,"2/9*(a*x^3+b)^(3/2)-b*(2/3*(a*x^3+b)^(1/2)-2/3*b^(1/2)*arctanh((a*x^3+b)^(1/2)/b^(1/2)))","A"
667,1,43,37,0.473000," ","int(x^2/(x^4-1)/(x^4+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(-\frac{\arctanh \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{4}-\frac{\arctan \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{4}\right) \sqrt{2}}{2}$&$43$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x +\sqrt{x^{4}+1}}{\left(-1+x \right) \left(1+x \right)}\right)}{8}+\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+2\right) x +\sqrt{x^{4}+1}}{x^{2}+1}\right)}{8}$&$73$\\ default&$-\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{2 \sqrt{x^{4}+1}}+\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{2 \sqrt{x^{4}+1}}$&$102$\\ \hline \end{longtable}"," ",0,"1/2*(-1/4*arctanh(1/2*2^(1/2)/x*(x^4+1)^(1/2))-1/4*arctan(1/2*2^(1/2)/x*(x^4+1)^(1/2)))*2^(1/2)","A"
668,1,65,37,0.388000," ","int((x^4+1)^(1/2)/(x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\ln \left(-1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{4}-\frac{\ln \left(1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{4}+\frac{\arctan \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{2}\right) \sqrt{2}}{2}$&$65$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x +\sqrt{x^{4}+1}}{x^{2}+1}\right)}{4}-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x +\sqrt{x^{4}+1}}{\left(-1+x \right) \left(1+x \right)}\right)}{4}$&$72$\\ default&$\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{i \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticE \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{2 \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{i \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \left(\EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)-\EllipticE \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)\right)}{2 \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{\sqrt{x^{4}+1}}-\frac{i \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{2 \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{\sqrt{x^{4}+1}}$&$362$\\ \hline \end{longtable}"," ",0,"1/2*(1/4*ln(-1+1/2*2^(1/2)/x*(x^4+1)^(1/2))-1/4*ln(1+1/2*2^(1/2)/x*(x^4+1)^(1/2))+1/2*arctan(1/2*2^(1/2)/x*(x^4+1)^(1/2)))*2^(1/2)","A"
669,1,48,45,0.280000," ","int((a*x^3+b)*(x^4+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{x \left(2 a \,x^{3}+a +4 b \right) \sqrt{x^{4}+x}}{12}-\frac{\left(a -4 b \right) \ln \left(-2 x^{3}-2 x \sqrt{x^{4}+x}-1\right)}{24}$&$48$\\ meijerg&$-\frac{a \left(-\frac{\sqrt{\pi}\, x^{\frac{3}{2}} \left(6 x^{3}+3\right) \sqrt{x^{3}+1}}{6}+\frac{\sqrt{\pi}\, \arcsinh \left(x^{\frac{3}{2}}\right)}{2}\right)}{6 \sqrt{\pi}}-\frac{b \left(-2 \sqrt{\pi}\, x^{\frac{3}{2}} \sqrt{x^{3}+1}-2 \sqrt{\pi}\, \arcsinh \left(x^{\frac{3}{2}}\right)\right)}{6 \sqrt{\pi}}$&$71$\\ elliptic&$\frac{a \,x^{4} \sqrt{x^{4}+x}}{6}+\left(\frac{a}{12}+\frac{b}{3}\right) x \sqrt{x^{4}+x}-\frac{2 \left(\frac{b}{2}-\frac{a}{8}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$327$\\ risch&$\frac{x^{2} \left(2 a \,x^{3}+a +4 b \right) \left(x^{3}+1\right)}{12 \sqrt{x \left(x^{3}+1\right)}}-\frac{2 \left(\frac{b}{2}-\frac{a}{8}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$328$\\ default&$a \left(\frac{x^{4} \sqrt{x^{4}+x}}{6}+\frac{x \sqrt{x^{4}+x}}{12}+\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{4 \left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+b \left(\frac{x \sqrt{x^{4}+x}}{3}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)$&$618$\\ \hline \end{longtable}"," ",0,"1/12*x*(2*a*x^3+a+4*b)*(x^4+x)^(1/2)-1/24*(a-4*b)*ln(-2*x^3-2*x*(x^4+x)^(1/2)-1)","A"
670,1,17,41,3.611000," ","int((x^4+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{2 x^{\frac{3}{2}} \hypergeom \left(\left[-\frac{1}{4}, \frac{3}{4}\right], \left[\frac{7}{4}\right], -x^{2}\right)}{3}$&$17$\\ trager&$\frac{x \left(x^{4}+x^{2}\right)^{\frac{1}{4}}}{2}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-2 \sqrt{x^{4}+x^{2}}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x +2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{4}+x^{2}\right)^{\frac{3}{4}}-2 x^{2} \left(x^{4}+x^{2}\right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{2}+1\right) x}{x}\right)}{8}-\frac{\ln \left(\frac{2 \left(x^{4}+x^{2}\right)^{\frac{3}{4}}-2 \sqrt{x^{4}+x^{2}}\, x +2 x^{2} \left(x^{4}+x^{2}\right)^{\frac{1}{4}}-2 x^{3}-x}{x}\right)}{8}$&$143$\\ risch&$\frac{x \left(x^{2} \left(x^{2}+1\right)\right)^{\frac{1}{4}}}{2}+\frac{\left(\frac{\ln \left(\frac{2 x^{6}+2 \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{1}{4}} x^{4}+2 \sqrt{x^{8}+3 x^{6}+3 x^{4}+x^{2}}\, x^{2}+5 x^{4}+2 \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{3}{4}}+4 \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{1}{4}} x^{2}+2 \sqrt{x^{8}+3 x^{6}+3 x^{4}+x^{2}}+4 x^{2}+2 \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{1}{4}}+1}{\left(x^{2}+1\right)^{2}}\right)}{8}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{1}{4}} x^{4}+2 x^{6}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{3}{4}}-4 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{1}{4}} x^{2}-2 \sqrt{x^{8}+3 x^{6}+3 x^{4}+x^{2}}\, x^{2}+5 x^{4}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{1}{4}}-2 \sqrt{x^{8}+3 x^{6}+3 x^{4}+x^{2}}+4 x^{2}+1}{\left(x^{2}+1\right)^{2}}\right)}{8}\right) \left(x^{2} \left(x^{2}+1\right)\right)^{\frac{1}{4}} \left(x^{2} \left(x^{2}+1\right)^{3}\right)^{\frac{1}{4}}}{x \left(x^{2}+1\right)}$&$409$\\ \hline \end{longtable}"," ",0,"2/3*x^(3/2)*hypergeom([-1/4,3/4],[7/4],-x^2)","C"
671,1,60,43,0.385000," ","int((x^4-1)*(x^4+1)^(1/2)/(x^4+3*x^2+1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(-\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{4 x \left(\frac{x^{4}+1}{2 x^{2}}+\frac{3}{2}\right)}+\frac{\sqrt{6}\, \arctan \left(\frac{\sqrt{6}\, \sqrt{2}\, \sqrt{x^{4}+1}}{6 x}\right)}{6}\right) \sqrt{2}}{2}$&$60$\\ trager&$-\frac{x \sqrt{x^{4}+1}}{2 \left(x^{4}+3 x^{2}+1\right)}-\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) x^{4}-3 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{2}+6 \sqrt{x^{4}+1}\, x +\RootOf \left(\textit{\_Z}^{2}+3\right)}{x^{4}+3 x^{2}+1}\right)}{12}$&$85$\\ risch&$-\frac{x \sqrt{x^{4}+1}}{2 \left(x^{4}+3 x^{2}+1\right)}+\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{2 \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+3 \textit{\_Z}^{2}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\sqrt{3}\, \arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}-3\right)}{\sqrt{-3 \underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{x^{4}+1}}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{6 \left(-1\right)^{\frac{3}{4}} \left(-\underline{\hspace{1.25 ex}}\alpha^{3}-3 \underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \underline{\hspace{1.25 ex}}\alpha^{2}+3 i, i\right)}{\sqrt{x^{4}+1}}\right)\right)}{24}$&$202$\\ default&$-\frac{x \sqrt{x^{4}+1}}{2 \left(x^{4}+3 x^{2}+1\right)}+\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{2 \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+3 \textit{\_Z}^{2}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(12 \underline{\hspace{1.25 ex}}\alpha^{2}+23\right) \left(-\frac{\sqrt{3}\, \arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}-3\right)}{\sqrt{-3 \underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{x^{4}+1}}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{6 \left(-1\right)^{\frac{3}{4}} \left(-\underline{\hspace{1.25 ex}}\alpha^{3}-3 \underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \underline{\hspace{1.25 ex}}\alpha^{2}+3 i, i\right)}{\sqrt{x^{4}+1}}\right)\right)}{120}-\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+3 \textit{\_Z}^{2}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2}+3\right) \left(-\frac{\sqrt{3}\, \arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}-3\right)}{\sqrt{-3 \underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{x^{4}+1}}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{6 \left(-1\right)^{\frac{3}{4}} \left(-\underline{\hspace{1.25 ex}}\alpha^{3}-3 \underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \underline{\hspace{1.25 ex}}\alpha^{2}+3 i, i\right)}{\sqrt{x^{4}+1}}\right)\right)}{20}$&$334$\\ \hline \end{longtable}"," ",0,"1/2*(-1/4*2^(1/2)/x*(x^4+1)^(1/2)/(1/2/x^2*(x^4+1)+3/2)+1/6*6^(1/2)*arctan(1/6*6^(1/2)*2^(1/2)/x*(x^4+1)^(1/2)))*2^(1/2)","A"
672,1,15,49,0.086000," ","int(1/x^8/(x^4+x^3)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{4 \hypergeom \left(\left[-\frac{31}{4}, \frac{1}{4}\right], \left[-\frac{27}{4}\right], -x \right)}{31 x^{\frac{31}{4}}}$&$15$\\ trager&$\frac{4 \left(x^{4}+x^{3}\right)^{\frac{3}{4}} \left(262144 x^{7}-196608 x^{6}+172032 x^{5}-157696 x^{4}+147840 x^{3}-140448 x^{2}+134596 x -129789\right)}{4023459 x^{10}}$&$50$\\ gosper&$\frac{4 \left(1+x \right) \left(262144 x^{7}-196608 x^{6}+172032 x^{5}-157696 x^{4}+147840 x^{3}-140448 x^{2}+134596 x -129789\right)}{4023459 x^{7} \left(x^{4}+x^{3}\right)^{\frac{1}{4}}}$&$53$\\ risch&$\frac{-\frac{4}{31}+\frac{4}{837} x -\frac{112}{19251} x^{2}+\frac{896}{121923} x^{3}-\frac{3584}{365769} x^{4}+\frac{57344}{4023459} x^{5}-\frac{32768}{1341153} x^{6}+\frac{262144}{4023459} x^{7}+\frac{1048576}{4023459} x^{8}}{x^{7} \left(x^{3} \left(1+x \right)\right)^{\frac{1}{4}}}$&$55$\\ \hline \end{longtable}"," ",0,"-4/31/x^(31/4)*hypergeom([-31/4,1/4],[-27/4],-x)","C"
673,1,92,51,1.287000," ","int((1+4*x)/(x^4+2*x^3+3*x^2-2*x+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(-x^{4}+\sqrt{x^{4}+2 x^{3}+3 x^{2}-2 x +1}\, x^{2}-3 x^{3}+2 \sqrt{x^{4}+2 x^{3}+3 x^{2}-2 x +1}\, x -5 x^{2}+2 \sqrt{x^{4}+2 x^{3}+3 x^{2}-2 x +1}-2 x \right)$&$92$\\ default&$\text{Expression too large to display}$&$2700$\\ elliptic&$\text{Expression too large to display}$&$2700$\\ \hline \end{longtable}"," ",0,"-ln(-x^4+(x^4+2*x^3+3*x^2-2*x+1)^(1/2)*x^2-3*x^3+2*(x^4+2*x^3+3*x^2-2*x+1)^(1/2)*x-5*x^2+2*(x^4+2*x^3+3*x^2-2*x+1)^(1/2)-2*x)","A"
674,1,160,37,1.104000," ","int(1/(x^4-1)^(1/4)/(3*x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{4 \RootOf \left(\textit{\_Z}^{2}-2\right) \sqrt{x^{4}-1}\, x^{2}+5 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{4}+4 \left(x^{4}-1\right)^{\frac{3}{4}} x +8 x^{3} \left(x^{4}-1\right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}-2\right)}{3 x^{4}+1}\right)}{8}+\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{-4 \RootOf \left(\textit{\_Z}^{2}+2\right) \sqrt{x^{4}-1}\, x^{2}+5 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{4}+4 \left(x^{4}-1\right)^{\frac{3}{4}} x -8 x^{3} \left(x^{4}-1\right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+2\right)}{3 x^{4}+1}\right)}{8}$&$160$\\ \hline \end{longtable}"," ",0,"1/8*RootOf(_Z^2-2)*ln((4*RootOf(_Z^2-2)*(x^4-1)^(1/2)*x^2+5*RootOf(_Z^2-2)*x^4+4*(x^4-1)^(3/4)*x+8*x^3*(x^4-1)^(1/4)-RootOf(_Z^2-2))/(3*x^4+1))+1/8*RootOf(_Z^2+2)*ln((-4*RootOf(_Z^2+2)*(x^4-1)^(1/2)*x^2+5*RootOf(_Z^2+2)*x^4+4*(x^4-1)^(3/4)*x-8*x^3*(x^4-1)^(1/4)-RootOf(_Z^2+2))/(3*x^4+1))","C"
675,0,0,49,0.022000," ","int((a*x^4-3*b)/(a*x^4-x^3+b)/(a*x^5+b*x)^(1/4),x)","\[\int \frac{a \,x^{4}-3 b}{\left(a \,x^{4}-x^{3}+b \right) \left(a \,x^{5}+b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^4-3*b)/(a*x^4-x^3+b)/(a*x^5+b*x)^(1/4),x)","F"
676,1,47,45,0.233000," ","int(x^20*(x^6-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{x^{3} \left(48 x^{18}-8 x^{12}-10 x^{6}-15\right) \sqrt{x^{6}-1}}{1152}+\frac{5 \ln \left(x^{3}-\sqrt{x^{6}-1}\right)}{384}$&$47$\\ risch&$\frac{x^{3} \left(48 x^{18}-8 x^{12}-10 x^{6}-15\right) \sqrt{x^{6}-1}}{1152}-\frac{5 \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \arcsin \left(x^{3}\right)}{384 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}$&$55$\\ meijerg&$-\frac{i \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(-\frac{i \sqrt{\pi}\, x^{3} \left(-336 x^{18}+56 x^{12}+70 x^{6}+105\right) \sqrt{-x^{6}+1}}{672}+\frac{5 i \sqrt{\pi}\, \arcsin \left(x^{3}\right)}{32}\right)}{12 \sqrt{\pi}\, \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}}$&$71$\\ \hline \end{longtable}"," ",0,"1/1152*x^3*(48*x^18-8*x^12-10*x^6-15)*(x^6-1)^(1/2)+5/384*ln(x^3-(x^6-1)^(1/2))","A"
677,1,58,41,0.543000," ","int((x^3-1)*(x^6-1)^(1/2)/x^4/(x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}-1}}{3 x^{3}}+\frac{\ln \left(x^{3}+\sqrt{x^{6}-1}\right)}{3}+\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)-\sqrt{x^{6}-1}}{x^{3}}\right)}{3}$&$58$\\ risch&$\frac{\sqrt{x^{6}-1}}{3 x^{3}}+\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \arcsin \left(x^{3}\right)}{3 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}-\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(-2 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right)+\left(-2 \ln \left(2\right)+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}\right)}{3 \sqrt{\pi}\, \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}$&$98$\\ \hline \end{longtable}"," ",0,"1/3*(x^6-1)^(1/2)/x^3+1/3*ln(x^3+(x^6-1)^(1/2))+2/3*RootOf(_Z^2+1)*ln(-(RootOf(_Z^2+1)-(x^6-1)^(1/2))/x^3)","C"
678,1,52,41,0.668000," ","int((x^6+1)/(x^4-x^2+1)^(1/2)/(-x^6+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{x^{4}-x^{2}+1}}{x}\right)}{3}-\frac{2 \arctan \left(\frac{\sqrt{2}\, \sqrt{x^{4}-x^{2}+1}}{2 x}\right)}{3}\right) \sqrt{2}}{2}$&$52$\\ trager&$-\frac{\ln \left(-\frac{\sqrt{x^{4}-x^{2}+1}-x}{\left(-1+x \right) \left(1+x \right)}\right)}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x^{4}-3 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{2}+4 \sqrt{x^{4}-x^{2}+1}\, x +\RootOf \left(\textit{\_Z}^{2}+2\right)}{\left(x^{2}-x +1\right) \left(x^{2}+x +1\right)}\right)}{6}$&$105$\\ default&$-\frac{2 \sqrt{1-\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}}\, \sqrt{1-\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{2+2 i \sqrt{3}}}{2}, \frac{\sqrt{-2-2 i \sqrt{3}}}{2}\right)}{\sqrt{2+2 i \sqrt{3}}\, \sqrt{x^{4}-x^{2}+1}}+\frac{2 \sqrt{1-\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}}\, \sqrt{1-\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , \frac{1}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \frac{\sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}-x^{2}+1}}-\frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{\arctanh \left(\frac{\left(-2+i \sqrt{3}\right) \left(7 x^{2}-\frac{13}{2}-\frac{3 i \sqrt{3}}{2}\right)}{14 \sqrt{1-i \sqrt{3}}\, \sqrt{x^{4}-x^{2}+1}}\right)}{2 \sqrt{1-i \sqrt{3}}}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{1-\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}}\, \sqrt{1-\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , \frac{i \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{2}-\frac{1}{4}-\frac{i \sqrt{3}}{4}, \frac{\sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}-x^{2}+1}}\right)}{3}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-\frac{\arctanh \left(\frac{\left(-2-i \sqrt{3}\right) \left(7 x^{2}-\frac{13}{2}+\frac{3 i \sqrt{3}}{2}\right)}{14 \sqrt{1+i \sqrt{3}}\, \sqrt{x^{4}-x^{2}+1}}\right)}{2 \sqrt{1+i \sqrt{3}}}-\frac{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{1-\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}}\, \sqrt{1-\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , \frac{i \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{2}-\frac{1}{4}+\frac{i \sqrt{3}}{4}, \frac{\sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{4}-x^{2}+1}}\right)}{3}-\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{\arctanh \left(\frac{\left(2+i \sqrt{3}\right) \left(7 x^{2}-\frac{13}{2}+\frac{3 i \sqrt{3}}{2}\right)}{14 \sqrt{1+i \sqrt{3}}\, \sqrt{x^{4}-x^{2}+1}}\right)}{2 \sqrt{1+i \sqrt{3}}}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{1-\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}}\, \sqrt{1-\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , -\frac{i \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{2}-\frac{1}{4}+\frac{i \sqrt{3}}{4}, \frac{\sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}-x^{2}+1}}\right)}{3}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(\frac{\arctanh \left(\frac{\left(2-i \sqrt{3}\right) \left(7 x^{2}-\frac{13}{2}-\frac{3 i \sqrt{3}}{2}\right)}{14 \sqrt{1-i \sqrt{3}}\, \sqrt{x^{4}-x^{2}+1}}\right)}{2 \sqrt{1-i \sqrt{3}}}-\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{1-\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}}\, \sqrt{1-\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , -\frac{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{2}-\frac{1}{4}-\frac{i \sqrt{3}}{4}, \frac{\sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}-x^{2}+1}}\right)}{3}$&$944$\\ \hline \end{longtable}"," ",0,"1/2*(1/3*2^(1/2)*arctanh(1/x*(x^4-x^2+1)^(1/2))-2/3*arctan(1/2*2^(1/2)/x*(x^4-x^2+1)^(1/2)))*2^(1/2)","A"
679,1,88,41,1.616000," ","int((x^6-2)*(x^6-1)^(1/2)/x^7/(x^6+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}-1}}{6 x^{6}}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) x^{6}+6 \sqrt{x^{6}-1}-4 \RootOf \left(\textit{\_Z}^{2}+3\right)}{x^{6}+2}\right)}{6}$&$88$\\ risch&$\frac{\sqrt{x^{6}-1}}{6 x^{6}}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+3\right) x^{6}+6 \sqrt{x^{6}-1}+4 \RootOf \left(\textit{\_Z}^{2}+3\right)}{x^{6}+2}\right)}{6}$&$89$\\ \hline \end{longtable}"," ",0,"1/6*(x^6-1)^(1/2)/x^6+1/2*RootOf(_Z^2+1)*ln((-RootOf(_Z^2+1)+(x^6-1)^(1/2))/x^3)-1/6*RootOf(_Z^2+3)*ln((RootOf(_Z^2+3)*x^6+6*(x^6-1)^(1/2)-4*RootOf(_Z^2+3))/(x^6+2))","C"
680,0,0,49,0.021000," ","int(x*(5*a*x-6*b)/(a*x^3-b*x^2)^(1/4)/(x^6-a*x+b),x)","\[\int \frac{x \left(5 a x -6 b \right)}{\left(a \,x^{3}-b \,x^{2}\right)^{\frac{1}{4}} \left(x^{6}-a x +b \right)}\, dx\]"," ",0,"int(x*(5*a*x-6*b)/(a*x^3-b*x^2)^(1/4)/(x^6-a*x+b),x)","F"
681,1,85,38,0.679000," ","int((x^3+1)^(1/2)*(x^6+2*x^3+2)/x/(x^6-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \sqrt{x^{3}+1}}{3}+\frac{2 \ln \left(-\frac{x^{3}+2 \sqrt{x^{3}+1}+2}{x^{3}}\right)}{3}-\frac{5 \RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x^{3}+3 \RootOf \left(\textit{\_Z}^{2}-2\right)+4 \sqrt{x^{3}+1}}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right)}{6}$&$85$\\ default&$\frac{2 \sqrt{x^{3}+1}}{3}+\frac{4 \arctanh \left(\sqrt{x^{3}+1}\right)}{3}-\frac{5 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{3}{4}-\frac{i \sqrt{3}}{4}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}+1}}+\frac{10 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{3}{4}-\frac{3 i \sqrt{3}}{4}+\frac{i \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{2}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}+1}}+\frac{10 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{3}{4}+\frac{3 i \sqrt{3}}{4}+\frac{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{2}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}+1}}$&$434$\\ elliptic&$\frac{2 \sqrt{x^{3}+1}}{3}+\frac{4 \arctanh \left(\sqrt{x^{3}+1}\right)}{3}-\frac{5 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{3}{4}-\frac{i \sqrt{3}}{4}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}}+\frac{5 i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{3}{4}-\frac{i \sqrt{3}}{4}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{6 \sqrt{x^{3}+1}}-\frac{10 i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{3}{4}-\frac{3 i \sqrt{3}}{4}+\frac{i \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{2}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{3 \sqrt{x^{3}+1}}+\frac{5 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{3}{4}+\frac{3 i \sqrt{3}}{4}+\frac{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{2}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{5 i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{3}{4}+\frac{3 i \sqrt{3}}{4}+\frac{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{2}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{3 \sqrt{x^{3}+1}}$&$905$\\ \hline \end{longtable}"," ",0,"2/3*(x^3+1)^(1/2)+2/3*ln(-(x^3+2*(x^3+1)^(1/2)+2)/x^3)-5/6*RootOf(_Z^2-2)*ln(-(RootOf(_Z^2-2)*x^3+3*RootOf(_Z^2-2)+4*(x^3+1)^(1/2))/(-1+x)/(x^2+x+1))","C"
682,1,79,37,1.110000," ","int((x^4-1)*(x^4+1)^(1/2)/(x^8+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(\frac{2^{\frac{1}{4}} \arctan \left(\frac{2^{\frac{3}{4}} \sqrt{x^{4}+1}}{2 x}\right)}{2}-\frac{2^{\frac{1}{4}} \ln \left(\frac{\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}+\frac{2^{\frac{3}{4}}}{2}}{\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}-\frac{2^{\frac{3}{4}}}{2}}\right)}{4}\right) \sqrt{2}}{2}$&$79$\\ elliptic&$\frac{\left(\frac{2^{\frac{1}{4}} \arctan \left(\frac{2^{\frac{3}{4}} \sqrt{x^{4}+1}}{2 x}\right)}{2}-\frac{2^{\frac{1}{4}} \ln \left(\frac{\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}+\frac{2^{\frac{3}{4}}}{2}}{\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}-\frac{2^{\frac{3}{4}}}{2}}\right)}{4}\right) \sqrt{2}}{2}$&$79$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{2} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{4}+8 \sqrt{x^{4}+1}\, x +2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right)}{2 x^{4}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+2}\right)}{8}+\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{2}-2 x^{4} \RootOf \left(\textit{\_Z}^{4}-8\right)+8 \sqrt{x^{4}+1}\, x -2 \RootOf \left(\textit{\_Z}^{4}-8\right)}{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 x^{4}-2}\right)}{8}$&$186$\\ \hline \end{longtable}"," ",0,"1/2*(1/2*2^(1/4)*arctan(1/2*2^(3/4)/x*(x^4+1)^(1/2))-1/4*2^(1/4)*ln((1/2*2^(1/2)/x*(x^4+1)^(1/2)+1/2*2^(3/4))/(1/2*2^(1/2)/x*(x^4+1)^(1/2)-1/2*2^(3/4))))*2^(1/2)","B"
683,1,79,37,0.938000," ","int((x^8-1)/(x^4+1)^(1/2)/(x^8+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{2^{\frac{1}{4}} \arctan \left(\frac{2^{\frac{3}{4}} \sqrt{x^{4}+1}}{2 x}\right)}{2}-\frac{2^{\frac{1}{4}} \ln \left(\frac{\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}+\frac{2^{\frac{3}{4}}}{2}}{\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}-\frac{2^{\frac{3}{4}}}{2}}\right)}{4}\right) \sqrt{2}}{2}$&$79$\\ default&$\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{8}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{6}+x^{2}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}+1}\, \sqrt{x^{4}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}+1}}-\frac{2 \left(-1\right)^{\frac{3}{4}} \underline{\hspace{1.25 ex}}\alpha^{7} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \underline{\hspace{1.25 ex}}\alpha^{6}, i\right)}{\sqrt{x^{4}+1}}\right)\right)}{8}$&$161$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{2}-2 x^{4} \RootOf \left(\textit{\_Z}^{4}-8\right)+8 \sqrt{x^{4}+1}\, x -2 \RootOf \left(\textit{\_Z}^{4}-8\right)}{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 x^{4}-2}\right)}{8}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{2} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{4}-8 \sqrt{x^{4}+1}\, x -2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right)}{2 x^{4}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+2}\right)}{8}$&$184$\\ \hline \end{longtable}"," ",0,"1/2*(1/2*2^(1/4)*arctan(1/2*2^(3/4)/x*(x^4+1)^(1/2))-1/4*2^(1/4)*ln((1/2*2^(1/2)/x*(x^4+1)^(1/2)+1/2*2^(3/4))/(1/2*2^(1/2)/x*(x^4+1)^(1/2)-1/2*2^(3/4))))*2^(1/2)","B"
684,1,79,37,1.146000," ","int((x^4-2)^(1/2)*(x^4+2)/(x^8-6*x^4+4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(\frac{2^{\frac{1}{4}} \arctan \left(\frac{2^{\frac{3}{4}} \sqrt{x^{4}-2}}{2 x}\right)}{2}-\frac{2^{\frac{1}{4}} \ln \left(\frac{\frac{\sqrt{x^{4}-2}\, \sqrt{2}}{2 x}+\frac{2^{\frac{3}{4}}}{2}}{\frac{\sqrt{x^{4}-2}\, \sqrt{2}}{2 x}-\frac{2^{\frac{3}{4}}}{2}}\right)}{4}\right) \sqrt{2}}{2}$&$79$\\ elliptic&$\frac{\left(\frac{2^{\frac{1}{4}} \arctan \left(\frac{2^{\frac{3}{4}} \sqrt{x^{4}-2}}{2 x}\right)}{2}-\frac{2^{\frac{1}{4}} \ln \left(\frac{\frac{\sqrt{x^{4}-2}\, \sqrt{2}}{2 x}+\frac{2^{\frac{3}{4}}}{2}}{\frac{\sqrt{x^{4}-2}\, \sqrt{2}}{2 x}-\frac{2^{\frac{3}{4}}}{2}}\right)}{4}\right) \sqrt{2}}{2}$&$79$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{2}+2 x^{4} \RootOf \left(\textit{\_Z}^{4}-8\right)+8 \sqrt{x^{4}-2}\, x -4 \RootOf \left(\textit{\_Z}^{4}-8\right)}{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 x^{4}+4}\right)}{8}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{2} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{4}+8 \sqrt{x^{4}-2}\, x +4 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right)}{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+2 x^{4}-4}\right)}{8}$&$182$\\ \hline \end{longtable}"," ",0,"1/2*(1/2*2^(1/4)*arctan(1/2*2^(3/4)/x*(x^4-2)^(1/2))-1/4*2^(1/4)*ln((1/2*(x^4-2)^(1/2)*2^(1/2)/x+1/2*2^(3/4))/(1/2*(x^4-2)^(1/2)*2^(1/2)/x-1/2*2^(3/4))))*2^(1/2)","B"
685,0,0,11,0.018000," ","int((a*x^4-2*b)/(a*x^4-b)^(1/4)/(2*x^8+a*x^4-b),x)","\[\int \frac{a \,x^{4}-2 b}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(2 x^{8}+a \,x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^4-2*b)/(a*x^4-b)^(1/4)/(2*x^8+a*x^4-b),x)","F"
686,1,22,41,0.063000," ","int(1/x^2/(x+(x^2+1)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{2}\, \hypergeom \left(\left[\frac{1}{4}, \frac{3}{4}, \frac{3}{4}\right], \left[\frac{3}{2}, \frac{7}{4}\right], -\frac{1}{x^{2}}\right)}{3 x^{\frac{3}{2}}}$&$22$\\ \hline \end{longtable}"," ",0,"-1/3*2^(1/2)/x^(3/2)*hypergeom([1/4,3/4,3/4],[3/2,7/4],-1/x^2)","C"
687,1,157,50,0.193000," ","int((-1+k^(1/2)*x)/(1+k^(1/2)*x)/((-x^2+1)*(-k^2*x^2+1))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\arctan \left(\frac{\sqrt{\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)}}{x \left(-1+k \right)}\right)}{-1+k}+\frac{\ln \left(\frac{-2 k^{2}+4 k -2+\left(-k^{3}+2 k^{2}-k \right) \left(x^{2}-\frac{1}{k}\right)+2 \sqrt{-\left(-1+k \right)^{2}}\, \sqrt{k^{3} \left(x^{2}-\frac{1}{k}\right)^{2}+\left(-k^{3}+2 k^{2}-k \right) \left(x^{2}-\frac{1}{k}\right)-k^{2}+2 k -1}}{x^{2}-\frac{1}{k}}\right)}{\sqrt{-\left(-1+k \right)^{2}}}$&$157$\\ default&$\frac{\sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticF \left(x , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}+\frac{\ln \left(\frac{-2 k^{2}+4 k -2+\left(-k^{3}+2 k^{2}-k \right) \left(x^{2}-\frac{1}{k}\right)+2 \sqrt{-\left(-1+k \right)^{2}}\, \sqrt{k^{3} \left(x^{2}-\frac{1}{k}\right)^{2}+\left(-k^{3}+2 k^{2}-k \right) \left(x^{2}-\frac{1}{k}\right)-k^{2}+2 k -1}}{x^{2}-\frac{1}{k}}\right)}{\sqrt{-\left(-1+k \right)^{2}}}-\frac{2 \sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticPi \left(x , k , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}$&$221$\\ \hline \end{longtable}"," ",0,"1/(-1+k)*arctan(((-x^2+1)*(-k^2*x^2+1))^(1/2)/x/(-1+k))+1/(-(-1+k)^2)^(1/2)*ln((-2*k^2+4*k-2+(-k^3+2*k^2-k)*(x^2-1/k)+2*(-(-1+k)^2)^(1/2)*(k^3*(x^2-1/k)^2+(-k^3+2*k^2-k)*(x^2-1/k)-k^2+2*k-1)^(1/2))/(x^2-1/k))","B"
688,1,158,50,0.143000," ","int((1+k^(1/2)*x)/(-1+k^(1/2)*x)/((-x^2+1)*(-k^2*x^2+1))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\arctan \left(\frac{\sqrt{\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)}}{x \left(-1+k \right)}\right)}{-1+k}-\frac{\ln \left(\frac{-2 k^{2}+4 k -2+\left(-k^{3}+2 k^{2}-k \right) \left(x^{2}-\frac{1}{k}\right)+2 \sqrt{-\left(-1+k \right)^{2}}\, \sqrt{k^{3} \left(x^{2}-\frac{1}{k}\right)^{2}+\left(-k^{3}+2 k^{2}-k \right) \left(x^{2}-\frac{1}{k}\right)-k^{2}+2 k -1}}{x^{2}-\frac{1}{k}}\right)}{\sqrt{-\left(-1+k \right)^{2}}}$&$158$\\ default&$\frac{\sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticF \left(x , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}-\frac{2 \sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticPi \left(x , k , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}-\frac{\ln \left(\frac{-2 k^{2}+4 k -2+\left(-k^{3}+2 k^{2}-k \right) \left(x^{2}-\frac{1}{k}\right)+2 \sqrt{-\left(-1+k \right)^{2}}\, \sqrt{k^{3} \left(x^{2}-\frac{1}{k}\right)^{2}+\left(-k^{3}+2 k^{2}-k \right) \left(x^{2}-\frac{1}{k}\right)-k^{2}+2 k -1}}{x^{2}-\frac{1}{k}}\right)}{\sqrt{-\left(-1+k \right)^{2}}}$&$222$\\ \hline \end{longtable}"," ",0,"1/(-1+k)*arctan(((-x^2+1)*(-k^2*x^2+1))^(1/2)/x/(-1+k))-1/(-(-1+k)^2)^(1/2)*ln((-2*k^2+4*k-2+(-k^3+2*k^2-k)*(x^2-1/k)+2*(-(-1+k)^2)^(1/2)*(k^3*(x^2-1/k)^2+(-k^3+2*k^2-k)*(x^2-1/k)-k^2+2*k-1)^(1/2))/(x^2-1/k))","B"
689,1,3008,48,0.743000," ","int((2+x)/(-1+x)/(-a*x^2+x^3+3*x-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$3008$\\ elliptic&$\text{Expression too large to display}$&$3008$\\ \hline \end{longtable}"," ",0,"2/3*I*3^(1/2)*(1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3))*(-I*(x+1/12*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-1/3*a+1/2*I*3^(1/2)*(1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))^(1/2)*((x-1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-1/3*a)/(-1/4*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+9*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-1/2*I*3^(1/2)*(1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3))))^(1/2)*(I*(x+1/12*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-1/3*a-1/2*I*3^(1/2)*(1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))^(1/2)/(-a*x^2+x^3+3*x-1)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/12*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-1/3*a+1/2*I*3^(1/2)*(1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))^(1/2),(-I*3^(1/2)*(1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3))/(-1/4*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+9*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-1/2*I*3^(1/2)*(1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3))))^(1/2))+2*I*3^(1/2)*(1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3))*(-I*(x+1/12*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-1/3*a+1/2*I*3^(1/2)*(1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))^(1/2)*((x-1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-1/3*a)/(-1/4*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+9*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-1/2*I*3^(1/2)*(1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3))))^(1/2)*(I*(x+1/12*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-1/3*a-1/2*I*3^(1/2)*(1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))^(1/2)/(-a*x^2+x^3+3*x-1)^(1/2)/(-1/12*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+3*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+1/3*a-1/2*I*3^(1/2)*(1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3))-1)*EllipticPi(1/3*3^(1/2)*(-I*(x+1/12*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-1/3*a+1/2*I*3^(1/2)*(1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)))^(1/2),-I*3^(1/2)*(1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3))/(-1/12*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+3*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+1/3*a-1/2*I*3^(1/2)*(1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3))-1),(-I*3^(1/2)*(1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3))/(-1/4*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+9*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)-1/2*I*3^(1/2)*(1/6*(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a+108+8*a^3+12*(12*a^3-27*a^2-162*a+405)^(1/2))^(1/3))))^(1/2))","C"
690,1,3008,48,0.755000," ","int((-2+x)/(1+x)/(-a*x^2+x^3+3*x+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$3008$\\ elliptic&$\text{Expression too large to display}$&$3008$\\ \hline \end{longtable}"," ",0,"2/3*I*3^(1/2)*(1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3))*(-I*(x+1/12*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-1/3*a+1/2*I*3^(1/2)*(1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))^(1/2)*((x-1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-1/3*a)/(-1/4*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+9*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-1/2*I*3^(1/2)*(1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3))))^(1/2)*(I*(x+1/12*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-1/3*a-1/2*I*3^(1/2)*(1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))^(1/2)/(-a*x^2+x^3+3*x+1)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/12*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-1/3*a+1/2*I*3^(1/2)*(1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))^(1/2),(-I*3^(1/2)*(1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3))/(-1/4*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+9*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-1/2*I*3^(1/2)*(1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3))))^(1/2))-2*I*3^(1/2)*(1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3))*(-I*(x+1/12*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-1/3*a+1/2*I*3^(1/2)*(1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))^(1/2)*((x-1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-1/3*a)/(-1/4*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+9*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-1/2*I*3^(1/2)*(1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3))))^(1/2)*(I*(x+1/12*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-1/3*a-1/2*I*3^(1/2)*(1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))^(1/2)/(-a*x^2+x^3+3*x+1)^(1/2)/(-1/12*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+3*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+1/3*a-1/2*I*3^(1/2)*(1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3))+1)*EllipticPi(1/3*3^(1/2)*(-I*(x+1/12*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-3*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-1/3*a+1/2*I*3^(1/2)*(1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))*3^(1/2)/(1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)))^(1/2),-I*3^(1/2)*(1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3))/(-1/12*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+3*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+1/3*a-1/2*I*3^(1/2)*(1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3))+1),(-I*3^(1/2)*(1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3))/(-1/4*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+9*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)-1/2*I*3^(1/2)*(1/6*(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3)+6*(1-1/9*a^2)/(-108*a-108+8*a^3+12*(-12*a^3-27*a^2+162*a+405)^(1/2))^(1/3))))^(1/2))","C"
691,1,33,42,4.212000," ","int((x^4-1)*(x^4+1)^(1/4)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\hypergeom \left(\left[-\frac{1}{4}, -\frac{1}{4}\right], \left[\frac{3}{4}\right], -x^{4}\right)}{x}+\frac{x^{3} \hypergeom \left(\left[-\frac{1}{4}, \frac{3}{4}\right], \left[\frac{7}{4}\right], -x^{4}\right)}{3}$&$33$\\ risch&$\frac{x^{8}+5 x^{4}+4}{4 x \left(x^{4}+1\right)^{\frac{3}{4}}}-\frac{x^{3} \hypergeom \left(\left[\frac{3}{4}, \frac{3}{4}\right], \left[\frac{7}{4}\right], -x^{4}\right)}{4}$&$40$\\ trager&$\frac{\left(x^{4}+1\right)^{\frac{1}{4}} \left(x^{4}+4\right)}{4 x}-\frac{3 \ln \left(-2 \left(x^{4}+1\right)^{\frac{3}{4}} x -2 x^{2} \sqrt{x^{4}+1}-2 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}-2 x^{4}-1\right)}{16}+\frac{3 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}\, x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-2 \left(x^{4}+1\right)^{\frac{3}{4}} x +2 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{16}$&$132$\\ \hline \end{longtable}"," ",0,"1/x*hypergeom([-1/4,-1/4],[3/4],-x^4)+1/3*x^3*hypergeom([-1/4,3/4],[7/4],-x^4)","C"
692,0,0,44,0.017000," ","int((a*x^2+2*b)/(a*x^2+b)^(1/4)/(x^4-2*a*x^2-2*b),x)","\[\int \frac{a \,x^{2}+2 b}{\left(a \,x^{2}+b \right)^{\frac{1}{4}} \left(x^{4}-2 a \,x^{2}-2 b \right)}\, dx\]"," ",0,"int((a*x^2+2*b)/(a*x^2+b)^(1/4)/(x^4-2*a*x^2-2*b),x)","F"
693,1,27,44,0.797000," ","int((x^4-x^3)^(1/4)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{4 \mathrm{signum}\left(-1+x \right)^{\frac{1}{4}} x^{\frac{3}{4}} \hypergeom \left(\left[-\frac{1}{4}, \frac{3}{4}\right], \left[\frac{7}{4}\right], x\right)}{3 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{4}}}$&$27$\\ trager&$\left(x^{4}-x^{3}\right)^{\frac{1}{4}}+\frac{\ln \left(\frac{2 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}-2 \sqrt{x^{4}-x^{3}}\, x +2 x^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}-2 x^{3}+x^{2}}{x^{2}}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-2 \sqrt{x^{4}-x^{3}}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x +2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}-2 x^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}}{x^{2}}\right)}{4}$&$157$\\ risch&$\left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}}+\frac{\left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{2}+1\right)+5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{3}{4}}-2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x^{2}-4 \RootOf \left(\textit{\_Z}^{2}+1\right) x +4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x +\RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}}}{\left(-1+x \right)^{2}}\right)}{4}+\frac{\ln \left(\frac{2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{3}{4}}-2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, x +2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x^{2}-2 x^{3}+2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}-4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x +5 x^{2}+2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}}-4 x +1}{\left(-1+x \right)^{2}}\right)}{4}\right) \left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}} \left(x \left(-1+x \right)^{3}\right)^{\frac{1}{4}}}{x \left(-1+x \right)}$&$390$\\ \hline \end{longtable}"," ",0,"4/3*signum(-1+x)^(1/4)/(-signum(-1+x))^(1/4)*x^(3/4)*hypergeom([-1/4,3/4],[7/4],x)","C"
694,1,47,46,0.395000," ","int((x^3-1)*(x^6-1)^(1/2)/x^13,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{8 x^{15}-3 x^{12}-16 x^{9}+9 x^{6}+8 x^{3}-6}{72 x^{12} \sqrt{x^{6}-1}}+\frac{\arcsin \left(\frac{1}{x^{3}}\right)}{24}$&$47$\\ trager&$\frac{\sqrt{x^{6}-1}\, \left(8 x^{9}-3 x^{6}-8 x^{3}+6\right)}{72 x^{12}}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{24}$&$60$\\ meijerg&$\frac{\sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(-\frac{\sqrt{\pi}\, \left(x^{12}-8 x^{6}+8\right)}{8 x^{12}}+\frac{\sqrt{\pi}\, \left(-4 x^{6}+8\right) \sqrt{-x^{6}+1}}{8 x^{12}}-\frac{\sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right)}{2}+\frac{\left(\frac{1}{2}-2 \ln \left(2\right)+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}}{4}+\frac{\sqrt{\pi}}{x^{12}}-\frac{\sqrt{\pi}}{x^{6}}\right)}{12 \sqrt{\pi}\, \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}}-\frac{\sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(-x^{6}+1\right)^{\frac{3}{2}}}{9 \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, x^{9}}$&$153$\\ \hline \end{longtable}"," ",0,"1/72*(8*x^15-3*x^12-16*x^9+9*x^6+8*x^3-6)/x^12/(x^6-1)^(1/2)+1/24*arcsin(1/x^3)","A"
695,1,12056,11,127.877000," ","int((x^3+2)*(-x^4+x)^(1/3)/(x^6-x^5-x^4-2*x^3+x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$12056$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
696,1,15547,11,119.270000," ","int((x^3+2)*(-x^4+x)^(1/3)/(x^6-x^5-x^4-2*x^3+x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$15547$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
697,0,0,42,0.003000," ","int(1/(x^8+2*x^4+1)^(1/8),x)","\[\int \frac{1}{\left(x^{8}+2 x^{4}+1\right)^{\frac{1}{8}}}\, dx\]"," ",0,"int(1/(x^8+2*x^4+1)^(1/8),x)","F"
698,1,22,42,0.040000," ","int(1/x/(x+(x^2+1)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{2}\, \hypergeom \left(\left[\frac{1}{4}, \frac{1}{4}, \frac{3}{4}\right], \left[\frac{5}{4}, \frac{3}{2}\right], -\frac{1}{x^{2}}\right)}{\sqrt{x}}$&$22$\\ \hline \end{longtable}"," ",0,"-2^(1/2)/x^(1/2)*hypergeom([1/4,1/4,3/4],[5/4,3/2],-1/x^2)","C"
699,1,2705,49,0.253000," ","int((k^2*x^2-2*x+1)/((1-x)*x*(-k^2*x+1))^(1/2)/(-1+2*x+(k^2-2)*x^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(k^{2}-2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{-\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}+\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}+\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) \sqrt{k^{2}-1}}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}-\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) \sqrt{k^{2}-1}}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}-\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right)}+\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right)}-\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}+\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}-\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) \sqrt{k^{2}-1}}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}+\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) \sqrt{k^{2}-1}}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}-\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right)}+\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right)}}{k^{2}-2}$&$2705$\\ elliptic&$-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(k^{2}-2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}-\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)^{2}}+\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)^{2}}+\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) \sqrt{k^{2}-1}}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)^{2}}-\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) \sqrt{k^{2}-1}}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)^{2}}-\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}+\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}-\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)^{2}}+\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)^{2}}-\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) \sqrt{k^{2}-1}}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)^{2}}+\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) \sqrt{k^{2}-1}}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)^{2}}-\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}+\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}$&$2727$\\ \hline \end{longtable}"," ",0,"-2/(k^2-2)*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticF((-(x-1/k^2)*k^2)^(1/2),(1/k^2/(1/k^2-1))^(1/2))+2/(k^2-2)*(-4/(-2*k^2/(k^2-2)+2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)-4/(k^2-2)*(k^2-1)^(1/2)+2)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)-1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-(-1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2))/(k^2-2)+4/(-2*k^2/(k^2-2)+2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)-4/(k^2-2)*(k^2-1)^(1/2)+2)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)-1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-(-1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2))/(k^2-2)+4/(-2*k^2/(k^2-2)+2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)-4/(k^2-2)*(k^2-1)^(1/2)+2)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)-1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-(-1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2))/(k^2-2)*(k^2-1)^(1/2)-4/(-2*k^2/(k^2-2)+2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)-4/(k^2-2)*(k^2-1)^(1/2)+2)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)-1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-(-1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2))/(k^2-2)*(k^2-1)^(1/2)-2/(-2*k^2/(k^2-2)+2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)-4/(k^2-2)*(k^2-1)^(1/2)+2)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)-1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-(-1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2))+2/(-2*k^2/(k^2-2)+2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)-4/(k^2-2)*(k^2-1)^(1/2)+2)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)-1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-(-1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2))-4/(-2*k^2/(k^2-2)-2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)+4/(k^2-2)*(k^2-1)^(1/2)+2)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)+1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+(1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2))/(k^2-2)+4/(-2*k^2/(k^2-2)-2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)+4/(k^2-2)*(k^2-1)^(1/2)+2)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)+1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+(1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2))/(k^2-2)-4/(-2*k^2/(k^2-2)-2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)+4/(k^2-2)*(k^2-1)^(1/2)+2)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)+1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+(1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2))/(k^2-2)*(k^2-1)^(1/2)+4/(-2*k^2/(k^2-2)-2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)+4/(k^2-2)*(k^2-1)^(1/2)+2)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)+1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+(1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2))/(k^2-2)*(k^2-1)^(1/2)-2/(-2*k^2/(k^2-2)-2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)+4/(k^2-2)*(k^2-1)^(1/2)+2)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)+1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+(1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2))+2/(-2*k^2/(k^2-2)-2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)+4/(k^2-2)*(k^2-1)^(1/2)+2)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)+1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+(1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2)))","C"
700,0,0,39,0.016000," ","int(1/x/(a*x^3+b)^(3/4),x)","\[\int \frac{1}{x \left(a \,x^{3}+b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x/(a*x^3+b)^(3/4),x)","F"
701,1,44,43,0.306000," ","int((a*x^3-b)*(a*x^3+b)^(1/2)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\sqrt{a \,x^{3}+b}\, \left(2 a \,x^{3}+b \right)}{3 x^{3}}-\frac{a \sqrt{b}\, \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{3}$&$44$\\ elliptic&$\frac{b \sqrt{a \,x^{3}+b}}{3 x^{3}}+\frac{2 a \sqrt{a \,x^{3}+b}}{3}-\frac{a \sqrt{b}\, \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{3}$&$49$\\ default&$-b \left(-\frac{\sqrt{a \,x^{3}+b}}{3 x^{3}}-\frac{a \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{3 \sqrt{b}}\right)+a \left(\frac{2 \sqrt{a \,x^{3}+b}}{3}-\frac{2 \sqrt{b}\, \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{3}\right)$&$73$\\ \hline \end{longtable}"," ",0,"1/3*(a*x^3+b)^(1/2)*(2*a*x^3+b)/x^3-1/3*a*b^(1/2)*arctanh((a*x^3+b)^(1/2)/b^(1/2))","A"
702,1,2705,49,0.176000," ","int((k^2*x^2-2*x+1)/(k^2*x^2-2*x^2+2*x-1)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(k^{2}-2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{-\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}+\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}+\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) \sqrt{k^{2}-1}}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}-\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) \sqrt{k^{2}-1}}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}-\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right)}+\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right)}-\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}+\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}-\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) \sqrt{k^{2}-1}}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}+\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) \sqrt{k^{2}-1}}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}-\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right)}+\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right)}}{k^{2}-2}$&$2705$\\ elliptic&$-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(k^{2}-2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}-\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)^{2}}+\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)^{2}}+\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) \sqrt{k^{2}-1}}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)^{2}}-\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) \sqrt{k^{2}-1}}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)^{2}}-\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}+\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}+\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}-\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}-\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}-\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)^{2}}+\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)^{2}}-\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) \sqrt{k^{2}-1}}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)^{2}}+\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) \sqrt{k^{2}-1}}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)^{2}}-\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}+\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1+\sqrt{k^{2}-1}}{k^{2}-2}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-\frac{2 k^{2}}{k^{2}-2}-\frac{2 k^{2} \sqrt{k^{2}-1}}{k^{2}-2}+\frac{4}{k^{2}-2}+\frac{4 \sqrt{k^{2}-1}}{k^{2}-2}+2\right) k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k^{2}-2}+\frac{\sqrt{k^{2}-1}}{k^{2}-2}\right) \left(k^{2}-2\right)}$&$2727$\\ \hline \end{longtable}"," ",0,"-2/(k^2-2)*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticF((-(x-1/k^2)*k^2)^(1/2),(1/k^2/(1/k^2-1))^(1/2))+2/(k^2-2)*(-4/(-2*k^2/(k^2-2)+2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)-4/(k^2-2)*(k^2-1)^(1/2)+2)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)-1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-(-1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2))/(k^2-2)+4/(-2*k^2/(k^2-2)+2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)-4/(k^2-2)*(k^2-1)^(1/2)+2)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)-1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-(-1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2))/(k^2-2)+4/(-2*k^2/(k^2-2)+2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)-4/(k^2-2)*(k^2-1)^(1/2)+2)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)-1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-(-1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2))/(k^2-2)*(k^2-1)^(1/2)-4/(-2*k^2/(k^2-2)+2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)-4/(k^2-2)*(k^2-1)^(1/2)+2)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)-1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-(-1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2))/(k^2-2)*(k^2-1)^(1/2)-2/(-2*k^2/(k^2-2)+2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)-4/(k^2-2)*(k^2-1)^(1/2)+2)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)-1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-(-1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2))+2/(-2*k^2/(k^2-2)+2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)-4/(k^2-2)*(k^2-1)^(1/2)+2)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)-1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-(-1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2))-4/(-2*k^2/(k^2-2)-2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)+4/(k^2-2)*(k^2-1)^(1/2)+2)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)+1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+(1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2))/(k^2-2)+4/(-2*k^2/(k^2-2)-2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)+4/(k^2-2)*(k^2-1)^(1/2)+2)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)+1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+(1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2))/(k^2-2)-4/(-2*k^2/(k^2-2)-2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)+4/(k^2-2)*(k^2-1)^(1/2)+2)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)+1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+(1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2))/(k^2-2)*(k^2-1)^(1/2)+4/(-2*k^2/(k^2-2)-2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)+4/(k^2-2)*(k^2-1)^(1/2)+2)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)+1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+(1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2))/(k^2-2)*(k^2-1)^(1/2)-2/(-2*k^2/(k^2-2)-2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)+4/(k^2-2)*(k^2-1)^(1/2)+2)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)+1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+(1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2))+2/(-2*k^2/(k^2-2)-2/(k^2-2)*k^2*(k^2-1)^(1/2)+4/(k^2-2)+4/(k^2-2)*(k^2-1)^(1/2)+2)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/(k^2-2)+1/(k^2-2)*(k^2-1)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+(1+(k^2-1)^(1/2))/(k^2-2)),(1/k^2/(1/k^2-1))^(1/2)))","C"
703,1,73,43,21.327000," ","int((2+x)/x/(x^4+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\sqrt{2}\, \Gamma \left(\frac{3}{4}\right) \left(-\frac{\pi  \sqrt{2}\, x^{4} \hypergeom \left(\left[1, 1, \frac{5}{4}\right], \left[2, 2\right], -x^{4}\right)}{4 \Gamma \left(\frac{3}{4}\right)}+\frac{\left(-3 \ln \left(2\right)-\frac{\pi}{2}+4 \ln \left(x \right)\right) \pi  \sqrt{2}}{\Gamma \left(\frac{3}{4}\right)}\right)}{4 \pi}+x \hypergeom \left(\left[\frac{1}{4}, \frac{1}{4}\right], \left[\frac{5}{4}\right], -x^{4}\right)$&$73$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}\, x^{10}-8 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}\, x^{9}+16 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}\, x^{8}-24 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}\, x^{7}+32 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}\, x^{6}-40 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}\, x^{5}+40 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}\, x^{4}-32 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}\, x^{3}-32 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}\, x +32 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}\, x^{2}+24 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{9}-33 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{8}+40 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{7}-48 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}+56 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{5}-48 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+8 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{11}-16 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{10}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{12}+16 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}-8 x^{10} \left(x^{4}+1\right)^{\frac{1}{4}}-40 x^{6} \left(x^{4}+1\right)^{\frac{1}{4}}-32 x^{2} \left(x^{4}+1\right)^{\frac{1}{4}}-16 \left(x^{4}+1\right)^{\frac{1}{4}}+16 \left(x^{4}+1\right)^{\frac{3}{4}}+32 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}-16 \RootOf \left(\textit{\_Z}^{2}+1\right)+32 \RootOf \left(\textit{\_Z}^{2}+1\right) x +32 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-32 \left(x^{4}+1\right)^{\frac{3}{4}} x -32 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-2 \left(x^{4}+1\right)^{\frac{3}{4}} x^{9}+2 \left(x^{4}+1\right)^{\frac{1}{4}} x^{11}+8 \left(x^{4}+1\right)^{\frac{3}{4}} x^{8}-16 \left(x^{4}+1\right)^{\frac{3}{4}} x^{7}+16 \left(x^{4}+1\right)^{\frac{1}{4}} x^{9}+24 \left(x^{4}+1\right)^{\frac{3}{4}} x^{6}-24 \left(x^{4}+1\right)^{\frac{1}{4}} x^{8}-32 \left(x^{4}+1\right)^{\frac{3}{4}} x^{5}+32 \left(x^{4}+1\right)^{\frac{1}{4}} x^{7}+36 \left(x^{4}+1\right)^{\frac{3}{4}} x^{4}-32 \left(x^{4}+1\right)^{\frac{3}{4}} x^{3}+48 \left(x^{4}+1\right)^{\frac{1}{4}} x^{5}+32 \left(x^{4}+1\right)^{\frac{3}{4}} x^{2}-44 \left(x^{4}+1\right)^{\frac{1}{4}} x^{4}+32 \left(x^{4}+1\right)^{\frac{1}{4}} x}{x^{8}}\right)}{4}-\frac{\ln \left(\frac{-16+32 x -40 x^{4} \sqrt{x^{4}+1}+32 \sqrt{x^{4}+1}\, x -8 x^{10} \left(x^{4}+1\right)^{\frac{1}{4}}-40 x^{6} \left(x^{4}+1\right)^{\frac{1}{4}}-32 x^{2} \left(x^{4}+1\right)^{\frac{1}{4}}+24 x^{9}-16 x^{10}+40 x^{7}-16 \sqrt{x^{4}+1}-16 \left(x^{4}+1\right)^{\frac{1}{4}}+56 x^{5}-48 x^{6}-16 \left(x^{4}+1\right)^{\frac{3}{4}}-32 x^{2}+32 x^{3}-33 x^{8}-48 x^{4}+32 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}-32 x^{2} \sqrt{x^{4}+1}+8 x^{11}-2 x^{12}+32 \left(x^{4}+1\right)^{\frac{3}{4}} x +2 \left(x^{4}+1\right)^{\frac{3}{4}} x^{9}+2 \left(x^{4}+1\right)^{\frac{1}{4}} x^{11}-8 \left(x^{4}+1\right)^{\frac{3}{4}} x^{8}+16 \left(x^{4}+1\right)^{\frac{3}{4}} x^{7}+16 \left(x^{4}+1\right)^{\frac{1}{4}} x^{9}-24 \left(x^{4}+1\right)^{\frac{3}{4}} x^{6}-24 \left(x^{4}+1\right)^{\frac{1}{4}} x^{8}+32 \left(x^{4}+1\right)^{\frac{3}{4}} x^{5}+32 \left(x^{4}+1\right)^{\frac{1}{4}} x^{7}-36 \left(x^{4}+1\right)^{\frac{3}{4}} x^{4}+32 \left(x^{4}+1\right)^{\frac{3}{4}} x^{3}+48 \left(x^{4}+1\right)^{\frac{1}{4}} x^{5}-32 \left(x^{4}+1\right)^{\frac{3}{4}} x^{2}-44 \left(x^{4}+1\right)^{\frac{1}{4}} x^{4}+32 \left(x^{4}+1\right)^{\frac{1}{4}} x -2 \sqrt{x^{4}+1}\, x^{10}+8 \sqrt{x^{4}+1}\, x^{9}-16 \sqrt{x^{4}+1}\, x^{8}+24 \sqrt{x^{4}+1}\, x^{7}-32 \sqrt{x^{4}+1}\, x^{6}+40 \sqrt{x^{4}+1}\, x^{5}+32 \sqrt{x^{4}+1}\, x^{3}}{x^{8}}\right)}{4}$&$1050$\\ \hline \end{longtable}"," ",0,"1/4/Pi*2^(1/2)*GAMMA(3/4)*(-1/4*Pi*2^(1/2)/GAMMA(3/4)*x^4*hypergeom([1,1,5/4],[2,2],-x^4)+(-3*ln(2)-1/2*Pi+4*ln(x))*Pi*2^(1/2)/GAMMA(3/4))+x*hypergeom([1/4,1/4],[5/4],-x^4)","C"
704,1,17,43,1.898000," ","int(x^6*(x^4+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{x^{7} \hypergeom \left(\left[-\frac{1}{4}, \frac{7}{4}\right], \left[\frac{11}{4}\right], -x^{4}\right)}{7}$&$17$\\ risch&$\frac{x^{3} \left(4 x^{4}+1\right) \left(x^{4}+1\right)^{\frac{1}{4}}}{32}-\frac{x^{3} \hypergeom \left(\left[\frac{3}{4}, \frac{3}{4}\right], \left[\frac{7}{4}\right], -x^{4}\right)}{32}$&$37$\\ trager&$\frac{x^{3} \left(4 x^{4}+1\right) \left(x^{4}+1\right)^{\frac{1}{4}}}{32}-\frac{3 \ln \left(2 \left(x^{4}+1\right)^{\frac{3}{4}} x +2 x^{2} \sqrt{x^{4}+1}+2 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}+2 x^{4}+1\right)}{128}+\frac{3 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}\, x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \left(x^{4}+1\right)^{\frac{3}{4}} x -2 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{128}$&$132$\\ \hline \end{longtable}"," ",0,"1/7*x^7*hypergeom([-1/4,7/4],[11/4],-x^4)","C"
705,1,33,43,5.468000," ","int((x^4-x)^(1/4)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{4 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{1}{4}, -\frac{1}{4}\right], \left[\frac{3}{4}\right], x^{3}\right)}{3 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}} x^{\frac{3}{4}}}$&$33$\\ trager&$-\frac{4 \left(x^{4}-x \right)^{\frac{1}{4}}}{3 x}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(2 \sqrt{x^{4}-x}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-2 \left(x^{4}-x \right)^{\frac{3}{4}}+2 x^{2} \left(x^{4}-x \right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{3}-\frac{\ln \left(-2 \left(x^{4}-x \right)^{\frac{3}{4}}+2 x \sqrt{x^{4}-x}-2 x^{2} \left(x^{4}-x \right)^{\frac{1}{4}}+2 x^{3}-1\right)}{3}$&$133$\\ risch&$-\frac{4 \left(x \left(x^{3}-1\right)\right)^{\frac{1}{4}}}{3 x}+\frac{\left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{2 x^{9}-2 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}-5 x^{6}-2 \sqrt{x^{12}-3 x^{9}+3 x^{6}-x^{3}}\, x^{3}+4 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{3}{4}}+4 x^{3}+2 \sqrt{x^{12}-3 x^{9}+3 x^{6}-x^{3}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}}-1}{\left(-1+x \right)^{2} \left(x^{2}+x +1\right)^{2}}\right)}{3}-\frac{\ln \left(-\frac{-2 x^{9}+2 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}} x^{6}+5 x^{6}-2 \sqrt{x^{12}-3 x^{9}+3 x^{6}-x^{3}}\, x^{3}-4 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}} x^{3}+2 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{3}{4}}-4 x^{3}+2 \sqrt{x^{12}-3 x^{9}+3 x^{6}-x^{3}}+2 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}}+1}{\left(-1+x \right)^{2} \left(x^{2}+x +1\right)^{2}}\right)}{3}\right) \left(x \left(x^{3}-1\right)\right)^{\frac{1}{4}} \left(x^{3} \left(x^{3}-1\right)^{3}\right)^{\frac{1}{4}}}{x \left(x^{3}-1\right)}$&$444$\\ \hline \end{longtable}"," ",0,"-4/3*signum(x^3-1)^(1/4)/(-signum(x^3-1))^(1/4)/x^(3/4)*hypergeom([-1/4,-1/4],[3/4],x^3)","C"
706,1,33,43,5.235000," ","int(x*(x^4-x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{4 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}} x^{\frac{9}{4}} \hypergeom \left(\left[-\frac{1}{4}, \frac{3}{4}\right], \left[\frac{7}{4}\right], x^{3}\right)}{9 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}}}$&$33$\\ trager&$\frac{x^{2} \left(x^{4}-x \right)^{\frac{1}{4}}}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(2 \sqrt{x^{4}-x}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-2 \left(x^{4}-x \right)^{\frac{3}{4}}+2 x^{2} \left(x^{4}-x \right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{12}+\frac{\ln \left(-2 \left(x^{4}-x \right)^{\frac{3}{4}}+2 x \sqrt{x^{4}-x}-2 x^{2} \left(x^{4}-x \right)^{\frac{1}{4}}+2 x^{3}-1\right)}{12}$&$133$\\ risch&$\frac{x^{2} \left(x \left(x^{3}-1\right)\right)^{\frac{1}{4}}}{3}+\frac{\left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{2 x^{9}-2 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}-5 x^{6}-2 \sqrt{x^{12}-3 x^{9}+3 x^{6}-x^{3}}\, x^{3}+4 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{3}{4}}+4 x^{3}+2 \sqrt{x^{12}-3 x^{9}+3 x^{6}-x^{3}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}}-1}{\left(-1+x \right)^{2} \left(x^{2}+x +1\right)^{2}}\right)}{12}+\frac{\ln \left(-\frac{-2 x^{9}+2 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}} x^{6}+5 x^{6}-2 \sqrt{x^{12}-3 x^{9}+3 x^{6}-x^{3}}\, x^{3}-4 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}} x^{3}+2 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{3}{4}}-4 x^{3}+2 \sqrt{x^{12}-3 x^{9}+3 x^{6}-x^{3}}+2 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}}+1}{\left(-1+x \right)^{2} \left(x^{2}+x +1\right)^{2}}\right)}{12}\right) \left(x \left(x^{3}-1\right)\right)^{\frac{1}{4}} \left(x^{3} \left(x^{3}-1\right)^{3}\right)^{\frac{1}{4}}}{x \left(x^{3}-1\right)}$&$444$\\ \hline \end{longtable}"," ",0,"4/9*signum(x^3-1)^(1/4)/(-signum(x^3-1))^(1/4)*x^(9/4)*hypergeom([-1/4,3/4],[7/4],x^3)","C"
707,1,52,47,0.337000," ","int((a*x^3-b)*(x^4-x)^(1/2)/x^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(a \,x^{3}+2 b \right) \sqrt{x^{4}-x}}{3 x^{2}}-\frac{\left(a +2 b \right) \ln \left(-2 x^{3}-2 x \sqrt{x^{4}-x}+1\right)}{6}$&$52$\\ meijerg&$\frac{i a \sqrt{\mathrm{signum}\left(x^{3}-1\right)}\, \left(-2 i \sqrt{\pi}\, x^{\frac{3}{2}} \sqrt{-x^{3}+1}-2 i \sqrt{\pi}\, \arcsin \left(x^{\frac{3}{2}}\right)\right)}{6 \sqrt{\pi}\, \sqrt{-\mathrm{signum}\left(x^{3}-1\right)}}+\frac{i b \sqrt{\mathrm{signum}\left(x^{3}-1\right)}\, \left(-\frac{4 i \sqrt{\pi}\, \sqrt{-x^{3}+1}}{x^{\frac{3}{2}}}-4 i \sqrt{\pi}\, \arcsin \left(x^{\frac{3}{2}}\right)\right)}{6 \sqrt{\pi}\, \sqrt{-\mathrm{signum}\left(x^{3}-1\right)}}$&$110$\\ risch&$\frac{\left(x^{3}-1\right) \left(a \,x^{3}+2 b \right)}{3 x \sqrt{x \left(x^{3}-1\right)}}+\frac{2 \left(-\frac{a}{2}-b \right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$324$\\ elliptic&$\frac{2 b \sqrt{x^{4}-x}}{3 x^{2}}+\frac{a x \sqrt{x^{4}-x}}{3}+\frac{2 \left(-\frac{a}{2}-b \right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$324$\\ default&$a \left(\frac{x \sqrt{x^{4}-x}}{3}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-b \left(-\frac{2 \sqrt{x^{4}-x}}{3 x^{2}}+\frac{2 \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)$&$609$\\ \hline \end{longtable}"," ",0,"1/3*(a*x^3+2*b)*(x^4-x)^(1/2)/x^2-1/6*(a+2*b)*ln(-2*x^3-2*x*(x^4-x)^(1/2)+1)","A"
708,1,27,49,0.728000," ","int((x^4-x^3)^(1/4)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{4 \mathrm{signum}\left(-1+x \right)^{\frac{1}{4}} \hypergeom \left(\left[-\frac{1}{4}, -\frac{1}{4}\right], \left[\frac{3}{4}\right], x\right)}{\left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{4}} x^{\frac{1}{4}}}$&$27$\\ trager&$-\frac{4 \left(x^{4}-x^{3}\right)^{\frac{1}{4}}}{x}-\ln \left(\frac{2 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}-2 \sqrt{x^{4}-x^{3}}\, x +2 x^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}-2 x^{3}+x^{2}}{x^{2}}\right)+\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \sqrt{x^{4}-x^{3}}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}-2 x^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}}{x^{2}}\right)$&$160$\\ risch&$-\frac{4 \left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}}}{x}+\frac{\left(-\ln \left(\frac{2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{3}{4}}-2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, x +2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x^{2}-2 x^{3}+2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}-4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x +5 x^{2}+2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}}-4 x +1}{\left(-1+x \right)^{2}}\right)+\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{2}+1\right)+5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{3}{4}}+2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x^{2}-4 \RootOf \left(\textit{\_Z}^{2}+1\right) x -4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x +\RootOf \left(\textit{\_Z}^{2}+1\right)+2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}}}{\left(-1+x \right)^{2}}\right)\right) \left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}} \left(x \left(-1+x \right)^{3}\right)^{\frac{1}{4}}}{x \left(-1+x \right)}$&$395$\\ \hline \end{longtable}"," ",0,"-4*signum(-1+x)^(1/4)/(-signum(-1+x))^(1/4)/x^(1/4)*hypergeom([-1/4,-1/4],[3/4],x)","C"
709,1,91,51,1.174000," ","int(x/(x^4+6*x^3-11*x^2+18*x-17)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\ln \left(-2 x^{4}+2 \sqrt{x^{4}+6 x^{3}-11 x^{2}+18 x -17}\, x^{2}-24 x^{3}+18 x \sqrt{x^{4}+6 x^{3}-11 x^{2}+18 x -17}-68 x^{2}+34 \sqrt{x^{4}+6 x^{3}-11 x^{2}+18 x -17}-11\right)}{4}$&$91$\\ default&$\text{Expression too large to display}$&$1610$\\ elliptic&$\text{Expression too large to display}$&$1610$\\ \hline \end{longtable}"," ",0,"-1/4*ln(-2*x^4+2*(x^4+6*x^3-11*x^2+18*x-17)^(1/2)*x^2-24*x^3+18*x*(x^4+6*x^3-11*x^2+18*x-17)^(1/2)-68*x^2+34*(x^4+6*x^3-11*x^2+18*x-17)^(1/2)-11)","A"
710,1,162,47,17.705000," ","int((x^4-x^2-x-1)^(1/2)*(2*x^4+x+2)/(x^4-x-1)/(x^4+x^2-x-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \sqrt{x^{4}-x^{2}-x -1}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right) x -\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{4}-x -1}\right)+\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+2\right) x^{4}+3 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{2}+4 \sqrt{x^{4}-x^{2}-x -1}\, x +\RootOf \left(\textit{\_Z}^{2}+2\right) x +\RootOf \left(\textit{\_Z}^{2}+2\right)}{\left(-1+x \right) \left(x^{3}+x^{2}+2 x +1\right)}\right)$&$162$\\ default&$\text{Expression too large to display}$&$7840$\\ elliptic&$\text{Expression too large to display}$&$1138832$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2+1)*ln(-(RootOf(_Z^2+1)*x^4-2*RootOf(_Z^2+1)*x^2+2*(x^4-x^2-x-1)^(1/2)*x-RootOf(_Z^2+1)*x-RootOf(_Z^2+1))/(x^4-x-1))+RootOf(_Z^2+2)*ln(-(-RootOf(_Z^2+2)*x^4+3*RootOf(_Z^2+2)*x^2+4*(x^4-x^2-x-1)^(1/2)*x+RootOf(_Z^2+2)*x+RootOf(_Z^2+2))/(-1+x)/(x^3+x^2+2*x+1))","C"
711,0,0,39,0.018000," ","int(1/x/(a*x^4+b)^(3/4),x)","\[\int \frac{1}{x \left(a \,x^{4}+b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x/(a*x^4+b)^(3/4),x)","F"
712,0,0,39,0.016000," ","int(1/x/(a*x^4+b)^(1/4),x)","\[\int \frac{1}{x \left(a \,x^{4}+b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/x/(a*x^4+b)^(1/4),x)","F"
713,0,0,39,0.015000," ","int(1/x/(a*x^5+b)^(3/4),x)","\[\int \frac{1}{x \left(a \,x^{5}+b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x/(a*x^5+b)^(3/4),x)","F"
714,1,63,43,0.516000," ","int((2*x^3+1)*(x^6-1)^(1/2)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\left(\frac{x^{3}}{3}+\frac{1}{3}\right) \sqrt{x^{6}-1}+\frac{\ln \left(-x^{3}+\sqrt{x^{6}-1}\right)}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)-\sqrt{x^{6}-1}}{x^{3}}\right)}{3}$&$63$\\ meijerg&$-\frac{\sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(4 \sqrt{\pi}-4 \sqrt{\pi}\, \sqrt{-x^{6}+1}+4 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right)-2 \left(2-2 \ln \left(2\right)+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}\right)}{12 \sqrt{\pi}\, \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}}+\frac{i \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(-2 i \sqrt{\pi}\, x^{3} \sqrt{-x^{6}+1}-2 i \sqrt{\pi}\, \arcsin \left(x^{3}\right)\right)}{6 \sqrt{\pi}\, \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}}$&$136$\\ \hline \end{longtable}"," ",0,"(1/3*x^3+1/3)*(x^6-1)^(1/2)+1/3*ln(-x^3+(x^6-1)^(1/2))+1/3*RootOf(_Z^2+1)*ln(-(RootOf(_Z^2+1)-(x^6-1)^(1/2))/x^3)","C"
715,1,2240,9,15.020000," ","int((x^3-2)*(x^4+x^3+x)^(1/3)/(x^6+x^5+x^4+2*x^3+x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2240$\\ \hline \end{longtable}"," ",0,"18*RootOf(27*_Z^6+9*_Z^3+1)^5*ln((75087*RootOf(27*_Z^6+9*_Z^3+1)^7*x^3-150174*RootOf(27*_Z^6+9*_Z^3+1)^7*x^2+75087*RootOf(27*_Z^6+9*_Z^3+1)^7-106272*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)^5*x+56304*RootOf(27*_Z^6+9*_Z^3+1)^4*x^3-54207*RootOf(27*_Z^6+9*_Z^3+1)^4*x^2+31275*(x^4+x^3+x)^(2/3)*RootOf(27*_Z^6+9*_Z^3+1)^3+56304*RootOf(27*_Z^6+9*_Z^3+1)^4-13191*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)^2*x+10192*RootOf(27*_Z^6+9*_Z^3+1)*x^3-2548*RootOf(27*_Z^6+9*_Z^3+1)*x^2+7411*(x^4+x^3+x)^(2/3)+10192*RootOf(27*_Z^6+9*_Z^3+1))/(9*RootOf(27*_Z^6+9*_Z^3+1)^3*x^3-18*RootOf(27*_Z^6+9*_Z^3+1)^3*x^2+9*RootOf(27*_Z^6+9*_Z^3+1)^3-x^3-5*x^2-1))-9*RootOf(27*_Z^6+9*_Z^3+1)^5*ln(-(16659*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)^5*x+2880*RootOf(27*_Z^6+9*_Z^3+1)^4*x^3+5760*RootOf(27*_Z^6+9*_Z^3+1)^4*x^2-2673*(x^4+x^3+x)^(2/3)*RootOf(27*_Z^6+9*_Z^3+1)^3+2880*RootOf(27*_Z^6+9*_Z^3+1)^4+2811*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)^2*x+23*RootOf(27*_Z^6+9*_Z^3+1)*x^3+46*RootOf(27*_Z^6+9*_Z^3+1)*x^2-914*(x^4+x^3+x)^(2/3)+23*RootOf(27*_Z^6+9*_Z^3+1))/(9*RootOf(27*_Z^6+9*_Z^3+1)^3*x^3-18*RootOf(27*_Z^6+9*_Z^3+1)^3*x^2+9*RootOf(27*_Z^6+9*_Z^3+1)^3-x^3-5*x^2-1))-9*RootOf(27*_Z^6+9*_Z^3+1)^4*ln((207*RootOf(27*_Z^6+9*_Z^3+1)^5*x^3+414*RootOf(27*_Z^6+9*_Z^3+1)^5*x^2-207*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)^4*x+207*RootOf(27*_Z^6+9*_Z^3+1)^5-2673*(x^4+x^3+x)^(2/3)*RootOf(27*_Z^6+9*_Z^3+1)^3+960*RootOf(27*_Z^6+9*_Z^3+1)^2*x^3+1920*RootOf(27*_Z^6+9*_Z^3+1)^2*x^2-960*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)*x+960*RootOf(27*_Z^6+9*_Z^3+1)^2+23*(x^4+x^3+x)^(2/3))/(9*RootOf(27*_Z^6+9*_Z^3+1)^3*x^3-18*RootOf(27*_Z^6+9*_Z^3+1)^3*x^2+9*RootOf(27*_Z^6+9*_Z^3+1)^3+4*x^3-x^2+4))+3*RootOf(27*_Z^6+9*_Z^3+1)^2*ln((75087*RootOf(27*_Z^6+9*_Z^3+1)^7*x^3-150174*RootOf(27*_Z^6+9*_Z^3+1)^7*x^2+75087*RootOf(27*_Z^6+9*_Z^3+1)^7-106272*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)^5*x+56304*RootOf(27*_Z^6+9*_Z^3+1)^4*x^3-54207*RootOf(27*_Z^6+9*_Z^3+1)^4*x^2+31275*(x^4+x^3+x)^(2/3)*RootOf(27*_Z^6+9*_Z^3+1)^3+56304*RootOf(27*_Z^6+9*_Z^3+1)^4-13191*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)^2*x+10192*RootOf(27*_Z^6+9*_Z^3+1)*x^3-2548*RootOf(27*_Z^6+9*_Z^3+1)*x^2+7411*(x^4+x^3+x)^(2/3)+10192*RootOf(27*_Z^6+9*_Z^3+1))/(9*RootOf(27*_Z^6+9*_Z^3+1)^3*x^3-18*RootOf(27*_Z^6+9*_Z^3+1)^3*x^2+9*RootOf(27*_Z^6+9*_Z^3+1)^3-x^3-5*x^2-1))-3*RootOf(27*_Z^6+9*_Z^3+1)^2*ln(-(16659*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)^5*x+2880*RootOf(27*_Z^6+9*_Z^3+1)^4*x^3+5760*RootOf(27*_Z^6+9*_Z^3+1)^4*x^2-2673*(x^4+x^3+x)^(2/3)*RootOf(27*_Z^6+9*_Z^3+1)^3+2880*RootOf(27*_Z^6+9*_Z^3+1)^4+2811*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)^2*x+23*RootOf(27*_Z^6+9*_Z^3+1)*x^3+46*RootOf(27*_Z^6+9*_Z^3+1)*x^2-914*(x^4+x^3+x)^(2/3)+23*RootOf(27*_Z^6+9*_Z^3+1))/(9*RootOf(27*_Z^6+9*_Z^3+1)^3*x^3-18*RootOf(27*_Z^6+9*_Z^3+1)^3*x^2+9*RootOf(27*_Z^6+9*_Z^3+1)^3-x^3-5*x^2-1))+RootOf(27*_Z^6+9*_Z^3+1)*ln((206388*RootOf(27*_Z^6+9*_Z^3+1)^8*x^3-412776*RootOf(27*_Z^6+9*_Z^3+1)^8*x^2+206388*RootOf(27*_Z^6+9*_Z^3+1)^8+2097*RootOf(27*_Z^6+9*_Z^3+1)^5*x^3-164718*RootOf(27*_Z^6+9*_Z^3+1)^5*x^2+27126*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)^4*x+2097*RootOf(27*_Z^6+9*_Z^3+1)^5-31275*(x^4+x^3+x)^(2/3)*RootOf(27*_Z^6+9*_Z^3+1)^3-2781*RootOf(27*_Z^6+9*_Z^3+1)^2*x^3-13905*RootOf(27*_Z^6+9*_Z^3+1)^2*x^2-1383*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)*x-2781*RootOf(27*_Z^6+9*_Z^3+1)^2-3014*(x^4+x^3+x)^(2/3))/(9*RootOf(27*_Z^6+9*_Z^3+1)^3*x^3-18*RootOf(27*_Z^6+9*_Z^3+1)^3*x^2+9*RootOf(27*_Z^6+9*_Z^3+1)^3+4*x^3-x^2+4))-2*RootOf(27*_Z^6+9*_Z^3+1)*ln((207*RootOf(27*_Z^6+9*_Z^3+1)^5*x^3+414*RootOf(27*_Z^6+9*_Z^3+1)^5*x^2-207*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)^4*x+207*RootOf(27*_Z^6+9*_Z^3+1)^5-2673*(x^4+x^3+x)^(2/3)*RootOf(27*_Z^6+9*_Z^3+1)^3+960*RootOf(27*_Z^6+9*_Z^3+1)^2*x^3+1920*RootOf(27*_Z^6+9*_Z^3+1)^2*x^2-960*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)*x+960*RootOf(27*_Z^6+9*_Z^3+1)^2+23*(x^4+x^3+x)^(2/3))/(9*RootOf(27*_Z^6+9*_Z^3+1)^3*x^3-18*RootOf(27*_Z^6+9*_Z^3+1)^3*x^2+9*RootOf(27*_Z^6+9*_Z^3+1)^3+4*x^3-x^2+4))","B"
716,1,2189,9,14.835000," ","int((x^3-2)*(x^4+x^3+x)^(1/3)/(x^6+x^5+x^4+2*x^3+x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2189$\\ \hline \end{longtable}"," ",0,"-9*RootOf(27*_Z^6+9*_Z^3+1)^5*ln((3*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)^2*x-RootOf(27*_Z^6+9*_Z^3+1)*x^3-2*RootOf(27*_Z^6+9*_Z^3+1)*x^2+(x^4+x^3+x)^(2/3)-RootOf(27*_Z^6+9*_Z^3+1))/(9*RootOf(27*_Z^6+9*_Z^3+1)^3*x^3-18*RootOf(27*_Z^6+9*_Z^3+1)^3*x^2+9*RootOf(27*_Z^6+9*_Z^3+1)^3-x^3-5*x^2-1))-9*ln(-(131301*RootOf(27*_Z^6+9*_Z^3+1)^7*x^3-262602*RootOf(27*_Z^6+9*_Z^3+1)^7*x^2+131301*RootOf(27*_Z^6+9*_Z^3+1)^7-93825*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)^5*x+79191*RootOf(27*_Z^6+9*_Z^3+1)^4*x^3-56259*RootOf(27*_Z^6+9*_Z^3+1)^4*x^2-31275*(x^4+x^3+x)^(2/3)*RootOf(27*_Z^6+9*_Z^3+1)^3+79191*RootOf(27*_Z^6+9*_Z^3+1)^4-22233*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)^2*x+9260*RootOf(27*_Z^6+9*_Z^3+1)*x^3-2315*RootOf(27*_Z^6+9*_Z^3+1)*x^2-7411*(x^4+x^3+x)^(2/3)+9260*RootOf(27*_Z^6+9*_Z^3+1))/(9*RootOf(27*_Z^6+9*_Z^3+1)^3*x^3-18*RootOf(27*_Z^6+9*_Z^3+1)^3*x^2+9*RootOf(27*_Z^6+9*_Z^3+1)^3-x^3-5*x^2-1))*RootOf(27*_Z^6+9*_Z^3+1)^5-9*ln(-(187515*RootOf(27*_Z^6+9*_Z^3+1)^8*x^3-375030*RootOf(27*_Z^6+9*_Z^3+1)^8*x^2+187515*RootOf(27*_Z^6+9*_Z^3+1)^8+22932*RootOf(27*_Z^6+9*_Z^3+1)^5*x^3-191709*RootOf(27*_Z^6+9*_Z^3+1)^5*x^2-39573*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)^4*x+22932*RootOf(27*_Z^6+9*_Z^3+1)^5+31275*(x^4+x^3+x)^(2/3)*RootOf(27*_Z^6+9*_Z^3+1)^3-4863*RootOf(27*_Z^6+9*_Z^3+1)^2*x^3-24315*RootOf(27*_Z^6+9*_Z^3+1)^2*x^2-11808*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)*x-4863*RootOf(27*_Z^6+9*_Z^3+1)^2+3014*(x^4+x^3+x)^(2/3))/(9*RootOf(27*_Z^6+9*_Z^3+1)^3*x^3-18*RootOf(27*_Z^6+9*_Z^3+1)^3*x^2+9*RootOf(27*_Z^6+9*_Z^3+1)^3+4*x^3-x^2+4))*RootOf(27*_Z^6+9*_Z^3+1)^4+9*ln((8226*RootOf(27*_Z^6+9*_Z^3+1)^5*x^3+16452*RootOf(27*_Z^6+9*_Z^3+1)^5*x^2+8433*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)^4*x+8226*RootOf(27*_Z^6+9*_Z^3+1)^5-2673*(x^4+x^3+x)^(2/3)*RootOf(27*_Z^6+9*_Z^3+1)^3+891*RootOf(27*_Z^6+9*_Z^3+1)^2*x^3+1782*RootOf(27*_Z^6+9*_Z^3+1)^2*x^2+1851*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)*x+891*RootOf(27*_Z^6+9*_Z^3+1)^2+23*(x^4+x^3+x)^(2/3))/(9*RootOf(27*_Z^6+9*_Z^3+1)^3*x^3-18*RootOf(27*_Z^6+9*_Z^3+1)^3*x^2+9*RootOf(27*_Z^6+9*_Z^3+1)^3+4*x^3-x^2+4))*RootOf(27*_Z^6+9*_Z^3+1)^4-3*ln(-(131301*RootOf(27*_Z^6+9*_Z^3+1)^7*x^3-262602*RootOf(27*_Z^6+9*_Z^3+1)^7*x^2+131301*RootOf(27*_Z^6+9*_Z^3+1)^7-93825*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)^5*x+79191*RootOf(27*_Z^6+9*_Z^3+1)^4*x^3-56259*RootOf(27*_Z^6+9*_Z^3+1)^4*x^2-31275*(x^4+x^3+x)^(2/3)*RootOf(27*_Z^6+9*_Z^3+1)^3+79191*RootOf(27*_Z^6+9*_Z^3+1)^4-22233*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)^2*x+9260*RootOf(27*_Z^6+9*_Z^3+1)*x^3-2315*RootOf(27*_Z^6+9*_Z^3+1)*x^2-7411*(x^4+x^3+x)^(2/3)+9260*RootOf(27*_Z^6+9*_Z^3+1))/(9*RootOf(27*_Z^6+9*_Z^3+1)^3*x^3-18*RootOf(27*_Z^6+9*_Z^3+1)^3*x^2+9*RootOf(27*_Z^6+9*_Z^3+1)^3-x^3-5*x^2-1))*RootOf(27*_Z^6+9*_Z^3+1)^2-2*ln(-(187515*RootOf(27*_Z^6+9*_Z^3+1)^8*x^3-375030*RootOf(27*_Z^6+9*_Z^3+1)^8*x^2+187515*RootOf(27*_Z^6+9*_Z^3+1)^8+22932*RootOf(27*_Z^6+9*_Z^3+1)^5*x^3-191709*RootOf(27*_Z^6+9*_Z^3+1)^5*x^2-39573*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)^4*x+22932*RootOf(27*_Z^6+9*_Z^3+1)^5+31275*(x^4+x^3+x)^(2/3)*RootOf(27*_Z^6+9*_Z^3+1)^3-4863*RootOf(27*_Z^6+9*_Z^3+1)^2*x^3-24315*RootOf(27*_Z^6+9*_Z^3+1)^2*x^2-11808*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)*x-4863*RootOf(27*_Z^6+9*_Z^3+1)^2+3014*(x^4+x^3+x)^(2/3))/(9*RootOf(27*_Z^6+9*_Z^3+1)^3*x^3-18*RootOf(27*_Z^6+9*_Z^3+1)^3*x^2+9*RootOf(27*_Z^6+9*_Z^3+1)^3+4*x^3-x^2+4))*RootOf(27*_Z^6+9*_Z^3+1)+ln((8226*RootOf(27*_Z^6+9*_Z^3+1)^5*x^3+16452*RootOf(27*_Z^6+9*_Z^3+1)^5*x^2+8433*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)^4*x+8226*RootOf(27*_Z^6+9*_Z^3+1)^5-2673*(x^4+x^3+x)^(2/3)*RootOf(27*_Z^6+9*_Z^3+1)^3+891*RootOf(27*_Z^6+9*_Z^3+1)^2*x^3+1782*RootOf(27*_Z^6+9*_Z^3+1)^2*x^2+1851*(x^4+x^3+x)^(1/3)*RootOf(27*_Z^6+9*_Z^3+1)*x+891*RootOf(27*_Z^6+9*_Z^3+1)^2+23*(x^4+x^3+x)^(2/3))/(9*RootOf(27*_Z^6+9*_Z^3+1)^3*x^3-18*RootOf(27*_Z^6+9*_Z^3+1)^3*x^2+9*RootOf(27*_Z^6+9*_Z^3+1)^3+4*x^3-x^2+4))*RootOf(27*_Z^6+9*_Z^3+1)","B"
717,0,0,39,0.017000," ","int(1/x/(a*x^6+b)^(3/4),x)","\[\int \frac{1}{x \left(a \,x^{6}+b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x/(a*x^6+b)^(3/4),x)","F"
718,0,0,11,0.021000," ","int((a*x^4-2*b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x)","\[\int \frac{a \,x^{4}-2 b}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(x^{8}+a \,x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^4-2*b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x)","F"
719,0,0,11,0.001000," ","int((a*x^4-2*b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x)","\[\int \frac{a \,x^{4}-2 b}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(x^{8}+a \,x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^4-2*b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x)","F"
720,0,0,14,0.029000," ","int(x^2/(a*x^4+b)^(3/4)/(a^2*x^8+b^2),x)","\[\int \frac{x^{2}}{\left(a \,x^{4}+b \right)^{\frac{3}{4}} \left(a^{2} x^{8}+b^{2}\right)}\, dx\]"," ",0,"int(x^2/(a*x^4+b)^(3/4)/(a^2*x^8+b^2),x)","F"
721,1,59,41,0.110000," ","int(1/(-1+x)/(-x^(1/2)+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(1-3 \sqrt{x}\right) \sqrt{2}}{4 \sqrt{\left(1+\sqrt{x}\right)^{2}-3 \sqrt{x}-1}}\right)}{2}-\frac{2 \sqrt{\left(-1+\sqrt{x}\right)^{2}+\sqrt{x}-1}}{-1+\sqrt{x}}$&$59$\\ default&$-\frac{\sqrt{-\sqrt{x}+x}\, \left(2 \sqrt{2}\, \sqrt{x}\, \arctanh \left(\frac{\left(-1+3 \sqrt{x}\right) \sqrt{2}}{4 \sqrt{-\sqrt{x}+x}}\right)-\sqrt{2}\, x \arctanh \left(\frac{\left(-1+3 \sqrt{x}\right) \sqrt{2}}{4 \sqrt{-\sqrt{x}+x}}\right)+4 \left(-\sqrt{x}+x \right)^{\frac{3}{2}}-\sqrt{2}\, \arctanh \left(\frac{\left(-1+3 \sqrt{x}\right) \sqrt{2}}{4 \sqrt{-\sqrt{x}+x}}\right)+8 \sqrt{-\sqrt{x}+x}\, \sqrt{x}-4 \sqrt{-\sqrt{x}+x}\, x -4 \sqrt{-\sqrt{x}+x}\right)}{2 \sqrt{\sqrt{x}\, \left(-1+\sqrt{x}\right)}\, \left(-1+\sqrt{x}\right)^{2}}$&$164$\\ \hline \end{longtable}"," ",0,"-1/2*2^(1/2)*arctanh(1/4*(1-3*x^(1/2))*2^(1/2)/((1+x^(1/2))^2-3*x^(1/2)-1)^(1/2))-2/(-1+x^(1/2))*((-1+x^(1/2))^2+x^(1/2)-1)^(1/2)","A"
722,0,0,45,0.050000," ","int(1/(1+2*x)/(2*x^2+2*x+1)^(1/4),x)","\[\int \frac{1}{\left(1+2 x \right) \left(2 x^{2}+2 x +1\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(1+2*x)/(2*x^2+2*x+1)^(1/4),x)","F"
723,1,49,44,0.111000," ","int((a*x^3+b)^(1/2)*(a*x^3+2*b)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\frac{2 b \sqrt{a \,x^{3}+b}}{3 x^{3}}+\frac{2 a \sqrt{a \,x^{3}+b}}{3}-\frac{4 a \sqrt{b}\, \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{3}$&$49$\\ risch&$-\frac{2 b \sqrt{a \,x^{3}+b}}{3 x^{3}}+a \left(\frac{2 \sqrt{a \,x^{3}+b}}{3}-\frac{4 \sqrt{b}\, \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{3}\right)$&$50$\\ default&$2 b \left(-\frac{\sqrt{a \,x^{3}+b}}{3 x^{3}}-\frac{a \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{3 \sqrt{b}}\right)+a \left(\frac{2 \sqrt{a \,x^{3}+b}}{3}-\frac{2 \sqrt{b}\, \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{3}\right)$&$73$\\ \hline \end{longtable}"," ",0,"-2/3*b*(a*x^3+b)^(1/2)/x^3+2/3*a*(a*x^3+b)^(1/2)-4/3*a*b^(1/2)*arctanh((a*x^3+b)^(1/2)/b^(1/2))","A"
724,1,877,44,0.671000," ","int((p*x^3-2*q)*(p*x^3+q)^(1/2)/x^2/(a*p*x^3+b*x^2+a*q),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{2 \sqrt{p \,x^{3}+q}}{a x}+\frac{2 i b \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}}{-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{p \left(-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right)}}\right)}{3 a^{2} p \sqrt{p \,x^{3}+q}}-\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a p \,\textit{\_Z}^{3}+b \,\textit{\_Z}^{2}+a q \right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2} b +3 a q \right) \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i p \left(2 x +\frac{-i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}+\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{p \left(x -\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{-3 \left(-q \,p^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i p \left(2 x +\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}+\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{2 \left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \left(-i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a \,p^{2}+i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a p -i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  p b +\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a \,p^{2}+i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, b +\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  a p +\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  b p +2 a \,p^{2} q +\left(-q \,p^{2}\right)^{\frac{2}{3}} b \right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{-i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a p +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a \,p^{2} q -i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  b -2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, a p q -3 \underline{\hspace{1.25 ex}}\alpha^{2} \left(-q \,p^{2}\right)^{\frac{2}{3}} a p +i \sqrt{3}\, b p q -3 \underline{\hspace{1.25 ex}}\alpha  a q \,p^{2}-3 \left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  b -3 b p q}{2 p q b}, \sqrt{\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{p \left(-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right)}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  \left(3 \underline{\hspace{1.25 ex}}\alpha  a p +2 b \right) \sqrt{p \,x^{3}+q}}\right)}{a^{2} p^{2} q}$&$877$\\ risch&$\frac{2 \sqrt{p \,x^{3}+q}}{a x}-\frac{b \left(-\frac{2 i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}}{-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{p \left(-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right)}}\right)}{3 a p \sqrt{p \,x^{3}+q}}-\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a p \,\textit{\_Z}^{3}+b \,\textit{\_Z}^{2}+a q \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{2} b -3 a q \right) \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i p \left(2 x +\frac{-i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}+\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{p \left(x -\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{-3 \left(-q \,p^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i p \left(2 x +\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}+\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{2 \left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \left(-i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a \,p^{2}+i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a p -i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  p b +\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a \,p^{2}+i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, b +\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  a p +\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  b p +2 a \,p^{2} q +\left(-q \,p^{2}\right)^{\frac{2}{3}} b \right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{-i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a p +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a \,p^{2} q -i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  b -2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, a p q -3 \underline{\hspace{1.25 ex}}\alpha^{2} \left(-q \,p^{2}\right)^{\frac{2}{3}} a p +i \sqrt{3}\, b p q -3 \underline{\hspace{1.25 ex}}\alpha  a q \,p^{2}-3 \left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  b -3 b p q}{2 p q b}, \sqrt{\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{p \left(-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right)}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  \left(3 \underline{\hspace{1.25 ex}}\alpha  a p +2 b \right) \sqrt{p \,x^{3}+q}}\right)}{a q \,p^{2} b}\right)}{a}$&$887$\\ default&$\frac{\frac{2 i b \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}}{-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{p \left(-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right)}}\right)}{3 a p \sqrt{p \,x^{3}+q}}-\frac{2 i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}}{-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{p \left(-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right)}}\right)+\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{p \left(-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right)}}\right)}{p}\right)}{\sqrt{p \,x^{3}+q}}-\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a p \,\textit{\_Z}^{3}+b \,\textit{\_Z}^{2}+a q \right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2} b +3 a q \right) \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i p \left(2 x +\frac{-i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}+\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{p \left(x -\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{-3 \left(-q \,p^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i p \left(2 x +\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}+\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{2 \left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \left(-i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a \,p^{2}+i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a p -i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  p b +\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a \,p^{2}+i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, b +\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  a p +\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  b p +2 a \,p^{2} q +\left(-q \,p^{2}\right)^{\frac{2}{3}} b \right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{-i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a p +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a \,p^{2} q -i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  b -2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, a p q -3 \underline{\hspace{1.25 ex}}\alpha^{2} \left(-q \,p^{2}\right)^{\frac{2}{3}} a p +i \sqrt{3}\, b p q -3 \underline{\hspace{1.25 ex}}\alpha  a q \,p^{2}-3 \left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  b -3 b p q}{2 p q b}, \sqrt{\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{p \left(-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right)}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  \left(3 \underline{\hspace{1.25 ex}}\alpha  a p +2 b \right) \sqrt{p \,x^{3}+q}}\right)}{a \,p^{2} q}}{a}-\frac{2 \left(-\frac{\sqrt{p \,x^{3}+q}}{x}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}}{-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{p \left(-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right)}}\right)+\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{p \left(-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right)}}\right)}{p}\right)}{\sqrt{p \,x^{3}+q}}\right)}{a}$&$1747$\\ \hline \end{longtable}"," ",0,"2*(p*x^3+q)^(1/2)/a/x+2/3*I/a^2*b*3^(1/2)/p*(-q*p^2)^(1/3)*(I*(x+1/2/p*(-q*p^2)^(1/3)-1/2*I*3^(1/2)/p*(-q*p^2)^(1/3))*3^(1/2)*p/(-q*p^2)^(1/3))^(1/2)*((x-1/p*(-q*p^2)^(1/3))/(-3/2/p*(-q*p^2)^(1/3)+1/2*I*3^(1/2)/p*(-q*p^2)^(1/3)))^(1/2)*(-I*(x+1/2/p*(-q*p^2)^(1/3)+1/2*I*3^(1/2)/p*(-q*p^2)^(1/3))*3^(1/2)*p/(-q*p^2)^(1/3))^(1/2)/(p*x^3+q)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2/p*(-q*p^2)^(1/3)-1/2*I*3^(1/2)/p*(-q*p^2)^(1/3))*3^(1/2)*p/(-q*p^2)^(1/3))^(1/2),(I*3^(1/2)/p*(-q*p^2)^(1/3)/(-3/2/p*(-q*p^2)^(1/3)+1/2*I*3^(1/2)/p*(-q*p^2)^(1/3)))^(1/2))-I/a^2/p^2/q*2^(1/2)*sum((_alpha^2*b+3*a*q)/_alpha/(3*_alpha*a*p+2*b)*(-q*p^2)^(1/3)*(1/2*I*p*(2*x+1/p*(-I*3^(1/2)*(-q*p^2)^(1/3)+(-q*p^2)^(1/3)))/(-q*p^2)^(1/3))^(1/2)*(p*(x-1/p*(-q*p^2)^(1/3))/(-3*(-q*p^2)^(1/3)+I*3^(1/2)*(-q*p^2)^(1/3)))^(1/2)*(-1/2*I*p*(2*x+1/p*(I*3^(1/2)*(-q*p^2)^(1/3)+(-q*p^2)^(1/3)))/(-q*p^2)^(1/3))^(1/2)/(p*x^3+q)^(1/2)*(-I*(-q*p^2)^(1/3)*3^(1/2)*_alpha^2*a*p^2+I*(-q*p^2)^(2/3)*3^(1/2)*_alpha*a*p-I*(-q*p^2)^(1/3)*3^(1/2)*_alpha*p*b+(-q*p^2)^(1/3)*_alpha^2*a*p^2+I*(-q*p^2)^(2/3)*3^(1/2)*b+(-q*p^2)^(2/3)*_alpha*a*p+(-q*p^2)^(1/3)*_alpha*b*p+2*a*p^2*q+(-q*p^2)^(2/3)*b)*EllipticPi(1/3*3^(1/2)*(I*(x+1/2/p*(-q*p^2)^(1/3)-1/2*I*3^(1/2)/p*(-q*p^2)^(1/3))*3^(1/2)*p/(-q*p^2)^(1/3))^(1/2),-1/2/p*(-I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^2*a*p+I*3^(1/2)*_alpha*a*p^2*q-I*(-q*p^2)^(2/3)*3^(1/2)*_alpha*b-2*I*(-q*p^2)^(1/3)*3^(1/2)*a*p*q-3*_alpha^2*(-q*p^2)^(2/3)*a*p+I*3^(1/2)*b*p*q-3*_alpha*a*q*p^2-3*(-q*p^2)^(2/3)*_alpha*b-3*b*p*q)/q/b,(I*3^(1/2)/p*(-q*p^2)^(1/3)/(-3/2/p*(-q*p^2)^(1/3)+1/2*I*3^(1/2)/p*(-q*p^2)^(1/3)))^(1/2)),_alpha=RootOf(_Z^3*a*p+_Z^2*b+a*q))","C"
725,1,91,52,1.195000," ","int((-1+2*x)/(x^4-10*x^3-3*x^2+4*x-8)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(x^{4}+\sqrt{x^{4}-10 x^{3}-3 x^{2}+4 x -8}\, x^{2}-18 x^{3}-13 \sqrt{x^{4}-10 x^{3}-3 x^{2}+4 x -8}\, x +89 x^{2}+38 \sqrt{x^{4}-10 x^{3}-3 x^{2}+4 x -8}-76 x -90\right)}{2}$&$91$\\ default&$\text{Expression too large to display}$&$2702$\\ elliptic&$\text{Expression too large to display}$&$2702$\\ \hline \end{longtable}"," ",0,"1/2*ln(x^4+(x^4-10*x^3-3*x^2+4*x-8)^(1/2)*x^2-18*x^3-13*(x^4-10*x^3-3*x^2+4*x-8)^(1/2)*x+89*x^2+38*(x^4-10*x^3-3*x^2+4*x-8)^(1/2)-76*x-90)","A"
726,1,94,52,1.026000," ","int((-1+x)/(x^4-8*x^3+12*x^2-16*x+4)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(-x^{4}-\sqrt{x^{4}-8 x^{3}+12 x^{2}-16 x +4}\, x^{2}+12 x^{3}+8 \sqrt{x^{4}-8 x^{3}+12 x^{2}-16 x +4}\, x -44 x^{2}-14 \sqrt{x^{4}-8 x^{3}+12 x^{2}-16 x +4}+56 x -36\right)}{4}$&$94$\\ default&$\text{Expression too large to display}$&$2700$\\ elliptic&$\text{Expression too large to display}$&$2700$\\ \hline \end{longtable}"," ",0,"1/4*ln(-x^4-(x^4-8*x^3+12*x^2-16*x+4)^(1/2)*x^2+12*x^3+8*(x^4-8*x^3+12*x^2-16*x+4)^(1/2)*x-44*x^2-14*(x^4-8*x^3+12*x^2-16*x+4)^(1/2)+56*x-36)","A"
727,0,0,44,0.013000," ","int((p*x^5+q)^(1/2)*(3*p*x^5-2*q)/x^2/(a*p*x^5+b*x^2+a*q),x)","\[\int \frac{\sqrt{p \,x^{5}+q}\, \left(3 p \,x^{5}-2 q \right)}{x^{2} \left(a p \,x^{5}+b \,x^{2}+a q \right)}\, dx\]"," ",0,"int((p*x^5+q)^(1/2)*(3*p*x^5-2*q)/x^2/(a*p*x^5+b*x^2+a*q),x)","F"
728,0,0,46,0.053000," ","int(x^2*(4*x^5-1)/(x^5+1)^2/(a*x^5+a-x)/(x^6+x)^(1/2),x)","\[\int \frac{x^{2} \left(4 x^{5}-1\right)}{\left(x^{5}+1\right)^{2} \left(a \,x^{5}+a -x \right) \sqrt{x^{6}+x}}\, dx\]"," ",0,"int(x^2*(4*x^5-1)/(x^5+1)^2/(a*x^5+a-x)/(x^6+x)^(1/2),x)","F"
729,1,55,48,0.322000," ","int((x^4-x)^(1/2)*(a*x^6-b)/x^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{4}-x}\, \left(3 a \,x^{6}-2 b \,x^{3}+2 b \right)}{9 x^{5}}-\frac{a \ln \left(-2 x^{3}-2 x \sqrt{x^{4}-x}+1\right)}{6}$&$55$\\ meijerg&$\frac{i a \sqrt{\mathrm{signum}\left(x^{3}-1\right)}\, \left(-2 i \sqrt{\pi}\, x^{\frac{3}{2}} \sqrt{-x^{3}+1}-2 i \sqrt{\pi}\, \arcsin \left(x^{\frac{3}{2}}\right)\right)}{6 \sqrt{\pi}\, \sqrt{-\mathrm{signum}\left(x^{3}-1\right)}}+\frac{2 \sqrt{\mathrm{signum}\left(x^{3}-1\right)}\, b \left(-x^{3}+1\right)^{\frac{3}{2}}}{9 \sqrt{-\mathrm{signum}\left(x^{3}-1\right)}\, x^{\frac{9}{2}}}$&$89$\\ risch&$\frac{\left(x^{3}-1\right) \left(3 a \,x^{6}-2 b \,x^{3}+2 b \right)}{9 x^{4} \sqrt{x \left(x^{3}-1\right)}}-\frac{a \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$325$\\ elliptic&$\frac{2 b \sqrt{x^{4}-x}}{9 x^{5}}-\frac{2 b \sqrt{x^{4}-x}}{9 x^{2}}+\frac{a x \sqrt{x^{4}-x}}{3}-\frac{a \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$333$\\ default&$a \left(\frac{x \sqrt{x^{4}-x}}{3}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-b \left(-\frac{2 \sqrt{x^{4}-x}}{9 x^{5}}+\frac{2 \sqrt{x^{4}-x}}{9 x^{2}}\right)$&$336$\\ \hline \end{longtable}"," ",0,"1/9*(x^4-x)^(1/2)*(3*a*x^6-2*b*x^3+2*b)/x^5-1/6*a*ln(-2*x^3-2*x*(x^4-x)^(1/2)+1)","A"
730,0,0,44,0.013000," ","int((p*x^6-2*q)*(p*x^6+q)^(1/2)/x^3/(a*p*x^6+b*x^4+a*q),x)","\[\int \frac{\left(p \,x^{6}-2 q \right) \sqrt{p \,x^{6}+q}}{x^{3} \left(a p \,x^{6}+b \,x^{4}+a q \right)}\, dx\]"," ",0,"int((p*x^6-2*q)*(p*x^6+q)^(1/2)/x^3/(a*p*x^6+b*x^4+a*q),x)","F"
731,1,33,52,0.108000," ","int(2*(p*x^6-2*q)*(p*x^6+q)^(1/2)*(a*p*x^6+b*x^4+a*q)/x^11,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{2 \left(p \,x^{6}+q \right)^{\frac{3}{2}} \left(3 a p \,x^{6}+5 b \,x^{4}+3 a q \right)}{15 x^{10}}$&$33$\\ trager&$\frac{2 \sqrt{p \,x^{6}+q}\, \left(3 a \,p^{2} x^{12}+5 b p \,x^{10}+6 a p q \,x^{6}+5 b q \,x^{4}+3 a \,q^{2}\right)}{15 x^{10}}$&$53$\\ risch&$\frac{2 \sqrt{p \,x^{6}+q}\, \left(3 a \,p^{2} x^{12}+5 b p \,x^{10}+6 a p q \,x^{6}+5 b q \,x^{4}+3 a \,q^{2}\right)}{15 x^{10}}$&$53$\\ \hline \end{longtable}"," ",0,"2/15*(p*x^6+q)^(3/2)*(3*a*p*x^6+5*b*x^4+3*a*q)/x^10","A"
732,1,49,42,0.069000," ","int(1/x^3/(x^8-16*x^6+96*x^4-256*x^2+256)^(1/8),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x^{2}-4}{8 x^{2} \left(\left(x^{2}-4\right)^{4}\right)^{\frac{1}{8}}}-\frac{\arctan \left(\frac{2}{\sqrt{x^{2}-4}}\right) \sqrt{x^{2}-4}}{16 \left(\left(x^{2}-4\right)^{4}\right)^{\frac{1}{8}}}$&$49$\\ \hline \end{longtable}"," ",0,"1/8*(x^2-4)/x^2/((x^2-4)^4)^(1/8)-1/16*arctan(2/(x^2-4)^(1/2))/((x^2-4)^4)^(1/8)*(x^2-4)^(1/2)","A"
733,0,0,46,0.019000," ","int(x^3*(8*a*x^3+5*b)/(a*x^4+b*x)^(1/4)/(a*x^8+b*x^5-2),x)","\[\int \frac{x^{3} \left(8 a \,x^{3}+5 b \right)}{\left(a \,x^{4}+b x \right)^{\frac{1}{4}} \left(a \,x^{8}+b \,x^{5}-2\right)}\, dx\]"," ",0,"int(x^3*(8*a*x^3+5*b)/(a*x^4+b*x)^(1/4)/(a*x^8+b*x^5-2),x)","F"
734,1,45,46,0.074000," ","int((-y^4-x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{x \sqrt{-y^{4}-x^{2}+1}}{2}-\frac{\left(4 y^{4}-4\right) \arctan \left(\frac{x}{\sqrt{-y^{4}-x^{2}+1}}\right)}{8}$&$45$\\ risch&$-\frac{x \left(y^{4}+x^{2}-1\right)}{2 \sqrt{-y^{4}-x^{2}+1}}-\frac{\arctan \left(\frac{x}{\sqrt{-y^{4}-x^{2}+1}}\right) y^{4}}{2}+\frac{\arctan \left(\frac{x}{\sqrt{-y^{4}-x^{2}+1}}\right)}{2}$&$68$\\ \hline \end{longtable}"," ",0,"1/2*x*(-y^4-x^2+1)^(1/2)-1/8*(4*y^4-4)*arctan(1/(-y^4-x^2+1)^(1/2)*x)","A"
735,1,4588,47,0.299000," ","int((k^2*x^2-2*k^2*x+1)/((1-x)*x*(-k^2*x+1))^(1/2)/(-a-b*x+(a*k^2+b*k^2)*x^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$4588$\\ elliptic&$\text{Expression too large to display}$&$4605$\\ \hline \end{longtable}"," ",0,"-2/(a+b)/k^2*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticF((-(x-1/k^2)*k^2)^(1/2),(1/k^2/(1/k^2-1))^(1/2))+1/(a+b)*(2/(1/(a+b)*a*b+1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*a+1/(a+b)*b^2+1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*b-b)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-1/2*b/k^2/(a+b)-1/2/k^2/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-1/2*(b+(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))/k^2/(a+b)),(1/k^2/(1/k^2-1))^(1/2))/(a+b)*a*b+2/(1/(a+b)*a*b+1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*a+1/(a+b)*b^2+1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*b-b)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-1/2*b/k^2/(a+b)-1/2/k^2/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-1/2*(b+(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))/k^2/(a+b)),(1/k^2/(1/k^2-1))^(1/2))/(a+b)*b^2-1/(1/(a+b)*a*b+1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*a+1/(a+b)*b^2+1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*b-b)/k^4*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-1/2*b/k^2/(a+b)-1/2/k^2/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-1/2*(b+(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))/k^2/(a+b)),(1/k^2/(1/k^2-1))^(1/2))/(a+b)*b^2+2/(1/(a+b)*a*b+1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*a+1/(a+b)*b^2+1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*b-b)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-1/2*b/k^2/(a+b)-1/2/k^2/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-1/2*(b+(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))/k^2/(a+b)),(1/k^2/(1/k^2-1))^(1/2))/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*a+2/(1/(a+b)*a*b+1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*a+1/(a+b)*b^2+1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*b-b)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-1/2*b/k^2/(a+b)-1/2/k^2/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-1/2*(b+(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))/k^2/(a+b)),(1/k^2/(1/k^2-1))^(1/2))/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*b-1/(1/(a+b)*a*b+1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*a+1/(a+b)*b^2+1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*b-b)/k^4*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-1/2*b/k^2/(a+b)-1/2/k^2/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-1/2*(b+(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))/k^2/(a+b)),(1/k^2/(1/k^2-1))^(1/2))/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*b-4/(1/(a+b)*a*b+1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*a+1/(a+b)*b^2+1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*b-b)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-1/2*b/k^2/(a+b)-1/2/k^2/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-1/2*(b+(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))/k^2/(a+b)),(1/k^2/(1/k^2-1))^(1/2))*a-2/(1/(a+b)*a*b+1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*a+1/(a+b)*b^2+1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*b-b)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-1/2*b/k^2/(a+b)-1/2/k^2/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-1/2*(b+(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))/k^2/(a+b)),(1/k^2/(1/k^2-1))^(1/2))*b+2/(1/(a+b)*a*b-1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*a+1/(a+b)*b^2-1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*b-b)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-1/2*b/k^2/(a+b)+1/2/k^2/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+1/2*(-b+(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))/k^2/(a+b)),(1/k^2/(1/k^2-1))^(1/2))/(a+b)*a*b+2/(1/(a+b)*a*b-1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*a+1/(a+b)*b^2-1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*b-b)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-1/2*b/k^2/(a+b)+1/2/k^2/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+1/2*(-b+(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))/k^2/(a+b)),(1/k^2/(1/k^2-1))^(1/2))/(a+b)*b^2-1/(1/(a+b)*a*b-1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*a+1/(a+b)*b^2-1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*b-b)/k^4*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-1/2*b/k^2/(a+b)+1/2/k^2/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+1/2*(-b+(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))/k^2/(a+b)),(1/k^2/(1/k^2-1))^(1/2))/(a+b)*b^2-2/(1/(a+b)*a*b-1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*a+1/(a+b)*b^2-1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*b-b)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-1/2*b/k^2/(a+b)+1/2/k^2/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+1/2*(-b+(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))/k^2/(a+b)),(1/k^2/(1/k^2-1))^(1/2))/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*a-2/(1/(a+b)*a*b-1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*a+1/(a+b)*b^2-1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*b-b)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-1/2*b/k^2/(a+b)+1/2/k^2/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+1/2*(-b+(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))/k^2/(a+b)),(1/k^2/(1/k^2-1))^(1/2))/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*b+1/(1/(a+b)*a*b-1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*a+1/(a+b)*b^2-1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*b-b)/k^4*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-1/2*b/k^2/(a+b)+1/2/k^2/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+1/2*(-b+(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))/k^2/(a+b)),(1/k^2/(1/k^2-1))^(1/2))/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*b-4/(1/(a+b)*a*b-1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*a+1/(a+b)*b^2-1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*b-b)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-1/2*b/k^2/(a+b)+1/2/k^2/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+1/2*(-b+(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))/k^2/(a+b)),(1/k^2/(1/k^2-1))^(1/2))*a-2/(1/(a+b)*a*b-1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*a+1/(a+b)*b^2-1/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2)*b-b)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-1/2*b/k^2/(a+b)+1/2/k^2/(a+b)*(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+1/2*(-b+(4*a^2*k^2+4*a*b*k^2+b^2)^(1/2))/k^2/(a+b)),(1/k^2/(1/k^2-1))^(1/2))*b)","C"
736,1,565,51,0.186000," ","int((a*b*c-(a+b+c)*x^2+2*x^3)/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)/(-a*b*c*d+(a*b*d+a*c*d+b*c*d-1)*x-(a+b+c)*d*x^2+d*x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{4 a \sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}\, \left(-c +x \right)^{2} \sqrt{\frac{c \left(-b +x \right)}{b \left(-c +x \right)}}\, \sqrt{\frac{c \left(-a +x \right)}{a \left(-c +x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)}{d \left(a -c \right) c \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}-\frac{2 a \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(d \,\textit{\_Z}^{3}+\left(-a d -b d -c d \right) \textit{\_Z}^{2}+\left(a b d +a c d +b c d -1\right) \textit{\_Z} -a b c d \right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2} a d +\underline{\hspace{1.25 ex}}\alpha^{2} b d +\underline{\hspace{1.25 ex}}\alpha^{2} c d -2 \underline{\hspace{1.25 ex}}\alpha  a b d -2 \underline{\hspace{1.25 ex}}\alpha  a c d -2 \underline{\hspace{1.25 ex}}\alpha  b c d +3 a b c d +2 \underline{\hspace{1.25 ex}}\alpha  \right) \left(-c +x \right)^{2} \left(d \,\underline{\hspace{1.25 ex}}\alpha^{2}-d \underline{\hspace{1.25 ex}}\alpha  a -d \underline{\hspace{1.25 ex}}\alpha  b +a b d -1\right) \sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}\, \sqrt{\frac{c \left(-b +x \right)}{b \left(-c +x \right)}}\, \sqrt{\frac{c \left(-a +x \right)}{a \left(-c +x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)-\frac{\left(d \,\underline{\hspace{1.25 ex}}\alpha^{2}-d \underline{\hspace{1.25 ex}}\alpha  a -d \underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  c d +a b d +a c d +b c d -1\right) \EllipticPi \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, -\frac{d \,\underline{\hspace{1.25 ex}}\alpha^{2}-d \underline{\hspace{1.25 ex}}\alpha  a -d \underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  c d +a c d +b c d -1}{b d \left(a -c \right)}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)}{a b d}\right)}{\left(-3 d \,\underline{\hspace{1.25 ex}}\alpha^{2}+2 d \underline{\hspace{1.25 ex}}\alpha  a +2 d \underline{\hspace{1.25 ex}}\alpha  b +2 \underline{\hspace{1.25 ex}}\alpha  c d -a b d -a c d -b c d +1\right) \left(a -c \right) \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}\right)}{d \,c^{2}}$&$565$\\ elliptic&$-\frac{4 a \sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}\, \left(-c +x \right)^{2} \sqrt{\frac{c \left(-b +x \right)}{b \left(-c +x \right)}}\, \sqrt{\frac{c \left(-a +x \right)}{a \left(-c +x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)}{d \left(a -c \right) c \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}-\frac{2 a \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(d \,\textit{\_Z}^{3}+\left(-a d -b d -c d \right) \textit{\_Z}^{2}+\left(a b d +a c d +b c d -1\right) \textit{\_Z} -a b c d \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{2} a d -\underline{\hspace{1.25 ex}}\alpha^{2} b d -\underline{\hspace{1.25 ex}}\alpha^{2} c d +2 \underline{\hspace{1.25 ex}}\alpha  a b d +2 \underline{\hspace{1.25 ex}}\alpha  a c d +2 \underline{\hspace{1.25 ex}}\alpha  b c d -3 a b c d -2 \underline{\hspace{1.25 ex}}\alpha  \right) \left(-c +x \right)^{2} \left(d \,\underline{\hspace{1.25 ex}}\alpha^{2}-d \underline{\hspace{1.25 ex}}\alpha  a -d \underline{\hspace{1.25 ex}}\alpha  b +a b d -1\right) \sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}\, \sqrt{\frac{c \left(-b +x \right)}{b \left(-c +x \right)}}\, \sqrt{\frac{c \left(-a +x \right)}{a \left(-c +x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)-\frac{\left(d \,\underline{\hspace{1.25 ex}}\alpha^{2}-d \underline{\hspace{1.25 ex}}\alpha  a -d \underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  c d +a b d +a c d +b c d -1\right) \EllipticPi \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, -\frac{d \,\underline{\hspace{1.25 ex}}\alpha^{2}-d \underline{\hspace{1.25 ex}}\alpha  a -d \underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  c d +a c d +b c d -1}{b d \left(a -c \right)}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)}{a b d}\right)}{\left(3 d \,\underline{\hspace{1.25 ex}}\alpha^{2}-2 d \underline{\hspace{1.25 ex}}\alpha  a -2 d \underline{\hspace{1.25 ex}}\alpha  b -2 \underline{\hspace{1.25 ex}}\alpha  c d +a b d +a c d +b c d -1\right) \left(a -c \right) \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}\right)}{d \,c^{2}}$&$565$\\ \hline \end{longtable}"," ",0,"-4/d*a*((a-c)*x/a/(-c+x))^(1/2)*(-c+x)^2*(c*(-b+x)/b/(-c+x))^(1/2)*(c*(-a+x)/a/(-c+x))^(1/2)/(a-c)/c/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)*EllipticF(((a-c)*x/a/(-c+x))^(1/2),((-b+c)*a/b/(c-a))^(1/2))-2/d*a/c^2*sum((_alpha^2*a*d+_alpha^2*b*d+_alpha^2*c*d-2*_alpha*a*b*d-2*_alpha*a*c*d-2*_alpha*b*c*d+3*a*b*c*d+2*_alpha)/(-3*_alpha^2*d+2*_alpha*a*d+2*_alpha*b*d+2*_alpha*c*d-a*b*d-a*c*d-b*c*d+1)*(-c+x)^2/(a-c)*(_alpha^2*d-_alpha*a*d-_alpha*b*d+a*b*d-1)*((a-c)*x/a/(-c+x))^(1/2)*(c*(-b+x)/b/(-c+x))^(1/2)*(c*(-a+x)/a/(-c+x))^(1/2)/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)*(EllipticF(((a-c)*x/a/(-c+x))^(1/2),((-b+c)*a/b/(c-a))^(1/2))-(_alpha^2*d-_alpha*a*d-_alpha*b*d-_alpha*c*d+a*b*d+a*c*d+b*c*d-1)/a/b/d*EllipticPi(((a-c)*x/a/(-c+x))^(1/2),-(_alpha^2*d-_alpha*a*d-_alpha*b*d-_alpha*c*d+a*c*d+b*c*d-1)/b/d/(a-c),((-b+c)*a/b/(c-a))^(1/2))),_alpha=RootOf(d*_Z^3+(-a*d-b*d-c*d)*_Z^2+(a*b*d+a*c*d+b*c*d-1)*_Z-a*b*c*d))","C"
737,1,33,45,1.955000," ","int(x^6*(x^4-1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}} x^{7} \hypergeom \left(\left[-\frac{1}{4}, \frac{7}{4}\right], \left[\frac{11}{4}\right], x^{4}\right)}{7 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}}}$&$33$\\ risch&$\frac{x^{3} \left(4 x^{4}-1\right) \left(x^{4}-1\right)^{\frac{1}{4}}}{32}-\frac{\left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{3}{4}} x^{3} \hypergeom \left(\left[\frac{3}{4}, \frac{3}{4}\right], \left[\frac{7}{4}\right], x^{4}\right)}{32 \mathrm{signum}\left(x^{4}-1\right)^{\frac{3}{4}}}$&$53$\\ trager&$\frac{x^{3} \left(4 x^{4}-1\right) \left(x^{4}-1\right)^{\frac{1}{4}}}{32}+\frac{3 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}-1}\, x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \left(x^{4}-1\right)^{\frac{3}{4}} x -2 x^{3} \left(x^{4}-1\right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{128}-\frac{3 \ln \left(2 \left(x^{4}-1\right)^{\frac{3}{4}} x +2 x^{2} \sqrt{x^{4}-1}+2 x^{3} \left(x^{4}-1\right)^{\frac{1}{4}}+2 x^{4}-1\right)}{128}$&$134$\\ \hline \end{longtable}"," ",0,"1/7*signum(x^4-1)^(1/4)/(-signum(x^4-1))^(1/4)*x^7*hypergeom([-1/4,7/4],[11/4],x^4)","C"
738,1,30,45,0.774000," ","int((-1+2*x)*(x^4+x^3)^(1/4)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{4 x^{\frac{3}{4}} \hypergeom \left(\left[-\frac{1}{4}, \frac{3}{4}\right], \left[\frac{7}{4}\right], -x \right)}{3}+\frac{8 x^{\frac{7}{4}} \hypergeom \left(\left[-\frac{1}{4}, \frac{7}{4}\right], \left[\frac{11}{4}\right], -x \right)}{7}$&$30$\\ trager&$\left(-\frac{3}{4}+x \right) \left(x^{4}+x^{3}\right)^{\frac{1}{4}}-\frac{7 \ln \left(\frac{2 \left(x^{4}+x^{3}\right)^{\frac{3}{4}}+2 \sqrt{x^{4}+x^{3}}\, x +2 \left(x^{4}+x^{3}\right)^{\frac{1}{4}} x^{2}+2 x^{3}+x^{2}}{x^{2}}\right)}{16}+\frac{7 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-2 \sqrt{x^{4}+x^{3}}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x +2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{4}+x^{3}\right)^{\frac{3}{4}}-2 \left(x^{4}+x^{3}\right)^{\frac{1}{4}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}}{x^{2}}\right)}{16}$&$146$\\ risch&$\frac{\left(-3+4 x \right) \left(x^{3} \left(1+x \right)\right)^{\frac{1}{4}}}{4}+\frac{\left(\frac{7 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, \RootOf \left(\textit{\_Z}^{2}+1\right)-5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{3}{4}}-2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x^{2}-4 \RootOf \left(\textit{\_Z}^{2}+1\right) x -4 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x -\RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}}}{\left(1+x \right)^{2}}\right)}{16}-\frac{7 \ln \left(\frac{2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{3}{4}}+2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, x +2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x^{2}+2 x^{3}+2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}+4 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x +5 x^{2}+2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}}+4 x +1}{\left(1+x \right)^{2}}\right)}{16}\right) \left(x^{3} \left(1+x \right)\right)^{\frac{1}{4}} \left(\left(1+x \right)^{3} x \right)^{\frac{1}{4}}}{x \left(1+x \right)}$&$375$\\ \hline \end{longtable}"," ",0,"-4/3*x^(3/4)*hypergeom([-1/4,3/4],[7/4],-x)+8/7*x^(7/4)*hypergeom([-1/4,7/4],[11/4],-x)","C"
739,1,142,46,1.438000," ","int((x^4-2*x^3+x^2-1)^(1/2)*(x^4-x^3+1)/(x^4-2*x^3-1)/(2*x^4-4*x^3-x^2-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(-\frac{x^{4}-2 x^{3}+2 \sqrt{x^{4}-2 x^{3}+x^{2}-1}\, x +2 x^{2}-1}{x^{4}-2 x^{3}-1}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}-6\right) \ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{2}-6\right) x^{4}+4 \RootOf \left(\textit{\_Z}^{2}-6\right) x^{3}-5 \RootOf \left(\textit{\_Z}^{2}-6\right) x^{2}+12 \sqrt{x^{4}-2 x^{3}+x^{2}-1}\, x +2 \RootOf \left(\textit{\_Z}^{2}-6\right)}{2 x^{4}-4 x^{3}-x^{2}-2}\right)}{4}$&$142$\\ default&$-\frac{i \left(-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{\frac{\left(\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{\frac{i \sqrt{3}\, \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)}{\left(-\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{i \sqrt{3}\, \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}{\left(\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{3}\, \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \sqrt{\frac{\left(\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}{\left(\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(-\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right)}}\right)}{3 \left(\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}}+\frac{i \sqrt{16}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}-1\right)}{\sum}\frac{2 \underline{\hspace{1.25 ex}}\alpha  \left(-i \sqrt{3}-\sqrt{5}\right) \sqrt{\frac{\left(\sqrt{5}-i \sqrt{3}\right) \left(i \sqrt{3}+2 x -1\right)}{\left(\sqrt{5}+i \sqrt{3}\right) \left(-1+2 x -i \sqrt{3}\right)}}\, \left(-1+2 x -i \sqrt{3}\right)^{2} \sqrt{\frac{i \left(2 x -1+\sqrt{5}\right)}{\left(i \sqrt{3}-\sqrt{5}\right) \left(-1+2 x -i \sqrt{3}\right)}}\, \sqrt{\frac{i \left(-1+2 x -\sqrt{5}\right)}{\left(\sqrt{5}+i \sqrt{3}\right) \left(-1+2 x -i \sqrt{3}\right)}}\, \left(\underline{\hspace{1.25 ex}}\alpha^{3}-3 \underline{\hspace{1.25 ex}}\alpha^{2}+3+i \sqrt{3}\, \left(\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}-2 \underline{\hspace{1.25 ex}}\alpha  -1\right)\right) \left(2 \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \sqrt{\frac{\left(\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}{\left(\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(-\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right)}}\right)+i \sqrt{3}\, \left(\underline{\hspace{1.25 ex}}\alpha^{3}-3 \underline{\hspace{1.25 ex}}\alpha^{2}+3+i \sqrt{3}\, \left(-\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha^{2}+2 \underline{\hspace{1.25 ex}}\alpha  +1\right)\right) \EllipticPi \left(\sqrt{\frac{\left(\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \frac{3 i \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{5}\, \sqrt{3}}{8}-\frac{i \sqrt{5}\, \sqrt{3}}{8}+\frac{3 i \sqrt{3}}{8}+\frac{i \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{3}}{8}-\frac{9 \sqrt{5}}{8}-\frac{3 i \underline{\hspace{1.25 ex}}\alpha  \sqrt{5}\, \sqrt{3}}{4}-\frac{3 \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{5}}{8}+\frac{9 \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{5}}{8}-\frac{3 i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{5}\, \sqrt{3}}{8}+\frac{3 \underline{\hspace{1.25 ex}}\alpha^{3}}{8}-\frac{1}{8}-\frac{3 \underline{\hspace{1.25 ex}}\alpha^{2}}{8}-\frac{3 \underline{\hspace{1.25 ex}}\alpha }{4}-\frac{3 i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{8}, \sqrt{\frac{\left(\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}{\left(\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(-\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\sqrt{5}-i \sqrt{3}\right) \sqrt{\left(i \sqrt{3}+2 x -1\right) \left(-1+2 x -i \sqrt{3}\right) \left(2 x -1+\sqrt{5}\right) \left(-1+2 x -\sqrt{5}\right)}}\right)}{16}-\frac{i \sqrt{16}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(2 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}-\textit{\_Z}^{2}-2\right)}{\sum}\frac{2 \underline{\hspace{1.25 ex}}\alpha  \left(-i \sqrt{3}-\sqrt{5}\right) \sqrt{\frac{\left(\sqrt{5}-i \sqrt{3}\right) \left(i \sqrt{3}+2 x -1\right)}{\left(\sqrt{5}+i \sqrt{3}\right) \left(-1+2 x -i \sqrt{3}\right)}}\, \left(-1+2 x -i \sqrt{3}\right)^{2} \sqrt{\frac{i \left(2 x -1+\sqrt{5}\right)}{\left(i \sqrt{3}-\sqrt{5}\right) \left(-1+2 x -i \sqrt{3}\right)}}\, \sqrt{\frac{i \left(-1+2 x -\sqrt{5}\right)}{\left(\sqrt{5}+i \sqrt{3}\right) \left(-1+2 x -i \sqrt{3}\right)}}\, \left(2 \underline{\hspace{1.25 ex}}\alpha^{3}-6 \underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +7+i \sqrt{3}\, \left(2 \underline{\hspace{1.25 ex}}\alpha^{3}-2 \underline{\hspace{1.25 ex}}\alpha^{2}-5 \underline{\hspace{1.25 ex}}\alpha  -3\right)\right) \left(6 \EllipticF \left(\sqrt{\frac{\left(\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \sqrt{\frac{\left(\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}{\left(\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(-\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right)}}\right)+i \sqrt{3}\, \left(2 \underline{\hspace{1.25 ex}}\alpha^{3}-6 \underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +7+i \sqrt{3}\, \left(-2 \underline{\hspace{1.25 ex}}\alpha^{3}+2 \underline{\hspace{1.25 ex}}\alpha^{2}+5 \underline{\hspace{1.25 ex}}\alpha  +3\right)\right) \EllipticPi \left(\sqrt{\frac{\left(\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, -\frac{1}{8}-\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha }{24}+\frac{\underline{\hspace{1.25 ex}}\alpha  \sqrt{5}}{8}+\frac{3 \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{5}}{4}-\frac{\underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{5}}{4}-\frac{7 \sqrt{5}}{8}+\frac{i \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{5}\, \sqrt{3}}{4}-\frac{5 \underline{\hspace{1.25 ex}}\alpha }{8}-\frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{5}\, \sqrt{3}}{4}-\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{4}-\frac{i \sqrt{5}\, \sqrt{3}}{8}+\frac{\underline{\hspace{1.25 ex}}\alpha^{3}}{4}-\frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{4}-\frac{5 i \underline{\hspace{1.25 ex}}\alpha  \sqrt{5}\, \sqrt{3}}{8}+\frac{7 i \sqrt{3}}{24}+\frac{i \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{3}}{12}, \sqrt{\frac{\left(\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}{\left(\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(-\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\sqrt{5}-i \sqrt{3}\right) \sqrt{\left(i \sqrt{3}+2 x -1\right) \left(-1+2 x -i \sqrt{3}\right) \left(2 x -1+\sqrt{5}\right) \left(-1+2 x -\sqrt{5}\right)}}\right)}{96}$&$1574$\\ elliptic&$\text{Expression too large to display}$&$15410$\\ \hline \end{longtable}"," ",0,"1/2*ln(-(x^4-2*x^3+2*(x^4-2*x^3+x^2-1)^(1/2)*x+2*x^2-1)/(x^4-2*x^3-1))+1/4*RootOf(_Z^2-6)*ln(-(-2*RootOf(_Z^2-6)*x^4+4*RootOf(_Z^2-6)*x^3-5*RootOf(_Z^2-6)*x^2+12*(x^4-2*x^3+x^2-1)^(1/2)*x+2*RootOf(_Z^2-6))/(2*x^4-4*x^3-x^2-2))","C"
740,0,0,41,0.016000," ","int(x^2/(a*x^4+b)^(3/4),x)","\[\int \frac{x^{2}}{\left(a \,x^{4}+b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(x^2/(a*x^4+b)^(3/4),x)","F"
741,0,0,14,0.028000," ","int(1/(a*x^4+b)^(1/4)/(a*x^8-b),x)","\[\int \frac{1}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(a \,x^{8}-b \right)}\, dx\]"," ",0,"int(1/(a*x^4+b)^(1/4)/(a*x^8-b),x)","F"
742,0,0,41,0.020000," ","int((a*x^8-b)/(a*x^8+b)^(1/4)/(a*x^8-c*x^4+b),x)","\[\int \frac{a \,x^{8}-b}{\left(a \,x^{8}+b \right)^{\frac{1}{4}} \left(a \,x^{8}-c \,x^{4}+b \right)}\, dx\]"," ",0,"int((a*x^8-b)/(a*x^8+b)^(1/4)/(a*x^8-c*x^4+b),x)","F"
743,1,177,49,7.960000," ","int((2*x^5-3)*(x^10+x^6+2*x^5+1)/x^6/(x^5-x^3+1)/(x^6+x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(3 x^{5}+7 x^{3}+3\right) \left(x^{6}+x \right)^{\frac{3}{4}}}{21 x^{6}}+2 \ln \left(-\frac{-x^{5}+2 \left(x^{6}+x \right)^{\frac{3}{4}}-2 x \sqrt{x^{6}+x}+2 \left(x^{6}+x \right)^{\frac{1}{4}} x^{2}-x^{3}-1}{x^{5}-x^{3}+1}\right)+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{5}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{6}+x}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{6}+x \right)^{\frac{3}{4}}-2 \left(x^{6}+x \right)^{\frac{1}{4}} x^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{5}-x^{3}+1}\right)$&$177$\\ risch&$\frac{\frac{4}{7} x^{10}+\frac{4}{3} x^{8}+\frac{8}{7} x^{5}+\frac{4}{3} x^{3}+\frac{4}{7}}{x^{5} \left(x \left(x^{5}+1\right)\right)^{\frac{1}{4}}}+2 \ln \left(-\frac{-x^{5}+2 \left(x^{6}+x \right)^{\frac{3}{4}}-2 x \sqrt{x^{6}+x}+2 \left(x^{6}+x \right)^{\frac{1}{4}} x^{2}-x^{3}-1}{x^{5}-x^{3}+1}\right)+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{5}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{6}+x}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{6}+x \right)^{\frac{3}{4}}-2 \left(x^{6}+x \right)^{\frac{1}{4}} x^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{5}-x^{3}+1}\right)$&$189$\\ \hline \end{longtable}"," ",0,"4/21*(3*x^5+7*x^3+3)*(x^6+x)^(3/4)/x^6+2*ln(-(-x^5+2*(x^6+x)^(3/4)-2*x*(x^6+x)^(1/2)+2*(x^6+x)^(1/4)*x^2-x^3-1)/(x^5-x^3+1))+2*RootOf(_Z^2+1)*ln(-(-RootOf(_Z^2+1)*x^5+2*RootOf(_Z^2+1)*(x^6+x)^(1/2)*x-RootOf(_Z^2+1)*x^3+2*(x^6+x)^(3/4)-2*(x^6+x)^(1/4)*x^2-RootOf(_Z^2+1))/(x^5-x^3+1))","C"
744,1,22,41,0.045000," ","int((x^2+(x^4+1)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\sqrt{2}\, x^{2} \hypergeom \left(\left[-\frac{1}{2}, -\frac{1}{4}, \frac{1}{4}\right], \left[\frac{1}{2}, \frac{1}{2}\right], -\frac{1}{x^{4}}\right)}{2}$&$22$\\ \hline \end{longtable}"," ",0,"1/2*2^(1/2)*x^2*hypergeom([-1/2,-1/4,1/4],[1/2,1/2],-1/x^4)","C"
745,1,210,46,1.498000," ","int((x^2-x-1)/(x^2+1)/(x^3-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticF \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}}-\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}-\frac{3 i \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}-\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}+\frac{3 i \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}$&$210$\\ elliptic&$\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticF \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}}-\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}-\frac{3 i \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}-\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}+\frac{3 i \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}$&$210$\\ trager&$\frac{3 \ln \left(-\frac{464 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right)^{2} x^{2}-696 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right)^{2} x -771 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right) x^{2}+400 \sqrt{x^{3}-x}\, \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right)-464 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right)^{2}+794 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right) x +315 x^{2}-275 \sqrt{x^{3}-x}+771 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right)-210 x -315}{\left(4 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right) x -8 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right)-x +7\right)^{2}}\right)}{4}-\frac{\ln \left(-\frac{464 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right)^{2} x^{2}-696 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right)^{2} x -771 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right) x^{2}+400 \sqrt{x^{3}-x}\, \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right)-464 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right)^{2}+794 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right) x +315 x^{2}-275 \sqrt{x^{3}-x}+771 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right)-210 x -315}{\left(4 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right) x -8 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right)-x +7\right)^{2}}\right) \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right)}{2}+\frac{\RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right) \ln \left(\frac{-928 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right)^{2} x^{2}+1392 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right)^{2} x +1242 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right) x^{2}+800 \sqrt{x^{3}-x}\, \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right)+928 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right)^{2}-2588 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right) x -405 x^{2}-650 \sqrt{x^{3}-x}-1242 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right)+1170 x +405}{\left(4 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right) x -8 \RootOf \left(8 \textit{\_Z}^{2}-12 \textit{\_Z} +5\right)-5 x +5\right)^{2}}\right)}{2}$&$545$\\ \hline \end{longtable}"," ",0,"(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticF((1+x)^(1/2),1/2*2^(1/2))-1/4*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticPi((1+x)^(1/2),1/2-1/2*I,1/2*2^(1/2))-3/4*I*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticPi((1+x)^(1/2),1/2-1/2*I,1/2*2^(1/2))-1/4*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticPi((1+x)^(1/2),1/2+1/2*I,1/2*2^(1/2))+3/4*I*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticPi((1+x)^(1/2),1/2+1/2*I,1/2*2^(1/2))","C"
746,1,210,46,1.567000," ","int((x^2+x-1)/(x^2+1)/(x^3-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticF \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}}-\frac{3 \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}-\frac{i \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}-\frac{3 \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}+\frac{i \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}$&$210$\\ elliptic&$\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticF \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}}-\frac{3 \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}-\frac{i \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}-\frac{3 \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}+\frac{i \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}$&$210$\\ trager&$-\frac{\ln \left(\frac{464 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right)^{2} x^{2}-696 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right)^{2} x +457 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right) x^{2}+1200 \sqrt{x^{3}-x}\, \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right)-464 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right)^{2}+402 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right) x +65 x^{2}+75 \sqrt{x^{3}-x}-457 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right)+90 x -65}{\left(4 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right) x -8 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right)-5 x -5\right)^{2}}\right)}{4}-\frac{\ln \left(\frac{464 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right)^{2} x^{2}-696 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right)^{2} x +457 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right) x^{2}+1200 \sqrt{x^{3}-x}\, \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right)-464 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right)^{2}+402 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right) x +65 x^{2}+75 \sqrt{x^{3}-x}-457 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right)+90 x -65}{\left(4 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right) x -8 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right)-5 x -5\right)^{2}}\right) \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right)}{2}+\frac{\RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right) \ln \left(-\frac{-928 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right)^{2} x^{2}+1392 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right)^{2} x -14 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right) x^{2}+2400 \sqrt{x^{3}-x}\, \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right)+928 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right)^{2}+2196 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right) x +95 x^{2}+1050 \sqrt{x^{3}-x}+14 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right)+570 x -95}{\left(4 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right) x -8 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +5\right)+7 x +1\right)^{2}}\right)}{2}$&$544$\\ \hline \end{longtable}"," ",0,"(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticF((1+x)^(1/2),1/2*2^(1/2))-3/4*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticPi((1+x)^(1/2),1/2-1/2*I,1/2*2^(1/2))-1/4*I*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticPi((1+x)^(1/2),1/2-1/2*I,1/2*2^(1/2))-3/4*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticPi((1+x)^(1/2),1/2+1/2*I,1/2*2^(1/2))+1/4*I*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticPi((1+x)^(1/2),1/2+1/2*I,1/2*2^(1/2))","C"
747,1,211,46,1.605000," ","int((7*x^2+x-7)/(x^2+1)/(x^3-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{7 \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticF \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}}-\frac{15 \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}-\frac{13 i \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}-\frac{15 \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}+\frac{13 i \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}$&$211$\\ elliptic&$\frac{7 \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticF \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}}-\frac{15 \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}-\frac{13 i \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}-\frac{15 \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}+\frac{13 i \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}$&$211$\\ trager&$-\frac{13 \ln \left(\frac{464 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right)^{2} x^{2}-696 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right)^{2} x +4141 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right) x^{2}+6000 \sqrt{x^{3}-x}\, \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right)-464 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right)^{2}-774 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right) x +8051 x^{2}+13875 \sqrt{x^{3}-x}-4141 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right)+3486 x -8051}{\left(4 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right) x -8 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right)-17 x -41\right)^{2}}\right)}{4}-\frac{\ln \left(\frac{464 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right)^{2} x^{2}-696 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right)^{2} x +4141 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right) x^{2}+6000 \sqrt{x^{3}-x}\, \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right)-464 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right)^{2}-774 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right) x +8051 x^{2}+13875 \sqrt{x^{3}-x}-4141 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right)+3486 x -8051}{\left(4 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right) x -8 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right)-17 x -41\right)^{2}}\right) \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right)}{2}+\frac{\RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right) \ln \left(-\frac{-928 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right)^{2} x^{2}+1392 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right)^{2} x -3782 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right) x^{2}+12000 \sqrt{x^{3}-x}\, \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right)+928 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right)^{2}+16548 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right) x -1477 x^{2}+50250 \sqrt{x^{3}-x}+3782 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right)+41778 x +1477}{\left(4 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right) x -8 \RootOf \left(8 \textit{\_Z}^{2}+52 \textit{\_Z} +197\right)+43 x -11\right)^{2}}\right)}{2}$&$544$\\ \hline \end{longtable}"," ",0,"7*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticF((1+x)^(1/2),1/2*2^(1/2))-15/4*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticPi((1+x)^(1/2),1/2-1/2*I,1/2*2^(1/2))-13/4*I*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticPi((1+x)^(1/2),1/2-1/2*I,1/2*2^(1/2))-15/4*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticPi((1+x)^(1/2),1/2+1/2*I,1/2*2^(1/2))+13/4*I*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticPi((1+x)^(1/2),1/2+1/2*I,1/2*2^(1/2))","C"
748,1,200,48,2.281000," ","int(1/(-2+x)/(x^3-x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{4 \RootOf \left(\textit{\_Z}^{2}+2\right) \sqrt{x^{3}-x^{2}}\, x -\RootOf \left(\textit{\_Z}^{2}+2\right) x^{3}+8 \left(x^{3}-x^{2}\right)^{\frac{3}{4}}-4 \left(x^{3}-x^{2}\right)^{\frac{1}{4}} x^{2}-4 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{2}+4 \RootOf \left(\textit{\_Z}^{2}+2\right) x}{\left(-2+x \right)^{2} x}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{-4 \RootOf \left(\textit{\_Z}^{2}-2\right) \sqrt{x^{3}-x^{2}}\, x -\RootOf \left(\textit{\_Z}^{2}-2\right) x^{3}+8 \left(x^{3}-x^{2}\right)^{\frac{3}{4}}+4 \left(x^{3}-x^{2}\right)^{\frac{1}{4}} x^{2}-4 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}+4 \RootOf \left(\textit{\_Z}^{2}-2\right) x}{\left(-2+x \right)^{2} x}\right)}{4}$&$200$\\ \hline \end{longtable}"," ",0,"1/4*RootOf(_Z^2+2)*ln((4*RootOf(_Z^2+2)*(x^3-x^2)^(1/2)*x-RootOf(_Z^2+2)*x^3+8*(x^3-x^2)^(3/4)-4*(x^3-x^2)^(1/4)*x^2-4*RootOf(_Z^2+2)*x^2+4*RootOf(_Z^2+2)*x)/(-2+x)^2/x)+1/4*RootOf(_Z^2-2)*ln((-4*RootOf(_Z^2-2)*(x^3-x^2)^(1/2)*x-RootOf(_Z^2-2)*x^3+8*(x^3-x^2)^(3/4)+4*(x^3-x^2)^(1/4)*x^2-4*RootOf(_Z^2-2)*x^2+4*RootOf(_Z^2-2)*x)/(-2+x)^2/x)","C"
749,1,54,50,0.304000," ","int((a*x^3+b)*(x^4-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{x \left(2 a \,x^{3}-a +4 b \right) \sqrt{x^{4}-x}}{12}-\frac{\left(a +4 b \right) \ln \left(-2 x^{3}-2 x \sqrt{x^{4}-x}+1\right)}{24}$&$54$\\ meijerg&$-\frac{i a \sqrt{\mathrm{signum}\left(x^{3}-1\right)}\, \left(-\frac{i \sqrt{\pi}\, x^{\frac{3}{2}} \left(-6 x^{3}+3\right) \sqrt{-x^{3}+1}}{6}+\frac{i \sqrt{\pi}\, \arcsin \left(x^{\frac{3}{2}}\right)}{2}\right)}{6 \sqrt{\pi}\, \sqrt{-\mathrm{signum}\left(x^{3}-1\right)}}+\frac{i b \sqrt{\mathrm{signum}\left(x^{3}-1\right)}\, \left(-2 i \sqrt{\pi}\, x^{\frac{3}{2}} \sqrt{-x^{3}+1}-2 i \sqrt{\pi}\, \arcsin \left(x^{\frac{3}{2}}\right)\right)}{6 \sqrt{\pi}\, \sqrt{-\mathrm{signum}\left(x^{3}-1\right)}}$&$117$\\ risch&$\frac{x^{2} \left(2 a \,x^{3}-a +4 b \right) \left(x^{3}-1\right)}{12 \sqrt{x \left(x^{3}-1\right)}}+\frac{2 \left(-\frac{b}{2}-\frac{a}{8}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$328$\\ elliptic&$\frac{a \,x^{4} \sqrt{x^{4}-x}}{6}+\left(-\frac{a}{12}+\frac{b}{3}\right) x \sqrt{x^{4}-x}+\frac{2 \left(-\frac{b}{2}-\frac{a}{8}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}$&$329$\\ default&$a \left(\frac{x^{4} \sqrt{x^{4}-x}}{6}-\frac{x \sqrt{x^{4}-x}}{12}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{4 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+b \left(\frac{x \sqrt{x^{4}-x}}{3}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)$&$620$\\ \hline \end{longtable}"," ",0,"1/12*x*(2*a*x^3-a+4*b)*(x^4-x)^(1/2)-1/24*(a+4*b)*ln(-2*x^3-2*x*(x^4-x)^(1/2)+1)","A"
750,1,46,52,1.149000," ","int((2*x^2-x-2)/(x^2+1)/(x^4+x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\arctanh \left(\frac{-x^{2}+1}{2 \sqrt{\left(x^{2}+1\right)^{2}-x^{2}}}\right)}{2}+2 \arctan \left(\frac{\sqrt{x^{4}+x^{2}+1}}{x}\right)$&$46$\\ trager&$-\frac{\ln \left(-\frac{6 \RootOf \left(4 \textit{\_Z}^{2}+4 \textit{\_Z} +17\right) x +8 x^{2}+4 \sqrt{x^{4}+x^{2}+1}+3 x -8}{\left(2 \RootOf \left(4 \textit{\_Z}^{2}+4 \textit{\_Z} +17\right) x +x -4\right)^{2}}\right) \RootOf \left(4 \textit{\_Z}^{2}+4 \textit{\_Z} +17\right)}{2}-\frac{\ln \left(-\frac{6 \RootOf \left(4 \textit{\_Z}^{2}+4 \textit{\_Z} +17\right) x +8 x^{2}+4 \sqrt{x^{4}+x^{2}+1}+3 x -8}{\left(2 \RootOf \left(4 \textit{\_Z}^{2}+4 \textit{\_Z} +17\right) x +x -4\right)^{2}}\right)}{2}+\frac{\RootOf \left(4 \textit{\_Z}^{2}+4 \textit{\_Z} +17\right) \ln \left(\frac{6 \RootOf \left(4 \textit{\_Z}^{2}+4 \textit{\_Z} +17\right) x -8 x^{2}-4 \sqrt{x^{4}+x^{2}+1}+3 x +8}{\left(2 \RootOf \left(4 \textit{\_Z}^{2}+4 \textit{\_Z} +17\right) x +x +4\right)^{2}}\right)}{2}$&$203$\\ default&$\frac{4 \sqrt{1-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{-2+2 i \sqrt{3}}}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}-\frac{\arctanh \left(\frac{x^{2}}{2 \sqrt{x^{4}+x^{2}+1}}-\frac{1}{2 \sqrt{x^{4}+x^{2}+1}}\right)}{2}-\frac{4 \sqrt{1+\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}}\, \sqrt{1+\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , -\frac{1}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+x^{2}+1}}$&$219$\\ \hline \end{longtable}"," ",0,"1/2*arctanh(1/2*(-x^2+1)/((x^2+1)^2-x^2)^(1/2))+2*arctan(1/x*(x^4+x^2+1)^(1/2))","A"
751,0,0,48,0.020000," ","int(x^3*(9*a*x^4-5*b)/(a*x^5-b*x)^(1/4)/(a*x^9-b*x^5-2),x)","\[\int \frac{x^{3} \left(9 a \,x^{4}-5 b \right)}{\left(a \,x^{5}-b x \right)^{\frac{1}{4}} \left(a \,x^{9}-b \,x^{5}-2\right)}\, dx\]"," ",0,"int(x^3*(9*a*x^4-5*b)/(a*x^5-b*x)^(1/4)/(a*x^9-b*x^5-2),x)","F"
752,1,102,51,0.604000," ","int((x^2+1)/(x^2-1)/(x^3+x^2+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) x^{2}+4 \RootOf \left(\textit{\_Z}^{2}-3\right) x +6 \sqrt{x^{3}+x^{2}+x}+\RootOf \left(\textit{\_Z}^{2}-3\right)}{\left(-1+x \right)^{2}}\right)}{6}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \sqrt{x^{3}+x^{2}+x}-\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(1+x \right)^{2}}\right)}{2}$&$102$\\ default&$\frac{2 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}}-\frac{2 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}\, \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}+\frac{2 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}$&$420$\\ elliptic&$\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}}+\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{\sqrt{x^{3}+x^{2}+x}}-\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}\, \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{\sqrt{x^{3}+x^{2}+x}\, \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}+\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{\sqrt{x^{3}+x^{2}+x}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}$&$910$\\ \hline \end{longtable}"," ",0,"-1/6*RootOf(_Z^2-3)*ln((RootOf(_Z^2-3)*x^2+4*RootOf(_Z^2-3)*x+6*(x^3+x^2+x)^(1/2)+RootOf(_Z^2-3))/(-1+x)^2)+1/2*RootOf(_Z^2+1)*ln((-RootOf(_Z^2+1)*x^2+2*(x^3+x^2+x)^(1/2)-RootOf(_Z^2+1))/(1+x)^2)","C"
753,1,522,53,0.138000," ","int((a*b*c-(a+b+c)*x^2+2*x^3)/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)/(-a*b*c+(a*b+a*c+b*c-d)*x-(a+b+c)*x^2+x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{4 a \sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}\, \left(-c +x \right)^{2} \sqrt{\frac{c \left(-b +x \right)}{b \left(-c +x \right)}}\, \sqrt{\frac{c \left(-a +x \right)}{a \left(-c +x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)}{\left(a -c \right) c \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}-\frac{2 a \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+\left(-a -b -c \right) \textit{\_Z}^{2}+\left(a b +a c +b c -d \right) \textit{\_Z} -a b c \right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2} a +\underline{\hspace{1.25 ex}}\alpha^{2} b +\underline{\hspace{1.25 ex}}\alpha^{2} c -2 \underline{\hspace{1.25 ex}}\alpha  a b -2 \underline{\hspace{1.25 ex}}\alpha  a c -2 \underline{\hspace{1.25 ex}}\alpha  b c +3 a b c +2 \underline{\hspace{1.25 ex}}\alpha  d \right) \left(-c +x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  b +a b -d \right) \sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}\, \sqrt{\frac{c \left(-b +x \right)}{b \left(-c +x \right)}}\, \sqrt{\frac{c \left(-a +x \right)}{a \left(-c +x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)-\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  c +a b +a c +b c -d \right) \EllipticPi \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, -\frac{\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  c +a c +b c -d}{b \left(a -c \right)}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)}{a b}\right)}{\left(-3 \underline{\hspace{1.25 ex}}\alpha^{2}+2 \underline{\hspace{1.25 ex}}\alpha  a +2 \underline{\hspace{1.25 ex}}\alpha  b +2 \underline{\hspace{1.25 ex}}\alpha  c -a b -a c -b c +d \right) \left(a -c \right) \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}\right)}{c^{2} d}$&$522$\\ elliptic&$-\frac{4 a \sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}\, \left(-c +x \right)^{2} \sqrt{\frac{c \left(-b +x \right)}{b \left(-c +x \right)}}\, \sqrt{\frac{c \left(-a +x \right)}{a \left(-c +x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)}{\left(a -c \right) c \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}+\frac{2 a \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+\left(-a -b -c \right) \textit{\_Z}^{2}+\left(a b +a c +b c -d \right) \textit{\_Z} -a b c \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{2} a -\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha^{2} c +2 \underline{\hspace{1.25 ex}}\alpha  a b +2 \underline{\hspace{1.25 ex}}\alpha  a c +2 \underline{\hspace{1.25 ex}}\alpha  b c -3 a b c -2 \underline{\hspace{1.25 ex}}\alpha  d \right) \left(-c +x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  b +a b -d \right) \sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}\, \sqrt{\frac{c \left(-b +x \right)}{b \left(-c +x \right)}}\, \sqrt{\frac{c \left(-a +x \right)}{a \left(-c +x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)-\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  c +a b +a c +b c -d \right) \EllipticPi \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, -\frac{\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  c +a c +b c -d}{b \left(a -c \right)}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)}{a b}\right)}{\left(-3 \underline{\hspace{1.25 ex}}\alpha^{2}+2 \underline{\hspace{1.25 ex}}\alpha  a +2 \underline{\hspace{1.25 ex}}\alpha  b +2 \underline{\hspace{1.25 ex}}\alpha  c -a b -a c -b c +d \right) \left(a -c \right) \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}\right)}{c^{2} d}$&$525$\\ \hline \end{longtable}"," ",0,"-4*a*((a-c)*x/a/(-c+x))^(1/2)*(-c+x)^2*(c*(-b+x)/b/(-c+x))^(1/2)*(c*(-a+x)/a/(-c+x))^(1/2)/(a-c)/c/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)*EllipticF(((a-c)*x/a/(-c+x))^(1/2),((-b+c)*a/b/(c-a))^(1/2))-2*a/c^2/d*sum((_alpha^2*a+_alpha^2*b+_alpha^2*c-2*_alpha*a*b-2*_alpha*a*c-2*_alpha*b*c+3*a*b*c+2*_alpha*d)/(-3*_alpha^2+2*_alpha*a+2*_alpha*b+2*_alpha*c-a*b-a*c-b*c+d)*(-c+x)^2/(a-c)*(_alpha^2-_alpha*a-_alpha*b+a*b-d)*((a-c)*x/a/(-c+x))^(1/2)*(c*(-b+x)/b/(-c+x))^(1/2)*(c*(-a+x)/a/(-c+x))^(1/2)/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)*(EllipticF(((a-c)*x/a/(-c+x))^(1/2),((-b+c)*a/b/(c-a))^(1/2))-(_alpha^2-_alpha*a-_alpha*b-_alpha*c+a*b+a*c+b*c-d)/a/b*EllipticPi(((a-c)*x/a/(-c+x))^(1/2),-(_alpha^2-_alpha*a-_alpha*b-_alpha*c+a*c+b*c-d)/b/(a-c),((-b+c)*a/b/(c-a))^(1/2))),_alpha=RootOf(_Z^3+(-a-b-c)*_Z^2+(a*b+a*c+b*c-d)*_Z-a*b*c))","C"
754,1,48,47,0.124000," ","int((a*x^3-b)*(a*x^3+b)^(1/2)/x^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{\sqrt{a \,x^{3}+b}\, \left(3 a \,x^{3}-2 b \right)}{12 x^{6}}-\frac{5 a^{2} \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{12 \sqrt{b}}$&$48$\\ elliptic&$\frac{b \sqrt{a \,x^{3}+b}}{6 x^{6}}-\frac{a \sqrt{a \,x^{3}+b}}{4 x^{3}}-\frac{5 a^{2} \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{12 \sqrt{b}}$&$54$\\ default&$a \left(-\frac{\sqrt{a \,x^{3}+b}}{3 x^{3}}-\frac{a \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{3 \sqrt{b}}\right)-b \left(-\frac{\sqrt{a \,x^{3}+b}}{6 x^{6}}-\frac{a \sqrt{a \,x^{3}+b}}{12 b \,x^{3}}+\frac{a^{2} \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{12 b^{\frac{3}{2}}}\right)$&$97$\\ \hline \end{longtable}"," ",0,"-1/12*(a*x^3+b)^(1/2)*(3*a*x^3-2*b)/x^6-5/12*a^2*arctanh((a*x^3+b)^(1/2)/b^(1/2))/b^(1/2)","A"
755,1,48,47,0.108000," ","int((a*x^3+b)^(1/2)*(a*x^3+2*b)/x^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{\sqrt{a \,x^{3}+b}\, \left(3 a \,x^{3}+2 b \right)}{6 x^{6}}-\frac{a^{2} \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{6 \sqrt{b}}$&$48$\\ elliptic&$-\frac{b \sqrt{a \,x^{3}+b}}{3 x^{6}}-\frac{a \sqrt{a \,x^{3}+b}}{2 x^{3}}-\frac{a^{2} \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{6 \sqrt{b}}$&$54$\\ default&$a \left(-\frac{\sqrt{a \,x^{3}+b}}{3 x^{3}}-\frac{a \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{3 \sqrt{b}}\right)+2 b \left(-\frac{\sqrt{a \,x^{3}+b}}{6 x^{6}}-\frac{a \sqrt{a \,x^{3}+b}}{12 b \,x^{3}}+\frac{a^{2} \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{12 b^{\frac{3}{2}}}\right)$&$97$\\ \hline \end{longtable}"," ",0,"-1/6*(a*x^3+b)^(1/2)*(3*a*x^3+2*b)/x^6-1/6*a^2*arctanh((a*x^3+b)^(1/2)/b^(1/2))/b^(1/2)","A"
756,1,628,53,0.158000," ","int((3*a*b*c*x-2*(a*b+a*c+b*c)*x^2+(a+b+c)*x^3)/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)/(a*b*c-(a*b+a*c+b*c)*x+(a+b+c)*x^2+(-1+d)*x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 \left(a +b +c \right) a \sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}\, \left(-c +x \right)^{2} \sqrt{\frac{c \left(-b +x \right)}{b \left(-c +x \right)}}\, \sqrt{\frac{c \left(-a +x \right)}{a \left(-c +x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)}{\left(-1+d \right) \left(a -c \right) c \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}-\frac{2 a \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\left(-1+d \right) \textit{\_Z}^{3}+\left(a +b +c \right) \textit{\_Z}^{2}+\left(-a b -a c -b c \right) \textit{\_Z} +a b c \right)}{\sum}\frac{\left(-2 \underline{\hspace{1.25 ex}}\alpha^{2} a b d -2 \underline{\hspace{1.25 ex}}\alpha^{2} a c d -2 \underline{\hspace{1.25 ex}}\alpha^{2} b c d +3 \underline{\hspace{1.25 ex}}\alpha  a b c d -\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-\underline{\hspace{1.25 ex}}\alpha^{2} b^{2}-\underline{\hspace{1.25 ex}}\alpha^{2} c^{2}+\underline{\hspace{1.25 ex}}\alpha  \,a^{2} b +\underline{\hspace{1.25 ex}}\alpha  \,a^{2} c +\underline{\hspace{1.25 ex}}\alpha  a \,b^{2}+\underline{\hspace{1.25 ex}}\alpha  a \,c^{2}+\underline{\hspace{1.25 ex}}\alpha  \,b^{2} c +\underline{\hspace{1.25 ex}}\alpha  b \,c^{2}-a^{2} b c -a \,b^{2} c -a b \,c^{2}\right) \left(-c +x \right)^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{2} d -\underline{\hspace{1.25 ex}}\alpha  c d -c^{2} d +\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  b +a b \right) \sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}\, \sqrt{\frac{c \left(-b +x \right)}{b \left(-c +x \right)}}\, \sqrt{\frac{c \left(-a +x \right)}{a \left(-c +x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)-\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{2} d +\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  c +a b +a c +b c \right) \EllipticPi \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, -\frac{-\underline{\hspace{1.25 ex}}\alpha^{2} d +\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  c +a c +b c}{b \left(a -c \right)}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)}{a b}\right)}{\left(-3 \underline{\hspace{1.25 ex}}\alpha^{2} d +3 \underline{\hspace{1.25 ex}}\alpha^{2}-2 \underline{\hspace{1.25 ex}}\alpha  a -2 \underline{\hspace{1.25 ex}}\alpha  b -2 \underline{\hspace{1.25 ex}}\alpha  c +a b +a c +b c \right) \left(a -c \right) \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}\right)}{\left(-1+d \right) c^{4} d}$&$628$\\ elliptic&$-\frac{2 \left(a +b +c \right) a \sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}\, \left(-c +x \right)^{2} \sqrt{\frac{c \left(-b +x \right)}{b \left(-c +x \right)}}\, \sqrt{\frac{c \left(-a +x \right)}{a \left(-c +x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)}{\left(-1+d \right) \left(a -c \right) c \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}-\frac{2 a \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\left(-1+d \right) \textit{\_Z}^{3}+\left(a +b +c \right) \textit{\_Z}^{2}+\left(-a b -a c -b c \right) \textit{\_Z} +a b c \right)}{\sum}\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2} a b d +2 \underline{\hspace{1.25 ex}}\alpha^{2} a c d +2 \underline{\hspace{1.25 ex}}\alpha^{2} b c d -3 \underline{\hspace{1.25 ex}}\alpha  a b c d +\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+\underline{\hspace{1.25 ex}}\alpha^{2} b^{2}+\underline{\hspace{1.25 ex}}\alpha^{2} c^{2}-\underline{\hspace{1.25 ex}}\alpha  \,a^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2} c -\underline{\hspace{1.25 ex}}\alpha  a \,b^{2}-\underline{\hspace{1.25 ex}}\alpha  a \,c^{2}-\underline{\hspace{1.25 ex}}\alpha  \,b^{2} c -\underline{\hspace{1.25 ex}}\alpha  b \,c^{2}+a^{2} b c +a \,b^{2} c +a b \,c^{2}\right) \left(-c +x \right)^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{2} d -\underline{\hspace{1.25 ex}}\alpha  c d -c^{2} d +\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  b +a b \right) \sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}\, \sqrt{\frac{c \left(-b +x \right)}{b \left(-c +x \right)}}\, \sqrt{\frac{c \left(-a +x \right)}{a \left(-c +x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)-\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{2} d +\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  c +a b +a c +b c \right) \EllipticPi \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, -\frac{-\underline{\hspace{1.25 ex}}\alpha^{2} d +\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  c +a c +b c}{b \left(a -c \right)}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)}{a b}\right)}{\left(-1+d \right) \left(3 \underline{\hspace{1.25 ex}}\alpha^{2} d -3 \underline{\hspace{1.25 ex}}\alpha^{2}+2 \underline{\hspace{1.25 ex}}\alpha  a +2 \underline{\hspace{1.25 ex}}\alpha  b +2 \underline{\hspace{1.25 ex}}\alpha  c -a b -a c -b c \right) \left(a -c \right) \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}\right)}{c^{4} d}$&$631$\\ \hline \end{longtable}"," ",0,"-2*(a+b+c)/(-1+d)*a*((a-c)*x/a/(-c+x))^(1/2)*(-c+x)^2*(c*(-b+x)/b/(-c+x))^(1/2)*(c*(-a+x)/a/(-c+x))^(1/2)/(a-c)/c/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)*EllipticF(((a-c)*x/a/(-c+x))^(1/2),((-b+c)*a/b/(c-a))^(1/2))-2/(-1+d)*a/c^4/d*sum((-2*_alpha^2*a*b*d-2*_alpha^2*a*c*d-2*_alpha^2*b*c*d+3*_alpha*a*b*c*d-_alpha^2*a^2-_alpha^2*b^2-_alpha^2*c^2+_alpha*a^2*b+_alpha*a^2*c+_alpha*a*b^2+_alpha*a*c^2+_alpha*b^2*c+_alpha*b*c^2-a^2*b*c-a*b^2*c-a*b*c^2)/(-3*_alpha^2*d+3*_alpha^2-2*_alpha*a-2*_alpha*b-2*_alpha*c+a*b+a*c+b*c)*(-c+x)^2/(a-c)*(-_alpha^2*d-_alpha*c*d-c^2*d+_alpha^2-_alpha*a-_alpha*b+a*b)*((a-c)*x/a/(-c+x))^(1/2)*(c*(-b+x)/b/(-c+x))^(1/2)*(c*(-a+x)/a/(-c+x))^(1/2)/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)*(EllipticF(((a-c)*x/a/(-c+x))^(1/2),((-b+c)*a/b/(c-a))^(1/2))-(-_alpha^2*d+_alpha^2-_alpha*a-_alpha*b-_alpha*c+a*b+a*c+b*c)/a/b*EllipticPi(((a-c)*x/a/(-c+x))^(1/2),-(-_alpha^2*d+_alpha^2-_alpha*a-_alpha*b-_alpha*c+a*c+b*c)/b/(a-c),((-b+c)*a/b/(c-a))^(1/2))),_alpha=RootOf((-1+d)*_Z^3+(a+b+c)*_Z^2+(-a*b-a*c-b*c)*_Z+a*b*c))","C"
757,1,671,53,0.165000," ","int(x*(3*a*b*c-2*(a*b+a*c+b*c)*x+(a+b+c)*x^2)/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)/(-a*b*c*d+(a*b+a*c+b*c)*d*x-(a+b+c)*d*x^2+(-1+d)*x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\frac{2 \left(a +b +c \right) a \sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}\, \left(-c +x \right)^{2} \sqrt{\frac{c \left(-b +x \right)}{b \left(-c +x \right)}}\, \sqrt{\frac{c \left(-a +x \right)}{a \left(-c +x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)}{\left(-1+d \right) \left(a -c \right) c \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}-\frac{2 a \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\left(-1+d \right) \textit{\_Z}^{3}+\left(-a d -b d -c d \right) \textit{\_Z}^{2}+\left(a b d +a c d +b c d \right) \textit{\_Z} -a b c d \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{2} a^{2} d -\underline{\hspace{1.25 ex}}\alpha^{2} b^{2} d -\underline{\hspace{1.25 ex}}\alpha^{2} c^{2} d +\underline{\hspace{1.25 ex}}\alpha  \,a^{2} b d +\underline{\hspace{1.25 ex}}\alpha  \,a^{2} c d +\underline{\hspace{1.25 ex}}\alpha  a \,b^{2} d +\underline{\hspace{1.25 ex}}\alpha  a \,c^{2} d +\underline{\hspace{1.25 ex}}\alpha  \,b^{2} c d +\underline{\hspace{1.25 ex}}\alpha  b \,c^{2} d -a^{2} b c d -a \,b^{2} c d -a b \,c^{2} d -2 \underline{\hspace{1.25 ex}}\alpha^{2} a b -2 \underline{\hspace{1.25 ex}}\alpha^{2} a c -2 \underline{\hspace{1.25 ex}}\alpha^{2} b c +3 \underline{\hspace{1.25 ex}}\alpha  a b c \right) \left(-c +x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2} d -d \underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  b d +a b d -\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  c -c^{2}\right) \sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}\, \sqrt{\frac{c \left(-b +x \right)}{b \left(-c +x \right)}}\, \sqrt{\frac{c \left(-a +x \right)}{a \left(-c +x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)-\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2} d -d \underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  b d -\underline{\hspace{1.25 ex}}\alpha  c d +a b d +a c d +b c d -\underline{\hspace{1.25 ex}}\alpha^{2}\right) \EllipticPi \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, -\frac{\underline{\hspace{1.25 ex}}\alpha^{2} d -d \underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  b d -\underline{\hspace{1.25 ex}}\alpha  c d +a c d +b c d -\underline{\hspace{1.25 ex}}\alpha^{2}}{b d \left(a -c \right)}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)}{a b d}\right)}{\left(-1+d \right) \left(3 \underline{\hspace{1.25 ex}}\alpha^{2} d -2 d \underline{\hspace{1.25 ex}}\alpha  a -2 \underline{\hspace{1.25 ex}}\alpha  b d -2 \underline{\hspace{1.25 ex}}\alpha  c d +a b d +a c d +b c d -3 \underline{\hspace{1.25 ex}}\alpha^{2}\right) \left(a -c \right) \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}\right)}{c^{4}}$&$671$\\ default&$-\frac{2 \left(a +b +c \right) a \sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}\, \left(-c +x \right)^{2} \sqrt{\frac{c \left(-b +x \right)}{b \left(-c +x \right)}}\, \sqrt{\frac{c \left(-a +x \right)}{a \left(-c +x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)}{\left(-1+d \right) \left(a -c \right) c \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}-\frac{2 a \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\left(-1+d \right) \textit{\_Z}^{3}+\left(-a d -b d -c d \right) \textit{\_Z}^{2}+\left(a b d +a c d +b c d \right) \textit{\_Z} -a b c d \right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2} a^{2} d +\underline{\hspace{1.25 ex}}\alpha^{2} b^{2} d +\underline{\hspace{1.25 ex}}\alpha^{2} c^{2} d -\underline{\hspace{1.25 ex}}\alpha  \,a^{2} b d -\underline{\hspace{1.25 ex}}\alpha  \,a^{2} c d -\underline{\hspace{1.25 ex}}\alpha  a \,b^{2} d -\underline{\hspace{1.25 ex}}\alpha  a \,c^{2} d -\underline{\hspace{1.25 ex}}\alpha  \,b^{2} c d -\underline{\hspace{1.25 ex}}\alpha  b \,c^{2} d +a^{2} b c d +a \,b^{2} c d +a b \,c^{2} d +2 \underline{\hspace{1.25 ex}}\alpha^{2} a b +2 \underline{\hspace{1.25 ex}}\alpha^{2} a c +2 \underline{\hspace{1.25 ex}}\alpha^{2} b c -3 \underline{\hspace{1.25 ex}}\alpha  a b c \right) \left(-c +x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2} d -d \underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  b d +a b d -\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  c -c^{2}\right) \sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}\, \sqrt{\frac{c \left(-b +x \right)}{b \left(-c +x \right)}}\, \sqrt{\frac{c \left(-a +x \right)}{a \left(-c +x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)-\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2} d -d \underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  b d -\underline{\hspace{1.25 ex}}\alpha  c d +a b d +a c d +b c d -\underline{\hspace{1.25 ex}}\alpha^{2}\right) \EllipticPi \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, -\frac{\underline{\hspace{1.25 ex}}\alpha^{2} d -d \underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  b d -\underline{\hspace{1.25 ex}}\alpha  c d +a c d +b c d -\underline{\hspace{1.25 ex}}\alpha^{2}}{b d \left(a -c \right)}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)}{a b d}\right)}{\left(-3 \underline{\hspace{1.25 ex}}\alpha^{2} d +2 d \underline{\hspace{1.25 ex}}\alpha  a +2 \underline{\hspace{1.25 ex}}\alpha  b d +2 \underline{\hspace{1.25 ex}}\alpha  c d -a b d -a c d -b c d +3 \underline{\hspace{1.25 ex}}\alpha^{2}\right) \left(a -c \right) \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}\right)}{\left(-1+d \right) c^{4}}$&$674$\\ \hline \end{longtable}"," ",0,"-2*(a+b+c)/(-1+d)*a*((a-c)*x/a/(-c+x))^(1/2)*(-c+x)^2*(c*(-b+x)/b/(-c+x))^(1/2)*(c*(-a+x)/a/(-c+x))^(1/2)/(a-c)/c/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)*EllipticF(((a-c)*x/a/(-c+x))^(1/2),((-b+c)*a/b/(c-a))^(1/2))-2*a/c^4*sum((-_alpha^2*a^2*d-_alpha^2*b^2*d-_alpha^2*c^2*d+_alpha*a^2*b*d+_alpha*a^2*c*d+_alpha*a*b^2*d+_alpha*a*c^2*d+_alpha*b^2*c*d+_alpha*b*c^2*d-a^2*b*c*d-a*b^2*c*d-a*b*c^2*d-2*_alpha^2*a*b-2*_alpha^2*a*c-2*_alpha^2*b*c+3*_alpha*a*b*c)/(-1+d)/(3*_alpha^2*d-2*_alpha*a*d-2*_alpha*b*d-2*_alpha*c*d+a*b*d+a*c*d+b*c*d-3*_alpha^2)*(-c+x)^2/(a-c)*(_alpha^2*d-_alpha*a*d-_alpha*b*d+a*b*d-_alpha^2-_alpha*c-c^2)*((a-c)*x/a/(-c+x))^(1/2)*(c*(-b+x)/b/(-c+x))^(1/2)*(c*(-a+x)/a/(-c+x))^(1/2)/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)*(EllipticF(((a-c)*x/a/(-c+x))^(1/2),((-b+c)*a/b/(c-a))^(1/2))-(_alpha^2*d-_alpha*a*d-_alpha*b*d-_alpha*c*d+a*b*d+a*c*d+b*c*d-_alpha^2)/a/b/d*EllipticPi(((a-c)*x/a/(-c+x))^(1/2),-(_alpha^2*d-_alpha*a*d-_alpha*b*d-_alpha*c*d+a*c*d+b*c*d-_alpha^2)/b/d/(a-c),((-b+c)*a/b/(c-a))^(1/2))),_alpha=RootOf((-1+d)*_Z^3+(-a*d-b*d-c*d)*_Z^2+(a*b*d+a*c*d+b*c*d)*_Z-a*b*c*d))","C"
758,1,33,47,3.405000," ","int((x^4-x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{2 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{4}} x^{\frac{3}{2}} \hypergeom \left(\left[-\frac{1}{4}, \frac{3}{4}\right], \left[\frac{7}{4}\right], x^{2}\right)}{3 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{4}}}$&$33$\\ trager&$\frac{x \left(x^{4}-x^{2}\right)^{\frac{1}{4}}}{2}-\frac{\ln \left(\frac{2 \left(x^{4}-x^{2}\right)^{\frac{3}{4}}+2 \sqrt{x^{4}-x^{2}}\, x +2 x^{2} \left(x^{4}-x^{2}\right)^{\frac{1}{4}}+2 x^{3}-x}{x}\right)}{8}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \sqrt{x^{4}-x^{2}}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{4}-x^{2}\right)^{\frac{3}{4}}-2 x^{2} \left(x^{4}-x^{2}\right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{2}+1\right) x}{x}\right)}{8}$&$157$\\ risch&$\frac{x \left(x^{2} \left(x^{2}-1\right)\right)^{\frac{1}{4}}}{2}+\frac{\left(-\frac{\ln \left(\frac{2 x^{6}+2 \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}} x^{4}+2 \sqrt{x^{8}-3 x^{6}+3 x^{4}-x^{2}}\, x^{2}-5 x^{4}+2 \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{3}{4}}-4 \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}} x^{2}-2 \sqrt{x^{8}-3 x^{6}+3 x^{4}-x^{2}}+4 x^{2}+2 \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}}-1}{\left(-1+x \right)^{2} \left(1+x \right)^{2}}\right)}{8}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-2 \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-2 x^{6}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{3}{4}}+2 \sqrt{x^{8}-3 x^{6}+3 x^{4}-x^{2}}\, x^{2}+4 \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+5 x^{4}-2 \sqrt{x^{8}-3 x^{6}+3 x^{4}-x^{2}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}}-4 x^{2}+1}{\left(-1+x \right)^{2} \left(1+x \right)^{2}}\right)}{8}\right) \left(x^{2} \left(x^{2}-1\right)\right)^{\frac{1}{4}} \left(x^{2} \left(x^{2}-1\right)^{3}\right)^{\frac{1}{4}}}{x \left(x^{2}-1\right)}$&$438$\\ \hline \end{longtable}"," ",0,"2/3*signum(x^2-1)^(1/4)/(-signum(x^2-1))^(1/4)*x^(3/2)*hypergeom([-1/4,3/4],[7/4],x^2)","C"
759,1,17,47,3.085000," ","int(x^2*(x^4+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{2 x^{\frac{7}{2}} \hypergeom \left(\left[-\frac{1}{4}, \frac{7}{4}\right], \left[\frac{11}{4}\right], -x^{2}\right)}{7}$&$17$\\ trager&$\frac{x \left(4 x^{2}+1\right) \left(x^{4}+x^{2}\right)^{\frac{1}{4}}}{16}-\frac{3 \ln \left(\frac{2 \left(x^{4}+x^{2}\right)^{\frac{3}{4}}+2 \sqrt{x^{4}+x^{2}}\, x +2 x^{2} \left(x^{4}+x^{2}\right)^{\frac{1}{4}}+2 x^{3}+x}{x}\right)}{64}-\frac{3 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \sqrt{x^{4}+x^{2}}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{4}+x^{2}\right)^{\frac{3}{4}}-2 x^{2} \left(x^{4}+x^{2}\right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right) x}{x}\right)}{64}$&$149$\\ risch&$\frac{x \left(4 x^{2}+1\right) \left(x^{2} \left(x^{2}+1\right)\right)^{\frac{1}{4}}}{16}+\frac{\left(-\frac{3 \ln \left(\frac{2 x^{6}+2 \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{1}{4}} x^{4}+2 \sqrt{x^{8}+3 x^{6}+3 x^{4}+x^{2}}\, x^{2}+5 x^{4}+2 \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{3}{4}}+4 \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{1}{4}} x^{2}+2 \sqrt{x^{8}+3 x^{6}+3 x^{4}+x^{2}}+4 x^{2}+2 \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{1}{4}}+1}{\left(x^{2}+1\right)^{2}}\right)}{64}+\frac{3 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{1}{4}} x^{4}+2 x^{6}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{3}{4}}-4 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{1}{4}} x^{2}-2 \sqrt{x^{8}+3 x^{6}+3 x^{4}+x^{2}}\, x^{2}+5 x^{4}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{1}{4}}-2 \sqrt{x^{8}+3 x^{6}+3 x^{4}+x^{2}}+4 x^{2}+1}{\left(x^{2}+1\right)^{2}}\right)}{64}\right) \left(x^{2} \left(x^{2}+1\right)\right)^{\frac{1}{4}} \left(x^{2} \left(x^{2}+1\right)^{3}\right)^{\frac{1}{4}}}{x \left(x^{2}+1\right)}$&$416$\\ \hline \end{longtable}"," ",0,"2/7*x^(7/2)*hypergeom([-1/4,7/4],[11/4],-x^2)","C"
760,1,74,51,0.272000," ","int((2*x^4-1)*(2*x^4+3*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(-\frac{\sqrt{2 x^{4}+3 x^{2}+1}\, \sqrt{2}}{4 x \left(\frac{2 x^{4}+3 x^{2}+1}{2 x^{2}}-\frac{1}{2}\right)}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{2 x^{4}+3 x^{2}+1}}{x}\right)}{2}\right) \sqrt{2}}{2}$&$74$\\ trager&$-\frac{x \sqrt{2 x^{4}+3 x^{2}+1}}{2 \left(2 x^{4}+2 x^{2}+1\right)}-\frac{\ln \left(-\frac{2 x^{4}+2 \sqrt{2 x^{4}+3 x^{2}+1}\, x +4 x^{2}+1}{2 x^{4}+2 x^{2}+1}\right)}{4}$&$81$\\ risch&$-\frac{x \sqrt{2 x^{4}+3 x^{2}+1}}{2 \left(2 x^{4}+2 x^{2}+1\right)}-\frac{i \sqrt{x^{2}+1}\, \sqrt{2 x^{2}+1}\, \EllipticF \left(i x , \sqrt{2}\right)}{2 \sqrt{2 x^{4}+3 x^{2}+1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(2 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\left(4 \underline{\hspace{1.25 ex}}\alpha^{2}+3\right) \left(\underline{\hspace{1.25 ex}}\alpha^{2}+5 x^{2}+4\right)}{10 \sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{2 x^{4}+3 x^{2}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{4 i \left(-\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{x^{2}+1}\, \sqrt{2 x^{2}+1}\, \EllipticPi \left(i x , 2 \underline{\hspace{1.25 ex}}\alpha^{2}+2, i \sqrt{-2}\right)}{\sqrt{2 x^{4}+3 x^{2}+1}}\right)\right)}{8}$&$201$\\ default&$-\frac{i \sqrt{x^{2}+1}\, \sqrt{2 x^{2}+1}\, \EllipticF \left(i x , \sqrt{2}\right)}{2 \sqrt{2 x^{4}+3 x^{2}+1}}-\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(2 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2}+1\right) \left(-\frac{\arctanh \left(\frac{\left(4 \underline{\hspace{1.25 ex}}\alpha^{2}+3\right) \left(\underline{\hspace{1.25 ex}}\alpha^{2}+5 x^{2}+4\right)}{10 \sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{2 x^{4}+3 x^{2}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{4 i \left(-\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{x^{2}+1}\, \sqrt{2 x^{2}+1}\, \EllipticPi \left(i x , 2 \underline{\hspace{1.25 ex}}\alpha^{2}+2, i \sqrt{-2}\right)}{\sqrt{2 x^{4}+3 x^{2}+1}}\right)\right)}{8}-\frac{x \sqrt{2 x^{4}+3 x^{2}+1}}{2 \left(2 x^{4}+2 x^{2}+1\right)}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(2 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2}+1\right) \left(-\frac{\arctanh \left(\frac{\left(4 \underline{\hspace{1.25 ex}}\alpha^{2}+3\right) \left(\underline{\hspace{1.25 ex}}\alpha^{2}+5 x^{2}+4\right)}{10 \sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{2 x^{4}+3 x^{2}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{4 i \left(-\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{x^{2}+1}\, \sqrt{2 x^{2}+1}\, \EllipticPi \left(i x , 2 \underline{\hspace{1.25 ex}}\alpha^{2}+2, i \sqrt{-2}\right)}{\sqrt{2 x^{4}+3 x^{2}+1}}\right)\right)}{4}$&$340$\\ \hline \end{longtable}"," ",0,"1/2*(-1/4*(2*x^4+3*x^2+1)^(1/2)*2^(1/2)/x/(1/2*(2*x^4+3*x^2+1)/x^2-1/2)-1/2*2^(1/2)*arctanh((2*x^4+3*x^2+1)^(1/2)/x))*2^(1/2)","A"
761,1,140,51,12.117000," ","int((2*x^4-2*x^3+x^2-2)^(1/2)*(2*x^4-x^3+2)/(x^4-x^3-1)/(2*x^4-2*x^3-x^2-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{4}+2 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{3}-3 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}+4 \sqrt{2 x^{4}-2 x^{3}+x^{2}-2}\, x +2 \RootOf \left(\textit{\_Z}^{2}-2\right)}{2 x^{4}-2 x^{3}-x^{2}-2}\right)+\ln \left(-\frac{x^{4}-x^{3}+\sqrt{2 x^{4}-2 x^{3}+x^{2}-2}\, x +x^{2}-1}{x^{4}-x^{3}-1}\right)$&$140$\\ default&$\text{Expression too large to display}$&$12512$\\ elliptic&$\text{Expression too large to display}$&$1159913$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2-2)*ln(-(-2*RootOf(_Z^2-2)*x^4+2*RootOf(_Z^2-2)*x^3-3*RootOf(_Z^2-2)*x^2+4*(2*x^4-2*x^3+x^2-2)^(1/2)*x+2*RootOf(_Z^2-2))/(2*x^4-2*x^3-x^2-2))+ln(-(x^4-x^3+(2*x^4-2*x^3+x^2-2)^(1/2)*x+x^2-1)/(x^4-x^3-1))","C"
762,1,38,45,0.135000," ","int((a*x^2-b)/(a*x^2+b)/(a^2*x^4+b^2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\arctan \left(\frac{\sqrt{a^{2} x^{4}+b^{2}}\, \sqrt{2}}{2 x \sqrt{a b}}\right) \sqrt{2}}{2 \sqrt{a b}}$&$38$\\ default&$\frac{\sqrt{1-\frac{i a \,x^{2}}{b}}\, \sqrt{1+\frac{i a \,x^{2}}{b}}\, \EllipticF \left(x \sqrt{\frac{i a}{b}}, i\right)}{\sqrt{\frac{i a}{b}}\, \sqrt{a^{2} x^{4}+b^{2}}}-\frac{2 \sqrt{1-\frac{i a \,x^{2}}{b}}\, \sqrt{1+\frac{i a \,x^{2}}{b}}\, \EllipticPi \left(x \sqrt{\frac{i a}{b}}, i, \frac{\sqrt{-\frac{i a}{b}}}{\sqrt{\frac{i a}{b}}}\right)}{\sqrt{\frac{i a}{b}}\, \sqrt{a^{2} x^{4}+b^{2}}}$&$152$\\ \hline \end{longtable}"," ",0,"1/2/(a*b)^(1/2)*arctan(1/2*(a^2*x^4+b^2)^(1/2)*2^(1/2)/x/(a*b)^(1/2))*2^(1/2)","A"
763,0,0,55,0.021000," ","int((a*x^4+3*b)/(a*x^4-x^3-b)/(a*x^5-b*x)^(1/4),x)","\[\int \frac{a \,x^{4}+3 b}{\left(a \,x^{4}-x^{3}-b \right) \left(a \,x^{5}-b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^4+3*b)/(a*x^4-x^3-b)/(a*x^5-b*x)^(1/4),x)","F"
764,1,58,47,0.462000," ","int((x^3-1)*(x^6-1)^(1/2)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\left(\frac{x^{3}}{6}-\frac{1}{3}\right) \sqrt{x^{6}-1}-\frac{\ln \left(x^{3}+\sqrt{x^{6}-1}\right)}{6}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{3}$&$58$\\ meijerg&$\frac{\sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(4 \sqrt{\pi}-4 \sqrt{\pi}\, \sqrt{-x^{6}+1}+4 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right)-2 \left(2-2 \ln \left(2\right)+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}\right)}{12 \sqrt{\pi}\, \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}}+\frac{i \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(-2 i \sqrt{\pi}\, x^{3} \sqrt{-x^{6}+1}-2 i \sqrt{\pi}\, \arcsin \left(x^{3}\right)\right)}{12 \sqrt{\pi}\, \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}}$&$136$\\ \hline \end{longtable}"," ",0,"(1/6*x^3-1/3)*(x^6-1)^(1/2)-1/6*ln(x^3+(x^6-1)^(1/2))+1/3*RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)+(x^6-1)^(1/2))/x^3)","C"
765,1,7038,11,43.898000," ","int(x*(3+4*x)*(x^3-2*x-1)^(1/3)/(x^6-8*x^2-8*x-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$7038$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
766,1,11032,11,43.208000," ","int(x*(3+4*x)*(x^3-2*x-1)^(1/3)/(x^6-8*x^2-8*x-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$11032$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
767,1,1598,11,6.095000," ","int((3+2*x)*(x^3+x+1)^(2/3)/(x^6+x^4+x^3+x^2+2*x+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{5} \ln \left(-\frac{18 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{5} x^{3}+9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{4} \left(x^{3}+x +1\right)^{\frac{1}{3}} x^{2}+3 \left(x^{3}+x +1\right)^{\frac{2}{3}} \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x +9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{5} x +9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{5}-4 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{2} x^{3}-2 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right) \left(x^{3}+x +1\right)^{\frac{1}{3}} x^{2}-\left(x^{3}+x +1\right)^{\frac{2}{3}} x -2 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{2} x -2 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{2}}{9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x^{3}-x^{3}+x +1}\right)+18 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{5} \ln \left(-\frac{-81 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{7} x^{3}+27 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{4} x^{3}+3 \left(x^{3}+x +1\right)^{\frac{2}{3}} \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{2} x +9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{4} x +9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{4}-2 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right) x^{3}+\left(x^{3}+x +1\right)^{\frac{1}{3}} x^{2}-\RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right) x -\RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)}{9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x^{3}-x^{3}+x +1}\right)-9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{4} \ln \left(\frac{54 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{7} x^{3}+9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{5} \left(x^{3}+x +1\right)^{\frac{1}{3}} x^{2}-15 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{4} x^{3}+3 \left(x^{3}+x +1\right)^{\frac{2}{3}} \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x -3 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{2} \left(x^{3}+x +1\right)^{\frac{1}{3}} x^{2}+6 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{4} x +6 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{4}+\RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right) x^{3}-\left(x^{3}+x +1\right)^{\frac{2}{3}} x -\RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right) x -\RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)}{9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x^{3}-2 x^{3}-x -1}\right)+3 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{2} \ln \left(-\frac{18 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{5} x^{3}+9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{4} \left(x^{3}+x +1\right)^{\frac{1}{3}} x^{2}+3 \left(x^{3}+x +1\right)^{\frac{2}{3}} \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x +9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{5} x +9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{5}-4 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{2} x^{3}-2 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right) \left(x^{3}+x +1\right)^{\frac{1}{3}} x^{2}-\left(x^{3}+x +1\right)^{\frac{2}{3}} x -2 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{2} x -2 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{2}}{9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x^{3}-x^{3}+x +1}\right)-3 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{2} \ln \left(-\frac{-81 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{7} x^{3}+27 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{4} x^{3}+3 \left(x^{3}+x +1\right)^{\frac{2}{3}} \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{2} x +9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{4} x +9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{4}-2 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right) x^{3}+\left(x^{3}+x +1\right)^{\frac{1}{3}} x^{2}-\RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right) x -\RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)}{9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x^{3}-x^{3}+x +1}\right)+\RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right) \ln \left(\frac{3 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{2} \left(x^{3}+x +1\right)^{\frac{1}{3}} x^{2}+2 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right) x^{3}+\left(x^{3}+x +1\right)^{\frac{2}{3}} x +\RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right) x +\RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)}{9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x^{3}-2 x^{3}-x -1}\right)+\RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right) \ln \left(\frac{54 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{7} x^{3}+9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{5} \left(x^{3}+x +1\right)^{\frac{1}{3}} x^{2}-15 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{4} x^{3}+3 \left(x^{3}+x +1\right)^{\frac{2}{3}} \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x -3 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{2} \left(x^{3}+x +1\right)^{\frac{1}{3}} x^{2}+6 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{4} x +6 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{4}+\RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right) x^{3}-\left(x^{3}+x +1\right)^{\frac{2}{3}} x -\RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right) x -\RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)}{9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x^{3}-2 x^{3}-x -1}\right)$&$1598$\\ \hline \end{longtable}"," ",0,"-9*RootOf(27*_Z^6-9*_Z^3+1)^5*ln(-(18*RootOf(27*_Z^6-9*_Z^3+1)^5*x^3+9*RootOf(27*_Z^6-9*_Z^3+1)^4*(x^3+x+1)^(1/3)*x^2+3*(x^3+x+1)^(2/3)*RootOf(27*_Z^6-9*_Z^3+1)^3*x+9*RootOf(27*_Z^6-9*_Z^3+1)^5*x+9*RootOf(27*_Z^6-9*_Z^3+1)^5-4*RootOf(27*_Z^6-9*_Z^3+1)^2*x^3-2*RootOf(27*_Z^6-9*_Z^3+1)*(x^3+x+1)^(1/3)*x^2-(x^3+x+1)^(2/3)*x-2*RootOf(27*_Z^6-9*_Z^3+1)^2*x-2*RootOf(27*_Z^6-9*_Z^3+1)^2)/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-x^3+x+1))+18*RootOf(27*_Z^6-9*_Z^3+1)^5*ln(-(-81*RootOf(27*_Z^6-9*_Z^3+1)^7*x^3+27*RootOf(27*_Z^6-9*_Z^3+1)^4*x^3+3*(x^3+x+1)^(2/3)*RootOf(27*_Z^6-9*_Z^3+1)^2*x+9*RootOf(27*_Z^6-9*_Z^3+1)^4*x+9*RootOf(27*_Z^6-9*_Z^3+1)^4-2*RootOf(27*_Z^6-9*_Z^3+1)*x^3+(x^3+x+1)^(1/3)*x^2-RootOf(27*_Z^6-9*_Z^3+1)*x-RootOf(27*_Z^6-9*_Z^3+1))/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-x^3+x+1))-9*RootOf(27*_Z^6-9*_Z^3+1)^4*ln((54*RootOf(27*_Z^6-9*_Z^3+1)^7*x^3+9*RootOf(27*_Z^6-9*_Z^3+1)^5*(x^3+x+1)^(1/3)*x^2-15*RootOf(27*_Z^6-9*_Z^3+1)^4*x^3+3*(x^3+x+1)^(2/3)*RootOf(27*_Z^6-9*_Z^3+1)^3*x-3*RootOf(27*_Z^6-9*_Z^3+1)^2*(x^3+x+1)^(1/3)*x^2+6*RootOf(27*_Z^6-9*_Z^3+1)^4*x+6*RootOf(27*_Z^6-9*_Z^3+1)^4+RootOf(27*_Z^6-9*_Z^3+1)*x^3-(x^3+x+1)^(2/3)*x-RootOf(27*_Z^6-9*_Z^3+1)*x-RootOf(27*_Z^6-9*_Z^3+1))/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-2*x^3-x-1))+3*RootOf(27*_Z^6-9*_Z^3+1)^2*ln(-(18*RootOf(27*_Z^6-9*_Z^3+1)^5*x^3+9*RootOf(27*_Z^6-9*_Z^3+1)^4*(x^3+x+1)^(1/3)*x^2+3*(x^3+x+1)^(2/3)*RootOf(27*_Z^6-9*_Z^3+1)^3*x+9*RootOf(27*_Z^6-9*_Z^3+1)^5*x+9*RootOf(27*_Z^6-9*_Z^3+1)^5-4*RootOf(27*_Z^6-9*_Z^3+1)^2*x^3-2*RootOf(27*_Z^6-9*_Z^3+1)*(x^3+x+1)^(1/3)*x^2-(x^3+x+1)^(2/3)*x-2*RootOf(27*_Z^6-9*_Z^3+1)^2*x-2*RootOf(27*_Z^6-9*_Z^3+1)^2)/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-x^3+x+1))-3*RootOf(27*_Z^6-9*_Z^3+1)^2*ln(-(-81*RootOf(27*_Z^6-9*_Z^3+1)^7*x^3+27*RootOf(27*_Z^6-9*_Z^3+1)^4*x^3+3*(x^3+x+1)^(2/3)*RootOf(27*_Z^6-9*_Z^3+1)^2*x+9*RootOf(27*_Z^6-9*_Z^3+1)^4*x+9*RootOf(27*_Z^6-9*_Z^3+1)^4-2*RootOf(27*_Z^6-9*_Z^3+1)*x^3+(x^3+x+1)^(1/3)*x^2-RootOf(27*_Z^6-9*_Z^3+1)*x-RootOf(27*_Z^6-9*_Z^3+1))/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-x^3+x+1))+RootOf(27*_Z^6-9*_Z^3+1)*ln((3*RootOf(27*_Z^6-9*_Z^3+1)^2*(x^3+x+1)^(1/3)*x^2+2*RootOf(27*_Z^6-9*_Z^3+1)*x^3+(x^3+x+1)^(2/3)*x+RootOf(27*_Z^6-9*_Z^3+1)*x+RootOf(27*_Z^6-9*_Z^3+1))/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-2*x^3-x-1))+RootOf(27*_Z^6-9*_Z^3+1)*ln((54*RootOf(27*_Z^6-9*_Z^3+1)^7*x^3+9*RootOf(27*_Z^6-9*_Z^3+1)^5*(x^3+x+1)^(1/3)*x^2-15*RootOf(27*_Z^6-9*_Z^3+1)^4*x^3+3*(x^3+x+1)^(2/3)*RootOf(27*_Z^6-9*_Z^3+1)^3*x-3*RootOf(27*_Z^6-9*_Z^3+1)^2*(x^3+x+1)^(1/3)*x^2+6*RootOf(27*_Z^6-9*_Z^3+1)^4*x+6*RootOf(27*_Z^6-9*_Z^3+1)^4+RootOf(27*_Z^6-9*_Z^3+1)*x^3-(x^3+x+1)^(2/3)*x-RootOf(27*_Z^6-9*_Z^3+1)*x-RootOf(27*_Z^6-9*_Z^3+1))/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-2*x^3-x-1))","B"
768,1,1207,11,5.941000," ","int((3+2*x)*(x^3+x+1)^(2/3)/(x^6+x^4+x^3+x^2+2*x+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$18 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{5} \ln \left(-\frac{-18 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{5} x^{3}+3 \left(x^{3}+x +1\right)^{\frac{2}{3}} \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x -9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{5} x -9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{5}+2 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{2} x^{3}+\RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right) \left(x^{3}+x +1\right)^{\frac{1}{3}} x^{2}-\left(x^{3}+x +1\right)^{\frac{2}{3}} x +\RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{2} x +\RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{2}}{9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x^{3}-x^{3}+x +1}\right)-9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{5} \ln \left(-\frac{9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{4} x^{3}-9 \left(x^{3}+x +1\right)^{\frac{1}{3}} \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x^{2}+3 \left(x^{3}+x +1\right)^{\frac{2}{3}} \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{2} x -2 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right) x^{3}+\left(x^{3}+x +1\right)^{\frac{1}{3}} x^{2}-\RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right) x -\RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)}{9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x^{3}-x^{3}+x +1}\right)+9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{4} \ln \left(\frac{-18 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{4} \left(x^{3}+x +1\right)^{\frac{1}{3}} x^{2}+6 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x^{3}+3 \left(x^{3}+x +1\right)^{\frac{2}{3}} \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{2} x +3 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right) \left(x^{3}+x +1\right)^{\frac{1}{3}} x^{2}+3 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x +3 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3}-2 x^{3}-x -1}{9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x^{3}-2 x^{3}-x -1}\right)-3 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{2} \ln \left(-\frac{-18 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{5} x^{3}+3 \left(x^{3}+x +1\right)^{\frac{2}{3}} \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x -9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{5} x -9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{5}+2 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{2} x^{3}+\RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right) \left(x^{3}+x +1\right)^{\frac{1}{3}} x^{2}-\left(x^{3}+x +1\right)^{\frac{2}{3}} x +\RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{2} x +\RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{2}}{9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x^{3}-x^{3}+x +1}\right)-2 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right) \ln \left(\frac{-18 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{4} \left(x^{3}+x +1\right)^{\frac{1}{3}} x^{2}+6 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x^{3}+3 \left(x^{3}+x +1\right)^{\frac{2}{3}} \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{2} x +3 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right) \left(x^{3}+x +1\right)^{\frac{1}{3}} x^{2}+3 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x +3 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3}-2 x^{3}-x -1}{9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x^{3}-2 x^{3}-x -1}\right)+\RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right) \ln \left(\frac{-27 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{7} x^{3}+9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{5} \left(x^{3}+x +1\right)^{\frac{1}{3}} x^{2}+3 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{4} x^{3}+3 \left(x^{3}+x +1\right)^{\frac{2}{3}} \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x -3 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{4} x -3 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{4}-\left(x^{3}+x +1\right)^{\frac{2}{3}} x}{9 \RootOf \left(27 \textit{\_Z}^{6}-9 \textit{\_Z}^{3}+1\right)^{3} x^{3}-2 x^{3}-x -1}\right)$&$1207$\\ \hline \end{longtable}"," ",0,"18*RootOf(27*_Z^6-9*_Z^3+1)^5*ln(-(-18*RootOf(27*_Z^6-9*_Z^3+1)^5*x^3+3*(x^3+x+1)^(2/3)*RootOf(27*_Z^6-9*_Z^3+1)^3*x-9*RootOf(27*_Z^6-9*_Z^3+1)^5*x-9*RootOf(27*_Z^6-9*_Z^3+1)^5+2*RootOf(27*_Z^6-9*_Z^3+1)^2*x^3+RootOf(27*_Z^6-9*_Z^3+1)*(x^3+x+1)^(1/3)*x^2-(x^3+x+1)^(2/3)*x+RootOf(27*_Z^6-9*_Z^3+1)^2*x+RootOf(27*_Z^6-9*_Z^3+1)^2)/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-x^3+x+1))-9*RootOf(27*_Z^6-9*_Z^3+1)^5*ln(-(9*RootOf(27*_Z^6-9*_Z^3+1)^4*x^3-9*(x^3+x+1)^(1/3)*RootOf(27*_Z^6-9*_Z^3+1)^3*x^2+3*(x^3+x+1)^(2/3)*RootOf(27*_Z^6-9*_Z^3+1)^2*x-2*RootOf(27*_Z^6-9*_Z^3+1)*x^3+(x^3+x+1)^(1/3)*x^2-RootOf(27*_Z^6-9*_Z^3+1)*x-RootOf(27*_Z^6-9*_Z^3+1))/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-x^3+x+1))+9*RootOf(27*_Z^6-9*_Z^3+1)^4*ln((-18*RootOf(27*_Z^6-9*_Z^3+1)^4*(x^3+x+1)^(1/3)*x^2+6*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3+3*(x^3+x+1)^(2/3)*RootOf(27*_Z^6-9*_Z^3+1)^2*x+3*RootOf(27*_Z^6-9*_Z^3+1)*(x^3+x+1)^(1/3)*x^2+3*RootOf(27*_Z^6-9*_Z^3+1)^3*x+3*RootOf(27*_Z^6-9*_Z^3+1)^3-2*x^3-x-1)/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-2*x^3-x-1))-3*RootOf(27*_Z^6-9*_Z^3+1)^2*ln(-(-18*RootOf(27*_Z^6-9*_Z^3+1)^5*x^3+3*(x^3+x+1)^(2/3)*RootOf(27*_Z^6-9*_Z^3+1)^3*x-9*RootOf(27*_Z^6-9*_Z^3+1)^5*x-9*RootOf(27*_Z^6-9*_Z^3+1)^5+2*RootOf(27*_Z^6-9*_Z^3+1)^2*x^3+RootOf(27*_Z^6-9*_Z^3+1)*(x^3+x+1)^(1/3)*x^2-(x^3+x+1)^(2/3)*x+RootOf(27*_Z^6-9*_Z^3+1)^2*x+RootOf(27*_Z^6-9*_Z^3+1)^2)/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-x^3+x+1))-2*RootOf(27*_Z^6-9*_Z^3+1)*ln((-18*RootOf(27*_Z^6-9*_Z^3+1)^4*(x^3+x+1)^(1/3)*x^2+6*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3+3*(x^3+x+1)^(2/3)*RootOf(27*_Z^6-9*_Z^3+1)^2*x+3*RootOf(27*_Z^6-9*_Z^3+1)*(x^3+x+1)^(1/3)*x^2+3*RootOf(27*_Z^6-9*_Z^3+1)^3*x+3*RootOf(27*_Z^6-9*_Z^3+1)^3-2*x^3-x-1)/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-2*x^3-x-1))+RootOf(27*_Z^6-9*_Z^3+1)*ln((-27*RootOf(27*_Z^6-9*_Z^3+1)^7*x^3+9*RootOf(27*_Z^6-9*_Z^3+1)^5*(x^3+x+1)^(1/3)*x^2+3*RootOf(27*_Z^6-9*_Z^3+1)^4*x^3+3*(x^3+x+1)^(2/3)*RootOf(27*_Z^6-9*_Z^3+1)^3*x-3*RootOf(27*_Z^6-9*_Z^3+1)^4*x-3*RootOf(27*_Z^6-9*_Z^3+1)^4-(x^3+x+1)^(2/3)*x)/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-2*x^3-x-1))","B"
769,1,1808,11,13.590000," ","int((x^3+2)*(-x^4+x^3+x)^(1/3)/(x^6-x^5+x^4-2*x^3+x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1808$\\ \hline \end{longtable}"," ",0,"-9*RootOf(27*_Z^6-9*_Z^3+1)^5*ln((567*RootOf(27*_Z^6-9*_Z^3+1)^7*x^3-567*RootOf(27*_Z^6-9*_Z^3+1)^7+3132*(-x^4+x^3+x)^(1/3)*RootOf(27*_Z^6-9*_Z^3+1)^5*x+855*RootOf(27*_Z^6-9*_Z^3+1)^4*x^3+63*RootOf(27*_Z^6-9*_Z^3+1)^4*x^2-1107*RootOf(27*_Z^6-9*_Z^3+1)^3*(-x^4+x^3+x)^(2/3)-855*RootOf(27*_Z^6-9*_Z^3+1)^4-717*(-x^4+x^3+x)^(1/3)*RootOf(27*_Z^6-9*_Z^3+1)^2*x-218*RootOf(27*_Z^6-9*_Z^3+1)*x^3+109*RootOf(27*_Z^6-9*_Z^3+1)*x^2+130*(-x^4+x^3+x)^(2/3)+218*RootOf(27*_Z^6-9*_Z^3+1))/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-9*RootOf(27*_Z^6-9*_Z^3+1)^3-x^3-x^2+1))+18*ln(-(5751*(-x^4+x^3+x)^(1/3)*RootOf(27*_Z^6-9*_Z^3+1)^5*x-819*RootOf(27*_Z^6-9*_Z^3+1)^4*x^3+1638*RootOf(27*_Z^6-9*_Z^3+1)^4*x^2-2736*RootOf(27*_Z^6-9*_Z^3+1)^3*(-x^4+x^3+x)^(2/3)+819*RootOf(27*_Z^6-9*_Z^3+1)^4-1551*(-x^4+x^3+x)^(1/3)*RootOf(27*_Z^6-9*_Z^3+1)^2*x-122*RootOf(27*_Z^6-9*_Z^3+1)*x^3+244*RootOf(27*_Z^6-9*_Z^3+1)*x^2+395*(-x^4+x^3+x)^(2/3)+122*RootOf(27*_Z^6-9*_Z^3+1))/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-9*RootOf(27*_Z^6-9*_Z^3+1)^3-x^3-x^2+1))*RootOf(27*_Z^6-9*_Z^3+1)^5-9*ln((8829*RootOf(27*_Z^6-9*_Z^3+1)^8*x^3-8829*RootOf(27*_Z^6-9*_Z^3+1)^8-792*RootOf(27*_Z^6-9*_Z^3+1)^5*x^3-981*RootOf(27*_Z^6-9*_Z^3+1)^5*x^2-1170*RootOf(27*_Z^6-9*_Z^3+1)^4*(-x^4+x^3+x)^(1/3)*x+792*RootOf(27*_Z^6-9*_Z^3+1)^5+1107*RootOf(27*_Z^6-9*_Z^3+1)^3*(-x^4+x^3+x)^(2/3)-21*RootOf(27*_Z^6-9*_Z^3+1)^2*x^3-21*RootOf(27*_Z^6-9*_Z^3+1)^2*x^2+369*RootOf(27*_Z^6-9*_Z^3+1)*(-x^4+x^3+x)^(1/3)*x+21*RootOf(27*_Z^6-9*_Z^3+1)^2-239*(-x^4+x^3+x)^(2/3))/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-9*RootOf(27*_Z^6-9*_Z^3+1)^3-2*x^3+x^2+2))*RootOf(27*_Z^6-9*_Z^3+1)^4-3*ln(-(5751*(-x^4+x^3+x)^(1/3)*RootOf(27*_Z^6-9*_Z^3+1)^5*x-819*RootOf(27*_Z^6-9*_Z^3+1)^4*x^3+1638*RootOf(27*_Z^6-9*_Z^3+1)^4*x^2-2736*RootOf(27*_Z^6-9*_Z^3+1)^3*(-x^4+x^3+x)^(2/3)+819*RootOf(27*_Z^6-9*_Z^3+1)^4-1551*(-x^4+x^3+x)^(1/3)*RootOf(27*_Z^6-9*_Z^3+1)^2*x-122*RootOf(27*_Z^6-9*_Z^3+1)*x^3+244*RootOf(27*_Z^6-9*_Z^3+1)*x^2+395*(-x^4+x^3+x)^(2/3)+122*RootOf(27*_Z^6-9*_Z^3+1))/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-9*RootOf(27*_Z^6-9*_Z^3+1)^3-x^3-x^2+1))*RootOf(27*_Z^6-9*_Z^3+1)^2+ln((8829*RootOf(27*_Z^6-9*_Z^3+1)^8*x^3-8829*RootOf(27*_Z^6-9*_Z^3+1)^8-792*RootOf(27*_Z^6-9*_Z^3+1)^5*x^3-981*RootOf(27*_Z^6-9*_Z^3+1)^5*x^2-1170*RootOf(27*_Z^6-9*_Z^3+1)^4*(-x^4+x^3+x)^(1/3)*x+792*RootOf(27*_Z^6-9*_Z^3+1)^5+1107*RootOf(27*_Z^6-9*_Z^3+1)^3*(-x^4+x^3+x)^(2/3)-21*RootOf(27*_Z^6-9*_Z^3+1)^2*x^3-21*RootOf(27*_Z^6-9*_Z^3+1)^2*x^2+369*RootOf(27*_Z^6-9*_Z^3+1)*(-x^4+x^3+x)^(1/3)*x+21*RootOf(27*_Z^6-9*_Z^3+1)^2-239*(-x^4+x^3+x)^(2/3))/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-9*RootOf(27*_Z^6-9*_Z^3+1)^3-2*x^3+x^2+2))*RootOf(27*_Z^6-9*_Z^3+1)+RootOf(27*_Z^6-9*_Z^3+1)*ln(-(1098*RootOf(27*_Z^6-9*_Z^3+1)^5*x^3-2196*RootOf(27*_Z^6-9*_Z^3+1)^5*x^2-3555*RootOf(27*_Z^6-9*_Z^3+1)^4*(-x^4+x^3+x)^(1/3)*x-1098*RootOf(27*_Z^6-9*_Z^3+1)^5+2736*RootOf(27*_Z^6-9*_Z^3+1)^3*(-x^4+x^3+x)^(2/3)+273*RootOf(27*_Z^6-9*_Z^3+1)^2*x^3-546*RootOf(27*_Z^6-9*_Z^3+1)^2*x^2+912*RootOf(27*_Z^6-9*_Z^3+1)*(-x^4+x^3+x)^(1/3)*x-273*RootOf(27*_Z^6-9*_Z^3+1)^2-517*(-x^4+x^3+x)^(2/3))/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-9*RootOf(27*_Z^6-9*_Z^3+1)^3-2*x^3+x^2+2))","B"
770,1,2253,11,13.059000," ","int((x^3+2)*(-x^4+x^3+x)^(1/3)/(x^6-x^5+x^4-2*x^3+x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2253$\\ \hline \end{longtable}"," ",0,"-9*RootOf(27*_Z^6-9*_Z^3+1)^5*ln((9*RootOf(27*_Z^6-9*_Z^3+1)^5*x^3-18*RootOf(27*_Z^6-9*_Z^3+1)^5*x^2+18*(-x^4+x^3+x)^(2/3)*RootOf(27*_Z^6-9*_Z^3+1)^4-9*RootOf(27*_Z^6-9*_Z^3+1)^5-9*(-x^4+x^3+x)^(1/3)*RootOf(27*_Z^6-9*_Z^3+1)^3*x-3*RootOf(27*_Z^6-9*_Z^3+1)^2*x^3+6*RootOf(27*_Z^6-9*_Z^3+1)^2*x^2-3*(-x^4+x^3+x)^(2/3)*RootOf(27*_Z^6-9*_Z^3+1)+3*RootOf(27*_Z^6-9*_Z^3+1)^2+(-x^4+x^3+x)^(1/3)*x)/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-9*RootOf(27*_Z^6-9*_Z^3+1)^3-x^3-x^2+1))+18*RootOf(27*_Z^6-9*_Z^3+1)^5*ln((81*RootOf(27*_Z^6-9*_Z^3+1)^8*x^3-81*RootOf(27*_Z^6-9*_Z^3+1)^8-18*RootOf(27*_Z^6-9*_Z^3+1)^5*x^3+9*RootOf(27*_Z^6-9*_Z^3+1)^5*x^2+9*(-x^4+x^3+x)^(2/3)*RootOf(27*_Z^6-9*_Z^3+1)^4+18*RootOf(27*_Z^6-9*_Z^3+1)^5-9*(-x^4+x^3+x)^(1/3)*RootOf(27*_Z^6-9*_Z^3+1)^3*x-3*(-x^4+x^3+x)^(2/3)*RootOf(27*_Z^6-9*_Z^3+1)+2*(-x^4+x^3+x)^(1/3)*x)/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-9*RootOf(27*_Z^6-9*_Z^3+1)^3-x^3-x^2+1))-9*RootOf(27*_Z^6-9*_Z^3+1)^4*ln((9*RootOf(27*_Z^6-9*_Z^3+1)^5*x^3-18*RootOf(27*_Z^6-9*_Z^3+1)^5*x^2-9*RootOf(27*_Z^6-9*_Z^3+1)^4*(-x^4+x^3+x)^(1/3)*x-9*RootOf(27*_Z^6-9*_Z^3+1)^5+9*RootOf(27*_Z^6-9*_Z^3+1)^3*(-x^4+x^3+x)^(2/3)-3*RootOf(27*_Z^6-9*_Z^3+1)^2*x^3+6*RootOf(27*_Z^6-9*_Z^3+1)^2*x^2+3*RootOf(27*_Z^6-9*_Z^3+1)^2-2*(-x^4+x^3+x)^(2/3))/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-9*RootOf(27*_Z^6-9*_Z^3+1)^3-2*x^3+x^2+2))+9*RootOf(27*_Z^6-9*_Z^3+1)^4*ln((10530*RootOf(27*_Z^6-9*_Z^3+1)^8*x^3-10530*RootOf(27*_Z^6-9*_Z^3+1)^8-4491*RootOf(27*_Z^6-9*_Z^3+1)^5*x^3-1170*RootOf(27*_Z^6-9*_Z^3+1)^5*x^2-981*RootOf(27*_Z^6-9*_Z^3+1)^4*(-x^4+x^3+x)^(1/3)*x+4491*RootOf(27*_Z^6-9*_Z^3+1)^5+1107*RootOf(27*_Z^6-9*_Z^3+1)^3*(-x^4+x^3+x)^(2/3)+369*RootOf(27*_Z^6-9*_Z^3+1)^2*x^3+369*RootOf(27*_Z^6-9*_Z^3+1)^2*x^2-21*RootOf(27*_Z^6-9*_Z^3+1)*(-x^4+x^3+x)^(1/3)*x-369*RootOf(27*_Z^6-9*_Z^3+1)^2-239*(-x^4+x^3+x)^(2/3))/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-9*RootOf(27*_Z^6-9*_Z^3+1)^3-2*x^3+x^2+2))+3*RootOf(27*_Z^6-9*_Z^3+1)^2*ln((9*RootOf(27*_Z^6-9*_Z^3+1)^5*x^3-18*RootOf(27*_Z^6-9*_Z^3+1)^5*x^2+18*(-x^4+x^3+x)^(2/3)*RootOf(27*_Z^6-9*_Z^3+1)^4-9*RootOf(27*_Z^6-9*_Z^3+1)^5-9*(-x^4+x^3+x)^(1/3)*RootOf(27*_Z^6-9*_Z^3+1)^3*x-3*RootOf(27*_Z^6-9*_Z^3+1)^2*x^3+6*RootOf(27*_Z^6-9*_Z^3+1)^2*x^2-3*(-x^4+x^3+x)^(2/3)*RootOf(27*_Z^6-9*_Z^3+1)+3*RootOf(27*_Z^6-9*_Z^3+1)^2+(-x^4+x^3+x)^(1/3)*x)/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-9*RootOf(27*_Z^6-9*_Z^3+1)^3-x^3-x^2+1))-3*RootOf(27*_Z^6-9*_Z^3+1)^2*ln((81*RootOf(27*_Z^6-9*_Z^3+1)^8*x^3-81*RootOf(27*_Z^6-9*_Z^3+1)^8-18*RootOf(27*_Z^6-9*_Z^3+1)^5*x^3+9*RootOf(27*_Z^6-9*_Z^3+1)^5*x^2+9*(-x^4+x^3+x)^(2/3)*RootOf(27*_Z^6-9*_Z^3+1)^4+18*RootOf(27*_Z^6-9*_Z^3+1)^5-9*(-x^4+x^3+x)^(1/3)*RootOf(27*_Z^6-9*_Z^3+1)^3*x-3*(-x^4+x^3+x)^(2/3)*RootOf(27*_Z^6-9*_Z^3+1)+2*(-x^4+x^3+x)^(1/3)*x)/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-9*RootOf(27*_Z^6-9*_Z^3+1)^3-x^3-x^2+1))+RootOf(27*_Z^6-9*_Z^3+1)*ln((9*RootOf(27*_Z^6-9*_Z^3+1)^5*x^3-18*RootOf(27*_Z^6-9*_Z^3+1)^5*x^2-9*RootOf(27*_Z^6-9*_Z^3+1)^4*(-x^4+x^3+x)^(1/3)*x-9*RootOf(27*_Z^6-9*_Z^3+1)^5+9*RootOf(27*_Z^6-9*_Z^3+1)^3*(-x^4+x^3+x)^(2/3)-3*RootOf(27*_Z^6-9*_Z^3+1)^2*x^3+6*RootOf(27*_Z^6-9*_Z^3+1)^2*x^2+3*RootOf(27*_Z^6-9*_Z^3+1)^2-2*(-x^4+x^3+x)^(2/3))/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-9*RootOf(27*_Z^6-9*_Z^3+1)^3-2*x^3+x^2+2))-2*RootOf(27*_Z^6-9*_Z^3+1)*ln((10530*RootOf(27*_Z^6-9*_Z^3+1)^8*x^3-10530*RootOf(27*_Z^6-9*_Z^3+1)^8-4491*RootOf(27*_Z^6-9*_Z^3+1)^5*x^3-1170*RootOf(27*_Z^6-9*_Z^3+1)^5*x^2-981*RootOf(27*_Z^6-9*_Z^3+1)^4*(-x^4+x^3+x)^(1/3)*x+4491*RootOf(27*_Z^6-9*_Z^3+1)^5+1107*RootOf(27*_Z^6-9*_Z^3+1)^3*(-x^4+x^3+x)^(2/3)+369*RootOf(27*_Z^6-9*_Z^3+1)^2*x^3+369*RootOf(27*_Z^6-9*_Z^3+1)^2*x^2-21*RootOf(27*_Z^6-9*_Z^3+1)*(-x^4+x^3+x)^(1/3)*x-369*RootOf(27*_Z^6-9*_Z^3+1)^2-239*(-x^4+x^3+x)^(2/3))/(9*RootOf(27*_Z^6-9*_Z^3+1)^3*x^3-9*RootOf(27*_Z^6-9*_Z^3+1)^3-2*x^3+x^2+2))","B"
771,1,9017,9,31.328000," ","int((x^2+3)*(x^3+x^2+1)^(2/3)/(x^6+x^5-x^4+x^3-2*x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$9017$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
772,1,8381,9,51.426000," ","int((x^2+3)*(x^3+x^2+1)^(2/3)/(x^6+x^5-x^4+x^3-2*x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$8381$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
773,0,0,43,0.020000," ","int((a*x^8+b)/(-a*x^8+b)^(1/4)/(a*x^8+c*x^4-b),x)","\[\int \frac{a \,x^{8}+b}{\left(-a \,x^{8}+b \right)^{\frac{1}{4}} \left(a \,x^{8}+c \,x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^8+b)/(-a*x^8+b)^(1/4)/(a*x^8+c*x^4-b),x)","F"
774,0,0,11,180.000000," ","int(x*(x^8-x^3+2)^(1/3)*(5*x^8-6)/(x^16+4*x^8+x^6+4),x)","\[\int \frac{x \left(x^{8}-x^{3}+2\right)^{\frac{1}{3}} \left(5 x^{8}-6\right)}{x^{16}+4 x^{8}+x^{6}+4}\, dx\]"," ",0,"int(x*(x^8-x^3+2)^(1/3)*(5*x^8-6)/(x^16+4*x^8+x^6+4),x)","F"
775,1,8138,54,0.312000," ","int((a*b+a*c-2*a*x-b*c+x^2)/((-a+x)*(-b+x)*(-c+x))^(1/2)/(b*c+a*d-(b+c+d)*x+x^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$8138$\\ elliptic&$\text{Expression too large to display}$&$8296$\\ \hline \end{longtable}"," ",0,"result too large to display","C"
776,1,9198,54,0.344000," ","int((a*b+a*c-2*a*x-b*c+x^2)/((-a+x)*(-b+x)*(-c+x))^(1/2)/(a+b*c*d-(b*d+c*d+1)*x+d*x^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$9198$\\ elliptic&$\text{Expression too large to display}$&$9394$\\ \hline \end{longtable}"," ",0,"result too large to display","C"
777,1,341,54,0.108000," ","int((k^2*x^2-1)/((1-x)*x*(-k^2*x+1))^(1/2)/(k^2*x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}-\frac{2 i \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{i}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{3} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}-\frac{i}{k}\right)}+\frac{2 i \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{i}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{3} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{i}{k}\right)}$&$341$\\ elliptic&$-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}-\frac{2 i \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{i}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{3} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}-\frac{i}{k}\right)}+\frac{2 i \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{i}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{3} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{i}{k}\right)}$&$345$\\ \hline \end{longtable}"," ",0,"-2/k^2*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticF((-(x-1/k^2)*k^2)^(1/2),(1/k^2/(1/k^2-1))^(1/2))-2*I/k^3*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-I/k)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-I/k),(1/k^2/(1/k^2-1))^(1/2))+2*I/k^3*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+I/k)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+I/k),(1/k^2/(1/k^2-1))^(1/2))","C"
778,1,510,54,0.131000," ","int((a*(a*b+a*c-3*b*c)+(-2*a^2+a*b+a*c+3*b*c)*x+(a-2*b-2*c)*x^2+x^3)/((-a+x)*(-b+x)*(-c+x))^(1/2)/(-a^3-b*c*d+(3*a^2+b*d+c*d)*x-(3*a+d)*x^2+x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 \left(b -c \right) \sqrt{\frac{-c +x}{b -c}}\, \sqrt{\frac{-a +x}{c -a}}\, \sqrt{\frac{-b +x}{-b +c}}\, \EllipticF \left(\sqrt{\frac{-c +x}{b -c}}, \sqrt{\frac{-b +c}{c -a}}\right)}{\sqrt{-a b c +a b x +a c x -a \,x^{2}+b c x -b \,x^{2}-c \,x^{2}+x^{3}}}+2 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+\left(-3 a -d \right) \textit{\_Z}^{2}+\left(3 a^{2}+b d +c d \right) \textit{\_Z} -a^{3}-b c d \right)}{\sum}\frac{\left(4 \underline{\hspace{1.25 ex}}\alpha^{2} a -2 \underline{\hspace{1.25 ex}}\alpha^{2} b -2 \underline{\hspace{1.25 ex}}\alpha^{2} c +\underline{\hspace{1.25 ex}}\alpha^{2} d -5 \underline{\hspace{1.25 ex}}\alpha  \,a^{2}+\underline{\hspace{1.25 ex}}\alpha  a b +\underline{\hspace{1.25 ex}}\alpha  a c +3 \underline{\hspace{1.25 ex}}\alpha  b c -\underline{\hspace{1.25 ex}}\alpha  b d -\underline{\hspace{1.25 ex}}\alpha  c d +a^{3}+a^{2} b +a^{2} c -3 a b c +b c d \right) \left(b -c \right) \sqrt{\frac{-c +x}{b -c}}\, \sqrt{\frac{-a +x}{c -a}}\, \sqrt{\frac{-b +x}{-b +c}}\, \left(\underline{\hspace{1.25 ex}}\alpha^{2}-3 \underline{\hspace{1.25 ex}}\alpha  a +\underline{\hspace{1.25 ex}}\alpha  c -\underline{\hspace{1.25 ex}}\alpha  d +3 a^{2}-3 a c +b d +c^{2}\right) \EllipticPi \left(\sqrt{\frac{-c +x}{b -c}}, \frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2}-3 \underline{\hspace{1.25 ex}}\alpha  a +\underline{\hspace{1.25 ex}}\alpha  c -\underline{\hspace{1.25 ex}}\alpha  d +3 a^{2}-3 a c +b d +c^{2}\right) \left(b -c \right)}{a^{3}-3 a^{2} c +3 a \,c^{2}-c^{3}}, \sqrt{\frac{-b +c}{c -a}}\right)}{\left(-3 \underline{\hspace{1.25 ex}}\alpha^{2}+6 \underline{\hspace{1.25 ex}}\alpha  a +2 \underline{\hspace{1.25 ex}}\alpha  d -3 a^{2}-b d -c d \right) \sqrt{-a b c +a b x +a c x -a \,x^{2}+b c x -b \,x^{2}-c \,x^{2}+x^{3}}\, \left(a^{3}-3 a^{2} c +3 a \,c^{2}-c^{3}\right)}\right)$&$510$\\ elliptic&$\frac{2 \left(b -c \right) \sqrt{\frac{-c +x}{b -c}}\, \sqrt{\frac{-a +x}{c -a}}\, \sqrt{\frac{-b +x}{-b +c}}\, \EllipticF \left(\sqrt{\frac{-c +x}{b -c}}, \sqrt{\frac{-b +c}{c -a}}\right)}{\sqrt{-a b c +a b x +a c x -a \,x^{2}+b c x -b \,x^{2}-c \,x^{2}+x^{3}}}-2 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+\left(-3 a -d \right) \textit{\_Z}^{2}+\left(3 a^{2}+b d +c d \right) \textit{\_Z} -a^{3}-b c d \right)}{\sum}\frac{\left(-4 \underline{\hspace{1.25 ex}}\alpha^{2} a +2 \underline{\hspace{1.25 ex}}\alpha^{2} b +2 \underline{\hspace{1.25 ex}}\alpha^{2} c -\underline{\hspace{1.25 ex}}\alpha^{2} d +5 \underline{\hspace{1.25 ex}}\alpha  \,a^{2}-\underline{\hspace{1.25 ex}}\alpha  a b -\underline{\hspace{1.25 ex}}\alpha  a c -3 \underline{\hspace{1.25 ex}}\alpha  b c +\underline{\hspace{1.25 ex}}\alpha  b d +\underline{\hspace{1.25 ex}}\alpha  c d -a^{3}-a^{2} b -a^{2} c +3 a b c -b c d \right) \left(b -c \right) \sqrt{\frac{-c +x}{b -c}}\, \sqrt{\frac{-a +x}{c -a}}\, \sqrt{\frac{-b +x}{-b +c}}\, \left(\underline{\hspace{1.25 ex}}\alpha^{2}-3 \underline{\hspace{1.25 ex}}\alpha  a +\underline{\hspace{1.25 ex}}\alpha  c -\underline{\hspace{1.25 ex}}\alpha  d +3 a^{2}-3 a c +b d +c^{2}\right) \EllipticPi \left(\sqrt{\frac{-c +x}{b -c}}, \frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2}-3 \underline{\hspace{1.25 ex}}\alpha  a +\underline{\hspace{1.25 ex}}\alpha  c -\underline{\hspace{1.25 ex}}\alpha  d +3 a^{2}-3 a c +b d +c^{2}\right) \left(b -c \right)}{a^{3}-3 a^{2} c +3 a \,c^{2}-c^{3}}, \sqrt{\frac{-b +c}{c -a}}\right)}{\left(-3 \underline{\hspace{1.25 ex}}\alpha^{2}+6 \underline{\hspace{1.25 ex}}\alpha  a +2 \underline{\hspace{1.25 ex}}\alpha  d -3 a^{2}-b d -c d \right) \sqrt{-a b c +a b x +a c x -a \,x^{2}+b c x -b \,x^{2}-c \,x^{2}+x^{3}}\, \left(a^{3}-3 a^{2} c +3 a \,c^{2}-c^{3}\right)}\right)$&$516$\\ \hline \end{longtable}"," ",0,"2*(b-c)*((-c+x)/(b-c))^(1/2)*((-a+x)/(c-a))^(1/2)*((-b+x)/(-b+c))^(1/2)/(-a*b*c+a*b*x+a*c*x-a*x^2+b*c*x-b*x^2-c*x^2+x^3)^(1/2)*EllipticF(((-c+x)/(b-c))^(1/2),((-b+c)/(c-a))^(1/2))+2*sum((4*_alpha^2*a-2*_alpha^2*b-2*_alpha^2*c+_alpha^2*d-5*_alpha*a^2+_alpha*a*b+_alpha*a*c+3*_alpha*b*c-_alpha*b*d-_alpha*c*d+a^3+a^2*b+a^2*c-3*a*b*c+b*c*d)/(-3*_alpha^2+6*_alpha*a+2*_alpha*d-3*a^2-b*d-c*d)*(b-c)*((-c+x)/(b-c))^(1/2)*((-a+x)/(c-a))^(1/2)*((-b+x)/(-b+c))^(1/2)/(-a*b*c+a*b*x+a*c*x-a*x^2+b*c*x-b*x^2-c*x^2+x^3)^(1/2)*(_alpha^2-3*_alpha*a+_alpha*c-_alpha*d+3*a^2-3*a*c+b*d+c^2)/(a^3-3*a^2*c+3*a*c^2-c^3)*EllipticPi(((-c+x)/(b-c))^(1/2),(_alpha^2-3*_alpha*a+_alpha*c-_alpha*d+3*a^2-3*a*c+b*d+c^2)*(b-c)/(a^3-3*a^2*c+3*a*c^2-c^3),((-b+c)/(c-a))^(1/2)),_alpha=RootOf(_Z^3+(-3*a-d)*_Z^2+(3*a^2+b*d+c*d)*_Z-a^3-b*c*d))","C"
779,1,5094,52,2.383000," ","int((a*x^3-2*c)*(a*x^3+b*x^2+c)^(1/2)/(a*x^3+c)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\text{Expression too large to display}$&$5094$\\ default&$\text{Expression too large to display}$&$10183$\\ \hline \end{longtable}"," ",0,"result too large to display","C"
780,1,1081,46,0.279000," ","int((a^2*x^2-b)/(a^2*x^2+2*a*b*x+b)/(a^2*x^3+b*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\sqrt{-b}\, \sqrt{\frac{x a}{\sqrt{-b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}+b x}}+\frac{\sqrt{-b}\, \sqrt{\frac{x a}{\sqrt{-b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}, -\frac{\sqrt{-b}}{a \left(-\frac{\sqrt{-b}}{a}-\frac{-b +\sqrt{b^{2}-b}}{a}\right)}, \frac{\sqrt{2}}{2}\right) b^{2}}{a^{2} \sqrt{b^{2}-b}\, \sqrt{a^{2} x^{3}+b x}\, \left(-\frac{\sqrt{-b}}{a}+\frac{b}{a}-\frac{\sqrt{b^{2}-b}}{a}\right)}-\frac{\sqrt{-b}\, \sqrt{\frac{x a}{\sqrt{-b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}, -\frac{\sqrt{-b}}{a \left(-\frac{\sqrt{-b}}{a}-\frac{-b +\sqrt{b^{2}-b}}{a}\right)}, \frac{\sqrt{2}}{2}\right) b}{a^{2} \sqrt{a^{2} x^{3}+b x}\, \left(-\frac{\sqrt{-b}}{a}+\frac{b}{a}-\frac{\sqrt{b^{2}-b}}{a}\right)}-\frac{\sqrt{-b}\, \sqrt{\frac{x a}{\sqrt{-b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}, -\frac{\sqrt{-b}}{a \left(-\frac{\sqrt{-b}}{a}-\frac{-b +\sqrt{b^{2}-b}}{a}\right)}, \frac{\sqrt{2}}{2}\right) b}{a^{2} \sqrt{b^{2}-b}\, \sqrt{a^{2} x^{3}+b x}\, \left(-\frac{\sqrt{-b}}{a}+\frac{b}{a}-\frac{\sqrt{b^{2}-b}}{a}\right)}-\frac{\sqrt{-b}\, \sqrt{\frac{x a}{\sqrt{-b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}, -\frac{\sqrt{-b}}{a \left(-\frac{\sqrt{-b}}{a}-\frac{-b -\sqrt{b^{2}-b}}{a}\right)}, \frac{\sqrt{2}}{2}\right) b^{2}}{a^{2} \sqrt{b^{2}-b}\, \sqrt{a^{2} x^{3}+b x}\, \left(-\frac{\sqrt{-b}}{a}+\frac{b}{a}+\frac{\sqrt{b^{2}-b}}{a}\right)}-\frac{\sqrt{-b}\, \sqrt{\frac{x a}{\sqrt{-b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}, -\frac{\sqrt{-b}}{a \left(-\frac{\sqrt{-b}}{a}-\frac{-b -\sqrt{b^{2}-b}}{a}\right)}, \frac{\sqrt{2}}{2}\right) b}{a^{2} \sqrt{a^{2} x^{3}+b x}\, \left(-\frac{\sqrt{-b}}{a}+\frac{b}{a}+\frac{\sqrt{b^{2}-b}}{a}\right)}+\frac{\sqrt{-b}\, \sqrt{\frac{x a}{\sqrt{-b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}, -\frac{\sqrt{-b}}{a \left(-\frac{\sqrt{-b}}{a}-\frac{-b -\sqrt{b^{2}-b}}{a}\right)}, \frac{\sqrt{2}}{2}\right) b}{a^{2} \sqrt{b^{2}-b}\, \sqrt{a^{2} x^{3}+b x}\, \left(-\frac{\sqrt{-b}}{a}+\frac{b}{a}+\frac{\sqrt{b^{2}-b}}{a}\right)}$&$1081$\\ default&$\frac{\sqrt{-b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}\, \sqrt{-\frac{x a}{\sqrt{-b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}+b x}}-2 b \left(-\frac{\sqrt{-b}\, \sqrt{\frac{x a}{\sqrt{-b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}, -\frac{\sqrt{-b}}{a \left(-\frac{\sqrt{-b}}{a}-\frac{-b +\sqrt{b^{2}-b}}{a}\right)}, \frac{\sqrt{2}}{2}\right) b}{2 a^{2} \sqrt{b^{2}-b}\, \sqrt{a^{2} x^{3}+b x}\, \left(-\frac{\sqrt{-b}}{a}+\frac{b}{a}-\frac{\sqrt{b^{2}-b}}{a}\right)}+\frac{\sqrt{-b}\, \sqrt{\frac{x a}{\sqrt{-b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}, -\frac{\sqrt{-b}}{a \left(-\frac{\sqrt{-b}}{a}-\frac{-b +\sqrt{b^{2}-b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a^{2} x^{3}+b x}\, \left(-\frac{\sqrt{-b}}{a}+\frac{b}{a}-\frac{\sqrt{b^{2}-b}}{a}\right)}+\frac{\sqrt{-b}\, \sqrt{\frac{x a}{\sqrt{-b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}, -\frac{\sqrt{-b}}{a \left(-\frac{\sqrt{-b}}{a}-\frac{-b +\sqrt{b^{2}-b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{b^{2}-b}\, \sqrt{a^{2} x^{3}+b x}\, \left(-\frac{\sqrt{-b}}{a}+\frac{b}{a}-\frac{\sqrt{b^{2}-b}}{a}\right)}+\frac{\sqrt{-b}\, \sqrt{\frac{x a}{\sqrt{-b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}, -\frac{\sqrt{-b}}{a \left(-\frac{\sqrt{-b}}{a}-\frac{-b -\sqrt{b^{2}-b}}{a}\right)}, \frac{\sqrt{2}}{2}\right) b}{2 a^{2} \sqrt{b^{2}-b}\, \sqrt{a^{2} x^{3}+b x}\, \left(-\frac{\sqrt{-b}}{a}+\frac{b}{a}+\frac{\sqrt{b^{2}-b}}{a}\right)}+\frac{\sqrt{-b}\, \sqrt{\frac{x a}{\sqrt{-b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}, -\frac{\sqrt{-b}}{a \left(-\frac{\sqrt{-b}}{a}-\frac{-b -\sqrt{b^{2}-b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a^{2} x^{3}+b x}\, \left(-\frac{\sqrt{-b}}{a}+\frac{b}{a}+\frac{\sqrt{b^{2}-b}}{a}\right)}-\frac{\sqrt{-b}\, \sqrt{\frac{x a}{\sqrt{-b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}, -\frac{\sqrt{-b}}{a \left(-\frac{\sqrt{-b}}{a}-\frac{-b -\sqrt{b^{2}-b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{b^{2}-b}\, \sqrt{a^{2} x^{3}+b x}\, \left(-\frac{\sqrt{-b}}{a}+\frac{b}{a}+\frac{\sqrt{b^{2}-b}}{a}\right)}\right)$&$1096$\\ \hline \end{longtable}"," ",0,"(-b)^(1/2)/a*(x/(-b)^(1/2)*a+1)^(1/2)*(-2*x/(-b)^(1/2)*a+2)^(1/2)*(-x/(-b)^(1/2)*a)^(1/2)/(a^2*x^3+b*x)^(1/2)*EllipticF(((x+(-b)^(1/2)/a)/(-b)^(1/2)*a)^(1/2),1/2*2^(1/2))+1/a^2/(b^2-b)^(1/2)*(-b)^(1/2)*(x/(-b)^(1/2)*a+1)^(1/2)*(-2*x/(-b)^(1/2)*a+2)^(1/2)*(-x/(-b)^(1/2)*a)^(1/2)/(a^2*x^3+b*x)^(1/2)/(-(-b)^(1/2)/a+b/a-1/a*(b^2-b)^(1/2))*EllipticPi(((x+(-b)^(1/2)/a)/(-b)^(1/2)*a)^(1/2),-(-b)^(1/2)/a/(-(-b)^(1/2)/a-(-b+(b^2-b)^(1/2))/a),1/2*2^(1/2))*b^2-1/a^2*(-b)^(1/2)*(x/(-b)^(1/2)*a+1)^(1/2)*(-2*x/(-b)^(1/2)*a+2)^(1/2)*(-x/(-b)^(1/2)*a)^(1/2)/(a^2*x^3+b*x)^(1/2)/(-(-b)^(1/2)/a+b/a-1/a*(b^2-b)^(1/2))*EllipticPi(((x+(-b)^(1/2)/a)/(-b)^(1/2)*a)^(1/2),-(-b)^(1/2)/a/(-(-b)^(1/2)/a-(-b+(b^2-b)^(1/2))/a),1/2*2^(1/2))*b-1/a^2/(b^2-b)^(1/2)*(-b)^(1/2)*(x/(-b)^(1/2)*a+1)^(1/2)*(-2*x/(-b)^(1/2)*a+2)^(1/2)*(-x/(-b)^(1/2)*a)^(1/2)/(a^2*x^3+b*x)^(1/2)/(-(-b)^(1/2)/a+b/a-1/a*(b^2-b)^(1/2))*EllipticPi(((x+(-b)^(1/2)/a)/(-b)^(1/2)*a)^(1/2),-(-b)^(1/2)/a/(-(-b)^(1/2)/a-(-b+(b^2-b)^(1/2))/a),1/2*2^(1/2))*b-1/a^2/(b^2-b)^(1/2)*(-b)^(1/2)*(x/(-b)^(1/2)*a+1)^(1/2)*(-2*x/(-b)^(1/2)*a+2)^(1/2)*(-x/(-b)^(1/2)*a)^(1/2)/(a^2*x^3+b*x)^(1/2)/(-(-b)^(1/2)/a+b/a+1/a*(b^2-b)^(1/2))*EllipticPi(((x+(-b)^(1/2)/a)/(-b)^(1/2)*a)^(1/2),-(-b)^(1/2)/a/(-(-b)^(1/2)/a-(-b-(b^2-b)^(1/2))/a),1/2*2^(1/2))*b^2-1/a^2*(-b)^(1/2)*(x/(-b)^(1/2)*a+1)^(1/2)*(-2*x/(-b)^(1/2)*a+2)^(1/2)*(-x/(-b)^(1/2)*a)^(1/2)/(a^2*x^3+b*x)^(1/2)/(-(-b)^(1/2)/a+b/a+1/a*(b^2-b)^(1/2))*EllipticPi(((x+(-b)^(1/2)/a)/(-b)^(1/2)*a)^(1/2),-(-b)^(1/2)/a/(-(-b)^(1/2)/a-(-b-(b^2-b)^(1/2))/a),1/2*2^(1/2))*b+1/a^2/(b^2-b)^(1/2)*(-b)^(1/2)*(x/(-b)^(1/2)*a+1)^(1/2)*(-2*x/(-b)^(1/2)*a+2)^(1/2)*(-x/(-b)^(1/2)*a)^(1/2)/(a^2*x^3+b*x)^(1/2)/(-(-b)^(1/2)/a+b/a+1/a*(b^2-b)^(1/2))*EllipticPi(((x+(-b)^(1/2)/a)/(-b)^(1/2)*a)^(1/2),-(-b)^(1/2)/a/(-(-b)^(1/2)/a-(-b-(b^2-b)^(1/2))/a),1/2*2^(1/2))*b","C"
781,1,534,54,0.139000," ","int((a*(a*b+a*c-3*b*c)+(-2*a^2+a*b+a*c+3*b*c)*x+(a-2*b-2*c)*x^2+x^3)/((-a+x)*(-b+x)*(-c+x))^(1/2)/(-b*c-a^3*d+(3*a^2*d+b+c)*x-(3*a*d+1)*x^2+d*x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 \left(b -c \right) \sqrt{\frac{-c +x}{b -c}}\, \sqrt{\frac{-a +x}{c -a}}\, \sqrt{\frac{-b +x}{-b +c}}\, \EllipticF \left(\sqrt{\frac{-c +x}{b -c}}, \sqrt{\frac{-b +c}{c -a}}\right)}{d \sqrt{-a b c +a b x +a c x -a \,x^{2}+b c x -b \,x^{2}-c \,x^{2}+x^{3}}}+\frac{2 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(d \,\textit{\_Z}^{3}+\left(-3 a d -1\right) \textit{\_Z}^{2}+\left(3 a^{2} d +b +c \right) \textit{\_Z} -a^{3} d -b c \right)}{\sum}\frac{\left(4 \underline{\hspace{1.25 ex}}\alpha^{2} a d -2 \underline{\hspace{1.25 ex}}\alpha^{2} b d -2 \underline{\hspace{1.25 ex}}\alpha^{2} c d -5 \underline{\hspace{1.25 ex}}\alpha  \,a^{2} d +\underline{\hspace{1.25 ex}}\alpha  a b d +\underline{\hspace{1.25 ex}}\alpha  a c d +3 \underline{\hspace{1.25 ex}}\alpha  b c d +a^{3} d +a^{2} b d +a^{2} c d -3 a b c d +\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  c +b c \right) \left(b -c \right) \left(\underline{\hspace{1.25 ex}}\alpha^{2} d -3 \underline{\hspace{1.25 ex}}\alpha  a d +\underline{\hspace{1.25 ex}}\alpha  c d +3 a^{2} d -3 a c d +c^{2} d -\underline{\hspace{1.25 ex}}\alpha  +b \right) \sqrt{\frac{-c +x}{b -c}}\, \sqrt{\frac{-a +x}{c -a}}\, \sqrt{\frac{-b +x}{-b +c}}\, \EllipticPi \left(\sqrt{\frac{-c +x}{b -c}}, \frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2} d -3 \underline{\hspace{1.25 ex}}\alpha  a d +\underline{\hspace{1.25 ex}}\alpha  c d +3 a^{2} d -3 a c d +c^{2} d -\underline{\hspace{1.25 ex}}\alpha  +b \right) \left(b -c \right)}{d \left(a^{3}-3 a^{2} c +3 a \,c^{2}-c^{3}\right)}, \sqrt{\frac{-b +c}{c -a}}\right)}{\left(-3 \underline{\hspace{1.25 ex}}\alpha^{2} d +6 \underline{\hspace{1.25 ex}}\alpha  a d -3 a^{2} d +2 \underline{\hspace{1.25 ex}}\alpha  -b -c \right) \left(a^{3}-3 a^{2} c +3 a \,c^{2}-c^{3}\right) \sqrt{-a b c +a b x +a c x -a \,x^{2}+b c x -b \,x^{2}-c \,x^{2}+x^{3}}}\right)}{d^{2}}$&$534$\\ elliptic&$\frac{2 \left(b -c \right) \sqrt{\frac{-c +x}{b -c}}\, \sqrt{\frac{-a +x}{c -a}}\, \sqrt{\frac{-b +x}{-b +c}}\, \EllipticF \left(\sqrt{\frac{-c +x}{b -c}}, \sqrt{\frac{-b +c}{c -a}}\right)}{d \sqrt{-a b c +a b x +a c x -a \,x^{2}+b c x -b \,x^{2}-c \,x^{2}+x^{3}}}+\frac{2 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(d \,\textit{\_Z}^{3}+\left(-3 a d -1\right) \textit{\_Z}^{2}+\left(3 a^{2} d +b +c \right) \textit{\_Z} -a^{3} d -b c \right)}{\sum}\frac{\left(-4 \underline{\hspace{1.25 ex}}\alpha^{2} a d +2 \underline{\hspace{1.25 ex}}\alpha^{2} b d +2 \underline{\hspace{1.25 ex}}\alpha^{2} c d +5 \underline{\hspace{1.25 ex}}\alpha  \,a^{2} d -\underline{\hspace{1.25 ex}}\alpha  a b d -\underline{\hspace{1.25 ex}}\alpha  a c d -3 \underline{\hspace{1.25 ex}}\alpha  b c d -a^{3} d -a^{2} b d -a^{2} c d +3 a b c d -\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  b +\underline{\hspace{1.25 ex}}\alpha  c -b c \right) \left(b -c \right) \left(\underline{\hspace{1.25 ex}}\alpha^{2} d -3 \underline{\hspace{1.25 ex}}\alpha  a d +\underline{\hspace{1.25 ex}}\alpha  c d +3 a^{2} d -3 a c d +c^{2} d -\underline{\hspace{1.25 ex}}\alpha  +b \right) \sqrt{\frac{-c +x}{b -c}}\, \sqrt{\frac{-a +x}{c -a}}\, \sqrt{\frac{-b +x}{-b +c}}\, \EllipticPi \left(\sqrt{\frac{-c +x}{b -c}}, \frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2} d -3 \underline{\hspace{1.25 ex}}\alpha  a d +\underline{\hspace{1.25 ex}}\alpha  c d +3 a^{2} d -3 a c d +c^{2} d -\underline{\hspace{1.25 ex}}\alpha  +b \right) \left(b -c \right)}{d \left(a^{3}-3 a^{2} c +3 a \,c^{2}-c^{3}\right)}, \sqrt{\frac{-b +c}{c -a}}\right)}{\left(3 \underline{\hspace{1.25 ex}}\alpha^{2} d -6 \underline{\hspace{1.25 ex}}\alpha  a d +3 a^{2} d -2 \underline{\hspace{1.25 ex}}\alpha  +b +c \right) \left(a^{3}-3 a^{2} c +3 a \,c^{2}-c^{3}\right) \sqrt{-a b c +a b x +a c x -a \,x^{2}+b c x -b \,x^{2}-c \,x^{2}+x^{3}}}\right)}{d^{2}}$&$536$\\ \hline \end{longtable}"," ",0,"2/d*(b-c)*((-c+x)/(b-c))^(1/2)*((-a+x)/(c-a))^(1/2)*((-b+x)/(-b+c))^(1/2)/(-a*b*c+a*b*x+a*c*x-a*x^2+b*c*x-b*x^2-c*x^2+x^3)^(1/2)*EllipticF(((-c+x)/(b-c))^(1/2),((-b+c)/(c-a))^(1/2))+2/d^2*sum((4*_alpha^2*a*d-2*_alpha^2*b*d-2*_alpha^2*c*d-5*_alpha*a^2*d+_alpha*a*b*d+_alpha*a*c*d+3*_alpha*b*c*d+a^3*d+a^2*b*d+a^2*c*d-3*a*b*c*d+_alpha^2-_alpha*b-_alpha*c+b*c)/(-3*_alpha^2*d+6*_alpha*a*d-3*a^2*d+2*_alpha-b-c)*(b-c)*(_alpha^2*d-3*_alpha*a*d+_alpha*c*d+3*a^2*d-3*a*c*d+c^2*d-_alpha+b)/(a^3-3*a^2*c+3*a*c^2-c^3)*((-c+x)/(b-c))^(1/2)*((-a+x)/(c-a))^(1/2)*((-b+x)/(-b+c))^(1/2)/(-a*b*c+a*b*x+a*c*x-a*x^2+b*c*x-b*x^2-c*x^2+x^3)^(1/2)*EllipticPi(((-c+x)/(b-c))^(1/2),(_alpha^2*d-3*_alpha*a*d+_alpha*c*d+3*a^2*d-3*a*c*d+c^2*d-_alpha+b)*(b-c)/d/(a^3-3*a^2*c+3*a*c^2-c^3),((-b+c)/(c-a))^(1/2)),_alpha=RootOf(d*_Z^3+(-3*a*d-1)*_Z^2+(3*a^2*d+b+c)*_Z-a^3*d-b*c))","C"
782,1,42,48,0.400000," ","int((x^2-1)*(x^4+1)^(1/2)/x^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\arcsinh \left(x^{2}\right)}{2}+\frac{\sqrt{x^{4}+1}}{4 x^{4}}+\frac{\arctanh \left(\frac{1}{\sqrt{x^{4}+1}}\right)}{4}-\frac{\sqrt{x^{4}+1}}{2 x^{2}}$&$42$\\ risch&$-\frac{2 x^{6}-x^{4}+2 x^{2}-1}{4 x^{4} \sqrt{x^{4}+1}}+\frac{\arcsinh \left(x^{2}\right)}{2}+\frac{\arctanh \left(\frac{1}{\sqrt{x^{4}+1}}\right)}{4}$&$47$\\ default&$\frac{\left(x^{4}+1\right)^{\frac{3}{2}}}{4 x^{4}}-\frac{\sqrt{x^{4}+1}}{4}+\frac{\arctanh \left(\frac{1}{\sqrt{x^{4}+1}}\right)}{4}-\frac{\left(x^{4}+1\right)^{\frac{3}{2}}}{2 x^{2}}+\frac{x^{2} \sqrt{x^{4}+1}}{2}+\frac{\arcsinh \left(x^{2}\right)}{2}$&$63$\\ trager&$-\frac{\left(2 x^{2}-1\right) \sqrt{x^{4}+1}}{4 x^{4}}-\frac{\ln \left(-\frac{-2 x^{6}+2 x^{4} \sqrt{x^{4}+1}-2 x^{4}+2 x^{2} \sqrt{x^{4}+1}-2 x^{2}+\sqrt{x^{4}+1}-1}{x^{2}}\right)}{4}$&$77$\\ meijerg&$\frac{-\frac{\sqrt{\pi}\, \left(4 x^{4}+8\right)}{4 x^{4}}+\frac{2 \sqrt{\pi}\, \sqrt{x^{4}+1}}{x^{4}}+2 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{x^{4}+1}}{2}\right)-\left(-2 \ln \left(2\right)-1+4 \ln \left(x \right)\right) \sqrt{\pi}+\frac{2 \sqrt{\pi}}{x^{4}}}{8 \sqrt{\pi}}-\frac{\frac{4 \sqrt{\pi}\, \sqrt{x^{4}+1}}{x^{2}}-4 \sqrt{\pi}\, \arcsinh \left(x^{2}\right)}{8 \sqrt{\pi}}$&$108$\\ \hline \end{longtable}"," ",0,"1/2*arcsinh(x^2)+1/4/x^4*(x^4+1)^(1/2)+1/4*arctanh(1/(x^4+1)^(1/2))-1/2*(x^4+1)^(1/2)/x^2","A"
783,1,38,52,0.232000," ","int((x^2-1)*(x^4+1)^(1/2)/x^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{2}+1\right) \sqrt{x^{4}+1}}{2 x^{2}}-\ln \left(\frac{1+x^{2}+\sqrt{x^{4}+1}}{x}\right)$&$38$\\ risch&$\frac{\sqrt{x^{4}+1}}{2 x^{2}}+\frac{\sqrt{x^{4}+1}}{2}-\frac{\arcsinh \left(x^{2}\right)}{2}-\frac{\arctanh \left(\frac{1}{\sqrt{x^{4}+1}}\right)}{2}$&$39$\\ elliptic&$\frac{\sqrt{x^{4}+1}}{2 x^{2}}+\frac{\sqrt{x^{4}+1}}{2}-\frac{\arcsinh \left(x^{2}\right)}{2}-\frac{\arctanh \left(\frac{1}{\sqrt{x^{4}+1}}\right)}{2}$&$39$\\ default&$\frac{\sqrt{x^{4}+1}}{2}-\frac{\arctanh \left(\frac{1}{\sqrt{x^{4}+1}}\right)}{2}+\frac{\left(x^{4}+1\right)^{\frac{3}{2}}}{2 x^{2}}-\frac{x^{2} \sqrt{x^{4}+1}}{2}-\frac{\arcsinh \left(x^{2}\right)}{2}$&$51$\\ meijerg&$\frac{\frac{4 \sqrt{\pi}\, \sqrt{x^{4}+1}}{x^{2}}-4 \sqrt{\pi}\, \arcsinh \left(x^{2}\right)}{8 \sqrt{\pi}}-\frac{4 \sqrt{\pi}-4 \sqrt{\pi}\, \sqrt{x^{4}+1}+4 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{x^{4}+1}}{2}\right)-2 \left(2-2 \ln \left(2\right)+4 \ln \left(x \right)\right) \sqrt{\pi}}{8 \sqrt{\pi}}$&$87$\\ \hline \end{longtable}"," ",0,"1/2*(x^2+1)*(x^4+1)^(1/2)/x^2-ln((1+x^2+(x^4+1)^(1/2))/x)","A"
784,1,66,48,0.529000," ","int((2*x^3+1)*(x^6-1)^(1/2)/x^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(4 x^{3}+1\right) \sqrt{x^{6}-1}}{6 x^{6}}-\frac{2 \ln \left(-x^{3}+\sqrt{x^{6}-1}\right)}{3}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{6}$&$66$\\ risch&$-\frac{4 x^{9}+x^{6}-4 x^{3}-1}{6 x^{6} \sqrt{x^{6}-1}}+\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(-2 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right)+\left(-2 \ln \left(2\right)+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}\right)}{12 \sqrt{\pi}\, \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}+\frac{2 \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \arcsin \left(x^{3}\right)}{3 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}$&$113$\\ meijerg&$\frac{\sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(\frac{\sqrt{\pi}\, \left(-4 x^{6}+8\right)}{4 x^{6}}-\frac{2 \sqrt{\pi}\, \sqrt{-x^{6}+1}}{x^{6}}+2 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right)-\left(-2 \ln \left(2\right)-1+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}-\frac{2 \sqrt{\pi}}{x^{6}}\right)}{12 \sqrt{\pi}\, \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}}-\frac{i \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(-\frac{4 i \sqrt{\pi}\, \sqrt{-x^{6}+1}}{x^{3}}-4 i \sqrt{\pi}\, \arcsin \left(x^{3}\right)\right)}{6 \sqrt{\pi}\, \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}}$&$157$\\ \hline \end{longtable}"," ",0,"-1/6*(4*x^3+1)*(x^6-1)^(1/2)/x^6-2/3*ln(-x^3+(x^6-1)^(1/2))-1/6*RootOf(_Z^2+1)*ln((-RootOf(_Z^2+1)+(x^6-1)^(1/2))/x^3)","C"
785,1,64,48,0.528000," ","int((2*x^3+1)*(x^6-1)^(1/2)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(2 x^{3}-1\right) \sqrt{x^{6}-1}}{3 x^{3}}-\frac{\ln \left(-x^{3}+\sqrt{x^{6}-1}\right)}{3}-\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{3}$&$64$\\ meijerg&$-\frac{i \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(-\frac{4 i \sqrt{\pi}\, \sqrt{-x^{6}+1}}{x^{3}}-4 i \sqrt{\pi}\, \arcsin \left(x^{3}\right)\right)}{12 \sqrt{\pi}\, \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}}-\frac{\sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(4 \sqrt{\pi}-4 \sqrt{\pi}\, \sqrt{-x^{6}+1}+4 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right)-2 \left(2-2 \ln \left(2\right)+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}\right)}{6 \sqrt{\pi}\, \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}}$&$136$\\ risch&$-\frac{\sqrt{x^{6}-1}}{3 x^{3}}-\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(-2 \sqrt{\pi}+2 \sqrt{\pi}\, \sqrt{-x^{6}+1}\right)}{3 \sqrt{\pi}\, \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}+\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \arcsin \left(x^{3}\right)}{3 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}-\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(-2 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right)+\left(-2 \ln \left(2\right)+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}\right)}{3 \sqrt{\pi}\, \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}$&$141$\\ \hline \end{longtable}"," ",0,"1/3*(2*x^3-1)*(x^6-1)^(1/2)/x^3-1/3*ln(-x^3+(x^6-1)^(1/2))-2/3*RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)+(x^6-1)^(1/2))/x^3)","C"
786,1,371,11,0.159000," ","int((a^6*x^6+b^6)/(a^2*x^3-b^2*x)^(1/2)/(a^6*x^6-b^6+c*x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{b \sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{2 \left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}-b^{2} x}}+\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{6} \textit{\_Z}^{6}-b^{6}+c \,\textit{\_Z}^{3}\right)}{\sum}\frac{\left(-2 b^{6}+\underline{\hspace{1.25 ex}}\alpha^{3} c \right) \left(a^{8} \underline{\hspace{1.25 ex}}\alpha^{5}-a^{7} \underline{\hspace{1.25 ex}}\alpha^{4} b +a^{6} \underline{\hspace{1.25 ex}}\alpha^{3} b^{2}-a^{5} \underline{\hspace{1.25 ex}}\alpha^{2} b^{3}+a^{4} b^{4} \underline{\hspace{1.25 ex}}\alpha  -a^{3} b^{5}+a^{2} \underline{\hspace{1.25 ex}}\alpha^{2} c -\underline{\hspace{1.25 ex}}\alpha  a b c +b^{2} c \right) \sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{\left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{a^{8} \underline{\hspace{1.25 ex}}\alpha^{5}-a^{7} \underline{\hspace{1.25 ex}}\alpha^{4} b +a^{6} \underline{\hspace{1.25 ex}}\alpha^{3} b^{2}-a^{5} \underline{\hspace{1.25 ex}}\alpha^{2} b^{3}+a^{4} b^{4} \underline{\hspace{1.25 ex}}\alpha  -a^{3} b^{5}+a^{2} \underline{\hspace{1.25 ex}}\alpha^{2} c -\underline{\hspace{1.25 ex}}\alpha  a b c +b^{2} c}{b^{2} c}, \frac{\sqrt{2}}{2}\right)}{\underline{\hspace{1.25 ex}}\alpha^{2} \left(2 \underline{\hspace{1.25 ex}}\alpha^{3} a^{6}+c \right) \sqrt{x \left(a^{2} x^{2}-b^{2}\right)}}\right)}{3 b^{2} c}$&$371$\\ elliptic&$\frac{b \sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{2 \left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}-b^{2} x}}+\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{6} \textit{\_Z}^{6}-b^{6}+c \,\textit{\_Z}^{3}\right)}{\sum}\frac{\left(-2 b^{6}+\underline{\hspace{1.25 ex}}\alpha^{3} c \right) \left(a^{8} \underline{\hspace{1.25 ex}}\alpha^{5}-a^{7} \underline{\hspace{1.25 ex}}\alpha^{4} b +a^{6} \underline{\hspace{1.25 ex}}\alpha^{3} b^{2}-a^{5} \underline{\hspace{1.25 ex}}\alpha^{2} b^{3}+a^{4} b^{4} \underline{\hspace{1.25 ex}}\alpha  -a^{3} b^{5}+a^{2} \underline{\hspace{1.25 ex}}\alpha^{2} c -\underline{\hspace{1.25 ex}}\alpha  a b c +b^{2} c \right) \sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{\left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{a^{8} \underline{\hspace{1.25 ex}}\alpha^{5}-a^{7} \underline{\hspace{1.25 ex}}\alpha^{4} b +a^{6} \underline{\hspace{1.25 ex}}\alpha^{3} b^{2}-a^{5} \underline{\hspace{1.25 ex}}\alpha^{2} b^{3}+a^{4} b^{4} \underline{\hspace{1.25 ex}}\alpha  -a^{3} b^{5}+a^{2} \underline{\hspace{1.25 ex}}\alpha^{2} c -\underline{\hspace{1.25 ex}}\alpha  a b c +b^{2} c}{b^{2} c}, \frac{\sqrt{2}}{2}\right)}{\underline{\hspace{1.25 ex}}\alpha^{2} \left(2 \underline{\hspace{1.25 ex}}\alpha^{3} a^{6}+c \right) \sqrt{x \left(a^{2} x^{2}-b^{2}\right)}}\right)}{3 b^{2} c}$&$371$\\ \hline \end{longtable}"," ",0,"b/a*((x+b/a)/b*a)^(1/2)*(-2*(x-b/a)/b*a)^(1/2)*(-a*x/b)^(1/2)/(a^2*x^3-b^2*x)^(1/2)*EllipticF(((x+b/a)/b*a)^(1/2),1/2*2^(1/2))+1/3/b^2/c*2^(1/2)*sum((-2*b^6+_alpha^3*c)/_alpha^2/(2*_alpha^3*a^6+c)*(_alpha^5*a^8-_alpha^4*a^7*b+_alpha^3*a^6*b^2-_alpha^2*a^5*b^3+_alpha*a^4*b^4-a^3*b^5+_alpha^2*a^2*c-_alpha*a*b*c+b^2*c)*((x+b/a)/b*a)^(1/2)*(-(x-b/a)/b*a)^(1/2)*(-a*x/b)^(1/2)/(x*(a^2*x^2-b^2))^(1/2)*EllipticPi(((x+b/a)/b*a)^(1/2),(_alpha^5*a^8-_alpha^4*a^7*b+_alpha^3*a^6*b^2-_alpha^2*a^5*b^3+_alpha*a^4*b^4-a^3*b^5+_alpha^2*a^2*c-_alpha*a*b*c+b^2*c)/b^2/c,1/2*2^(1/2)),_alpha=RootOf(_Z^6*a^6-b^6+_Z^3*c))","B"
787,1,371,11,0.064000," ","int((a^6*x^6+b^6)/(a^2*x^3-b^2*x)^(1/2)/(a^6*x^6-b^6+c*x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{b \sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{2 \left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}-b^{2} x}}+\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{6} \textit{\_Z}^{6}-b^{6}+c \,\textit{\_Z}^{3}\right)}{\sum}\frac{\left(-2 b^{6}+\underline{\hspace{1.25 ex}}\alpha^{3} c \right) \left(a^{8} \underline{\hspace{1.25 ex}}\alpha^{5}-a^{7} \underline{\hspace{1.25 ex}}\alpha^{4} b +a^{6} \underline{\hspace{1.25 ex}}\alpha^{3} b^{2}-a^{5} \underline{\hspace{1.25 ex}}\alpha^{2} b^{3}+a^{4} b^{4} \underline{\hspace{1.25 ex}}\alpha  -a^{3} b^{5}+a^{2} \underline{\hspace{1.25 ex}}\alpha^{2} c -\underline{\hspace{1.25 ex}}\alpha  a b c +b^{2} c \right) \sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{\left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{a^{8} \underline{\hspace{1.25 ex}}\alpha^{5}-a^{7} \underline{\hspace{1.25 ex}}\alpha^{4} b +a^{6} \underline{\hspace{1.25 ex}}\alpha^{3} b^{2}-a^{5} \underline{\hspace{1.25 ex}}\alpha^{2} b^{3}+a^{4} b^{4} \underline{\hspace{1.25 ex}}\alpha  -a^{3} b^{5}+a^{2} \underline{\hspace{1.25 ex}}\alpha^{2} c -\underline{\hspace{1.25 ex}}\alpha  a b c +b^{2} c}{b^{2} c}, \frac{\sqrt{2}}{2}\right)}{\underline{\hspace{1.25 ex}}\alpha^{2} \left(2 \underline{\hspace{1.25 ex}}\alpha^{3} a^{6}+c \right) \sqrt{x \left(a^{2} x^{2}-b^{2}\right)}}\right)}{3 b^{2} c}$&$371$\\ elliptic&$\frac{b \sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{2 \left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}-b^{2} x}}+\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{6} \textit{\_Z}^{6}-b^{6}+c \,\textit{\_Z}^{3}\right)}{\sum}\frac{\left(-2 b^{6}+\underline{\hspace{1.25 ex}}\alpha^{3} c \right) \left(a^{8} \underline{\hspace{1.25 ex}}\alpha^{5}-a^{7} \underline{\hspace{1.25 ex}}\alpha^{4} b +a^{6} \underline{\hspace{1.25 ex}}\alpha^{3} b^{2}-a^{5} \underline{\hspace{1.25 ex}}\alpha^{2} b^{3}+a^{4} b^{4} \underline{\hspace{1.25 ex}}\alpha  -a^{3} b^{5}+a^{2} \underline{\hspace{1.25 ex}}\alpha^{2} c -\underline{\hspace{1.25 ex}}\alpha  a b c +b^{2} c \right) \sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{\left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{a^{8} \underline{\hspace{1.25 ex}}\alpha^{5}-a^{7} \underline{\hspace{1.25 ex}}\alpha^{4} b +a^{6} \underline{\hspace{1.25 ex}}\alpha^{3} b^{2}-a^{5} \underline{\hspace{1.25 ex}}\alpha^{2} b^{3}+a^{4} b^{4} \underline{\hspace{1.25 ex}}\alpha  -a^{3} b^{5}+a^{2} \underline{\hspace{1.25 ex}}\alpha^{2} c -\underline{\hspace{1.25 ex}}\alpha  a b c +b^{2} c}{b^{2} c}, \frac{\sqrt{2}}{2}\right)}{\underline{\hspace{1.25 ex}}\alpha^{2} \left(2 \underline{\hspace{1.25 ex}}\alpha^{3} a^{6}+c \right) \sqrt{x \left(a^{2} x^{2}-b^{2}\right)}}\right)}{3 b^{2} c}$&$371$\\ \hline \end{longtable}"," ",0,"b/a*((x+b/a)/b*a)^(1/2)*(-2*(x-b/a)/b*a)^(1/2)*(-a*x/b)^(1/2)/(a^2*x^3-b^2*x)^(1/2)*EllipticF(((x+b/a)/b*a)^(1/2),1/2*2^(1/2))+1/3/b^2/c*2^(1/2)*sum((-2*b^6+_alpha^3*c)/_alpha^2/(2*_alpha^3*a^6+c)*(_alpha^5*a^8-_alpha^4*a^7*b+_alpha^3*a^6*b^2-_alpha^2*a^5*b^3+_alpha*a^4*b^4-a^3*b^5+_alpha^2*a^2*c-_alpha*a*b*c+b^2*c)*((x+b/a)/b*a)^(1/2)*(-(x-b/a)/b*a)^(1/2)*(-a*x/b)^(1/2)/(x*(a^2*x^2-b^2))^(1/2)*EllipticPi(((x+b/a)/b*a)^(1/2),(_alpha^5*a^8-_alpha^4*a^7*b+_alpha^3*a^6*b^2-_alpha^2*a^5*b^3+_alpha*a^4*b^4-a^3*b^5+_alpha^2*a^2*c-_alpha*a*b*c+b^2*c)/b^2/c,1/2*2^(1/2)),_alpha=RootOf(_Z^6*a^6-b^6+_Z^3*c))","B"
788,0,0,48,0.015000," ","int((-3*x^5+x)/(x^5+x)^(1/2)/(x^8+2*x^4-a*x^2+1),x)","\[\int \frac{-3 x^{5}+x}{\sqrt{x^{5}+x}\, \left(x^{8}+2 x^{4}-a \,x^{2}+1\right)}\, dx\]"," ",0,"int((-3*x^5+x)/(x^5+x)^(1/2)/(x^8+2*x^4-a*x^2+1),x)","F"
789,1,72,52,0.665000," ","int((-2*x^8+1)^(1/2)*(2*x^8-1)*(2*x^8+1)/x^7/(2*x^8+x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{-2 x^{8}+1}\, \left(2 x^{8}-3 x^{4}-1\right)}{6 x^{6}}+\frac{\ln \left(\frac{-2 x^{8}+x^{4}+2 \sqrt{-2 x^{8}+1}\, x^{2}+1}{\left(x^{4}+1\right) \left(2 x^{4}-1\right)}\right)}{4}$&$72$\\ risch&$-\frac{4 x^{16}-6 x^{12}-4 x^{8}+3 x^{4}+1}{6 x^{6} \sqrt{-2 x^{8}+1}}+\frac{\ln \left(-\frac{-2 x^{8}+x^{4}+2 \sqrt{-2 x^{8}+1}\, x^{2}+1}{\left(x^{4}+1\right) \left(2 x^{4}-1\right)}\right)}{4}$&$83$\\ \hline \end{longtable}"," ",0,"1/6*(-2*x^8+1)^(1/2)*(2*x^8-3*x^4-1)/x^6+1/4*ln((-2*x^8+x^4+2*(-2*x^8+1)^(1/2)*x^2+1)/(x^4+1)/(2*x^4-1))","A"
790,0,0,48,0.016000," ","int((3*x^5-x)/(x^5+x)^(1/2)/(a*x^8+2*a*x^4-x^2+a),x)","\[\int \frac{3 x^{5}-x}{\sqrt{x^{5}+x}\, \left(a \,x^{8}+2 a \,x^{4}-x^{2}+a \right)}\, dx\]"," ",0,"int((3*x^5-x)/(x^5+x)^(1/2)/(a*x^8+2*a*x^4-x^2+a),x)","F"
791,0,0,50,0.020000," ","int(x^5*(9*a*x^2+7*b)/(a*x^5+b*x^3)^(1/4)/(a*x^9+b*x^7-2),x)","\[\int \frac{x^{5} \left(9 a \,x^{2}+7 b \right)}{\left(a \,x^{5}+b \,x^{3}\right)^{\frac{1}{4}} \left(a \,x^{9}+b \,x^{7}-2\right)}\, dx\]"," ",0,"int(x^5*(9*a*x^2+7*b)/(a*x^5+b*x^3)^(1/4)/(a*x^9+b*x^7-2),x)","F"
792,1,130,50,0.187000," ","int(x^2/(x^2+1)/(1024*x^10-16640*x^9+112000*x^8-401440*x^7+820340*x^6-954733*x^5+615255*x^4-225810*x^3+47250*x^2-5265*x+243)^(1/5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(-\frac{13}{340}+\frac{i}{340}\right) \left(4 x^{2}-13 x +3\right) \ln \left(i+x \right)}{\left(\left(4 x^{2}-13 x +3\right)^{5}\right)^{\frac{1}{5}}}+\frac{\left(-\frac{13}{340}-\frac{i}{340}\right) \left(4 x^{2}-13 x +3\right) \ln \left(-i+x \right)}{\left(\left(4 x^{2}-13 x +3\right)^{5}\right)^{\frac{1}{5}}}-\frac{\left(4 x^{2}-13 x +3\right) \ln \left(-1+4 x \right)}{187 \left(\left(4 x^{2}-13 x +3\right)^{5}\right)^{\frac{1}{5}}}+\frac{9 \left(4 x^{2}-13 x +3\right) \ln \left(-3+x \right)}{110 \left(\left(4 x^{2}-13 x +3\right)^{5}\right)^{\frac{1}{5}}}$&$130$\\ \hline \end{longtable}"," ",0,"(-13/340+1/340*I)/((4*x^2-13*x+3)^5)^(1/5)*(4*x^2-13*x+3)*ln(I+x)-(13/340+1/340*I)/((4*x^2-13*x+3)^5)^(1/5)*(4*x^2-13*x+3)*ln(-I+x)-1/187/((4*x^2-13*x+3)^5)^(1/5)*(4*x^2-13*x+3)*ln(-1+4*x)+9/110/((4*x^2-13*x+3)^5)^(1/5)*(4*x^2-13*x+3)*ln(-3+x)","C"
793,1,15639,23,17.818000," ","int((x^2-2*x+1)^(1/3)/(x^2+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$15639$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
794,1,2779,23,2.494000," ","int((x^2+2*x+1)^(1/3)/(x^2+3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2779$\\ \hline \end{longtable}"," ",0,"-1/3*ln(-(12*RootOf(108*_Z^6+18*_Z^3+1)^3*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)^2*x^2+36*(x^2+2*x+1)^(1/3)*RootOf(108*_Z^6+18*_Z^3+1)^3*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)*x+48*RootOf(108*_Z^6+18*_Z^3+1)^3*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)^2*x+36*(x^2+2*x+1)^(1/3)*RootOf(108*_Z^6+18*_Z^3+1)^3*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)+36*RootOf(108*_Z^6+18*_Z^3+1)^3*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)^2+RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)^2*x^2+6*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)*(x^2+2*x+1)^(1/3)*x+4*x*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)^2+12*(x^2+2*x+1)^(2/3)+6*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)*(x^2+2*x+1)^(1/3)+3*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)^2)/(1+x)/(12*x*RootOf(108*_Z^6+18*_Z^3+1)^3+x+1))*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)-3*ln(-(12*RootOf(108*_Z^6+18*_Z^3+1)^3*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)^2*x^2+36*(x^2+2*x+1)^(1/3)*RootOf(108*_Z^6+18*_Z^3+1)^3*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)*x+48*RootOf(108*_Z^6+18*_Z^3+1)^3*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)^2*x+36*(x^2+2*x+1)^(1/3)*RootOf(108*_Z^6+18*_Z^3+1)^3*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)+36*RootOf(108*_Z^6+18*_Z^3+1)^3*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)^2+RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)^2*x^2+6*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)*(x^2+2*x+1)^(1/3)*x+4*x*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)^2+12*(x^2+2*x+1)^(2/3)+6*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)*(x^2+2*x+1)^(1/3)+3*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)^2)/(1+x)/(12*x*RootOf(108*_Z^6+18*_Z^3+1)^3+x+1))*RootOf(108*_Z^6+18*_Z^3+1)^3*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)-18*RootOf(108*_Z^6+18*_Z^3+1)^4*ln((36*RootOf(108*_Z^6+18*_Z^3+1)^5*x^2+36*RootOf(108*_Z^6+18*_Z^3+1)^5*x+36*(x^2+2*x+1)^(1/3)*RootOf(108*_Z^6+18*_Z^3+1)^4*x+36*(x^2+2*x+1)^(1/3)*RootOf(108*_Z^6+18*_Z^3+1)^4+18*(x^2+2*x+1)^(2/3)*RootOf(108*_Z^6+18*_Z^3+1)^3+3*RootOf(108*_Z^6+18*_Z^3+1)^2*x^2+6*RootOf(108*_Z^6+18*_Z^3+1)^2*x+3*(x^2+2*x+1)^(1/3)*RootOf(108*_Z^6+18*_Z^3+1)*x+3*RootOf(108*_Z^6+18*_Z^3+1)^2+3*(x^2+2*x+1)^(1/3)*RootOf(108*_Z^6+18*_Z^3+1)+(x^2+2*x+1)^(2/3))/(1+x)/(12*x*RootOf(108*_Z^6+18*_Z^3+1)^3+x-1))-2*RootOf(108*_Z^6+18*_Z^3+1)*ln((36*RootOf(108*_Z^6+18*_Z^3+1)^5*x^2+36*RootOf(108*_Z^6+18*_Z^3+1)^5*x+36*(x^2+2*x+1)^(1/3)*RootOf(108*_Z^6+18*_Z^3+1)^4*x+36*(x^2+2*x+1)^(1/3)*RootOf(108*_Z^6+18*_Z^3+1)^4+18*(x^2+2*x+1)^(2/3)*RootOf(108*_Z^6+18*_Z^3+1)^3+3*RootOf(108*_Z^6+18*_Z^3+1)^2*x^2+6*RootOf(108*_Z^6+18*_Z^3+1)^2*x+3*(x^2+2*x+1)^(1/3)*RootOf(108*_Z^6+18*_Z^3+1)*x+3*RootOf(108*_Z^6+18*_Z^3+1)^2+3*(x^2+2*x+1)^(1/3)*RootOf(108*_Z^6+18*_Z^3+1)+(x^2+2*x+1)^(2/3))/(1+x)/(12*x*RootOf(108*_Z^6+18*_Z^3+1)^3+x-1))+18*RootOf(108*_Z^6+18*_Z^3+1)^4*ln((36*RootOf(108*_Z^6+18*_Z^3+1)^5*x^2+144*RootOf(108*_Z^6+18*_Z^3+1)^5*x+18*(x^2+2*x+1)^(1/3)*RootOf(108*_Z^6+18*_Z^3+1)^4*x+108*RootOf(108*_Z^6+18*_Z^3+1)^5+18*(x^2+2*x+1)^(1/3)*RootOf(108*_Z^6+18*_Z^3+1)^4+3*RootOf(108*_Z^6+18*_Z^3+1)^2*x^2+12*RootOf(108*_Z^6+18*_Z^3+1)^2*x+9*RootOf(108*_Z^6+18*_Z^3+1)^2-(x^2+2*x+1)^(2/3))/(1+x)/(12*x*RootOf(108*_Z^6+18*_Z^3+1)^3+x-1))+RootOf(108*_Z^6+18*_Z^3+1)*ln((36*RootOf(108*_Z^6+18*_Z^3+1)^5*x^2+144*RootOf(108*_Z^6+18*_Z^3+1)^5*x+18*(x^2+2*x+1)^(1/3)*RootOf(108*_Z^6+18*_Z^3+1)^4*x+108*RootOf(108*_Z^6+18*_Z^3+1)^5+18*(x^2+2*x+1)^(1/3)*RootOf(108*_Z^6+18*_Z^3+1)^4+3*RootOf(108*_Z^6+18*_Z^3+1)^2*x^2+12*RootOf(108*_Z^6+18*_Z^3+1)^2*x+9*RootOf(108*_Z^6+18*_Z^3+1)^2-(x^2+2*x+1)^(2/3))/(1+x)/(12*x*RootOf(108*_Z^6+18*_Z^3+1)^3+x-1))+3*ln(-(12*RootOf(108*_Z^6+18*_Z^3+1)^3*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)^2*x^2+72*(x^2+2*x+1)^(1/3)*RootOf(108*_Z^6+18*_Z^3+1)^3*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)*x+12*RootOf(108*_Z^6+18*_Z^3+1)^3*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)^2*x+216*(x^2+2*x+1)^(2/3)*RootOf(108*_Z^6+18*_Z^3+1)^3+72*(x^2+2*x+1)^(1/3)*RootOf(108*_Z^6+18*_Z^3+1)^3*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)+RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)^2*x^2+6*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)*(x^2+2*x+1)^(1/3)*x+24*(x^2+2*x+1)^(2/3)+6*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)*(x^2+2*x+1)^(1/3)-RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)^2)/(1+x)/(12*x*RootOf(108*_Z^6+18*_Z^3+1)^3+x+1))*RootOf(108*_Z^6+18*_Z^3+1)^3*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)+1/6*ln(-(12*RootOf(108*_Z^6+18*_Z^3+1)^3*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)^2*x^2+72*(x^2+2*x+1)^(1/3)*RootOf(108*_Z^6+18*_Z^3+1)^3*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)*x+12*RootOf(108*_Z^6+18*_Z^3+1)^3*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)^2*x+216*(x^2+2*x+1)^(2/3)*RootOf(108*_Z^6+18*_Z^3+1)^3+72*(x^2+2*x+1)^(1/3)*RootOf(108*_Z^6+18*_Z^3+1)^3*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)+RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)^2*x^2+6*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)*(x^2+2*x+1)^(1/3)*x+24*(x^2+2*x+1)^(2/3)+6*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)*(x^2+2*x+1)^(1/3)-RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)^2)/(1+x)/(12*x*RootOf(108*_Z^6+18*_Z^3+1)^3+x+1))*RootOf(_Z^3+216*RootOf(108*_Z^6+18*_Z^3+1)^3+36)","B"
795,1,507,45,9.637000," ","int(1/(-1+x)/(x^3+x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(\frac{-2 \sqrt{x^{3}+x}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{2}-4 \sqrt{x^{3}+x}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x -2 \left(x^{3}+x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}-2 \sqrt{x^{3}+x}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right)-6 \left(x^{3}+x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{4}+16 \left(x^{3}+x \right)^{\frac{3}{4}} x -6 \left(x^{3}+x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x +12 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{3}+16 \left(x^{3}+x \right)^{\frac{3}{4}}-2 \left(x^{3}+x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2}+6 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{2}+12 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right)}{\left(-1+x \right)^{4}}\right)}{8}-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(\frac{2 \sqrt{x^{3}+x}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{2}+4 \sqrt{x^{3}+x}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x +2 \left(x^{3}+x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}+2 \sqrt{x^{3}+x}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{3}+6 \left(x^{3}+x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+x^{4} \RootOf \left(\textit{\_Z}^{4}-8\right)+16 \left(x^{3}+x \right)^{\frac{3}{4}} x +6 \left(x^{3}+x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x +12 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{3}+16 \left(x^{3}+x \right)^{\frac{3}{4}}+2 \left(x^{3}+x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2}+6 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{2}+12 \RootOf \left(\textit{\_Z}^{4}-8\right) x +\RootOf \left(\textit{\_Z}^{4}-8\right)}{\left(-1+x \right)^{4}}\right)}{8}$&$507$\\ \hline \end{longtable}"," ",0,"-1/8*RootOf(_Z^2+RootOf(_Z^4-8)^2)*ln((-2*(x^3+x)^(1/2)*RootOf(_Z^4-8)^2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^2-4*(x^3+x)^(1/2)*RootOf(_Z^4-8)^2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x-2*(x^3+x)^(1/4)*RootOf(_Z^4-8)^2*x^3-2*(x^3+x)^(1/2)*RootOf(_Z^4-8)^2*RootOf(_Z^2+RootOf(_Z^4-8)^2)-6*(x^3+x)^(1/4)*RootOf(_Z^4-8)^2*x^2+RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^4+16*(x^3+x)^(3/4)*x-6*(x^3+x)^(1/4)*RootOf(_Z^4-8)^2*x+12*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^3+16*(x^3+x)^(3/4)-2*(x^3+x)^(1/4)*RootOf(_Z^4-8)^2+6*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^2+12*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x+RootOf(_Z^2+RootOf(_Z^4-8)^2))/(-1+x)^4)-1/8*RootOf(_Z^4-8)*ln((2*(x^3+x)^(1/2)*RootOf(_Z^4-8)^3*x^2+4*(x^3+x)^(1/2)*RootOf(_Z^4-8)^3*x+2*(x^3+x)^(1/4)*RootOf(_Z^4-8)^2*x^3+2*(x^3+x)^(1/2)*RootOf(_Z^4-8)^3+6*(x^3+x)^(1/4)*RootOf(_Z^4-8)^2*x^2+x^4*RootOf(_Z^4-8)+16*(x^3+x)^(3/4)*x+6*(x^3+x)^(1/4)*RootOf(_Z^4-8)^2*x+12*RootOf(_Z^4-8)*x^3+16*(x^3+x)^(3/4)+2*(x^3+x)^(1/4)*RootOf(_Z^4-8)^2+6*RootOf(_Z^4-8)*x^2+12*RootOf(_Z^4-8)*x+RootOf(_Z^4-8))/(-1+x)^4)","C"
796,1,151,49,1.573000," ","int((x^4-1)/(x^3+x)^(1/2)/(x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{i \sqrt{-i \left(i+x \right)}\, \sqrt{2}\, \sqrt{i \left(-i+x \right)}\, \sqrt{i x}\, \EllipticF \left(\sqrt{-i \left(i+x \right)}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}+x}}+\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+1\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{3}-i \underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +i\right) \sqrt{-i \left(i+x \right)}\, \sqrt{i \left(-i+x \right)}\, \sqrt{i x}\, \EllipticPi \left(\sqrt{-i \left(i+x \right)}, -\frac{1}{2} i \underline{\hspace{1.25 ex}}\alpha^{3}-\frac{1}{2} \underline{\hspace{1.25 ex}}\alpha^{2}+\frac{1}{2} i \underline{\hspace{1.25 ex}}\alpha  +\frac{1}{2}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x \left(x^{2}+1\right)}}\right)}{4}$&$151$\\ elliptic&$\frac{i \sqrt{-i \left(i+x \right)}\, \sqrt{2}\, \sqrt{i \left(-i+x \right)}\, \sqrt{i x}\, \EllipticF \left(\sqrt{-i \left(i+x \right)}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}+x}}+\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+1\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{3}-i \underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +i\right) \sqrt{-i \left(i+x \right)}\, \sqrt{i \left(-i+x \right)}\, \sqrt{i x}\, \EllipticPi \left(\sqrt{-i \left(i+x \right)}, -\frac{1}{2} i \underline{\hspace{1.25 ex}}\alpha^{3}-\frac{1}{2} \underline{\hspace{1.25 ex}}\alpha^{2}+\frac{1}{2} i \underline{\hspace{1.25 ex}}\alpha  +\frac{1}{2}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x \left(x^{2}+1\right)}}\right)}{4}$&$151$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{5} x^{2}-2 x \RootOf \left(\textit{\_Z}^{4}-8\right)^{5}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{5}-4 \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x -16 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{2}+16 \RootOf \left(\textit{\_Z}^{4}-8\right) x -16 \RootOf \left(\textit{\_Z}^{4}-8\right)-32 \sqrt{x^{3}+x}}{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 x \RootOf \left(\textit{\_Z}^{4}-8\right)^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}+4 x^{2}-4 x +4}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{4} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{4} x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{4}+4 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x -16 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{2}+16 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x -16 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right)+32 \sqrt{x^{3}+x}}{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 x \RootOf \left(\textit{\_Z}^{4}-8\right)^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}-4 x^{2}+4 x -4}\right)}{4}$&$350$\\ \hline \end{longtable}"," ",0,"I*(-I*(I+x))^(1/2)*2^(1/2)*(I*(-I+x))^(1/2)*(I*x)^(1/2)/(x^3+x)^(1/2)*EllipticF((-I*(I+x))^(1/2),1/2*2^(1/2))+1/4*I*2^(1/2)*sum(_alpha*(I+_alpha^3-I*_alpha^2-_alpha)*(-I*(I+x))^(1/2)*(I*(-I+x))^(1/2)*(I*x)^(1/2)/(x*(x^2+1))^(1/2)*EllipticPi((-I*(I+x))^(1/2),-1/2*I*_alpha^3-1/2*_alpha^2+1/2*I*_alpha+1/2,1/2*2^(1/2)),_alpha=RootOf(_Z^4+1))","C"
797,1,244,49,0.437000," ","int((x^3+1)/(x^3-1)/(x^4+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4 \sqrt{\left(x^{2}-1\right)^{2}+2 x^{2}}}\right)}{6}+\frac{\sqrt{2}\, \sqrt{\frac{2 \left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+2}\, \arctan \left(\frac{\sqrt{\frac{2 \left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+2}\, \left(x^{2}+1\right)}{\left(\frac{\left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+1\right) \left(-x^{2}+1\right)}\right)}{3 \sqrt{\frac{\frac{\left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+1}{\left(\frac{x^{2}+1}{-x^{2}+1}+1\right)^{2}}}\, \left(\frac{x^{2}+1}{-x^{2}+1}+1\right)}+\frac{\left(\frac{\ln \left(-1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{6}-\frac{\ln \left(1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{6}+\frac{2 \sqrt{2}\, \arctan \left(\frac{\sqrt{x^{4}+1}}{x}\right)}{3}\right) \sqrt{2}}{2}$&$244$\\ default&$\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4 \sqrt{x^{4}+1}}\right)}{6}+\frac{2 \left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{3 \sqrt{x^{4}+1}}+\frac{2 \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{\arctanh \left(\frac{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \left(x^{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{3}+\frac{2 \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(\frac{\arctanh \left(\frac{\sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}\, \left(x^{2}-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{3}$&$358$\\ \hline \end{longtable}"," ",0,"-1/6*2^(1/2)*arctanh(1/4*(2*x^2+2)*2^(1/2)/((x^2-1)^2+2*x^2)^(1/2))+1/3*2^(1/2)/(((x^2+1)^2/(-x^2+1)^2+1)/((x^2+1)/(-x^2+1)+1)^2)^(1/2)/((x^2+1)/(-x^2+1)+1)*(2*(x^2+1)^2/(-x^2+1)^2+2)^(1/2)*arctan(1/((x^2+1)^2/(-x^2+1)^2+1)*(2*(x^2+1)^2/(-x^2+1)^2+2)^(1/2)*(x^2+1)/(-x^2+1))+1/2*(1/6*ln(-1+1/2*2^(1/2)/x*(x^4+1)^(1/2))-1/6*ln(1+1/2*2^(1/2)/x*(x^4+1)^(1/2))+2/3*2^(1/2)*arctan((x^4+1)^(1/2)/x))*2^(1/2)","B"
798,1,73,45,1.988000," ","int((-1+x)/x/(x^4+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{2}\, \Gamma \left(\frac{3}{4}\right) \left(-\frac{\pi  \sqrt{2}\, x^{4} \hypergeom \left(\left[1, 1, \frac{5}{4}\right], \left[2, 2\right], -x^{4}\right)}{4 \Gamma \left(\frac{3}{4}\right)}+\frac{\left(-3 \ln \left(2\right)-\frac{\pi}{2}+4 \ln \left(x \right)\right) \pi  \sqrt{2}}{\Gamma \left(\frac{3}{4}\right)}\right)}{8 \pi}+x \hypergeom \left(\left[\frac{1}{4}, \frac{1}{4}\right], \left[\frac{5}{4}\right], -x^{4}\right)$&$73$\\ trager&$\frac{\ln \left(-\frac{\left(x^{4}+1\right)^{\frac{3}{4}} x +x^{2} \sqrt{x^{4}+1}+x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}+x^{4}+\left(x^{4}+1\right)^{\frac{3}{4}}+\sqrt{x^{4}+1}\, x +x^{2} \left(x^{4}+1\right)^{\frac{1}{4}}+x^{3}+\sqrt{x^{4}+1}+\left(x^{4}+1\right)^{\frac{1}{4}} x +\left(x^{4}+1\right)^{\frac{1}{4}}+x +1}{x^{2}}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}\, x^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+\left(x^{4}+1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}\, x -x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+\left(x^{4}+1\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}-x^{2} \left(x^{4}+1\right)^{\frac{1}{4}}-\left(x^{4}+1\right)^{\frac{1}{4}} x +\RootOf \left(\textit{\_Z}^{2}+1\right) x -\left(x^{4}+1\right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{2}}\right)}{2}$&$257$\\ \hline \end{longtable}"," ",0,"-1/8/Pi*2^(1/2)*GAMMA(3/4)*(-1/4*Pi*2^(1/2)/GAMMA(3/4)*x^4*hypergeom([1,1,5/4],[2,2],-x^4)+(-3*ln(2)-1/2*Pi+4*ln(x))*Pi*2^(1/2)/GAMMA(3/4))+x*hypergeom([1/4,1/4],[5/4],-x^4)","C"
799,0,0,45,0.017000," ","int(x^2/(a*x^4-b)^(3/4),x)","\[\int \frac{x^{2}}{\left(a \,x^{4}-b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(x^2/(a*x^4-b)^(3/4),x)","F"
800,1,111,53,0.637000," ","int((x^4+6)*(x^5+x^4-2*x)^(1/2)/(x^4-2)/(x^4-x^3-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(\frac{x^{4}+2 x^{3}+2 x \sqrt{x^{5}+x^{4}-2 x}-2}{x^{4}-2}\right)+\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}-2\right) x^{4}-3 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{3}+4 x \sqrt{x^{5}+x^{4}-2 x}+2 \RootOf \left(\textit{\_Z}^{2}-2\right)}{\left(1+x \right) \left(x^{3}-2 x^{2}+2 x -2\right)}\right)$&$111$\\ \hline \end{longtable}"," ",0,"ln((x^4+2*x^3+2*x*(x^5+x^4-2*x)^(1/2)-2)/(x^4-2))+RootOf(_Z^2-2)*ln((-RootOf(_Z^2-2)*x^4-3*RootOf(_Z^2-2)*x^3+4*x*(x^5+x^4-2*x)^(1/2)+2*RootOf(_Z^2-2))/(1+x)/(x^3-2*x^2+2*x-2))","C"
801,1,2078,9,21.155000," ","int((x^2-3)*(x^3-x^2+1)^(2/3)/(x^6+x^5+x^4-x^3-2*x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2078$\\ \hline \end{longtable}"," ",0,"-3*RootOf(3*_Z^6+3*_Z^3+1)^4*ln(-(30*RootOf(3*_Z^6+3*_Z^3+1)^7*x^3-12*(x^3-x^2+1)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^5*x^2+38*RootOf(3*_Z^6+3*_Z^3+1)^4*x^3-5*RootOf(3*_Z^6+3*_Z^3+1)^4*x^2-9*(x^3-x^2+1)^(2/3)*RootOf(3*_Z^6+3*_Z^3+1)^3*x-3*(x^3-x^2+1)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^2*x^2+5*RootOf(3*_Z^6+3*_Z^3+1)^4+12*RootOf(3*_Z^6+3*_Z^3+1)*x^3-3*RootOf(3*_Z^6+3*_Z^3+1)*x^2-4*(x^3-x^2+1)^(2/3)*x+3*RootOf(3*_Z^6+3*_Z^3+1))/(3*RootOf(3*_Z^6+3*_Z^3+1)^3*x^3+2*x^3+x^2-1))-3*RootOf(3*_Z^6+3*_Z^3+1)^3*ln((3*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^6*x^3+6*(x^3-x^2+1)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^3*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)^2*x^2+7*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x^3-RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x^2+3*(x^3-x^2+1)^(1/3)*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)^2*x^2+RootOf(3*_Z^6+3*_Z^3+1)^3*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)+4*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*x^3+(x^3-x^2+1)^(2/3)*x-RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*x^2+RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1))/(3*RootOf(3*_Z^6+3*_Z^3+1)^3*x^3+x^3-x^2+1))*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)-2*RootOf(3*_Z^6+3*_Z^3+1)*ln(-(30*RootOf(3*_Z^6+3*_Z^3+1)^7*x^3-12*(x^3-x^2+1)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^5*x^2+38*RootOf(3*_Z^6+3*_Z^3+1)^4*x^3-5*RootOf(3*_Z^6+3*_Z^3+1)^4*x^2-9*(x^3-x^2+1)^(2/3)*RootOf(3*_Z^6+3*_Z^3+1)^3*x-3*(x^3-x^2+1)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^2*x^2+5*RootOf(3*_Z^6+3*_Z^3+1)^4+12*RootOf(3*_Z^6+3*_Z^3+1)*x^3-3*RootOf(3*_Z^6+3*_Z^3+1)*x^2-4*(x^3-x^2+1)^(2/3)*x+3*RootOf(3*_Z^6+3*_Z^3+1))/(3*RootOf(3*_Z^6+3*_Z^3+1)^3*x^3+2*x^3+x^2-1))+RootOf(3*_Z^6+3*_Z^3+1)*ln((3*RootOf(3*_Z^6+3*_Z^3+1)^7*x^3+3*(x^3-x^2+1)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^5*x^2+2*RootOf(3*_Z^6+3*_Z^3+1)^4*x^3+RootOf(3*_Z^6+3*_Z^3+1)^4*x^2+3*(x^3-x^2+1)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^2*x^2-RootOf(3*_Z^6+3*_Z^3+1)^4-RootOf(3*_Z^6+3*_Z^3+1)*x^3+RootOf(3*_Z^6+3*_Z^3+1)*x^2+(x^3-x^2+1)^(2/3)*x-RootOf(3*_Z^6+3*_Z^3+1))/(3*RootOf(3*_Z^6+3*_Z^3+1)^3*x^3+2*x^3+x^2-1))+RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*ln((6*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^6*x^3-3*(x^3-x^2+1)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^3*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)^2*x^2-4*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x^3-9*(x^3-x^2+1)^(2/3)*RootOf(3*_Z^6+3*_Z^3+1)^3*x+RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x^2+3*(x^3-x^2+1)^(1/3)*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)^2*x^2-RootOf(3*_Z^6+3*_Z^3+1)^3*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)-2*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*x^3-5*(x^3-x^2+1)^(2/3)*x-RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*x^2+RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1))/(3*RootOf(3*_Z^6+3*_Z^3+1)^3*x^3+x^3-x^2+1))-2*ln((3*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^6*x^3+6*(x^3-x^2+1)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^3*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)^2*x^2+7*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x^3-RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x^2+3*(x^3-x^2+1)^(1/3)*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)^2*x^2+RootOf(3*_Z^6+3*_Z^3+1)^3*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)+4*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*x^3+(x^3-x^2+1)^(2/3)*x-RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*x^2+RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1))/(3*RootOf(3*_Z^6+3*_Z^3+1)^3*x^3+x^3-x^2+1))*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)","B"
802,1,2003,9,19.791000," ","int((x^2-3)*(x^3-x^2+1)^(2/3)/(x^6+x^5+x^4-x^3-2*x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2003$\\ \hline \end{longtable}"," ",0,"-3*RootOf(3*_Z^6+3*_Z^3+1)^4*ln(-(30*RootOf(3*_Z^6+3*_Z^3+1)^7*x^3-12*(x^3-x^2+1)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^5*x^2+38*RootOf(3*_Z^6+3*_Z^3+1)^4*x^3-5*RootOf(3*_Z^6+3*_Z^3+1)^4*x^2-9*(x^3-x^2+1)^(2/3)*RootOf(3*_Z^6+3*_Z^3+1)^3*x-3*(x^3-x^2+1)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^2*x^2+5*RootOf(3*_Z^6+3*_Z^3+1)^4+12*RootOf(3*_Z^6+3*_Z^3+1)*x^3-3*RootOf(3*_Z^6+3*_Z^3+1)*x^2-4*(x^3-x^2+1)^(2/3)*x+3*RootOf(3*_Z^6+3*_Z^3+1))/(3*RootOf(3*_Z^6+3*_Z^3+1)^3*x^3+2*x^3+x^2-1))+3*RootOf(3*_Z^6+3*_Z^3+1)^3*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*ln(-(30*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^6*x^3+12*(x^3-x^2+1)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^3*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)^2*x^2+22*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x^3+5*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x^2+9*(x^3-x^2+1)^(2/3)*RootOf(3*_Z^6+3*_Z^3+1)^3*x+9*(x^3-x^2+1)^(1/3)*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)^2*x^2-5*RootOf(3*_Z^6+3*_Z^3+1)^3*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)+4*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*x^3+2*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*x^2+5*(x^3-x^2+1)^(2/3)*x-2*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1))/(3*RootOf(3*_Z^6+3*_Z^3+1)^3*x^3+x^3-x^2+1))-2*RootOf(3*_Z^6+3*_Z^3+1)*ln(-(30*RootOf(3*_Z^6+3*_Z^3+1)^7*x^3-12*(x^3-x^2+1)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^5*x^2+38*RootOf(3*_Z^6+3*_Z^3+1)^4*x^3-5*RootOf(3*_Z^6+3*_Z^3+1)^4*x^2-9*(x^3-x^2+1)^(2/3)*RootOf(3*_Z^6+3*_Z^3+1)^3*x-3*(x^3-x^2+1)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^2*x^2+5*RootOf(3*_Z^6+3*_Z^3+1)^4+12*RootOf(3*_Z^6+3*_Z^3+1)*x^3-3*RootOf(3*_Z^6+3*_Z^3+1)*x^2-4*(x^3-x^2+1)^(2/3)*x+3*RootOf(3*_Z^6+3*_Z^3+1))/(3*RootOf(3*_Z^6+3*_Z^3+1)^3*x^3+2*x^3+x^2-1))+RootOf(3*_Z^6+3*_Z^3+1)*ln((3*RootOf(3*_Z^6+3*_Z^3+1)^7*x^3+3*(x^3-x^2+1)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^5*x^2+2*RootOf(3*_Z^6+3*_Z^3+1)^4*x^3+RootOf(3*_Z^6+3*_Z^3+1)^4*x^2+3*(x^3-x^2+1)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^2*x^2-RootOf(3*_Z^6+3*_Z^3+1)^4-RootOf(3*_Z^6+3*_Z^3+1)*x^3+RootOf(3*_Z^6+3*_Z^3+1)*x^2+(x^3-x^2+1)^(2/3)*x-RootOf(3*_Z^6+3*_Z^3+1))/(3*RootOf(3*_Z^6+3*_Z^3+1)^3*x^3+2*x^3+x^2-1))+RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*ln((3*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^6*x^3-3*(x^3-x^2+1)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^3*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)^2*x^2+4*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x^3-RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x^2+RootOf(3*_Z^6+3*_Z^3+1)^3*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)+(x^3-x^2+1)^(2/3)*x)/(3*RootOf(3*_Z^6+3*_Z^3+1)^3*x^3+x^3-x^2+1))+RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*ln(-(30*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^6*x^3+12*(x^3-x^2+1)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^3*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)^2*x^2+22*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x^3+5*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x^2+9*(x^3-x^2+1)^(2/3)*RootOf(3*_Z^6+3*_Z^3+1)^3*x+9*(x^3-x^2+1)^(1/3)*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)^2*x^2-5*RootOf(3*_Z^6+3*_Z^3+1)^3*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)+4*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*x^3+2*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*x^2+5*(x^3-x^2+1)^(2/3)*x-2*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1))/(3*RootOf(3*_Z^6+3*_Z^3+1)^3*x^3+x^3-x^2+1))","B"
803,1,101,45,1.043000," ","int((x^6-1)^(1/2)*(2*x^6-1)^2/x/(4*x^6-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\left(\frac{x^{6}}{9}-\frac{13}{36}\right) \sqrt{x^{6}-1}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(\frac{4 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{6}-7 \RootOf \left(\textit{\_Z}^{2}+3\right)+12 \sqrt{x^{6}-1}}{\left(2 x^{3}-1\right) \left(2 x^{3}+1\right)}\right)}{48}$&$101$\\ \hline \end{longtable}"," ",0,"(1/9*x^6-13/36)*(x^6-1)^(1/2)+1/3*RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)+(x^6-1)^(1/2))/x^3)+1/48*RootOf(_Z^2+3)*ln((4*RootOf(_Z^2+3)*x^6-7*RootOf(_Z^2+3)+12*(x^6-1)^(1/2))/(2*x^3-1)/(2*x^3+1))","C"
804,0,0,14,0.023000," ","int(1/(x^3+x)^(1/3)/(a*x^6+b),x)","\[\int \frac{1}{\left(x^{3}+x \right)^{\frac{1}{3}} \left(a \,x^{6}+b \right)}\, dx\]"," ",0,"int(1/(x^3+x)^(1/3)/(a*x^6+b),x)","F"
805,0,0,14,0.000000," ","int(1/(x^3+x)^(1/3)/(a*x^6+b),x)","\[\int \frac{1}{\left(x^{3}+x \right)^{\frac{1}{3}} \left(a \,x^{6}+b \right)}\, dx\]"," ",0,"int(1/(x^3+x)^(1/3)/(a*x^6+b),x)","F"
806,0,0,49,0.023000," ","int((a*x^4-b)/(a*x^4-2*x^2+b)/(a*x^6+b*x^2)^(1/4),x)","\[\int \frac{a \,x^{4}-b}{\left(a \,x^{4}-2 x^{2}+b \right) \left(a \,x^{6}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^4-b)/(a*x^4-2*x^2+b)/(a*x^6+b*x^2)^(1/4),x)","F"
807,1,67,53,0.772000," ","int((x^5+4)*(x^10+x^8-2*x^5+1)^(1/2)/x^9,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(-1+x \right) \left(x^{4}+x^{3}+x^{2}+x +1\right) \sqrt{x^{10}+x^{8}-2 x^{5}+1}}{2 x^{8}}-\frac{\ln \left(-\frac{-x^{5}+\sqrt{x^{10}+x^{8}-2 x^{5}+1}+1}{x^{4}}\right)}{2}$&$67$\\ risch&$\frac{x^{15}+x^{13}-3 x^{10}-x^{8}+3 x^{5}-1}{2 x^{8} \sqrt{x^{10}+x^{8}-2 x^{5}+1}}+\frac{\ln \left(-\frac{-1+x^{5}+\sqrt{x^{10}+x^{8}-2 x^{5}+1}}{x^{4}}\right)}{2}$&$73$\\ \hline \end{longtable}"," ",0,"1/2*(-1+x)*(x^4+x^3+x^2+x+1)/x^8*(x^10+x^8-2*x^5+1)^(1/2)-1/2*ln(-(-x^5+(x^10+x^8-2*x^5+1)^(1/2)+1)/x^4)","A"
808,1,2936,11,21.279000," ","int((x^6+1)*(x^6+x^3-1)^(2/3)/(x^12-x^6+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2936$\\ \hline \end{longtable}"," ",0,"-1/6*ln(-(17*RootOf(_Z^3+2)*x^12-1695*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^12-34*RootOf(_Z^3+2)*x^9+3390*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^9-3390*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^3-85*RootOf(_Z^3+2)*x^6+8475*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^6+17*RootOf(_Z^3+2)-1695*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)+34*RootOf(_Z^3+2)*x^3+5697*RootOf(_Z^3+2)^4*(x^6+x^3-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*x^4+1899*RootOf(_Z^3+2)^2*(x^6+x^3-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^7-10170*RootOf(_Z^3+2)^3*(x^6+x^3-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*x^5+102*RootOf(_Z^3+2)^4*(x^6+x^3-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^5-5085*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^8-5391*RootOf(_Z^3+2)^2*(x^6+x^3-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^4+1695*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^5-1899*RootOf(_Z^3+2)^2*(x^6+x^3-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x+5085*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^2+51*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)^2*x^8-17*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)^2*x^5-51*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)^2*x^2-20340*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^9+204*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^9-10170*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^6+102*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^6+20340*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^3-204*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^3-1164*(x^6+x^3-1)^(2/3)*x^7+1164*(x^6+x^3-1)^(2/3)*x+1164*(x^6+x^3-1)^(2/3)*x^4)/(x^12-x^6+1))*RootOf(_Z^3+2)-ln(-(17*RootOf(_Z^3+2)*x^12-1695*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^12-34*RootOf(_Z^3+2)*x^9+3390*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^9-3390*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^3-85*RootOf(_Z^3+2)*x^6+8475*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^6+17*RootOf(_Z^3+2)-1695*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)+34*RootOf(_Z^3+2)*x^3+5697*RootOf(_Z^3+2)^4*(x^6+x^3-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*x^4+1899*RootOf(_Z^3+2)^2*(x^6+x^3-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^7-10170*RootOf(_Z^3+2)^3*(x^6+x^3-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*x^5+102*RootOf(_Z^3+2)^4*(x^6+x^3-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^5-5085*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^8-5391*RootOf(_Z^3+2)^2*(x^6+x^3-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^4+1695*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^5-1899*RootOf(_Z^3+2)^2*(x^6+x^3-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x+5085*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^2+51*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)^2*x^8-17*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)^2*x^5-51*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)^2*x^2-20340*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^9+204*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^9-10170*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^6+102*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^6+20340*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^3-204*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^3-1164*(x^6+x^3-1)^(2/3)*x^7+1164*(x^6+x^3-1)^(2/3)*x+1164*(x^6+x^3-1)^(2/3)*x^4)/(x^12-x^6+1))*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)+1/6*RootOf(_Z^3+2)*ln(-(-34*RootOf(_Z^3+2)*x^12-3594*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^12-68*RootOf(_Z^3+2)*x^9-7188*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^9+7188*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^3+102*RootOf(_Z^3+2)*x^6+10782*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^6-34*RootOf(_Z^3+2)-3594*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)+68*RootOf(_Z^3+2)*x^3+11394*RootOf(_Z^3+2)^4*(x^6+x^3-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*x^4-3798*RootOf(_Z^3+2)^2*(x^6+x^3-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^7-1224*RootOf(_Z^3+2)^3*(x^6+x^3-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*x^5+3390*RootOf(_Z^3+2)^4*(x^6+x^3-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^5+612*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^8+3186*RootOf(_Z^3+2)^2*(x^6+x^3-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^4+204*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^5+3798*RootOf(_Z^3+2)^2*(x^6+x^3-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x-612*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^2-1695*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)^2*x^8-565*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)^2*x^5+1695*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)^2*x^2+43128*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^9+408*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^9+21564*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^6+204*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^6-43128*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^3-408*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^3-1062*(x^6+x^3-1)^(2/3)*x^7+1062*(x^6+x^3-1)^(2/3)*x)/(x^12-x^6+1))","B"
809,1,1958,11,21.161000," ","int((x^6+1)*(x^6+x^3-1)^(2/3)/(x^12-x^6+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1958$\\ \hline \end{longtable}"," ",0,"1/6*RootOf(_Z^3+2)*ln(-(565*RootOf(_Z^3+2)*x^12+3594*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^12-1130*RootOf(_Z^3+2)*x^9-7188*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^9+7188*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^3-2825*RootOf(_Z^3+2)*x^6-17970*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^6+565*RootOf(_Z^3+2)+3594*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)+1130*RootOf(_Z^3+2)*x^3+11394*RootOf(_Z^3+2)^4*(x^6+x^3-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*x^4+3798*RootOf(_Z^3+2)^2*(x^6+x^3-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^7-1224*RootOf(_Z^3+2)^3*(x^6+x^3-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*x^5-3594*RootOf(_Z^3+2)^4*(x^6+x^3-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^5-612*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^8-10782*RootOf(_Z^3+2)^2*(x^6+x^3-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^4+204*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^5-3798*RootOf(_Z^3+2)^2*(x^6+x^3-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x+612*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^2-1797*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)^2*x^8+599*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)^2*x^5+1797*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)^2*x^2+43128*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^9+6780*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^9+21564*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^6+3390*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^6-43128*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^3-6780*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^3-2328*(x^6+x^3-1)^(2/3)*x^7+2328*(x^6+x^3-1)^(2/3)*x+2328*(x^6+x^3-1)^(2/3)*x^4)/(x^12-x^6+1))+RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*ln(-(599*RootOf(_Z^3+2)*x^12+3390*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^12+1198*RootOf(_Z^3+2)*x^9+6780*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^9-6780*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^3-1797*RootOf(_Z^3+2)*x^6-10170*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^6+599*RootOf(_Z^3+2)+3390*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)-1198*RootOf(_Z^3+2)*x^3+11394*RootOf(_Z^3+2)^4*(x^6+x^3-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*x^4-3798*RootOf(_Z^3+2)^2*(x^6+x^3-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^7-20340*RootOf(_Z^3+2)^3*(x^6+x^3-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*x^5-3594*RootOf(_Z^3+2)^4*(x^6+x^3-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^5+10170*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^8+3186*RootOf(_Z^3+2)^2*(x^6+x^3-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^4+3390*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^5+3798*RootOf(_Z^3+2)^2*(x^6+x^3-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x-10170*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^2+1797*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)^2*x^8+599*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)^2*x^5-1797*(x^6+x^3-1)^(1/3)*RootOf(_Z^3+2)^2*x^2-40680*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^9-7188*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^9-20340*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^6-3594*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^6+40680*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^2*x^3+7188*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^3*x^3-1062*(x^6+x^3-1)^(2/3)*x^7+1062*(x^6+x^3-1)^(2/3)*x)/(x^12-x^6+1))","B"
810,0,0,11,180.000000," ","int((5*x^7-2)*(2*x^8+x^3+2*x)^(1/3)/(4*x^14+8*x^7+x^4+4),x)","\[\int \frac{\left(5 x^{7}-2\right) \left(2 x^{8}+x^{3}+2 x \right)^{\frac{1}{3}}}{4 x^{14}+8 x^{7}+x^{4}+4}\, dx\]"," ",0,"int((5*x^7-2)*(2*x^8+x^3+2*x)^(1/3)/(4*x^14+8*x^7+x^4+4),x)","F"
811,0,0,11,180.000000," ","int((5*x^7-2)*(2*x^8+x^3+2*x)^(1/3)/(4*x^14+8*x^7+x^4+4),x)","\[\int \frac{\left(5 x^{7}-2\right) \left(2 x^{8}+x^{3}+2 x \right)^{\frac{1}{3}}}{4 x^{14}+8 x^{7}+x^{4}+4}\, dx\]"," ",0,"int((5*x^7-2)*(2*x^8+x^3+2*x)^(1/3)/(4*x^14+8*x^7+x^4+4),x)","F"
812,0,0,51,180.000000," ","int(1/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{1}{\sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int(1/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","F"
813,1,33,50,1.875000," ","int(x^10*(x^4-1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}} x^{11} \hypergeom \left(\left[-\frac{1}{4}, \frac{11}{4}\right], \left[\frac{15}{4}\right], x^{4}\right)}{11 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}}}$&$33$\\ risch&$\frac{x^{3} \left(32 x^{8}-4 x^{4}-7\right) \left(x^{4}-1\right)^{\frac{1}{4}}}{384}-\frac{7 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{3}{4}} x^{3} \hypergeom \left(\left[\frac{3}{4}, \frac{3}{4}\right], \left[\frac{7}{4}\right], x^{4}\right)}{384 \mathrm{signum}\left(x^{4}-1\right)^{\frac{3}{4}}}$&$58$\\ trager&$\frac{x^{3} \left(32 x^{8}-4 x^{4}-7\right) \left(x^{4}-1\right)^{\frac{1}{4}}}{384}+\frac{7 \ln \left(2 \left(x^{4}-1\right)^{\frac{3}{4}} x -2 x^{2} \sqrt{x^{4}-1}+2 x^{3} \left(x^{4}-1\right)^{\frac{1}{4}}-2 x^{4}+1\right)}{512}+\frac{7 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}-1}\, x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \left(x^{4}-1\right)^{\frac{3}{4}} x -2 x^{3} \left(x^{4}-1\right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{512}$&$139$\\ \hline \end{longtable}"," ",0,"1/11*signum(x^4-1)^(1/4)/(-signum(x^4-1))^(1/4)*x^11*hypergeom([-1/4,11/4],[15/4],x^4)","C"
814,1,17,50,1.815000," ","int(x^10*(x^4+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{x^{11} \hypergeom \left(\left[-\frac{1}{4}, \frac{11}{4}\right], \left[\frac{15}{4}\right], -x^{4}\right)}{11}$&$17$\\ risch&$\frac{x^{3} \left(32 x^{8}+4 x^{4}-7\right) \left(x^{4}+1\right)^{\frac{1}{4}}}{384}+\frac{7 x^{3} \hypergeom \left(\left[\frac{3}{4}, \frac{3}{4}\right], \left[\frac{7}{4}\right], -x^{4}\right)}{384}$&$42$\\ trager&$\frac{x^{3} \left(32 x^{8}+4 x^{4}-7\right) \left(x^{4}+1\right)^{\frac{1}{4}}}{384}+\frac{7 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}\, x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \left(x^{4}+1\right)^{\frac{3}{4}} x -2 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{512}+\frac{7 \ln \left(2 \left(x^{4}+1\right)^{\frac{3}{4}} x +2 x^{2} \sqrt{x^{4}+1}+2 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}+2 x^{4}+1\right)}{512}$&$139$\\ \hline \end{longtable}"," ",0,"1/11*x^11*hypergeom([-1/4,11/4],[15/4],-x^4)","C"
815,1,1629,11,43.737000," ","int((x^2+1)/(x^4-x^2+1)/(x^4+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1629$\\ \hline \end{longtable}"," ",0,"1/6*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*ln(-(RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^8*x^3+4*RootOf(_Z^8+2187)^5*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*(x^4+x^2)^(1/2)*x-RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^8*x-264*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)^5*(x^4+x^2)^(1/4)*x^2-558*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^4*x^3+756*RootOf(_Z^8+2187)^4*(x^4+x^2)^(3/4)-4860*RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*(x^4+x^2)^(1/2)*x-144*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^4*x-7776*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)*(x^4+x^2)^(1/4)*x^2+23085*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*x^3+67068*(x^4+x^2)^(3/4)+8505*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*x)/x/(x^2*RootOf(_Z^8+2187)^4-RootOf(_Z^8+2187)^4+27*x^2+27))+1/6*RootOf(_Z^8+2187)*ln(-(RootOf(_Z^8+2187)^9*x^3-RootOf(_Z^8+2187)^9*x-4*(x^4+x^2)^(1/2)*RootOf(_Z^8+2187)^7*x+264*RootOf(_Z^8+2187)^6*(x^4+x^2)^(1/4)*x^2+558*RootOf(_Z^8+2187)^5*x^3-756*RootOf(_Z^8+2187)^4*(x^4+x^2)^(3/4)+144*RootOf(_Z^8+2187)^5*x-4860*(x^4+x^2)^(1/2)*RootOf(_Z^8+2187)^3*x-7776*RootOf(_Z^8+2187)^2*(x^4+x^2)^(1/4)*x^2+23085*RootOf(_Z^8+2187)*x^3+67068*(x^4+x^2)^(3/4)+8505*RootOf(_Z^8+2187)*x)/(x^2*RootOf(_Z^8+2187)^4-RootOf(_Z^8+2187)^4-27*x^2-27)/x)+1/6*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*ln(-(x^3*RootOf(_Z^8+2187)^8*RootOf(_Z^2+RootOf(_Z^8+2187)^2)-RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)^8*x+4*(x^4+x^2)^(1/2)*RootOf(_Z^8+2187)^6*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*x-264*RootOf(_Z^8+2187)^6*(x^4+x^2)^(1/4)*x^2+558*x^3*RootOf(_Z^8+2187)^4*RootOf(_Z^2+RootOf(_Z^8+2187)^2)-756*RootOf(_Z^8+2187)^4*(x^4+x^2)^(3/4)+144*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)^4*x+4860*(x^4+x^2)^(1/2)*RootOf(_Z^8+2187)^2*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*x+7776*RootOf(_Z^8+2187)^2*(x^4+x^2)^(1/4)*x^2+23085*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*x^3+67068*(x^4+x^2)^(3/4)+8505*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*x)/(x^2*RootOf(_Z^8+2187)^4-RootOf(_Z^8+2187)^4-27*x^2-27)/x)-1/13122*RootOf(_Z^8+2187)^7*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*ln(-(5*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^11*x^3-5*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)^11*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*x-2322*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^7*x^3-1188*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^7*x+972*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^6*(x^4+x^2)^(1/2)*x+64152*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)^5*(x^4+x^2)^(1/4)*x^2-124659*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^3*x^3+183708*RootOf(_Z^8+2187)^4*(x^4+x^2)^(3/4)-45927*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^3*x-1180980*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^2*(x^4+x^2)^(1/2)*x+1889568*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)*(x^4+x^2)^(1/4)*x^2+16297524*(x^4+x^2)^(3/4))/x/(x^2*RootOf(_Z^8+2187)^4-RootOf(_Z^8+2187)^4+27*x^2+27))","B"
816,0,0,14,0.030000," ","int(1/(a*x^4-b)/(a*x^4-b*x^2)^(1/4),x)","\[\int \frac{1}{\left(a \,x^{4}-b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(a*x^4-b)/(a*x^4-b*x^2)^(1/4),x)","F"
817,0,0,14,0.001000," ","int(1/(a*x^4-b)/(a*x^4-b*x^2)^(1/4),x)","\[\int \frac{1}{\left(a \,x^{4}-b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(a*x^4-b)/(a*x^4-b*x^2)^(1/4),x)","F"
818,1,3365,54,0.182000," ","int((-x^2+1)/x/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$3365$\\ elliptic&$\text{Expression too large to display}$&$3365$\\ \hline \end{longtable}"," ",0,"-2*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))^2*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2)*(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)*EllipticF(((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2),((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2))+(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*EllipticPi(((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2),(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)),((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)))+2*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))^2*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2)/RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)*(EllipticF(((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2),((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2))+(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1)*EllipticPi(((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2),RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)*(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)),((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)))","C"
819,0,0,52,0.051000," ","int(x^2*(3*x^4-1)/(x^4+1)^2/(a*x^4+a-x)/(x^5+x)^(1/2),x)","\[\int \frac{x^{2} \left(3 x^{4}-1\right)}{\left(x^{4}+1\right)^{2} \left(a \,x^{4}+a -x \right) \sqrt{x^{5}+x}}\, dx\]"," ",0,"int(x^2*(3*x^4-1)/(x^4+1)^2/(a*x^4+a-x)/(x^5+x)^(1/2),x)","F"
820,1,157,54,5.396000," ","int((x^4-3)*(x^8-x^7-x^6+2*x^4-x^3+1)/x^6/(x^4-x^3+1)/(x^5+x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{4}+1\right) \left(x^{5}+x \right)^{\frac{3}{4}}}{7 x^{6}}+\ln \left(\frac{x^{4}+2 \left(x^{5}+x \right)^{\frac{3}{4}}+2 \sqrt{x^{5}+x}\, x +2 x^{2} \left(x^{5}+x \right)^{\frac{1}{4}}+x^{3}+1}{x^{4}-x^{3}+1}\right)+\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{5}+x}\, x +\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{5}+x \right)^{\frac{3}{4}}-2 x^{2} \left(x^{5}+x \right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{4}-x^{3}+1}\right)$&$157$\\ risch&$\frac{\frac{4}{7} x^{8}+\frac{8}{7} x^{4}+\frac{4}{7}}{x^{5} \left(x \left(x^{4}+1\right)\right)^{\frac{1}{4}}}+\ln \left(-\frac{x^{4}+2 \left(x^{5}+x \right)^{\frac{3}{4}}+2 \sqrt{x^{5}+x}\, x +2 x^{2} \left(x^{5}+x \right)^{\frac{1}{4}}+x^{3}+1}{x^{4}-x^{3}+1}\right)+\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{5}+x}\, x +\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{5}+x \right)^{\frac{3}{4}}-2 x^{2} \left(x^{5}+x \right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{4}-x^{3}+1}\right)$&$165$\\ \hline \end{longtable}"," ",0,"4/7*(x^4+1)*(x^5+x)^(3/4)/x^6+ln((x^4+2*(x^5+x)^(3/4)+2*(x^5+x)^(1/2)*x+2*x^2*(x^5+x)^(1/4)+x^3+1)/(x^4-x^3+1))+RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)*x^4-2*RootOf(_Z^2+1)*(x^5+x)^(1/2)*x+RootOf(_Z^2+1)*x^3+2*(x^5+x)^(3/4)-2*x^2*(x^5+x)^(1/4)+RootOf(_Z^2+1))/(x^4-x^3+1))","C"
821,1,38,48,0.098000," ","int((x^2+1)/(1+(1+x)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\sqrt{2}\, x \hypergeom \left(\left[\frac{1}{4}, \frac{3}{4}, 1\right], \left[\frac{3}{2}, 2\right], -x \right)}{2}+\frac{\sqrt{2}\, x^{3} \hypergeom \left(\left[\frac{1}{4}, \frac{3}{4}, 3\right], \left[\frac{3}{2}, 4\right], -x \right)}{6}$&$38$\\ derivativedivides&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{11}{2}}}{11}-\frac{20 \left(1+\sqrt{1+x}\right)^{\frac{9}{2}}}{9}+\frac{32 \left(1+\sqrt{1+x}\right)^{\frac{7}{2}}}{7}-\frac{16 \left(1+\sqrt{1+x}\right)^{\frac{5}{2}}}{5}+\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}-4 \sqrt{1+\sqrt{1+x}}$&$68$\\ default&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{11}{2}}}{11}-\frac{20 \left(1+\sqrt{1+x}\right)^{\frac{9}{2}}}{9}+\frac{32 \left(1+\sqrt{1+x}\right)^{\frac{7}{2}}}{7}-\frac{16 \left(1+\sqrt{1+x}\right)^{\frac{5}{2}}}{5}+\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}-4 \sqrt{1+\sqrt{1+x}}$&$68$\\ \hline \end{longtable}"," ",0,"1/2*2^(1/2)*x*hypergeom([1/4,3/4,1],[3/2,2],-x)+1/6*2^(1/2)*x^3*hypergeom([1/4,3/4,3],[3/2,4],-x)","C"
822,0,0,60,0.033000," ","int((-1+2*x)/(1+x)/(-a^2*x^2+(1+x)^6)^(1/2),x)","\[\int \frac{-1+2 x}{\left(1+x \right) \sqrt{-a^{2} x^{2}+\left(1+x \right)^{6}}}\, dx\]"," ",0,"int((-1+2*x)/(1+x)/(-a^2*x^2+(1+x)^6)^(1/2),x)","F"
823,0,0,50,180.000000," ","int(x/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/4),x)","\[\int \frac{x}{\sqrt{a^{2} x^{2}-b}\, \left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(x/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/4),x)","F"
824,0,0,52,180.000000," ","int((a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","\[\int \sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}\, dx\]"," ",0,"int((a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","F"
825,1,52,47,0.090000," ","int(1/(1+x^(1/2))/(-x^(1/2)+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$2 \ln \left(-\frac{1}{2}+\sqrt{x}+\sqrt{-\sqrt{x}+x}\right)+\sqrt{2}\, \arctanh \left(\frac{\left(1-3 \sqrt{x}\right) \sqrt{2}}{4 \sqrt{\left(1+\sqrt{x}\right)^{2}-3 \sqrt{x}-1}}\right)$&$52$\\ default&$-\frac{\sqrt{-\sqrt{x}+x}\, \left(\sqrt{2}\, \arctanh \left(\frac{\left(-1+3 \sqrt{x}\right) \sqrt{2}}{4 \sqrt{-\sqrt{x}+x}}\right)-2 \ln \left(-\frac{1}{2}+\sqrt{x}+\sqrt{-\sqrt{x}+x}\right)\right)}{\sqrt{\sqrt{x}\, \left(-1+\sqrt{x}\right)}}$&$67$\\ \hline \end{longtable}"," ",0,"2*ln(-1/2+x^(1/2)+(-x^(1/2)+x)^(1/2))+2^(1/2)*arctanh(1/4*(1-3*x^(1/2))*2^(1/2)/((1+x^(1/2))^2-3*x^(1/2)-1)^(1/2))","A"
826,1,103,51,0.592000," ","int(x/(x^2-1)/(x^3+x^2+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}-3\right) x^{2}-4 \RootOf \left(\textit{\_Z}^{2}-3\right) x +6 \sqrt{x^{3}+x^{2}+x}-\RootOf \left(\textit{\_Z}^{2}-3\right)}{\left(-1+x \right)^{2}}\right)}{12}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)-2 \sqrt{x^{3}+x^{2}+x}}{\left(1+x \right)^{2}}\right)}{4}$&$103$\\ default&$\frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}\, \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}+\frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}$&$300$\\ elliptic&$\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{6 \sqrt{x^{3}+x^{2}+x}\, \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{2 \sqrt{x^{3}+x^{2}+x}\, \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}+\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{6 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{2 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}$&$646$\\ \hline \end{longtable}"," ",0,"1/12*RootOf(_Z^2-3)*ln((-RootOf(_Z^2-3)*x^2-4*RootOf(_Z^2-3)*x+6*(x^3+x^2+x)^(1/2)-RootOf(_Z^2-3))/(-1+x)^2)-1/4*RootOf(_Z^2+1)*ln(-(RootOf(_Z^2+1)*x^2+RootOf(_Z^2+1)-2*(x^3+x^2+x)^(1/2))/(1+x)^2)","C"
827,1,509,57,0.157000," ","int((-a*b*c+2*a*(b+c)*x-(3*a+b+c)*x^2+2*x^3)/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)/(a*d+(b*c-d)*x-(b+c)*x^2+x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{4 a \sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}\, \left(-c +x \right)^{2} \sqrt{\frac{c \left(-b +x \right)}{b \left(-c +x \right)}}\, \sqrt{\frac{c \left(-a +x \right)}{a \left(-c +x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)}{\left(a -c \right) c \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}+\frac{2 c \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+\left(-b -c \right) \textit{\_Z}^{2}+\left(b c -d \right) \textit{\_Z} +a d \right)}{\sum}\frac{\left(-3 \underline{\hspace{1.25 ex}}\alpha^{2} a +\underline{\hspace{1.25 ex}}\alpha^{2} b +\underline{\hspace{1.25 ex}}\alpha^{2} c +2 \underline{\hspace{1.25 ex}}\alpha  a b +2 \underline{\hspace{1.25 ex}}\alpha  a c -2 \underline{\hspace{1.25 ex}}\alpha  b c -a b c +2 \underline{\hspace{1.25 ex}}\alpha  d -2 a d \right) \left(-a +x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  c +a^{2}-a b -a c +b c -d \right) \sqrt{\frac{\left(c -a \right) x}{c \left(-a +x \right)}}\, \sqrt{\frac{a \left(-b +x \right)}{b \left(-a +x \right)}}\, \sqrt{\frac{a \left(-c +x \right)}{c \left(-a +x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(c -a \right) x}{c \left(-a +x \right)}}, \sqrt{\frac{\left(a -b \right) c}{b \left(a -c \right)}}\right)+\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  c +b c -d \right) \EllipticPi \left(\sqrt{\frac{\left(c -a \right) x}{c \left(-a +x \right)}}, -\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  c +b c \right) c}{d \left(a -c \right)}, \sqrt{\frac{\left(a -b \right) c}{b \left(a -c \right)}}\right)}{d}\right)}{\left(-3 \underline{\hspace{1.25 ex}}\alpha^{2}+2 \underline{\hspace{1.25 ex}}\alpha  b +2 \underline{\hspace{1.25 ex}}\alpha  c -b c +d \right) \left(c -a \right) \left(a^{2}-a b -a c +b c \right) \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}\right)}{a^{2}}$&$509$\\ elliptic&$-\frac{4 c \sqrt{\frac{\left(c -a \right) x}{c \left(-a +x \right)}}\, \left(-a +x \right)^{2} \sqrt{\frac{a \left(-b +x \right)}{b \left(-a +x \right)}}\, \sqrt{\frac{a \left(-c +x \right)}{c \left(-a +x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(c -a \right) x}{c \left(-a +x \right)}}, \sqrt{\frac{\left(a -b \right) c}{b \left(a -c \right)}}\right)}{\left(c -a \right) a \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}-\frac{2 c \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+\left(-b -c \right) \textit{\_Z}^{2}+\left(b c -d \right) \textit{\_Z} +a d \right)}{\sum}\frac{\left(3 \underline{\hspace{1.25 ex}}\alpha^{2} a -\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha^{2} c -2 \underline{\hspace{1.25 ex}}\alpha  a b -2 \underline{\hspace{1.25 ex}}\alpha  a c +2 \underline{\hspace{1.25 ex}}\alpha  b c +a b c -2 \underline{\hspace{1.25 ex}}\alpha  d +2 a d \right) \left(-a +x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  c +a^{2}-a b -a c +b c -d \right) \sqrt{\frac{\left(c -a \right) x}{c \left(-a +x \right)}}\, \sqrt{\frac{a \left(-b +x \right)}{b \left(-a +x \right)}}\, \sqrt{\frac{a \left(-c +x \right)}{c \left(-a +x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(c -a \right) x}{c \left(-a +x \right)}}, \sqrt{\frac{\left(a -b \right) c}{b \left(a -c \right)}}\right)+\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  c +b c -d \right) \EllipticPi \left(\sqrt{\frac{\left(c -a \right) x}{c \left(-a +x \right)}}, -\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  c +b c \right) c}{d \left(a -c \right)}, \sqrt{\frac{\left(a -b \right) c}{b \left(a -c \right)}}\right)}{d}\right)}{\left(-3 \underline{\hspace{1.25 ex}}\alpha^{2}+2 \underline{\hspace{1.25 ex}}\alpha  b +2 \underline{\hspace{1.25 ex}}\alpha  c -b c +d \right) \left(c -a \right) \left(a^{2}-a b -a c +b c \right) \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}\right)}{a^{2}}$&$510$\\ \hline \end{longtable}"," ",0,"-4*a*((a-c)*x/a/(-c+x))^(1/2)*(-c+x)^2*(c*(-b+x)/b/(-c+x))^(1/2)*(c*(-a+x)/a/(-c+x))^(1/2)/(a-c)/c/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)*EllipticF(((a-c)*x/a/(-c+x))^(1/2),((-b+c)*a/b/(c-a))^(1/2))+2*c/a^2*sum((-3*_alpha^2*a+_alpha^2*b+_alpha^2*c+2*_alpha*a*b+2*_alpha*a*c-2*_alpha*b*c-a*b*c+2*_alpha*d-2*a*d)/(-3*_alpha^2+2*_alpha*b+2*_alpha*c-b*c+d)*(-a+x)^2/(c-a)*(_alpha^2+_alpha*a-_alpha*b-_alpha*c+a^2-a*b-a*c+b*c-d)/(a^2-a*b-a*c+b*c)*((c-a)*x/c/(-a+x))^(1/2)*(a*(-b+x)/b/(-a+x))^(1/2)*(a*(-c+x)/c/(-a+x))^(1/2)/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)*(EllipticF(((c-a)*x/c/(-a+x))^(1/2),((a-b)*c/b/(a-c))^(1/2))+(_alpha^2-_alpha*b-_alpha*c+b*c-d)/d*EllipticPi(((c-a)*x/c/(-a+x))^(1/2),-(_alpha^2-_alpha*b-_alpha*c+b*c)*c/d/(a-c),((a-b)*c/b/(a-c))^(1/2))),_alpha=RootOf(_Z^3+(-b-c)*_Z^2+(b*c-d)*_Z+a*d))","C"
828,1,433,46,0.286000," ","int((a*x^3+3*b)/x/(a*x^3-b)/(a*x^3+b)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}-b \right)}{\sum}\frac{\left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i a \left(2 x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{a \left(x -\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{-3 \left(-a^{2} b \right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i a \left(2 x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{2 \left(-a^{2} b \right)^{\frac{1}{3}}}}\, \left(i \left(-a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  \sqrt{3}\, a -i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{2}{3}}+2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-\left(-a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  a -\left(-a^{2} b \right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a^{2} b \right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a -i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  +i \sqrt{3}\, a b -3 \left(-a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  -3 a b}{4 a b}, \sqrt{\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{2 \sqrt{a \,x^{3}+b}}\right)}{3 a^{2} b}+\frac{2 \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{\sqrt{b}}$&$433$\\ elliptic&$-\frac{\sqrt{2}\, \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{-\frac{i \left(i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}-2 a x -\left(-a^{2} b \right)^{\frac{1}{3}}\right)}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{-\frac{-a x +\left(-a^{2} b \right)^{\frac{1}{3}}}{\left(-a^{2} b \right)^{\frac{1}{3}} \left(-3+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(-a^{2} b \right)^{\frac{1}{3}}\right)}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{3}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}-b \right)}{\sum}\EllipticPi \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}-2 a x -\left(-a^{2} b \right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a^{2} b \right)^{\frac{1}{3}}}}}{6}, \frac{-2 i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a +i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  -i \sqrt{3}\, a b +3 \left(-a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +3 a b}{4 a b}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\right) \underline{\hspace{1.25 ex}}\alpha  \right)}{3 a b \sqrt{a \,x^{3}+b}}-\frac{\sqrt{2}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}-2 a x -\left(-a^{2} b \right)^{\frac{1}{3}}\right)}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{-\frac{-a x +\left(-a^{2} b \right)^{\frac{1}{3}}}{\left(-a^{2} b \right)^{\frac{1}{3}} \left(-3+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(-a^{2} b \right)^{\frac{1}{3}}\right)}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{3}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}-b \right)}{\sum}\EllipticPi \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}-2 a x -\left(-a^{2} b \right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a^{2} b \right)^{\frac{1}{3}}}}}{6}, \frac{-2 i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a +i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  -i \sqrt{3}\, a b +3 \left(-a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +3 a b}{4 a b}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\right)\right)}{3 \sqrt{a \,x^{3}+b}}+\frac{2 i \sqrt{2}\, \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{-\frac{i \left(i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}-2 a x -\left(-a^{2} b \right)^{\frac{1}{3}}\right)}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{-\frac{-a x +\left(-a^{2} b \right)^{\frac{1}{3}}}{\left(-a^{2} b \right)^{\frac{1}{3}} \left(-3+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(-a^{2} b \right)^{\frac{1}{3}}\right)}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}-b \right)}{\sum}\EllipticPi \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}-2 a x -\left(-a^{2} b \right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a^{2} b \right)^{\frac{1}{3}}}}}{6}, \frac{-2 i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a +i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  -i \sqrt{3}\, a b +3 \left(-a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +3 a b}{4 a b}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\right) \underline{\hspace{1.25 ex}}\alpha^{2}\right)}{3 b \sqrt{a \,x^{3}+b}}-\frac{i \sqrt{2}\, \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{-\frac{i \left(i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}-2 a x -\left(-a^{2} b \right)^{\frac{1}{3}}\right)}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{-\frac{-a x +\left(-a^{2} b \right)^{\frac{1}{3}}}{\left(-a^{2} b \right)^{\frac{1}{3}} \left(-3+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(-a^{2} b \right)^{\frac{1}{3}}\right)}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}-b \right)}{\sum}\EllipticPi \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}-2 a x -\left(-a^{2} b \right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a^{2} b \right)^{\frac{1}{3}}}}}{6}, \frac{-2 i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a +i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  -i \sqrt{3}\, a b +3 \left(-a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +3 a b}{4 a b}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\right) \underline{\hspace{1.25 ex}}\alpha  \right)}{3 a b \sqrt{a \,x^{3}+b}}+\frac{i \sqrt{2}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}-2 a x -\left(-a^{2} b \right)^{\frac{1}{3}}\right)}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{-\frac{-a x +\left(-a^{2} b \right)^{\frac{1}{3}}}{\left(-a^{2} b \right)^{\frac{1}{3}} \left(-3+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(-a^{2} b \right)^{\frac{1}{3}}\right)}{\left(-a^{2} b \right)^{\frac{1}{3}}}}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}-b \right)}{\sum}\EllipticPi \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(-a^{2} b \right)^{\frac{1}{3}}-2 a x -\left(-a^{2} b \right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(-a^{2} b \right)^{\frac{1}{3}}}}}{6}, \frac{-2 i \left(-a^{2} b \right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a +i \left(-a^{2} b \right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  -i \sqrt{3}\, a b +3 \left(-a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +3 a b}{4 a b}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\right)\right)}{3 \sqrt{a \,x^{3}+b}}+\frac{2 \arctanh \left(\frac{\sqrt{a \,x^{3}+b}}{\sqrt{b}}\right)}{\sqrt{b}}$&$1502$\\ \hline \end{longtable}"," ",0,"2/3*I/a^2/b*2^(1/2)*sum((-a^2*b)^(1/3)*(1/2*I*a*(2*x+1/a*((-a^2*b)^(1/3)-I*3^(1/2)*(-a^2*b)^(1/3)))/(-a^2*b)^(1/3))^(1/2)*(a*(x-1/a*(-a^2*b)^(1/3))/(-3*(-a^2*b)^(1/3)+I*3^(1/2)*(-a^2*b)^(1/3)))^(1/2)*(-1/2*I*a*(2*x+1/a*((-a^2*b)^(1/3)+I*3^(1/2)*(-a^2*b)^(1/3)))/(-a^2*b)^(1/3))^(1/2)/(a*x^3+b)^(1/2)*(I*(-a^2*b)^(1/3)*_alpha*3^(1/2)*a-I*3^(1/2)*(-a^2*b)^(2/3)+2*_alpha^2*a^2-(-a^2*b)^(1/3)*_alpha*a-(-a^2*b)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2/a*(-a^2*b)^(1/3)-1/2*I*3^(1/2)/a*(-a^2*b)^(1/3))*3^(1/2)*a/(-a^2*b)^(1/3))^(1/2),-1/4/a*(2*I*(-a^2*b)^(1/3)*3^(1/2)*_alpha^2*a-I*(-a^2*b)^(2/3)*3^(1/2)*_alpha+I*3^(1/2)*a*b-3*(-a^2*b)^(2/3)*_alpha-3*a*b)/b,(I*3^(1/2)/a*(-a^2*b)^(1/3)/(-3/2/a*(-a^2*b)^(1/3)+1/2*I*3^(1/2)/a*(-a^2*b)^(1/3)))^(1/2)),_alpha=RootOf(_Z^3*a-b))+2*arctanh((a*x^3+b)^(1/2)/b^(1/2))/b^(1/2)","C"
829,1,16170,51,7.399000," ","int((-a*x^3+2*c)*(a*x^3+b*x^2+c)^(1/2)/(c+(-3+b)*x^2+a*x^3)/(c+(-2+b)*x^2+a*x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$16170$\\ elliptic&$\text{Expression too large to display}$&$977321$\\ \hline \end{longtable}"," ",0,"result too large to display","C"
830,1,531,57,0.135000," ","int((-a*b*c+2*a*(b+c)*x-(3*a+b+c)*x^2+2*x^3)/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)/(a+(b*c*d-1)*x-(b+c)*d*x^2+d*x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{4 a \sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}\, \left(-c +x \right)^{2} \sqrt{\frac{c \left(-b +x \right)}{b \left(-c +x \right)}}\, \sqrt{\frac{c \left(-a +x \right)}{a \left(-c +x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(a -c \right) x}{a \left(-c +x \right)}}, \sqrt{\frac{\left(-b +c \right) a}{b \left(c -a \right)}}\right)}{d \left(a -c \right) c \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}+\frac{2 c \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(d \,\textit{\_Z}^{3}+\left(-b d -c d \right) \textit{\_Z}^{2}+\left(b c d -1\right) \textit{\_Z} +a \right)}{\sum}\frac{\left(-3 \underline{\hspace{1.25 ex}}\alpha^{2} a d +\underline{\hspace{1.25 ex}}\alpha^{2} b d +\underline{\hspace{1.25 ex}}\alpha^{2} c d +2 \underline{\hspace{1.25 ex}}\alpha  a b d +2 \underline{\hspace{1.25 ex}}\alpha  a c d -2 \underline{\hspace{1.25 ex}}\alpha  b c d -a b c d +2 \underline{\hspace{1.25 ex}}\alpha  -2 a \right) \left(-a +x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2} d +\underline{\hspace{1.25 ex}}\alpha  a d -\underline{\hspace{1.25 ex}}\alpha  b d -\underline{\hspace{1.25 ex}}\alpha  c d +a^{2} d -a b d -a c d +b c d -1\right) \sqrt{\frac{\left(c -a \right) x}{c \left(-a +x \right)}}\, \sqrt{\frac{a \left(-b +x \right)}{b \left(-a +x \right)}}\, \sqrt{\frac{a \left(-c +x \right)}{c \left(-a +x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(c -a \right) x}{c \left(-a +x \right)}}, \sqrt{\frac{\left(a -b \right) c}{b \left(a -c \right)}}\right)+\left(\underline{\hspace{1.25 ex}}\alpha^{2} d -\underline{\hspace{1.25 ex}}\alpha  b d -\underline{\hspace{1.25 ex}}\alpha  c d +b c d -1\right) \EllipticPi \left(\sqrt{\frac{\left(c -a \right) x}{c \left(-a +x \right)}}, -\frac{d \left(\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  c +b c \right) c}{a -c}, \sqrt{\frac{\left(a -b \right) c}{b \left(a -c \right)}}\right)\right)}{\left(-3 \underline{\hspace{1.25 ex}}\alpha^{2} d +2 \underline{\hspace{1.25 ex}}\alpha  b d +2 \underline{\hspace{1.25 ex}}\alpha  c d -b c d +1\right) \left(c -a \right) \left(a^{2}-a b -a c +b c \right) \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}\right)}{d^{2} a^{2}}$&$531$\\ elliptic&$-\frac{4 c \sqrt{\frac{\left(c -a \right) x}{c \left(-a +x \right)}}\, \left(-a +x \right)^{2} \sqrt{\frac{a \left(-b +x \right)}{b \left(-a +x \right)}}\, \sqrt{\frac{a \left(-c +x \right)}{c \left(-a +x \right)}}\, \EllipticF \left(\sqrt{\frac{\left(c -a \right) x}{c \left(-a +x \right)}}, \sqrt{\frac{\left(a -b \right) c}{b \left(a -c \right)}}\right)}{d \left(c -a \right) a \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}+\frac{2 c \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(d \,\textit{\_Z}^{3}+\left(-b d -c d \right) \textit{\_Z}^{2}+\left(b c d -1\right) \textit{\_Z} +a \right)}{\sum}\frac{\left(3 \underline{\hspace{1.25 ex}}\alpha^{2} a d -\underline{\hspace{1.25 ex}}\alpha^{2} b d -\underline{\hspace{1.25 ex}}\alpha^{2} c d -2 \underline{\hspace{1.25 ex}}\alpha  a b d -2 \underline{\hspace{1.25 ex}}\alpha  a c d +2 \underline{\hspace{1.25 ex}}\alpha  b c d +a b c d -2 \underline{\hspace{1.25 ex}}\alpha  +2 a \right) \left(-a +x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2} d +\underline{\hspace{1.25 ex}}\alpha  a d -\underline{\hspace{1.25 ex}}\alpha  b d -\underline{\hspace{1.25 ex}}\alpha  c d +a^{2} d -a b d -a c d +b c d -1\right) \sqrt{\frac{\left(c -a \right) x}{c \left(-a +x \right)}}\, \sqrt{\frac{a \left(-b +x \right)}{b \left(-a +x \right)}}\, \sqrt{\frac{a \left(-c +x \right)}{c \left(-a +x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(c -a \right) x}{c \left(-a +x \right)}}, \sqrt{\frac{\left(a -b \right) c}{b \left(a -c \right)}}\right)+\left(\underline{\hspace{1.25 ex}}\alpha^{2} d -\underline{\hspace{1.25 ex}}\alpha  b d -\underline{\hspace{1.25 ex}}\alpha  c d +b c d -1\right) \EllipticPi \left(\sqrt{\frac{\left(c -a \right) x}{c \left(-a +x \right)}}, -\frac{d \left(\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  b -\underline{\hspace{1.25 ex}}\alpha  c +b c \right) c}{a -c}, \sqrt{\frac{\left(a -b \right) c}{b \left(a -c \right)}}\right)\right)}{\left(3 \underline{\hspace{1.25 ex}}\alpha^{2} d -2 \underline{\hspace{1.25 ex}}\alpha  b d -2 \underline{\hspace{1.25 ex}}\alpha  c d +b c d -1\right) \left(c -a \right) \left(a^{2}-a b -a c +b c \right) \sqrt{x \left(-a +x \right) \left(-b +x \right) \left(-c +x \right)}}\right)}{d^{2} a^{2}}$&$531$\\ \hline \end{longtable}"," ",0,"-4/d*a*((a-c)*x/a/(-c+x))^(1/2)*(-c+x)^2*(c*(-b+x)/b/(-c+x))^(1/2)*(c*(-a+x)/a/(-c+x))^(1/2)/(a-c)/c/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)*EllipticF(((a-c)*x/a/(-c+x))^(1/2),((-b+c)*a/b/(c-a))^(1/2))+2/d^2*c/a^2*sum((-3*_alpha^2*a*d+_alpha^2*b*d+_alpha^2*c*d+2*_alpha*a*b*d+2*_alpha*a*c*d-2*_alpha*b*c*d-a*b*c*d+2*_alpha-2*a)/(-3*_alpha^2*d+2*_alpha*b*d+2*_alpha*c*d-b*c*d+1)*(-a+x)^2/(c-a)*(_alpha^2*d+_alpha*a*d-_alpha*b*d-_alpha*c*d+a^2*d-a*b*d-a*c*d+b*c*d-1)/(a^2-a*b-a*c+b*c)*((c-a)*x/c/(-a+x))^(1/2)*(a*(-b+x)/b/(-a+x))^(1/2)*(a*(-c+x)/c/(-a+x))^(1/2)/(x*(-a+x)*(-b+x)*(-c+x))^(1/2)*(EllipticF(((c-a)*x/c/(-a+x))^(1/2),((a-b)*c/b/(a-c))^(1/2))+(_alpha^2*d-_alpha*b*d-_alpha*c*d+b*c*d-1)*EllipticPi(((c-a)*x/c/(-a+x))^(1/2),-d*(_alpha^2-_alpha*b-_alpha*c+b*c)*c/(a-c),((a-b)*c/b/(a-c))^(1/2))),_alpha=RootOf(d*_Z^3+(-b*d-c*d)*_Z^2+(b*c*d-1)*_Z+a))","C"
831,1,244,51,0.391000," ","int((x^3-1)/(x^3+1)/(x^4+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4 \sqrt{\left(x^{2}-1\right)^{2}+2 x^{2}}}\right)}{6}-\frac{\sqrt{2}\, \sqrt{\frac{2 \left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+2}\, \arctan \left(\frac{\sqrt{\frac{2 \left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+2}\, \left(x^{2}+1\right)}{\left(\frac{\left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+1\right) \left(-x^{2}+1\right)}\right)}{3 \sqrt{\frac{\frac{\left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+1}{\left(\frac{x^{2}+1}{-x^{2}+1}+1\right)^{2}}}\, \left(\frac{x^{2}+1}{-x^{2}+1}+1\right)}+\frac{\left(\frac{\ln \left(-1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{6}-\frac{\ln \left(1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{6}+\frac{2 \sqrt{2}\, \arctan \left(\frac{\sqrt{x^{4}+1}}{x}\right)}{3}\right) \sqrt{2}}{2}$&$244$\\ default&$\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4 \sqrt{x^{4}+1}}\right)}{6}+\frac{2 \left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{3 \sqrt{x^{4}+1}}+\frac{2 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{\arctanh \left(\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x^{2}-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{3}+\frac{2 \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-\frac{\arctanh \left(\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x^{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{3}$&$374$\\ \hline \end{longtable}"," ",0,"1/6*2^(1/2)*arctanh(1/4*(2*x^2+2)*2^(1/2)/((x^2-1)^2+2*x^2)^(1/2))-1/3*2^(1/2)/(((x^2+1)^2/(-x^2+1)^2+1)/((x^2+1)/(-x^2+1)+1)^2)^(1/2)/((x^2+1)/(-x^2+1)+1)*(2*(x^2+1)^2/(-x^2+1)^2+2)^(1/2)*arctan(1/((x^2+1)^2/(-x^2+1)^2+1)*(2*(x^2+1)^2/(-x^2+1)^2+2)^(1/2)*(x^2+1)/(-x^2+1))+1/2*(1/6*ln(-1+1/2*2^(1/2)/x*(x^4+1)^(1/2))-1/6*ln(1+1/2*2^(1/2)/x*(x^4+1)^(1/2))+2/3*2^(1/2)*arctan((x^4+1)^(1/2)/x))*2^(1/2)","B"
832,1,33,51,5.260000," ","int(x^4*(x^4-x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{4 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}} x^{\frac{21}{4}} \hypergeom \left(\left[-\frac{1}{4}, \frac{7}{4}\right], \left[\frac{11}{4}\right], x^{3}\right)}{21 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}}}$&$33$\\ trager&$\frac{x^{2} \left(4 x^{3}-1\right) \left(x^{4}-x \right)^{\frac{1}{4}}}{24}+\frac{\ln \left(-2 \left(x^{4}-x \right)^{\frac{3}{4}}+2 x \sqrt{x^{4}-x}-2 x^{2} \left(x^{4}-x \right)^{\frac{1}{4}}+2 x^{3}-1\right)}{32}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-2 \sqrt{x^{4}-x}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x +2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-2 \left(x^{4}-x \right)^{\frac{3}{4}}+2 x^{2} \left(x^{4}-x \right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{32}$&$142$\\ risch&$\frac{x^{2} \left(4 x^{3}-1\right) \left(x \left(x^{3}-1\right)\right)^{\frac{1}{4}}}{24}+\frac{\left(\frac{\ln \left(-\frac{-2 x^{9}+2 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}} x^{6}+5 x^{6}-2 \sqrt{x^{12}-3 x^{9}+3 x^{6}-x^{3}}\, x^{3}-4 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}} x^{3}+2 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{3}{4}}-4 x^{3}+2 \sqrt{x^{12}-3 x^{9}+3 x^{6}-x^{3}}+2 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}}+1}{\left(-1+x \right)^{2} \left(x^{2}+x +1\right)^{2}}\right)}{32}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-2 x^{9}-2 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}+5 x^{6}+2 \sqrt{x^{12}-3 x^{9}+3 x^{6}-x^{3}}\, x^{3}+4 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{3}{4}}-4 x^{3}-2 \sqrt{x^{12}-3 x^{9}+3 x^{6}-x^{3}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}}+1}{\left(-1+x \right)^{2} \left(x^{2}+x +1\right)^{2}}\right)}{32}\right) \left(x \left(x^{3}-1\right)\right)^{\frac{1}{4}} \left(x^{3} \left(x^{3}-1\right)^{3}\right)^{\frac{1}{4}}}{x \left(x^{3}-1\right)}$&$450$\\ \hline \end{longtable}"," ",0,"4/21*signum(x^3-1)^(1/4)/(-signum(x^3-1))^(1/4)*x^(21/4)*hypergeom([-1/4,7/4],[11/4],x^3)","C"
833,1,27,51,0.672000," ","int((x^4-x^3)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{4 \mathrm{signum}\left(-1+x \right)^{\frac{1}{4}} x^{\frac{7}{4}} \hypergeom \left(\left[-\frac{1}{4}, \frac{7}{4}\right], \left[\frac{11}{4}\right], x\right)}{7 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{4}}}$&$27$\\ trager&$\left(-\frac{1}{8}+\frac{x}{2}\right) \left(x^{4}-x^{3}\right)^{\frac{1}{4}}-\frac{3 \ln \left(\frac{2 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}+2 \sqrt{x^{4}-x^{3}}\, x +2 x^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}+2 x^{3}-x^{2}}{x^{2}}\right)}{32}+\frac{3 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-2 \sqrt{x^{4}-x^{3}}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x +2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}-2 x^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}}{x^{2}}\right)}{32}$&$165$\\ risch&$\frac{\left(-1+4 x \right) \left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}}}{8}+\frac{\left(\frac{3 \ln \left(\frac{2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{3}{4}}-2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, x +2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x^{2}-2 x^{3}+2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}-4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x +5 x^{2}+2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}}-4 x +1}{\left(-1+x \right)^{2}}\right)}{32}+\frac{3 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{2}+1\right)+5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{3}{4}}-2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x^{2}-4 \RootOf \left(\textit{\_Z}^{2}+1\right) x +4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x +\RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}}}{\left(-1+x \right)^{2}}\right)}{32}\right) \left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}} \left(x \left(-1+x \right)^{3}\right)^{\frac{1}{4}}}{x \left(-1+x \right)}$&$397$\\ \hline \end{longtable}"," ",0,"4/7*signum(-1+x)^(1/4)/(-signum(-1+x))^(1/4)*x^(7/4)*hypergeom([-1/4,7/4],[11/4],x)","C"
834,1,167,55,4.768000," ","int((-x^4-x^3+2)^(1/2)*(2*x^4+x^3+4)/(x^4+x^3-3*x^2-2)/(x^4+x^3-x^2-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) x^{4}+\RootOf \left(\textit{\_Z}^{2}+3\right) x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{2}+6 \sqrt{-x^{4}-x^{3}+2}\, x -2 \RootOf \left(\textit{\_Z}^{2}+3\right)}{x^{4}+x^{3}-3 x^{2}-2}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \sqrt{-x^{4}-x^{3}+2}\, x -2 \RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{4}+x^{3}-x^{2}-2}\right)}{2}$&$167$\\ default&$\text{Expression too large to display}$&$5959$\\ elliptic&$\text{Expression too large to display}$&$433723$\\ \hline \end{longtable}"," ",0,"-1/2*RootOf(_Z^2+3)*ln(-(RootOf(_Z^2+3)*x^4+RootOf(_Z^2+3)*x^3+3*RootOf(_Z^2+3)*x^2+6*(-x^4-x^3+2)^(1/2)*x-2*RootOf(_Z^2+3))/(x^4+x^3-3*x^2-2))+1/2*RootOf(_Z^2+1)*ln(-(RootOf(_Z^2+1)*x^4+RootOf(_Z^2+1)*x^3+RootOf(_Z^2+1)*x^2+2*(-x^4-x^3+2)^(1/2)*x-2*RootOf(_Z^2+1))/(x^4+x^3-x^2-2))","C"
835,0,0,11,0.074000," ","int((a*x^4+b*x^3)^(1/4)/x/(a*x+x^2+b),x)","\[\int \frac{\left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}}{x \left(a x +x^{2}+b \right)}\, dx\]"," ",0,"int((a*x^4+b*x^3)^(1/4)/x/(a*x+x^2+b),x)","F"
836,0,0,11,0.000000," ","int((a*x^4+b*x^3)^(1/4)/x/(a*x+x^2+b),x)","\[\int \frac{\left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}}{x \left(a x +x^{2}+b \right)}\, dx\]"," ",0,"int((a*x^4+b*x^3)^(1/4)/x/(a*x+x^2+b),x)","F"
837,1,65,50,0.311000," ","int(x^2*(x^6-4)/(x^6-1)^(1/2)/(x^6+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(x^{3}+\sqrt{x^{6}-1}\right)}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}-6\right) \ln \left(\frac{-5 \RootOf \left(\textit{\_Z}^{2}-6\right) x^{6}+12 x^{3} \sqrt{x^{6}-1}+2 \RootOf \left(\textit{\_Z}^{2}-6\right)}{x^{6}+2}\right)}{6}$&$65$\\ \hline \end{longtable}"," ",0,"1/3*ln(x^3+(x^6-1)^(1/2))+1/6*RootOf(_Z^2-6)*ln((-5*RootOf(_Z^2-6)*x^6+12*x^3*(x^6-1)^(1/2)+2*RootOf(_Z^2-6))/(x^6+2))","C"
838,1,185,55,16.773000," ","int((x^5-1)*(x^5+x^3-1)*(2*x^5+3)/x^6/(x^5-x^3-1)/(x^6-x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(3 x^{5}+14 x^{3}-3\right) \left(x^{6}-x \right)^{\frac{3}{4}}}{21 x^{6}}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{5}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{6}-x}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{6}-x \right)^{\frac{3}{4}}-2 \left(x^{6}-x \right)^{\frac{1}{4}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{5}-x^{3}-1}\right)-2 \ln \left(-\frac{x^{5}+2 \left(x^{6}-x \right)^{\frac{3}{4}}+2 x \sqrt{x^{6}-x}+2 \left(x^{6}-x \right)^{\frac{1}{4}} x^{2}+x^{3}-1}{x^{5}-x^{3}-1}\right)$&$185$\\ risch&$\frac{\frac{4}{7} x^{10}+\frac{8}{3} x^{8}-\frac{8}{7} x^{5}-\frac{8}{3} x^{3}+\frac{4}{7}}{x^{5} \left(x \left(x^{5}-1\right)\right)^{\frac{1}{4}}}+2 \ln \left(-\frac{-x^{5}+2 \left(x^{6}-x \right)^{\frac{3}{4}}-2 x \sqrt{x^{6}-x}+2 \left(x^{6}-x \right)^{\frac{1}{4}} x^{2}-x^{3}+1}{x^{5}-x^{3}-1}\right)+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{5}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{6}-x}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{6}-x \right)^{\frac{3}{4}}-2 \left(x^{6}-x \right)^{\frac{1}{4}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{5}-x^{3}-1}\right)$&$198$\\ \hline \end{longtable}"," ",0,"4/21*(3*x^5+14*x^3-3)*(x^6-x)^(3/4)/x^6+2*RootOf(_Z^2+1)*ln(-(-RootOf(_Z^2+1)*x^5+2*RootOf(_Z^2+1)*(x^6-x)^(1/2)*x-RootOf(_Z^2+1)*x^3+2*(x^6-x)^(3/4)-2*(x^6-x)^(1/4)*x^2+RootOf(_Z^2+1))/(x^5-x^3-1))-2*ln(-(x^5+2*(x^6-x)^(3/4)+2*x*(x^6-x)^(1/2)+2*(x^6-x)^(1/4)*x^2+x^3-1)/(x^5-x^3-1))","C"
839,1,95,48,0.713000," ","int((x^3+1)^(1/2)*(x^6+2*x^3+2)/x^7/(x^6-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{3}+1}\, \left(5 x^{3}+2\right)}{6 x^{6}}+\frac{5 \ln \left(-\frac{x^{3}+2 \sqrt{x^{3}+1}+2}{x^{3}}\right)}{4}-\frac{5 \RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x^{3}+3 \RootOf \left(\textit{\_Z}^{2}-2\right)+4 \sqrt{x^{3}+1}}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right)}{6}$&$95$\\ default&$\frac{5 \sqrt{x^{3}+1}}{6 x^{3}}+\frac{5 \arctanh \left(\sqrt{x^{3}+1}\right)}{2}-\frac{5 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{3}{4}-\frac{i \sqrt{3}}{4}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}+1}}+\frac{10 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{3}{4}-\frac{3 i \sqrt{3}}{4}+\frac{i \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{2}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}+1}}+\frac{10 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{3}{4}+\frac{3 i \sqrt{3}}{4}+\frac{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{2}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}+1}}+\frac{\sqrt{x^{3}+1}}{3 x^{6}}$&$449$\\ risch&$\frac{5 x^{6}+7 x^{3}+2}{6 x^{6} \sqrt{x^{3}+1}}-\frac{5 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{3}{4}-\frac{i \sqrt{3}}{4}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}+1}}+\frac{5 \arctanh \left(\sqrt{x^{3}+1}\right)}{2}+\frac{10 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{3}{4}-\frac{3 i \sqrt{3}}{4}+\frac{i \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{2}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}+1}}+\frac{10 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{3}{4}+\frac{3 i \sqrt{3}}{4}+\frac{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{2}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}+1}}$&$449$\\ elliptic&$\frac{\sqrt{x^{3}+1}}{3 x^{6}}+\frac{5 \sqrt{x^{3}+1}}{6 x^{3}}+\frac{5 \arctanh \left(\sqrt{x^{3}+1}\right)}{2}-\frac{5 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{3}{4}-\frac{i \sqrt{3}}{4}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}}+\frac{5 i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{3}{4}-\frac{i \sqrt{3}}{4}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{6 \sqrt{x^{3}+1}}-\frac{10 i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{3}{4}-\frac{3 i \sqrt{3}}{4}+\frac{i \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{2}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{3 \sqrt{x^{3}+1}}+\frac{5 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{3}{4}+\frac{3 i \sqrt{3}}{4}+\frac{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{2}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{5 i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{3}{4}+\frac{3 i \sqrt{3}}{4}+\frac{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{2}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{3 \sqrt{x^{3}+1}}$&$920$\\ \hline \end{longtable}"," ",0,"1/6*(x^3+1)^(1/2)*(5*x^3+2)/x^6+5/4*ln(-(x^3+2*(x^3+1)^(1/2)+2)/x^3)-5/6*RootOf(_Z^2-2)*ln(-(RootOf(_Z^2-2)*x^3+3*RootOf(_Z^2-2)+4*(x^3+1)^(1/2))/(-1+x)/(x^2+x+1))","C"
840,1,484,51,3.751000," ","int((x^5+x^2-1)^(1/2)*(3*x^5+2)/(x^10-2*x^5+x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+4 \RootOf \left(8 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2}+2\right) \ln \left(\frac{-\RootOf \left(8 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2} x^{5} \RootOf \left(\textit{\_Z}^{2}+4 \RootOf \left(8 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2}+2\right)-4 \RootOf \left(\textit{\_Z}^{2}+4 \RootOf \left(8 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2}+2\right) \RootOf \left(8 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{4} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+4 \RootOf \left(8 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2}+2\right) \RootOf \left(8 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2} x^{2}+4 \sqrt{x^{5}+x^{2}-1}\, \RootOf \left(8 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2} x +\RootOf \left(8 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+4 \RootOf \left(8 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2}+2\right)+\sqrt{x^{5}+x^{2}-1}\, x}{-x^{5}+4 \RootOf \left(8 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2} x^{2}+x^{2}+1}\right)}{2}+\RootOf \left(8 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right) \ln \left(-\frac{-2 \RootOf \left(8 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{3} x^{5}+8 \RootOf \left(8 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{5} x^{2}-\RootOf \left(8 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right) x^{5}+2 \RootOf \left(8 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{3} x^{2}+4 \sqrt{x^{5}+x^{2}-1}\, \RootOf \left(8 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2} x +2 \RootOf \left(8 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{3}-\RootOf \left(8 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right) x^{2}+\sqrt{x^{5}+x^{2}-1}\, x +\RootOf \left(8 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)}{x^{5}+4 \RootOf \left(8 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2} x^{2}+x^{2}-1}\right)$&$484$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^2+4*RootOf(8*_Z^4+4*_Z^2+1)^2+2)*ln((-RootOf(8*_Z^4+4*_Z^2+1)^2*x^5*RootOf(_Z^2+4*RootOf(8*_Z^4+4*_Z^2+1)^2+2)-4*RootOf(_Z^2+4*RootOf(8*_Z^4+4*_Z^2+1)^2+2)*RootOf(8*_Z^4+4*_Z^2+1)^4*x^2-3*RootOf(_Z^2+4*RootOf(8*_Z^4+4*_Z^2+1)^2+2)*RootOf(8*_Z^4+4*_Z^2+1)^2*x^2+4*(x^5+x^2-1)^(1/2)*RootOf(8*_Z^4+4*_Z^2+1)^2*x+RootOf(8*_Z^4+4*_Z^2+1)^2*RootOf(_Z^2+4*RootOf(8*_Z^4+4*_Z^2+1)^2+2)+(x^5+x^2-1)^(1/2)*x)/(-x^5+4*RootOf(8*_Z^4+4*_Z^2+1)^2*x^2+x^2+1))+RootOf(8*_Z^4+4*_Z^2+1)*ln(-(-2*RootOf(8*_Z^4+4*_Z^2+1)^3*x^5+8*RootOf(8*_Z^4+4*_Z^2+1)^5*x^2-RootOf(8*_Z^4+4*_Z^2+1)*x^5+2*RootOf(8*_Z^4+4*_Z^2+1)^3*x^2+4*(x^5+x^2-1)^(1/2)*RootOf(8*_Z^4+4*_Z^2+1)^2*x+2*RootOf(8*_Z^4+4*_Z^2+1)^3-RootOf(8*_Z^4+4*_Z^2+1)*x^2+(x^5+x^2-1)^(1/2)*x+RootOf(8*_Z^4+4*_Z^2+1))/(x^5+4*RootOf(8*_Z^4+4*_Z^2+1)^2*x^2+x^2-1))","C"
841,0,0,49,0.031000," ","int(1/x/(x^2+x)^(1/2)/(x^2+x*(x^2+x)^(1/2))^(1/2),x)","\[\int \frac{1}{x \sqrt{x^{2}+x}\, \sqrt{x^{2}+x \sqrt{x^{2}+x}}}\, dx\]"," ",0,"int(1/x/(x^2+x)^(1/2)/(x^2+x*(x^2+x)^(1/2))^(1/2),x)","F"
842,1,118,49,0.051000," ","int((b+(a*x^2+b^2)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\left(b^{2}\right)^{\frac{1}{4}} \left(-\frac{32 \sqrt{\pi}\, \sqrt{2}\, x^{3} \sqrt{\frac{a}{b^{2}}}\, a \cosh \left(\frac{3 \arcsinh \left(\frac{x \sqrt{a}}{b}\right)}{2}\right)}{3 b^{2}}-\frac{8 \sqrt{\pi}\, \sqrt{2}\, \sqrt{\frac{a}{b^{2}}}\, \left(-\frac{4 x^{4} a^{2}}{3 b^{4}}-\frac{2 x^{2} a}{3 b^{2}}+\frac{2}{3}\right) \sinh \left(\frac{3 \arcsinh \left(\frac{x \sqrt{a}}{b}\right)}{2}\right) b}{\sqrt{a}\, \sqrt{\frac{x^{2} a}{b^{2}}+1}}\right)}{8 \sqrt{\pi}\, \sqrt{\frac{a}{b^{2}}}}$&$118$\\ \hline \end{longtable}"," ",0,"-1/8*(b^2)^(1/4)/Pi^(1/2)/(a/b^2)^(1/2)*(-32/3*Pi^(1/2)*2^(1/2)*x^3*(a/b^2)^(1/2)*a/b^2*cosh(3/2*arcsinh(x*a^(1/2)/b))-8*Pi^(1/2)*2^(1/2)*(a/b^2)^(1/2)*(-4/3*x^4*a^2/b^4-2/3*x^2*a/b^2+2/3)*sinh(3/2*arcsinh(x*a^(1/2)/b))/a^(1/2)*b/(x^2*a/b^2+1)^(1/2))","C"
843,0,0,47,0.021000," ","int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(1/2)/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\sqrt{x^{2}+1}\, \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(1/2)/(x+(x^2+1)^(1/2))^(1/2),x)","F"
844,1,231,50,0.149000," ","int((a*x-b)/(a*x+b)/(a^2*x^3+b^2*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{i b \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticF \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}+b^{2} x}}-\frac{2 i b^{2} \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, -\frac{i b}{a \left(-\frac{i b}{a}+\frac{b}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{a^{2} \sqrt{a^{2} x^{3}+b^{2} x}\, \left(-\frac{i b}{a}+\frac{b}{a}\right)}$&$231$\\ elliptic&$\frac{i b \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticF \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}+b^{2} x}}-\frac{2 i b^{2} \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, -\frac{i b}{a \left(-\frac{i b}{a}+\frac{b}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{a^{2} \sqrt{a^{2} x^{3}+b^{2} x}\, \left(-\frac{i b}{a}+\frac{b}{a}\right)}$&$231$\\ \hline \end{longtable}"," ",0,"I*b/a*(-I*(x+I*b/a)/b*a)^(1/2)*2^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(a^2*x^3+b^2*x)^(1/2)*EllipticF((-I*(x+I*b/a)/b*a)^(1/2),1/2*2^(1/2))-2*I*b^2/a^2*(-I*(x+I*b/a)/b*a)^(1/2)*2^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(a^2*x^3+b^2*x)^(1/2)/(-I*b/a+b/a)*EllipticPi((-I*(x+I*b/a)/b*a)^(1/2),-I*b/a/(-I*b/a+b/a),1/2*2^(1/2))","C"
845,1,233,50,0.094000," ","int((a*x+b)/(a*x-b)/(a^2*x^3+b^2*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{i b \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticF \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}+b^{2} x}}+\frac{2 i b^{2} \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, -\frac{i b}{a \left(-\frac{i b}{a}-\frac{b}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{a^{2} \sqrt{a^{2} x^{3}+b^{2} x}\, \left(-\frac{i b}{a}-\frac{b}{a}\right)}$&$233$\\ elliptic&$\frac{i b \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticF \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}+b^{2} x}}+\frac{2 i b^{2} \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, -\frac{i b}{a \left(-\frac{i b}{a}-\frac{b}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{a^{2} \sqrt{a^{2} x^{3}+b^{2} x}\, \left(-\frac{i b}{a}-\frac{b}{a}\right)}$&$233$\\ \hline \end{longtable}"," ",0,"I*b/a*(-I*(x+I*b/a)/b*a)^(1/2)*2^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(a^2*x^3+b^2*x)^(1/2)*EllipticF((-I*(x+I*b/a)/b*a)^(1/2),1/2*2^(1/2))+2*I*b^2/a^2*(-I*(x+I*b/a)/b*a)^(1/2)*2^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(a^2*x^3+b^2*x)^(1/2)/(-I*b/a-b/a)*EllipticPi((-I*(x+I*b/a)/b*a)^(1/2),-I*b/a/(-I*b/a-b/a),1/2*2^(1/2))","C"
846,1,231,50,0.072000," ","int((a*x^3-b*x^2)/(a*x^3+b*x^2)/(a^2*x^3+b^2*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{i b \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticF \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}+b^{2} x}}-\frac{2 i b^{2} \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, -\frac{i b}{a \left(-\frac{i b}{a}+\frac{b}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{a^{2} \sqrt{a^{2} x^{3}+b^{2} x}\, \left(-\frac{i b}{a}+\frac{b}{a}\right)}$&$231$\\ elliptic&$\frac{i b \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticF \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}+b^{2} x}}-\frac{2 i b^{2} \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, -\frac{i b}{a \left(-\frac{i b}{a}+\frac{b}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{a^{2} \sqrt{a^{2} x^{3}+b^{2} x}\, \left(-\frac{i b}{a}+\frac{b}{a}\right)}$&$231$\\ \hline \end{longtable}"," ",0,"I*b/a*(-I*(x+I*b/a)/b*a)^(1/2)*2^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(a^2*x^3+b^2*x)^(1/2)*EllipticF((-I*(x+I*b/a)/b*a)^(1/2),1/2*2^(1/2))-2*I*b^2/a^2*(-I*(x+I*b/a)/b*a)^(1/2)*2^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(a^2*x^3+b^2*x)^(1/2)/(-I*b/a+b/a)*EllipticPi((-I*(x+I*b/a)/b*a)^(1/2),-I*b/a/(-I*b/a+b/a),1/2*2^(1/2))","C"
847,1,123,62,1.239000," ","int((2+5*x)/(x^4+2*x^3+5*x^2+20*x-12)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(-x^{5}+\sqrt{x^{4}+2 x^{3}+5 x^{2}+20 x -12}\, x^{3}-3 x^{4}+2 \sqrt{x^{4}+2 x^{3}+5 x^{2}+20 x -12}\, x^{2}-8 x^{3}+4 \sqrt{x^{4}+2 x^{3}+5 x^{2}+20 x -12}\, x -24 x^{2}+8 \sqrt{x^{4}+2 x^{3}+5 x^{2}+20 x -12}-16 x -16\right)$&$123$\\ default&$\text{Expression too large to display}$&$2769$\\ elliptic&$\text{Expression too large to display}$&$2769$\\ \hline \end{longtable}"," ",0,"-ln(-x^5+(x^4+2*x^3+5*x^2+20*x-12)^(1/2)*x^3-3*x^4+2*(x^4+2*x^3+5*x^2+20*x-12)^(1/2)*x^2-8*x^3+4*(x^4+2*x^3+5*x^2+20*x-12)^(1/2)*x-24*x^2+8*(x^4+2*x^3+5*x^2+20*x-12)^(1/2)-16*x-16)","A"
848,1,66,52,0.528000," ","int((x^3-1)*(x^6-1)^(1/2)/x^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(2 x^{3}-1\right) \sqrt{x^{6}-1}}{6 x^{6}}-\frac{\ln \left(-x^{3}+\sqrt{x^{6}-1}\right)}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{6}$&$66$\\ risch&$-\frac{2 x^{9}-x^{6}-2 x^{3}+1}{6 x^{6} \sqrt{x^{6}-1}}-\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \left(-2 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right)+\left(-2 \ln \left(2\right)+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}\right)}{12 \sqrt{\pi}\, \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}+\frac{\sqrt{-\mathrm{signum}\left(x^{6}-1\right)}\, \arcsin \left(x^{3}\right)}{3 \sqrt{\mathrm{signum}\left(x^{6}-1\right)}}$&$115$\\ meijerg&$-\frac{\sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(\frac{\sqrt{\pi}\, \left(-4 x^{6}+8\right)}{4 x^{6}}-\frac{2 \sqrt{\pi}\, \sqrt{-x^{6}+1}}{x^{6}}+2 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{-x^{6}+1}}{2}\right)-\left(-2 \ln \left(2\right)-1+6 \ln \left(x \right)+i \pi \right) \sqrt{\pi}-\frac{2 \sqrt{\pi}}{x^{6}}\right)}{12 \sqrt{\pi}\, \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}}-\frac{i \sqrt{\mathrm{signum}\left(x^{6}-1\right)}\, \left(-\frac{4 i \sqrt{\pi}\, \sqrt{-x^{6}+1}}{x^{3}}-4 i \sqrt{\pi}\, \arcsin \left(x^{3}\right)\right)}{12 \sqrt{\pi}\, \sqrt{-\mathrm{signum}\left(x^{6}-1\right)}}$&$157$\\ \hline \end{longtable}"," ",0,"-1/6*(2*x^3-1)/x^6*(x^6-1)^(1/2)-1/3*ln(-x^3+(x^6-1)^(1/2))+1/6*RootOf(_Z^2+1)*ln((-RootOf(_Z^2+1)+(x^6-1)^(1/2))/x^3)","C"
849,1,105,48,1.563000," ","int((x^6-1)^(1/2)*(2*x^6-1)^2/x^7/(4*x^6-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}-1}\, \left(2 x^{6}+1\right)}{6 x^{6}}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{6}+\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(\frac{4 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{6}-7 \RootOf \left(\textit{\_Z}^{2}+3\right)+12 \sqrt{x^{6}-1}}{\left(2 x^{3}-1\right) \left(2 x^{3}+1\right)}\right)}{12}$&$105$\\ risch&$\frac{\sqrt{x^{6}-1}}{6 x^{6}}+\frac{\sqrt{x^{6}-1}}{3}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{6}-1}}{x^{3}}\right)}{6}+\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(\frac{4 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{6}-7 \RootOf \left(\textit{\_Z}^{2}+3\right)+12 \sqrt{x^{6}-1}}{\left(2 x^{3}-1\right) \left(2 x^{3}+1\right)}\right)}{12}$&$107$\\ \hline \end{longtable}"," ",0,"1/6*(x^6-1)^(1/2)*(2*x^6+1)/x^6-1/6*RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)+(x^6-1)^(1/2))/x^3)+1/12*RootOf(_Z^2+3)*ln((4*RootOf(_Z^2+3)*x^6-7*RootOf(_Z^2+3)+12*(x^6-1)^(1/2))/(2*x^3-1)/(2*x^3+1))","C"
850,1,225,46,2.736000," ","int((x^4-2)/(x^4+1)^(1/4)/(2*x^8+x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{x}{\left(x^{4}+1\right)^{\frac{1}{4}}}+\frac{\RootOf \left(\textit{\_Z}^{4}-27\right) \ln \left(-\frac{2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}-27\right)^{3} x^{2}+6 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-27\right)^{2} x^{3}+12 \RootOf \left(\textit{\_Z}^{4}-27\right) x^{4}+18 \left(x^{4}+1\right)^{\frac{3}{4}} x +3 \RootOf \left(\textit{\_Z}^{4}-27\right)}{2 x^{4}-1}\right)}{12}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-27\right)^{2}\right) \ln \left(-\frac{-2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}-27\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-27\right)^{2}\right) x^{2}-6 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-27\right)^{2} x^{3}+12 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-27\right)^{2}\right) x^{4}+18 \left(x^{4}+1\right)^{\frac{3}{4}} x +3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-27\right)^{2}\right)}{2 x^{4}-1}\right)}{12}$&$225$\\ risch&$\frac{x}{\left(x^{4}+1\right)^{\frac{1}{4}}}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-27\right)^{2}\right) \ln \left(-\frac{2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}-27\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-27\right)^{2}\right) x^{2}-6 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-27\right)^{2} x^{3}-12 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-27\right)^{2}\right) x^{4}+18 \left(x^{4}+1\right)^{\frac{3}{4}} x -3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-27\right)^{2}\right)}{2 x^{4}-1}\right)}{12}+\frac{\RootOf \left(\textit{\_Z}^{4}-27\right) \ln \left(-\frac{2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}-27\right)^{3} x^{2}+6 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-27\right)^{2} x^{3}+12 \RootOf \left(\textit{\_Z}^{4}-27\right) x^{4}+18 \left(x^{4}+1\right)^{\frac{3}{4}} x +3 \RootOf \left(\textit{\_Z}^{4}-27\right)}{2 x^{4}-1}\right)}{12}$&$225$\\ \hline \end{longtable}"," ",0,"x/(x^4+1)^(1/4)+1/12*RootOf(_Z^4-27)*ln(-(2*(x^4+1)^(1/2)*RootOf(_Z^4-27)^3*x^2+6*(x^4+1)^(1/4)*RootOf(_Z^4-27)^2*x^3+12*RootOf(_Z^4-27)*x^4+18*(x^4+1)^(3/4)*x+3*RootOf(_Z^4-27))/(2*x^4-1))+1/12*RootOf(_Z^2+RootOf(_Z^4-27)^2)*ln(-(-2*(x^4+1)^(1/2)*RootOf(_Z^4-27)^2*RootOf(_Z^2+RootOf(_Z^4-27)^2)*x^2-6*(x^4+1)^(1/4)*RootOf(_Z^4-27)^2*x^3+12*RootOf(_Z^2+RootOf(_Z^4-27)^2)*x^4+18*(x^4+1)^(3/4)*x+3*RootOf(_Z^2+RootOf(_Z^4-27)^2))/(2*x^4-1))","C"
851,1,74,50,0.330000," ","int((10*x^8-x^2)/(x^6-1)^(1/2)/(4*x^6-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{5 \ln \left(x^{3}+\sqrt{x^{6}-1}\right)}{6}-\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{6}-6 x^{3} \sqrt{x^{6}-1}+\RootOf \left(\textit{\_Z}^{2}+3\right)}{\left(2 x^{3}-1\right) \left(2 x^{3}+1\right)}\right)}{12}$&$74$\\ \hline \end{longtable}"," ",0,"5/6*ln(x^3+(x^6-1)^(1/2))-1/12*RootOf(_Z^2+3)*ln((2*RootOf(_Z^2+3)*x^6-6*x^3*(x^6-1)^(1/2)+RootOf(_Z^2+3))/(2*x^3-1)/(2*x^3+1))","C"
852,1,67,48,0.182000," ","int((x^2+1)/(x^2-1)/(2*x^2+1)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{x}{3 \sqrt{2 x^{2}+1}}+\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(-\frac{-5 \RootOf \left(\textit{\_Z}^{2}-3\right) x^{2}+6 \sqrt{2 x^{2}+1}\, x -\RootOf \left(\textit{\_Z}^{2}-3\right)}{\left(-1+x \right) \left(1+x \right)}\right)}{9}$&$67$\\ risch&$-\frac{x}{3 \sqrt{2 x^{2}+1}}-\frac{\sqrt{3}\, \arctanh \left(\frac{\left(2+4 x \right) \sqrt{3}}{6 \sqrt{2 \left(-1+x \right)^{2}-1+4 x}}\right)}{9}+\frac{\sqrt{3}\, \arctanh \left(\frac{\left(2-4 x \right) \sqrt{3}}{6 \sqrt{2 \left(1+x \right)^{2}-1-4 x}}\right)}{9}$&$74$\\ default&$\frac{x}{\sqrt{2 x^{2}+1}}-\frac{1}{3 \sqrt{2 \left(1+x \right)^{2}-1-4 x}}-\frac{2 x}{3 \sqrt{2 \left(1+x \right)^{2}-1-4 x}}+\frac{\sqrt{3}\, \arctanh \left(\frac{\left(2-4 x \right) \sqrt{3}}{6 \sqrt{2 \left(1+x \right)^{2}-1-4 x}}\right)}{9}+\frac{1}{3 \sqrt{2 \left(-1+x \right)^{2}-1+4 x}}-\frac{2 x}{3 \sqrt{2 \left(-1+x \right)^{2}-1+4 x}}-\frac{\sqrt{3}\, \arctanh \left(\frac{\left(2+4 x \right) \sqrt{3}}{6 \sqrt{2 \left(-1+x \right)^{2}-1+4 x}}\right)}{9}$&$139$\\ \hline \end{longtable}"," ",0,"-1/3*x/(2*x^2+1)^(1/2)+1/9*RootOf(_Z^2-3)*ln(-(-5*RootOf(_Z^2-3)*x^2+6*(2*x^2+1)^(1/2)*x-RootOf(_Z^2-3))/(-1+x)/(1+x))","C"
853,0,0,49,0.014000," ","int((a*x^2+b)^(3/4)/x,x)","\[\int \frac{\left(a \,x^{2}+b \right)^{\frac{3}{4}}}{x}\, dx\]"," ",0,"int((a*x^2+b)^(3/4)/x,x)","F"
854,1,102,49,0.559000," ","int((x^2-x+1)/(x^2-1)/(x^3+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+2\right) x +\RootOf \left(\textit{\_Z}^{2}+2\right)-4 \sqrt{x^{3}+x}}{\left(1+x \right)^{2}}\right)}{8}-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}+2 \RootOf \left(\textit{\_Z}^{2}-2\right) x +4 \sqrt{x^{3}+x}+\RootOf \left(\textit{\_Z}^{2}-2\right)}{\left(-1+x \right)^{2}}\right)}{8}$&$102$\\ default&$\frac{i \sqrt{-i \left(i+x \right)}\, \sqrt{2}\, \sqrt{i \left(-i+x \right)}\, \sqrt{i x}\, \EllipticF \left(\sqrt{-i \left(i+x \right)}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}+x}}+\frac{\left(\frac{3}{4}-\frac{3 i}{4}\right) \sqrt{-i \left(i+x \right)}\, \sqrt{2}\, \sqrt{i \left(-i+x \right)}\, \sqrt{i x}\, \EllipticPi \left(\sqrt{-i \left(i+x \right)}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}+x}}+\frac{\left(-\frac{1}{4}-\frac{i}{4}\right) \sqrt{-i \left(i+x \right)}\, \sqrt{2}\, \sqrt{i \left(-i+x \right)}\, \sqrt{i x}\, \EllipticPi \left(\sqrt{-i \left(i+x \right)}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}+x}}$&$166$\\ elliptic&$\frac{i \sqrt{-i x +1}\, \sqrt{2}\, \sqrt{i x +1}\, \sqrt{i x}\, \EllipticF \left(\sqrt{-i \left(i+x \right)}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}+x}}+\frac{3 \sqrt{-i x +1}\, \sqrt{2}\, \sqrt{i x +1}\, \sqrt{i x}\, \EllipticPi \left(\sqrt{-i \left(i+x \right)}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}+x}}-\frac{3 i \sqrt{-i x +1}\, \sqrt{2}\, \sqrt{i x +1}\, \sqrt{i x}\, \EllipticPi \left(\sqrt{-i \left(i+x \right)}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}+x}}-\frac{\sqrt{-i x +1}\, \sqrt{2}\, \sqrt{i x +1}\, \sqrt{i x}\, \EllipticPi \left(\sqrt{-i \left(i+x \right)}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}+x}}-\frac{i \sqrt{-i x +1}\, \sqrt{2}\, \sqrt{i x +1}\, \sqrt{i x}\, \EllipticPi \left(\sqrt{-i \left(i+x \right)}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}+x}}$&$262$\\ \hline \end{longtable}"," ",0,"3/8*RootOf(_Z^2+2)*ln((RootOf(_Z^2+2)*x^2-2*RootOf(_Z^2+2)*x+RootOf(_Z^2+2)-4*(x^3+x)^(1/2))/(1+x)^2)-1/8*RootOf(_Z^2-2)*ln((RootOf(_Z^2-2)*x^2+2*RootOf(_Z^2-2)*x+4*(x^3+x)^(1/2)+RootOf(_Z^2-2))/(-1+x)^2)","C"
855,1,92,54,0.475000," ","int((2*x^2-1)/(x^2+1)/(x^4-x^2-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}-5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-4 \sqrt{x^{4}-x^{2}-1}\, x^{3}-5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-2 x \sqrt{x^{4}-x^{2}-1}-\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(x^{2}+1\right)^{3}}\right)}{2}$&$92$\\ default&$\frac{4 \sqrt{1-\left(-\frac{1}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{-2-2 \sqrt{5}}}{2}, \frac{i \sqrt{5}}{2}-\frac{i}{2}\right)}{\sqrt{-2-2 \sqrt{5}}\, \sqrt{x^{4}-x^{2}-1}}-\frac{3 \sqrt{1+\frac{x^{2}}{2}+\frac{\sqrt{5}\, x^{2}}{2}}\, \sqrt{1-\frac{\sqrt{5}\, x^{2}}{2}+\frac{x^{2}}{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}-\frac{\sqrt{5}}{2}}\, x , -\frac{1}{-\frac{1}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}}}{\sqrt{-\frac{1}{2}-\frac{\sqrt{5}}{2}}}\right)}{\sqrt{-\frac{1}{2}-\frac{\sqrt{5}}{2}}\, \sqrt{x^{4}-x^{2}-1}}$&$178$\\ elliptic&$\frac{4 \sqrt{1+\frac{x^{2}}{2}+\frac{\sqrt{5}\, x^{2}}{2}}\, \sqrt{1-\frac{\sqrt{5}\, x^{2}}{2}+\frac{x^{2}}{2}}\, \EllipticF \left(\frac{x \sqrt{-2-2 \sqrt{5}}}{2}, \frac{i \sqrt{5}}{2}-\frac{i}{2}\right)}{\sqrt{-2-2 \sqrt{5}}\, \sqrt{x^{4}-x^{2}-1}}-\frac{3 \sqrt{1+\frac{x^{2}}{2}+\frac{\sqrt{5}\, x^{2}}{2}}\, \sqrt{1-\frac{\sqrt{5}\, x^{2}}{2}+\frac{x^{2}}{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}-\frac{\sqrt{5}}{2}}\, x , -\frac{1}{-\frac{1}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}}}{\sqrt{-\frac{1}{2}-\frac{\sqrt{5}}{2}}}\right)}{\sqrt{-\frac{1}{2}-\frac{\sqrt{5}}{2}}\, \sqrt{x^{4}-x^{2}-1}}$&$180$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^2+1)*ln(-(RootOf(_Z^2+1)*x^6-5*RootOf(_Z^2+1)*x^4-4*(x^4-x^2-1)^(1/2)*x^3-5*RootOf(_Z^2+1)*x^2-2*x*(x^4-x^2-1)^(1/2)-RootOf(_Z^2+1))/(x^2+1)^3)","C"
856,0,0,14,0.032000," ","int(1/(a*x^4-2*b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{1}{\left(a \,x^{4}-2 b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(a*x^4-2*b)/(a*x^4+b*x^2)^(1/4),x)","F"
857,0,0,14,0.000000," ","int(1/(a*x^4-2*b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{1}{\left(a \,x^{4}-2 b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(a*x^4-2*b)/(a*x^4+b*x^2)^(1/4),x)","F"
858,0,0,53,0.022000," ","int((c*x^2-2*b)/(c*x^2-b)/(a*x^4+c*x^2-b)^(1/4),x)","\[\int \frac{c \,x^{2}-2 b}{\left(c \,x^{2}-b \right) \left(a \,x^{4}+c \,x^{2}-b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((c*x^2-2*b)/(c*x^2-b)/(a*x^4+c*x^2-b)^(1/4),x)","F"
859,0,0,53,0.022000," ","int((a*x^3-4*b)/(a*x^3-b)/(c*x^4-a*x^3+b)^(1/4),x)","\[\int \frac{a \,x^{3}-4 b}{\left(a \,x^{3}-b \right) \left(c \,x^{4}-a \,x^{3}+b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^3-4*b)/(a*x^3-b)/(c*x^4-a*x^3+b)^(1/4),x)","F"
860,0,0,11,0.021000," ","int((a*x^6-b)/(a*x^6+b)/(a*x^6+a^3*x^3-b)^(1/3),x)","\[\int \frac{a \,x^{6}-b}{\left(a \,x^{6}+b \right) \left(a \,x^{6}+a^{3} x^{3}-b \right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a*x^6-b)/(a*x^6+b)/(a*x^6+a^3*x^3-b)^(1/3),x)","F"
861,0,0,11,0.001000," ","int((a*x^6-b)/(a*x^6+b)/(a*x^6+a^3*x^3-b)^(1/3),x)","\[\int \frac{a \,x^{6}-b}{\left(a \,x^{6}+b \right) \left(a \,x^{6}+a^{3} x^{3}-b \right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a*x^6-b)/(a*x^6+b)/(a*x^6+a^3*x^3-b)^(1/3),x)","F"
862,1,116,53,1.121000," ","int((-x^4+1)^(1/2)*(x^4+1)/(4*x^8-7*x^4+4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(-\frac{\sqrt{2}\, \arctan \left(\frac{2 \sqrt{-x^{4}+1}}{x}+1\right)}{8}-\frac{\sqrt{2}\, \arctan \left(\frac{2 \sqrt{-x^{4}+1}}{x}-1\right)}{8}-\frac{\sqrt{2}\, \ln \left(\frac{\frac{-x^{4}+1}{2 x^{2}}-\frac{\sqrt{-x^{4}+1}}{2 x}+\frac{1}{4}}{\frac{-x^{4}+1}{2 x^{2}}+\frac{\sqrt{-x^{4}+1}}{2 x}+\frac{1}{4}}\right)}{16}\right) \sqrt{2}}{2}$&$116$\\ elliptic&$\frac{\left(-\frac{\sqrt{2}\, \arctan \left(\frac{2 \sqrt{-x^{4}+1}}{x}+1\right)}{8}-\frac{\sqrt{2}\, \arctan \left(\frac{2 \sqrt{-x^{4}+1}}{x}-1\right)}{8}-\frac{\sqrt{2}\, \ln \left(\frac{\frac{-x^{4}+1}{2 x^{2}}-\frac{\sqrt{-x^{4}+1}}{2 x}+\frac{1}{4}}{\frac{-x^{4}+1}{2 x^{2}}+\frac{\sqrt{-x^{4}+1}}{2 x}+\frac{1}{4}}\right)}{16}\right) \sqrt{2}}{2}$&$116$\\ trager&$\RootOf \left(128 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right) \ln \left(-\frac{-8 \RootOf \left(128 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right) x^{4}-64 x^{2} \RootOf \left(128 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)^{2}+4 x^{2} \RootOf \left(128 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)+\sqrt{-x^{4}+1}\, x +8 \RootOf \left(128 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)}{-2 x^{4}+16 x^{2} \RootOf \left(128 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)-x^{2}+2}\right)+\frac{\ln \left(-\frac{16 \RootOf \left(128 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right) x^{4}-128 x^{2} \RootOf \left(128 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)^{2}-2 x^{4}+24 x^{2} \RootOf \left(128 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)+2 \sqrt{-x^{4}+1}\, x -x^{2}-16 \RootOf \left(128 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)+2}{2 x^{4}+16 x^{2} \RootOf \left(128 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)-x^{2}-2}\right)}{8}-\ln \left(-\frac{16 \RootOf \left(128 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right) x^{4}-128 x^{2} \RootOf \left(128 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)^{2}-2 x^{4}+24 x^{2} \RootOf \left(128 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)+2 \sqrt{-x^{4}+1}\, x -x^{2}-16 \RootOf \left(128 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)+2}{2 x^{4}+16 x^{2} \RootOf \left(128 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)-x^{2}-2}\right) \RootOf \left(128 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)$&$377$\\ \hline \end{longtable}"," ",0,"1/2*(-1/8*2^(1/2)*arctan(2*(-x^4+1)^(1/2)/x+1)-1/8*2^(1/2)*arctan(2*(-x^4+1)^(1/2)/x-1)-1/16*2^(1/2)*ln((1/2*(-x^4+1)/x^2-1/2*(-x^4+1)^(1/2)/x+1/4)/(1/2*(-x^4+1)/x^2+1/2*(-x^4+1)^(1/2)/x+1/4)))*2^(1/2)","B"
863,0,0,11,0.032000," ","int(x^4/(a*x^4-b)^(1/4)/(a*x^8-b),x)","\[\int \frac{x^{4}}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(a \,x^{8}-b \right)}\, dx\]"," ",0,"int(x^4/(a*x^4-b)^(1/4)/(a*x^8-b),x)","F"
864,0,0,9,0.015000," ","int((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1),x)","\[\int \frac{\sqrt{x +\sqrt{x^{2}+1}}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{x^{2}+1}\, dx\]"," ",0,"int((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1),x)","F"
865,0,0,9,0.001000," ","int((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1),x)","\[\int \frac{\sqrt{x +\sqrt{x^{2}+1}}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{x^{2}+1}\, dx\]"," ",0,"int((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1),x)","F"
866,1,458,50,0.457000," ","int((a*x^3-b)^(1/2)/x/(a*x^3+2*b),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{a \left(\frac{2 \sqrt{a \,x^{3}-b}}{3 a}-\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}+2 b \right)}{\sum}\frac{\left(a^{2} b \right)^{\frac{1}{3}} \sqrt{-\frac{i a \left(2 x +\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+\left(a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{2 \left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{a \left(x -\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{-3 \left(a^{2} b \right)^{\frac{1}{3}}-i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{2}\, \sqrt{\frac{i a \left(2 x +\frac{-i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+\left(a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \left(-i \left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  \sqrt{3}\, a +i \sqrt{3}\, \left(a^{2} b \right)^{\frac{2}{3}}+2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-\left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  a -\left(a^{2} b \right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(a^{2} b \right)^{\frac{1}{3}}}}}{3}, \frac{-2 i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a +i \sqrt{3}\, \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +i \sqrt{3}\, a b -3 \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +3 a b}{6 a b}, \sqrt{-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{2 \sqrt{a \,x^{3}-b}}\right)}{3 a^{3}}\right)}{2 b}+\frac{\frac{2 \sqrt{a \,x^{3}-b}}{3}+\frac{2 b \arctanh \left(\frac{\sqrt{a \,x^{3}-b}}{\sqrt{-b}}\right)}{3 \sqrt{-b}}}{2 b}$&$458$\\ elliptic&$\frac{\sqrt{2}\, \left(a^{2} b \right)^{\frac{2}{3}} \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(a^{2} b \right)^{\frac{1}{3}}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{-a x +\left(a^{2} b \right)^{\frac{1}{3}}}{\left(a^{2} b \right)^{\frac{1}{3}} \left(3+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}-2 a x -\left(a^{2} b \right)^{\frac{1}{3}}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{3}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}+2 b \right)}{\sum}\EllipticPi \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(a^{2} b \right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(a^{2} b \right)^{\frac{1}{3}}}}}{6}, \frac{-2 i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a +i \sqrt{3}\, \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +i \sqrt{3}\, a b -3 \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +3 a b}{6 a b}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{3+i \sqrt{3}}}\right) \underline{\hspace{1.25 ex}}\alpha  \right)}{12 a b \sqrt{a \,x^{3}-b}}-\frac{\sqrt{2}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(a^{2} b \right)^{\frac{1}{3}}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{-a x +\left(a^{2} b \right)^{\frac{1}{3}}}{\left(a^{2} b \right)^{\frac{1}{3}} \left(3+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}-2 a x -\left(a^{2} b \right)^{\frac{1}{3}}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{3}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}+2 b \right)}{\sum}\EllipticPi \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(a^{2} b \right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(a^{2} b \right)^{\frac{1}{3}}}}}{6}, \frac{-2 i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a +i \sqrt{3}\, \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +i \sqrt{3}\, a b -3 \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +3 a b}{6 a b}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{3+i \sqrt{3}}}\right)\right)}{12 \sqrt{a \,x^{3}-b}}+\frac{i \sqrt{2}\, \left(a^{2} b \right)^{\frac{1}{3}} \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(a^{2} b \right)^{\frac{1}{3}}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{-a x +\left(a^{2} b \right)^{\frac{1}{3}}}{\left(a^{2} b \right)^{\frac{1}{3}} \left(3+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}-2 a x -\left(a^{2} b \right)^{\frac{1}{3}}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}+2 b \right)}{\sum}\EllipticPi \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(a^{2} b \right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(a^{2} b \right)^{\frac{1}{3}}}}}{6}, \frac{-2 i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a +i \sqrt{3}\, \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +i \sqrt{3}\, a b -3 \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +3 a b}{6 a b}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{3+i \sqrt{3}}}\right) \underline{\hspace{1.25 ex}}\alpha^{2}\right)}{6 b \sqrt{a \,x^{3}-b}}-\frac{i \sqrt{2}\, \left(a^{2} b \right)^{\frac{2}{3}} \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(a^{2} b \right)^{\frac{1}{3}}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{-a x +\left(a^{2} b \right)^{\frac{1}{3}}}{\left(a^{2} b \right)^{\frac{1}{3}} \left(3+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}-2 a x -\left(a^{2} b \right)^{\frac{1}{3}}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}+2 b \right)}{\sum}\EllipticPi \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(a^{2} b \right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(a^{2} b \right)^{\frac{1}{3}}}}}{6}, \frac{-2 i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a +i \sqrt{3}\, \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +i \sqrt{3}\, a b -3 \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +3 a b}{6 a b}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{3+i \sqrt{3}}}\right) \underline{\hspace{1.25 ex}}\alpha  \right)}{12 a b \sqrt{a \,x^{3}-b}}-\frac{i \sqrt{2}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(a^{2} b \right)^{\frac{1}{3}}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{-a x +\left(a^{2} b \right)^{\frac{1}{3}}}{\left(a^{2} b \right)^{\frac{1}{3}} \left(3+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}-2 a x -\left(a^{2} b \right)^{\frac{1}{3}}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}+2 b \right)}{\sum}\EllipticPi \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(a^{2} b \right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(a^{2} b \right)^{\frac{1}{3}}}}}{6}, \frac{-2 i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a +i \sqrt{3}\, \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +i \sqrt{3}\, a b -3 \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +3 a b}{6 a b}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{3+i \sqrt{3}}}\right)\right)}{12 \sqrt{a \,x^{3}-b}}+\frac{\arctanh \left(\frac{\sqrt{a \,x^{3}-b}}{\sqrt{-b}}\right)}{3 \sqrt{-b}}$&$1430$\\ \hline \end{longtable}"," ",0,"-1/2*a/b*(2/3*(a*x^3-b)^(1/2)/a-1/3*I/a^3*2^(1/2)*sum((a^2*b)^(1/3)*(-1/2*I*a*(2*x+1/a*(I*3^(1/2)*(a^2*b)^(1/3)+(a^2*b)^(1/3)))/(a^2*b)^(1/3))^(1/2)*(a*(x-1/a*(a^2*b)^(1/3))/(-3*(a^2*b)^(1/3)-I*3^(1/2)*(a^2*b)^(1/3)))^(1/2)*(1/2*I*a*(2*x+1/a*(-I*3^(1/2)*(a^2*b)^(1/3)+(a^2*b)^(1/3)))/(a^2*b)^(1/3))^(1/2)/(a*x^3-b)^(1/2)*(-I*(a^2*b)^(1/3)*_alpha*3^(1/2)*a+I*3^(1/2)*(a^2*b)^(2/3)+2*_alpha^2*a^2-(a^2*b)^(1/3)*_alpha*a-(a^2*b)^(2/3))*EllipticPi(1/3*3^(1/2)*(-I*(x+1/2/a*(a^2*b)^(1/3)+1/2*I*3^(1/2)/a*(a^2*b)^(1/3))*3^(1/2)*a/(a^2*b)^(1/3))^(1/2),1/6/a*(-2*I*3^(1/2)*(a^2*b)^(1/3)*_alpha^2*a+I*3^(1/2)*(a^2*b)^(2/3)*_alpha+I*3^(1/2)*a*b-3*(a^2*b)^(2/3)*_alpha+3*a*b)/b,(-I*3^(1/2)/a*(a^2*b)^(1/3)/(-3/2/a*(a^2*b)^(1/3)-1/2*I*3^(1/2)/a*(a^2*b)^(1/3)))^(1/2)),_alpha=RootOf(_Z^3*a+2*b)))+1/2/b*(2/3*(a*x^3-b)^(1/2)+2/3*b*arctanh((a*x^3-b)^(1/2)/(-b)^(1/2))/(-b)^(1/2))","C"
867,1,418,49,0.165000," ","int((4*a*x^3-b)/x/(a*x^3-b)^(1/2)/(a*x^3+2*b),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}+2 b \right)}{\sum}\frac{\left(a^{2} b \right)^{\frac{1}{3}} \sqrt{-\frac{i a \left(2 x +\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+\left(a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{2 \left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{a \left(x -\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{-3 \left(a^{2} b \right)^{\frac{1}{3}}-i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{2}\, \sqrt{\frac{i a \left(2 x +\frac{-i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+\left(a^{2} b \right)^{\frac{1}{3}}}{a}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \left(-i \left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  \sqrt{3}\, a +i \sqrt{3}\, \left(a^{2} b \right)^{\frac{2}{3}}+2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-\left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  a -\left(a^{2} b \right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a^{2} b \right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(a^{2} b \right)^{\frac{1}{3}}}}}{3}, \frac{-2 i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a +i \sqrt{3}\, \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +i \sqrt{3}\, a b -3 \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +3 a b}{6 a b}, \sqrt{-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{2 \sqrt{a \,x^{3}-b}}\right)}{2 a^{2} b}+\frac{\arctanh \left(\frac{\sqrt{a \,x^{3}-b}}{\sqrt{-b}}\right)}{3 \sqrt{-b}}$&$418$\\ elliptic&$\frac{\sqrt{2}\, \left(a^{2} b \right)^{\frac{2}{3}} \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(a^{2} b \right)^{\frac{1}{3}}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{-a x +\left(a^{2} b \right)^{\frac{1}{3}}}{\left(a^{2} b \right)^{\frac{1}{3}} \left(3+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}-2 a x -\left(a^{2} b \right)^{\frac{1}{3}}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{3}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}+2 b \right)}{\sum}\EllipticPi \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(a^{2} b \right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(a^{2} b \right)^{\frac{1}{3}}}}}{6}, \frac{-2 i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a +i \sqrt{3}\, \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +i \sqrt{3}\, a b -3 \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +3 a b}{6 a b}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{3+i \sqrt{3}}}\right) \underline{\hspace{1.25 ex}}\alpha  \right)}{4 a b \sqrt{a \,x^{3}-b}}-\frac{\sqrt{2}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(a^{2} b \right)^{\frac{1}{3}}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{-a x +\left(a^{2} b \right)^{\frac{1}{3}}}{\left(a^{2} b \right)^{\frac{1}{3}} \left(3+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}-2 a x -\left(a^{2} b \right)^{\frac{1}{3}}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{3}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}+2 b \right)}{\sum}\EllipticPi \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(a^{2} b \right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(a^{2} b \right)^{\frac{1}{3}}}}}{6}, \frac{-2 i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a +i \sqrt{3}\, \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +i \sqrt{3}\, a b -3 \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +3 a b}{6 a b}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{3+i \sqrt{3}}}\right)\right)}{4 \sqrt{a \,x^{3}-b}}+\frac{i \sqrt{2}\, \left(a^{2} b \right)^{\frac{1}{3}} \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(a^{2} b \right)^{\frac{1}{3}}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{-a x +\left(a^{2} b \right)^{\frac{1}{3}}}{\left(a^{2} b \right)^{\frac{1}{3}} \left(3+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}-2 a x -\left(a^{2} b \right)^{\frac{1}{3}}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}+2 b \right)}{\sum}\EllipticPi \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(a^{2} b \right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(a^{2} b \right)^{\frac{1}{3}}}}}{6}, \frac{-2 i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a +i \sqrt{3}\, \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +i \sqrt{3}\, a b -3 \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +3 a b}{6 a b}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{3+i \sqrt{3}}}\right) \underline{\hspace{1.25 ex}}\alpha^{2}\right)}{2 b \sqrt{a \,x^{3}-b}}-\frac{i \sqrt{2}\, \left(a^{2} b \right)^{\frac{2}{3}} \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(a^{2} b \right)^{\frac{1}{3}}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{-a x +\left(a^{2} b \right)^{\frac{1}{3}}}{\left(a^{2} b \right)^{\frac{1}{3}} \left(3+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}-2 a x -\left(a^{2} b \right)^{\frac{1}{3}}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}+2 b \right)}{\sum}\EllipticPi \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(a^{2} b \right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(a^{2} b \right)^{\frac{1}{3}}}}}{6}, \frac{-2 i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a +i \sqrt{3}\, \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +i \sqrt{3}\, a b -3 \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +3 a b}{6 a b}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{3+i \sqrt{3}}}\right) \underline{\hspace{1.25 ex}}\alpha  \right)}{4 a b \sqrt{a \,x^{3}-b}}-\frac{i \sqrt{2}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(a^{2} b \right)^{\frac{1}{3}}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \sqrt{\frac{-a x +\left(a^{2} b \right)^{\frac{1}{3}}}{\left(a^{2} b \right)^{\frac{1}{3}} \left(3+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}-2 a x -\left(a^{2} b \right)^{\frac{1}{3}}\right)}{\left(a^{2} b \right)^{\frac{1}{3}}}}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}+2 b \right)}{\sum}\EllipticPi \left(\frac{\sqrt{3}\, \sqrt{2}\, \sqrt{-\frac{i \left(i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}}+2 a x +\left(a^{2} b \right)^{\frac{1}{3}}\right) \sqrt{3}}{\left(a^{2} b \right)^{\frac{1}{3}}}}}{6}, \frac{-2 i \sqrt{3}\, \left(a^{2} b \right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a +i \sqrt{3}\, \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +i \sqrt{3}\, a b -3 \left(a^{2} b \right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  +3 a b}{6 a b}, \sqrt{2}\, \sqrt{\frac{i \sqrt{3}}{3+i \sqrt{3}}}\right)\right)}{4 \sqrt{a \,x^{3}-b}}+\frac{\arctanh \left(\frac{\sqrt{a \,x^{3}-b}}{\sqrt{-b}}\right)}{3 \sqrt{-b}}$&$1430$\\ \hline \end{longtable}"," ",0,"1/2*I/a^2/b*2^(1/2)*sum((a^2*b)^(1/3)*(-1/2*I*a*(2*x+1/a*(I*3^(1/2)*(a^2*b)^(1/3)+(a^2*b)^(1/3)))/(a^2*b)^(1/3))^(1/2)*(a*(x-1/a*(a^2*b)^(1/3))/(-3*(a^2*b)^(1/3)-I*3^(1/2)*(a^2*b)^(1/3)))^(1/2)*(1/2*I*a*(2*x+1/a*(-I*3^(1/2)*(a^2*b)^(1/3)+(a^2*b)^(1/3)))/(a^2*b)^(1/3))^(1/2)/(a*x^3-b)^(1/2)*(-I*(a^2*b)^(1/3)*_alpha*3^(1/2)*a+I*3^(1/2)*(a^2*b)^(2/3)+2*_alpha^2*a^2-(a^2*b)^(1/3)*_alpha*a-(a^2*b)^(2/3))*EllipticPi(1/3*3^(1/2)*(-I*(x+1/2/a*(a^2*b)^(1/3)+1/2*I*3^(1/2)/a*(a^2*b)^(1/3))*3^(1/2)*a/(a^2*b)^(1/3))^(1/2),1/6/a*(-2*I*3^(1/2)*(a^2*b)^(1/3)*_alpha^2*a+I*3^(1/2)*(a^2*b)^(2/3)*_alpha+I*3^(1/2)*a*b-3*(a^2*b)^(2/3)*_alpha+3*a*b)/b,(-I*3^(1/2)/a*(a^2*b)^(1/3)/(-3/2/a*(a^2*b)^(1/3)-1/2*I*3^(1/2)/a*(a^2*b)^(1/3)))^(1/2)),_alpha=RootOf(_Z^3*a+2*b))+1/3*arctanh((a*x^3-b)^(1/2)/(-b)^(1/2))/(-b)^(1/2)","C"
868,1,80,54,0.515000," ","int((x^4+6*x^2+1)^(1/2)/(-1+x)/(1+x)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{4}+6 x^{2}+1}}{4 \left(1+x \right)^{2}}+\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{2}-2\right) x +2 \sqrt{x^{4}+6 x^{2}+1}-\RootOf \left(\textit{\_Z}^{2}-2\right)}{\left(-1+x \right)^{2}}\right)}{8}$&$80$\\ default&$\frac{\sqrt{x^{4}+6 x^{2}+1}}{4 \left(1+x \right)^{2}}-\frac{\sqrt{8}\, \arctanh \left(\frac{\left(8 x^{2}+8\right) \sqrt{8}}{16 \sqrt{x^{4}+6 x^{2}+1}}\right)}{16}+\frac{\sqrt{1-\left(-3+2 \sqrt{2}\right) x^{2}}\, \sqrt{1-\left(-3-2 \sqrt{2}\right) x^{2}}\, \EllipticF \left(x \left(i \sqrt{2}-i\right), 3+2 \sqrt{2}\right)}{2 \left(i \sqrt{2}-i\right) \sqrt{x^{4}+6 x^{2}+1}}-\frac{\sqrt{1-\left(-3+2 \sqrt{2}\right) x^{2}}\, \sqrt{1-\left(-3-2 \sqrt{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{-3+2 \sqrt{2}}\, x , \frac{1}{-3+2 \sqrt{2}}, \frac{\sqrt{-3-2 \sqrt{2}}}{\sqrt{-3+2 \sqrt{2}}}\right)}{\sqrt{-3+2 \sqrt{2}}\, \sqrt{x^{4}+6 x^{2}+1}}$&$222$\\ risch&$\frac{\sqrt{x^{4}+6 x^{2}+1}}{4 \left(1+x \right)^{2}}-\frac{\sqrt{8}\, \arctanh \left(\frac{\left(8 x^{2}+8\right) \sqrt{8}}{16 \sqrt{x^{4}+6 x^{2}+1}}\right)}{16}+\frac{\sqrt{1-\left(-3+2 \sqrt{2}\right) x^{2}}\, \sqrt{1-\left(-3-2 \sqrt{2}\right) x^{2}}\, \EllipticF \left(x \left(i \sqrt{2}-i\right), 3+2 \sqrt{2}\right)}{2 \left(i \sqrt{2}-i\right) \sqrt{x^{4}+6 x^{2}+1}}-\frac{\sqrt{1-\left(-3+2 \sqrt{2}\right) x^{2}}\, \sqrt{1-\left(-3-2 \sqrt{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{-3+2 \sqrt{2}}\, x , \frac{1}{-3+2 \sqrt{2}}, \frac{\sqrt{-3-2 \sqrt{2}}}{\sqrt{-3+2 \sqrt{2}}}\right)}{\sqrt{-3+2 \sqrt{2}}\, \sqrt{x^{4}+6 x^{2}+1}}$&$222$\\ elliptic&$\frac{\left(\left(x^{2}-1\right)^{2}+8 x^{2}\right)^{\frac{3}{2}}}{16 \left(x^{2}-1\right)^{2}}-\frac{\left(\left(x^{2}-1\right)^{2}+8 x^{2}\right)^{\frac{3}{2}}}{32 \left(x^{2}-1\right)}+\frac{\sqrt{\left(x^{2}-1\right)^{2}+8 x^{2}}}{16}-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(8 x^{2}+8\right) \sqrt{2}}{8 \sqrt{\left(x^{2}-1\right)^{2}+8 x^{2}}}\right)}{8}+\frac{\left(2 x^{2}+6\right) \sqrt{\left(x^{2}-1\right)^{2}+8 x^{2}}}{64}+\frac{\left(-\frac{1}{4 \left(2+\frac{\sqrt{x^{4}+6 x^{2}+1}\, \sqrt{2}}{2 x}\right)}-\frac{\ln \left(2+\frac{\sqrt{x^{4}+6 x^{2}+1}\, \sqrt{2}}{2 x}\right)}{8}-\frac{1}{4 \left(-2+\frac{\sqrt{x^{4}+6 x^{2}+1}\, \sqrt{2}}{2 x}\right)}+\frac{\ln \left(-2+\frac{\sqrt{x^{4}+6 x^{2}+1}\, \sqrt{2}}{2 x}\right)}{8}\right) \sqrt{2}}{2}$&$232$\\ \hline \end{longtable}"," ",0,"1/4*(x^4+6*x^2+1)^(1/2)/(1+x)^2+1/8*RootOf(_Z^2-2)*ln(-(-RootOf(_Z^2-2)*x^2-2*RootOf(_Z^2-2)*x+2*(x^4+6*x^2+1)^(1/2)-RootOf(_Z^2-2))/(-1+x)^2)","C"
869,0,0,48,0.016000," ","int((a*x^4+b)^(1/4)/x,x)","\[\int \frac{\left(a \,x^{4}+b \right)^{\frac{1}{4}}}{x}\, dx\]"," ",0,"int((a*x^4+b)^(1/4)/x,x)","F"
870,0,0,14,0.033000," ","int(1/(a*x^4-2*b)/(a*x^4-b*x^2)^(1/4),x)","\[\int \frac{1}{\left(a \,x^{4}-2 b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(a*x^4-2*b)/(a*x^4-b*x^2)^(1/4),x)","F"
871,0,0,14,0.000000," ","int(1/(a*x^4-2*b)/(a*x^4-b*x^2)^(1/4),x)","\[\int \frac{1}{\left(a \,x^{4}-2 b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(a*x^4-2*b)/(a*x^4-b*x^2)^(1/4),x)","F"
872,0,0,14,0.029000," ","int(x^6/(a*x^4+b)^(3/4)/(a^2*x^8+b^2),x)","\[\int \frac{x^{6}}{\left(a \,x^{4}+b \right)^{\frac{3}{4}} \left(a^{2} x^{8}+b^{2}\right)}\, dx\]"," ",0,"int(x^6/(a*x^4+b)^(3/4)/(a^2*x^8+b^2),x)","F"
873,0,0,52,0.018000," ","int((x^3+x^2*(x^2-1)^(1/2))^(1/2),x)","\[\int \sqrt{x^{3}+x^{2} \sqrt{x^{2}-1}}\, dx\]"," ",0,"int((x^3+x^2*(x^2-1)^(1/2))^(1/2),x)","F"
874,1,3422,59,0.376000," ","int((-a+x)*(-b+x)*(-a*b+x^2)/x/(x*(-a+x)*(-b+x))^(1/2)/(a*b-(a+b+d)*x+x^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$3422$\\ elliptic&$\text{Expression too large to display}$&$3462$\\ default&$\text{Expression too large to display}$&$3786$\\ \hline \end{longtable}"," ",0,"2*(a-x)*(b-x)/(x*(-a+x)*(-b+x))^(1/2)-d*(2*a*(-(-a+x)/a)^(1/2)*((-b+x)/(a-b))^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)*EllipticF((-(-a+x)/a)^(1/2),(a/(a-b))^(1/2))+1/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a^3*(1-1/a*x)^(1/2)*(-b/(a-b)+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))-2/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a^2*(1-1/a*x)^(1/2)*(-b/(a-b)+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*b+2/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a^2*(1-1/a*x)^(1/2)*(-b/(a-b)+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*d+a^2*(1-1/a*x)^(1/2)*(-b/(a-b)+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))+1/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a*(1-1/a*x)^(1/2)*(-b/(a-b)+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*b^2+2/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a*(1-1/a*x)^(1/2)*(-b/(a-b)+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*b*d+a*(1-1/a*x)^(1/2)*(-b/(a-b)+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*b+1/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a*(1-1/a*x)^(1/2)*(-b/(a-b)+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*d^2+a*(1-1/a*x)^(1/2)*(-b/(a-b)+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d-1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*d-1/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a^3*(1-1/a*x)^(1/2)*(-b/(a-b)+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))+2/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a^2*(1-1/a*x)^(1/2)*(-b/(a-b)+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*b-2/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a^2*(1-1/a*x)^(1/2)*(-b/(a-b)+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*d+a^2*(1-1/a*x)^(1/2)*(-b/(a-b)+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))-1/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a*(1-1/a*x)^(1/2)*(-b/(a-b)+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*b^2-2/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a*(1-1/a*x)^(1/2)*(-b/(a-b)+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*b*d+a*(1-1/a*x)^(1/2)*(-b/(a-b)+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*b-1/(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)*a*(1-1/a*x)^(1/2)*(-b/(a-b)+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*d^2+a*(1-1/a*x)^(1/2)*(-b/(a-b)+1/(a-b)*x)^(1/2)*(1/a*x)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-a+x)/a)^(1/2),a/(1/2*a-1/2*b-1/2*d+1/2*(a^2-2*a*b+2*a*d+b^2+2*b*d+d^2)^(1/2)),(a/(a-b))^(1/2))*d)","C"
875,0,0,14,0.031000," ","int(1/(a^3*x^2+b)/(a^3*x^3-b*x^2)^(1/3),x)","\[\int \frac{1}{\left(a^{3} x^{2}+b \right) \left(a^{3} x^{3}-b \,x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(a^3*x^2+b)/(a^3*x^3-b*x^2)^(1/3),x)","F"
876,0,0,14,0.000000," ","int(1/(a^3*x^2+b)/(a^3*x^3-b*x^2)^(1/3),x)","\[\int \frac{1}{\left(a^{3} x^{2}+b \right) \left(a^{3} x^{3}-b \,x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(a^3*x^2+b)/(a^3*x^3-b*x^2)^(1/3),x)","F"
877,1,101,51,0.601000," ","int((x^4-1)^(1/2)/(x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{x^{4}-1}}{x}+1\right)}{4}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{x^{4}-1}}{x}-1\right)}{4}+\frac{\sqrt{2}\, \ln \left(\frac{\frac{x^{4}-1}{2 x^{2}}-\frac{\sqrt{x^{4}-1}}{x}+1}{\frac{x^{4}-1}{2 x^{2}}+\frac{\sqrt{x^{4}-1}}{x}+1}\right)}{8}\right) \sqrt{2}}{2}$&$101$\\ elliptic&$\frac{\left(\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{x^{4}-1}}{x}+1\right)}{4}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{x^{4}-1}}{x}-1\right)}{4}+\frac{\sqrt{2}\, \ln \left(\frac{\frac{x^{4}-1}{2 x^{2}}-\frac{\sqrt{x^{4}-1}}{x}+1}{\frac{x^{4}-1}{2 x^{2}}+\frac{\sqrt{x^{4}-1}}{x}+1}\right)}{8}\right) \sqrt{2}}{2}$&$101$\\ trager&$-\frac{\ln \left(-\frac{-4 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) x +\sqrt{x^{4}-1}}{4 x^{2} \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right)+x^{2}-1}\right)}{2}-\ln \left(-\frac{-4 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) x +\sqrt{x^{4}-1}}{4 x^{2} \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right)+x^{2}-1}\right) \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right)+\RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) \ln \left(-\frac{4 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) x +\sqrt{x^{4}-1}+2 x}{4 x^{2} \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right)+x^{2}+1}\right)$&$176$\\ \hline \end{longtable}"," ",0,"1/2*(1/4*2^(1/2)*arctan((x^4-1)^(1/2)/x+1)+1/4*2^(1/2)*arctan((x^4-1)^(1/2)/x-1)+1/8*2^(1/2)*ln((1/2*(x^4-1)/x^2-(x^4-1)^(1/2)/x+1)/(1/2*(x^4-1)/x^2+(x^4-1)^(1/2)/x+1)))*2^(1/2)","A"
878,1,33,55,3.129000," ","int(x^2*(x^4-x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{2 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{4}} x^{\frac{7}{2}} \hypergeom \left(\left[-\frac{1}{4}, \frac{7}{4}\right], \left[\frac{11}{4}\right], x^{2}\right)}{7 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{4}}}$&$33$\\ trager&$\frac{x \left(4 x^{2}-1\right) \left(x^{4}-x^{2}\right)^{\frac{1}{4}}}{16}+\frac{3 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{2 \sqrt{x^{4}-x^{2}}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-2 \left(x^{4}-x^{2}\right)^{\frac{3}{4}}+2 x^{2} \left(x^{4}-x^{2}\right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{2}+1\right) x}{x}\right)}{64}-\frac{3 \ln \left(\frac{2 \left(x^{4}-x^{2}\right)^{\frac{3}{4}}+2 \sqrt{x^{4}-x^{2}}\, x +2 x^{2} \left(x^{4}-x^{2}\right)^{\frac{1}{4}}+2 x^{3}-x}{x}\right)}{64}$&$165$\\ risch&$\frac{x \left(4 x^{2}-1\right) \left(x^{2} \left(x^{2}-1\right)\right)^{\frac{1}{4}}}{16}+\frac{\left(\frac{3 \ln \left(-\frac{-2 x^{6}+2 \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}} x^{4}-2 \sqrt{x^{8}-3 x^{6}+3 x^{4}-x^{2}}\, x^{2}+5 x^{4}+2 \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{3}{4}}-4 \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}} x^{2}+2 \sqrt{x^{8}-3 x^{6}+3 x^{4}-x^{2}}-4 x^{2}+2 \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}}+1}{\left(-1+x \right)^{2} \left(1+x \right)^{2}}\right)}{64}-\frac{3 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-2 \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-2 x^{6}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{3}{4}}+2 \sqrt{x^{8}-3 x^{6}+3 x^{4}-x^{2}}\, x^{2}+4 \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+5 x^{4}-2 \sqrt{x^{8}-3 x^{6}+3 x^{4}-x^{2}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}}-4 x^{2}+1}{\left(-1+x \right)^{2} \left(1+x \right)^{2}}\right)}{64}\right) \left(x^{2} \left(x^{2}-1\right)\right)^{\frac{1}{4}} \left(x^{2} \left(x^{2}-1\right)^{3}\right)^{\frac{1}{4}}}{x \left(x^{2}-1\right)}$&$446$\\ \hline \end{longtable}"," ",0,"2/7*signum(x^2-1)^(1/4)/(-signum(x^2-1))^(1/4)*x^(7/2)*hypergeom([-1/4,7/4],[11/4],x^2)","C"
879,1,151,61,1.682000," ","int(x/(x^4-2*x^3+3*x^2+4*x+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\ln \left(-2 x^{6}+2 \sqrt{x^{4}-2 x^{3}+3 x^{2}+4 x +1}\, x^{4}+12 x^{5}-10 \sqrt{x^{4}-2 x^{3}+3 x^{2}+4 x +1}\, x^{3}-36 x^{4}+24 \sqrt{x^{4}-2 x^{3}+3 x^{2}+4 x +1}\, x^{2}+56 x^{3}-28 x \sqrt{x^{4}-2 x^{3}+3 x^{2}+4 x +1}-42 x^{2}+14 \sqrt{x^{4}-2 x^{3}+3 x^{2}+4 x +1}+13\right)}{6}$&$151$\\ default&$\text{Expression too large to display}$&$1609$\\ elliptic&$\text{Expression too large to display}$&$1609$\\ \hline \end{longtable}"," ",0,"-1/6*ln(-2*x^6+2*(x^4-2*x^3+3*x^2+4*x+1)^(1/2)*x^4+12*x^5-10*(x^4-2*x^3+3*x^2+4*x+1)^(1/2)*x^3-36*x^4+24*(x^4-2*x^3+3*x^2+4*x+1)^(1/2)*x^2+56*x^3-28*x*(x^4-2*x^3+3*x^2+4*x+1)^(1/2)-42*x^2+14*(x^4-2*x^3+3*x^2+4*x+1)^(1/2)+13)","B"
880,1,151,61,1.064000," ","int(x/(x^4+2*x^3+3*x^2-4*x+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(2 x^{6}+2 \sqrt{x^{4}+2 x^{3}+3 x^{2}-4 x +1}\, x^{4}+12 x^{5}+10 \sqrt{x^{4}+2 x^{3}+3 x^{2}-4 x +1}\, x^{3}+36 x^{4}+24 \sqrt{x^{4}+2 x^{3}+3 x^{2}-4 x +1}\, x^{2}+56 x^{3}+28 x \sqrt{x^{4}+2 x^{3}+3 x^{2}-4 x +1}+42 x^{2}+14 \sqrt{x^{4}+2 x^{3}+3 x^{2}-4 x +1}-13\right)}{6}$&$151$\\ default&$\text{Expression too large to display}$&$1609$\\ elliptic&$\text{Expression too large to display}$&$1609$\\ \hline \end{longtable}"," ",0,"1/6*ln(2*x^6+2*(x^4+2*x^3+3*x^2-4*x+1)^(1/2)*x^4+12*x^5+10*(x^4+2*x^3+3*x^2-4*x+1)^(1/2)*x^3+36*x^4+24*(x^4+2*x^3+3*x^2-4*x+1)^(1/2)*x^2+56*x^3+28*x*(x^4+2*x^3+3*x^2-4*x+1)^(1/2)+42*x^2+14*(x^4+2*x^3+3*x^2-4*x+1)^(1/2)-13)","B"
881,1,127,50,2.573000," ","int((2*x^4-3*x^2+3)/(x^2-1)^(1/4)/(x^4-3*x^2+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 x}{\left(x^{2}-1\right)^{\frac{1}{4}}}-\frac{5 \RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{\left(x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+2\right)+x \sqrt{x^{2}-1}-\RootOf \left(\textit{\_Z}^{2}+2\right) \left(x^{2}-1\right)^{\frac{1}{4}}-x}{x^{2}-2}\right)}{4}-\frac{5 \RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{\left(x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}-2\right)+x \sqrt{x^{2}-1}+\RootOf \left(\textit{\_Z}^{2}-2\right) \left(x^{2}-1\right)^{\frac{1}{4}}+x}{x^{2}-2}\right)}{4}$&$127$\\ risch&$\frac{4 x}{\left(x^{2}-1\right)^{\frac{1}{4}}}+\frac{5 \RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(-\frac{\left(x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+2\right)-x \sqrt{x^{2}-1}-\RootOf \left(\textit{\_Z}^{2}+2\right) \left(x^{2}-1\right)^{\frac{1}{4}}+x}{x^{2}-2}\right)}{4}+\frac{5 \RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{\left(x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}-2\right)-x \sqrt{x^{2}-1}+\RootOf \left(\textit{\_Z}^{2}-2\right) \left(x^{2}-1\right)^{\frac{1}{4}}-x}{x^{2}-2}\right)}{4}$&$131$\\ \hline \end{longtable}"," ",0,"4*x/(x^2-1)^(1/4)-5/4*RootOf(_Z^2+2)*ln(((x^2-1)^(3/4)*RootOf(_Z^2+2)+x*(x^2-1)^(1/2)-RootOf(_Z^2+2)*(x^2-1)^(1/4)-x)/(x^2-2))-5/4*RootOf(_Z^2-2)*ln(((x^2-1)^(3/4)*RootOf(_Z^2-2)+x*(x^2-1)^(1/2)+RootOf(_Z^2-2)*(x^2-1)^(1/4)+x)/(x^2-2))","C"
882,0,0,11,0.031000," ","int(x^2/(a*x^4-b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{x^{2}}{\left(a \,x^{4}-b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(x^2/(a*x^4-b)/(a*x^4+b*x^2)^(1/4),x)","F"
883,0,0,11,0.000000," ","int(x^2/(a*x^4-b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{x^{2}}{\left(a \,x^{4}-b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(x^2/(a*x^4-b)/(a*x^4+b*x^2)^(1/4),x)","F"
884,0,0,55,0.020000," ","int((x^3+4*b)/(x^3+b)/(a*x^4-x^3-b)^(1/4),x)","\[\int \frac{x^{3}+4 b}{\left(x^{3}+b \right) \left(a \,x^{4}-x^{3}-b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((x^3+4*b)/(x^3+b)/(a*x^4-x^3-b)^(1/4),x)","F"
885,0,0,55,0.022000," ","int((a*x^5+4*b)/(a*x^5-b)/(a*x^5+c*x^4-b)^(1/4),x)","\[\int \frac{a \,x^{5}+4 b}{\left(a \,x^{5}-b \right) \left(a \,x^{5}+c \,x^{4}-b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^5+4*b)/(a*x^5-b)/(a*x^5+c*x^4-b)^(1/4),x)","F"
886,1,132,55,0.577000," ","int((-2*x^6+x^2+1)^(1/2)*(4*x^6+1)/(2*x^6-4*x^2-1)/(2*x^6-2*x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}-2 \sqrt{-2 x^{6}+x^{2}+1}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right)}{2 x^{6}-2 x^{2}-1}\right)}{4}-\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{6}+2 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{2}+6 \sqrt{-2 x^{6}+x^{2}+1}\, x -\RootOf \left(\textit{\_Z}^{2}+3\right)}{2 x^{6}-4 x^{2}-1}\right)}{4}$&$132$\\ \hline \end{longtable}"," ",0,"-1/4*RootOf(_Z^2+1)*ln((2*RootOf(_Z^2+1)*x^6-2*(-2*x^6+x^2+1)^(1/2)*x-RootOf(_Z^2+1))/(2*x^6-2*x^2-1))-1/4*RootOf(_Z^2+3)*ln(-(2*RootOf(_Z^2+3)*x^6+2*RootOf(_Z^2+3)*x^2+6*(-2*x^6+x^2+1)^(1/2)*x-RootOf(_Z^2+3))/(2*x^6-4*x^2-1))","C"
887,1,217,47,2.080000," ","int(x^4/(x^4-1)^(1/4)/(x^8-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{x}{2 \left(x^{4}-1\right)^{\frac{1}{4}}}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(-\frac{\sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{4}-4 \left(x^{4}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right)}{x^{4}+1}\right)}{16}+\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(\frac{\sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{2}+2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}+3 x^{4} \RootOf \left(\textit{\_Z}^{4}-8\right)+4 \left(x^{4}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}-8\right)}{x^{4}+1}\right)}{16}$&$217$\\ risch&$-\frac{x}{2 \left(x^{4}-1\right)^{\frac{1}{4}}}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(-\frac{\sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{4}-4 \left(x^{4}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right)}{x^{4}+1}\right)}{16}+\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(\frac{\sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{2}+2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}+3 x^{4} \RootOf \left(\textit{\_Z}^{4}-8\right)+4 \left(x^{4}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}-8\right)}{x^{4}+1}\right)}{16}$&$217$\\ \hline \end{longtable}"," ",0,"-1/2*x/(x^4-1)^(1/4)+1/16*RootOf(_Z^2+RootOf(_Z^4-8)^2)*ln(-((x^4-1)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x^2+2*(x^4-1)^(1/4)*RootOf(_Z^4-8)^2*x^3-3*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^4-4*(x^4-1)^(3/4)*x+RootOf(_Z^2+RootOf(_Z^4-8)^2))/(x^4+1))+1/16*RootOf(_Z^4-8)*ln(((x^4-1)^(1/2)*RootOf(_Z^4-8)^3*x^2+2*(x^4-1)^(1/4)*RootOf(_Z^4-8)^2*x^3+3*x^4*RootOf(_Z^4-8)+4*(x^4-1)^(3/4)*x-RootOf(_Z^4-8))/(x^4+1))","C"
888,1,238,47,2.451000," ","int(1/(x^4+1)^(1/4)/(x^8-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{x}{2 \left(x^{4}+1\right)^{\frac{1}{4}}}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(-\frac{\sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{4}+4 \left(x^{4}+1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right)}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)}{16}-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(-\frac{\sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{2}+2 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}+3 x^{4} \RootOf \left(\textit{\_Z}^{4}-8\right)+4 \left(x^{4}+1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}-8\right)}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)}{16}$&$238$\\ risch&$-\frac{x}{2 \left(x^{4}+1\right)^{\frac{1}{4}}}+\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(-\frac{-\sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{2}+2 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}-3 x^{4} \RootOf \left(\textit{\_Z}^{4}-8\right)+4 \left(x^{4}+1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}-8\right)}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)}{16}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(-\frac{-\sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{4}+4 \left(x^{4}+1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right)}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)}{16}$&$240$\\ \hline \end{longtable}"," ",0,"-1/2*x/(x^4+1)^(1/4)+1/16*RootOf(_Z^2+RootOf(_Z^4-8)^2)*ln(-((x^4+1)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x^2-2*(x^4+1)^(1/4)*RootOf(_Z^4-8)^2*x^3-3*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^4+4*(x^4+1)^(3/4)*x-RootOf(_Z^2+RootOf(_Z^4-8)^2))/(-1+x)/(1+x)/(x^2+1))-1/16*RootOf(_Z^4-8)*ln(-((x^4+1)^(1/2)*RootOf(_Z^4-8)^3*x^2+2*(x^4+1)^(1/4)*RootOf(_Z^4-8)^2*x^3+3*x^4*RootOf(_Z^4-8)+4*(x^4+1)^(3/4)*x+RootOf(_Z^4-8))/(-1+x)/(1+x)/(x^2+1))","C"
889,1,215,47,2.132000," ","int((2*x^4-1)/(x^4-1)^(1/4)/(x^8-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{x}{2 \left(x^{4}-1\right)^{\frac{1}{4}}}-\frac{3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(\frac{\sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{4}+4 \left(x^{4}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right)}{x^{4}+1}\right)}{16}-\frac{3 \RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(\frac{-\sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{2}+2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}-3 x^{4} \RootOf \left(\textit{\_Z}^{4}-8\right)+4 \left(x^{4}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}-8\right)}{x^{4}+1}\right)}{16}$&$215$\\ trager&$-\frac{x}{2 \left(x^{4}-1\right)^{\frac{1}{4}}}+\frac{3 \RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(\frac{\sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{2}+2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}+3 x^{4} \RootOf \left(\textit{\_Z}^{4}-8\right)+4 \left(x^{4}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}-8\right)}{x^{4}+1}\right)}{16}-\frac{3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(\frac{\sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{4}+4 \left(x^{4}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right)}{x^{4}+1}\right)}{16}$&$216$\\ \hline \end{longtable}"," ",0,"-1/2*x/(x^4-1)^(1/4)-3/16*RootOf(_Z^2+RootOf(_Z^4-8)^2)*ln(((x^4-1)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x^2-2*(x^4-1)^(1/4)*RootOf(_Z^4-8)^2*x^3-3*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^4+4*(x^4-1)^(3/4)*x+RootOf(_Z^2+RootOf(_Z^4-8)^2))/(x^4+1))-3/16*RootOf(_Z^4-8)*ln((-(x^4-1)^(1/2)*RootOf(_Z^4-8)^3*x^2+2*(x^4-1)^(1/4)*RootOf(_Z^4-8)^2*x^3-3*x^4*RootOf(_Z^4-8)+4*(x^4-1)^(3/4)*x+RootOf(_Z^4-8))/(x^4+1))","C"
890,1,78,47,0.465000," ","int((x^8+1)/(x^4+1)^(1/2)/(x^8-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\ln \left(-1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{8}+\frac{\arctan \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{4}-\frac{\ln \left(1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{8}-\frac{\sqrt{2}\, x}{2 \sqrt{x^{4}+1}}\right) \sqrt{2}}{2}$&$78$\\ trager&$-\frac{x}{2 \sqrt{x^{4}+1}}+\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x -\sqrt{x^{4}+1}}{\left(-1+x \right) \left(1+x \right)}\right)}{8}-\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x -\sqrt{x^{4}+1}}{x^{2}+1}\right)}{8}$&$86$\\ default&$\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{2 \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{2 \sqrt{x^{4}+1}}+\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{2 \sqrt{x^{4}+1}}-\frac{x}{2 \sqrt{x^{4}+1}}$&$172$\\ risch&$-\frac{x}{2 \sqrt{x^{4}+1}}+\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{2 \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}-\frac{i \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{4 \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{2 \sqrt{x^{4}+1}}+\frac{i \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \left(\EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)-\EllipticE \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)\right)}{4 \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{i \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticE \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{4 \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{2 \sqrt{x^{4}+1}}$&$375$\\ \hline \end{longtable}"," ",0,"1/2*(1/8*ln(-1+1/2*2^(1/2)/x*(x^4+1)^(1/2))+1/4*arctan(1/2*2^(1/2)/x*(x^4+1)^(1/2))-1/8*ln(1+1/2*2^(1/2)/x*(x^4+1)^(1/2))-1/2*2^(1/2)*x/(x^4+1)^(1/2))*2^(1/2)","A"
891,1,104,47,1.316000," ","int((x^12-1)/(x^4+1)^(1/2)/(x^12+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\sqrt{2}\, 3^{\frac{3}{4}} \arctan \left(\frac{3^{\frac{3}{4}} \sqrt{x^{4}+1}}{3 x}\right)}{9}-\frac{\sqrt{2}\, 3^{\frac{3}{4}} \ln \left(\frac{\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}+\frac{\sqrt{2}\, 3^{\frac{1}{4}}}{2}}{\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}-\frac{\sqrt{2}\, 3^{\frac{1}{4}}}{2}}\right)}{18}-\frac{\sqrt{2}\, x}{3 \sqrt{x^{4}+1}}\right) \sqrt{2}}{2}$&$104$\\ default&$\frac{2 \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{3 \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{6}+\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}+1}\, \sqrt{x^{4}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}+1}}+\frac{2 \left(-1\right)^{\frac{3}{4}} \left(-\underline{\hspace{1.25 ex}}\alpha^{7}+\underline{\hspace{1.25 ex}}\alpha^{3}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \underline{\hspace{1.25 ex}}\alpha^{6}-i \underline{\hspace{1.25 ex}}\alpha^{2}, i\right)}{\sqrt{x^{4}+1}}\right)\right)}{12}-\frac{x}{3 \sqrt{x^{4}+1}}$&$193$\\ risch&$\frac{2 \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{3 \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{6}+\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}+1}\, \sqrt{x^{4}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}+1}}+\frac{2 \left(-1\right)^{\frac{3}{4}} \left(-\underline{\hspace{1.25 ex}}\alpha^{7}+\underline{\hspace{1.25 ex}}\alpha^{3}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \underline{\hspace{1.25 ex}}\alpha^{6}-i \underline{\hspace{1.25 ex}}\alpha^{2}, i\right)}{\sqrt{x^{4}+1}}\right)\right)}{12}-\frac{x}{3 \sqrt{x^{4}+1}}$&$193$\\ trager&$-\frac{x}{3 \sqrt{x^{4}+1}}+\frac{\RootOf \left(\textit{\_Z}^{4}-27\right) \ln \left(-\frac{-x^{2} \RootOf \left(\textit{\_Z}^{4}-27\right)^{3}-3 \RootOf \left(\textit{\_Z}^{4}-27\right) x^{4}+18 \sqrt{x^{4}+1}\, x -3 \RootOf \left(\textit{\_Z}^{4}-27\right)}{\RootOf \left(\textit{\_Z}^{4}-27\right)^{2} x^{2}-3 x^{4}-3}\right)}{18}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-27\right)^{2}\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-27\right)^{2}\right) x^{2} \RootOf \left(\textit{\_Z}^{4}-27\right)^{2}+3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-27\right)^{2}\right) x^{4}+18 \sqrt{x^{4}+1}\, x +3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-27\right)^{2}\right)}{3 x^{4}+\RootOf \left(\textit{\_Z}^{4}-27\right)^{2} x^{2}+3}\right)}{18}$&$196$\\ \hline \end{longtable}"," ",0,"1/2*(1/9*2^(1/2)*3^(3/4)*arctan(1/3*3^(3/4)/x*(x^4+1)^(1/2))-1/18*2^(1/2)*3^(3/4)*ln((1/2*2^(1/2)/x*(x^4+1)^(1/2)+1/2*2^(1/2)*3^(1/4))/(1/2*2^(1/2)/x*(x^4+1)^(1/2)-1/2*2^(1/2)*3^(1/4)))-1/3*2^(1/2)*x/(x^4+1)^(1/2))*2^(1/2)","B"
892,0,0,53,0.013000," ","int((x^2-1)/(x^2+1)^(1/2)/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{x^{2}-1}{\sqrt{x^{2}+1}\, \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^2-1)/(x^2+1)^(1/2)/(x+(x^2+1)^(1/2))^(1/2),x)","F"
893,0,0,53,0.012000," ","int((x^2+1)^(1/2)/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{x^{2}+1}}{\sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^2+1)^(1/2)/(x+(x^2+1)^(1/2))^(1/2),x)","F"
894,0,0,14,0.032000," ","int(1/(a^3*x^2-b)/(a^3*x^3-b*x^2)^(1/3),x)","\[\int \frac{1}{\left(a^{3} x^{2}-b \right) \left(a^{3} x^{3}-b \,x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(a^3*x^2-b)/(a^3*x^3-b*x^2)^(1/3),x)","F"
895,0,0,14,0.000000," ","int(1/(a^3*x^2-b)/(a^3*x^3-b*x^2)^(1/3),x)","\[\int \frac{1}{\left(a^{3} x^{2}-b \right) \left(a^{3} x^{3}-b \,x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(a^3*x^2-b)/(a^3*x^3-b*x^2)^(1/3),x)","F"
896,0,0,14,0.030000," ","int(1/(a*x^2+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{1}{\left(a \,x^{2}+b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(a*x^2+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
897,0,0,14,0.000000," ","int(1/(a*x^2+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{1}{\left(a \,x^{2}+b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(a*x^2+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
898,1,33,56,4.879000," ","int(x^7*(x^4-x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{4 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{4}} x^{\frac{33}{4}} \hypergeom \left(\left[-\frac{1}{4}, \frac{11}{4}\right], \left[\frac{15}{4}\right], x^{3}\right)}{33 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{4}}}$&$33$\\ trager&$\frac{x^{2} \left(32 x^{6}-4 x^{3}-7\right) \left(x^{4}-x \right)^{\frac{1}{4}}}{288}-\frac{7 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-2 \sqrt{x^{4}-x}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x +2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-2 \left(x^{4}-x \right)^{\frac{3}{4}}+2 x^{2} \left(x^{4}-x \right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{384}-\frac{7 \ln \left(-2 \left(x^{4}-x \right)^{\frac{3}{4}}-2 x \sqrt{x^{4}-x}-2 x^{2} \left(x^{4}-x \right)^{\frac{1}{4}}-2 x^{3}+1\right)}{384}$&$147$\\ risch&$\frac{x^{2} \left(32 x^{6}-4 x^{3}-7\right) \left(x \left(x^{3}-1\right)\right)^{\frac{1}{4}}}{288}+\frac{\left(\frac{7 \ln \left(-\frac{-2 x^{9}+2 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}} x^{6}+5 x^{6}-2 \sqrt{x^{12}-3 x^{9}+3 x^{6}-x^{3}}\, x^{3}-4 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}} x^{3}+2 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{3}{4}}-4 x^{3}+2 \sqrt{x^{12}-3 x^{9}+3 x^{6}-x^{3}}+2 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}}+1}{\left(-1+x \right)^{2} \left(x^{2}+x +1\right)^{2}}\right)}{384}-\frac{7 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-2 x^{9}-2 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}+5 x^{6}+2 \sqrt{x^{12}-3 x^{9}+3 x^{6}-x^{3}}\, x^{3}+4 \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{3}{4}}-4 x^{3}-2 \sqrt{x^{12}-3 x^{9}+3 x^{6}-x^{3}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{12}-3 x^{9}+3 x^{6}-x^{3}\right)^{\frac{1}{4}}+1}{\left(-1+x \right)^{2} \left(x^{2}+x +1\right)^{2}}\right)}{384}\right) \left(x \left(x^{3}-1\right)\right)^{\frac{1}{4}} \left(x^{3} \left(x^{3}-1\right)^{3}\right)^{\frac{1}{4}}}{x \left(x^{3}-1\right)}$&$455$\\ \hline \end{longtable}"," ",0,"4/33*signum(x^3-1)^(1/4)/(-signum(x^3-1))^(1/4)*x^(33/4)*hypergeom([-1/4,11/4],[15/4],x^3)","C"
899,1,201,60,8.744000," ","int((x^2+2)*(x^4-x^2-1)^(1/4)*(x^4+x^2+1)/x^6/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{2 \left(x^{4}-x^{2}-1\right)^{\frac{1}{4}} \left(4 x^{4}+x^{2}+1\right)}{5 x^{5}}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}-x^{2}-1}\, x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \left(x^{4}-x^{2}-1\right)^{\frac{3}{4}} x -2 \left(x^{4}-x^{2}-1\right)^{\frac{1}{4}} x^{3}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{2}+1}\right)}{2}+\frac{\ln \left(\frac{2 \left(x^{4}-x^{2}-1\right)^{\frac{3}{4}} x +2 \sqrt{x^{4}-x^{2}-1}\, x^{2}+2 \left(x^{4}-x^{2}-1\right)^{\frac{1}{4}} x^{3}+2 x^{4}-x^{2}-1}{x^{2}+1}\right)}{2}$&$201$\\ risch&$-\frac{2 \left(4 x^{8}-3 x^{6}-4 x^{4}-2 x^{2}-1\right)}{5 x^{5} \left(x^{4}-x^{2}-1\right)^{\frac{3}{4}}}+\frac{\left(-\frac{\ln \left(\frac{-2 x^{12}+2 \left(x^{12}-3 x^{10}+5 x^{6}-3 x^{2}-1\right)^{\frac{1}{4}} x^{9}+5 x^{10}-2 \sqrt{x^{12}-3 x^{10}+5 x^{6}-3 x^{2}-1}\, x^{6}-4 \left(x^{12}-3 x^{10}+5 x^{6}-3 x^{2}-1\right)^{\frac{1}{4}} x^{7}+x^{8}+2 \left(x^{12}-3 x^{10}+5 x^{6}-3 x^{2}-1\right)^{\frac{3}{4}} x^{3}+2 \sqrt{x^{12}-3 x^{10}+5 x^{6}-3 x^{2}-1}\, x^{4}-2 \left(x^{12}-3 x^{10}+5 x^{6}-3 x^{2}-1\right)^{\frac{1}{4}} x^{5}-7 x^{6}+2 \sqrt{x^{12}-3 x^{10}+5 x^{6}-3 x^{2}-1}\, x^{2}+4 \left(x^{12}-3 x^{10}+5 x^{6}-3 x^{2}-1\right)^{\frac{1}{4}} x^{3}-x^{4}+2 \left(x^{12}-3 x^{10}+5 x^{6}-3 x^{2}-1\right)^{\frac{1}{4}} x +3 x^{2}+1}{\left(x^{2}+1\right) \left(x^{4}-x^{2}-1\right)^{2}}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-2 x^{12}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{12}-3 x^{10}+5 x^{6}-3 x^{2}-1\right)^{\frac{1}{4}} x^{9}+5 x^{10}+4 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{12}-3 x^{10}+5 x^{6}-3 x^{2}-1\right)^{\frac{1}{4}} x^{7}+2 \sqrt{x^{12}-3 x^{10}+5 x^{6}-3 x^{2}-1}\, x^{6}+x^{8}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{12}-3 x^{10}+5 x^{6}-3 x^{2}-1\right)^{\frac{3}{4}} x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{12}-3 x^{10}+5 x^{6}-3 x^{2}-1\right)^{\frac{1}{4}} x^{5}-2 \sqrt{x^{12}-3 x^{10}+5 x^{6}-3 x^{2}-1}\, x^{4}-7 x^{6}-4 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{12}-3 x^{10}+5 x^{6}-3 x^{2}-1\right)^{\frac{1}{4}} x^{3}-2 \sqrt{x^{12}-3 x^{10}+5 x^{6}-3 x^{2}-1}\, x^{2}-x^{4}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{12}-3 x^{10}+5 x^{6}-3 x^{2}-1\right)^{\frac{1}{4}} x +3 x^{2}+1}{\left(x^{2}+1\right) \left(x^{4}-x^{2}-1\right)^{2}}\right)}{2}\right) \left(\left(x^{4}-x^{2}-1\right)^{3}\right)^{\frac{1}{4}}}{\left(x^{4}-x^{2}-1\right)^{\frac{3}{4}}}$&$700$\\ \hline \end{longtable}"," ",0,"-2/5*(x^4-x^2-1)^(1/4)*(4*x^4+x^2+1)/x^5+1/2*RootOf(_Z^2+1)*ln((2*RootOf(_Z^2+1)*(x^4-x^2-1)^(1/2)*x^2-2*RootOf(_Z^2+1)*x^4+2*(x^4-x^2-1)^(3/4)*x-2*(x^4-x^2-1)^(1/4)*x^3+RootOf(_Z^2+1)*x^2+RootOf(_Z^2+1))/(x^2+1))+1/2*ln((2*(x^4-x^2-1)^(3/4)*x+2*(x^4-x^2-1)^(1/2)*x^2+2*(x^4-x^2-1)^(1/4)*x^3+2*x^4-x^2-1)/(x^2+1))","C"
900,1,246,54,2.133000," ","int((x^4+x^3)^(1/4)/x^2/(x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{4}+x^{3}\right)^{\frac{1}{4}}}{x}-\frac{\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(\frac{3 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{3}+4 \left(x^{4}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{2}+4 \sqrt{x^{4}+x^{3}}\, \RootOf \left(\textit{\_Z}^{4}-2\right) x +4 \left(x^{4}+x^{3}\right)^{\frac{3}{4}}}{\left(-1+x \right) x^{2}}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(\frac{3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{3}-4 \left(x^{4}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}-4 \sqrt{x^{4}+x^{3}}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x +4 \left(x^{4}+x^{3}\right)^{\frac{3}{4}}}{\left(-1+x \right) x^{2}}\right)}{2}$&$246$\\ risch&$\frac{4 \left(x^{3} \left(1+x \right)\right)^{\frac{1}{4}}}{x}+\frac{\left(\frac{\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(\frac{-2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x -2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}+2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}+4 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x -3 \RootOf \left(\textit{\_Z}^{4}-2\right) x^{3}+4 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{3}{4}}+2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-7 \RootOf \left(\textit{\_Z}^{4}-2\right) x^{2}-5 \RootOf \left(\textit{\_Z}^{4}-2\right) x -\RootOf \left(\textit{\_Z}^{4}-2\right)}{\left(-1+x \right) \left(1+x \right)^{2}}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(\frac{-2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x -2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}-4 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x +3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{3}+4 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{3}{4}}-2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+7 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{2}+5 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)}{\left(-1+x \right) \left(1+x \right)^{2}}\right)}{2}\right) \left(x^{3} \left(1+x \right)\right)^{\frac{1}{4}} \left(\left(1+x \right)^{3} x \right)^{\frac{1}{4}}}{x \left(1+x \right)}$&$541$\\ \hline \end{longtable}"," ",0,"4*(x^4+x^3)^(1/4)/x-1/2*RootOf(_Z^4-2)*ln((3*RootOf(_Z^4-2)^3*x^3+4*(x^4+x^3)^(1/4)*RootOf(_Z^4-2)^2*x^2+RootOf(_Z^4-2)^3*x^2+4*(x^4+x^3)^(1/2)*RootOf(_Z^4-2)*x+4*(x^4+x^3)^(3/4))/(-1+x)/x^2)+1/2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln((3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*x^3-4*(x^4+x^3)^(1/4)*RootOf(_Z^4-2)^2*x^2+RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*x^2-4*(x^4+x^3)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x+4*(x^4+x^3)^(3/4))/(-1+x)/x^2)","C"
901,0,0,54,0.009000," ","int((2*a*x^4+b)/x^2/(a*x^4+b)^(3/4),x)","\[\int \frac{2 a \,x^{4}+b}{x^{2} \left(a \,x^{4}+b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int((2*a*x^4+b)/x^2/(a*x^4+b)^(3/4),x)","F"
902,0,0,54,0.013000," ","int((x^2+1)*(x^6+x^2)^(1/4)/x^2/(x^2-1),x)","\[\int \frac{\left(x^{2}+1\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}}}{x^{2} \left(x^{2}-1\right)}\, dx\]"," ",0,"int((x^2+1)*(x^6+x^2)^(1/4)/x^2/(x^2-1),x)","F"
903,1,113,53,0.993000," ","int((x^3-1)^(1/2)*(x^6-x^3+1)/x^10/(x^3+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(12 x^{6}-5 x^{3}+2\right) \sqrt{x^{3}-1}}{36 x^{9}}-\frac{13 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-2 \RootOf \left(\textit{\_Z}^{2}+1\right)+2 \sqrt{x^{3}-1}}{x^{3}}\right)}{48}-\frac{7 \RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) x^{3}-4 \RootOf \left(\textit{\_Z}^{2}+3\right)-6 \sqrt{x^{3}-1}}{x^{3}+2}\right)}{48}$&$113$\\ risch&$-\frac{12 x^{9}-17 x^{6}+7 x^{3}-2}{36 x^{9} \sqrt{x^{3}-1}}+\frac{13 \arctan \left(\sqrt{x^{3}-1}\right)}{24}-\frac{7 \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+2\right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(-3-i \sqrt{3}\right) \sqrt{\frac{-1+x}{-3-i \sqrt{3}}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{3-i \sqrt{3}}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{\underline{\hspace{1.25 ex}}\alpha}{2}+\frac{1}{2}+\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{6}+\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha }{6}+\frac{i \sqrt{3}}{6}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}\right)}{48}$&$211$\\ default&$-\frac{\sqrt{x^{3}-1}}{18 x^{9}}+\frac{5 \sqrt{x^{3}-1}}{36 x^{6}}-\frac{\sqrt{x^{3}-1}}{3 x^{3}}+\frac{13 \arctan \left(\sqrt{x^{3}-1}\right)}{24}-\frac{7 \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+2\right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(-3-i \sqrt{3}\right) \sqrt{\frac{-1+x}{-3-i \sqrt{3}}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{3-i \sqrt{3}}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{\underline{\hspace{1.25 ex}}\alpha}{2}+\frac{1}{2}+\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{6}+\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha }{6}+\frac{i \sqrt{3}}{6}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}\right)}{48}$&$218$\\ elliptic&$-\frac{\sqrt{x^{3}-1}}{18 x^{9}}+\frac{5 \sqrt{x^{3}-1}}{36 x^{6}}-\frac{\sqrt{x^{3}-1}}{3 x^{3}}+\frac{13 \arctan \left(\sqrt{x^{3}-1}\right)}{24}+\frac{7 \sqrt{2}\, \left(3+i \sqrt{3}\right) \sqrt{-\frac{-1+x}{3+i \sqrt{3}}}\, \sqrt{\frac{i \sqrt{3}-2 x -1}{-3+i \sqrt{3}}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{3+i \sqrt{3}}}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+2\right)}{\sum}\EllipticPi \left(\sqrt{-\frac{2 \left(-1+x \right)}{3+i \sqrt{3}}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{\underline{\hspace{1.25 ex}}\alpha}{2}+\frac{1}{2}+\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{6}+\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha }{6}+\frac{i \sqrt{3}}{6}, \sqrt{-\frac{3+i \sqrt{3}}{-3+i \sqrt{3}}}\right) \underline{\hspace{1.25 ex}}\alpha^{2}\right)}{48 \sqrt{x^{3}-1}}+\frac{7 \sqrt{2}\, \left(3+i \sqrt{3}\right) \sqrt{-\frac{-1+x}{3+i \sqrt{3}}}\, \sqrt{\frac{i \sqrt{3}-2 x -1}{-3+i \sqrt{3}}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{3+i \sqrt{3}}}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+2\right)}{\sum}\EllipticPi \left(\sqrt{-\frac{2 \left(-1+x \right)}{3+i \sqrt{3}}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{\underline{\hspace{1.25 ex}}\alpha}{2}+\frac{1}{2}+\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{6}+\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha }{6}+\frac{i \sqrt{3}}{6}, \sqrt{-\frac{3+i \sqrt{3}}{-3+i \sqrt{3}}}\right) \underline{\hspace{1.25 ex}}\alpha  \right)}{48 \sqrt{x^{3}-1}}+\frac{7 \sqrt{2}\, \left(3+i \sqrt{3}\right) \sqrt{-\frac{-1+x}{3+i \sqrt{3}}}\, \sqrt{\frac{i \sqrt{3}-2 x -1}{-3+i \sqrt{3}}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{3+i \sqrt{3}}}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{3}+2\right)}{\sum}\EllipticPi \left(\sqrt{-\frac{2 \left(-1+x \right)}{3+i \sqrt{3}}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{\underline{\hspace{1.25 ex}}\alpha}{2}+\frac{1}{2}+\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{6}+\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha }{6}+\frac{i \sqrt{3}}{6}, \sqrt{-\frac{3+i \sqrt{3}}{-3+i \sqrt{3}}}\right)\right)}{48 \sqrt{x^{3}-1}}$&$552$\\ \hline \end{longtable}"," ",0,"-1/36*(12*x^6-5*x^3+2)/x^9*(x^3-1)^(1/2)-13/48*RootOf(_Z^2+1)*ln(-(RootOf(_Z^2+1)*x^3-2*RootOf(_Z^2+1)+2*(x^3-1)^(1/2))/x^3)-7/48*RootOf(_Z^2+3)*ln((RootOf(_Z^2+3)*x^3-4*RootOf(_Z^2+3)-6*(x^3-1)^(1/2))/(x^3+2))","C"
904,0,0,52,0.017000," ","int((x^2+x*(x^2+x)^(1/2))^(1/2)/x/(x^2+x)^(1/2),x)","\[\int \frac{\sqrt{x^{2}+x \sqrt{x^{2}+x}}}{x \sqrt{x^{2}+x}}\, dx\]"," ",0,"int((x^2+x*(x^2+x)^(1/2))^(1/2)/x/(x^2+x)^(1/2),x)","F"
905,0,0,14,0.031000," ","int(1/(a*x^2-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{1}{\left(a \,x^{2}-b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(a*x^2-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
906,0,0,14,0.000000," ","int(1/(a*x^2-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{1}{\left(a \,x^{2}-b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(a*x^2-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
907,1,321,61,0.179000," ","int((-a+x)*(-b+x)*(3*a*b-2*(a+b)*x+x^2)/x^2/(x*(-a+x)*(-b+x))^(1/2)/(-a*b+(a+b)*x-x^2+d*x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{2 \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}{x^{2}}-\frac{2 b \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}-\frac{2 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(d \,\textit{\_Z}^{3}-\textit{\_Z}^{2}+\left(a +b \right) \textit{\_Z} -a b \right)}{\sum}\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2} a d +2 \underline{\hspace{1.25 ex}}\alpha^{2} b d -3 \underline{\hspace{1.25 ex}}\alpha  a b d -\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  a +\underline{\hspace{1.25 ex}}\alpha  b -a b \right) \left(\underline{\hspace{1.25 ex}}\alpha^{2} d +\underline{\hspace{1.25 ex}}\alpha  b d +b^{2} d -\underline{\hspace{1.25 ex}}\alpha  +a \right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2} d +\underline{\hspace{1.25 ex}}\alpha  b d +b^{2} d -\underline{\hspace{1.25 ex}}\alpha  +a}{b^{2} d}, \sqrt{\frac{b}{-a +b}}\right)}{\left(-3 \underline{\hspace{1.25 ex}}\alpha^{2} d +2 \underline{\hspace{1.25 ex}}\alpha  -a -b \right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}\right)}{b^{2} d}$&$321$\\ risch&$\frac{2 \left(a -x \right) \left(b -x \right)}{x \sqrt{x \left(-a +x \right) \left(-b +x \right)}}+d \left(-\frac{2 a \sqrt{-\frac{-a +x}{a}}\, \sqrt{\frac{-b +x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticF \left(\sqrt{-\frac{-a +x}{a}}, \sqrt{\frac{a}{a -b}}\right)}{d \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}+\frac{2 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(d \,\textit{\_Z}^{3}-\textit{\_Z}^{2}+\left(a +b \right) \textit{\_Z} -a b \right)}{\sum}\frac{\left(-2 \underline{\hspace{1.25 ex}}\alpha^{2} a d -2 \underline{\hspace{1.25 ex}}\alpha^{2} b d +3 \underline{\hspace{1.25 ex}}\alpha  a b d +\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  b +a b \right) \left(\underline{\hspace{1.25 ex}}\alpha^{2} d +\underline{\hspace{1.25 ex}}\alpha  a d +a^{2} d -\underline{\hspace{1.25 ex}}\alpha  +b \right) \sqrt{-\frac{-a +x}{a}}\, \sqrt{\frac{-b +x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2} d +\underline{\hspace{1.25 ex}}\alpha  a d +a^{2} d -\underline{\hspace{1.25 ex}}\alpha  +b}{a^{2} d}, \sqrt{\frac{a}{a -b}}\right)}{\left(-3 \underline{\hspace{1.25 ex}}\alpha^{2} d +2 \underline{\hspace{1.25 ex}}\alpha  -a -b \right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}\right)}{d^{2} a^{2}}\right)$&$328$\\ default&$\frac{2 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(d \,\textit{\_Z}^{3}-\textit{\_Z}^{2}+\left(a +b \right) \textit{\_Z} -a b \right)}{\sum}\frac{\left(-2 \underline{\hspace{1.25 ex}}\alpha^{2} a d -2 \underline{\hspace{1.25 ex}}\alpha^{2} b d +3 \underline{\hspace{1.25 ex}}\alpha  a b d +\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  a -\underline{\hspace{1.25 ex}}\alpha  b +a b \right) \left(\underline{\hspace{1.25 ex}}\alpha^{2} d +\underline{\hspace{1.25 ex}}\alpha  b d +b^{2} d -\underline{\hspace{1.25 ex}}\alpha  +a \right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2} d +\underline{\hspace{1.25 ex}}\alpha  b d +b^{2} d -\underline{\hspace{1.25 ex}}\alpha  +a}{b^{2} d}, \sqrt{\frac{b}{-a +b}}\right)}{\left(-3 \underline{\hspace{1.25 ex}}\alpha^{2} d +2 \underline{\hspace{1.25 ex}}\alpha  -a -b \right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}\right)}{b^{2} d}-3 a b \left(-\frac{2 \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}{3 a b \,x^{2}}-\frac{4 \left(a b -a x -b x +x^{2}\right) \left(a +b \right)}{3 a^{2} b^{2} \sqrt{x \left(a b -a x -b x +x^{2}\right)}}-\frac{2 \left(-\frac{1}{3 a b}+\frac{2 \left(a +b \right)^{2}}{3 a^{2} b^{2}}+\frac{2 \left(-a -b \right) \left(a +b \right)}{3 a^{2} b^{2}}\right) b \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}-\frac{4 \left(a +b \right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \left(\left(-a +b \right) \EllipticE \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)+a \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)\right)}{3 a^{2} b \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}\right)-\left(-2 a -2 b \right) \left(-\frac{2 \left(a b -a x -b x +x^{2}\right)}{a b \sqrt{x \left(a b -a x -b x +x^{2}\right)}}-\frac{2 \left(\frac{a +b}{a b}+\frac{-a -b}{a b}\right) b \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}-\frac{2 \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \left(\left(-a +b \right) \EllipticE \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)+a \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)\right)}{a \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}\right)$&$818$\\ \hline \end{longtable}"," ",0,"2*(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/x^2-2*b*(-(-b+x)/b)^(1/2)*((-a+x)/(-a+b))^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)*EllipticF((-(-b+x)/b)^(1/2),(b/(-a+b))^(1/2))-2/b^2/d*sum((2*_alpha^2*a*d+2*_alpha^2*b*d-3*_alpha*a*b*d-_alpha^2+_alpha*a+_alpha*b-a*b)/(-3*_alpha^2*d+2*_alpha-a-b)*(_alpha^2*d+_alpha*b*d+b^2*d-_alpha+a)*(-(-b+x)/b)^(1/2)*((-a+x)/(-a+b))^(1/2)*(x/b)^(1/2)/(x*(a*b-a*x-b*x+x^2))^(1/2)*EllipticPi((-(-b+x)/b)^(1/2),(_alpha^2*d+_alpha*b*d+b^2*d-_alpha+a)/b^2/d,(b/(-a+b))^(1/2)),_alpha=RootOf(d*_Z^3-_Z^2+(a+b)*_Z-a*b))","C"
908,1,230,53,5.291000," ","int(1/(x^3+1)/(x^4-x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(-\frac{\sqrt{x^{4}-x}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x -2 \left(x^{4}-x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{3}+4 \left(x^{4}-x \right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right)}{\left(x^{2}-x +1\right) \left(1+x \right)}\right)}{6}+\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(-\frac{\sqrt{x^{4}-x}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x +2 \left(x^{4}-x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+3 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{3}+4 \left(x^{4}-x \right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}-8\right)}{\left(x^{2}-x +1\right) \left(1+x \right)}\right)}{6}$&$230$\\ \hline \end{longtable}"," ",0,"-1/6*RootOf(_Z^2+RootOf(_Z^4-8)^2)*ln(-((x^4-x)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x-2*(x^4-x)^(1/4)*RootOf(_Z^4-8)^2*x^2-3*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^3+4*(x^4-x)^(3/4)+RootOf(_Z^2+RootOf(_Z^4-8)^2))/(x^2-x+1)/(1+x))+1/6*RootOf(_Z^4-8)*ln(-((x^4-x)^(1/2)*RootOf(_Z^4-8)^3*x+2*(x^4-x)^(1/4)*RootOf(_Z^4-8)^2*x^2+3*RootOf(_Z^4-8)*x^3+4*(x^4-x)^(3/4)-RootOf(_Z^4-8))/(x^2-x+1)/(1+x))","C"
909,1,90,55,0.375000," ","int(x*(x^4-x^2)^(1/2)/(2*x^2-3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{4}-x^{2}}}{4}+\frac{\ln \left(\frac{x^{2}+\sqrt{x^{4}-x^{2}}}{x}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}-3\right) x^{2}-3 \RootOf \left(\textit{\_Z}^{2}-3\right)-6 \sqrt{x^{4}-x^{2}}}{2 x^{2}-3}\right)}{8}$&$90$\\ default&$-\frac{\sqrt{x^{4}-x^{2}}\, \left(\sqrt{6}\, \sqrt{2}\, \arctanh \left(\frac{\left(\sqrt{6}\, x +2\right) \sqrt{2}}{2 \sqrt{x^{2}-1}}\right)+\sqrt{6}\, \sqrt{2}\, \arctanh \left(\frac{\left(\sqrt{6}\, x -2\right) \sqrt{2}}{2 \sqrt{x^{2}-1}}\right)-8 \ln \left(x +\sqrt{x^{2}-1}\right)-4 x \sqrt{x^{2}-1}\right)}{16 x \sqrt{x^{2}-1}}$&$101$\\ risch&$\frac{\sqrt{x^{2} \left(x^{2}-1\right)}}{4}+\frac{\left(\frac{\ln \left(x +\sqrt{x^{2}-1}\right)}{2}-\frac{\sqrt{6}\, \sqrt{2}\, \arctanh \left(\frac{\left(1+\sqrt{6}\, \left(x -\frac{\sqrt{6}}{2}\right)\right) \sqrt{2}}{\sqrt{4 \left(x -\frac{\sqrt{6}}{2}\right)^{2}+4 \sqrt{6}\, \left(x -\frac{\sqrt{6}}{2}\right)+2}}\right)}{16}+\frac{\sqrt{6}\, \sqrt{2}\, \arctanh \left(\frac{\left(1-\sqrt{6}\, \left(x +\frac{\sqrt{6}}{2}\right)\right) \sqrt{2}}{\sqrt{4 \left(x +\frac{\sqrt{6}}{2}\right)^{2}-4 \sqrt{6}\, \left(x +\frac{\sqrt{6}}{2}\right)+2}}\right)}{16}\right) \sqrt{x^{2} \left(x^{2}-1\right)}}{x \sqrt{x^{2}-1}}$&$157$\\ \hline \end{longtable}"," ",0,"1/4*(x^4-x^2)^(1/2)+1/2*ln((x^2+(x^4-x^2)^(1/2))/x)+1/8*RootOf(_Z^2-3)*ln(-(4*RootOf(_Z^2-3)*x^2-3*RootOf(_Z^2-3)-6*(x^4-x^2)^(1/2))/(2*x^2-3))","C"
910,1,75,54,0.531000," ","int((x^4-1)*(x^4+1)*(x^4-x^2-1)^(1/2)/(2*x^4-x^2-2)^2/(2*x^4+x^2-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\sqrt{3}\, \arctan \left(\frac{\sqrt{x^{4}-x^{2}-1}\, \sqrt{2}\, \sqrt{3}}{3 x}\right)}{16}-\frac{\sqrt{x^{4}-x^{2}-1}\, \sqrt{2}}{64 x \left(\frac{x^{4}-x^{2}-1}{2 x^{2}}+\frac{1}{4}\right)}\right) \sqrt{2}}{2}$&$75$\\ trager&$-\frac{x \sqrt{x^{4}-x^{2}-1}}{16 \left(2 x^{4}-x^{2}-2\right)}-\frac{\RootOf \left(\textit{\_Z}^{2}+6\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+6\right) x^{4}-5 \RootOf \left(\textit{\_Z}^{2}+6\right) x^{2}+12 x \sqrt{x^{4}-x^{2}-1}-2 \RootOf \left(\textit{\_Z}^{2}+6\right)}{2 x^{4}+x^{2}-2}\right)}{64}$&$100$\\ default&$-\frac{x \sqrt{x^{4}-x^{2}-1}}{16 \left(2 x^{4}-x^{2}-2\right)}+\frac{3 \sqrt{1-\left(-\frac{1}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{-2-2 \sqrt{5}}}{2}, \frac{i \sqrt{5}}{2}-\frac{i}{2}\right)}{16 \sqrt{-2-2 \sqrt{5}}\, \sqrt{x^{4}-x^{2}-1}}+\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(2 \textit{\_Z}^{4}+\textit{\_Z}^{2}-2\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{2 \sqrt{3}\, \arctanh \left(\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \left(-5 \underline{\hspace{1.25 ex}}\alpha^{2}+2 x^{2}-6\right)}{4 \sqrt{-\frac{3 \underline{\hspace{1.25 ex}}\alpha^{2}}{2}}\, \sqrt{x^{4}-x^{2}-1}}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{2}}}-\frac{3 \left(2 \underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{x^{2}+2+\sqrt{5}\, x^{2}}\, \sqrt{x^{2}+2-\sqrt{5}\, x^{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}-\frac{\sqrt{5}}{2}}\, x , \frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{2}-\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{5}}{2}+\frac{1}{4}-\frac{\sqrt{5}}{4}, \frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}}}{\sqrt{-\frac{1}{2}-\frac{\sqrt{5}}{2}}}\right)}{\sqrt{-\sqrt{5}-1}\, \sqrt{x^{4}-x^{2}-1}}\right)\right)}{256}$&$293$\\ risch&$-\frac{x \sqrt{x^{4}-x^{2}-1}}{16 \left(2 x^{4}-x^{2}-2\right)}+\frac{3 \sqrt{1-\left(-\frac{1}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{-2-2 \sqrt{5}}}{2}, \frac{i \sqrt{5}}{2}-\frac{i}{2}\right)}{16 \sqrt{-2-2 \sqrt{5}}\, \sqrt{x^{4}-x^{2}-1}}+\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(2 \textit{\_Z}^{4}+\textit{\_Z}^{2}-2\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{2 \sqrt{3}\, \arctanh \left(\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \left(-5 \underline{\hspace{1.25 ex}}\alpha^{2}+2 x^{2}-6\right)}{4 \sqrt{-\frac{3 \underline{\hspace{1.25 ex}}\alpha^{2}}{2}}\, \sqrt{x^{4}-x^{2}-1}}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{2}}}-\frac{3 \left(2 \underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{x^{2}+2+\sqrt{5}\, x^{2}}\, \sqrt{x^{2}+2-\sqrt{5}\, x^{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}-\frac{\sqrt{5}}{2}}\, x , \frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{2}-\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{5}}{2}+\frac{1}{4}-\frac{\sqrt{5}}{4}, \frac{\sqrt{\frac{\sqrt{5}}{2}-\frac{1}{2}}}{\sqrt{-\frac{1}{2}-\frac{\sqrt{5}}{2}}}\right)}{\sqrt{-\sqrt{5}-1}\, \sqrt{x^{4}-x^{2}-1}}\right)\right)}{256}$&$293$\\ \hline \end{longtable}"," ",0,"1/2*(1/16*3^(1/2)*arctan(1/3*(x^4-x^2-1)^(1/2)*2^(1/2)/x*3^(1/2))-1/64*(x^4-x^2-1)^(1/2)*2^(1/2)/x/(1/2*(x^4-x^2-1)/x^2+1/4))*2^(1/2)","A"
911,0,0,11,0.021000," ","int((a*x^2+b)/(x^4+a*x^2+b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{a \,x^{2}+b}{\left(x^{4}+a \,x^{2}+b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2+b)/(x^4+a*x^2+b)/(a*x^4+b*x^2)^(1/4),x)","F"
912,0,0,11,0.001000," ","int((a*x^2+b)/(x^4+a*x^2+b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{a \,x^{2}+b}{\left(x^{4}+a \,x^{2}+b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2+b)/(x^4+a*x^2+b)/(a*x^4+b*x^2)^(1/4),x)","F"
913,1,63,53,0.177000," ","int((a*x^2-b)*(a^2*x^4+b^2)^(1/2)/x^2/(a*x^2+b),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\sqrt{a^{2} x^{4}+b^{2}}\, \sqrt{2}}{x}-\frac{2 a b \arctan \left(\frac{\sqrt{a^{2} x^{4}+b^{2}}\, \sqrt{2}}{2 x \sqrt{a b}}\right)}{\sqrt{a b}}\right) \sqrt{2}}{2}$&$63$\\ risch&$\frac{\sqrt{a^{2} x^{4}+b^{2}}}{x}-2 b a \left(\frac{\sqrt{1-\frac{i a \,x^{2}}{b}}\, \sqrt{1+\frac{i a \,x^{2}}{b}}\, \EllipticF \left(x \sqrt{\frac{i a}{b}}, i\right)}{\sqrt{\frac{i a}{b}}\, \sqrt{a^{2} x^{4}+b^{2}}}-\frac{2 \sqrt{1-\frac{i a \,x^{2}}{b}}\, \sqrt{1+\frac{i a \,x^{2}}{b}}\, \EllipticPi \left(x \sqrt{\frac{i a}{b}}, i, \frac{\sqrt{-\frac{i a}{b}}}{\sqrt{\frac{i a}{b}}}\right)}{\sqrt{\frac{i a}{b}}\, \sqrt{a^{2} x^{4}+b^{2}}}\right)$&$174$\\ default&$2 a \left(-\frac{b \sqrt{1-\frac{i a \,x^{2}}{b}}\, \sqrt{1+\frac{i a \,x^{2}}{b}}\, \EllipticF \left(x \sqrt{\frac{i a}{b}}, i\right)}{\sqrt{\frac{i a}{b}}\, \sqrt{a^{2} x^{4}+b^{2}}}+\frac{i b \sqrt{1-\frac{i a \,x^{2}}{b}}\, \sqrt{1+\frac{i a \,x^{2}}{b}}\, \EllipticF \left(x \sqrt{\frac{i a}{b}}, i\right)}{\sqrt{\frac{i a}{b}}\, \sqrt{a^{2} x^{4}+b^{2}}}-\frac{i b \sqrt{1-\frac{i a \,x^{2}}{b}}\, \sqrt{1+\frac{i a \,x^{2}}{b}}\, \EllipticE \left(x \sqrt{\frac{i a}{b}}, i\right)}{\sqrt{\frac{i a}{b}}\, \sqrt{a^{2} x^{4}+b^{2}}}+\frac{2 b \sqrt{1-\frac{i a \,x^{2}}{b}}\, \sqrt{1+\frac{i a \,x^{2}}{b}}\, \EllipticPi \left(x \sqrt{\frac{i a}{b}}, i, \frac{\sqrt{-\frac{i a}{b}}}{\sqrt{\frac{i a}{b}}}\right)}{\sqrt{\frac{i a}{b}}\, \sqrt{a^{2} x^{4}+b^{2}}}\right)+\frac{\sqrt{a^{2} x^{4}+b^{2}}}{x}-\frac{2 i a b \sqrt{1-\frac{i a \,x^{2}}{b}}\, \sqrt{1+\frac{i a \,x^{2}}{b}}\, \left(\EllipticF \left(x \sqrt{\frac{i a}{b}}, i\right)-\EllipticE \left(x \sqrt{\frac{i a}{b}}, i\right)\right)}{\sqrt{\frac{i a}{b}}\, \sqrt{a^{2} x^{4}+b^{2}}}$&$398$\\ \hline \end{longtable}"," ",0,"1/2*((a^2*x^4+b^2)^(1/2)*2^(1/2)/x-2*a*b/(a*b)^(1/2)*arctan(1/2*(a^2*x^4+b^2)^(1/2)*2^(1/2)/x/(a*b)^(1/2)))*2^(1/2)","A"
914,0,0,57,0.023000," ","int((a*x^3+4*b)/(a*x^3+b)/(c*x^4-a*x^3-b)^(1/4),x)","\[\int \frac{a \,x^{3}+4 b}{\left(a \,x^{3}+b \right) \left(c \,x^{4}-a \,x^{3}-b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^3+4*b)/(a*x^3+b)/(c*x^4-a*x^3-b)^(1/4),x)","F"
915,1,172,61,5.196000," ","int((x^4-3)*(x^4+1)*(x^4+x^3+1)/x^6/(x^4-x^3+1)/(x^5+x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(3 x^{4}+14 x^{3}+3\right) \left(x^{5}+x \right)^{\frac{3}{4}}}{21 x^{6}}-2 \ln \left(-\frac{x^{4}+2 \left(x^{5}+x \right)^{\frac{3}{4}}+2 \sqrt{x^{5}+x}\, x +2 x^{2} \left(x^{5}+x \right)^{\frac{1}{4}}+x^{3}+1}{x^{4}-x^{3}+1}\right)+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{5}+x}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{5}+x \right)^{\frac{3}{4}}-2 x^{2} \left(x^{5}+x \right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{4}-x^{3}+1}\right)$&$172$\\ risch&$\frac{\frac{4}{7} x^{8}+\frac{8}{7} x^{4}+\frac{4}{7}+\frac{8}{3} x^{7}+\frac{8}{3} x^{3}}{x^{5} \left(x \left(x^{4}+1\right)\right)^{\frac{1}{4}}}+2 \ln \left(-\frac{-x^{4}+2 \left(x^{5}+x \right)^{\frac{3}{4}}-2 \sqrt{x^{5}+x}\, x +2 x^{2} \left(x^{5}+x \right)^{\frac{1}{4}}-x^{3}-1}{x^{4}-x^{3}+1}\right)+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{5}+x}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{5}+x \right)^{\frac{3}{4}}-2 x^{2} \left(x^{5}+x \right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{4}-x^{3}+1}\right)$&$188$\\ \hline \end{longtable}"," ",0,"4/21*(3*x^4+14*x^3+3)*(x^5+x)^(3/4)/x^6-2*ln(-(x^4+2*(x^5+x)^(3/4)+2*(x^5+x)^(1/2)*x+2*x^2*(x^5+x)^(1/4)+x^3+1)/(x^4-x^3+1))+2*RootOf(_Z^2+1)*ln((-RootOf(_Z^2+1)*x^4+2*RootOf(_Z^2+1)*(x^5+x)^(1/2)*x-RootOf(_Z^2+1)*x^3+2*(x^5+x)^(3/4)-2*x^2*(x^5+x)^(1/4)-RootOf(_Z^2+1))/(x^4-x^3+1))","C"
916,1,172,61,4.785000," ","int((x^4-3)*(x^8+x^6+2*x^4+1)/x^6/(x^4-x^3+1)/(x^5+x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(3 x^{4}+7 x^{3}+3\right) \left(x^{5}+x \right)^{\frac{3}{4}}}{21 x^{6}}-2 \ln \left(-\frac{x^{4}+2 \left(x^{5}+x \right)^{\frac{3}{4}}+2 \sqrt{x^{5}+x}\, x +2 x^{2} \left(x^{5}+x \right)^{\frac{1}{4}}+x^{3}+1}{x^{4}-x^{3}+1}\right)+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{5}+x}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{5}+x \right)^{\frac{3}{4}}-2 x^{2} \left(x^{5}+x \right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{4}-x^{3}+1}\right)$&$172$\\ risch&$\frac{\frac{4}{7} x^{8}+\frac{8}{7} x^{4}+\frac{4}{7}+\frac{4}{3} x^{7}+\frac{4}{3} x^{3}}{x^{5} \left(x \left(x^{4}+1\right)\right)^{\frac{1}{4}}}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{5}+x}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{5}+x \right)^{\frac{3}{4}}-2 x^{2} \left(x^{5}+x \right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{4}-x^{3}+1}\right)+2 \ln \left(\frac{-x^{4}+2 \left(x^{5}+x \right)^{\frac{3}{4}}-2 \sqrt{x^{5}+x}\, x +2 x^{2} \left(x^{5}+x \right)^{\frac{1}{4}}-x^{3}-1}{x^{4}-x^{3}+1}\right)$&$187$\\ \hline \end{longtable}"," ",0,"4/21*(3*x^4+7*x^3+3)*(x^5+x)^(3/4)/x^6-2*ln(-(x^4+2*(x^5+x)^(3/4)+2*(x^5+x)^(1/2)*x+2*x^2*(x^5+x)^(1/4)+x^3+1)/(x^4-x^3+1))+2*RootOf(_Z^2+1)*ln((-RootOf(_Z^2+1)*x^4+2*RootOf(_Z^2+1)*(x^5+x)^(1/2)*x-RootOf(_Z^2+1)*x^3+2*(x^5+x)^(3/4)-2*x^2*(x^5+x)^(1/4)-RootOf(_Z^2+1))/(x^4-x^3+1))","C"
917,0,0,50,0.018000," ","int((a*x^3+b)^(3/4)/x,x)","\[\int \frac{\left(a \,x^{3}+b \right)^{\frac{3}{4}}}{x}\, dx\]"," ",0,"int((a*x^3+b)^(3/4)/x,x)","F"
918,1,90,52,11.625000," ","int((3*x^4+3*x+1)/x/(x^4+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\sqrt{2}\, \Gamma \left(\frac{3}{4}\right) \left(-\frac{\pi  \sqrt{2}\, x^{4} \hypergeom \left(\left[1, 1, \frac{5}{4}\right], \left[2, 2\right], -x^{4}\right)}{4 \Gamma \left(\frac{3}{4}\right)}+\frac{\left(-3 \ln \left(2\right)-\frac{\pi}{2}+4 \ln \left(x \right)\right) \pi  \sqrt{2}}{\Gamma \left(\frac{3}{4}\right)}\right)}{8 \pi}+\frac{3 x^{4} \hypergeom \left(\left[\frac{1}{4}, 1\right], \left[2\right], -x^{4}\right)}{4}+3 x \hypergeom \left(\left[\frac{1}{4}, \frac{1}{4}\right], \left[\frac{5}{4}\right], -x^{4}\right)$&$90$\\ trager&$\left(x^{4}+1\right)^{\frac{3}{4}}-\frac{\ln \left(-\frac{-1+3 x -4 x^{4} \sqrt{x^{4}+1}+3 \sqrt{x^{4}+1}\, x +3 x \left(x^{4}+1\right)^{\frac{1}{4}}-8 x^{6} \left(x^{4}+1\right)^{\frac{1}{4}}-5 x^{2} \left(x^{4}+1\right)^{\frac{1}{4}}+8 x^{7}-\sqrt{x^{4}+1}-\left(x^{4}+1\right)^{\frac{1}{4}}+4 x^{5}-4 x^{6}-\left(x^{4}+1\right)^{\frac{3}{4}}-4 x^{2}+7 x^{3}-8 x^{8}-9 x^{4}+7 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}-5 x^{2} \sqrt{x^{4}+1}+3 \left(x^{4}+1\right)^{\frac{3}{4}} x +8 \left(x^{4}+1\right)^{\frac{3}{4}} x^{5}+8 \left(x^{4}+1\right)^{\frac{1}{4}} x^{7}-8 x^{4} \left(x^{4}+1\right)^{\frac{3}{4}}+4 x^{3} \left(x^{4}+1\right)^{\frac{3}{4}}+4 \left(x^{4}+1\right)^{\frac{1}{4}} x^{5}-4 \left(x^{4}+1\right)^{\frac{3}{4}} x^{2}-4 \left(x^{4}+1\right)^{\frac{1}{4}} x^{4}-8 \sqrt{x^{4}+1}\, x^{6}+8 \sqrt{x^{4}+1}\, x^{5}+4 \sqrt{x^{4}+1}\, x^{3}}{x^{2}}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-3 x \left(x^{4}+1\right)^{\frac{1}{4}}+8 x^{6} \left(x^{4}+1\right)^{\frac{1}{4}}+5 x^{2} \left(x^{4}+1\right)^{\frac{1}{4}}+\left(x^{4}+1\right)^{\frac{1}{4}}-\left(x^{4}+1\right)^{\frac{3}{4}}-7 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right)+7 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-9 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+3 \left(x^{4}+1\right)^{\frac{3}{4}} x -4 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+3 \RootOf \left(\textit{\_Z}^{2}+1\right) x +5 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}\, x^{2}+8 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}-8 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x^{5}+4 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-4 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}\, x +8 \left(x^{4}+1\right)^{\frac{3}{4}} x^{5}-8 \left(x^{4}+1\right)^{\frac{1}{4}} x^{7}-8 x^{4} \left(x^{4}+1\right)^{\frac{3}{4}}+4 x^{3} \left(x^{4}+1\right)^{\frac{3}{4}}-4 \left(x^{4}+1\right)^{\frac{1}{4}} x^{5}-4 \left(x^{4}+1\right)^{\frac{3}{4}} x^{2}+4 \left(x^{4}+1\right)^{\frac{1}{4}} x^{4}-8 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{8}+8 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{7}-4 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}+4 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{5}+\RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}}{x^{2}}\right)}{2}$&$679$\\ \hline \end{longtable}"," ",0,"1/8/Pi*2^(1/2)*GAMMA(3/4)*(-1/4*Pi*2^(1/2)/GAMMA(3/4)*x^4*hypergeom([1,1,5/4],[2,2],-x^4)+(-3*ln(2)-1/2*Pi+4*ln(x))*Pi*2^(1/2)/GAMMA(3/4))+3/4*x^4*hypergeom([1/4,1],[2],-x^4)+3*x*hypergeom([1/4,1/4],[5/4],-x^4)","C"
919,0,0,50,0.015000," ","int((a*x^4+b)^(3/4)/x,x)","\[\int \frac{\left(a \,x^{4}+b \right)^{\frac{3}{4}}}{x}\, dx\]"," ",0,"int((a*x^4+b)^(3/4)/x,x)","F"
920,1,79345,60,0.174000," ","int((x^2-1)/(x^2+1)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$79345$\\ elliptic&$\text{Expression too large to display}$&$90322$\\ \hline \end{longtable}"," ",0,"result too large to display","C"
921,1,63,54,0.154000," ","int((a*x^2+b)*(a^2*x^4+b^2)^(1/2)/x^2/(a*x^2-b),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\sqrt{a^{2} x^{4}+b^{2}}\, \sqrt{2}}{x}-\frac{2 a b \arctanh \left(\frac{\sqrt{a^{2} x^{4}+b^{2}}\, \sqrt{2}}{2 x \sqrt{a b}}\right)}{\sqrt{a b}}\right) \sqrt{2}}{2}$&$63$\\ risch&$\frac{\sqrt{a^{2} x^{4}+b^{2}}}{x}+2 b a \left(\frac{\sqrt{1-\frac{i a \,x^{2}}{b}}\, \sqrt{1+\frac{i a \,x^{2}}{b}}\, \EllipticF \left(x \sqrt{\frac{i a}{b}}, i\right)}{\sqrt{\frac{i a}{b}}\, \sqrt{a^{2} x^{4}+b^{2}}}-\frac{2 \sqrt{1-\frac{i a \,x^{2}}{b}}\, \sqrt{1+\frac{i a \,x^{2}}{b}}\, \EllipticPi \left(x \sqrt{\frac{i a}{b}}, -i, \frac{\sqrt{-\frac{i a}{b}}}{\sqrt{\frac{i a}{b}}}\right)}{\sqrt{\frac{i a}{b}}\, \sqrt{a^{2} x^{4}+b^{2}}}\right)$&$174$\\ default&$2 a \left(\frac{b \sqrt{1-\frac{i a \,x^{2}}{b}}\, \sqrt{1+\frac{i a \,x^{2}}{b}}\, \EllipticF \left(x \sqrt{\frac{i a}{b}}, i\right)}{\sqrt{\frac{i a}{b}}\, \sqrt{a^{2} x^{4}+b^{2}}}+\frac{i b \sqrt{1-\frac{i a \,x^{2}}{b}}\, \sqrt{1+\frac{i a \,x^{2}}{b}}\, \EllipticF \left(x \sqrt{\frac{i a}{b}}, i\right)}{\sqrt{\frac{i a}{b}}\, \sqrt{a^{2} x^{4}+b^{2}}}-\frac{i b \sqrt{1-\frac{i a \,x^{2}}{b}}\, \sqrt{1+\frac{i a \,x^{2}}{b}}\, \EllipticE \left(x \sqrt{\frac{i a}{b}}, i\right)}{\sqrt{\frac{i a}{b}}\, \sqrt{a^{2} x^{4}+b^{2}}}-\frac{2 b \sqrt{1-\frac{i a \,x^{2}}{b}}\, \sqrt{1+\frac{i a \,x^{2}}{b}}\, \EllipticPi \left(x \sqrt{\frac{i a}{b}}, -i, \frac{\sqrt{-\frac{i a}{b}}}{\sqrt{\frac{i a}{b}}}\right)}{\sqrt{\frac{i a}{b}}\, \sqrt{a^{2} x^{4}+b^{2}}}\right)+\frac{\sqrt{a^{2} x^{4}+b^{2}}}{x}-\frac{2 i a b \sqrt{1-\frac{i a \,x^{2}}{b}}\, \sqrt{1+\frac{i a \,x^{2}}{b}}\, \left(\EllipticF \left(x \sqrt{\frac{i a}{b}}, i\right)-\EllipticE \left(x \sqrt{\frac{i a}{b}}, i\right)\right)}{\sqrt{\frac{i a}{b}}\, \sqrt{a^{2} x^{4}+b^{2}}}$&$397$\\ \hline \end{longtable}"," ",0,"1/2*((a^2*x^4+b^2)^(1/2)*2^(1/2)/x-2*a*b/(a*b)^(1/2)*arctanh(1/2*(a^2*x^4+b^2)^(1/2)*2^(1/2)/x/(a*b)^(1/2)))*2^(1/2)","A"
922,0,0,50,0.018000," ","int((a*x^5+b)^(3/4)/x,x)","\[\int \frac{\left(a \,x^{5}+b \right)^{\frac{3}{4}}}{x}\, dx\]"," ",0,"int((a*x^5+b)^(3/4)/x,x)","F"
923,1,102,62,0.937000," ","int((2*x^5+3)*(-x^6-2*x^4+x)^(1/2)/(x^5-1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{x \sqrt{-x^{6}-2 x^{4}+x}}{x^{5}-1}-\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x^{5}+4 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{3}+4 \sqrt{-x^{6}-2 x^{4}+x}\, x -\RootOf \left(\textit{\_Z}^{2}+2\right)}{\left(-1+x \right) \left(x^{4}+x^{3}+x^{2}+x +1\right)}\right)}{4}$&$102$\\ risch&$\frac{x^{2} \left(x^{5}+2 x^{3}-1\right)}{\left(x^{5}-1\right) \sqrt{-x \left(x^{5}+2 x^{3}-1\right)}}+\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x^{5}+4 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{3}-4 \sqrt{-x^{6}-2 x^{4}+x}\, x -\RootOf \left(\textit{\_Z}^{2}+2\right)}{\left(-1+x \right) \left(x^{4}+x^{3}+x^{2}+x +1\right)}\right)}{4}$&$115$\\ \hline \end{longtable}"," ",0,"-x*(-x^6-2*x^4+x)^(1/2)/(x^5-1)-1/4*RootOf(_Z^2+2)*ln((RootOf(_Z^2+2)*x^5+4*RootOf(_Z^2+2)*x^3+4*(-x^6-2*x^4+x)^(1/2)*x-RootOf(_Z^2+2))/(-1+x)/(x^4+x^3+x^2+x+1))","C"
924,1,216,62,16.849000," ","int((x^6-2)*(x^6+1)*(x^6-x^4+1)^(1/4)/x^6/(x^6-2*x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{6}-x^{4}+1\right)^{\frac{1}{4}} \left(x^{6}+9 x^{4}+1\right)}{5 x^{5}}+\ln \left(-\frac{-x^{6}+2 \left(x^{6}-x^{4}+1\right)^{\frac{3}{4}} x -2 \sqrt{x^{6}-x^{4}+1}\, x^{2}+2 \left(x^{6}-x^{4}+1\right)^{\frac{1}{4}} x^{3}-1}{\left(-1+x \right) \left(1+x \right) \left(x^{4}-x^{2}-1\right)}\right)+\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{6}-x^{4}+1}\, x^{2}-2 \left(x^{6}-x^{4}+1\right)^{\frac{3}{4}} x +2 \left(x^{6}-x^{4}+1\right)^{\frac{1}{4}} x^{3}-\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(-1+x \right) \left(1+x \right) \left(x^{4}-x^{2}-1\right)}\right)$&$216$\\ risch&$\frac{\frac{2}{5} x^{12}+\frac{16}{5} x^{10}+\frac{4}{5} x^{6}-\frac{18}{5} x^{8}+\frac{16}{5} x^{4}+\frac{2}{5}}{x^{5} \left(x^{6}-x^{4}+1\right)^{\frac{3}{4}}}+\frac{\left(-\ln \left(-\frac{x^{18}-2 x^{16}+2 \left(x^{18}-3 x^{16}+3 x^{14}+2 x^{12}-6 x^{10}+3 x^{8}+3 x^{6}-3 x^{4}+1\right)^{\frac{1}{4}} x^{13}+x^{14}-4 \left(x^{18}-3 x^{16}+3 x^{14}+2 x^{12}-6 x^{10}+3 x^{8}+3 x^{6}-3 x^{4}+1\right)^{\frac{1}{4}} x^{11}+3 x^{12}+2 \sqrt{x^{18}-3 x^{16}+3 x^{14}+2 x^{12}-6 x^{10}+3 x^{8}+3 x^{6}-3 x^{4}+1}\, x^{8}+2 \left(x^{18}-3 x^{16}+3 x^{14}+2 x^{12}-6 x^{10}+3 x^{8}+3 x^{6}-3 x^{4}+1\right)^{\frac{1}{4}} x^{9}-4 x^{10}-2 \sqrt{x^{18}-3 x^{16}+3 x^{14}+2 x^{12}-6 x^{10}+3 x^{8}+3 x^{6}-3 x^{4}+1}\, x^{6}+4 \left(x^{18}-3 x^{16}+3 x^{14}+2 x^{12}-6 x^{10}+3 x^{8}+3 x^{6}-3 x^{4}+1\right)^{\frac{1}{4}} x^{7}+x^{8}+2 \left(x^{18}-3 x^{16}+3 x^{14}+2 x^{12}-6 x^{10}+3 x^{8}+3 x^{6}-3 x^{4}+1\right)^{\frac{3}{4}} x^{3}-4 \left(x^{18}-3 x^{16}+3 x^{14}+2 x^{12}-6 x^{10}+3 x^{8}+3 x^{6}-3 x^{4}+1\right)^{\frac{1}{4}} x^{5}+3 x^{6}+2 \sqrt{x^{18}-3 x^{16}+3 x^{14}+2 x^{12}-6 x^{10}+3 x^{8}+3 x^{6}-3 x^{4}+1}\, x^{2}-2 x^{4}+2 \left(x^{18}-3 x^{16}+3 x^{14}+2 x^{12}-6 x^{10}+3 x^{8}+3 x^{6}-3 x^{4}+1\right)^{\frac{1}{4}} x +1}{\left(x^{6}-x^{4}+1\right)^{2} \left(-1+x \right) \left(1+x \right) \left(x^{4}-x^{2}-1\right)}\right)-\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{18}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{16}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{14}-2 \left(x^{18}-3 x^{16}+3 x^{14}+2 x^{12}-6 x^{10}+3 x^{8}+3 x^{6}-3 x^{4}+1\right)^{\frac{1}{4}} x^{13}+3 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{12}+4 \left(x^{18}-3 x^{16}+3 x^{14}+2 x^{12}-6 x^{10}+3 x^{8}+3 x^{6}-3 x^{4}+1\right)^{\frac{1}{4}} x^{11}-2 \sqrt{x^{18}-3 x^{16}+3 x^{14}+2 x^{12}-6 x^{10}+3 x^{8}+3 x^{6}-3 x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x^{8}-4 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{10}-2 \left(x^{18}-3 x^{16}+3 x^{14}+2 x^{12}-6 x^{10}+3 x^{8}+3 x^{6}-3 x^{4}+1\right)^{\frac{1}{4}} x^{9}+2 \sqrt{x^{18}-3 x^{16}+3 x^{14}+2 x^{12}-6 x^{10}+3 x^{8}+3 x^{6}-3 x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{8}-4 \left(x^{18}-3 x^{16}+3 x^{14}+2 x^{12}-6 x^{10}+3 x^{8}+3 x^{6}-3 x^{4}+1\right)^{\frac{1}{4}} x^{7}+3 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}+2 \left(x^{18}-3 x^{16}+3 x^{14}+2 x^{12}-6 x^{10}+3 x^{8}+3 x^{6}-3 x^{4}+1\right)^{\frac{3}{4}} x^{3}+4 \left(x^{18}-3 x^{16}+3 x^{14}+2 x^{12}-6 x^{10}+3 x^{8}+3 x^{6}-3 x^{4}+1\right)^{\frac{1}{4}} x^{5}-2 \sqrt{x^{18}-3 x^{16}+3 x^{14}+2 x^{12}-6 x^{10}+3 x^{8}+3 x^{6}-3 x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-2 \left(x^{18}-3 x^{16}+3 x^{14}+2 x^{12}-6 x^{10}+3 x^{8}+3 x^{6}-3 x^{4}+1\right)^{\frac{1}{4}} x +\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(x^{6}-x^{4}+1\right)^{2} \left(-1+x \right) \left(1+x \right) \left(x^{4}-x^{2}-1\right)}\right)\right) \left(\left(x^{6}-x^{4}+1\right)^{3}\right)^{\frac{1}{4}}}{\left(x^{6}-x^{4}+1\right)^{\frac{3}{4}}}$&$1238$\\ \hline \end{longtable}"," ",0,"2/5*(x^6-x^4+1)^(1/4)*(x^6+9*x^4+1)/x^5+ln(-(-x^6+2*(x^6-x^4+1)^(3/4)*x-2*(x^6-x^4+1)^(1/2)*x^2+2*(x^6-x^4+1)^(1/4)*x^3-1)/(-1+x)/(1+x)/(x^4-x^2-1))+RootOf(_Z^2+1)*ln((-RootOf(_Z^2+1)*x^6+2*RootOf(_Z^2+1)*(x^6-x^4+1)^(1/2)*x^2-2*(x^6-x^4+1)^(3/4)*x+2*(x^6-x^4+1)^(1/4)*x^3-RootOf(_Z^2+1))/(-1+x)/(1+x)/(x^4-x^2-1))","C"
925,0,0,50,0.018000," ","int((a*x^6+b)^(3/4)/x,x)","\[\int \frac{\left(a \,x^{6}+b \right)^{\frac{3}{4}}}{x}\, dx\]"," ",0,"int((a*x^6+b)^(3/4)/x,x)","F"
926,1,47,50,0.033000," ","int((1+x)^(1/2)/(x+(1+x)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\sqrt{1+x}\, \sqrt{x +\sqrt{1+x}}-\frac{3 \sqrt{x +\sqrt{1+x}}}{2}+\frac{7 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{4}$&$47$\\ default&$\sqrt{1+x}\, \sqrt{x +\sqrt{1+x}}-\frac{3 \sqrt{x +\sqrt{1+x}}}{2}+\frac{7 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{4}$&$47$\\ \hline \end{longtable}"," ",0,"(1+x)^(1/2)*(x+(1+x)^(1/2))^(1/2)-3/2*(x+(1+x)^(1/2))^(1/2)+7/4*ln(1/2+(1+x)^(1/2)+(x+(1+x)^(1/2))^(1/2))","A"
927,1,41,50,0.026000," ","int((x+(1+x)^(1/2))^(1/2)/(1+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\left(2 \sqrt{1+x}+1\right) \sqrt{x +\sqrt{1+x}}}{2}-\frac{5 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{4}$&$41$\\ default&$\frac{\left(2 \sqrt{1+x}+1\right) \sqrt{x +\sqrt{1+x}}}{2}-\frac{5 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{4}$&$41$\\ \hline \end{longtable}"," ",0,"1/2*(2*(1+x)^(1/2)+1)*(x+(1+x)^(1/2))^(1/2)-5/4*ln(1/2+(1+x)^(1/2)+(x+(1+x)^(1/2))^(1/2))","A"
928,0,0,52,0.016000," ","int((x^2-1)*(1+(x^2+1)^(1/2))^(1/2)/(x^2+1),x)","\[\int \frac{\left(x^{2}-1\right) \sqrt{1+\sqrt{x^{2}+1}}}{x^{2}+1}\, dx\]"," ",0,"int((x^2-1)*(1+(x^2+1)^(1/2))^(1/2)/(x^2+1),x)","F"
929,1,51,55,0.060000," ","int(1/(x^2+(x^4+1)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{-\frac{\sqrt{\pi}\, \sqrt{2}\, \hypergeom \left(\left[1, 1, \frac{5}{4}, \frac{7}{4}\right], \left[2, 2, \frac{5}{2}\right], -\frac{1}{x^{4}}\right)}{4 x^{4}}+2 \left(-4 \ln \left(2\right)-2-4 \ln \left(x \right)\right) \sqrt{\pi}\, \sqrt{2}}{16 \sqrt{\pi}}$&$51$\\ \hline \end{longtable}"," ",0,"-1/16/Pi^(1/2)*(-1/4*Pi^(1/2)*2^(1/2)/x^4*hypergeom([1,1,5/4,7/4],[2,2,5/2],-1/x^4)+2*(-4*ln(2)-2-4*ln(x))*Pi^(1/2)*2^(1/2))","C"
930,1,51,56,0.052000," ","int((x^2+(x^4+1)^(1/2))^(1/2)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{-\frac{\sqrt{\pi}\, \sqrt{2}\, \hypergeom \left(\left[\frac{3}{4}, 1, 1, \frac{5}{4}\right], \left[\frac{3}{2}, 2, 2\right], -\frac{1}{x^{4}}\right)}{2 x^{4}}-4 \left(-4 \ln \left(2\right)+4-4 \ln \left(x \right)\right) \sqrt{\pi}\, \sqrt{2}}{16 \sqrt{\pi}}$&$51$\\ \hline \end{longtable}"," ",0,"1/16/Pi^(1/2)*(-1/2*Pi^(1/2)*2^(1/2)/x^4*hypergeom([3/4,1,1,5/4],[3/2,2,2],-1/x^4)-4*(-4*ln(2)+4-4*ln(x))*Pi^(1/2)*2^(1/2))","C"
931,1,67,52,0.061000," ","int(1/((-1+x)^(1/2)+2*x^(1/2))^2/(-1+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{-1+x}}{4 \left(1+3 x \right)}+\frac{4 \sqrt{3}\, \arctan \left(\frac{\sqrt{-1+x}\, \sqrt{3}}{2}\right)}{9}+\frac{4 \sqrt{x}}{9 \left(\frac{1}{3}+x \right)}-\frac{4 \sqrt{3}\, \arctan \left(\sqrt{x}\, \sqrt{3}\right)}{9}-\frac{5 \sqrt{-1+x}}{36 \left(\frac{1}{3}+x \right)}$&$67$\\ \hline \end{longtable}"," ",0,"-1/4*(-1+x)^(1/2)/(1+3*x)+4/9*3^(1/2)*arctan(1/2*(-1+x)^(1/2)*3^(1/2))+4/9*x^(1/2)/(1/3+x)-4/9*3^(1/2)*arctan(x^(1/2)*3^(1/2))-5/36*(-1+x)^(1/2)/(1/3+x)","A"
932,1,52,59,0.245000," ","int(1/(x^2-1)^(1/2)/(3*x^2-4)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{3 x \sqrt{x^{2}-1}}{8 \left(3 x^{2}-4\right)}-\frac{5 \ln \left(-\frac{4 x \sqrt{x^{2}-1}-5 x^{2}+4}{3 x^{2}-4}\right)}{32}$&$52$\\ risch&$-\frac{3 x \sqrt{x^{2}-1}}{8 \left(3 x^{2}-4\right)}+\frac{5 \arctanh \left(\frac{3 \left(\frac{2}{3}+\frac{4 \left(x -\frac{2 \sqrt{3}}{3}\right) \sqrt{3}}{3}\right) \sqrt{3}}{2 \sqrt{9 \left(x -\frac{2 \sqrt{3}}{3}\right)^{2}+12 \left(x -\frac{2 \sqrt{3}}{3}\right) \sqrt{3}+3}}\right)}{32}-\frac{5 \arctanh \left(\frac{3 \left(\frac{2}{3}-\frac{4 \left(x +\frac{2 \sqrt{3}}{3}\right) \sqrt{3}}{3}\right) \sqrt{3}}{2 \sqrt{9 \left(x +\frac{2 \sqrt{3}}{3}\right)^{2}-12 \left(x +\frac{2 \sqrt{3}}{3}\right) \sqrt{3}+3}}\right)}{32}$&$119$\\ default&$-\frac{\sqrt{\left(x -\frac{2 \sqrt{3}}{3}\right)^{2}+\frac{4 \left(x -\frac{2 \sqrt{3}}{3}\right) \sqrt{3}}{3}+\frac{1}{3}}}{16 \left(x -\frac{2 \sqrt{3}}{3}\right)}+\frac{5 \arctanh \left(\frac{3 \left(\frac{2}{3}+\frac{4 \left(x -\frac{2 \sqrt{3}}{3}\right) \sqrt{3}}{3}\right) \sqrt{3}}{2 \sqrt{9 \left(x -\frac{2 \sqrt{3}}{3}\right)^{2}+12 \left(x -\frac{2 \sqrt{3}}{3}\right) \sqrt{3}+3}}\right)}{32}-\frac{5 \arctanh \left(\frac{3 \left(\frac{2}{3}-\frac{4 \left(x +\frac{2 \sqrt{3}}{3}\right) \sqrt{3}}{3}\right) \sqrt{3}}{2 \sqrt{9 \left(x +\frac{2 \sqrt{3}}{3}\right)^{2}-12 \left(x +\frac{2 \sqrt{3}}{3}\right) \sqrt{3}+3}}\right)}{32}-\frac{\sqrt{\left(x +\frac{2 \sqrt{3}}{3}\right)^{2}-\frac{4 \left(x +\frac{2 \sqrt{3}}{3}\right) \sqrt{3}}{3}+\frac{1}{3}}}{16 \left(x +\frac{2 \sqrt{3}}{3}\right)}$&$172$\\ \hline \end{longtable}"," ",0,"-3/8*x/(3*x^2-4)*(x^2-1)^(1/2)-5/32*ln(-(4*x*(x^2-1)^(1/2)-5*x^2+4)/(3*x^2-4))","A"
933,1,63,56,2.532000," ","int(1/x/(x^3+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\frac{2 \pi  \sqrt{3}\, x^{3} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], -x^{3}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{6 \pi}$&$63$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\frac{-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}-2 x^{3}-9 \left(x^{3}+1\right)^{\frac{2}{3}}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-9 \left(x^{3}+1\right)^{\frac{1}{3}}+19 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-5}{x^{3}}\right)}{3}-\frac{\ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+17 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}+15 x^{3}+24 \left(x^{3}+1\right)^{\frac{2}{3}}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+24 \left(x^{3}+1\right)^{\frac{1}{3}}+11 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+20}{x^{3}}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{3}-\frac{\ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+17 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}+15 x^{3}+24 \left(x^{3}+1\right)^{\frac{2}{3}}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+24 \left(x^{3}+1\right)^{\frac{1}{3}}+11 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+20}{x^{3}}\right)}{3}$&$348$\\ \hline \end{longtable}"," ",0,"1/6/Pi*3^(1/2)*GAMMA(2/3)*(-2/9*Pi*3^(1/2)/GAMMA(2/3)*x^3*hypergeom([1,1,4/3],[2,2],-x^3)+2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)+3*ln(x))*Pi*3^(1/2)/GAMMA(2/3))","C"
934,0,0,59,0.017000," ","int(x^2*(3-2*(1+k)*x+k*x^2)/((1-x)*x*(-k*x+1))^(3/4)/(-1+(1+k)*x-k*x^2+d*x^3),x)","\[\int \frac{x^{2} \left(3-2 \left(1+k \right) x +k \,x^{2}\right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{3}{4}} \left(-1+\left(1+k \right) x -k \,x^{2}+d \,x^{3}\right)}\, dx\]"," ",0,"int(x^2*(3-2*(1+k)*x+k*x^2)/((1-x)*x*(-k*x+1))^(3/4)/(-1+(1+k)*x-k*x^2+d*x^3),x)","F"
935,0,0,11,0.022000," ","int((a*x^2-b)/(x^4+a*x^2-b)/(a*x^4-b*x^2)^(1/4),x)","\[\int \frac{a \,x^{2}-b}{\left(x^{4}+a \,x^{2}-b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2-b)/(x^4+a*x^2-b)/(a*x^4-b*x^2)^(1/4),x)","F"
936,0,0,11,0.001000," ","int((a*x^2-b)/(x^4+a*x^2-b)/(a*x^4-b*x^2)^(1/4),x)","\[\int \frac{a \,x^{2}-b}{\left(x^{4}+a \,x^{2}-b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2-b)/(x^4+a*x^2-b)/(a*x^4-b*x^2)^(1/4),x)","F"
937,0,0,14,0.036000," ","int((x^3-x)^(1/3)/(a*x^6+b),x)","\[\int \frac{\left(x^{3}-x \right)^{\frac{1}{3}}}{a \,x^{6}+b}\, dx\]"," ",0,"int((x^3-x)^(1/3)/(a*x^6+b),x)","F"
938,0,0,14,0.002000," ","int((x^3-x)^(1/3)/(a*x^6+b),x)","\[\int \frac{\left(x^{3}-x \right)^{\frac{1}{3}}}{a \,x^{6}+b}\, dx\]"," ",0,"int((x^3-x)^(1/3)/(a*x^6+b),x)","F"
939,0,0,55,0.012000," ","int((a*x^6-2*b)*(a*x^6+b)^(3/4)/x^4/(a*x^6-c*x^4+b),x)","\[\int \frac{\left(a \,x^{6}-2 b \right) \left(a \,x^{6}+b \right)^{\frac{3}{4}}}{x^{4} \left(a \,x^{6}-c \,x^{4}+b \right)}\, dx\]"," ",0,"int((a*x^6-2*b)*(a*x^6+b)^(3/4)/x^4/(a*x^6-c*x^4+b),x)","F"
940,0,0,55,0.021000," ","int((a*x^8+b)/(a*x^8-b)/(a*x^8+c*x^4-b)^(1/4),x)","\[\int \frac{a \,x^{8}+b}{\left(a \,x^{8}-b \right) \left(a \,x^{8}+c \,x^{4}-b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^8+b)/(a*x^8-b)/(a*x^8+c*x^4-b)^(1/4),x)","F"
941,1,153,59,1.528000," ","int((x^5+1)^(1/2)*(3*x^5-2)/(x^10+2*x^5+x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{5}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{5} x^{2}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+2 \sqrt{x^{5}+1}\, x}{-x^{5}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}-1}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}+1\right) x^{5}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}+2 \sqrt{x^{5}+1}\, x -\RootOf \left(\textit{\_Z}^{4}+1\right)}{x^{5}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}+1}\right)}{2}$&$153$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^4+1)^3*ln((-RootOf(_Z^4+1)^3*x^5-RootOf(_Z^4+1)^5*x^2-RootOf(_Z^4+1)^3+2*(x^5+1)^(1/2)*x)/(-x^5+RootOf(_Z^4+1)^2*x^2-1))+1/2*RootOf(_Z^4+1)*ln((-RootOf(_Z^4+1)*x^5+RootOf(_Z^4+1)^3*x^2+2*(x^5+1)^(1/2)*x-RootOf(_Z^4+1))/(x^5+RootOf(_Z^4+1)^2*x^2+1))","C"
942,1,72,56,0.223000," ","int(1/(2*x+(x^2+1)^(1/2))^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{4 x}{3 \left(3 x^{2}-1\right)}+\frac{2 \sqrt{x^{2}+1}}{3 \left(3 x^{2}-1\right)}-\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}-3\right)-3 \sqrt{x^{2}+1}}{\RootOf \left(\textit{\_Z}^{2}-3\right) x -1}\right)}{9}$&$72$\\ default&$-\frac{x}{2 \left(3 x^{2}-1\right)}-\frac{\sqrt{3}\, \arctanh \left(x \sqrt{3}\right)}{9}-\frac{5 x}{18 \left(x^{2}-\frac{1}{3}\right)}-\sqrt{3}\, \left(-\frac{\left(\left(x -\frac{\sqrt{3}}{3}\right)^{2}+\frac{2 \left(x -\frac{\sqrt{3}}{3}\right) \sqrt{3}}{3}+\frac{4}{3}\right)^{\frac{3}{2}}}{12 \left(x -\frac{\sqrt{3}}{3}\right)}+\frac{\sqrt{3}\, \left(\frac{\sqrt{9 \left(x -\frac{\sqrt{3}}{3}\right)^{2}+6 \left(x -\frac{\sqrt{3}}{3}\right) \sqrt{3}+12}}{3}+\frac{\sqrt{3}\, \arcsinh \left(x \right)}{3}-\frac{2 \sqrt{3}\, \arctanh \left(\frac{3 \left(\frac{8}{3}+\frac{2 \left(x -\frac{\sqrt{3}}{3}\right) \sqrt{3}}{3}\right) \sqrt{3}}{4 \sqrt{9 \left(x -\frac{\sqrt{3}}{3}\right)^{2}+6 \left(x -\frac{\sqrt{3}}{3}\right) \sqrt{3}+12}}\right)}{3}\right)}{36}+\frac{x \sqrt{\left(x -\frac{\sqrt{3}}{3}\right)^{2}+\frac{2 \left(x -\frac{\sqrt{3}}{3}\right) \sqrt{3}}{3}+\frac{4}{3}}}{12}+\frac{\arcsinh \left(x \right)}{12}\right)+\sqrt{3}\, \left(-\frac{\left(\left(x +\frac{\sqrt{3}}{3}\right)^{2}-\frac{2 \left(x +\frac{\sqrt{3}}{3}\right) \sqrt{3}}{3}+\frac{4}{3}\right)^{\frac{3}{2}}}{12 \left(x +\frac{\sqrt{3}}{3}\right)}-\frac{\sqrt{3}\, \left(\frac{\sqrt{9 \left(x +\frac{\sqrt{3}}{3}\right)^{2}-6 \left(x +\frac{\sqrt{3}}{3}\right) \sqrt{3}+12}}{3}-\frac{\sqrt{3}\, \arcsinh \left(x \right)}{3}-\frac{2 \sqrt{3}\, \arctanh \left(\frac{3 \left(\frac{8}{3}-\frac{2 \left(x +\frac{\sqrt{3}}{3}\right) \sqrt{3}}{3}\right) \sqrt{3}}{4 \sqrt{9 \left(x +\frac{\sqrt{3}}{3}\right)^{2}-6 \left(x +\frac{\sqrt{3}}{3}\right) \sqrt{3}+12}}\right)}{3}\right)}{36}+\frac{x \sqrt{\left(x +\frac{\sqrt{3}}{3}\right)^{2}-\frac{2 \left(x +\frac{\sqrt{3}}{3}\right) \sqrt{3}}{3}+\frac{4}{3}}}{12}+\frac{\arcsinh \left(x \right)}{12}\right)$&$370$\\ \hline \end{longtable}"," ",0,"-4/3*x/(3*x^2-1)+2/3/(3*x^2-1)*(x^2+1)^(1/2)-1/9*RootOf(_Z^2-3)*ln((2*RootOf(_Z^2-3)-3*(x^2+1)^(1/2))/(RootOf(_Z^2-3)*x-1))","C"
943,0,0,57,0.033000," ","int((a*x^2+x*(a^2*x^2-b)^(1/2))^(1/2)/x/(a^2*x^2-b)^(1/2),x)","\[\int \frac{\sqrt{a \,x^{2}+x \sqrt{a^{2} x^{2}-b}}}{x \sqrt{a^{2} x^{2}-b}}\, dx\]"," ",0,"int((a*x^2+x*(a^2*x^2-b)^(1/2))^(1/2)/x/(a^2*x^2-b)^(1/2),x)","F"
944,0,0,9,0.014000," ","int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1),x)","\[\int \frac{\sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{x^{2}+1}\, dx\]"," ",0,"int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1),x)","F"
945,0,0,9,0.001000," ","int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1),x)","\[\int \frac{\sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{x^{2}+1}\, dx\]"," ",0,"int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1),x)","F"
946,0,0,22,180.000000," ","int((x^2+2*x+1)^(1/3)/(x^3+x^2+x+4),x)","\[\int \frac{\left(x^{2}+2 x +1\right)^{\frac{1}{3}}}{x^{3}+x^{2}+x +4}\, dx\]"," ",0,"int((x^2+2*x+1)^(1/3)/(x^3+x^2+x+4),x)","F"
947,1,198,63,1.049000," ","int((x^2-1)*(x^4+1)^(1/2)/(x^2-x+1)/(x^2+x+1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{4}+1}}{2 x^{2}+2 x +2}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{8}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{7}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}+4 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{5}-2 \sqrt{x^{4}+1}\, x^{5}+5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-2 x^{4} \sqrt{x^{4}+1}+4 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-2 \sqrt{x^{4}+1}\, x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-2 x^{2} \sqrt{x^{4}+1}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \sqrt{x^{4}+1}\, x +\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(x^{2}-x +1\right) \left(x^{2}+x +1\right)^{3}}\right)}{4}$&$198$\\ risch&$\frac{\sqrt{x^{4}+1}}{2 x^{2}+2 x +2}+\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{2 \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{3 \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{\arctanh \left(\frac{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \left(x^{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{4}+\frac{3 \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(\frac{\arctanh \left(\frac{\sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}\, \left(x^{2}-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{4}-\frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{\arctanh \left(\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x^{2}-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{4}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-\frac{\arctanh \left(\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x^{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{4}$&$539$\\ elliptic&$-\frac{\sqrt{2}\, \sqrt{\frac{2 \left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+2}\, \left(\sqrt{3}\, \arctanh \left(\frac{\sqrt{\frac{2 \left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+2}\, \sqrt{3}}{2}\right)-9 \arctan \left(\frac{\sqrt{\frac{2 \left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+2}\, \left(x^{2}+1\right)}{\left(\frac{\left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+1\right) \left(-x^{2}+1\right)}\right)\right)}{12 \sqrt{\frac{\frac{\left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+1}{\left(\frac{x^{2}+1}{-x^{2}+1}+1\right)^{2}}}\, \left(\frac{x^{2}+1}{-x^{2}+1}+1\right)}+\frac{\left(\frac{3 \sqrt{3}\, \arctanh \left(\frac{\sqrt{\frac{2 \left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+2}\, \sqrt{3}}{2}\right) \left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}-\frac{9 \arctan \left(\frac{\sqrt{\frac{2 \left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+2}\, \left(x^{2}+1\right)}{\left(\frac{\left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+1\right) \left(-x^{2}+1\right)}\right) \left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+\sqrt{3}\, \arctanh \left(\frac{\sqrt{\frac{2 \left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+2}\, \sqrt{3}}{2}\right)+\frac{6 \sqrt{\frac{2 \left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+2}\, \left(x^{2}+1\right)}{-x^{2}+1}-3 \arctan \left(\frac{\sqrt{\frac{2 \left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+2}\, \left(x^{2}+1\right)}{\left(\frac{\left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+1\right) \left(-x^{2}+1\right)}\right)\right) \sqrt{\frac{2 \left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+2}\, \sqrt{2}}{12 \left(\frac{3 \left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+1\right) \sqrt{\frac{\frac{\left(x^{2}+1\right)^{2}}{\left(-x^{2}+1\right)^{2}}+1}{\left(\frac{x^{2}+1}{-x^{2}+1}+1\right)^{2}}}\, \left(\frac{x^{2}+1}{-x^{2}+1}+1\right)}+\frac{\left(-\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{4 x \left(\frac{x^{4}+1}{2 x^{2}}+\frac{1}{2}\right)}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{x^{4}+1}}{x}\right)}{2}\right) \sqrt{2}}{2}$&$602$\\ default&$\frac{\sqrt{x^{4}+1}}{2 x^{2}+2 x +2}+\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{2 \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}-\frac{i \sqrt{3}\, \left(\frac{\arctanh \left(\frac{\sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}\, \left(x^{2}-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{3}+\frac{i \sqrt{3}\, \left(\frac{\arctanh \left(\frac{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \left(x^{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{3}-\frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{\arctanh \left(\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x^{2}-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{4}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-\frac{\arctanh \left(\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x^{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{4}-\frac{\left(\frac{3}{2}-\frac{i \sqrt{3}}{6}\right) \left(\frac{\arctanh \left(\frac{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \left(x^{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{4}-\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{6}\right) \left(\frac{\arctanh \left(\frac{\sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}\, \left(x^{2}-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{4}$&$753$\\ \hline \end{longtable}"," ",0,"1/2*(x^4+1)^(1/2)/(x^2+x+1)+1/4*RootOf(_Z^2+1)*ln(-(RootOf(_Z^2+1)*x^8+2*RootOf(_Z^2+1)*x^7+2*RootOf(_Z^2+1)*x^6+4*RootOf(_Z^2+1)*x^5-2*(x^4+1)^(1/2)*x^5+5*RootOf(_Z^2+1)*x^4-2*x^4*(x^4+1)^(1/2)+4*RootOf(_Z^2+1)*x^3-2*(x^4+1)^(1/2)*x^3+2*RootOf(_Z^2+1)*x^2-2*x^2*(x^4+1)^(1/2)+2*RootOf(_Z^2+1)*x-2*(x^4+1)^(1/2)*x+RootOf(_Z^2+1))/(x^2-x+1)/(x^2+x+1)^3)","C"
948,1,33,60,3.200000," ","int(x^4*(x^4-x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{2 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{4}} x^{\frac{11}{2}} \hypergeom \left(\left[-\frac{1}{4}, \frac{11}{4}\right], \left[\frac{15}{4}\right], x^{2}\right)}{11 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{4}}}$&$33$\\ trager&$\frac{x \left(32 x^{4}-4 x^{2}-7\right) \left(x^{4}-x^{2}\right)^{\frac{1}{4}}}{192}+\frac{7 \ln \left(\frac{2 \left(x^{4}-x^{2}\right)^{\frac{3}{4}}-2 \sqrt{x^{4}-x^{2}}\, x +2 x^{2} \left(x^{4}-x^{2}\right)^{\frac{1}{4}}-2 x^{3}+x}{x}\right)}{256}+\frac{7 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-2 \sqrt{x^{4}-x^{2}}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x +2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{4}-x^{2}\right)^{\frac{3}{4}}-2 x^{2} \left(x^{4}-x^{2}\right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right) x}{x}\right)}{256}$&$168$\\ risch&$\frac{x \left(32 x^{4}-4 x^{2}-7\right) \left(x^{2} \left(x^{2}-1\right)\right)^{\frac{1}{4}}}{192}+\frac{\left(\frac{7 \ln \left(-\frac{-2 x^{6}+2 \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}} x^{4}-2 \sqrt{x^{8}-3 x^{6}+3 x^{4}-x^{2}}\, x^{2}+5 x^{4}+2 \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{3}{4}}-4 \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}} x^{2}+2 \sqrt{x^{8}-3 x^{6}+3 x^{4}-x^{2}}-4 x^{2}+2 \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}}+1}{\left(-1+x \right)^{2} \left(1+x \right)^{2}}\right)}{256}-\frac{7 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-2 \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-2 x^{6}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{3}{4}}+2 \sqrt{x^{8}-3 x^{6}+3 x^{4}-x^{2}}\, x^{2}+4 \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+5 x^{4}-2 \sqrt{x^{8}-3 x^{6}+3 x^{4}-x^{2}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}}-4 x^{2}+1}{\left(-1+x \right)^{2} \left(1+x \right)^{2}}\right)}{256}\right) \left(x^{2} \left(x^{2}-1\right)\right)^{\frac{1}{4}} \left(x^{2} \left(x^{2}-1\right)^{3}\right)^{\frac{1}{4}}}{x \left(x^{2}-1\right)}$&$451$\\ \hline \end{longtable}"," ",0,"2/11*signum(x^2-1)^(1/4)/(-signum(x^2-1))^(1/4)*x^(11/2)*hypergeom([-1/4,11/4],[15/4],x^2)","C"
949,1,15,60,0.692000," ","int(x^4*(x^4+x^3)^(1/4)/(1+x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{4 x^{\frac{23}{4}} \hypergeom \left(\left[\frac{3}{4}, \frac{23}{4}\right], \left[\frac{27}{4}\right], -x \right)}{23}$&$15$\\ trager&$\left(\frac{1}{5} x^{4}-\frac{19}{80} x^{3}+\frac{19}{64} x^{2}-\frac{209}{512} x +\frac{1463}{2048}\right) \left(x^{4}+x^{3}\right)^{\frac{1}{4}}-\frac{4389 \ln \left(\frac{2 \left(x^{4}+x^{3}\right)^{\frac{3}{4}}+2 \sqrt{x^{4}+x^{3}}\, x +2 x^{2} \left(x^{4}+x^{3}\right)^{\frac{1}{4}}+2 x^{3}+x^{2}}{x^{2}}\right)}{8192}+\frac{4389 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-2 \sqrt{x^{4}+x^{3}}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x +2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{4}+x^{3}\right)^{\frac{3}{4}}-2 x^{2} \left(x^{4}+x^{3}\right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}}{x^{2}}\right)}{8192}$&$163$\\ risch&$\frac{\left(2048 x^{4}-2432 x^{3}+3040 x^{2}-4180 x +7315\right) \left(x^{3} \left(1+x \right)\right)^{\frac{1}{4}}}{10240}+\frac{\left(\frac{4389 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, \RootOf \left(\textit{\_Z}^{2}+1\right)-5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{3}{4}}-2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x^{2}-4 \RootOf \left(\textit{\_Z}^{2}+1\right) x -4 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x -\RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}}}{\left(1+x \right)^{2}}\right)}{8192}+\frac{4389 \ln \left(\frac{2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{3}{4}}-2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, x +2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x^{2}-2 x^{3}-2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}+4 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x -5 x^{2}+2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}}-4 x -1}{\left(1+x \right)^{2}}\right)}{8192}\right) \left(x^{3} \left(1+x \right)\right)^{\frac{1}{4}} \left(\left(1+x \right)^{3} x \right)^{\frac{1}{4}}}{x \left(1+x \right)}$&$390$\\ \hline \end{longtable}"," ",0,"4/23*x^(23/4)*hypergeom([3/4,23/4],[27/4],-x)","C"
950,0,0,57,0.012000," ","int((a*x^3+4*b)*(-a*x^3+x^4-b)/x^4/(a*x^3+b)^(1/4)/(-a*x^3+2*x^4-b),x)","\[\int \frac{\left(a \,x^{3}+4 b \right) \left(-a \,x^{3}+x^{4}-b \right)}{x^{4} \left(a \,x^{3}+b \right)^{\frac{1}{4}} \left(-a \,x^{3}+2 x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^3+4*b)*(-a*x^3+x^4-b)/x^4/(a*x^3+b)^(1/4)/(-a*x^3+2*x^4-b),x)","F"
951,0,0,11,0.029000," ","int((a*x^2+b)/(a*x^4+b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{a \,x^{2}+b}{\left(a \,x^{4}+b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2+b)/(a*x^4+b)/(a*x^4+b*x^2)^(1/4),x)","F"
952,0,0,11,0.001000," ","int((a*x^2+b)/(a*x^4+b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{a \,x^{2}+b}{\left(a \,x^{4}+b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2+b)/(a*x^4+b)/(a*x^4+b*x^2)^(1/4),x)","F"
953,1,64,64,0.157000," ","int((1-x)/(x^6+2*x^5+x^4-4*x^3-5*x^2+2*x+3)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(x^{2}-1\right) \sqrt{x^{2}+2 x +3}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{2}}{\sqrt{x^{2}+2 x +3}}\right)}{2 \sqrt{x^{6}+2 x^{5}+x^{4}-4 x^{3}-5 x^{2}+2 x +3}}$&$64$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}+\sqrt{x^{6}+2 x^{5}+x^{4}-4 x^{3}-5 x^{2}+2 x +3}+\RootOf \left(\textit{\_Z}^{2}-2\right)}{\left(-1+x \right) \left(1+x \right)^{2}}\right)}{2}$&$68$\\ \hline \end{longtable}"," ",0,"1/2/(x^6+2*x^5+x^4-4*x^3-5*x^2+2*x+3)^(1/2)*(x^2-1)*(x^2+2*x+3)^(1/2)*2^(1/2)*arctanh(2^(1/2)/(x^2+2*x+3)^(1/2))","A"
954,1,90,64,0.746000," ","int((3*x^4-1)*(x^8+2*x^4+x^2+1)^(1/2)/(x^4-x+1)^2/(x^4+x+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\sqrt{x^{8}+2 x^{4}+x^{2}+1}}{2 \left(x^{4}-x +1\right)}-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x^{4}-\RootOf \left(\textit{\_Z}^{2}-2\right) x +\RootOf \left(\textit{\_Z}^{2}-2\right)-2 \sqrt{x^{8}+2 x^{4}+x^{2}+1}}{x^{4}+x +1}\right)}{4}$&$90$\\ risch&$-\frac{\sqrt{x^{8}+2 x^{4}+x^{2}+1}}{2 \left(x^{4}-x +1\right)}-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x^{4}-\RootOf \left(\textit{\_Z}^{2}-2\right) x +\RootOf \left(\textit{\_Z}^{2}-2\right)-2 \sqrt{x^{8}+2 x^{4}+x^{2}+1}}{x^{4}+x +1}\right)}{4}$&$90$\\ \hline \end{longtable}"," ",0,"-1/2/(x^4-x+1)*(x^8+2*x^4+x^2+1)^(1/2)-1/4*RootOf(_Z^2-2)*ln((RootOf(_Z^2-2)*x^4-RootOf(_Z^2-2)*x+RootOf(_Z^2-2)-2*(x^8+2*x^4+x^2+1)^(1/2))/(x^4+x+1))","C"
955,1,65,61,0.190000," ","int((a*x^2+b*x+c)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(2 a x +b \right) \sqrt{a \,x^{2}+b x +c}}{4 a}+\frac{\left(4 a c -b^{2}\right) \ln \left(\frac{\frac{b}{2}+a x}{\sqrt{a}}+\sqrt{a \,x^{2}+b x +c}\right)}{8 a^{\frac{3}{2}}}$&$65$\\ risch&$\frac{\left(2 a x +b \right) \sqrt{a \,x^{2}+b x +c}}{4 a}+\frac{\ln \left(\frac{\frac{b}{2}+a x}{\sqrt{a}}+\sqrt{a \,x^{2}+b x +c}\right) c}{2 \sqrt{a}}-\frac{\ln \left(\frac{\frac{b}{2}+a x}{\sqrt{a}}+\sqrt{a \,x^{2}+b x +c}\right) b^{2}}{8 a^{\frac{3}{2}}}$&$89$\\ \hline \end{longtable}"," ",0,"1/4*(2*a*x+b)*(a*x^2+b*x+c)^(1/2)/a+1/8*(4*a*c-b^2)/a^(3/2)*ln((1/2*b+a*x)/a^(1/2)+(a*x^2+b*x+c)^(1/2))","A"
956,1,116,57,1.223000," ","int((-1+x)/(x^2-2*x-1)/(x^3-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{1}{-2-\sqrt{2}}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{3}-x}\, \left(-2-\sqrt{2}\right)}+\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{1}{-2+\sqrt{2}}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{3}-x}\, \left(-2+\sqrt{2}\right)}$&$116$\\ elliptic&$\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{1}{-2-\sqrt{2}}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{3}-x}\, \left(-2-\sqrt{2}\right)}+\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{1}{-2+\sqrt{2}}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{3}-x}\, \left(-2+\sqrt{2}\right)}$&$116$\\ trager&$\frac{\RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) \ln \left(-\frac{278808 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2} x^{2}-1394040 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2} x +63721 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) x^{2}+1672848 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2}-1038514 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) \sqrt{x^{3}-x}-2862728 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) x -148735 x^{2}+2926449 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)-886429 \sqrt{x^{3}-x}-1427856 x +1279121}{\left(4 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) x -8 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)+3 x -7\right)^{2}}\right)}{2}-\frac{\ln \left(-\frac{278808 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2} x^{2}-1394040 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2} x +493895 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) x^{2}+1672848 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2}+1038514 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) \sqrt{x^{3}-x}+74648 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) x +66352 x^{2}+419247 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)+152085 \sqrt{x^{3}-x}+40832 x +25520}{\left(4 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) x -8 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)+x -1\right)^{2}}\right) \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)}{2}-\frac{\ln \left(-\frac{278808 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2} x^{2}-1394040 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2} x +493895 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) x^{2}+1672848 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2}+1038514 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) \sqrt{x^{3}-x}+74648 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) x +66352 x^{2}+419247 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)+152085 \sqrt{x^{3}-x}+40832 x +25520}{\left(4 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) x -8 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)+x -1\right)^{2}}\right)}{2}$&$542$\\ \hline \end{longtable}"," ",0,"1/2*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/(-2-2^(1/2))*EllipticPi((1+x)^(1/2),-1/(-2-2^(1/2)),1/2*2^(1/2))+1/2*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/(-2+2^(1/2))*EllipticPi((1+x)^(1/2),-1/(-2+2^(1/2)),1/2*2^(1/2))","C"
957,1,273,57,1.303000," ","int((x^2+3*x-2)/(x^2-2*x-1)/(x^3-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticF \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}}+\frac{\sqrt{2}\, \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{1}{-2-\sqrt{2}}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}\, \left(-2-\sqrt{2}\right)}+\frac{5 \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{1}{-2-\sqrt{2}}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{3}-x}\, \left(-2-\sqrt{2}\right)}-\frac{\sqrt{2}\, \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{1}{-2+\sqrt{2}}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}\, \left(-2+\sqrt{2}\right)}+\frac{5 \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{1}{-2+\sqrt{2}}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{3}-x}\, \left(-2+\sqrt{2}\right)}$&$273$\\ elliptic&$\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticF \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}}+\frac{\sqrt{2}\, \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{1}{-2-\sqrt{2}}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}\, \left(-2-\sqrt{2}\right)}+\frac{5 \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{1}{-2-\sqrt{2}}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{3}-x}\, \left(-2-\sqrt{2}\right)}-\frac{\sqrt{2}\, \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{1}{-2+\sqrt{2}}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}\, \left(-2+\sqrt{2}\right)}+\frac{5 \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{1}{-2+\sqrt{2}}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{3}-x}\, \left(-2+\sqrt{2}\right)}$&$273$\\ trager&$\frac{\RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right) \ln \left(-\frac{-278808 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right)^{2} x^{2}+1394040 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right)^{2} x +621337 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right) x^{2}+1038514 \sqrt{x^{3}-x}\, \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right)-1672848 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right)^{2}-5650808 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right) x -193794 x^{2}-1924943 \sqrt{x^{3}-x}+6272145 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right)+5684624 x -5878418}{\left(4 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right) x -8 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right)-7 x +15\right)^{2}}\right)}{2}-\frac{\ln \left(\frac{278808 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right)^{2} x^{2}-1394040 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right)^{2} x -1051511 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right) x^{2}+1038514 \sqrt{x^{3}-x}\, \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right)+1672848 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right)^{2}+2713432 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right) x +839055 x^{2}-1190599 \sqrt{x^{3}-x}-3764943 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right)-1278560 x +2117615}{\left(4 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right) x -8 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right)-5 x +9\right)^{2}}\right) \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right)}{2}+\frac{3 \ln \left(\frac{278808 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right)^{2} x^{2}-1394040 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right)^{2} x -1051511 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right) x^{2}+1038514 \sqrt{x^{3}-x}\, \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right)+1672848 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right)^{2}+2713432 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right) x +839055 x^{2}-1190599 \sqrt{x^{3}-x}-3764943 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right)-1278560 x +2117615}{\left(4 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right) x -8 \RootOf \left(8 \textit{\_Z}^{2}-24 \textit{\_Z} +17\right)-5 x +9\right)^{2}}\right)}{2}$&$544$\\ \hline \end{longtable}"," ",0,"(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticF((1+x)^(1/2),1/2*2^(1/2))+2^(1/2)*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/(-2-2^(1/2))*EllipticPi((1+x)^(1/2),-1/(-2-2^(1/2)),1/2*2^(1/2))+5/2*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/(-2-2^(1/2))*EllipticPi((1+x)^(1/2),-1/(-2-2^(1/2)),1/2*2^(1/2))-2^(1/2)*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/(-2+2^(1/2))*EllipticPi((1+x)^(1/2),-1/(-2+2^(1/2)),1/2*2^(1/2))+5/2*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/(-2+2^(1/2))*EllipticPi((1+x)^(1/2),-1/(-2+2^(1/2)),1/2*2^(1/2))","C"
958,1,288,59,0.883000," ","int(x*(x^2-3)/(x^2-1)^(2/3)/(x^3-x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 x \left(x^{2}-1\right)^{\frac{2}{3}}+3 \left(x^{2}-1\right)^{\frac{1}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+2 x^{2}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2}{x^{3}-x^{2}+1}\right)-\ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{2}{3}} x +\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{1}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+2 x \left(x^{2}-1\right)^{\frac{2}{3}}+2 \left(x^{2}-1\right)^{\frac{1}{3}} x^{2}+x^{3}+x^{2}-1}{x^{3}-x^{2}+1}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-\ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{2}{3}} x +\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{1}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+2 x \left(x^{2}-1\right)^{\frac{2}{3}}+2 \left(x^{2}-1\right)^{\frac{1}{3}} x^{2}+x^{3}+x^{2}-1}{x^{3}-x^{2}+1}\right)$&$288$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2+_Z+1)*ln((-RootOf(_Z^2+_Z+1)^2*x^3-2*RootOf(_Z^2+_Z+1)*x^3+3*x*(x^2-1)^(2/3)+3*(x^2-1)^(1/3)*x^2+RootOf(_Z^2+_Z+1)*x^2+2*x^2-RootOf(_Z^2+_Z+1)-2)/(x^3-x^2+1))-ln((RootOf(_Z^2+_Z+1)*(x^2-1)^(2/3)*x+RootOf(_Z^2+_Z+1)*(x^2-1)^(1/3)*x^2+RootOf(_Z^2+_Z+1)*x^3+2*x*(x^2-1)^(2/3)+2*(x^2-1)^(1/3)*x^2+x^3+x^2-1)/(x^3-x^2+1))*RootOf(_Z^2+_Z+1)-ln((RootOf(_Z^2+_Z+1)*(x^2-1)^(2/3)*x+RootOf(_Z^2+_Z+1)*(x^2-1)^(1/3)*x^2+RootOf(_Z^2+_Z+1)*x^3+2*x*(x^2-1)^(2/3)+2*(x^2-1)^(1/3)*x^2+x^3+x^2-1)/(x^3-x^2+1))","C"
959,1,27,61,0.681000," ","int(x^2*(x^4-x^3)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{4 \mathrm{signum}\left(-1+x \right)^{\frac{1}{4}} x^{\frac{15}{4}} \hypergeom \left(\left[-\frac{1}{4}, \frac{15}{4}\right], \left[\frac{19}{4}\right], x\right)}{15 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{4}}}$&$27$\\ trager&$\left(\frac{1}{4} x^{3}-\frac{1}{48} x^{2}-\frac{11}{384} x -\frac{77}{1536}\right) \left(x^{4}-x^{3}\right)^{\frac{1}{4}}+\frac{77 \ln \left(\frac{2 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}-2 \sqrt{x^{4}-x^{3}}\, x +2 x^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}-2 x^{3}+x^{2}}{x^{2}}\right)}{2048}+\frac{77 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-2 \sqrt{x^{4}-x^{3}}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x +2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}-2 x^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}}{x^{2}}\right)}{2048}$&$173$\\ risch&$\frac{\left(384 x^{3}-32 x^{2}-44 x -77\right) \left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}}}{1536}+\frac{\left(-\frac{77 \ln \left(\frac{2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{3}{4}}+2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, x +2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x^{2}+2 x^{3}-2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}-4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x -5 x^{2}+2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}}+4 x -1}{\left(-1+x \right)^{2}}\right)}{2048}+\frac{77 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{3}{4}}-2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x^{2}+5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x -4 \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(-1+x \right)^{2}}\right)}{2048}\right) \left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}} \left(x \left(-1+x \right)^{3}\right)^{\frac{1}{4}}}{x \left(-1+x \right)}$&$407$\\ \hline \end{longtable}"," ",0,"4/15*signum(-1+x)^(1/4)/(-signum(-1+x))^(1/4)*x^(15/4)*hypergeom([-1/4,15/4],[19/4],x)","C"
960,1,111,65,0.597000," ","int((x^4+3)*(-x^5+x^4+x)^(1/2)/(x^4-1)/(x^4+x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(\frac{x^{4}-2 x^{3}+2 x \sqrt{-x^{5}+x^{4}+x}-1}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)+\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x^{4}-3 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{3}-4 x \sqrt{-x^{5}+x^{4}+x}-\RootOf \left(\textit{\_Z}^{2}-2\right)}{x^{4}+x^{3}-1}\right)$&$111$\\ \hline \end{longtable}"," ",0,"ln((x^4-2*x^3+2*x*(-x^5+x^4+x)^(1/2)-1)/(-1+x)/(1+x)/(x^2+1))+RootOf(_Z^2-2)*ln(-(RootOf(_Z^2-2)*x^4-3*RootOf(_Z^2-2)*x^3-4*x*(-x^5+x^4+x)^(1/2)-RootOf(_Z^2-2))/(x^4+x^3-1))","C"
961,1,385,61,0.167000," ","int((a*x^2-b)*(a*x^3+b*x)^(1/2)/(b^2*x+2*(a*b-1)*x^3+a^2*x^5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}+b x}}-\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{2} \textit{\_Z}^{4}+\left(2 a b -2\right) \textit{\_Z}^{2}+b^{2}\right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2} a b -\underline{\hspace{1.25 ex}}\alpha^{2}+b^{2}\right) \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{\left(x -\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \left(a \left(a^{2} \underline{\hspace{1.25 ex}}\alpha^{3}+a b \underline{\hspace{1.25 ex}}\alpha  -2 \underline{\hspace{1.25 ex}}\alpha  \right)-a^{2} \sqrt{-a b}\, \underline{\hspace{1.25 ex}}\alpha^{2}-\sqrt{-a b}\, a b +2 \sqrt{-a b}\right) \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}\, \underline{\hspace{1.25 ex}}\alpha^{3} a^{2}+\underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b +\sqrt{-a b}\, \underline{\hspace{1.25 ex}}\alpha  a b +a \,b^{2}-2 \sqrt{-a b}\, \underline{\hspace{1.25 ex}}\alpha  -2 b}{2 b}, \frac{\sqrt{2}}{2}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+a b -1\right) \sqrt{x \left(a \,x^{2}+b \right)}}\right)}{4 a b}$&$385$\\ default&$\frac{\frac{2 \sqrt{a \,x^{3}+b x}}{3}+\frac{5 b \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{3 a \sqrt{a \,x^{3}+b x}}-\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{2} \textit{\_Z}^{4}+\left(2 a b -2\right) \textit{\_Z}^{2}+b^{2}\right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2} a b -\underline{\hspace{1.25 ex}}\alpha^{2}+b^{2}\right) \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{\left(x -\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \left(a \left(a^{2} \underline{\hspace{1.25 ex}}\alpha^{3}+a b \underline{\hspace{1.25 ex}}\alpha  -2 \underline{\hspace{1.25 ex}}\alpha  \right)-a^{2} \sqrt{-a b}\, \underline{\hspace{1.25 ex}}\alpha^{2}-\sqrt{-a b}\, a b +2 \sqrt{-a b}\right) \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}\, \underline{\hspace{1.25 ex}}\alpha^{3} a^{2}+\underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b +\sqrt{-a b}\, \underline{\hspace{1.25 ex}}\alpha  a b +a \,b^{2}-2 \sqrt{-a b}\, \underline{\hspace{1.25 ex}}\alpha  -2 b}{2 b}, \frac{\sqrt{2}}{2}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+a b -1\right) \sqrt{x \left(a \,x^{2}+b \right)}}\right)}{4 a}}{b}-\frac{\frac{2 \sqrt{a \,x^{3}+b x}}{3}+\frac{2 b \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{3 a \sqrt{a \,x^{3}+b x}}}{b}$&$530$\\ \hline \end{longtable}"," ",0,"1/a*(-a*b)^(1/2)*((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2)*(-2*(x-1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)*EllipticF(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))-1/4/a/b*2^(1/2)*sum((_alpha^2*a*b-_alpha^2+b^2)/_alpha/(_alpha^2*a^2+a*b-1)*(-a*b)^(1/2)*((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2)*(-(x-1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(x*(a*x^2+b))^(1/2)*(a*(_alpha^3*a^2+_alpha*a*b-2*_alpha)-a^2*(-a*b)^(1/2)*_alpha^2-(-a*b)^(1/2)*a*b+2*(-a*b)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/2*((-a*b)^(1/2)*_alpha^3*a^2+_alpha^2*a^2*b+(-a*b)^(1/2)*_alpha*a*b+a*b^2-2*(-a*b)^(1/2)*_alpha-2*b)/b,1/2*2^(1/2)),_alpha=RootOf(a^2*_Z^4+(2*a*b-2)*_Z^2+b^2))","C"
962,1,7428,24,163.232000," ","int((x^3-2)*(x^3+1)^(2/3)/x^3/(x^6+x^3+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$7428$\\ trager&$\text{Expression too large to display}$&$13494$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
963,1,5531,24,161.736000," ","int((x^3-2)*(x^3+1)^(2/3)/x^3/(x^6+x^3+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$5531$\\ trager&$\text{Expression too large to display}$&$9663$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
964,1,121,65,0.681000," ","int((2*x^5-3)*(x^6+2*x^4+x)^(1/2)/(x^5+1)/(x^5+x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}-2\right) x^{5}-4 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{3}+4 \sqrt{x^{6}+2 x^{4}+x}\, x -\RootOf \left(\textit{\_Z}^{2}-2\right)}{\left(1+x \right) \left(x^{4}-x^{3}+x^{2}-x +1\right)}\right)-\ln \left(\frac{-x^{5}-3 x^{3}+2 \sqrt{x^{6}+2 x^{4}+x}\, x -1}{x^{5}+x^{3}+1}\right)$&$121$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2-2)*ln((-RootOf(_Z^2-2)*x^5-4*RootOf(_Z^2-2)*x^3+4*(x^6+2*x^4+x)^(1/2)*x-RootOf(_Z^2-2))/(1+x)/(x^4-x^3+x^2-x+1))-ln((-x^5-3*x^3+2*(x^6+2*x^4+x)^(1/2)*x-1)/(x^5+x^3+1))","C"
965,1,590,57,3.824000," ","int((x^6+x^4+x^2-1)^(1/2)*(2*x^6+x^4+1)/(x^12+2*x^10+x^8-2*x^6-x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+16 \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right)^{2}+2\right) \ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+16 \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right)^{2}+2\right) \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right)^{2} x^{6}+64 \RootOf \left(\textit{\_Z}^{2}+16 \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right)^{2}+2\right) \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right)^{4} x^{2}+4 \RootOf \left(\textit{\_Z}^{2}+16 \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right)^{2}+2\right) \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right)^{2} x^{4}+12 \RootOf \left(\textit{\_Z}^{2}+16 \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right)^{2}+2\right) \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right)^{2} x^{2}-16 \sqrt{x^{6}+x^{4}+x^{2}-1}\, \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right)^{2} x -4 \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+16 \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right)^{2}+2\right)-\sqrt{x^{6}+x^{4}+x^{2}-1}\, x}{-x^{6}+16 x^{2} \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right)^{2}-x^{4}+x^{2}+1}\right)}{4}+\RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right) \ln \left(-\frac{-16 \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right)^{3} x^{6}+256 \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right)^{5} x^{2}-16 \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right)^{3} x^{4}-2 \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right) x^{6}+16 \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right)^{3} x^{2}-2 \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right) x^{4}+16 \sqrt{x^{6}+x^{4}+x^{2}-1}\, \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right)^{2} x +16 \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right)^{3}-2 x^{2} \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right)+\sqrt{x^{6}+x^{4}+x^{2}-1}\, x +2 \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right)}{x^{6}+16 x^{2} \RootOf \left(128 \textit{\_Z}^{4}+16 \textit{\_Z}^{2}+1\right)^{2}+x^{4}+x^{2}-1}\right)$&$590$\\ \hline \end{longtable}"," ",0,"1/4*RootOf(_Z^2+16*RootOf(128*_Z^4+16*_Z^2+1)^2+2)*ln(-(4*RootOf(_Z^2+16*RootOf(128*_Z^4+16*_Z^2+1)^2+2)*RootOf(128*_Z^4+16*_Z^2+1)^2*x^6+64*RootOf(_Z^2+16*RootOf(128*_Z^4+16*_Z^2+1)^2+2)*RootOf(128*_Z^4+16*_Z^2+1)^4*x^2+4*RootOf(_Z^2+16*RootOf(128*_Z^4+16*_Z^2+1)^2+2)*RootOf(128*_Z^4+16*_Z^2+1)^2*x^4+12*RootOf(_Z^2+16*RootOf(128*_Z^4+16*_Z^2+1)^2+2)*RootOf(128*_Z^4+16*_Z^2+1)^2*x^2-16*(x^6+x^4+x^2-1)^(1/2)*RootOf(128*_Z^4+16*_Z^2+1)^2*x-4*RootOf(128*_Z^4+16*_Z^2+1)^2*RootOf(_Z^2+16*RootOf(128*_Z^4+16*_Z^2+1)^2+2)-(x^6+x^4+x^2-1)^(1/2)*x)/(-x^6+16*x^2*RootOf(128*_Z^4+16*_Z^2+1)^2-x^4+x^2+1))+RootOf(128*_Z^4+16*_Z^2+1)*ln(-(-16*RootOf(128*_Z^4+16*_Z^2+1)^3*x^6+256*RootOf(128*_Z^4+16*_Z^2+1)^5*x^2-16*RootOf(128*_Z^4+16*_Z^2+1)^3*x^4-2*RootOf(128*_Z^4+16*_Z^2+1)*x^6+16*RootOf(128*_Z^4+16*_Z^2+1)^3*x^2-2*RootOf(128*_Z^4+16*_Z^2+1)*x^4+16*(x^6+x^4+x^2-1)^(1/2)*RootOf(128*_Z^4+16*_Z^2+1)^2*x+16*RootOf(128*_Z^4+16*_Z^2+1)^3-2*x^2*RootOf(128*_Z^4+16*_Z^2+1)+(x^6+x^4+x^2-1)^(1/2)*x+2*RootOf(128*_Z^4+16*_Z^2+1))/(x^6+16*x^2*RootOf(128*_Z^4+16*_Z^2+1)^2+x^4+x^2-1))","C"
966,0,0,59,0.014000," ","int((x^2-x*(x^2-x)^(1/2))^(1/2)/x^3,x)","\[\int \frac{\sqrt{x^{2}-x \sqrt{x^{2}-x}}}{x^{3}}\, dx\]"," ",0,"int((x^2-x*(x^2-x)^(1/2))^(1/2)/x^3,x)","F"
967,1,46,56,1.674000," ","int(1/x/(x^2+1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{-\frac{2 \Gamma \left(\frac{2}{3}\right) x^{2} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 2\right], -x^{2}\right)}{3}+\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+2 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)}{2 \Gamma \left(\frac{2}{3}\right)}$&$46$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}}+17 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+24 \left(x^{2}+1\right)^{\frac{2}{3}}+15 \left(x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+15 x^{2}+24 \left(x^{2}+1\right)^{\frac{1}{3}}+11 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+20}{x^{2}}\right)}{2}-\frac{\ln \left(\frac{-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}}+9 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-9 \left(x^{2}+1\right)^{\frac{2}{3}}+15 \left(x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-2 x^{2}-9 \left(x^{2}+1\right)^{\frac{1}{3}}+19 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-5}{x^{2}}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{2}-\frac{\ln \left(\frac{-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}}+9 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-9 \left(x^{2}+1\right)^{\frac{2}{3}}+15 \left(x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-2 x^{2}-9 \left(x^{2}+1\right)^{\frac{1}{3}}+19 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-5}{x^{2}}\right)}{2}$&$347$\\ \hline \end{longtable}"," ",0,"1/2/GAMMA(2/3)*(-2/3*GAMMA(2/3)*x^2*hypergeom([1,1,5/3],[2,2],-x^2)+(1/6*Pi*3^(1/2)-3/2*ln(3)+2*ln(x))*GAMMA(2/3))","C"
968,1,63,56,1.395000," ","int(1/x/(x^2+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\frac{2 \pi  \sqrt{3}\, x^{2} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], -x^{2}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+2 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{4 \pi}$&$63$\\ trager&$\frac{\ln \left(\frac{-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}}+9 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-9 \left(x^{2}+1\right)^{\frac{2}{3}}+15 \left(x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-2 x^{2}-9 \left(x^{2}+1\right)^{\frac{1}{3}}+19 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-5}{x^{2}}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}}+17 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+24 \left(x^{2}+1\right)^{\frac{2}{3}}+15 \left(x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+15 x^{2}+24 \left(x^{2}+1\right)^{\frac{1}{3}}+11 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+20}{x^{2}}\right)}{2}-\frac{\ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}}+17 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+24 \left(x^{2}+1\right)^{\frac{2}{3}}+15 \left(x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+15 x^{2}+24 \left(x^{2}+1\right)^{\frac{1}{3}}+11 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+20}{x^{2}}\right)}{2}$&$348$\\ \hline \end{longtable}"," ",0,"1/4/Pi*3^(1/2)*GAMMA(2/3)*(-2/9*Pi*3^(1/2)/GAMMA(2/3)*x^2*hypergeom([1,1,4/3],[2,2],-x^2)+2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)+2*ln(x))*Pi*3^(1/2)/GAMMA(2/3))","C"
969,1,2082,34,9.104000," ","int(1/(x^3-1)/(x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$2082$\\ trager&$\text{Expression too large to display}$&$2138$\\ \hline \end{longtable}"," ",0,"-x/((-1+x)*x^2)^(1/3)+1/6*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*ln(-(69*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^6*x^2-138*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^6*x+183*(x^3-x^2)^(1/3)*RootOf(3*_Z^6-24*_Z^3+64)^3*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)^2*x-1268*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^3*x^2+228*(x^3-x^2)^(2/3)*RootOf(3*_Z^6-24*_Z^3+64)^3+1340*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^3*x-1920*(x^3-x^2)^(1/3)*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)^2*x+4640*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*x^2+1952*(x^3-x^2)^(2/3)-3248*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*x)/(3*x*RootOf(3*_Z^6-24*_Z^3+64)^3-6*RootOf(3*_Z^6-24*_Z^3+64)^3+8*x+40)/x)+1/6*RootOf(3*_Z^6-24*_Z^3+64)*ln(-(-87*x^2*RootOf(3*_Z^6-24*_Z^3+64)^7+174*x*RootOf(3*_Z^6-24*_Z^3+64)^7-2892*(x^3-x^2)^(1/3)*RootOf(3*_Z^6-24*_Z^3+64)^5*x+2992*RootOf(3*_Z^6-24*_Z^3+64)^4*x^2+3120*(x^3-x^2)^(2/3)*RootOf(3*_Z^6-24*_Z^3+64)^3-1576*RootOf(3*_Z^6-24*_Z^3+64)^4*x+8448*(x^3-x^2)^(1/3)*RootOf(3*_Z^6-24*_Z^3+64)^2*x+832*x^2*RootOf(3*_Z^6-24*_Z^3+64)-27904*(x^3-x^2)^(2/3)-448*x*RootOf(3*_Z^6-24*_Z^3+64))/(3*x*RootOf(3*_Z^6-24*_Z^3+64)^3-6*RootOf(3*_Z^6-24*_Z^3+64)^3-32*x+8)/x)+1/16*ln((-183*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^6*x^2+366*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^6*x+276*(x^3-x^2)^(1/3)*RootOf(3*_Z^6-24*_Z^3+64)^3*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)^2*x-4136*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^3*x^2+3120*(x^3-x^2)^(2/3)*RootOf(3*_Z^6-24*_Z^3+64)^3-1000*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^3*x-8448*(x^3-x^2)^(1/3)*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)^2*x+19840*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*x^2+2944*(x^3-x^2)^(2/3)-1984*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*x)/(3*x*RootOf(3*_Z^6-24*_Z^3+64)^3-6*RootOf(3*_Z^6-24*_Z^3+64)^3+8*x+40)/x)*RootOf(3*_Z^6-24*_Z^3+64)^3*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)-1/3*ln((-183*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^6*x^2+366*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^6*x+276*(x^3-x^2)^(1/3)*RootOf(3*_Z^6-24*_Z^3+64)^3*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)^2*x-4136*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^3*x^2+3120*(x^3-x^2)^(2/3)*RootOf(3*_Z^6-24*_Z^3+64)^3-1000*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^3*x-8448*(x^3-x^2)^(1/3)*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)^2*x+19840*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*x^2+2944*(x^3-x^2)^(2/3)-1984*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*x)/(3*x*RootOf(3*_Z^6-24*_Z^3+64)^3-6*RootOf(3*_Z^6-24*_Z^3+64)^3+8*x+40)/x)*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)+1/16*ln((15*x^2*RootOf(3*_Z^6-24*_Z^3+64)^7-30*x*RootOf(3*_Z^6-24*_Z^3+64)^7-1074*(x^3-x^2)^(1/3)*RootOf(3*_Z^6-24*_Z^3+64)^5*x+368*RootOf(3*_Z^6-24*_Z^3+64)^4*x^2+456*(x^3-x^2)^(2/3)*RootOf(3*_Z^6-24*_Z^3+64)^3-476*RootOf(3*_Z^6-24*_Z^3+64)^4*x+3840*(x^3-x^2)^(1/3)*RootOf(3*_Z^6-24*_Z^3+64)^2*x+1536*x^2*RootOf(3*_Z^6-24*_Z^3+64)-7552*(x^3-x^2)^(2/3)+1920*x*RootOf(3*_Z^6-24*_Z^3+64))/(3*x*RootOf(3*_Z^6-24*_Z^3+64)^3-6*RootOf(3*_Z^6-24*_Z^3+64)^3-32*x+8)/x)*RootOf(3*_Z^6-24*_Z^3+64)^4-1/3*ln((15*x^2*RootOf(3*_Z^6-24*_Z^3+64)^7-30*x*RootOf(3*_Z^6-24*_Z^3+64)^7-1074*(x^3-x^2)^(1/3)*RootOf(3*_Z^6-24*_Z^3+64)^5*x+368*RootOf(3*_Z^6-24*_Z^3+64)^4*x^2+456*(x^3-x^2)^(2/3)*RootOf(3*_Z^6-24*_Z^3+64)^3-476*RootOf(3*_Z^6-24*_Z^3+64)^4*x+3840*(x^3-x^2)^(1/3)*RootOf(3*_Z^6-24*_Z^3+64)^2*x+1536*x^2*RootOf(3*_Z^6-24*_Z^3+64)-7552*(x^3-x^2)^(2/3)+1920*x*RootOf(3*_Z^6-24*_Z^3+64))/(3*x*RootOf(3*_Z^6-24*_Z^3+64)^3-6*RootOf(3*_Z^6-24*_Z^3+64)^3-32*x+8)/x)*RootOf(3*_Z^6-24*_Z^3+64)","B"
970,1,2083,34,8.136000," ","int(1/(x^3-1)/(x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$2083$\\ trager&$\text{Expression too large to display}$&$2579$\\ \hline \end{longtable}"," ",0,"-x/((-1+x)*x^2)^(1/3)+1/6*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*ln(-(69*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^6*x^2-138*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^6*x+183*(x^3-x^2)^(1/3)*RootOf(3*_Z^6-24*_Z^3+64)^3*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)^2*x-1268*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^3*x^2+228*(x^3-x^2)^(2/3)*RootOf(3*_Z^6-24*_Z^3+64)^3+1340*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^3*x-1920*(x^3-x^2)^(1/3)*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)^2*x+4640*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*x^2+1952*(x^3-x^2)^(2/3)-3248*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*x)/(3*x*RootOf(3*_Z^6-24*_Z^3+64)^3-6*RootOf(3*_Z^6-24*_Z^3+64)^3+8*x+40)/x)+1/6*RootOf(3*_Z^6-24*_Z^3+64)*ln((-69*x^2*RootOf(3*_Z^6-24*_Z^3+64)^7+138*x*RootOf(3*_Z^6-24*_Z^3+64)^7+183*(x^3-x^2)^(1/3)*RootOf(3*_Z^6-24*_Z^3+64)^5*x-164*RootOf(3*_Z^6-24*_Z^3+64)^4*x^2+228*(x^3-x^2)^(2/3)*RootOf(3*_Z^6-24*_Z^3+64)^3-868*RootOf(3*_Z^6-24*_Z^3+64)^4*x+456*(x^3-x^2)^(1/3)*RootOf(3*_Z^6-24*_Z^3+64)^2*x+1088*x^2*RootOf(3*_Z^6-24*_Z^3+64)-3776*(x^3-x^2)^(2/3)+1360*x*RootOf(3*_Z^6-24*_Z^3+64))/(3*x*RootOf(3*_Z^6-24*_Z^3+64)^3-6*RootOf(3*_Z^6-24*_Z^3+64)^3-32*x+8)/x)+1/16*ln((-183*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^6*x^2+366*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^6*x+276*(x^3-x^2)^(1/3)*RootOf(3*_Z^6-24*_Z^3+64)^3*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)^2*x-4136*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^3*x^2+3120*(x^3-x^2)^(2/3)*RootOf(3*_Z^6-24*_Z^3+64)^3-1000*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^3*x-8448*(x^3-x^2)^(1/3)*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)^2*x+19840*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*x^2+2944*(x^3-x^2)^(2/3)-1984*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*x)/(3*x*RootOf(3*_Z^6-24*_Z^3+64)^3-6*RootOf(3*_Z^6-24*_Z^3+64)^3+8*x+40)/x)*RootOf(3*_Z^6-24*_Z^3+64)^3*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)-1/3*ln((-183*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^6*x^2+366*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^6*x+276*(x^3-x^2)^(1/3)*RootOf(3*_Z^6-24*_Z^3+64)^3*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)^2*x-4136*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^3*x^2+3120*(x^3-x^2)^(2/3)*RootOf(3*_Z^6-24*_Z^3+64)^3-1000*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*RootOf(3*_Z^6-24*_Z^3+64)^3*x-8448*(x^3-x^2)^(1/3)*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)^2*x+19840*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*x^2+2944*(x^3-x^2)^(2/3)-1984*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)*x)/(3*x*RootOf(3*_Z^6-24*_Z^3+64)^3-6*RootOf(3*_Z^6-24*_Z^3+64)^3+8*x+40)/x)*RootOf(RootOf(3*_Z^6-24*_Z^3+64)^3+_Z^3-8)-1/16*ln(-(183*x^2*RootOf(3*_Z^6-24*_Z^3+64)^7-366*x*RootOf(3*_Z^6-24*_Z^3+64)^7+276*(x^3-x^2)^(1/3)*RootOf(3*_Z^6-24*_Z^3+64)^5*x-7064*RootOf(3*_Z^6-24*_Z^3+64)^4*x^2+3120*(x^3-x^2)^(2/3)*RootOf(3*_Z^6-24*_Z^3+64)^3+4856*RootOf(3*_Z^6-24*_Z^3+64)^4*x+6240*(x^3-x^2)^(1/3)*RootOf(3*_Z^6-24*_Z^3+64)^2*x+24960*x^2*RootOf(3*_Z^6-24*_Z^3+64)-27904*(x^3-x^2)^(2/3)-13440*x*RootOf(3*_Z^6-24*_Z^3+64))/(3*x*RootOf(3*_Z^6-24*_Z^3+64)^3-6*RootOf(3*_Z^6-24*_Z^3+64)^3-32*x+8)/x)*RootOf(3*_Z^6-24*_Z^3+64)^4+1/6*ln(-(183*x^2*RootOf(3*_Z^6-24*_Z^3+64)^7-366*x*RootOf(3*_Z^6-24*_Z^3+64)^7+276*(x^3-x^2)^(1/3)*RootOf(3*_Z^6-24*_Z^3+64)^5*x-7064*RootOf(3*_Z^6-24*_Z^3+64)^4*x^2+3120*(x^3-x^2)^(2/3)*RootOf(3*_Z^6-24*_Z^3+64)^3+4856*RootOf(3*_Z^6-24*_Z^3+64)^4*x+6240*(x^3-x^2)^(1/3)*RootOf(3*_Z^6-24*_Z^3+64)^2*x+24960*x^2*RootOf(3*_Z^6-24*_Z^3+64)-27904*(x^3-x^2)^(2/3)-13440*x*RootOf(3*_Z^6-24*_Z^3+64))/(3*x*RootOf(3*_Z^6-24*_Z^3+64)^3-6*RootOf(3*_Z^6-24*_Z^3+64)^3-32*x+8)/x)*RootOf(3*_Z^6-24*_Z^3+64)","B"
971,1,107,59,0.608000," ","int((x^3-1)^(1/2)*(x^3+2)*(x^3-x^2-1)^2/x^6/(2*x^3-3*x^2-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{3}-1}\, \left(12 x^{6}-10 x^{5}+15 x^{4}-24 x^{3}+10 x^{2}+12\right)}{60 x^{5}}+\frac{\RootOf \left(\textit{\_Z}^{2}-6\right) \ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{2}-6\right) x^{3}-3 \RootOf \left(\textit{\_Z}^{2}-6\right) x^{2}+12 x \sqrt{x^{3}-1}+2 \RootOf \left(\textit{\_Z}^{2}-6\right)}{2 x^{3}-3 x^{2}-2}\right)}{16}$&$107$\\ risch&$\frac{12 x^{9}-10 x^{8}+15 x^{7}-36 x^{6}+20 x^{5}-15 x^{4}+36 x^{3}-10 x^{2}-12}{60 x^{5} \sqrt{x^{3}-1}}+\frac{3 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{8 \sqrt{x^{3}-1}}+\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(2 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}-2\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(-2 \underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(-3-i \sqrt{3}\right) \sqrt{\frac{-1+x}{-3-i \sqrt{3}}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{3-i \sqrt{3}}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\underline{\hspace{1.25 ex}}\alpha^{2}+\frac{\underline{\hspace{1.25 ex}}\alpha}{2}+\frac{1}{2}-\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{3}+\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha }{6}+\frac{i \sqrt{3}}{6}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}\right)}{16}$&$351$\\ default&$\frac{x \sqrt{x^{3}-1}}{5}+\frac{3 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{8 \sqrt{x^{3}-1}}+\frac{\sqrt{x^{3}-1}}{6 x^{3}}+\frac{\sqrt{x^{3}-1}}{4 x}-\frac{\sqrt{x^{3}-1}}{6}+\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(2 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}-2\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(-2 \underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(-3-i \sqrt{3}\right) \sqrt{\frac{-1+x}{-3-i \sqrt{3}}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{3-i \sqrt{3}}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\underline{\hspace{1.25 ex}}\alpha^{2}+\frac{\underline{\hspace{1.25 ex}}\alpha}{2}+\frac{1}{2}-\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{3}+\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha }{6}+\frac{i \sqrt{3}}{6}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}\right)}{16}-\frac{2 \sqrt{x^{3}-1}}{5 x^{2}}+\frac{\sqrt{x^{3}-1}}{5 x^{5}}$&$364$\\ elliptic&$\frac{x \sqrt{x^{3}-1}}{5}+\frac{3 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{8 \sqrt{x^{3}-1}}+\frac{\sqrt{x^{3}-1}}{6 x^{3}}+\frac{\sqrt{x^{3}-1}}{4 x}-\frac{\sqrt{x^{3}-1}}{6}+\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(2 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}-2\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(-2 \underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(-3-i \sqrt{3}\right) \sqrt{\frac{-1+x}{-3-i \sqrt{3}}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{3-i \sqrt{3}}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\underline{\hspace{1.25 ex}}\alpha^{2}+\frac{\underline{\hspace{1.25 ex}}\alpha}{2}+\frac{1}{2}-\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{3}+\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha }{6}+\frac{i \sqrt{3}}{6}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}\right)}{16}-\frac{2 \sqrt{x^{3}-1}}{5 x^{2}}+\frac{\sqrt{x^{3}-1}}{5 x^{5}}$&$364$\\ \hline \end{longtable}"," ",0,"1/60*(x^3-1)^(1/2)*(12*x^6-10*x^5+15*x^4-24*x^3+10*x^2+12)/x^5+1/16*RootOf(_Z^2-6)*ln(-(-2*RootOf(_Z^2-6)*x^3-3*RootOf(_Z^2-6)*x^2+12*x*(x^3-1)^(1/2)+2*RootOf(_Z^2-6))/(2*x^3-3*x^2-2))","C"
972,0,0,22,180.000000," ","int((x^3-3*x^2+3*x-1)^(1/4)/(3*x^3+x^2-2*x-1),x)","\[\int \frac{\left(x^{3}-3 x^{2}+3 x -1\right)^{\frac{1}{4}}}{3 x^{3}+x^{2}-2 x -1}\, dx\]"," ",0,"int((x^3-3*x^2+3*x-1)^(1/4)/(3*x^3+x^2-2*x-1),x)","F"
973,1,83,68,1.209000," ","int((x^2+x+1)*(x^2+2*x)*(-x^4+x^2+2*x+1)^(1/2)/(1+x)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{-x^{4}+x^{2}+2 x +1}\, \left(2 x^{4}+3 x^{3}+x^{2}-4 x -2\right)}{6 \left(1+x \right)^{3}}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{-x^{4}+x^{2}+2 x +1}+x^{2}}{1+x}\right)}{2}$&$83$\\ risch&$-\frac{2 x^{8}+3 x^{7}-x^{6}-11 x^{5}-11 x^{4}-x^{3}+9 x^{2}+8 x +2}{6 \left(1+x \right)^{3} \sqrt{-x^{4}+x^{2}+2 x +1}}-\frac{i \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{\frac{i \sqrt{3}\, \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)}{\left(1-\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{i \sqrt{3}\, \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{3}\, \left(\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticF \left(\sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \sqrt{\frac{\left(-1+\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}{\left(-1-\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1+\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}}\right)-i \sqrt{3}\, \EllipticPi \left(\sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \frac{1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}}{1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-1+\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}{\left(-1-\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1+\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}}\right)\right)}{3 \left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-\left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}}-\frac{i \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{\frac{i \sqrt{3}\, \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)}{\left(1-\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{i \sqrt{3}\, \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{3}\, \EllipticF \left(\sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \sqrt{\frac{\left(-1+\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}{\left(-1-\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1+\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}}\right)}{3 \left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-\left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}}+\frac{i \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{\frac{i \sqrt{3}\, \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)}{\left(1-\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{i \sqrt{3}\, \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{3}\, \left(\EllipticF \left(\sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \sqrt{\frac{\left(-1+\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}{\left(-1-\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1+\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}}\right)+\frac{i \sqrt{3}\, \EllipticPi \left(\sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right)}, \sqrt{\frac{\left(-1+\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}{\left(-1-\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1+\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}}\right)}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}\right)}{3 \left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-\left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}\, \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}$&$1392$\\ default&$\frac{x \sqrt{-x^{4}+x^{2}+2 x +1}}{3}-\frac{i \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{\frac{i \sqrt{3}\, \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)}{\left(1-\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{i \sqrt{3}\, \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{3}\, \left(\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticF \left(\sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \sqrt{\frac{\left(-1+\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}{\left(-1-\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1+\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}}\right)-i \sqrt{3}\, \EllipticPi \left(\sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \frac{1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}}{1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-1+\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}{\left(-1-\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1+\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}}\right)\right)}{3 \left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-\left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}}-\frac{i \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{\frac{i \sqrt{3}\, \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)}{\left(1-\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{i \sqrt{3}\, \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{3}\, \EllipticF \left(\sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \sqrt{\frac{\left(-1+\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}{\left(-1-\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1+\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}}\right)}{3 \left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-\left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}}-\frac{\sqrt{-x^{4}+x^{2}+2 x +1}}{2}+\frac{i \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{\frac{i \sqrt{3}\, \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)}{\left(1-\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{i \sqrt{3}\, \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{3}\, \left(\EllipticF \left(\sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \sqrt{\frac{\left(-1+\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}{\left(-1-\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1+\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}}\right)+\frac{i \sqrt{3}\, \EllipticPi \left(\sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right)}, \sqrt{\frac{\left(-1+\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}{\left(-1-\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1+\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}}\right)}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}\right)}{3 \left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-\left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}\, \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}-\frac{5 \sqrt{-x^{4}+x^{2}+2 x +1}}{6 \left(1+x \right)^{2}}+\frac{2 \sqrt{-x^{4}+x^{2}+2 x +1}}{3 \left(1+x \right)}+\frac{\sqrt{-x^{4}+x^{2}+2 x +1}}{3 \left(1+x \right)^{3}}$&$1431$\\ elliptic&$\frac{x \sqrt{-x^{4}+x^{2}+2 x +1}}{3}-\frac{i \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{\frac{i \sqrt{3}\, \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)}{\left(1-\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{i \sqrt{3}\, \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{3}\, \left(\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticF \left(\sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \sqrt{\frac{\left(-1+\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}{\left(-1-\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1+\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}}\right)-i \sqrt{3}\, \EllipticPi \left(\sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \frac{1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}}{1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-1+\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}{\left(-1-\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1+\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}}\right)\right)}{3 \left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-\left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}}-\frac{i \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{\frac{i \sqrt{3}\, \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)}{\left(1-\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{i \sqrt{3}\, \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{3}\, \EllipticF \left(\sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \sqrt{\frac{\left(-1+\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}{\left(-1-\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1+\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}}\right)}{3 \left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-\left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}}-\frac{\sqrt{-x^{4}+x^{2}+2 x +1}}{2}+\frac{i \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{\frac{i \sqrt{3}\, \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)}{\left(1-\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{i \sqrt{3}\, \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{3}\, \left(\EllipticF \left(\sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \sqrt{\frac{\left(-1+\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}{\left(-1-\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1+\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}}\right)+\frac{i \sqrt{3}\, \EllipticPi \left(\sqrt{\frac{\left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}, \frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+\frac{\sqrt{5}}{2}+\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right)}, \sqrt{\frac{\left(-1+\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1-\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}{\left(-1-\frac{i \sqrt{3}}{2}+\frac{\sqrt{5}}{2}\right) \left(-1+\frac{i \sqrt{3}}{2}-\frac{\sqrt{5}}{2}\right)}}\right)}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}\right)}{3 \left(1+\frac{\sqrt{5}}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-\left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}\, \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}-\frac{5 \sqrt{-x^{4}+x^{2}+2 x +1}}{6 \left(1+x \right)^{2}}+\frac{2 \sqrt{-x^{4}+x^{2}+2 x +1}}{3 \left(1+x \right)}+\frac{\sqrt{-x^{4}+x^{2}+2 x +1}}{3 \left(1+x \right)^{3}}$&$1431$\\ \hline \end{longtable}"," ",0,"1/6*(-x^4+x^2+2*x+1)^(1/2)*(2*x^4+3*x^3+x^2-4*x-2)/(1+x)^3+1/2*RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)*(-x^4+x^2+2*x+1)^(1/2)+x^2)/(1+x))","C"
974,1,90,54,2.938000," ","int((x^4-x-1)/x/(x^4+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{2}\, \Gamma \left(\frac{3}{4}\right) \left(-\frac{\pi  \sqrt{2}\, x^{4} \hypergeom \left(\left[1, 1, \frac{5}{4}\right], \left[2, 2\right], -x^{4}\right)}{4 \Gamma \left(\frac{3}{4}\right)}+\frac{\left(-3 \ln \left(2\right)-\frac{\pi}{2}+4 \ln \left(x \right)\right) \pi  \sqrt{2}}{\Gamma \left(\frac{3}{4}\right)}\right)}{8 \pi}+\frac{x^{4} \hypergeom \left(\left[\frac{1}{4}, 1\right], \left[2\right], -x^{4}\right)}{4}-x \hypergeom \left(\left[\frac{1}{4}, \frac{1}{4}\right], \left[\frac{5}{4}\right], -x^{4}\right)$&$90$\\ trager&$\frac{\left(x^{4}+1\right)^{\frac{3}{4}}}{3}-\frac{\ln \left(-\frac{\left(x^{4}+1\right)^{\frac{3}{4}} x +x^{2} \sqrt{x^{4}+1}+x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}+x^{4}-\left(x^{4}+1\right)^{\frac{3}{4}}-\sqrt{x^{4}+1}\, x -x^{2} \left(x^{4}+1\right)^{\frac{1}{4}}-x^{3}+\sqrt{x^{4}+1}+x \left(x^{4}+1\right)^{\frac{1}{4}}-\left(x^{4}+1\right)^{\frac{1}{4}}-x +1}{x^{2}}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}\, x^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+\left(x^{4}+1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}\, x -x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-\left(x^{4}+1\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}+x^{2} \left(x^{4}+1\right)^{\frac{1}{4}}-x \left(x^{4}+1\right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right) x +\left(x^{4}+1\right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{2}}\right)}{2}$&$275$\\ \hline \end{longtable}"," ",0,"-1/8/Pi*2^(1/2)*GAMMA(3/4)*(-1/4*Pi*2^(1/2)/GAMMA(3/4)*x^4*hypergeom([1,1,5/4],[2,2],-x^4)+(-3*ln(2)-1/2*Pi+4*ln(x))*Pi*2^(1/2)/GAMMA(3/4))+1/4*x^4*hypergeom([1/4,1],[2],-x^4)-x*hypergeom([1/4,1/4],[5/4],-x^4)","C"
975,1,260,60,2.957000," ","int((x^4-x^3)^(1/4)/x^2/(x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{4}-x^{3}\right)^{\frac{1}{4}}}{x}+\frac{\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(\frac{-3 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{3}+4 \left(x^{4}-x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{2}-4 \sqrt{x^{4}-x^{3}}\, \RootOf \left(\textit{\_Z}^{4}-2\right) x +4 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(1+x \right)}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(\frac{-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{3}-4 \left(x^{4}-x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}+4 \sqrt{x^{4}-x^{3}}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x +4 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(1+x \right)}\right)}{2}$&$260$\\ risch&$\frac{4 \left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}}}{x}+\frac{\left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(-\frac{2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x -2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+2 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{3}-4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x +7 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{2}+2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{3}{4}}-5 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)}{\left(-1+x \right)^{2} \left(1+x \right)}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(-\frac{2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x -2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}-2 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x^{2}+4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x +3 \RootOf \left(\textit{\_Z}^{4}-2\right) x^{3}-2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-7 \RootOf \left(\textit{\_Z}^{4}-2\right) x^{2}-4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{3}{4}}+5 \RootOf \left(\textit{\_Z}^{4}-2\right) x -\RootOf \left(\textit{\_Z}^{4}-2\right)}{\left(-1+x \right)^{2} \left(1+x \right)}\right)}{2}\right) \left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}} \left(x \left(-1+x \right)^{3}\right)^{\frac{1}{4}}}{x \left(-1+x \right)}$&$567$\\ \hline \end{longtable}"," ",0,"4*(x^4-x^3)^(1/4)/x+1/2*RootOf(_Z^4-2)*ln((-3*RootOf(_Z^4-2)^3*x^3+4*(x^4-x^3)^(1/4)*RootOf(_Z^4-2)^2*x^2+RootOf(_Z^4-2)^3*x^2-4*(x^4-x^3)^(1/2)*RootOf(_Z^4-2)*x+4*(x^4-x^3)^(3/4))/x^2/(1+x))-1/2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln((-3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*x^3-4*(x^4-x^3)^(1/4)*RootOf(_Z^4-2)^2*x^2+RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*x^2+4*(x^4-x^3)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x+4*(x^4-x^3)^(3/4))/x^2/(1+x))","C"
976,1,260,60,3.768000," ","int((x^4-3)/(x^4+1)^(1/3)/(x^4-x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x +\left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-x^{4}+2 \left(x^{4}+1\right)^{\frac{2}{3}} x -x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}-x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1}{x^{4}-x^{3}+1}\right)+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x -2 \left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+x^{4}-\left(x^{4}+1\right)^{\frac{2}{3}} x -x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1}{x^{4}-x^{3}+1}\right)$&$260$\\ \hline \end{longtable}"," ",0,"ln(-(-RootOf(_Z^2+_Z+1)^2*x^3-RootOf(_Z^2+_Z+1)*x^4+RootOf(_Z^2+_Z+1)*(x^4+1)^(2/3)*x+(x^4+1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2-2*RootOf(_Z^2+_Z+1)*x^3-x^4+2*(x^4+1)^(2/3)*x-x^2*(x^4+1)^(1/3)-x^3-RootOf(_Z^2+_Z+1)-1)/(x^4-x^3+1))+RootOf(_Z^2+_Z+1)*ln((-RootOf(_Z^2+_Z+1)^2*x^3+RootOf(_Z^2+_Z+1)*x^4+RootOf(_Z^2+_Z+1)*(x^4+1)^(2/3)*x-2*(x^4+1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2-RootOf(_Z^2+_Z+1)*x^3+x^4-(x^4+1)^(2/3)*x-x^2*(x^4+1)^(1/3)+RootOf(_Z^2+_Z+1)+1)/(x^4-x^3+1))","C"
977,0,0,11,0.023000," ","int((a*x^2+b)/(x^4-a*x^2+b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{a \,x^{2}+b}{\left(x^{4}-a \,x^{2}+b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2+b)/(x^4-a*x^2+b)/(a*x^4+b*x^2)^(1/4),x)","F"
978,0,0,11,0.000000," ","int((a*x^2+b)/(x^4-a*x^2+b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{a \,x^{2}+b}{\left(x^{4}-a \,x^{2}+b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2+b)/(x^4-a*x^2+b)/(a*x^4+b*x^2)^(1/4),x)","F"
979,0,0,60,0.010000," ","int((2*a*x^4-b)/x^2/(a*x^4-b)^(3/4),x)","\[\int \frac{2 a \,x^{4}-b}{x^{2} \left(a \,x^{4}-b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int((2*a*x^4-b)/x^2/(a*x^4-b)^(3/4),x)","F"
980,1,63,56,6.480000," ","int(1/x/(x^6+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\frac{2 \pi  \sqrt{3}\, x^{6} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], -x^{6}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+6 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{12 \pi}$&$63$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\frac{-353837768 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}+523021641 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+369307790 x^{6}+1600004967 \left(x^{6}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+569431707 \left(x^{6}+1\right)^{\frac{2}{3}}+1600004967 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}}+353837768 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+569431707 \left(x^{6}+1\right)^{\frac{1}{3}}+1953842735 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+923269475}{x^{6}}\right)}{6}-\frac{\ln \left(-\frac{1417676 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}+5413001 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+3479919 x^{6}+5928407 \left(x^{6}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+6057568 \left(x^{6}+1\right)^{\frac{2}{3}}+5928407 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}}-1417676 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+6057568 \left(x^{6}+1\right)^{\frac{1}{3}}+4510731 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+4639892}{x^{6}}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{6}-\frac{\ln \left(-\frac{1417676 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}+5413001 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+3479919 x^{6}+5928407 \left(x^{6}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+6057568 \left(x^{6}+1\right)^{\frac{2}{3}}+5928407 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}}-1417676 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+6057568 \left(x^{6}+1\right)^{\frac{1}{3}}+4510731 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+4639892}{x^{6}}\right)}{6}$&$348$\\ \hline \end{longtable}"," ",0,"1/12/Pi*3^(1/2)*GAMMA(2/3)*(-2/9*Pi*3^(1/2)/GAMMA(2/3)*x^6*hypergeom([1,1,4/3],[2,2],-x^6)+2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)+6*ln(x))*Pi*3^(1/2)/GAMMA(2/3))","C"
981,1,102,70,0.299000," ","int((2*x^6-9*x^4+3)/x/(x^2+1)^2/(2*x^2-1)/((-2*x^2+1)/(2*x^2+1))^(1/2)/(2*x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{2 \left(x^{2}-1\right) \left(2 x^{2}+1\right) \sqrt{-\frac{2 x^{2}-1}{2 x^{2}+1}}}{3 \left(2 x^{4}+x^{2}-1\right)}+\frac{3 \ln \left(\frac{2 \sqrt{-\frac{2 x^{2}-1}{2 x^{2}+1}}\, x^{2}+\sqrt{-\frac{2 x^{2}-1}{2 x^{2}+1}}+1}{x^{2}}\right)}{2}$&$102$\\ default&$-\frac{64 \sqrt{-4 x^{4}+1}\, x^{6}+16 \left(-4 x^{4}+1\right)^{\frac{3}{2}} x^{2}-32 \sqrt{-4 x^{4}+1}\, x^{4}+162 \arctanh \left(\frac{1}{\sqrt{-4 x^{4}+1}}\right) x^{4}-8 \left(-4 x^{4}+1\right)^{\frac{3}{2}}-52 x^{2} \sqrt{-4 x^{4}+1}+81 \arctanh \left(\frac{1}{\sqrt{-4 x^{4}+1}}\right) x^{2}+44 \sqrt{-4 x^{4}+1}-81 \arctanh \left(\frac{1}{\sqrt{-4 x^{4}+1}}\right)}{54 \left(x^{2}+1\right) \sqrt{-\left(2 x^{2}+1\right) \left(2 x^{2}-1\right)}\, \sqrt{-\frac{2 x^{2}-1}{2 x^{2}+1}}}$&$169$\\ \hline \end{longtable}"," ",0,"-2/3*(x^2-1)*(2*x^2+1)/(2*x^4+x^2-1)*(-(2*x^2-1)/(2*x^2+1))^(1/2)+3/2*ln((2*(-(2*x^2-1)/(2*x^2+1))^(1/2)*x^2+(-(2*x^2-1)/(2*x^2+1))^(1/2)+1)/x^2)","A"
982,1,196,62,4.373000," ","int((2*x^4-1)^(1/4)*(x^8-2)/x^6/(x^4-1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(2 x^{4}-1\right)^{\frac{1}{4}} \left(69 x^{8}-56 x^{4}-8\right)}{20 x^{5} \left(x^{4}-1\right)}+\frac{15 \ln \left(\frac{2 \left(2 x^{4}-1\right)^{\frac{3}{4}} x -2 \sqrt{2 x^{4}-1}\, x^{2}+2 \left(2 x^{4}-1\right)^{\frac{1}{4}} x^{3}-3 x^{4}+1}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)}{16}+\frac{15 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-2 \sqrt{2 x^{4}-1}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+3 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \left(2 x^{4}-1\right)^{\frac{3}{4}} x -2 \left(2 x^{4}-1\right)^{\frac{1}{4}} x^{3}-\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)}{16}$&$196$\\ risch&$\frac{138 x^{12}-181 x^{8}+40 x^{4}+8}{20 x^{5} \left(x^{4}-1\right) \left(2 x^{4}-1\right)^{\frac{3}{4}}}+\frac{\left(-\frac{15 \ln \left(\frac{12 x^{12}+8 \left(8 x^{12}-12 x^{8}+6 x^{4}-1\right)^{\frac{1}{4}} x^{9}+4 \sqrt{8 x^{12}-12 x^{8}+6 x^{4}-1}\, x^{6}-16 x^{8}+2 \left(8 x^{12}-12 x^{8}+6 x^{4}-1\right)^{\frac{3}{4}} x^{3}-8 \left(8 x^{12}-12 x^{8}+6 x^{4}-1\right)^{\frac{1}{4}} x^{5}-2 \sqrt{8 x^{12}-12 x^{8}+6 x^{4}-1}\, x^{2}+7 x^{4}+2 \left(8 x^{12}-12 x^{8}+6 x^{4}-1\right)^{\frac{1}{4}} x -1}{\left(2 x^{4}-1\right)^{2} \left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)}{16}+\frac{15 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{12 x^{12}-8 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(8 x^{12}-12 x^{8}+6 x^{4}-1\right)^{\frac{1}{4}} x^{9}-4 \sqrt{8 x^{12}-12 x^{8}+6 x^{4}-1}\, x^{6}-16 x^{8}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(8 x^{12}-12 x^{8}+6 x^{4}-1\right)^{\frac{3}{4}} x^{3}+8 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(8 x^{12}-12 x^{8}+6 x^{4}-1\right)^{\frac{1}{4}} x^{5}+2 \sqrt{8 x^{12}-12 x^{8}+6 x^{4}-1}\, x^{2}+7 x^{4}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(8 x^{12}-12 x^{8}+6 x^{4}-1\right)^{\frac{1}{4}} x -1}{\left(2 x^{4}-1\right)^{2} \left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)}{16}\right) \left(\left(2 x^{4}-1\right)^{3}\right)^{\frac{1}{4}}}{\left(2 x^{4}-1\right)^{\frac{3}{4}}}$&$471$\\ \hline \end{longtable}"," ",0,"1/20*(2*x^4-1)^(1/4)*(69*x^8-56*x^4-8)/x^5/(x^4-1)+15/16*ln((2*(2*x^4-1)^(3/4)*x-2*(2*x^4-1)^(1/2)*x^2+2*(2*x^4-1)^(1/4)*x^3-3*x^4+1)/(-1+x)/(1+x)/(x^2+1))+15/16*RootOf(_Z^2+1)*ln((-2*(2*x^4-1)^(1/2)*RootOf(_Z^2+1)*x^2+3*RootOf(_Z^2+1)*x^4+2*(2*x^4-1)^(3/4)*x-2*(2*x^4-1)^(1/4)*x^3-RootOf(_Z^2+1))/(-1+x)/(1+x)/(x^2+1))","C"
983,0,0,55,0.005000," ","int((a*x^2+b)^(3/4)/x^3,x)","\[\int \frac{\left(a \,x^{2}+b \right)^{\frac{3}{4}}}{x^{3}}\, dx\]"," ",0,"int((a*x^2+b)^(3/4)/x^3,x)","F"
984,0,0,63,0.013000," ","int((3-2*(1+k)*x+k*x^2)/((1-x)*x*(-k*x+1))^(1/4)/(-d+d*(1+k)*x-d*k*x^2+x^3),x)","\[\int \frac{3-2 \left(1+k \right) x +k \,x^{2}}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{4}} \left(-d +d \left(1+k \right) x -d k \,x^{2}+x^{3}\right)}\, dx\]"," ",0,"int((3-2*(1+k)*x+k*x^2)/((1-x)*x*(-k*x+1))^(1/4)/(-d+d*(1+k)*x-d*k*x^2+x^3),x)","F"
985,0,0,22,180.000000," ","int(1/(x^3-3*x^2+3*x-1)^(1/4)/(3*x^3+x^2-2*x-1),x)","\[\int \frac{1}{\left(x^{3}-3 x^{2}+3 x -1\right)^{\frac{1}{4}} \left(3 x^{3}+x^{2}-2 x -1\right)}\, dx\]"," ",0,"int(1/(x^3-3*x^2+3*x-1)^(1/4)/(3*x^3+x^2-2*x-1),x)","F"
986,0,0,55,0.004000," ","int((a*x^3+b)^(3/4)/x^4,x)","\[\int \frac{\left(a \,x^{3}+b \right)^{\frac{3}{4}}}{x^{4}}\, dx\]"," ",0,"int((a*x^3+b)^(3/4)/x^4,x)","F"
987,1,259,60,8.527000," ","int((x^4+x^2)^(1/4)/x^4/(x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{2}+1\right) \left(x^{4}+x^{2}\right)^{\frac{1}{4}}}{5 x^{3}}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(\frac{-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{3}-4 \left(x^{4}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}+4 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \sqrt{x^{4}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x +4 \left(x^{4}+x^{2}\right)^{\frac{3}{4}}}{x \left(-1+x \right) \left(1+x \right)}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(\frac{-3 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{3}+4 \left(x^{4}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}-4 \sqrt{x^{4}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}-2\right) x -\RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x +4 \left(x^{4}+x^{2}\right)^{\frac{3}{4}}}{x \left(-1+x \right) \left(1+x \right)}\right)}{4}$&$259$\\ risch&$\frac{2 \left(x^{4}+2 x^{2}+1\right) \left(x^{2} \left(x^{2}+1\right)\right)^{\frac{1}{4}}}{5 x^{3} \left(x^{2}+1\right)}+\frac{\left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{1}{4}} x^{4}+3 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{6}+4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{1}{4}} x^{2}+7 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{4}+2 \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+5 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}-4 \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)-4 \sqrt{x^{8}+3 x^{6}+3 x^{4}+x^{2}}\, x^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-4 \sqrt{x^{8}+3 x^{6}+3 x^{4}+x^{2}}}{\left(x^{2}+1\right)^{2} \left(-1+x \right) \left(1+x \right)}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{1}{4}} x^{4}-3 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{6}+4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{1}{4}} x^{2}-7 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{4}+2 \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}-5 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}+4 \left(x^{8}+3 x^{6}+3 x^{4}+x^{2}\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)-4 \sqrt{x^{8}+3 x^{6}+3 x^{4}+x^{2}}\, x^{2}-\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-4 \sqrt{x^{8}+3 x^{6}+3 x^{4}+x^{2}}}{\left(x^{2}+1\right)^{2} \left(-1+x \right) \left(1+x \right)}\right)}{4}\right) \left(x^{2} \left(x^{2}+1\right)\right)^{\frac{1}{4}} \left(x^{2} \left(x^{2}+1\right)^{3}\right)^{\frac{1}{4}}}{x \left(x^{2}+1\right)}$&$606$\\ \hline \end{longtable}"," ",0,"2/5*(x^2+1)*(x^4+x^2)^(1/4)/x^3-1/4*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln((-3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*x^3-4*(x^4+x^2)^(1/4)*RootOf(_Z^4-2)^2*x^2+4*RootOf(_Z^2+RootOf(_Z^4-2)^2)*(x^4+x^2)^(1/2)*x-RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x+4*(x^4+x^2)^(3/4))/x/(-1+x)/(1+x))+1/4*RootOf(_Z^4-2)*ln((-3*RootOf(_Z^4-2)^3*x^3+4*(x^4+x^2)^(1/4)*RootOf(_Z^4-2)^2*x^2-4*(x^4+x^2)^(1/2)*RootOf(_Z^4-2)*x-RootOf(_Z^4-2)^3*x+4*(x^4+x^2)^(3/4))/x/(-1+x)/(1+x))","C"
988,1,287,61,1.960000," ","int(x*(x^4-3)/(x^4+1)^(2/3)/(x^4+x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x -\left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+x^{4}-\left(x^{4}+1\right)^{\frac{2}{3}} x +x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}+1}{x^{4}+x^{3}+1}\right)-\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x -\left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-x^{4}+2 \left(x^{4}+1\right)^{\frac{2}{3}} x -2 x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}+x^{3}-1}{x^{4}+x^{3}+1}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x -\left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-x^{4}+2 \left(x^{4}+1\right)^{\frac{2}{3}} x -2 x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}+x^{3}-1}{x^{4}+x^{3}+1}\right)$&$287$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2+_Z+1)*ln((RootOf(_Z^2+_Z+1)*(x^4+1)^(2/3)*x-(x^4+1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2+RootOf(_Z^2+_Z+1)*x^3+x^4-(x^4+1)^(2/3)*x+x^2*(x^4+1)^(1/3)+1)/(x^4+x^3+1))-ln(-(RootOf(_Z^2+_Z+1)*(x^4+1)^(2/3)*x-(x^4+1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2+RootOf(_Z^2+_Z+1)*x^3-x^4+2*(x^4+1)^(2/3)*x-2*x^2*(x^4+1)^(1/3)+x^3-1)/(x^4+x^3+1))*RootOf(_Z^2+_Z+1)-ln(-(RootOf(_Z^2+_Z+1)*(x^4+1)^(2/3)*x-(x^4+1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2+RootOf(_Z^2+_Z+1)*x^3-x^4+2*(x^4+1)^(2/3)*x-2*x^2*(x^4+1)^(1/3)+x^3-1)/(x^4+x^3+1))","C"
989,1,61,67,0.675000," ","int((-4*x^4-x^2+2)^(1/2)*(2*x^4+1)/(2*x^4-1)/(2*x^4-x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(-\sqrt{6}\, \arctan \left(\frac{\sqrt{6}\, \sqrt{-4 x^{4}-x^{2}+2}\, \sqrt{2}}{6 x}\right)+\sqrt{2}\, \arctan \left(\frac{\sqrt{-4 x^{4}-x^{2}+2}}{x}\right)\right) \sqrt{2}}{2}$&$61$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{4}+2 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{2}+3 \sqrt{-4 x^{4}-x^{2}+2}\, x -\RootOf \left(\textit{\_Z}^{2}+3\right)}{\left(-1+x \right) \left(1+x \right) \left(2 x^{2}+1\right)}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+\sqrt{-4 x^{4}-x^{2}+2}\, x +\RootOf \left(\textit{\_Z}^{2}+1\right)}{2 x^{4}-1}\right)}{2}$&$145$\\ default&$-\frac{6 \sqrt{1-\left(\frac{1}{4}+\frac{\sqrt{33}}{4}\right) x^{2}}\, \sqrt{1-\left(\frac{1}{4}-\frac{\sqrt{33}}{4}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{1+\sqrt{33}}}{2}, \frac{i \sqrt{66}}{8}-\frac{i \sqrt{2}}{8}\right)}{\sqrt{1+\sqrt{33}}\, \sqrt{-4 x^{4}-x^{2}+2}}-\frac{32 \sqrt{1-\left(\frac{1}{4}+\frac{\sqrt{33}}{4}\right) x^{2}}\, \sqrt{1-\left(\frac{1}{4}-\frac{\sqrt{33}}{4}\right) x^{2}}\, \left(\EllipticF \left(\frac{x \sqrt{1+\sqrt{33}}}{2}, \frac{i \sqrt{66}}{8}-\frac{i \sqrt{2}}{8}\right)-\EllipticE \left(\frac{x \sqrt{1+\sqrt{33}}}{2}, \frac{i \sqrt{66}}{8}-\frac{i \sqrt{2}}{8}\right)\right)}{\sqrt{1+\sqrt{33}}\, \sqrt{-4 x^{4}-x^{2}+2}\, \left(-1+\sqrt{33}\right)}+\frac{3 \sqrt{1-\left(\frac{1}{4}+\frac{\sqrt{33}}{4}\right) x^{2}}\, \sqrt{1-\left(\frac{1}{4}-\frac{\sqrt{33}}{4}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{1}{4}+\frac{\sqrt{33}}{4}}\, x , \frac{1}{\frac{1}{4}+\frac{\sqrt{33}}{4}}, \frac{\sqrt{\frac{1}{4}-\frac{\sqrt{33}}{4}}}{\sqrt{\frac{1}{4}+\frac{\sqrt{33}}{4}}}\right)}{\sqrt{\frac{1}{4}+\frac{\sqrt{33}}{4}}\, \sqrt{-4 x^{4}-x^{2}+2}}+\frac{2 \sqrt{1-\frac{x^{2}}{4}-\frac{x^{2} \sqrt{33}}{4}}\, \sqrt{1-\frac{x^{2}}{4}+\frac{x^{2} \sqrt{33}}{4}}\, \EllipticF \left(\frac{x \sqrt{1+\sqrt{33}}}{2}, \frac{i \sqrt{66}}{8}-\frac{i \sqrt{2}}{8}\right)}{\sqrt{1+\sqrt{33}}\, \sqrt{-4 x^{4}-x^{2}+2}}+\frac{32 \sqrt{1-\frac{x^{2}}{4}-\frac{x^{2} \sqrt{33}}{4}}\, \sqrt{1-\frac{x^{2}}{4}+\frac{x^{2} \sqrt{33}}{4}}\, \EllipticF \left(\frac{x \sqrt{1+\sqrt{33}}}{2}, \frac{i \sqrt{66}}{8}-\frac{i \sqrt{2}}{8}\right)}{\sqrt{1+\sqrt{33}}\, \sqrt{-4 x^{4}-x^{2}+2}\, \left(-1+\sqrt{33}\right)}-\frac{32 \sqrt{1-\frac{x^{2}}{4}-\frac{x^{2} \sqrt{33}}{4}}\, \sqrt{1-\frac{x^{2}}{4}+\frac{x^{2} \sqrt{33}}{4}}\, \EllipticE \left(\frac{x \sqrt{1+\sqrt{33}}}{2}, \frac{i \sqrt{66}}{8}-\frac{i \sqrt{2}}{8}\right)}{\sqrt{1+\sqrt{33}}\, \sqrt{-4 x^{4}-x^{2}+2}\, \left(-1+\sqrt{33}\right)}+\frac{3 \sqrt{1-\frac{x^{2}}{4}-\frac{x^{2} \sqrt{33}}{4}}\, \sqrt{1-\frac{x^{2}}{4}+\frac{x^{2} \sqrt{33}}{4}}\, \EllipticPi \left(\sqrt{\frac{1}{4}+\frac{\sqrt{33}}{4}}\, x , -\frac{2}{\frac{1}{4}+\frac{\sqrt{33}}{4}}, \frac{\sqrt{\frac{1}{4}-\frac{\sqrt{33}}{4}}}{\sqrt{\frac{1}{4}+\frac{\sqrt{33}}{4}}}\right)}{\sqrt{\frac{1}{4}+\frac{\sqrt{33}}{4}}\, \sqrt{-4 x^{4}-x^{2}+2}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(2 \textit{\_Z}^{4}-1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(\frac{\arctanh \left(\frac{\left(8 \underline{\hspace{1.25 ex}}\alpha^{2}+1\right) \left(-33 \underline{\hspace{1.25 ex}}\alpha^{2}+31 x^{2}+8\right)}{62 \sqrt{-\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{-4 x^{4}-x^{2}+2}}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{2}}}-\frac{\sqrt{4}\, \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{-x^{2}+4-x^{2} \sqrt{33}}\, \sqrt{-x^{2}+4+x^{2} \sqrt{33}}\, \EllipticPi \left(\sqrt{\frac{1}{4}+\frac{\sqrt{33}}{4}}\, x , \frac{\underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{33}}{4}-\frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{4}, \frac{\sqrt{\frac{1}{4}-\frac{\sqrt{33}}{4}}}{\sqrt{\frac{1}{4}+\frac{\sqrt{33}}{4}}}\right)}{\sqrt{1+\sqrt{33}}\, \sqrt{-4 x^{4}-x^{2}+2}}\right)\right)}{4}$&$823$\\ \hline \end{longtable}"," ",0,"1/2*(-6^(1/2)*arctan(1/6*6^(1/2)*(-4*x^4-x^2+2)^(1/2)*2^(1/2)/x)+2^(1/2)*arctan((-4*x^4-x^2+2)^(1/2)/x))*2^(1/2)","A"
990,0,0,55,0.013000," ","int((a*x^4+b)^(3/4),x)","\[\int \left(a \,x^{4}+b \right)^{\frac{3}{4}}\, dx\]"," ",0,"int((a*x^4+b)^(3/4),x)","F"
991,0,0,55,0.005000," ","int((a*x^4+b)^(3/4)/x^4,x)","\[\int \frac{\left(a \,x^{4}+b \right)^{\frac{3}{4}}}{x^{4}}\, dx\]"," ",0,"int((a*x^4+b)^(3/4)/x^4,x)","F"
992,0,0,55,0.006000," ","int((a*x^5+b)^(3/4)/x^6,x)","\[\int \frac{\left(a \,x^{5}+b \right)^{\frac{3}{4}}}{x^{6}}\, dx\]"," ",0,"int((a*x^5+b)^(3/4)/x^6,x)","F"
993,1,348,61,5.813000," ","int((-3*x^5+2)/(x^5-x^2+1)/(x^6+x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(-\frac{540903516171 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{5}+17275317817 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{5}-2129063429050 x^{5}-1081807032342 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}+1553609277245 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+x \right)^{\frac{2}{3}}-4781755056454 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+x \right)^{\frac{1}{3}} x +3751773977563 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+3228145779209 \left(x^{6}+x \right)^{\frac{2}{3}}+1553609277245 x \left(x^{6}+x \right)^{\frac{1}{3}}+540903516171 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}-3193595143575 x^{2}+17275317817 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-2129063429050}{x^{5}-x^{2}+1}\right)+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(-\frac{-25445006 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{5}+110741541 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{5}-103219569 x^{5}+50890012 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}+70252591 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+x \right)^{\frac{2}{3}}-163071098 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+x \right)^{\frac{1}{3}} x -43368040 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+92818507 \left(x^{6}+x \right)^{\frac{2}{3}}+70252591 x \left(x^{6}+x \right)^{\frac{1}{3}}-25445006 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}-34406523 x^{2}+110741541 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-103219569}{x^{5}-x^{2}+1}\right)$&$348$\\ \hline \end{longtable}"," ",0,"-ln(-(540903516171*RootOf(_Z^2-_Z+1)^2*x^5+17275317817*RootOf(_Z^2-_Z+1)*x^5-2129063429050*x^5-1081807032342*RootOf(_Z^2-_Z+1)^2*x^2+1553609277245*RootOf(_Z^2-_Z+1)*(x^6+x)^(2/3)-4781755056454*RootOf(_Z^2-_Z+1)*(x^6+x)^(1/3)*x+3751773977563*RootOf(_Z^2-_Z+1)*x^2+3228145779209*(x^6+x)^(2/3)+1553609277245*x*(x^6+x)^(1/3)+540903516171*RootOf(_Z^2-_Z+1)^2-3193595143575*x^2+17275317817*RootOf(_Z^2-_Z+1)-2129063429050)/(x^5-x^2+1))+RootOf(_Z^2-_Z+1)*ln(-(-25445006*RootOf(_Z^2-_Z+1)^2*x^5+110741541*RootOf(_Z^2-_Z+1)*x^5-103219569*x^5+50890012*RootOf(_Z^2-_Z+1)^2*x^2+70252591*RootOf(_Z^2-_Z+1)*(x^6+x)^(2/3)-163071098*RootOf(_Z^2-_Z+1)*(x^6+x)^(1/3)*x-43368040*RootOf(_Z^2-_Z+1)*x^2+92818507*(x^6+x)^(2/3)+70252591*x*(x^6+x)^(1/3)-25445006*RootOf(_Z^2-_Z+1)^2-34406523*x^2+110741541*RootOf(_Z^2-_Z+1)-103219569)/(x^5-x^2+1))","C"
994,0,0,55,0.006000," ","int((a*x^6+b)^(3/4)/x^7,x)","\[\int \frac{\left(a \,x^{6}+b \right)^{\frac{3}{4}}}{x^{7}}\, dx\]"," ",0,"int((a*x^6+b)^(3/4)/x^7,x)","F"
995,0,0,65,0.023000," ","int((a*x^6+2*b)/(a*x^6-b)^(1/4)/(a*x^6-2*x^4-b),x)","\[\int \frac{a \,x^{6}+2 b}{\left(a \,x^{6}-b \right)^{\frac{1}{4}} \left(a \,x^{6}-2 x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^6+2*b)/(a*x^6-b)^(1/4)/(a*x^6-2*x^4-b),x)","F"
996,1,102,59,0.957000," ","int((x^4-1)*(x^4+1)^(1/2)/(x^8+3*x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(\frac{\ln \left(\frac{x^{4}+1}{x^{2}}-\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{x}+1\right)}{4}+\frac{\arctan \left(-1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{x}\right)}{2}-\frac{\ln \left(\frac{x^{4}+1}{x^{2}}+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{x}+1\right)}{4}+\frac{\arctan \left(1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{x}\right)}{2}\right) \sqrt{2}}{2}$&$102$\\ elliptic&$\frac{\left(\frac{\ln \left(\frac{x^{4}+1}{x^{2}}-\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{x}+1\right)}{4}+\frac{\arctan \left(-1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{x}\right)}{2}-\frac{\ln \left(\frac{x^{4}+1}{x^{2}}+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{x}+1\right)}{4}+\frac{\arctan \left(1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{x}\right)}{2}\right) \sqrt{2}}{2}$&$102$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{5} x^{2}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{4}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+2 \sqrt{x^{4}+1}\, x}{\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}-x^{4}-1}\right)}{4}-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}+\RootOf \left(\textit{\_Z}^{4}+1\right) x^{4}+2 \sqrt{x^{4}+1}\, x +\RootOf \left(\textit{\_Z}^{4}+1\right)}{\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}+x^{4}+1}\right)}{4}$&$147$\\ \hline \end{longtable}"," ",0,"1/2*(1/4*ln(1/x^2*(x^4+1)-2^(1/2)/x*(x^4+1)^(1/2)+1)+1/2*arctan(-1+2^(1/2)/x*(x^4+1)^(1/2))-1/4*ln(1/x^2*(x^4+1)+2^(1/2)/x*(x^4+1)^(1/2)+1)+1/2*arctan(1+2^(1/2)/x*(x^4+1)^(1/2)))*2^(1/2)","A"
997,1,1175,66,0.270000," ","int((k^2*x^2-1)/((1-x)*x*(-k^2*x+1))^(1/2)/(a*k^2*x^2+b*x+a),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{a \,k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-b +\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\sqrt{-4 a^{2} k^{2}+b^{2}}\, k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{b}{2 a \,k^{2}}-\frac{\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right)}-\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-b +\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b^{2}}{\sqrt{-4 a^{2} k^{2}+b^{2}}\, k^{4} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{b}{2 a \,k^{2}}-\frac{\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right) a^{2}}+\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-b +\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{k^{4} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{b}{2 a \,k^{2}}-\frac{\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right) a^{2}}-\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{b +\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\sqrt{-4 a^{2} k^{2}+b^{2}}\, k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{b}{2 a \,k^{2}}+\frac{\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right)}+\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{b +\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b^{2}}{\sqrt{-4 a^{2} k^{2}+b^{2}}\, k^{4} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{b}{2 a \,k^{2}}+\frac{\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right) a^{2}}+\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{b +\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{k^{4} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{b}{2 a \,k^{2}}+\frac{\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right) a^{2}}$&$1175$\\ default&$-\frac{2 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{a \,k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{-\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-b +\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b^{2}}{\sqrt{-4 a^{2} k^{2}+b^{2}}\, k^{4} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{b}{2 a \,k^{2}}-\frac{\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right) a}+\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-b +\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{k^{4} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{b}{2 a \,k^{2}}-\frac{\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right) a}+\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{-b +\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) a}{\sqrt{-4 a^{2} k^{2}+b^{2}}\, k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{b}{2 a \,k^{2}}-\frac{\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right)}+\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{b +\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b^{2}}{\sqrt{-4 a^{2} k^{2}+b^{2}}\, k^{4} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{b}{2 a \,k^{2}}+\frac{\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right) a}+\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{b +\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{k^{4} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{b}{2 a \,k^{2}}+\frac{\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right) a}-\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{b +\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) a}{\sqrt{-4 a^{2} k^{2}+b^{2}}\, k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{b}{2 a \,k^{2}}+\frac{\sqrt{-4 a^{2} k^{2}+b^{2}}}{2 a \,k^{2}}\right)}}{a}$&$1178$\\ \hline \end{longtable}"," ",0,"-2/a/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticF((-(x-1/k^2)*k^2)^(1/2),(1/k^2/(1/k^2-1))^(1/2))+4/(-4*a^2*k^2+b^2)^(1/2)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/2*b/a/k^2-1/2/a/k^2*(-4*a^2*k^2+b^2)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-1/2/a/k^2*(-b+(-4*a^2*k^2+b^2)^(1/2))),(1/k^2/(1/k^2-1))^(1/2))-1/(-4*a^2*k^2+b^2)^(1/2)/k^4*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/2*b/a/k^2-1/2/a/k^2*(-4*a^2*k^2+b^2)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-1/2/a/k^2*(-b+(-4*a^2*k^2+b^2)^(1/2))),(1/k^2/(1/k^2-1))^(1/2))*b^2/a^2+1/k^4*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/2*b/a/k^2-1/2/a/k^2*(-4*a^2*k^2+b^2)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-1/2/a/k^2*(-b+(-4*a^2*k^2+b^2)^(1/2))),(1/k^2/(1/k^2-1))^(1/2))*b/a^2-4/(-4*a^2*k^2+b^2)^(1/2)/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/2*b/a/k^2+1/2/a/k^2*(-4*a^2*k^2+b^2)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+1/2*(b+(-4*a^2*k^2+b^2)^(1/2))/a/k^2),(1/k^2/(1/k^2-1))^(1/2))+1/(-4*a^2*k^2+b^2)^(1/2)/k^4*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/2*b/a/k^2+1/2/a/k^2*(-4*a^2*k^2+b^2)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+1/2*(b+(-4*a^2*k^2+b^2)^(1/2))/a/k^2),(1/k^2/(1/k^2-1))^(1/2))*b^2/a^2+1/k^4*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/2*b/a/k^2+1/2/a/k^2*(-4*a^2*k^2+b^2)^(1/2))*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+1/2*(b+(-4*a^2*k^2+b^2)^(1/2))/a/k^2),(1/k^2/(1/k^2-1))^(1/2))*b/a^2","C"
998,1,83,58,3.418000," ","int(1/x/(x^4-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{3}} \left(\frac{2 \pi  \sqrt{3}\, x^{4} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], x^{4}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{8 \pi  \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{3}}}$&$83$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(-\frac{-13019 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{4}+173029 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{4}+333840 x^{4}+186849 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}}-853728 \left(x^{4}-1\right)^{\frac{2}{3}}-186849 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{1}{3}}+208304 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}+853728 \left(x^{4}-1\right)^{\frac{1}{3}}-21455 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-645424}{x^{4}}\right)}{4}-\frac{\ln \left(-\frac{13085182254449 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{4}+153030407784045 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{4}-422270012895374 x^{4}+103124015072835 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}}+601470785188317 \left(x^{4}-1\right)^{\frac{2}{3}}-103124015072835 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{1}{3}}-209362916071184 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}-601470785188317 \left(x^{4}-1\right)^{\frac{1}{3}}+312486931144019 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+392107869117133}{x^{4}}\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)}{4}+\frac{\ln \left(-\frac{13085182254449 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{4}+153030407784045 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{4}-422270012895374 x^{4}+103124015072835 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}}+601470785188317 \left(x^{4}-1\right)^{\frac{2}{3}}-103124015072835 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{1}{3}}-209362916071184 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}-601470785188317 \left(x^{4}-1\right)^{\frac{1}{3}}+312486931144019 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+392107869117133}{x^{4}}\right)}{4}$&$389$\\ \hline \end{longtable}"," ",0,"1/8/Pi*3^(1/2)*GAMMA(2/3)/signum(x^4-1)^(1/3)*(-signum(x^4-1))^(1/3)*(2/9*Pi*3^(1/2)/GAMMA(2/3)*x^4*hypergeom([1,1,4/3],[2,2],x^4)+2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)+4*ln(x)+I*Pi)*Pi*3^(1/2)/GAMMA(2/3))","C"
999,0,0,67,0.024000," ","int(x^2*(a*x^2-2*b)/(a*x^2-b)^(3/4)/(x^4-4*a*x^2+4*b),x)","\[\int \frac{x^{2} \left(a \,x^{2}-2 b \right)}{\left(a \,x^{2}-b \right)^{\frac{3}{4}} \left(x^{4}-4 a \,x^{2}+4 b \right)}\, dx\]"," ",0,"int(x^2*(a*x^2-2*b)/(a*x^2-b)^(3/4)/(x^4-4*a*x^2+4*b),x)","F"
1000,1,289,64,0.096000," ","int((-a*b*x+x^3)/(x*(-a+x)*(-b+x))^(1/2)/(a^2*b^2-2*a*b*(a+b)*x+(a^2+4*a*b+b^2-d)*x^2-2*(a+b)*x^3+x^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+\left(-2 a -2 b \right) \textit{\_Z}^{3}+\left(a^{2}+4 a b +b^{2}-d \right) \textit{\_Z}^{2}+\left(-2 a^{2} b -2 a \,b^{2}\right) \textit{\_Z} +a^{2} b^{2}\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2}-a b \right) \left(-\underline{\hspace{1.25 ex}}\alpha^{3}+2 \underline{\hspace{1.25 ex}}\alpha^{2} a +\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2}-2 \underline{\hspace{1.25 ex}}\alpha  a b +a^{2} b +\underline{\hspace{1.25 ex}}\alpha  d +b d \right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{-\underline{\hspace{1.25 ex}}\alpha^{3}+2 \underline{\hspace{1.25 ex}}\alpha^{2} a +\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2}-2 \underline{\hspace{1.25 ex}}\alpha  a b +a^{2} b +\underline{\hspace{1.25 ex}}\alpha  d +b d}{b d}, \sqrt{\frac{b}{-a +b}}\right)}{\left(-2 \underline{\hspace{1.25 ex}}\alpha^{3}+3 \underline{\hspace{1.25 ex}}\alpha^{2} a +3 \underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2}-4 \underline{\hspace{1.25 ex}}\alpha  a b -\underline{\hspace{1.25 ex}}\alpha  \,b^{2}+a^{2} b +a \,b^{2}+\underline{\hspace{1.25 ex}}\alpha  d \right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}}{b d}$&$289$\\ elliptic&$\frac{\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+\left(-2 a -2 b \right) \textit{\_Z}^{3}+\left(a^{2}+4 a b +b^{2}-d \right) \textit{\_Z}^{2}+\left(-2 a^{2} b -2 a \,b^{2}\right) \textit{\_Z} +a^{2} b^{2}\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2}-a b \right) \left(-\underline{\hspace{1.25 ex}}\alpha^{3}+2 \underline{\hspace{1.25 ex}}\alpha^{2} a +\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2}-2 \underline{\hspace{1.25 ex}}\alpha  a b +a^{2} b +\underline{\hspace{1.25 ex}}\alpha  d +b d \right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{-\underline{\hspace{1.25 ex}}\alpha^{3}+2 \underline{\hspace{1.25 ex}}\alpha^{2} a +\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2}-2 \underline{\hspace{1.25 ex}}\alpha  a b +a^{2} b +\underline{\hspace{1.25 ex}}\alpha  d +b d}{b d}, \sqrt{\frac{b}{-a +b}}\right)}{\left(-2 \underline{\hspace{1.25 ex}}\alpha^{3}+3 \underline{\hspace{1.25 ex}}\alpha^{2} a +3 \underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2}-4 \underline{\hspace{1.25 ex}}\alpha  a b -\underline{\hspace{1.25 ex}}\alpha  \,b^{2}+a^{2} b +a \,b^{2}+\underline{\hspace{1.25 ex}}\alpha  d \right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}}{b d}$&$289$\\ \hline \end{longtable}"," ",0,"1/b/d*sum(_alpha*(_alpha^2-a*b)/(-2*_alpha^3+3*_alpha^2*a+3*_alpha^2*b-_alpha*a^2-4*_alpha*a*b-_alpha*b^2+a^2*b+a*b^2+_alpha*d)*(-_alpha^3+2*_alpha^2*a+_alpha^2*b-_alpha*a^2-2*_alpha*a*b+a^2*b+_alpha*d+b*d)*(-(-b+x)/b)^(1/2)*((-a+x)/(-a+b))^(1/2)*(x/b)^(1/2)/(x*(a*b-a*x-b*x+x^2))^(1/2)*EllipticPi((-(-b+x)/b)^(1/2),(-_alpha^3+2*_alpha^2*a+_alpha^2*b-_alpha*a^2-2*_alpha*a*b+a^2*b+_alpha*d+b*d)/b/d,(b/(-a+b))^(1/2)),_alpha=RootOf(_Z^4+(-2*a-2*b)*_Z^3+(a^2+4*a*b+b^2-d)*_Z^2+(-2*a^2*b-2*a*b^2)*_Z+a^2*b^2))","C"
1001,1,152,64,3.102000," ","int((-x^4-1)^(1/4)*(x^4-1)/x^6/(2*x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(14 x^{4}-1\right) \left(-x^{4}-1\right)^{\frac{1}{4}}}{5 x^{5}}-\frac{3 \ln \left(\frac{2 \left(-x^{4}-1\right)^{\frac{3}{4}} x -2 \sqrt{-x^{4}-1}\, x^{2}+2 \left(-x^{4}-1\right)^{\frac{1}{4}} x^{3}+1}{2 x^{4}+1}\right)}{4}-\frac{3 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-2 \sqrt{-x^{4}-1}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \left(-x^{4}-1\right)^{\frac{3}{4}} x -2 \left(-x^{4}-1\right)^{\frac{1}{4}} x^{3}-\RootOf \left(\textit{\_Z}^{2}+1\right)}{2 x^{4}+1}\right)}{4}$&$152$\\ risch&$\frac{14 x^{8}+13 x^{4}-1}{5 x^{5} \left(-x^{4}-1\right)^{\frac{3}{4}}}+\frac{\left(-\frac{3 \ln \left(\frac{2 \left(-x^{12}-3 x^{8}-3 x^{4}-1\right)^{\frac{1}{4}} x^{9}+2 \sqrt{-x^{12}-3 x^{8}-3 x^{4}-1}\, x^{6}+x^{8}+2 \left(-x^{12}-3 x^{8}-3 x^{4}-1\right)^{\frac{3}{4}} x^{3}+4 \left(-x^{12}-3 x^{8}-3 x^{4}-1\right)^{\frac{1}{4}} x^{5}+2 \sqrt{-x^{12}-3 x^{8}-3 x^{4}-1}\, x^{2}+2 x^{4}+2 \left(-x^{12}-3 x^{8}-3 x^{4}-1\right)^{\frac{1}{4}} x +1}{\left(x^{4}+1\right)^{2} \left(2 x^{4}+1\right)}\right)}{4}-\frac{3 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(-x^{12}-3 x^{8}-3 x^{4}-1\right)^{\frac{1}{4}} x^{9}+2 \sqrt{-x^{12}-3 x^{8}-3 x^{4}-1}\, x^{6}-x^{8}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(-x^{12}-3 x^{8}-3 x^{4}-1\right)^{\frac{3}{4}} x^{3}-4 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(-x^{12}-3 x^{8}-3 x^{4}-1\right)^{\frac{1}{4}} x^{5}+2 \sqrt{-x^{12}-3 x^{8}-3 x^{4}-1}\, x^{2}-2 x^{4}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(-x^{12}-3 x^{8}-3 x^{4}-1\right)^{\frac{1}{4}} x -1}{\left(x^{4}+1\right)^{2} \left(2 x^{4}+1\right)}\right)}{4}\right) \left(-\left(x^{4}+1\right)^{3}\right)^{\frac{1}{4}}}{\left(-x^{4}-1\right)^{\frac{3}{4}}}$&$426$\\ \hline \end{longtable}"," ",0,"-1/5*(14*x^4-1)/x^5*(-x^4-1)^(1/4)-3/4*ln((2*(-x^4-1)^(3/4)*x-2*(-x^4-1)^(1/2)*x^2+2*(-x^4-1)^(1/4)*x^3+1)/(2*x^4+1))-3/4*RootOf(_Z^2+1)*ln((-2*(-x^4-1)^(1/2)*RootOf(_Z^2+1)*x^2+2*(-x^4-1)^(3/4)*x-2*(-x^4-1)^(1/4)*x^3-RootOf(_Z^2+1))/(2*x^4+1))","C"
1002,1,304,64,0.094000," ","int((a*b*x-x^3)/(x*(-a+x)*(-b+x))^(1/2)/(a^2*b^2*d-2*a*b*(a+b)*d*x+(a^2*d+4*a*b*d+b^2*d-1)*x^2-2*(a+b)*d*x^3+d*x^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(d \,\textit{\_Z}^{4}+\left(-2 a d -2 b d \right) \textit{\_Z}^{3}+\left(a^{2} d +4 a b d +b^{2} d -1\right) \textit{\_Z}^{2}+\left(-2 a^{2} b d -2 a \,b^{2} d \right) \textit{\_Z} +a^{2} b^{2} d \right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2}-a b \right) \left(-d \,\underline{\hspace{1.25 ex}}\alpha^{3}+2 d \,\underline{\hspace{1.25 ex}}\alpha^{2} a +d \,\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2} d -2 \underline{\hspace{1.25 ex}}\alpha  a d b +a^{2} b d +\underline{\hspace{1.25 ex}}\alpha  +b \right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{-d \,\underline{\hspace{1.25 ex}}\alpha^{3}+2 d \,\underline{\hspace{1.25 ex}}\alpha^{2} a +d \,\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2} d -2 \underline{\hspace{1.25 ex}}\alpha  a d b +a^{2} b d +\underline{\hspace{1.25 ex}}\alpha  +b}{b}, \sqrt{\frac{b}{-a +b}}\right)}{\left(-2 d \,\underline{\hspace{1.25 ex}}\alpha^{3}+3 d \,\underline{\hspace{1.25 ex}}\alpha^{2} a +3 d \,\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2} d -4 \underline{\hspace{1.25 ex}}\alpha  a d b -\underline{\hspace{1.25 ex}}\alpha  \,b^{2} d +a^{2} b d +a \,b^{2} d +\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}}{b}$&$304$\\ elliptic&$-\frac{\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(d \,\textit{\_Z}^{4}+\left(-2 a d -2 b d \right) \textit{\_Z}^{3}+\left(a^{2} d +4 a b d +b^{2} d -1\right) \textit{\_Z}^{2}+\left(-2 a^{2} b d -2 a \,b^{2} d \right) \textit{\_Z} +a^{2} b^{2} d \right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2}-a b \right) \left(-d \,\underline{\hspace{1.25 ex}}\alpha^{3}+2 d \,\underline{\hspace{1.25 ex}}\alpha^{2} a +d \,\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2} d -2 \underline{\hspace{1.25 ex}}\alpha  a d b +a^{2} b d +\underline{\hspace{1.25 ex}}\alpha  +b \right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{-d \,\underline{\hspace{1.25 ex}}\alpha^{3}+2 d \,\underline{\hspace{1.25 ex}}\alpha^{2} a +d \,\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2} d -2 \underline{\hspace{1.25 ex}}\alpha  a d b +a^{2} b d +\underline{\hspace{1.25 ex}}\alpha  +b}{b}, \sqrt{\frac{b}{-a +b}}\right)}{\left(-2 d \,\underline{\hspace{1.25 ex}}\alpha^{3}+3 d \,\underline{\hspace{1.25 ex}}\alpha^{2} a +3 d \,\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2} d -4 \underline{\hspace{1.25 ex}}\alpha  a d b -\underline{\hspace{1.25 ex}}\alpha  \,b^{2} d +a^{2} b d +a \,b^{2} d +\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}}{b}$&$304$\\ \hline \end{longtable}"," ",0,"-1/b*sum(_alpha*(_alpha^2-a*b)/(-2*_alpha^3*d+3*_alpha^2*a*d+3*_alpha^2*b*d-_alpha*a^2*d-4*_alpha*a*b*d-_alpha*b^2*d+a^2*b*d+a*b^2*d+_alpha)*(-_alpha^3*d+2*_alpha^2*a*d+_alpha^2*b*d-_alpha*a^2*d-2*_alpha*a*b*d+a^2*b*d+_alpha+b)*(-(-b+x)/b)^(1/2)*((-a+x)/(-a+b))^(1/2)*(x/b)^(1/2)/(x*(a*b-a*x-b*x+x^2))^(1/2)*EllipticPi((-(-b+x)/b)^(1/2),(-_alpha^3*d+2*_alpha^2*a*d+_alpha^2*b*d-_alpha*a^2*d-2*_alpha*a*b*d+a^2*b*d+_alpha+b)/b,(b/(-a+b))^(1/2)),_alpha=RootOf(d*_Z^4+(-2*a*d-2*b*d)*_Z^3+(a^2*d+4*a*b*d+b^2*d-1)*_Z^2+(-2*a^2*b*d-2*a*b^2*d)*_Z+a^2*b^2*d))","C"
1003,1,303,64,0.075000," ","int((-a*b*x+x^3)/(x*(-a+x)*(-b+x))^(1/2)/(a^2*b^2*d-2*a*b*(a+b)*d*x+(a^2*d+4*a*b*d+b^2*d-1)*x^2-2*(a+b)*d*x^3+d*x^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(d \,\textit{\_Z}^{4}+\left(-2 a d -2 b d \right) \textit{\_Z}^{3}+\left(a^{2} d +4 a b d +b^{2} d -1\right) \textit{\_Z}^{2}+\left(-2 a^{2} b d -2 a \,b^{2} d \right) \textit{\_Z} +a^{2} b^{2} d \right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2}-a b \right) \left(-d \,\underline{\hspace{1.25 ex}}\alpha^{3}+2 d \,\underline{\hspace{1.25 ex}}\alpha^{2} a +d \,\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2} d -2 \underline{\hspace{1.25 ex}}\alpha  a d b +a^{2} b d +\underline{\hspace{1.25 ex}}\alpha  +b \right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{-d \,\underline{\hspace{1.25 ex}}\alpha^{3}+2 d \,\underline{\hspace{1.25 ex}}\alpha^{2} a +d \,\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2} d -2 \underline{\hspace{1.25 ex}}\alpha  a d b +a^{2} b d +\underline{\hspace{1.25 ex}}\alpha  +b}{b}, \sqrt{\frac{b}{-a +b}}\right)}{\left(-2 d \,\underline{\hspace{1.25 ex}}\alpha^{3}+3 d \,\underline{\hspace{1.25 ex}}\alpha^{2} a +3 d \,\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2} d -4 \underline{\hspace{1.25 ex}}\alpha  a d b -\underline{\hspace{1.25 ex}}\alpha  \,b^{2} d +a^{2} b d +a \,b^{2} d +\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}}{b}$&$303$\\ elliptic&$\frac{\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(d \,\textit{\_Z}^{4}+\left(-2 a d -2 b d \right) \textit{\_Z}^{3}+\left(a^{2} d +4 a b d +b^{2} d -1\right) \textit{\_Z}^{2}+\left(-2 a^{2} b d -2 a \,b^{2} d \right) \textit{\_Z} +a^{2} b^{2} d \right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2}-a b \right) \left(-d \,\underline{\hspace{1.25 ex}}\alpha^{3}+2 d \,\underline{\hspace{1.25 ex}}\alpha^{2} a +d \,\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2} d -2 \underline{\hspace{1.25 ex}}\alpha  a d b +a^{2} b d +\underline{\hspace{1.25 ex}}\alpha  +b \right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{-d \,\underline{\hspace{1.25 ex}}\alpha^{3}+2 d \,\underline{\hspace{1.25 ex}}\alpha^{2} a +d \,\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2} d -2 \underline{\hspace{1.25 ex}}\alpha  a d b +a^{2} b d +\underline{\hspace{1.25 ex}}\alpha  +b}{b}, \sqrt{\frac{b}{-a +b}}\right)}{\left(-2 d \,\underline{\hspace{1.25 ex}}\alpha^{3}+3 d \,\underline{\hspace{1.25 ex}}\alpha^{2} a +3 d \,\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2} d -4 \underline{\hspace{1.25 ex}}\alpha  a d b -\underline{\hspace{1.25 ex}}\alpha  \,b^{2} d +a^{2} b d +a \,b^{2} d +\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}}{b}$&$303$\\ \hline \end{longtable}"," ",0,"1/b*sum(_alpha*(_alpha^2-a*b)/(-2*_alpha^3*d+3*_alpha^2*a*d+3*_alpha^2*b*d-_alpha*a^2*d-4*_alpha*a*b*d-_alpha*b^2*d+a^2*b*d+a*b^2*d+_alpha)*(-_alpha^3*d+2*_alpha^2*a*d+_alpha^2*b*d-_alpha*a^2*d-2*_alpha*a*b*d+a^2*b*d+_alpha+b)*(-(-b+x)/b)^(1/2)*((-a+x)/(-a+b))^(1/2)*(x/b)^(1/2)/(x*(a*b-a*x-b*x+x^2))^(1/2)*EllipticPi((-(-b+x)/b)^(1/2),(-_alpha^3*d+2*_alpha^2*a*d+_alpha^2*b*d-_alpha*a^2*d-2*_alpha*a*b*d+a^2*b*d+_alpha+b)/b,(b/(-a+b))^(1/2)),_alpha=RootOf(d*_Z^4+(-2*a*d-2*b*d)*_Z^3+(a^2*d+4*a*b*d+b^2*d-1)*_Z^2+(-2*a^2*b*d-2*a*b^2*d)*_Z+a^2*b^2*d))","C"
1004,1,83,58,7.242000," ","int(1/x/(x^6-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} \left(\frac{2 \pi  \sqrt{3}\, x^{6} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], x^{6}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+6 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{12 \pi  \mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}}}$&$83$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(-\frac{1505024575790858565046 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}-94448748446849318458973 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}-23171389162410581752275 x^{6}+68267310132857019576606 \left(x^{6}-1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+142296551347461340528569 \left(x^{6}-1\right)^{\frac{2}{3}}-68267310132857019576606 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}}-96321572850614948162944 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}-142296551347461340528569 \left(x^{6}-1\right)^{\frac{1}{3}}+164588882983471967739550 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+45974978496846392365625}{x^{6}}\right)}{6}-\frac{\ln \left(\frac{-1505024575790858565046 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}-91438699295267601328881 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}+116115113033469041646202 x^{6}+68267310132857019576606 \left(x^{6}-1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-210563861480318360105175 \left(x^{6}-1\right)^{\frac{2}{3}}-68267310132857019576606 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}}+96321572850614948162944 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}+210563861480318360105175 \left(x^{6}-1\right)^{\frac{1}{3}}-28054262717757928586338 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-114242288629703411942231}{x^{6}}\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)}{6}+\frac{\ln \left(\frac{-1505024575790858565046 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}-91438699295267601328881 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}+116115113033469041646202 x^{6}+68267310132857019576606 \left(x^{6}-1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-210563861480318360105175 \left(x^{6}-1\right)^{\frac{2}{3}}-68267310132857019576606 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}}+96321572850614948162944 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}+210563861480318360105175 \left(x^{6}-1\right)^{\frac{1}{3}}-28054262717757928586338 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-114242288629703411942231}{x^{6}}\right)}{6}$&$387$\\ \hline \end{longtable}"," ",0,"1/12/Pi*3^(1/2)*GAMMA(2/3)/signum(x^6-1)^(1/3)*(-signum(x^6-1))^(1/3)*(2/9*Pi*3^(1/2)/GAMMA(2/3)*x^6*hypergeom([1,1,4/3],[2,2],x^6)+2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)+6*ln(x)+I*Pi)*Pi*3^(1/2)/GAMMA(2/3))","C"
1005,1,1837,29,22.319000," ","int((x^3+1)^(2/3)*(2*x^6+x^3+2)/x^6/(x^6+x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$1837$\\ trager&$\text{Expression too large to display}$&$4248$\\ \hline \end{longtable}"," ",0,"1/10*(x^6-3*x^3-4)/x^5/(x^3+1)^(1/3)+1458*ln((729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x^3+243*(x^3+1)^(1/3)*RootOf(19683*_Z^6+243*_Z^3+1)^3*x^2+27*RootOf(19683*_Z^6+243*_Z^3+1)^2*(x^3+1)^(2/3)*x+6*RootOf(19683*_Z^6+243*_Z^3+1)*x^3+x^2*(x^3+1)^(1/3)+3*RootOf(19683*_Z^6+243*_Z^3+1))/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+54*RootOf(19683*_Z^6+243*_Z^3+1)^2*x-1)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x+1)/(27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x+1))*RootOf(19683*_Z^6+243*_Z^3+1)^5-729*ln((-4374*RootOf(19683*_Z^6+243*_Z^3+1)^5*x^3+81*(x^3+1)^(2/3)*RootOf(19683*_Z^6+243*_Z^3+1)^3*x-2187*RootOf(19683*_Z^6+243*_Z^3+1)^5-18*RootOf(19683*_Z^6+243*_Z^3+1)^2*x^3+3*(x^3+1)^(1/3)*RootOf(19683*_Z^6+243*_Z^3+1)*x^2+x*(x^3+1)^(2/3)-9*RootOf(19683*_Z^6+243*_Z^3+1)^2)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+54*RootOf(19683*_Z^6+243*_Z^3+1)^2*x-1)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x+1)/(27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x+1))*RootOf(19683*_Z^6+243*_Z^3+1)^5+243*ln(-(-59049*RootOf(19683*_Z^6+243*_Z^3+1)^7*x^3-4374*(x^3+1)^(1/3)*RootOf(19683*_Z^6+243*_Z^3+1)^5*x^2-972*RootOf(19683*_Z^6+243*_Z^3+1)^4*x^3+81*(x^3+1)^(2/3)*RootOf(19683*_Z^6+243*_Z^3+1)^3*x-27*(x^3+1)^(1/3)*RootOf(19683*_Z^6+243*_Z^3+1)^2*x^2+243*RootOf(19683*_Z^6+243*_Z^3+1)^4-3*RootOf(19683*_Z^6+243*_Z^3+1)*x^3+x*(x^3+1)^(2/3)+3*RootOf(19683*_Z^6+243*_Z^3+1))/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x-1)/(1458*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x+1)/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x-1))*RootOf(19683*_Z^6+243*_Z^3+1)^4+9*ln((729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x^3+243*(x^3+1)^(1/3)*RootOf(19683*_Z^6+243*_Z^3+1)^3*x^2+27*RootOf(19683*_Z^6+243*_Z^3+1)^2*(x^3+1)^(2/3)*x+6*RootOf(19683*_Z^6+243*_Z^3+1)*x^3+x^2*(x^3+1)^(1/3)+3*RootOf(19683*_Z^6+243*_Z^3+1))/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+54*RootOf(19683*_Z^6+243*_Z^3+1)^2*x-1)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x+1)/(27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x+1))*RootOf(19683*_Z^6+243*_Z^3+1)^2-9*ln((-4374*RootOf(19683*_Z^6+243*_Z^3+1)^5*x^3+81*(x^3+1)^(2/3)*RootOf(19683*_Z^6+243*_Z^3+1)^3*x-2187*RootOf(19683*_Z^6+243*_Z^3+1)^5-18*RootOf(19683*_Z^6+243*_Z^3+1)^2*x^3+3*(x^3+1)^(1/3)*RootOf(19683*_Z^6+243*_Z^3+1)*x^2+x*(x^3+1)^(2/3)-9*RootOf(19683*_Z^6+243*_Z^3+1)^2)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+54*RootOf(19683*_Z^6+243*_Z^3+1)^2*x-1)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x+1)/(27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x+1))*RootOf(19683*_Z^6+243*_Z^3+1)^2+ln(-(-59049*RootOf(19683*_Z^6+243*_Z^3+1)^7*x^3-4374*(x^3+1)^(1/3)*RootOf(19683*_Z^6+243*_Z^3+1)^5*x^2-972*RootOf(19683*_Z^6+243*_Z^3+1)^4*x^3+81*(x^3+1)^(2/3)*RootOf(19683*_Z^6+243*_Z^3+1)^3*x-27*(x^3+1)^(1/3)*RootOf(19683*_Z^6+243*_Z^3+1)^2*x^2+243*RootOf(19683*_Z^6+243*_Z^3+1)^4-3*RootOf(19683*_Z^6+243*_Z^3+1)*x^3+x*(x^3+1)^(2/3)+3*RootOf(19683*_Z^6+243*_Z^3+1))/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x-1)/(1458*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x+1)/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x-1))*RootOf(19683*_Z^6+243*_Z^3+1)+RootOf(19683*_Z^6+243*_Z^3+1)*ln(-(729*(x^3+1)^(1/3)*RootOf(19683*_Z^6+243*_Z^3+1)^4*x^2+324*x^3*RootOf(19683*_Z^6+243*_Z^3+1)^3+27*RootOf(19683*_Z^6+243*_Z^3+1)^2*(x^3+1)^(2/3)*x+9*(x^3+1)^(1/3)*RootOf(19683*_Z^6+243*_Z^3+1)*x^2+162*RootOf(19683*_Z^6+243*_Z^3+1)^3+2*x^3+1)/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x-1)/(1458*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x+1)/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x-1))","B"
1006,1,1732,29,21.146000," ","int((x^3+1)^(2/3)*(2*x^6+x^3+2)/x^6/(x^6+x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$1732$\\ trager&$\text{Expression too large to display}$&$4476$\\ \hline \end{longtable}"," ",0,"1/10*(x^6-3*x^3-4)/x^5/(x^3+1)^(1/3)-729*ln((-4374*RootOf(19683*_Z^6+243*_Z^3+1)^5*x^3+81*(x^3+1)^(2/3)*RootOf(19683*_Z^6+243*_Z^3+1)^3*x-2187*RootOf(19683*_Z^6+243*_Z^3+1)^5-18*RootOf(19683*_Z^6+243*_Z^3+1)^2*x^3+3*(x^3+1)^(1/3)*RootOf(19683*_Z^6+243*_Z^3+1)*x^2+x*(x^3+1)^(2/3)-9*RootOf(19683*_Z^6+243*_Z^3+1)^2)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+54*RootOf(19683*_Z^6+243*_Z^3+1)^2*x-1)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x+1)/(27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x+1))*RootOf(19683*_Z^6+243*_Z^3+1)^5+1458*RootOf(19683*_Z^6+243*_Z^3+1)^5*ln((-531441*RootOf(19683*_Z^6+243*_Z^3+1)^8*x^3-4374*RootOf(19683*_Z^6+243*_Z^3+1)^5*x^3+1458*(x^3+1)^(1/3)*RootOf(19683*_Z^6+243*_Z^3+1)^4*x^2+243*(x^3+1)^(2/3)*RootOf(19683*_Z^6+243*_Z^3+1)^3*x-2187*RootOf(19683*_Z^6+243*_Z^3+1)^5+9*(x^3+1)^(1/3)*RootOf(19683*_Z^6+243*_Z^3+1)*x^2+x*(x^3+1)^(2/3))/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+54*RootOf(19683*_Z^6+243*_Z^3+1)^2*x-1)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x+1)/(27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x+1))-243*RootOf(19683*_Z^6+243*_Z^3+1)^4*ln(-(27*(x^3+1)^(1/3)*RootOf(19683*_Z^6+243*_Z^3+1)^2*x^2-6*RootOf(19683*_Z^6+243*_Z^3+1)*x^3+x*(x^3+1)^(2/3)-3*RootOf(19683*_Z^6+243*_Z^3+1))/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x-1)/(1458*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x+1)/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x-1))-9*ln((-4374*RootOf(19683*_Z^6+243*_Z^3+1)^5*x^3+81*(x^3+1)^(2/3)*RootOf(19683*_Z^6+243*_Z^3+1)^3*x-2187*RootOf(19683*_Z^6+243*_Z^3+1)^5-18*RootOf(19683*_Z^6+243*_Z^3+1)^2*x^3+3*(x^3+1)^(1/3)*RootOf(19683*_Z^6+243*_Z^3+1)*x^2+x*(x^3+1)^(2/3)-9*RootOf(19683*_Z^6+243*_Z^3+1)^2)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+54*RootOf(19683*_Z^6+243*_Z^3+1)^2*x-1)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x+1)/(27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x+1))*RootOf(19683*_Z^6+243*_Z^3+1)^2+9*RootOf(19683*_Z^6+243*_Z^3+1)^2*ln((-531441*RootOf(19683*_Z^6+243*_Z^3+1)^8*x^3-4374*RootOf(19683*_Z^6+243*_Z^3+1)^5*x^3+1458*(x^3+1)^(1/3)*RootOf(19683*_Z^6+243*_Z^3+1)^4*x^2+243*(x^3+1)^(2/3)*RootOf(19683*_Z^6+243*_Z^3+1)^3*x-2187*RootOf(19683*_Z^6+243*_Z^3+1)^5+9*(x^3+1)^(1/3)*RootOf(19683*_Z^6+243*_Z^3+1)*x^2+x*(x^3+1)^(2/3))/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+54*RootOf(19683*_Z^6+243*_Z^3+1)^2*x-1)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x+1)/(27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x+1))-2*RootOf(19683*_Z^6+243*_Z^3+1)*ln(-(27*(x^3+1)^(1/3)*RootOf(19683*_Z^6+243*_Z^3+1)^2*x^2-6*RootOf(19683*_Z^6+243*_Z^3+1)*x^3+x*(x^3+1)^(2/3)-3*RootOf(19683*_Z^6+243*_Z^3+1))/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x-1)/(1458*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x+1)/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x-1))+RootOf(19683*_Z^6+243*_Z^3+1)*ln(-(118098*RootOf(19683*_Z^6+243*_Z^3+1)^7*x^3+2187*(x^3+1)^(1/3)*RootOf(19683*_Z^6+243*_Z^3+1)^5*x^2+1215*RootOf(19683*_Z^6+243*_Z^3+1)^4*x^3+81*(x^3+1)^(2/3)*RootOf(19683*_Z^6+243*_Z^3+1)^3*x+27*(x^3+1)^(1/3)*RootOf(19683*_Z^6+243*_Z^3+1)^2*x^2-486*RootOf(19683*_Z^6+243*_Z^3+1)^4+3*RootOf(19683*_Z^6+243*_Z^3+1)*x^3+x*(x^3+1)^(2/3)-3*RootOf(19683*_Z^6+243*_Z^3+1))/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x-1)/(1458*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x+1)/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x-1))","B"
1007,1,86,62,0.987000," ","int((x^4-1)*(x^4-x^2+1)*(4*x^4-x^2+4)^(1/2)/(x^4+1)/(4*x^8+7*x^4+4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{4 x^{4}-x^{2}+4}}{x}\right)}{4}-\sqrt{2}\, \arctan \left(\frac{\sqrt{4 x^{4}-x^{2}+4}}{x}\right)+\frac{3 \sqrt{6}\, \arctan \left(\frac{\sqrt{6}\, \sqrt{4 x^{4}-x^{2}+4}\, \sqrt{2}}{6 x}\right)}{4}\right) \sqrt{2}}{2}$&$86$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-\sqrt{4 x^{4}-x^{2}+4}\, x +2 \RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{4}+1}\right)}{2}-\frac{3 \RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{2}+3 \sqrt{4 x^{4}-x^{2}+4}\, x +2 \RootOf \left(\textit{\_Z}^{2}+3\right)}{2 x^{4}+x^{2}+2}\right)}{8}-\frac{\ln \left(-\frac{-2 x^{4}+\sqrt{4 x^{4}-x^{2}+4}\, x -2}{2 x^{4}-x^{2}+2}\right)}{8}$&$180$\\ default&$-\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(2 \textit{\_Z}^{4}-\textit{\_Z}^{2}+2\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{8 \arctanh \left(\frac{\left(8 \underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \left(-63 \underline{\hspace{1.25 ex}}\alpha^{2}+61 x^{2}+16\right)}{122 \sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{4 x^{4}-x^{2}+4}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}}-\frac{\sqrt{8}\, \left(-2 \underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{-x^{2}+8-3 i x^{2} \sqrt{7}}\, \sqrt{-x^{2}+8+3 i x^{2} \sqrt{7}}\, \EllipticPi \left(\sqrt{\frac{1}{8}+\frac{3 i \sqrt{7}}{8}}\, x , \frac{3 i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{7}}{8}-\frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{8}-\frac{3 i \sqrt{7}}{16}+\frac{1}{16}, \frac{\sqrt{\frac{1}{8}-\frac{3 i \sqrt{7}}{8}}}{\sqrt{\frac{1}{8}+\frac{3 i \sqrt{7}}{8}}}\right)}{\sqrt{1+3 i \sqrt{7}}\, \sqrt{4 x^{4}-x^{2}+4}}\right)\right)}{128}+\frac{4 \sqrt{1-\left(\frac{1}{8}+\frac{3 i \sqrt{7}}{8}\right) x^{2}}\, \sqrt{1-\left(\frac{1}{8}-\frac{3 i \sqrt{7}}{8}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{2+6 i \sqrt{7}}}{4}, \frac{\sqrt{-62-6 i \sqrt{7}}}{8}\right)}{\sqrt{2+6 i \sqrt{7}}\, \sqrt{4 x^{4}-x^{2}+4}}+\frac{3 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(2 \textit{\_Z}^{4}+\textit{\_Z}^{2}+2\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{8 \sqrt{3}\, \arctanh \left(\frac{\left(8 \underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \left(-21 \underline{\hspace{1.25 ex}}\alpha^{2}+23 x^{2}-16\right)}{46 \sqrt{-3 \underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{4 x^{4}-x^{2}+4}}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{2}}}-\frac{3 \sqrt{8}\, \left(-2 \underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{-x^{2}+8-3 i x^{2} \sqrt{7}}\, \sqrt{-x^{2}+8+3 i x^{2} \sqrt{7}}\, \EllipticPi \left(\sqrt{\frac{1}{8}+\frac{3 i \sqrt{7}}{8}}\, x , \frac{3 i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{7}}{8}-\frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{8}+\frac{3 i \sqrt{7}}{16}-\frac{1}{16}, \frac{\sqrt{\frac{1}{8}-\frac{3 i \sqrt{7}}{8}}}{\sqrt{\frac{1}{8}+\frac{3 i \sqrt{7}}{8}}}\right)}{\sqrt{1+3 i \sqrt{7}}\, \sqrt{4 x^{4}-x^{2}+4}}\right)\right)}{128}-\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{4 \arctanh \left(\frac{\left(8 \underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \left(-63 \underline{\hspace{1.25 ex}}\alpha^{2}+65 x^{2}-16\right)}{130 \sqrt{-\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{4 x^{4}-x^{2}+4}}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{\sqrt{8}\, \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{-x^{2}+8-3 i x^{2} \sqrt{7}}\, \sqrt{-x^{2}+8+3 i x^{2} \sqrt{7}}\, \EllipticPi \left(\sqrt{\frac{1}{8}+\frac{3 i \sqrt{7}}{8}}\, x , \frac{3 i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{7}}{8}-\frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{8}, \frac{\sqrt{\frac{1}{8}-\frac{3 i \sqrt{7}}{8}}}{\sqrt{\frac{1}{8}+\frac{3 i \sqrt{7}}{8}}}\right)}{\sqrt{1+3 i \sqrt{7}}\, \sqrt{4 x^{4}-x^{2}+4}}\right)\right)}{16}$&$671$\\ \hline \end{longtable}"," ",0,"1/2*(1/4*2^(1/2)*arctanh(1/x*(4*x^4-x^2+4)^(1/2))-2^(1/2)*arctan(1/x*(4*x^4-x^2+4)^(1/2))+3/4*6^(1/2)*arctan(1/6*6^(1/2)*(4*x^4-x^2+4)^(1/2)*2^(1/2)/x))*2^(1/2)","A"
1008,1,46,72,0.054000," ","int((-3*x^10+x^9-9*x^7+3*x^6-9*x^4+3*x^3-3*x+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(-\left(-1+3 x \right) \left(x^{3}+1\right)^{3}\right)^{\frac{1}{3}} \left(210 x^{4}-7 x^{3}-3 x^{2}+681 x -229\right)}{910 x^{3}+910}$&$46$\\ trager&$\frac{\left(210 x^{4}-7 x^{3}-3 x^{2}+681 x -229\right) \left(-3 x^{10}+x^{9}-9 x^{7}+3 x^{6}-9 x^{4}+3 x^{3}-3 x +1\right)^{\frac{1}{3}}}{910 x^{3}+910}$&$65$\\ gosper&$\frac{\left(-1+3 x \right) \left(70 x^{3}+21 x^{2}+6 x +229\right) \left(-3 x^{10}+x^{9}-9 x^{7}+3 x^{6}-9 x^{4}+3 x^{3}-3 x +1\right)^{\frac{1}{3}}}{910 \left(1+x \right) \left(x^{2}-x +1\right)}$&$73$\\ \hline \end{longtable}"," ",0,"1/910*(-(-1+3*x)*(x^3+1)^3)^(1/3)/(x^3+1)*(210*x^4-7*x^3-3*x^2+681*x-229)","A"
1009,1,2341,69,0.283000," ","int(x*(-b+x)*(a*b-2*a*x+x^2)/(-a+x)/(x*(-a+x)*(-b+x))^(1/2)/(a*d+(-b-d)*x+x^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{-2 b x +2 x^{2}}{\sqrt{\left(-a +x \right) \left(-b x +x^{2}\right)}}-\frac{2 d b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}+\frac{4 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) a \,d^{2}}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}+\frac{2 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) d a}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{b^{3} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) d}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{2 b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) d^{2}}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) d}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) d^{3}}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) d^{2}}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{4 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) a \,d^{2}}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}+\frac{2 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) d a}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}+\frac{b^{3} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) d}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}+\frac{2 b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) d^{2}}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) d}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}+\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) d^{3}}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) d^{2}}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}$&$2341$\\ default&$\frac{2 a b \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}-\frac{2 d b \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}-\frac{2 b \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \left(\left(-a +b \right) \EllipticE \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)+a \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}-a \left(a -b \right) \left(-\frac{2 \left(-b x +x^{2}\right)}{a \left(a -b \right) \sqrt{\left(-a +x \right) \left(-b x +x^{2}\right)}}+\frac{2 \left(\frac{1}{a}+\frac{b}{a \left(a -b \right)}\right) b \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}-\frac{2 b \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \left(\left(-a +b \right) \EllipticE \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)+a \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)\right)}{a \left(a -b \right) \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}\right)+d \left(\frac{4 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) a d}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}+\frac{2 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) a}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{b^{3} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{2 b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) d}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) d^{2}}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) d}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}-\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{4 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) a d}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}+\frac{2 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) a}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}+\frac{b^{3} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}+\frac{2 b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) d}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}+\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) d^{2}}{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}-\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}}, \sqrt{\frac{b}{-a +b}}\right) d}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{d}{2}+\frac{\sqrt{-4 a d +b^{2}+2 b d +d^{2}}}{2}\right)}\right)$&$2765$\\ \hline \end{longtable}"," ",0,"2*(-b*x+x^2)/((-a+x)*(-b*x+x^2))^(1/2)-2*d*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)*EllipticF((-(-b+x)/b)^(1/2),(b/(-a+b))^(1/2))+4/(-4*a*d+b^2+2*b*d+d^2)^(1/2)*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(b/(-a+b))^(1/2))*a*d^2+2*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(b/(-a+b))^(1/2))*d*a-1/(-4*a*d+b^2+2*b*d+d^2)^(1/2)*b^3*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(b/(-a+b))^(1/2))*d-2/(-4*a*d+b^2+2*b*d+d^2)^(1/2)*b^2*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(b/(-a+b))^(1/2))*d^2-b^2*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(b/(-a+b))^(1/2))*d-1/(-4*a*d+b^2+2*b*d+d^2)^(1/2)*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(b/(-a+b))^(1/2))*d^3-b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(1/2*b-1/2*d-1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(b/(-a+b))^(1/2))*d^2-4/(-4*a*d+b^2+2*b*d+d^2)^(1/2)*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(b/(-a+b))^(1/2))*a*d^2+2*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(b/(-a+b))^(1/2))*d*a+1/(-4*a*d+b^2+2*b*d+d^2)^(1/2)*b^3*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(b/(-a+b))^(1/2))*d+2/(-4*a*d+b^2+2*b*d+d^2)^(1/2)*b^2*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(b/(-a+b))^(1/2))*d^2-b^2*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(b/(-a+b))^(1/2))*d+1/(-4*a*d+b^2+2*b*d+d^2)^(1/2)*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(b/(-a+b))^(1/2))*d^3-b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(1/2*b-1/2*d+1/2*(-4*a*d+b^2+2*b*d+d^2)^(1/2)),(b/(-a+b))^(1/2))*d^2","C"
1010,1,323,73,0.115000," ","int((k^2*x^2+1)/((1-x)*x*(-k^2*x+1))^(1/2)/(k^2*x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{2 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{3} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}-\frac{2 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{3} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}$&$323$\\ elliptic&$-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{3} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{3} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}$&$335$\\ \hline \end{longtable}"," ",0,"-2/k^2*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticF((-(x-1/k^2)*k^2)^(1/2),(1/k^2/(1/k^2-1))^(1/2))+2/k^3*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/k)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+1/k),(1/k^2/(1/k^2-1))^(1/2))-2/k^3*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-1/k)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-1/k),(1/k^2/(1/k^2-1))^(1/2))","C"
1011,1,14,62,1.515000," ","int(1/(x^3+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{3}\right)$&$14$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x -3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}-4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}+1\right)^{\frac{2}{3}}+3 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}+4 x^{3}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+2\right)}{3}-\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+x^{3}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+1\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)}{3}+\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+x^{3}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+1\right)}{3}$&$304$\\ \hline \end{longtable}"," ",0,"x*hypergeom([1/3,1/3],[4/3],-x^3)","C"
1012,1,273,61,1.030000," ","int((x^2+x)/(x^2-2*x-1)/(x^3-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticF \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}}+\frac{\sqrt{2}\, \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{1}{-2-\sqrt{2}}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}\, \left(-2-\sqrt{2}\right)}+\frac{3 \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{1}{-2-\sqrt{2}}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{3}-x}\, \left(-2-\sqrt{2}\right)}-\frac{\sqrt{2}\, \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{1}{-2+\sqrt{2}}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}\, \left(-2+\sqrt{2}\right)}+\frac{3 \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{1}{-2+\sqrt{2}}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{3}-x}\, \left(-2+\sqrt{2}\right)}$&$273$\\ elliptic&$\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticF \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}}+\frac{\sqrt{2}\, \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{1}{-2-\sqrt{2}}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}\, \left(-2-\sqrt{2}\right)}+\frac{3 \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{1}{-2-\sqrt{2}}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{3}-x}\, \left(-2-\sqrt{2}\right)}-\frac{\sqrt{2}\, \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{1}{-2+\sqrt{2}}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}\, \left(-2+\sqrt{2}\right)}+\frac{3 \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{1}{-2+\sqrt{2}}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{3}-x}\, \left(-2+\sqrt{2}\right)}$&$273$\\ trager&$\frac{\ln \left(-\frac{278808 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2} x^{2}-1394040 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2} x +493895 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) x^{2}+1672848 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2}+1038514 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) \sqrt{x^{3}-x}+74648 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) x +66352 x^{2}+419247 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)+152085 \sqrt{x^{3}-x}+40832 x +25520}{\left(4 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) x -8 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)+x -1\right)^{2}}\right) \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)}{2}-\frac{\ln \left(\frac{-278808 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2} x^{2}+1394040 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2} x -63721 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) x^{2}+1038514 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) \sqrt{x^{3}-x}-1672848 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2}+2862728 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) x +148735 x^{2}+886429 \sqrt{x^{3}-x}-2926449 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)+1427856 x -1279121}{\left(4 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) x -8 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)+3 x -7\right)^{2}}\right) \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)}{2}-\frac{\ln \left(\frac{-278808 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2} x^{2}+1394040 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2} x -63721 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) x^{2}+1038514 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) \sqrt{x^{3}-x}-1672848 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2}+2862728 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) x +148735 x^{2}+886429 \sqrt{x^{3}-x}-2926449 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)+1427856 x -1279121}{\left(4 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) x -8 \RootOf \left(8 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)+3 x -7\right)^{2}}\right)}{2}$&$542$\\ \hline \end{longtable}"," ",0,"(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticF((1+x)^(1/2),1/2*2^(1/2))+2^(1/2)*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/(-2-2^(1/2))*EllipticPi((1+x)^(1/2),-1/(-2-2^(1/2)),1/2*2^(1/2))+3/2*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/(-2-2^(1/2))*EllipticPi((1+x)^(1/2),-1/(-2-2^(1/2)),1/2*2^(1/2))-2^(1/2)*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/(-2+2^(1/2))*EllipticPi((1+x)^(1/2),-1/(-2+2^(1/2)),1/2*2^(1/2))+3/2*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)/(-2+2^(1/2))*EllipticPi((1+x)^(1/2),-1/(-2+2^(1/2)),1/2*2^(1/2))","C"
1013,0,0,65,0.019000," ","int(x^2*(3*a*b-2*(a+b)*x+x^2)/(x*(-a+x)*(-b+x))^(3/4)/(-a*b+(a+b)*x-x^2+d*x^3),x)","\[\int \frac{x^{2} \left(3 a b -2 \left(a +b \right) x +x^{2}\right)}{\left(x \left(-a +x \right) \left(-b +x \right)\right)^{\frac{3}{4}} \left(-a b +\left(a +b \right) x -x^{2}+d \,x^{3}\right)}\, dx\]"," ",0,"int(x^2*(3*a*b-2*(a+b)*x+x^2)/(x*(-a+x)*(-b+x))^(3/4)/(-a*b+(a+b)*x-x^2+d*x^3),x)","F"
1014,1,79,57,7.311000," ","int(1/x/(x^4-1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\sqrt{2}\, \Gamma \left(\frac{3}{4}\right) \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \left(\frac{\pi  \sqrt{2}\, x^{4} \hypergeom \left(\left[1, 1, \frac{5}{4}\right], \left[2, 2\right], x^{4}\right)}{4 \Gamma \left(\frac{3}{4}\right)}+\frac{\left(-3 \ln \left(2\right)-\frac{\pi}{2}+4 \ln \left(x \right)+i \pi \right) \pi  \sqrt{2}}{\Gamma \left(\frac{3}{4}\right)}\right)}{8 \pi  \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}}}$&$79$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{4}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)+2 \left(x^{4}-1\right)^{\frac{3}{4}}}{x^{4}}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}-\RootOf \left(\textit{\_Z}^{4}+1\right) x^{4}-2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+2 \left(x^{4}-1\right)^{\frac{3}{4}}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)}{x^{4}}\right)}{4}$&$157$\\ \hline \end{longtable}"," ",0,"1/8/Pi*2^(1/2)*GAMMA(3/4)/signum(x^4-1)^(1/4)*(-signum(x^4-1))^(1/4)*(1/4*Pi*2^(1/2)/GAMMA(3/4)*x^4*hypergeom([1,1,5/4],[2,2],x^4)+(-3*ln(2)-1/2*Pi+4*ln(x)+I*Pi)*Pi*2^(1/2)/GAMMA(3/4))","C"
1015,1,425,65,0.102000," ","int((-a+x)*(-b+x)*(-a*b+x^2)/(x*(-a+x)*(-b+x))^(1/2)/(a^2*b^2-2*a*b*(a+b)*x+(a^2+4*a*b+b^2-d)*x^2-2*(a+b)*x^3+x^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 b \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}+\frac{\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+\left(-2 a -2 b \right) \textit{\_Z}^{3}+\left(a^{2}+4 a b +b^{2}-d \right) \textit{\_Z}^{2}+\left(-2 a^{2} b -2 a \,b^{2}\right) \textit{\_Z} +a^{2} b^{2}\right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{3} a +\underline{\hspace{1.25 ex}}\alpha^{3} b -\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-4 \underline{\hspace{1.25 ex}}\alpha^{2} a b -\underline{\hspace{1.25 ex}}\alpha^{2} b^{2}+3 \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b +3 \underline{\hspace{1.25 ex}}\alpha  a \,b^{2}-2 a^{2} b^{2}+\underline{\hspace{1.25 ex}}\alpha^{2} d \right) \left(-\underline{\hspace{1.25 ex}}\alpha^{3}+2 \underline{\hspace{1.25 ex}}\alpha^{2} a +\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2}-2 \underline{\hspace{1.25 ex}}\alpha  a b +a^{2} b +\underline{\hspace{1.25 ex}}\alpha  d +b d \right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{-\underline{\hspace{1.25 ex}}\alpha^{3}+2 \underline{\hspace{1.25 ex}}\alpha^{2} a +\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2}-2 \underline{\hspace{1.25 ex}}\alpha  a b +a^{2} b +\underline{\hspace{1.25 ex}}\alpha  d +b d}{b d}, \sqrt{\frac{b}{-a +b}}\right)}{\left(-2 \underline{\hspace{1.25 ex}}\alpha^{3}+3 \underline{\hspace{1.25 ex}}\alpha^{2} a +3 \underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2}-4 \underline{\hspace{1.25 ex}}\alpha  a b -\underline{\hspace{1.25 ex}}\alpha  \,b^{2}+a^{2} b +a \,b^{2}+\underline{\hspace{1.25 ex}}\alpha  d \right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}}{b d}$&$425$\\ elliptic&$-\frac{2 b \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}-\frac{\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+\left(-2 a -2 b \right) \textit{\_Z}^{3}+\left(a^{2}+4 a b +b^{2}-d \right) \textit{\_Z}^{2}+\left(-2 a^{2} b -2 a \,b^{2}\right) \textit{\_Z} +a^{2} b^{2}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{3} a -\underline{\hspace{1.25 ex}}\alpha^{3} b +\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+4 \underline{\hspace{1.25 ex}}\alpha^{2} a b +\underline{\hspace{1.25 ex}}\alpha^{2} b^{2}-3 \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b -3 \underline{\hspace{1.25 ex}}\alpha  a \,b^{2}+2 a^{2} b^{2}-\underline{\hspace{1.25 ex}}\alpha^{2} d \right) \left(-\underline{\hspace{1.25 ex}}\alpha^{3}+2 \underline{\hspace{1.25 ex}}\alpha^{2} a +\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2}-2 \underline{\hspace{1.25 ex}}\alpha  a b +a^{2} b +\underline{\hspace{1.25 ex}}\alpha  d +b d \right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{-\underline{\hspace{1.25 ex}}\alpha^{3}+2 \underline{\hspace{1.25 ex}}\alpha^{2} a +\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2}-2 \underline{\hspace{1.25 ex}}\alpha  a b +a^{2} b +\underline{\hspace{1.25 ex}}\alpha  d +b d}{b d}, \sqrt{\frac{b}{-a +b}}\right)}{\left(-2 \underline{\hspace{1.25 ex}}\alpha^{3}+3 \underline{\hspace{1.25 ex}}\alpha^{2} a +3 \underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2}-4 \underline{\hspace{1.25 ex}}\alpha  a b -\underline{\hspace{1.25 ex}}\alpha  \,b^{2}+a^{2} b +a \,b^{2}+\underline{\hspace{1.25 ex}}\alpha  d \right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}}{b d}$&$427$\\ \hline \end{longtable}"," ",0,"-2*b*(-(-b+x)/b)^(1/2)*((-a+x)/(-a+b))^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)*EllipticF((-(-b+x)/b)^(1/2),(b/(-a+b))^(1/2))+1/b/d*sum((_alpha^3*a+_alpha^3*b-_alpha^2*a^2-4*_alpha^2*a*b-_alpha^2*b^2+3*_alpha*a^2*b+3*_alpha*a*b^2-2*a^2*b^2+_alpha^2*d)/(-2*_alpha^3+3*_alpha^2*a+3*_alpha^2*b-_alpha*a^2-4*_alpha*a*b-_alpha*b^2+a^2*b+a*b^2+_alpha*d)*(-_alpha^3+2*_alpha^2*a+_alpha^2*b-_alpha*a^2-2*_alpha*a*b+a^2*b+_alpha*d+b*d)*(-(-b+x)/b)^(1/2)*((-a+x)/(-a+b))^(1/2)*(x/b)^(1/2)/(x*(a*b-a*x-b*x+x^2))^(1/2)*EllipticPi((-(-b+x)/b)^(1/2),(-_alpha^3+2*_alpha^2*a+_alpha^2*b-_alpha*a^2-2*_alpha*a*b+a^2*b+_alpha*d+b*d)/b/d,(b/(-a+b))^(1/2)),_alpha=RootOf(_Z^4+(-2*a-2*b)*_Z^3+(a^2+4*a*b+b^2-d)*_Z^2+(-2*a^2*b-2*a*b^2)*_Z+a^2*b^2))","C"
1016,0,0,57,0.007000," ","int(x^2*(a*x^4-b)/(a*x^4+b)^(3/4),x)","\[\int \frac{x^{2} \left(a \,x^{4}-b \right)}{\left(a \,x^{4}+b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(x^2*(a*x^4-b)/(a*x^4+b)^(3/4),x)","F"
1017,0,0,61,0.028000," ","int(1/(a*x^4+b*x)^(1/4),x)","\[\int \frac{1}{\left(a \,x^{4}+b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(a*x^4+b*x)^(1/4),x)","F"
1018,1,451,65,0.105000," ","int((-a+x)*(-b+x)*(-a*b+x^2)/(x*(-a+x)*(-b+x))^(1/2)/(a^2*b^2*d-2*a*b*(a+b)*d*x+(a^2*d+4*a*b*d+b^2*d-1)*x^2-2*(a+b)*d*x^3+d*x^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 b \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)}{d \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}+\frac{\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(d \,\textit{\_Z}^{4}+\left(-2 a d -2 b d \right) \textit{\_Z}^{3}+\left(a^{2} d +4 a b d +b^{2} d -1\right) \textit{\_Z}^{2}+\left(-2 a^{2} b d -2 a \,b^{2} d \right) \textit{\_Z} +a^{2} b^{2} d \right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{3} a d +\underline{\hspace{1.25 ex}}\alpha^{3} b d -\underline{\hspace{1.25 ex}}\alpha^{2} a^{2} d -4 \underline{\hspace{1.25 ex}}\alpha^{2} a b d -\underline{\hspace{1.25 ex}}\alpha^{2} b^{2} d +3 \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b d +3 \underline{\hspace{1.25 ex}}\alpha  a \,b^{2} d -2 a^{2} b^{2} d +\underline{\hspace{1.25 ex}}\alpha^{2}\right) \left(-d \,\underline{\hspace{1.25 ex}}\alpha^{3}+2 d \,\underline{\hspace{1.25 ex}}\alpha^{2} a +d \,\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2} d -2 \underline{\hspace{1.25 ex}}\alpha  a d b +a^{2} b d +\underline{\hspace{1.25 ex}}\alpha  +b \right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{-d \,\underline{\hspace{1.25 ex}}\alpha^{3}+2 d \,\underline{\hspace{1.25 ex}}\alpha^{2} a +d \,\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2} d -2 \underline{\hspace{1.25 ex}}\alpha  a d b +a^{2} b d +\underline{\hspace{1.25 ex}}\alpha  +b}{b}, \sqrt{\frac{b}{-a +b}}\right)}{\left(-2 d \,\underline{\hspace{1.25 ex}}\alpha^{3}+3 d \,\underline{\hspace{1.25 ex}}\alpha^{2} a +3 d \,\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2} d -4 \underline{\hspace{1.25 ex}}\alpha  a d b -\underline{\hspace{1.25 ex}}\alpha  \,b^{2} d +a^{2} b d +a \,b^{2} d +\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}}{d b}$&$451$\\ elliptic&$-\frac{2 b \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)}{d \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}+\frac{\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(d \,\textit{\_Z}^{4}+\left(-2 a d -2 b d \right) \textit{\_Z}^{3}+\left(a^{2} d +4 a b d +b^{2} d -1\right) \textit{\_Z}^{2}+\left(-2 a^{2} b d -2 a \,b^{2} d \right) \textit{\_Z} +a^{2} b^{2} d \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{3} a d -\underline{\hspace{1.25 ex}}\alpha^{3} b d +\underline{\hspace{1.25 ex}}\alpha^{2} a^{2} d +4 \underline{\hspace{1.25 ex}}\alpha^{2} a b d +\underline{\hspace{1.25 ex}}\alpha^{2} b^{2} d -3 \underline{\hspace{1.25 ex}}\alpha  \,a^{2} b d -3 \underline{\hspace{1.25 ex}}\alpha  a \,b^{2} d +2 a^{2} b^{2} d -\underline{\hspace{1.25 ex}}\alpha^{2}\right) \left(-d \,\underline{\hspace{1.25 ex}}\alpha^{3}+2 d \,\underline{\hspace{1.25 ex}}\alpha^{2} a +d \,\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2} d -2 \underline{\hspace{1.25 ex}}\alpha  a d b +a^{2} b d +\underline{\hspace{1.25 ex}}\alpha  +b \right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{-d \,\underline{\hspace{1.25 ex}}\alpha^{3}+2 d \,\underline{\hspace{1.25 ex}}\alpha^{2} a +d \,\underline{\hspace{1.25 ex}}\alpha^{2} b -\underline{\hspace{1.25 ex}}\alpha  \,a^{2} d -2 \underline{\hspace{1.25 ex}}\alpha  a d b +a^{2} b d +\underline{\hspace{1.25 ex}}\alpha  +b}{b}, \sqrt{\frac{b}{-a +b}}\right)}{\left(2 d \,\underline{\hspace{1.25 ex}}\alpha^{3}-3 d \,\underline{\hspace{1.25 ex}}\alpha^{2} a -3 d \,\underline{\hspace{1.25 ex}}\alpha^{2} b +\underline{\hspace{1.25 ex}}\alpha  \,a^{2} d +4 \underline{\hspace{1.25 ex}}\alpha  a d b +\underline{\hspace{1.25 ex}}\alpha  \,b^{2} d -a^{2} b d -a \,b^{2} d -\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}}{d b}$&$455$\\ \hline \end{longtable}"," ",0,"-2/d*b*(-(-b+x)/b)^(1/2)*((-a+x)/(-a+b))^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)*EllipticF((-(-b+x)/b)^(1/2),(b/(-a+b))^(1/2))+1/d/b*sum((_alpha^3*a*d+_alpha^3*b*d-_alpha^2*a^2*d-4*_alpha^2*a*b*d-_alpha^2*b^2*d+3*_alpha*a^2*b*d+3*_alpha*a*b^2*d-2*a^2*b^2*d+_alpha^2)/(-2*_alpha^3*d+3*_alpha^2*a*d+3*_alpha^2*b*d-_alpha*a^2*d-4*_alpha*a*b*d-_alpha*b^2*d+a^2*b*d+a*b^2*d+_alpha)*(-_alpha^3*d+2*_alpha^2*a*d+_alpha^2*b*d-_alpha*a^2*d-2*_alpha*a*b*d+a^2*b*d+_alpha+b)*(-(-b+x)/b)^(1/2)*((-a+x)/(-a+b))^(1/2)*(x/b)^(1/2)/(x*(a*b-a*x-b*x+x^2))^(1/2)*EllipticPi((-(-b+x)/b)^(1/2),(-_alpha^3*d+2*_alpha^2*a*d+_alpha^2*b*d-_alpha*a^2*d-2*_alpha*a*b*d+a^2*b*d+_alpha+b)/b,(b/(-a+b))^(1/2)),_alpha=RootOf(d*_Z^4+(-2*a*d-2*b*d)*_Z^3+(a^2*d+4*a*b*d+b^2*d-1)*_Z^2+(-2*a^2*b*d-2*a*b^2*d)*_Z+a^2*b^2*d))","C"
1019,1,79,57,9.684000," ","int(1/x/(x^6-1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\sqrt{2}\, \Gamma \left(\frac{3}{4}\right) \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{4}} \left(\frac{\pi  \sqrt{2}\, x^{6} \hypergeom \left(\left[1, 1, \frac{5}{4}\right], \left[2, 2\right], x^{6}\right)}{4 \Gamma \left(\frac{3}{4}\right)}+\frac{\left(-3 \ln \left(2\right)-\frac{\pi}{2}+6 \ln \left(x \right)+i \pi \right) \pi  \sqrt{2}}{\Gamma \left(\frac{3}{4}\right)}\right)}{12 \pi  \mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{4}}}$&$79$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{6}+2 \left(x^{6}-1\right)^{\frac{3}{4}}+2 \sqrt{x^{6}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)+2 \left(x^{6}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{x^{6}}\right)}{6}+\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}+1\right) x^{6}+2 \sqrt{x^{6}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+2 \left(x^{6}-1\right)^{\frac{3}{4}}-2 \left(x^{6}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)}{x^{6}}\right)}{6}$&$160$\\ \hline \end{longtable}"," ",0,"1/12/Pi*2^(1/2)*GAMMA(3/4)/signum(x^6-1)^(1/4)*(-signum(x^6-1))^(1/4)*(1/4*Pi*2^(1/2)/GAMMA(3/4)*x^6*hypergeom([1,1,5/4],[2,2],x^6)+(-3*ln(2)-1/2*Pi+6*ln(x)+I*Pi)*Pi*2^(1/2)/GAMMA(3/4))","C"
1020,0,0,14,0.034000," ","int(1/(a*x^3-b*x)^(1/3)/(c*x^6+d),x)","\[\int \frac{1}{\left(a \,x^{3}-b x \right)^{\frac{1}{3}} \left(c \,x^{6}+d \right)}\, dx\]"," ",0,"int(1/(a*x^3-b*x)^(1/3)/(c*x^6+d),x)","F"
1021,0,0,14,0.002000," ","int(1/(a*x^3-b*x)^(1/3)/(c*x^6+d),x)","\[\int \frac{1}{\left(a \,x^{3}-b x \right)^{\frac{1}{3}} \left(c \,x^{6}+d \right)}\, dx\]"," ",0,"int(1/(a*x^3-b*x)^(1/3)/(c*x^6+d),x)","F"
1022,1,75,64,0.250000," ","int((x^2-1)*(-1+x*(-x^4+3*x^2-1)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\frac{x^{3}}{3}+x +\frac{x^{4} \sqrt{-x^{4}+3 x^{2}-1}}{6}-\frac{3 x^{2} \sqrt{-x^{4}+3 x^{2}-1}}{8}-\frac{\sqrt{-x^{4}+3 x^{2}-1}}{48}+\frac{5 \arcsin \left(\frac{2 \sqrt{5}\, \left(x^{2}-\frac{3}{2}\right)}{5}\right)}{32}$&$75$\\ trager&$-\frac{x \left(x^{2}-3\right)}{3}+\left(\frac{1}{6} x^{4}-\frac{3}{8} x^{2}-\frac{1}{48}\right) \sqrt{-x^{4}+3 x^{2}-1}+\frac{5 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \sqrt{-x^{4}+3 x^{2}-1}+3 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{32}$&$82$\\ default&$\frac{x^{4} \sqrt{-x^{4}+3 x^{2}-1}}{6}-\frac{x^{2} \sqrt{-x^{4}+3 x^{2}-1}}{8}-\frac{19 \sqrt{-x^{4}+3 x^{2}-1}}{48}+\frac{5 \arcsin \left(\frac{2 \sqrt{5}\, \left(x^{2}-\frac{3}{2}\right)}{5}\right)}{32}+\frac{\left(-2 x^{2}+3\right) \sqrt{-x^{4}+3 x^{2}-1}}{8}-\frac{x^{3}}{3}+x$&$98$\\ \hline \end{longtable}"," ",0,"-1/3*x^3+x+1/6*x^4*(-x^4+3*x^2-1)^(1/2)-3/8*x^2*(-x^4+3*x^2-1)^(1/2)-1/48*(-x^4+3*x^2-1)^(1/2)+5/32*arcsin(2/5*5^(1/2)*(x^2-3/2))","A"
1023,0,0,9,0.017000," ","int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(x^{2}+1\right) \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)/(x+(x^2+1)^(1/2))^(1/2),x)","F"
1024,0,0,9,0.000000," ","int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(x^{2}+1\right) \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)/(x+(x^2+1)^(1/2))^(1/2),x)","F"
1025,0,0,61,0.030000," ","int((c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2)/(a^2*x^2+b)^(1/2),x)","\[\int \frac{\sqrt{c +\sqrt{a x +\sqrt{a^{2} x^{2}+b}}}}{\sqrt{a^{2} x^{2}+b}}\, dx\]"," ",0,"int((c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2)/(a^2*x^2+b)^(1/2),x)","F"
1026,1,65,63,0.152000," ","int((x^2-1)^(1/2)/(-I+x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{\sqrt{x^{2}-1}}{-i+x}+\ln \left(x +\sqrt{x^{2}-1}\right)+\frac{i \sqrt{2}\, \arctan \left(\frac{\left(-4+2 i \left(-i+x \right)\right) \sqrt{2}}{4 \sqrt{\left(-i+x \right)^{2}+2 i \left(-i+x \right)-2}}\right)}{2}$&$65$\\ default&$\frac{\left(\left(-i+x \right)^{2}+2 i \left(-i+x \right)-2\right)^{\frac{3}{2}}}{-2 i+2 x}-\frac{i \left(\sqrt{\left(-i+x \right)^{2}+2 i \left(-i+x \right)-2}+i \ln \left(x +\sqrt{\left(-i+x \right)^{2}+2 i \left(-i+x \right)-2}\right)-\sqrt{2}\, \arctan \left(\frac{\left(-4+2 i \left(-i+x \right)\right) \sqrt{2}}{4 \sqrt{\left(-i+x \right)^{2}+2 i \left(-i+x \right)-2}}\right)\right)}{2}-\frac{x \sqrt{\left(-i+x \right)^{2}+2 i \left(-i+x \right)-2}}{2}+\frac{\ln \left(x +\sqrt{\left(-i+x \right)^{2}+2 i \left(-i+x \right)-2}\right)}{2}$&$150$\\ \hline \end{longtable}"," ",0,"-(x^2-1)^(1/2)/(-I+x)+ln(x+(x^2-1)^(1/2))+1/2*I*2^(1/2)*arctan(1/4*(-4+2*I*(-I+x))*2^(1/2)/((-I+x)^2+2*I*(-I+x)-2)^(1/2))","A"
1027,0,0,58,0.005000," ","int(1/x^3/(a*x^2+b)^(3/4),x)","\[\int \frac{1}{x^{3} \left(a \,x^{2}+b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x^3/(a*x^2+b)^(3/4),x)","F"
1028,1,73,74,0.075000," ","int((3*x^3+x^2-2*x-1)^4/(x^3-3*x^2+3*x-1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{4 \left(-1+x \right) \left(1949108765175 x^{12}+4908866519700 x^{11}+609206533650 x^{10}-9283999210200 x^{9}-8805988591725 x^{8}+3131067556500 x^{7}+9260757242646 x^{6}+4070651298324 x^{5}-2008108342110 x^{4}-2834315032620 x^{3}-1158885626660 x^{2}+32327777464 x +1308401597431\right)}{1179090487575 \left(\left(-1+x \right)^{3}\right)^{\frac{1}{4}}}$&$73$\\ gosper&$\frac{4 \left(-1+x \right) \left(1949108765175 x^{12}+4908866519700 x^{11}+609206533650 x^{10}-9283999210200 x^{9}-8805988591725 x^{8}+3131067556500 x^{7}+9260757242646 x^{6}+4070651298324 x^{5}-2008108342110 x^{4}-2834315032620 x^{3}-1158885626660 x^{2}+32327777464 x +1308401597431\right)}{1179090487575 \left(x^{3}-3 x^{2}+3 x -1\right)^{\frac{1}{4}}}$&$81$\\ trager&$\frac{4 \left(1949108765175 x^{12}+4908866519700 x^{11}+609206533650 x^{10}-9283999210200 x^{9}-8805988591725 x^{8}+3131067556500 x^{7}+9260757242646 x^{6}+4070651298324 x^{5}-2008108342110 x^{4}-2834315032620 x^{3}-1158885626660 x^{2}+32327777464 x +1308401597431\right) \left(x^{3}-3 x^{2}+3 x -1\right)^{\frac{3}{4}}}{1179090487575 \left(-1+x \right)^{2}}$&$83$\\ \hline \end{longtable}"," ",0,"4/1179090487575*(-1+x)*(1949108765175*x^12+4908866519700*x^11+609206533650*x^10-9283999210200*x^9-8805988591725*x^8+3131067556500*x^7+9260757242646*x^6+4070651298324*x^5-2008108342110*x^4-2834315032620*x^3-1158885626660*x^2+32327777464*x+1308401597431)/((-1+x)^3)^(1/4)","A"
1029,0,0,58,0.005000," ","int(1/x^4/(a*x^3+b)^(3/4),x)","\[\int \frac{1}{x^{4} \left(a \,x^{3}+b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x^4/(a*x^3+b)^(3/4),x)","F"
1030,1,148,74,1.104000," ","int(x/(x^4+10*x^2-96*x-71)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(x^{8}+\sqrt{x^{4}+10 x^{2}-96 x -71}\, x^{6}+20 x^{6}+15 \sqrt{x^{4}+10 x^{2}-96 x -71}\, x^{4}-128 x^{5}-80 \sqrt{x^{4}+10 x^{2}-96 x -71}\, x^{3}+54 x^{4}+27 \sqrt{x^{4}+10 x^{2}-96 x -71}\, x^{2}-1408 x^{3}-528 x \sqrt{x^{4}+10 x^{2}-96 x -71}+3124 x^{2}+781 \sqrt{x^{4}+10 x^{2}-96 x -71}+10001\right)}{8}$&$148$\\ default&$\text{Expression too large to display}$&$1290$\\ elliptic&$\text{Expression too large to display}$&$1290$\\ \hline \end{longtable}"," ",0,"1/8*ln(x^8+(x^4+10*x^2-96*x-71)^(1/2)*x^6+20*x^6+15*(x^4+10*x^2-96*x-71)^(1/2)*x^4-128*x^5-80*(x^4+10*x^2-96*x-71)^(1/2)*x^3+54*x^4+27*(x^4+10*x^2-96*x-71)^(1/2)*x^2-1408*x^3-528*x*(x^4+10*x^2-96*x-71)^(1/2)+3124*x^2+781*(x^4+10*x^2-96*x-71)^(1/2)+10001)","A"
1031,1,303,64,9.736000," ","int((8+3*x)*(2*x^4-x-2)^(1/4)/x^2/(x^4+x+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{4 \left(2 x^{4}-x -2\right)^{\frac{1}{4}}}{x}-\RootOf \left(\textit{\_Z}^{4}-3\right) \ln \left(\frac{-5 \RootOf \left(\textit{\_Z}^{4}-3\right)^{3} x^{4}+6 \left(2 x^{4}-x -2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{3}-6 \sqrt{2 x^{4}-x -2}\, \RootOf \left(\textit{\_Z}^{4}-3\right) x^{2}+6 \left(2 x^{4}-x -2\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}-3\right)^{3} x +2 \RootOf \left(\textit{\_Z}^{4}-3\right)^{3}}{x^{4}+x +2}\right)-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) \ln \left(\frac{5 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) x^{4}-6 \left(2 x^{4}-x -2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{3}-6 \sqrt{2 x^{4}-x -2}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) x^{2}+6 \left(2 x^{4}-x -2\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}-3\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) x -2 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right)}{x^{4}+x +2}\right)$&$303$\\ risch&$-\frac{4 \left(2 x^{4}-x -2\right)^{\frac{1}{4}}}{x}+\frac{\left(-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) \ln \left(-\frac{-20 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{12}+8 \left(8 x^{12}-12 x^{9}-24 x^{8}+6 x^{6}+24 x^{5}+24 x^{4}-x^{3}-6 x^{2}-12 x -8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{9}+24 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{9}-8 \left(8 x^{12}-12 x^{9}-24 x^{8}+6 x^{6}+24 x^{5}+24 x^{4}-x^{3}-6 x^{2}-12 x -8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{6}+48 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{8}-16 \left(8 x^{12}-12 x^{9}-24 x^{8}+6 x^{6}+24 x^{5}+24 x^{4}-x^{3}-6 x^{2}-12 x -8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{5}-9 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{6}+12 \sqrt{8 x^{12}-12 x^{9}-24 x^{8}+6 x^{6}+24 x^{5}+24 x^{4}-x^{3}-6 x^{2}-12 x -8}\, x^{6}+2 \left(8 x^{12}-12 x^{9}-24 x^{8}+6 x^{6}+24 x^{5}+24 x^{4}-x^{3}-6 x^{2}-12 x -8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{3}-6 \left(8 x^{12}-12 x^{9}-24 x^{8}+6 x^{6}+24 x^{5}+24 x^{4}-x^{3}-6 x^{2}-12 x -8\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) x^{3}-36 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{5}+8 \left(8 x^{12}-12 x^{9}-24 x^{8}+6 x^{6}+24 x^{5}+24 x^{4}-x^{3}-6 x^{2}-12 x -8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{2}-36 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{4}+8 \left(8 x^{12}-12 x^{9}-24 x^{8}+6 x^{6}+24 x^{5}+24 x^{4}-x^{3}-6 x^{2}-12 x -8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x +\RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{3}-6 \sqrt{8 x^{12}-12 x^{9}-24 x^{8}+6 x^{6}+24 x^{5}+24 x^{4}-x^{3}-6 x^{2}-12 x -8}\, x^{3}+6 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{2}-12 \sqrt{8 x^{12}-12 x^{9}-24 x^{8}+6 x^{6}+24 x^{5}+24 x^{4}-x^{3}-6 x^{2}-12 x -8}\, x^{2}+12 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x +8 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2}}{\left(x^{4}+x +2\right) \left(2 x^{4}-x -2\right)^{2}}\right)-\RootOf \left(\textit{\_Z}^{4}-3\right) \ln \left(\frac{-20 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{12}+8 \left(8 x^{12}-12 x^{9}-24 x^{8}+6 x^{6}+24 x^{5}+24 x^{4}-x^{3}-6 x^{2}-12 x -8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-3\right)^{3} x^{9}+24 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{9}-8 \left(8 x^{12}-12 x^{9}-24 x^{8}+6 x^{6}+24 x^{5}+24 x^{4}-x^{3}-6 x^{2}-12 x -8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-3\right)^{3} x^{6}+48 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{8}-16 \left(8 x^{12}-12 x^{9}-24 x^{8}+6 x^{6}+24 x^{5}+24 x^{4}-x^{3}-6 x^{2}-12 x -8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-3\right)^{3} x^{5}-9 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{6}-12 \sqrt{8 x^{12}-12 x^{9}-24 x^{8}+6 x^{6}+24 x^{5}+24 x^{4}-x^{3}-6 x^{2}-12 x -8}\, x^{6}+2 \left(8 x^{12}-12 x^{9}-24 x^{8}+6 x^{6}+24 x^{5}+24 x^{4}-x^{3}-6 x^{2}-12 x -8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-3\right)^{3} x^{3}-36 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{5}+6 \left(8 x^{12}-12 x^{9}-24 x^{8}+6 x^{6}+24 x^{5}+24 x^{4}-x^{3}-6 x^{2}-12 x -8\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{4}-3\right) x^{3}+8 \left(8 x^{12}-12 x^{9}-24 x^{8}+6 x^{6}+24 x^{5}+24 x^{4}-x^{3}-6 x^{2}-12 x -8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-3\right)^{3} x^{2}-36 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{4}+8 \left(8 x^{12}-12 x^{9}-24 x^{8}+6 x^{6}+24 x^{5}+24 x^{4}-x^{3}-6 x^{2}-12 x -8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-3\right)^{3} x +\RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{3}+6 \sqrt{8 x^{12}-12 x^{9}-24 x^{8}+6 x^{6}+24 x^{5}+24 x^{4}-x^{3}-6 x^{2}-12 x -8}\, x^{3}+6 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{2}+12 \sqrt{8 x^{12}-12 x^{9}-24 x^{8}+6 x^{6}+24 x^{5}+24 x^{4}-x^{3}-6 x^{2}-12 x -8}\, x^{2}+12 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x +8 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2}}{\left(x^{4}+x +2\right) \left(2 x^{4}-x -2\right)^{2}}\right)\right) \left(\left(2 x^{4}-x -2\right)^{3}\right)^{\frac{1}{4}}}{\left(2 x^{4}-x -2\right)^{\frac{3}{4}}}$&$1594$\\ \hline \end{longtable}"," ",0,"-4*(2*x^4-x-2)^(1/4)/x-RootOf(_Z^4-3)*ln((-5*RootOf(_Z^4-3)^3*x^4+6*(2*x^4-x-2)^(1/4)*RootOf(_Z^4-3)^2*x^3-6*(2*x^4-x-2)^(1/2)*RootOf(_Z^4-3)*x^2+6*(2*x^4-x-2)^(3/4)*x+RootOf(_Z^4-3)^3*x+2*RootOf(_Z^4-3)^3)/(x^4+x+2))-RootOf(_Z^2+RootOf(_Z^4-3)^2)*ln((5*RootOf(_Z^4-3)^2*RootOf(_Z^2+RootOf(_Z^4-3)^2)*x^4-6*(2*x^4-x-2)^(1/4)*RootOf(_Z^4-3)^2*x^3-6*(2*x^4-x-2)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-3)^2)*x^2+6*(2*x^4-x-2)^(3/4)*x-RootOf(_Z^4-3)^2*RootOf(_Z^2+RootOf(_Z^4-3)^2)*x-2*RootOf(_Z^4-3)^2*RootOf(_Z^2+RootOf(_Z^4-3)^2))/(x^4+x+2))","C"
1032,0,0,58,0.005000," ","int(1/x^5/(a*x^4+b)^(3/4),x)","\[\int \frac{1}{x^{5} \left(a \,x^{4}+b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x^5/(a*x^4+b)^(3/4),x)","F"
1033,0,0,58,0.005000," ","int(1/x^6/(a*x^5+b)^(3/4),x)","\[\int \frac{1}{x^{6} \left(a \,x^{5}+b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x^6/(a*x^5+b)^(3/4),x)","F"
1034,1,1461,31,26.342000," ","int((x^3-1)^(2/3)*(x^6-2*x^3+1)/x^6/(x^6-x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{7 x^{6}-9 x^{3}+2}{10 x^{5} \left(x^{3}-1\right)^{\frac{1}{3}}}-729 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{5} \ln \left(\frac{-177147 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{7} x^{3}-2916 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{4} x^{3}-243 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{3} x^{2}+27 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{2} \left(x^{3}-1\right)^{\frac{2}{3}} x +729 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{4}-12 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right) x^{3}-2 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}+6 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)}{\left(27 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{2} x -1\right) \left(6561 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{5} x +27 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{2} x -1\right) \left(6561 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{5} x +54 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{2} x +1\right)}\right)+1458 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{5} \ln \left(\frac{729 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{4} \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+81 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{3} x -18 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{2} x^{3}+3 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+x \left(x^{3}-1\right)^{\frac{2}{3}}+9 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{2}}{\left(27 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{2} x -1\right) \left(6561 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{5} x +27 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{2} x -1\right) \left(6561 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{5} x +54 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{2} x +1\right)}\right)-243 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{4} \ln \left(-\frac{27 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{2} \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-6 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right) x^{3}+x \left(x^{3}-1\right)^{\frac{2}{3}}+3 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)}{\left(1458 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{4} x +9 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right) x -1\right) \left(729 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{4} x +9 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right) x +1\right) \left(729 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{4} x +1\right)}\right)+9 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{2} \ln \left(\frac{729 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{4} \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+81 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{3} x -18 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{2} x^{3}+3 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+x \left(x^{3}-1\right)^{\frac{2}{3}}+9 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{2}}{\left(27 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{2} x -1\right) \left(6561 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{5} x +27 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{2} x -1\right) \left(6561 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{5} x +54 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{2} x +1\right)}\right)+\RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right) \ln \left(-\frac{177147 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{7} x^{3}+6561 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{5} \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+1458 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{4} x^{3}+243 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{3} x +54 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{2} \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+729 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{4}+3 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right) x^{3}+2 x \left(x^{3}-1\right)^{\frac{2}{3}}+3 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)}{\left(1458 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{4} x +9 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right) x -1\right) \left(729 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{4} x +9 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right) x +1\right) \left(729 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{4} x +1\right)}\right)-2 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right) \ln \left(-\frac{27 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{2} \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-6 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right) x^{3}+x \left(x^{3}-1\right)^{\frac{2}{3}}+3 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)}{\left(1458 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{4} x +9 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right) x -1\right) \left(729 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{4} x +9 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right) x +1\right) \left(729 \RootOf \left(19683 \textit{\_Z}^{6}+243 \textit{\_Z}^{3}+1\right)^{4} x +1\right)}\right)$&$1461$\\ trager&$\text{Expression too large to display}$&$4455$\\ \hline \end{longtable}"," ",0,"1/10*(7*x^6-9*x^3+2)/x^5/(x^3-1)^(1/3)-729*RootOf(19683*_Z^6+243*_Z^3+1)^5*ln((-177147*RootOf(19683*_Z^6+243*_Z^3+1)^7*x^3-2916*RootOf(19683*_Z^6+243*_Z^3+1)^4*x^3-243*(x^3-1)^(1/3)*RootOf(19683*_Z^6+243*_Z^3+1)^3*x^2+27*RootOf(19683*_Z^6+243*_Z^3+1)^2*(x^3-1)^(2/3)*x+729*RootOf(19683*_Z^6+243*_Z^3+1)^4-12*RootOf(19683*_Z^6+243*_Z^3+1)*x^3-2*x^2*(x^3-1)^(1/3)+6*RootOf(19683*_Z^6+243*_Z^3+1))/(27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x-1)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x-1)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+54*RootOf(19683*_Z^6+243*_Z^3+1)^2*x+1))+1458*RootOf(19683*_Z^6+243*_Z^3+1)^5*ln((729*RootOf(19683*_Z^6+243*_Z^3+1)^4*(x^3-1)^(1/3)*x^2+81*(x^3-1)^(2/3)*RootOf(19683*_Z^6+243*_Z^3+1)^3*x-18*RootOf(19683*_Z^6+243*_Z^3+1)^2*x^3+3*RootOf(19683*_Z^6+243*_Z^3+1)*(x^3-1)^(1/3)*x^2+x*(x^3-1)^(2/3)+9*RootOf(19683*_Z^6+243*_Z^3+1)^2)/(27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x-1)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x-1)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+54*RootOf(19683*_Z^6+243*_Z^3+1)^2*x+1))-243*RootOf(19683*_Z^6+243*_Z^3+1)^4*ln(-(27*RootOf(19683*_Z^6+243*_Z^3+1)^2*(x^3-1)^(1/3)*x^2-6*RootOf(19683*_Z^6+243*_Z^3+1)*x^3+x*(x^3-1)^(2/3)+3*RootOf(19683*_Z^6+243*_Z^3+1))/(1458*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x-1)/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x+1)/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+1))+9*RootOf(19683*_Z^6+243*_Z^3+1)^2*ln((729*RootOf(19683*_Z^6+243*_Z^3+1)^4*(x^3-1)^(1/3)*x^2+81*(x^3-1)^(2/3)*RootOf(19683*_Z^6+243*_Z^3+1)^3*x-18*RootOf(19683*_Z^6+243*_Z^3+1)^2*x^3+3*RootOf(19683*_Z^6+243*_Z^3+1)*(x^3-1)^(1/3)*x^2+x*(x^3-1)^(2/3)+9*RootOf(19683*_Z^6+243*_Z^3+1)^2)/(27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x-1)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x-1)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+54*RootOf(19683*_Z^6+243*_Z^3+1)^2*x+1))+RootOf(19683*_Z^6+243*_Z^3+1)*ln(-(177147*RootOf(19683*_Z^6+243*_Z^3+1)^7*x^3+6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*(x^3-1)^(1/3)*x^2+1458*RootOf(19683*_Z^6+243*_Z^3+1)^4*x^3+243*(x^3-1)^(2/3)*RootOf(19683*_Z^6+243*_Z^3+1)^3*x+54*RootOf(19683*_Z^6+243*_Z^3+1)^2*(x^3-1)^(1/3)*x^2+729*RootOf(19683*_Z^6+243*_Z^3+1)^4+3*RootOf(19683*_Z^6+243*_Z^3+1)*x^3+2*x*(x^3-1)^(2/3)+3*RootOf(19683*_Z^6+243*_Z^3+1))/(1458*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x-1)/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x+1)/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+1))-2*RootOf(19683*_Z^6+243*_Z^3+1)*ln(-(27*RootOf(19683*_Z^6+243*_Z^3+1)^2*(x^3-1)^(1/3)*x^2-6*RootOf(19683*_Z^6+243*_Z^3+1)*x^3+x*(x^3-1)^(2/3)+3*RootOf(19683*_Z^6+243*_Z^3+1))/(1458*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x-1)/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x+1)/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+1))","B"
1035,1,2011,31,23.452000," ","int((x^3-1)^(2/3)*(x^6-2*x^3+1)/x^6/(x^6-x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$2011$\\ trager&$\text{Expression too large to display}$&$4238$\\ \hline \end{longtable}"," ",0,"1/10*(7*x^6-9*x^3+2)/x^5/(x^3-1)^(1/3)+1458*RootOf(19683*_Z^6+243*_Z^3+1)^5*ln((729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x^3+243*(x^3-1)^(1/3)*RootOf(19683*_Z^6+243*_Z^3+1)^3*x^2+27*RootOf(19683*_Z^6+243*_Z^3+1)^2*(x^3-1)^(2/3)*x+6*RootOf(19683*_Z^6+243*_Z^3+1)*x^3+x^2*(x^3-1)^(1/3)-3*RootOf(19683*_Z^6+243*_Z^3+1))/(27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x-1)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x-1)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+54*RootOf(19683*_Z^6+243*_Z^3+1)^2*x+1))-729*RootOf(19683*_Z^6+243*_Z^3+1)^5*ln((4374*RootOf(19683*_Z^6+243*_Z^3+1)^5*x^3+1458*RootOf(19683*_Z^6+243*_Z^3+1)^4*(x^3-1)^(1/3)*x^2+243*(x^3-1)^(2/3)*RootOf(19683*_Z^6+243*_Z^3+1)^3*x-2187*RootOf(19683*_Z^6+243*_Z^3+1)^5+54*RootOf(19683*_Z^6+243*_Z^3+1)^2*x^3+9*RootOf(19683*_Z^6+243*_Z^3+1)*(x^3-1)^(1/3)*x^2+x*(x^3-1)^(2/3)-27*RootOf(19683*_Z^6+243*_Z^3+1)^2)/(27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x-1)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x-1)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+54*RootOf(19683*_Z^6+243*_Z^3+1)^2*x+1))+243*RootOf(19683*_Z^6+243*_Z^3+1)^4*ln((1458*RootOf(19683*_Z^6+243*_Z^3+1)^4*(x^3-1)^(1/3)*x^2+162*x^3*RootOf(19683*_Z^6+243*_Z^3+1)^3-27*RootOf(19683*_Z^6+243*_Z^3+1)^2*(x^3-1)^(2/3)*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*(x^3-1)^(1/3)*x^2-81*RootOf(19683*_Z^6+243*_Z^3+1)^3+2*x^3-1)/(1458*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x-1)/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x+1)/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+1))-243*RootOf(19683*_Z^6+243*_Z^3+1)^4*ln((59049*RootOf(19683*_Z^6+243*_Z^3+1)^7*x^3-2187*RootOf(19683*_Z^6+243*_Z^3+1)^5*(x^3-1)^(1/3)*x^2+243*RootOf(19683*_Z^6+243*_Z^3+1)^4*x^3-81*(x^3-1)^(2/3)*RootOf(19683*_Z^6+243*_Z^3+1)^3*x+243*RootOf(19683*_Z^6+243*_Z^3+1)^4-x*(x^3-1)^(2/3))/(1458*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x-1)/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x+1)/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+1))+9*RootOf(19683*_Z^6+243*_Z^3+1)^2*ln((729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x^3+243*(x^3-1)^(1/3)*RootOf(19683*_Z^6+243*_Z^3+1)^3*x^2+27*RootOf(19683*_Z^6+243*_Z^3+1)^2*(x^3-1)^(2/3)*x+6*RootOf(19683*_Z^6+243*_Z^3+1)*x^3+x^2*(x^3-1)^(1/3)-3*RootOf(19683*_Z^6+243*_Z^3+1))/(27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x-1)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x-1)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+54*RootOf(19683*_Z^6+243*_Z^3+1)^2*x+1))-9*RootOf(19683*_Z^6+243*_Z^3+1)^2*ln((4374*RootOf(19683*_Z^6+243*_Z^3+1)^5*x^3+1458*RootOf(19683*_Z^6+243*_Z^3+1)^4*(x^3-1)^(1/3)*x^2+243*(x^3-1)^(2/3)*RootOf(19683*_Z^6+243*_Z^3+1)^3*x-2187*RootOf(19683*_Z^6+243*_Z^3+1)^5+54*RootOf(19683*_Z^6+243*_Z^3+1)^2*x^3+9*RootOf(19683*_Z^6+243*_Z^3+1)*(x^3-1)^(1/3)*x^2+x*(x^3-1)^(2/3)-27*RootOf(19683*_Z^6+243*_Z^3+1)^2)/(27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x-1)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+27*RootOf(19683*_Z^6+243*_Z^3+1)^2*x-1)/(6561*RootOf(19683*_Z^6+243*_Z^3+1)^5*x+54*RootOf(19683*_Z^6+243*_Z^3+1)^2*x+1))+RootOf(19683*_Z^6+243*_Z^3+1)*ln((1458*RootOf(19683*_Z^6+243*_Z^3+1)^4*(x^3-1)^(1/3)*x^2+162*x^3*RootOf(19683*_Z^6+243*_Z^3+1)^3-27*RootOf(19683*_Z^6+243*_Z^3+1)^2*(x^3-1)^(2/3)*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*(x^3-1)^(1/3)*x^2-81*RootOf(19683*_Z^6+243*_Z^3+1)^3+2*x^3-1)/(1458*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x-1)/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x+1)/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+1))-2*RootOf(19683*_Z^6+243*_Z^3+1)*ln((59049*RootOf(19683*_Z^6+243*_Z^3+1)^7*x^3-2187*RootOf(19683*_Z^6+243*_Z^3+1)^5*(x^3-1)^(1/3)*x^2+243*RootOf(19683*_Z^6+243*_Z^3+1)^4*x^3-81*(x^3-1)^(2/3)*RootOf(19683*_Z^6+243*_Z^3+1)^3*x+243*RootOf(19683*_Z^6+243*_Z^3+1)^4-x*(x^3-1)^(2/3))/(1458*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x-1)/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+9*RootOf(19683*_Z^6+243*_Z^3+1)*x+1)/(729*RootOf(19683*_Z^6+243*_Z^3+1)^4*x+1))","B"
1036,0,0,58,0.005000," ","int(1/x^7/(a*x^6+b)^(3/4),x)","\[\int \frac{1}{x^{7} \left(a \,x^{6}+b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x^7/(a*x^6+b)^(3/4),x)","F"
1037,1,3771,31,17.087000," ","int((x^4-1)^(1/4)*(x^8-1)/x^6/(x^8+1),x)","\[\text{output too large to display}\]"," ",0,"-1/5*(x^8-2*x^4+1)/x^5/(x^4-1)^(3/4)+(-256*ln((8192*x^12*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-16384*x^8*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2-6*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*x^12-(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x^9+262144*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^6+65536*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*x^3+8192*x^4*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2+14*x^8*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2+2*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x^5-262144*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^2-128*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6-32*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*x^3-10*x^4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2-(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x+128*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2+2*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2)/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^4-x^4-1)/(-1+x)^2/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x-x-1)^2/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x-x+1)^2/(1+x)^2)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)+1/16*ln((8192*x^12*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-16384*x^8*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2-6*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*x^12-(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x^9+262144*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^6+65536*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*x^3+8192*x^4*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2+14*x^8*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2+2*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x^5-262144*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^2-128*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6-32*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*x^3-10*x^4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2-(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x+128*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2+2*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2)/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^4-x^4-1)/(-1+x)^2/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x-x-1)^2/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x-x+1)^2/(1+x)^2)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)-8192*ln((-4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^12+8192*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^8-x^12+16*RootOf(8388608*_Z^8-4096*_Z^4+1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9-128*RootOf(8388608*_Z^8-4096*_Z^4+1)^2*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6+1024*RootOf(8388608*_Z^8-4096*_Z^4+1)^3*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3-4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^4+3*x^8-32*RootOf(8388608*_Z^8-4096*_Z^4+1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5+128*RootOf(8388608*_Z^8-4096*_Z^4+1)^2*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2-3*x^4+16*RootOf(8388608*_Z^8-4096*_Z^4+1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x+1)/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^4-x^4+1)/(-1+x)^2/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x-x-1)^2/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x-x+1)^2/(1+x)^2)*RootOf(8388608*_Z^8-4096*_Z^4+1)^5+2*ln((-4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^12+8192*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^8-x^12+16*RootOf(8388608*_Z^8-4096*_Z^4+1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9-128*RootOf(8388608*_Z^8-4096*_Z^4+1)^2*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6+1024*RootOf(8388608*_Z^8-4096*_Z^4+1)^3*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3-4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^4+3*x^8-32*RootOf(8388608*_Z^8-4096*_Z^4+1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5+128*RootOf(8388608*_Z^8-4096*_Z^4+1)^2*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2-3*x^4+16*RootOf(8388608*_Z^8-4096*_Z^4+1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x+1)/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^4-x^4+1)/(-1+x)^2/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x-x-1)^2/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x-x+1)^2/(1+x)^2)*RootOf(8388608*_Z^8-4096*_Z^4+1)-1/16*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*ln((-8192*x^12*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-4096*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^9+16384*x^8*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2+6*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*x^12+8192*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^5+(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x^9+262144*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^6+65536*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*x^3-8192*x^4*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2-14*x^8*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2-4096*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x-2*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x^5-262144*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^2-128*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6+10*x^4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2+(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x+128*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2-2*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2)/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^4-x^4-1)/(-1+x)^2/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x-x-1)^2/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x-x+1)^2/(1+x)^2)-2*RootOf(8388608*_Z^8-4096*_Z^4+1)*ln(-(-8192*x^12*RootOf(8388608*_Z^8-4096*_Z^4+1)^5-131072*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^6*x^9+16384*RootOf(8388608*_Z^8-4096*_Z^4+1)^5*x^8-2*x^12*RootOf(8388608*_Z^8-4096*_Z^4+1)+262144*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^6*x^5+32*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^2*x^9+256*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)^3*x^6+2048*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^3-8192*RootOf(8388608*_Z^8-4096*_Z^4+1)^5*x^4+6*RootOf(8388608*_Z^8-4096*_Z^4+1)*x^8-131072*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^6*x-64*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^2*x^5-256*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)^3*x^2-(x^12-3*x^8+3*x^4-1)^(3/4)*x^3-6*RootOf(8388608*_Z^8-4096*_Z^4+1)*x^4+32*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^2*x+2*RootOf(8388608*_Z^8-4096*_Z^4+1))/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^4-x^4+1)/(-1+x)^2/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x-x-1)^2/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x-x+1)^2/(1+x)^2))/(x^4-1)^(3/4)*((x^4-1)^3)^(1/4)","B"
1038,1,1245,36,15.275000," ","int((x^8-1)/(x^4+1)^(1/4)/(x^8+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1245$\\ \hline \end{longtable}"," ",0,"1/4*RootOf(_Z^2+1)*ln(-2*RootOf(_Z^2+1)*(x^4+1)^(1/2)*x^2+2*RootOf(_Z^2+1)*x^4+2*(x^4+1)^(3/4)*x-2*x^3*(x^4+1)^(1/4)+RootOf(_Z^2+1))-1/4*ln(2*(x^4+1)^(3/4)*x-2*x^2*(x^4+1)^(1/2)+2*x^3*(x^4+1)^(1/4)-2*x^4-1)-1/8*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*ln(-((x^4+1)^(1/2)*RootOf(_Z^2+1)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^3*x^2+3*(x^4+1)^(1/2)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^3*x^2+2*(x^4+1)^(1/4)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^2*RootOf(_Z^2+1)*x^3-4*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x^4+6*(x^4+1)^(1/4)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^2*x^3+6*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x^4+16*(x^4+1)^(3/4)*RootOf(_Z^2+1)*x+4*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*x^4+8*(x^4+1)^(3/4)*x+4*RootOf(_Z^2+1)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)+2*RootOf(_Z^4-8*RootOf(_Z^2+1)-8))/(RootOf(_Z^2+1)*x^4+1))+1/8*RootOf(_Z^2+1)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*ln(-(3*(x^4+1)^(1/2)*RootOf(_Z^2+1)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^3*x^2-(x^4+1)^(1/2)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^3*x^2-2*(x^4+1)^(1/4)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^2*RootOf(_Z^2+1)*x^3+2*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x^4-6*(x^4+1)^(1/4)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^2*x^3-8*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x^4+16*(x^4+1)^(3/4)*RootOf(_Z^2+1)*x+8*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*x^4+8*(x^4+1)^(3/4)*x-2*RootOf(_Z^2+1)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)+4*RootOf(_Z^4-8*RootOf(_Z^2+1)-8))/(RootOf(_Z^2+1)*x^4+1))+1/8*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*ln((-(x^4+1)^(1/2)*RootOf(_Z^2+1)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^3*x^2+(x^4+1)^(1/2)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^3*x^2+2*(x^4+1)^(1/4)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^2*RootOf(_Z^2+1)*x^3-2*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x^4-2*(x^4+1)^(1/4)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^2*x^3-4*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x^4+8*(x^4+1)^(3/4)*RootOf(_Z^2+1)*x-2*RootOf(_Z^2+1)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8))/(RootOf(_Z^2+1)*x^4-1))-1/8*RootOf(_Z^2+1)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*ln(((x^4+1)^(1/2)*RootOf(_Z^2+1)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^3*x^2+2*(x^4+1)^(1/2)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^3*x^2-4*(x^4+1)^(1/4)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^2*RootOf(_Z^2+1)*x^3+RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x^4+2*(x^4+1)^(1/4)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^2*x^3-RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x^4+12*(x^4+1)^(3/4)*RootOf(_Z^2+1)*x-6*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*x^4+4*(x^4+1)^(3/4)*x+RootOf(_Z^2+1)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)-3*RootOf(_Z^4+8*RootOf(_Z^2+1)-8))/(RootOf(_Z^2+1)*x^4-1))","B"
1039,1,1289,36,14.363000," ","int((x^8-1)/(x^4+1)^(1/4)/(x^8+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1289$\\ \hline \end{longtable}"," ",0,"1/4*RootOf(_Z^2+1)*ln(-2*RootOf(_Z^2+1)*(x^4+1)^(1/2)*x^2+2*RootOf(_Z^2+1)*x^4+2*(x^4+1)^(3/4)*x-2*x^3*(x^4+1)^(1/4)+RootOf(_Z^2+1))+1/4*ln(2*(x^4+1)^(3/4)*x+2*x^2*(x^4+1)^(1/2)+2*x^3*(x^4+1)^(1/4)+2*x^4+1)+1/8*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*ln(((x^4+1)^(1/2)*RootOf(_Z^2+1)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^3*x^2+3*(x^4+1)^(1/2)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^3*x^2-2*(x^4+1)^(1/4)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^2*RootOf(_Z^2+1)*x^3-4*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x^4-6*(x^4+1)^(1/4)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^2*x^3+6*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x^4+4*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*x^4-16*(x^4+1)^(3/4)*RootOf(_Z^2+1)*x-8*(x^4+1)^(3/4)*x+4*RootOf(_Z^2+1)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)+2*RootOf(_Z^4-8*RootOf(_Z^2+1)-8))/(RootOf(_Z^2+1)*x^4+1))-1/8*RootOf(_Z^2+1)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*ln(((x^4+1)^(1/2)*RootOf(_Z^2+1)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^3*x^2-2*(x^4+1)^(1/2)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^3*x^2+4*(x^4+1)^(1/4)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^2*RootOf(_Z^2+1)*x^3-RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x^4+2*(x^4+1)^(1/4)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^2*x^3-RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x^4+6*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*x^4-12*(x^4+1)^(3/4)*RootOf(_Z^2+1)*x+4*(x^4+1)^(3/4)*x+RootOf(_Z^2+1)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)+3*RootOf(_Z^4-8*RootOf(_Z^2+1)-8))/(RootOf(_Z^2+1)*x^4+1))+1/8*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*ln((-(x^4+1)^(1/2)*RootOf(_Z^2+1)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^3*x^2+3*(x^4+1)^(1/2)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^3*x^2+2*(x^4+1)^(1/4)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^2*RootOf(_Z^2+1)*x^3-4*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x^4-6*(x^4+1)^(1/4)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^2*x^3-6*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x^4+16*(x^4+1)^(3/4)*RootOf(_Z^2+1)*x+4*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*x^4-8*(x^4+1)^(3/4)*x-4*RootOf(_Z^2+1)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)+2*RootOf(_Z^4+8*RootOf(_Z^2+1)-8))/(RootOf(_Z^2+1)*x^4-1))-1/8*RootOf(_Z^2+1)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*ln((3*(x^4+1)^(1/2)*RootOf(_Z^2+1)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^3*x^2+(x^4+1)^(1/2)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^3*x^2-2*(x^4+1)^(1/4)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^2*RootOf(_Z^2+1)*x^3-2*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x^4+6*(x^4+1)^(1/4)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^2*x^3-8*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x^4+16*(x^4+1)^(3/4)*RootOf(_Z^2+1)*x-8*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*x^4-8*(x^4+1)^(3/4)*x-2*RootOf(_Z^2+1)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)-4*RootOf(_Z^4+8*RootOf(_Z^2+1)-8))/(RootOf(_Z^2+1)*x^4-1))","B"
1040,0,0,31,180.000000," ","int((x^4-1)^(1/4)*(x^8-x^4+1)/x^6/(2*x^8+1),x)","\[\int \frac{\left(x^{4}-1\right)^{\frac{1}{4}} \left(x^{8}-x^{4}+1\right)}{x^{6} \left(2 x^{8}+1\right)}\, dx\]"," ",0,"int((x^4-1)^(1/4)*(x^8-x^4+1)/x^6/(2*x^8+1),x)","F"
1041,0,0,31,180.000000," ","int((x^4-1)^(1/4)*(x^8-x^4+1)/x^6/(2*x^8+1),x)","\[\int \frac{\left(x^{4}-1\right)^{\frac{1}{4}} \left(x^{8}-x^{4}+1\right)}{x^{6} \left(2 x^{8}+1\right)}\, dx\]"," ",0,"int((x^4-1)^(1/4)*(x^8-x^4+1)/x^6/(2*x^8+1),x)","F"
1042,1,68,60,0.553000," ","int((2*x^4+1)*(2*x^8+1)^(1/2)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\left(\frac{x^{4}}{4}+\frac{1}{4}\right) \sqrt{2 x^{8}+1}-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}-2\right) x^{4}-\sqrt{2 x^{8}+1}\right)}{8}+\frac{\ln \left(\frac{\sqrt{2 x^{8}+1}-1}{x^{4}}\right)}{4}$&$68$\\ meijerg&$-\frac{4 \sqrt{\pi}-4 \sqrt{\pi}\, \sqrt{2 x^{8}+1}+4 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{2 x^{8}+1}}{2}\right)-2 \left(2-\ln \left(2\right)+8 \ln \left(x \right)\right) \sqrt{\pi}}{16 \sqrt{\pi}}-\frac{\sqrt{2}\, \left(-2 \sqrt{\pi}\, \sqrt{2}\, x^{4} \sqrt{2 x^{8}+1}-2 \sqrt{\pi}\, \arcsinh \left(\sqrt{2}\, x^{4}\right)\right)}{16 \sqrt{\pi}}$&$103$\\ \hline \end{longtable}"," ",0,"(1/4*x^4+1/4)*(2*x^8+1)^(1/2)-1/8*RootOf(_Z^2-2)*ln(RootOf(_Z^2-2)*x^4-(2*x^8+1)^(1/2))+1/4*ln(((2*x^8+1)^(1/2)-1)/x^4)","C"
1043,1,52,56,0.011000," ","int((x+(1+x)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{2 \left(x +\sqrt{1+x}\right)^{\frac{3}{2}}}{3}-\frac{\left(2 \sqrt{1+x}+1\right) \sqrt{x +\sqrt{1+x}}}{4}+\frac{5 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{8}$&$52$\\ default&$\frac{2 \left(x +\sqrt{1+x}\right)^{\frac{3}{2}}}{3}-\frac{\left(2 \sqrt{1+x}+1\right) \sqrt{x +\sqrt{1+x}}}{4}+\frac{5 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{8}$&$52$\\ \hline \end{longtable}"," ",0,"2/3*(x+(1+x)^(1/2))^(3/2)-1/4*(2*(1+x)^(1/2)+1)*(x+(1+x)^(1/2))^(1/2)+5/8*ln(1/2+(1+x)^(1/2)+(x+(1+x)^(1/2))^(1/2))","A"
1044,0,0,65,0.020000," ","int((a*x^2+2*b)/x/(a^2*x^2+b^2)^(3/4),x)","\[\int \frac{a \,x^{2}+2 b}{x \left(a^{2} x^{2}+b^{2}\right)^{\frac{3}{4}}}\, dx\]"," ",0,"int((a*x^2+2*b)/x/(a^2*x^2+b^2)^(3/4),x)","F"
1045,1,4026,71,0.376000," ","int((-a*b*x+x^3)/(-a+x)/(-b+x)/(x*(-a+x)*(-b+x))^(1/2)/(a*b*d-(a*d+b*d+1)*x+d*x^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\text{Expression too large to display}$&$4026$\\ default&$\text{Expression too large to display}$&$4442$\\ \hline \end{longtable}"," ",0,"2*x/((a*b+(-a-b)*x+x^2)*x)^(1/2)-2*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)*EllipticF((-(-b+x)/b)^(1/2),(b/(-a+b))^(1/2))-1/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*a-1/2/d-1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(b-1/2/d*(a*d+b*d+1+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))),(b/(-a+b))^(1/2))*a^2*d+2/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*b^2*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*a-1/2/d-1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(b-1/2/d*(a*d+b*d+1+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))),(b/(-a+b))^(1/2))*a*d-2/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*a-1/2/d-1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(b-1/2/d*(a*d+b*d+1+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))),(b/(-a+b))^(1/2))*a-1/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*b^3*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*a-1/2/d-1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(b-1/2/d*(a*d+b*d+1+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))),(b/(-a+b))^(1/2))*d-2/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*b^2*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*a-1/2/d-1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(b-1/2/d*(a*d+b*d+1+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))),(b/(-a+b))^(1/2))-1/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*a-1/2/d-1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(b-1/2/d*(a*d+b*d+1+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))),(b/(-a+b))^(1/2))/d-b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*a-1/2/d-1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(b-1/2/d*(a*d+b*d+1+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))),(b/(-a+b))^(1/2))*a-b^2*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*a-1/2/d-1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(b-1/2/d*(a*d+b*d+1+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))),(b/(-a+b))^(1/2))-b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*a-1/2/d-1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(b-1/2/d*(a*d+b*d+1+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2))),(b/(-a+b))^(1/2))/d+1/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*a+1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-b+x)/b)^(1/2),b/(b+1/2*(-a*d-b*d+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1)/d),(b/(-a+b))^(1/2))*a^2*d-2/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*b^2*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*a+1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-b+x)/b)^(1/2),b/(b+1/2*(-a*d-b*d+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1)/d),(b/(-a+b))^(1/2))*a*d+2/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*a+1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-b+x)/b)^(1/2),b/(b+1/2*(-a*d-b*d+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1)/d),(b/(-a+b))^(1/2))*a+1/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*b^3*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*a+1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-b+x)/b)^(1/2),b/(b+1/2*(-a*d-b*d+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1)/d),(b/(-a+b))^(1/2))*d+2/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*b^2*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*a+1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-b+x)/b)^(1/2),b/(b+1/2*(-a*d-b*d+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1)/d),(b/(-a+b))^(1/2))-b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*a+1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-b+x)/b)^(1/2),b/(b+1/2*(-a*d-b*d+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1)/d),(b/(-a+b))^(1/2))*a-b^2*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*a+1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-b+x)/b)^(1/2),b/(b+1/2*(-a*d-b*d+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1)/d),(b/(-a+b))^(1/2))-b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*a+1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-b+x)/b)^(1/2),b/(b+1/2*(-a*d-b*d+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1)/d),(b/(-a+b))^(1/2))/d+1/(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2*a+1/2/d*(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-b+x)/b)^(1/2),b/(b+1/2*(-a*d-b*d+(a^2*d^2-2*a*b*d^2+b^2*d^2+2*a*d+2*b*d+1)^(1/2)-1)/d),(b/(-a+b))^(1/2))/d","C"
1046,0,0,67,0.010000," ","int((-1+2*(-1+k)*x+k*x^2)/((1-x)*x*(-k*x+1))^(1/4)/(-1+(3+d)*x-(d*k+3)*x^2+x^3),x)","\[\int \frac{-1+2 \left(-1+k \right) x +k \,x^{2}}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{4}} \left(-1+\left(3+d \right) x -\left(d k +3\right) x^{2}+x^{3}\right)}\, dx\]"," ",0,"int((-1+2*(-1+k)*x+k*x^2)/((1-x)*x*(-k*x+1))^(1/4)/(-1+(3+d)*x-(d*k+3)*x^2+x^3),x)","F"
1047,1,223,65,1.510000," ","int((x^4+1)/(x^3-x)^(1/2)/(x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{x}{\sqrt{x \left(x^{2}-1\right)}}+\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticF \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{3}-x}}-\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}-\frac{i \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}-\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}+\frac{i \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}$&$223$\\ elliptic&$-\frac{x}{\sqrt{x \left(x^{2}-1\right)}}+\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticF \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{3}-x}}-\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}-\frac{i \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}-\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}+\frac{i \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}$&$223$\\ default&$\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticF \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{3}-x}}-\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}-\frac{i \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}-\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}+\frac{i \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}+\frac{x^{2}-x}{2 \sqrt{\left(1+x \right) \left(x^{2}-x \right)}}-\frac{x^{2}+x}{2 \sqrt{\left(-1+x \right) \left(x^{2}+x \right)}}$&$251$\\ trager&$-\frac{\sqrt{x^{3}-x}}{x^{2}-1}+9 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right) \ln \left(\frac{-150336 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)^{2} x^{2}+225504 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)^{2} x +2826 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right) x^{2}+7200 \sqrt{x^{3}-x}\, \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)+150336 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)^{2}-10764 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right) x -8 x^{2}-125 \sqrt{x^{3}-x}-2826 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)+112 x +8}{\left(72 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right) x -144 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)-3 x +1\right)^{2}}\right)+\frac{\ln \left(-\frac{300672 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)^{2} x^{2}-451008 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)^{2} x -11052 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right) x^{2}+14400 \sqrt{x^{3}-x}\, \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)-300672 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)^{2}+3528 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right) x +91 x^{2}-150 \sqrt{x^{3}-x}+11052 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)+26 x -91}{\left(72 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right) x -144 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)+x +3\right)^{2}}\right)}{4}-9 \ln \left(-\frac{300672 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)^{2} x^{2}-451008 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)^{2} x -11052 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right) x^{2}+14400 \sqrt{x^{3}-x}\, \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)-300672 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)^{2}+3528 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right) x +91 x^{2}-150 \sqrt{x^{3}-x}+11052 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)+26 x -91}{\left(72 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right) x -144 \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)+x +3\right)^{2}}\right) \RootOf \left(2592 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)$&$559$\\ \hline \end{longtable}"," ",0,"-x/(x*(x^2-1))^(1/2)+1/2*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticF((1+x)^(1/2),1/2*2^(1/2))-1/4*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticPi((1+x)^(1/2),1/2-1/2*I,1/2*2^(1/2))-1/4*I*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticPi((1+x)^(1/2),1/2-1/2*I,1/2*2^(1/2))-1/4*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticPi((1+x)^(1/2),1/2+1/2*I,1/2*2^(1/2))+1/4*I*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticPi((1+x)^(1/2),1/2+1/2*I,1/2*2^(1/2))","C"
1048,1,107,70,0.666000," ","int((x^2+2)*(x^4-5*x^2+4)^(1/2)/x^2/(x^2+2*x-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{4}-5 x^{2}+4}}{x}+\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}-3\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}-3\right) x +3 \sqrt{x^{4}-5 x^{2}+4}-4 \RootOf \left(\textit{\_Z}^{2}-3\right)}{x^{2}+2 x -2}\right)+2 \ln \left(-\frac{-x^{2}+\sqrt{x^{4}-5 x^{2}+4}+2}{x}\right)$&$107$\\ elliptic&$-\ln \left(-\frac{5}{2}+x^{2}+\sqrt{x^{4}-5 x^{2}+4}\right)+\frac{9 \sqrt{3}\, \arctanh \left(\frac{24-12 \sqrt{3}+\left(3-4 \sqrt{3}\right) \left(x^{2}-4+2 \sqrt{3}\right)}{2 \left(3-\sqrt{3}\right) \sqrt{\left(x^{2}-4+2 \sqrt{3}\right)^{2}+\left(3-4 \sqrt{3}\right) \left(x^{2}-4+2 \sqrt{3}\right)+12-6 \sqrt{3}}}\right)}{2 \left(\sqrt{3}-2\right) \left(3-\sqrt{3}\right)}-\frac{15 \arctanh \left(\frac{24-12 \sqrt{3}+\left(3-4 \sqrt{3}\right) \left(x^{2}-4+2 \sqrt{3}\right)}{2 \left(3-\sqrt{3}\right) \sqrt{\left(x^{2}-4+2 \sqrt{3}\right)^{2}+\left(3-4 \sqrt{3}\right) \left(x^{2}-4+2 \sqrt{3}\right)+12-6 \sqrt{3}}}\right)}{2 \left(\sqrt{3}-2\right) \left(3-\sqrt{3}\right)}-\frac{\arctanh \left(\frac{-5 x^{2}+8}{4 \sqrt{x^{4}-5 x^{2}+4}}\right)}{\left(2+\sqrt{3}\right) \left(\sqrt{3}-2\right)}+\frac{9 \sqrt{3}\, \arctanh \left(\frac{24+12 \sqrt{3}+\left(3+4 \sqrt{3}\right) \left(x^{2}-4-2 \sqrt{3}\right)}{2 \left(3+\sqrt{3}\right) \sqrt{\left(x^{2}-4-2 \sqrt{3}\right)^{2}+\left(3+4 \sqrt{3}\right) \left(x^{2}-4-2 \sqrt{3}\right)+12+6 \sqrt{3}}}\right)}{2 \left(2+\sqrt{3}\right) \left(3+\sqrt{3}\right)}+\frac{15 \arctanh \left(\frac{24+12 \sqrt{3}+\left(3+4 \sqrt{3}\right) \left(x^{2}-4-2 \sqrt{3}\right)}{2 \left(3+\sqrt{3}\right) \sqrt{\left(x^{2}-4-2 \sqrt{3}\right)^{2}+\left(3+4 \sqrt{3}\right) \left(x^{2}-4-2 \sqrt{3}\right)+12+6 \sqrt{3}}}\right)}{2 \left(2+\sqrt{3}\right) \left(3+\sqrt{3}\right)}+\frac{\left(\frac{\sqrt{x^{4}-5 x^{2}+4}\, \sqrt{2}}{x}-\sqrt{6}\, \arctanh \left(\frac{\sqrt{6}\, \sqrt{x^{4}-5 x^{2}+4}\, \sqrt{2}}{6 x}\right)\right) \sqrt{2}}{2}$&$488$\\ risch&$\frac{\sqrt{x^{4}-5 x^{2}+4}}{x}-\ln \left(-\frac{5}{2}+x^{2}+\sqrt{x^{4}-5 x^{2}+4}\right)+\frac{3 \sqrt{-x^{2}+1}\, \sqrt{-x^{2}+4}\, \EllipticF \left(x , \frac{1}{2}\right)}{2 \sqrt{x^{4}-5 x^{2}+4}}+\arctanh \left(\frac{-5 x^{2}+8}{4 \sqrt{x^{4}-5 x^{2}+4}}\right)-\frac{3 \arctanh \left(\frac{3}{2 \sqrt{-\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}-\frac{5 \sqrt{3}}{4 \sqrt{-\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}-\frac{3 x^{2}}{8 \sqrt{-\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}+\frac{\sqrt{3}\, x^{2}}{2 \sqrt{-\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}\right)}{2 \sqrt{-\frac{3 \sqrt{3}}{2}+3}}+\frac{3 \sqrt{-x^{2}+1}\, \sqrt{-x^{2}+4}\, \EllipticPi \left(x , \frac{1}{\left(\sqrt{3}-1\right)^{2}}, \frac{1}{2}\right)}{2 \sqrt{x^{4}-5 x^{2}+4}\, \left(\sqrt{3}-1\right)}+\frac{3 \sqrt{3}\, \arctanh \left(\frac{3}{2 \sqrt{-\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}-\frac{5 \sqrt{3}}{4 \sqrt{-\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}-\frac{3 x^{2}}{8 \sqrt{-\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}+\frac{\sqrt{3}\, x^{2}}{2 \sqrt{-\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}\right)}{2 \sqrt{-\frac{3 \sqrt{3}}{2}+3}}-\frac{3 \sqrt{3}\, \sqrt{-x^{2}+1}\, \sqrt{-x^{2}+4}\, \EllipticPi \left(x , \frac{1}{\left(\sqrt{3}-1\right)^{2}}, \frac{1}{2}\right)}{2 \sqrt{x^{4}-5 x^{2}+4}\, \left(\sqrt{3}-1\right)}+\frac{3 \sqrt{3}\, \arctanh \left(-\frac{3}{2 \sqrt{\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}-\frac{5 \sqrt{3}}{4 \sqrt{\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}+\frac{3 x^{2}}{8 \sqrt{\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}+\frac{\sqrt{3}\, x^{2}}{2 \sqrt{\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}\right)}{2 \sqrt{\frac{3 \sqrt{3}}{2}+3}}+\frac{3 \sqrt{3}\, \sqrt{-x^{2}+1}\, \sqrt{-x^{2}+4}\, \EllipticPi \left(x , \frac{1}{\left(-1-\sqrt{3}\right)^{2}}, \frac{1}{2}\right)}{2 \sqrt{x^{4}-5 x^{2}+4}\, \left(-1-\sqrt{3}\right)}+\frac{3 \arctanh \left(-\frac{3}{2 \sqrt{\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}-\frac{5 \sqrt{3}}{4 \sqrt{\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}+\frac{3 x^{2}}{8 \sqrt{\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}+\frac{\sqrt{3}\, x^{2}}{2 \sqrt{\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}\right)}{2 \sqrt{\frac{3 \sqrt{3}}{2}+3}}+\frac{3 \sqrt{-x^{2}+1}\, \sqrt{-x^{2}+4}\, \EllipticPi \left(x , \frac{1}{\left(-1-\sqrt{3}\right)^{2}}, \frac{1}{2}\right)}{2 \sqrt{x^{4}-5 x^{2}+4}\, \left(-1-\sqrt{3}\right)}$&$811$\\ default&$\frac{\sqrt{x^{4}-5 x^{2}+4}}{x}+\frac{11 \sqrt{-x^{2}+1}\, \sqrt{-x^{2}+4}\, \EllipticF \left(x , \frac{1}{2}\right)}{2 \sqrt{x^{4}-5 x^{2}+4}}-\frac{4 \sqrt{-x^{2}+1}\, \sqrt{-x^{2}+4}\, \left(\EllipticF \left(x , \frac{1}{2}\right)-\EllipticE \left(x , \frac{1}{2}\right)\right)}{\sqrt{x^{4}-5 x^{2}+4}}+\frac{5 \ln \left(-\frac{5}{2}+x^{2}+\sqrt{x^{4}-5 x^{2}+4}\right)}{4}+\arctanh \left(\frac{-5 x^{2}+8}{4 \sqrt{x^{4}-5 x^{2}+4}}\right)+9 \ln \left(2\right)-\frac{9 \ln \left(2 x^{2}-5+2 \sqrt{x^{4}-5 x^{2}+4}\right)}{2}-\frac{4 \sqrt{-x^{2}+1}\, \sqrt{-x^{2}+4}\, \EllipticE \left(x , \frac{1}{2}\right)}{\sqrt{x^{4}-5 x^{2}+4}}-\frac{3 \arctanh \left(\frac{3}{2 \sqrt{-\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}-\frac{5 \sqrt{3}}{4 \sqrt{-\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}-\frac{3 x^{2}}{8 \sqrt{-\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}+\frac{\sqrt{3}\, x^{2}}{2 \sqrt{-\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}\right)}{2 \sqrt{-\frac{3 \sqrt{3}}{2}+3}}+\frac{3 \sqrt{-x^{2}+1}\, \sqrt{-x^{2}+4}\, \EllipticPi \left(x , \frac{1}{\left(\sqrt{3}-1\right)^{2}}, \frac{1}{2}\right)}{2 \sqrt{x^{4}-5 x^{2}+4}\, \left(\sqrt{3}-1\right)}+\frac{3 \sqrt{3}\, \arctanh \left(\frac{3}{2 \sqrt{-\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}-\frac{5 \sqrt{3}}{4 \sqrt{-\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}-\frac{3 x^{2}}{8 \sqrt{-\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}+\frac{\sqrt{3}\, x^{2}}{2 \sqrt{-\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}\right)}{2 \sqrt{-\frac{3 \sqrt{3}}{2}+3}}-\frac{3 \sqrt{3}\, \sqrt{-x^{2}+1}\, \sqrt{-x^{2}+4}\, \EllipticPi \left(x , \frac{1}{\left(\sqrt{3}-1\right)^{2}}, \frac{1}{2}\right)}{2 \sqrt{x^{4}-5 x^{2}+4}\, \left(\sqrt{3}-1\right)}+\frac{3 \sqrt{3}\, \arctanh \left(-\frac{3}{2 \sqrt{\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}-\frac{5 \sqrt{3}}{4 \sqrt{\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}+\frac{3 x^{2}}{8 \sqrt{\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}+\frac{\sqrt{3}\, x^{2}}{2 \sqrt{\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}\right)}{2 \sqrt{\frac{3 \sqrt{3}}{2}+3}}+\frac{3 \sqrt{3}\, \sqrt{-x^{2}+1}\, \sqrt{-x^{2}+4}\, \EllipticPi \left(x , \frac{1}{\left(-1-\sqrt{3}\right)^{2}}, \frac{1}{2}\right)}{2 \sqrt{x^{4}-5 x^{2}+4}\, \left(-1-\sqrt{3}\right)}+\frac{3 \arctanh \left(-\frac{3}{2 \sqrt{\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}-\frac{5 \sqrt{3}}{4 \sqrt{\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}+\frac{3 x^{2}}{8 \sqrt{\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}+\frac{\sqrt{3}\, x^{2}}{2 \sqrt{\frac{3 \sqrt{3}}{2}+3}\, \sqrt{\frac{1}{4} x^{4}-\frac{5}{4} x^{2}+1}}\right)}{2 \sqrt{\frac{3 \sqrt{3}}{2}+3}}+\frac{3 \sqrt{-x^{2}+1}\, \sqrt{-x^{2}+4}\, \EllipticPi \left(x , \frac{1}{\left(-1-\sqrt{3}\right)^{2}}, \frac{1}{2}\right)}{2 \sqrt{x^{4}-5 x^{2}+4}\, \left(-1-\sqrt{3}\right)}$&$915$\\ \hline \end{longtable}"," ",0,"(x^4-5*x^2+4)^(1/2)/x+RootOf(_Z^2-3)*ln(-(2*RootOf(_Z^2-3)*x^2+RootOf(_Z^2-3)*x+3*(x^4-5*x^2+4)^(1/2)-4*RootOf(_Z^2-3))/(x^2+2*x-2))+2*ln(-(-x^2+(x^4-5*x^2+4)^(1/2)+2)/x)","C"
1049,1,241,61,6.338000," ","int(x^2/(x^4-1)/(x^4+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x}{\left(x^{2} \left(x^{2}+1\right)\right)^{\frac{1}{4}}}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(-\frac{\sqrt{x^{4}+x^{2}}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x +2 \left(x^{4}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{3}-4 \left(x^{4}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x}{x \left(-1+x \right) \left(1+x \right)}\right)}{8}-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(\frac{\sqrt{x^{4}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x +2 \left(x^{4}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+3 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{3}+4 \left(x^{4}+x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}-8\right) x}{x \left(-1+x \right) \left(1+x \right)}\right)}{8}$&$241$\\ trager&$\frac{\left(x^{4}+x^{2}\right)^{\frac{3}{4}}}{x \left(x^{2}+1\right)}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(-\frac{\sqrt{x^{4}+x^{2}}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x +2 \left(x^{4}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{3}-4 \left(x^{4}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x}{x \left(-1+x \right) \left(1+x \right)}\right)}{8}+\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(\frac{-\sqrt{x^{4}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x +2 \left(x^{4}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-3 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{3}+4 \left(x^{4}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}-8\right) x}{x \left(-1+x \right) \left(1+x \right)}\right)}{8}$&$250$\\ \hline \end{longtable}"," ",0,"x/(x^2*(x^2+1))^(1/4)-1/8*RootOf(_Z^2+RootOf(_Z^4-8)^2)*ln(-((x^4+x^2)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x+2*(x^4+x^2)^(1/4)*RootOf(_Z^4-8)^2*x^2-3*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^3-4*(x^4+x^2)^(3/4)-RootOf(_Z^2+RootOf(_Z^4-8)^2)*x)/x/(-1+x)/(1+x))-1/8*RootOf(_Z^4-8)*ln(((x^4+x^2)^(1/2)*RootOf(_Z^4-8)^3*x+2*(x^4+x^2)^(1/4)*RootOf(_Z^4-8)^2*x^2+3*RootOf(_Z^4-8)*x^3+4*(x^4+x^2)^(3/4)+RootOf(_Z^4-8)*x)/x/(-1+x)/(1+x))","C"
1050,1,77,62,0.979000," ","int((x^6-2)*(x^6-1)^(1/2)/x^4/(x^6+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}-1}}{3 x^{3}}+\frac{\ln \left(x^{3}+\sqrt{x^{6}-1}\right)}{3}-\frac{\RootOf \left(\textit{\_Z}^{2}-6\right) \ln \left(\frac{5 \RootOf \left(\textit{\_Z}^{2}-6\right) x^{6}+12 x^{3} \sqrt{x^{6}-1}-2 \RootOf \left(\textit{\_Z}^{2}-6\right)}{x^{6}+2}\right)}{6}$&$77$\\ risch&$\frac{\sqrt{x^{6}-1}}{3 x^{3}}+\frac{\ln \left(x^{3}+\sqrt{x^{6}-1}\right)}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}-6\right) \ln \left(\frac{-5 \RootOf \left(\textit{\_Z}^{2}-6\right) x^{6}+12 x^{3} \sqrt{x^{6}-1}+2 \RootOf \left(\textit{\_Z}^{2}-6\right)}{x^{6}+2}\right)}{6}$&$77$\\ \hline \end{longtable}"," ",0,"1/3*(x^6-1)^(1/2)/x^3+1/3*ln(x^3+(x^6-1)^(1/2))-1/6*RootOf(_Z^2-6)*ln((5*RootOf(_Z^2-6)*x^6+12*x^3*(x^6-1)^(1/2)-2*RootOf(_Z^2-6))/(x^6+2))","C"
1051,1,117,71,0.850000," ","int((x^6-4)*(x^6-x^4+2)^(5/2)/x^7/(x^6+2)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}-x^{4}+2}\, \left(2 x^{12}-14 x^{10}-3 x^{8}+8 x^{6}-28 x^{4}+8\right)}{6 x^{6} \left(x^{6}+2\right)}+\frac{5 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-2 \sqrt{x^{6}-x^{4}+2}\, x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{6}+2}\right)}{4}$&$117$\\ risch&$\frac{2 x^{18}-16 x^{16}+11 x^{14}+15 x^{12}-64 x^{10}+22 x^{8}+24 x^{6}-64 x^{4}+16}{6 x^{6} \sqrt{x^{6}-x^{4}+2}\, \left(x^{6}+2\right)}-\frac{5 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \sqrt{x^{6}-x^{4}+2}\, x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{6}+2}\right)}{4}$&$133$\\ \hline \end{longtable}"," ",0,"1/6*(x^6-x^4+2)^(1/2)*(2*x^12-14*x^10-3*x^8+8*x^6-28*x^4+8)/x^6/(x^6+2)+5/4*RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)*x^6-2*RootOf(_Z^2+1)*x^4-2*(x^6-x^4+2)^(1/2)*x^2+2*RootOf(_Z^2+1))/(x^6+2))","C"
1052,1,6506,24,280.109000," ","int((x^3-1)^(2/3)*(x^3+2)/x^6/(2*x^6+x^3+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$6506$\\ trager&$\text{Expression too large to display}$&$12148$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1053,1,6630,24,265.566000," ","int((x^3-1)^(2/3)*(x^3+2)/x^6/(2*x^6+x^3+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$6630$\\ trager&$\text{Expression too large to display}$&$7528$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1054,1,436,63,1.416000," ","int((x^7+x)/(x^6-1)^(2/3)/(x^6+x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(-\frac{-6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}-x^{6}-18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x -9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{2}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+3 x \left(x^{6}-1\right)^{\frac{2}{3}}-3 x^{2} \left(x^{6}-1\right)^{\frac{1}{3}}+6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+1}{x^{6}+x^{3}-1}\right)-\frac{\ln \left(\frac{-6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}-x^{6}+18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x -9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{2}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+x^{3}+6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+1}{x^{6}+x^{3}-1}\right)}{3}-\ln \left(\frac{-6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}-x^{6}+18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x -9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{2}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+x^{3}+6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+1}{x^{6}+x^{3}-1}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)$&$436$\\ \hline \end{longtable}"," ",0,"RootOf(9*_Z^2+3*_Z+1)*ln(-(-6*RootOf(9*_Z^2+3*_Z+1)*x^6-x^6-18*RootOf(9*_Z^2+3*_Z+1)^2*x^3+9*RootOf(9*_Z^2+3*_Z+1)*(x^6-1)^(2/3)*x-9*RootOf(9*_Z^2+3*_Z+1)*(x^6-1)^(1/3)*x^2-3*RootOf(9*_Z^2+3*_Z+1)*x^3+3*x*(x^6-1)^(2/3)-3*x^2*(x^6-1)^(1/3)+6*RootOf(9*_Z^2+3*_Z+1)+1)/(x^6+x^3-1))-1/3*ln((-6*RootOf(9*_Z^2+3*_Z+1)*x^6-x^6+18*RootOf(9*_Z^2+3*_Z+1)^2*x^3+9*RootOf(9*_Z^2+3*_Z+1)*(x^6-1)^(2/3)*x-9*RootOf(9*_Z^2+3*_Z+1)*(x^6-1)^(1/3)*x^2+9*RootOf(9*_Z^2+3*_Z+1)*x^3+x^3+6*RootOf(9*_Z^2+3*_Z+1)+1)/(x^6+x^3-1))-ln((-6*RootOf(9*_Z^2+3*_Z+1)*x^6-x^6+18*RootOf(9*_Z^2+3*_Z+1)^2*x^3+9*RootOf(9*_Z^2+3*_Z+1)*(x^6-1)^(2/3)*x-9*RootOf(9*_Z^2+3*_Z+1)*(x^6-1)^(1/3)*x^2+9*RootOf(9*_Z^2+3*_Z+1)*x^3+x^3+6*RootOf(9*_Z^2+3*_Z+1)+1)/(x^6+x^3-1))*RootOf(9*_Z^2+3*_Z+1)","C"
1055,1,157,63,1.496000," ","int((-x^6+1)^(1/2)*(2*x^6+1)/(x^12-2*x^6+x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{6}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{5} x^{2}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+2 \sqrt{-x^{6}+1}\, x}{x^{6}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}-1}\right)}{4}-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) x^{6}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}+2 \sqrt{-x^{6}+1}\, x -\RootOf \left(\textit{\_Z}^{4}+1\right)}{-x^{6}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}+1}\right)}{4}$&$157$\\ \hline \end{longtable}"," ",0,"-1/4*RootOf(_Z^4+1)^3*ln(-(RootOf(_Z^4+1)^3*x^6-RootOf(_Z^4+1)^5*x^2-RootOf(_Z^4+1)^3+2*(-x^6+1)^(1/2)*x)/(x^6+RootOf(_Z^4+1)^2*x^2-1))-1/4*RootOf(_Z^4+1)*ln(-(RootOf(_Z^4+1)*x^6+RootOf(_Z^4+1)^3*x^2+2*(-x^6+1)^(1/2)*x-RootOf(_Z^4+1))/(-x^6+RootOf(_Z^4+1)^2*x^2+1))","C"
1056,0,0,58,0.014000," ","int((x^2+1)^(1/2)/(1+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{x^{2}+1}}{\sqrt{1+\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^2+1)^(1/2)/(1+(x^2+1)^(1/2))^(1/2),x)","F"
1057,1,84,65,0.059000," ","int((x^2+1)/(x+(x^2+1)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{-\frac{32 \sqrt{\pi}\, \sqrt{2}\, \cosh \left(\frac{3 \arcsinh \left(\frac{1}{x}\right)}{2}\right)}{3 x^{\frac{3}{2}}}-\frac{8 \sqrt{\pi}\, \sqrt{2}\, x^{\frac{3}{2}} \left(-\frac{4}{3 x^{4}}-\frac{2}{3 x^{2}}+\frac{2}{3}\right) \sinh \left(\frac{3 \arcsinh \left(\frac{1}{x}\right)}{2}\right)}{\sqrt{1+\frac{1}{x^{2}}}}}{8 \sqrt{\pi}}+\frac{\sqrt{2}\, x^{\frac{5}{2}} \hypergeom \left(\left[-\frac{5}{4}, \frac{1}{4}, \frac{3}{4}\right], \left[-\frac{1}{4}, \frac{3}{2}\right], -\frac{1}{x^{2}}\right)}{5}$&$84$\\ \hline \end{longtable}"," ",0,"-1/8/Pi^(1/2)*(-32/3*Pi^(1/2)*2^(1/2)/x^(3/2)*cosh(3/2*arcsinh(1/x))-8*Pi^(1/2)*2^(1/2)*x^(3/2)*(-4/3/x^4-2/3/x^2+2/3)*sinh(3/2*arcsinh(1/x))/(1+1/x^2)^(1/2))+1/5*2^(1/2)*x^(5/2)*hypergeom([-5/4,1/4,3/4],[-1/4,3/2],-1/x^2)","C"
1058,1,22,57,0.034000," ","int(x^2/(x^2+(x^4+1)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\sqrt{2}\, x^{2} \hypergeom \left(\left[-\frac{1}{2}, \frac{1}{4}, \frac{3}{4}\right], \left[\frac{1}{2}, \frac{3}{2}\right], -\frac{1}{x^{4}}\right)}{4}$&$22$\\ \hline \end{longtable}"," ",0,"1/4*2^(1/2)*x^2*hypergeom([-1/2,1/4,3/4],[1/2,3/2],-1/x^4)","C"
1059,0,0,57,0.019000," ","int((x^4+1)^(1/2)/(x^2+(x^4+1)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{x^{4}+1}}{\sqrt{x^{2}+\sqrt{x^{4}+1}}}\, dx\]"," ",0,"int((x^4+1)^(1/2)/(x^2+(x^4+1)^(1/2))^(1/2),x)","F"
1060,1,255,64,1.324000," ","int((x^2-3)/(x^2-1)^(1/3)/(x^3+x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{2}{3}} x -\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{1}{3}} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+2 x \left(x^{2}-1\right)^{\frac{2}{3}}+\left(x^{2}-1\right)^{\frac{1}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-x^{3}+x^{2}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1}{x^{3}+x^{2}-1}\right)+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{2}{3}} x +2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{1}{3}} x^{2}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-x \left(x^{2}-1\right)^{\frac{2}{3}}+\left(x^{2}-1\right)^{\frac{1}{3}} x^{2}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1}{x^{3}+x^{2}-1}\right)$&$255$\\ \hline \end{longtable}"," ",0,"ln(-(-RootOf(_Z^2+_Z+1)^2*x^3+RootOf(_Z^2+_Z+1)*(x^2-1)^(2/3)*x-RootOf(_Z^2+_Z+1)*(x^2-1)^(1/3)*x^2-2*RootOf(_Z^2+_Z+1)*x^3+2*x*(x^2-1)^(2/3)+(x^2-1)^(1/3)*x^2+RootOf(_Z^2+_Z+1)*x^2-x^3+x^2-RootOf(_Z^2+_Z+1)-1)/(x^3+x^2-1))+RootOf(_Z^2+_Z+1)*ln((-RootOf(_Z^2+_Z+1)^2*x^3+RootOf(_Z^2+_Z+1)*(x^2-1)^(2/3)*x+2*RootOf(_Z^2+_Z+1)*(x^2-1)^(1/3)*x^2-RootOf(_Z^2+_Z+1)*x^3-x*(x^2-1)^(2/3)+(x^2-1)^(1/3)*x^2-RootOf(_Z^2+_Z+1)*x^2-x^2+RootOf(_Z^2+_Z+1)+1)/(x^3+x^2-1))","C"
1061,1,2557,72,0.390000," ","int((-a^2*b+a*(2*a+b)*x-3*a*x^2+x^3)/x/(-b+x)/(x*(-a+x)*(-b+x))^(1/2)/(a-(b*d+1)*x+d*x^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\frac{2 \left(a b -a x -b x +x^{2}\right)}{b \sqrt{x \left(a b -a x -b x +x^{2}\right)}}+\frac{-2 a x +2 x^{2}}{b \sqrt{\left(-b +x \right) \left(-a x +x^{2}\right)}}-\frac{2 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}-\frac{b^{3} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) d}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}-\frac{2 b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}+\frac{4 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) a}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}-\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right) d}+\frac{2 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) a}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}-\frac{b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}-\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right) d}+\frac{b^{3} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) d}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}+\frac{2 b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}+\frac{2 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) a}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}-\frac{b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}-\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right) d}-\frac{4 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) a}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}+\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right) d}$&$2557$\\ risch&$-\frac{2 \left(a -x \right) \left(b -x \right)}{b \sqrt{x \left(-a +x \right) \left(-b +x \right)}}+\frac{-\frac{2 a \sqrt{-\frac{-a +x}{a}}\, \sqrt{\frac{-b +x}{a -b}}\, \sqrt{\frac{x}{a}}\, \left(\left(a -b \right) \EllipticE \left(\sqrt{-\frac{-a +x}{a}}, \sqrt{\frac{a}{a -b}}\right)+b \EllipticF \left(\sqrt{-\frac{-a +x}{a}}, \sqrt{\frac{a}{a -b}}\right)\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}-b \left(\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b^{2} d}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}+\frac{2 a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}-\frac{4 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}+\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right) d}-\frac{2 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}+\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}+\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right) d}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b^{2} d}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}-\frac{2 a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}-\frac{2 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}+\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}+\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right) d}+\frac{4 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right) d}\right)+\left(a -b \right) b \left(\frac{-2 a x +2 x^{2}}{b \left(a -b \right) \sqrt{\left(-b +x \right) \left(-a x +x^{2}\right)}}-\frac{2 \left(-\frac{1}{b}+\frac{a}{b \left(a -b \right)}\right) a \sqrt{-\frac{-a +x}{a}}\, \sqrt{\frac{-b +x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticF \left(\sqrt{-\frac{-a +x}{a}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}+\frac{2 a \sqrt{-\frac{-a +x}{a}}\, \sqrt{\frac{-b +x}{a -b}}\, \sqrt{\frac{x}{a}}\, \left(\left(a -b \right) \EllipticE \left(\sqrt{-\frac{-a +x}{a}}, \sqrt{\frac{a}{a -b}}\right)+b \EllipticF \left(\sqrt{-\frac{-a +x}{a}}, \sqrt{\frac{a}{a -b}}\right)\right)}{b \left(a -b \right) \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}\right)}{b}$&$2838$\\ default&$\left(a -b \right) \left(\frac{-2 a x +2 x^{2}}{b \left(a -b \right) \sqrt{\left(-b +x \right) \left(-a x +x^{2}\right)}}+\frac{2 \left(\frac{1}{b}-\frac{a}{b \left(a -b \right)}\right) b \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}+\frac{2 \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \left(\left(-a +b \right) \EllipticE \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)+a \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)\right)}{\left(a -b \right) \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}\right)+a \left(-\frac{2 \left(a b -a x -b x +x^{2}\right)}{a b \sqrt{x \left(a b -a x -b x +x^{2}\right)}}-\frac{2 \left(\frac{a +b}{a b}+\frac{-a -b}{a b}\right) b \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}-\frac{2 \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \left(\left(-a +b \right) \EllipticE \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)+a \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)\right)}{a \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}\right)-\frac{b^{3} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) d}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}-\frac{2 b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}+\frac{4 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) a}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}-\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right) d}+\frac{2 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) a}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}-\frac{b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}-\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right) d}+\frac{b^{3} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) d}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}+\frac{2 b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}+\frac{2 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) a}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}-\frac{b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}-\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right) d}-\frac{4 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) a}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}+\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right) d}$&$2937$\\ \hline \end{longtable}"," ",0,"-2*(a*b-a*x-b*x+x^2)/b/(x*(a*b-a*x-b*x+x^2))^(1/2)+2*(-a*x+x^2)/b/((-b+x)*(-a*x+x^2))^(1/2)-2*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)*EllipticF((-(-b+x)/b)^(1/2),(b/(-a+b))^(1/2))-1/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*b^3*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2/d-1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(b-1/2/d*(b*d+1+(b^2*d^2-4*a*d+2*b*d+1)^(1/2))),(b/(-a+b))^(1/2))*d-2/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*b^2*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2/d-1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(b-1/2/d*(b*d+1+(b^2*d^2-4*a*d+2*b*d+1)^(1/2))),(b/(-a+b))^(1/2))+4/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2/d-1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(b-1/2/d*(b*d+1+(b^2*d^2-4*a*d+2*b*d+1)^(1/2))),(b/(-a+b))^(1/2))*a-1/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2/d-1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(b-1/2/d*(b*d+1+(b^2*d^2-4*a*d+2*b*d+1)^(1/2))),(b/(-a+b))^(1/2))/d+2*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2/d-1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(b-1/2/d*(b*d+1+(b^2*d^2-4*a*d+2*b*d+1)^(1/2))),(b/(-a+b))^(1/2))*a-b^2*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2/d-1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(b-1/2/d*(b*d+1+(b^2*d^2-4*a*d+2*b*d+1)^(1/2))),(b/(-a+b))^(1/2))-b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2/d-1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(b-1/2/d*(b*d+1+(b^2*d^2-4*a*d+2*b*d+1)^(1/2))),(b/(-a+b))^(1/2))/d+1/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*b^3*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b+1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-b+x)/b)^(1/2),b/(b+1/2*(-b*d+(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1)/d),(b/(-a+b))^(1/2))*d+2/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*b^2*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b+1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-b+x)/b)^(1/2),b/(b+1/2*(-b*d+(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1)/d),(b/(-a+b))^(1/2))+2*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b+1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-b+x)/b)^(1/2),b/(b+1/2*(-b*d+(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1)/d),(b/(-a+b))^(1/2))*a-b^2*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b+1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-b+x)/b)^(1/2),b/(b+1/2*(-b*d+(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1)/d),(b/(-a+b))^(1/2))-b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b+1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-b+x)/b)^(1/2),b/(b+1/2*(-b*d+(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1)/d),(b/(-a+b))^(1/2))/d-4/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b+1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-b+x)/b)^(1/2),b/(b+1/2*(-b*d+(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1)/d),(b/(-a+b))^(1/2))*a+1/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b+1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-b+x)/b)^(1/2),b/(b+1/2*(-b*d+(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1)/d),(b/(-a+b))^(1/2))/d","C"
1062,0,0,14,0.028000," ","int(1/(a^3*x^3+b)/(a^3*x^3-b*x^2)^(1/3),x)","\[\int \frac{1}{\left(a^{3} x^{3}+b \right) \left(a^{3} x^{3}-b \,x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(a^3*x^3+b)/(a^3*x^3-b*x^2)^(1/3),x)","F"
1063,0,0,14,0.001000," ","int(1/(a^3*x^3+b)/(a^3*x^3-b*x^2)^(1/3),x)","\[\int \frac{1}{\left(a^{3} x^{3}+b \right) \left(a^{3} x^{3}-b \,x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(a^3*x^3+b)/(a^3*x^3-b*x^2)^(1/3),x)","F"
1064,1,206,64,1.399000," ","int(x^2*(x^3-4)/(x^3-1)^(3/4)/(x^4+x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{4}+2 \left(x^{3}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{3}+2 \sqrt{x^{3}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right) x^{2}+2 \left(x^{3}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{x^{4}+x^{3}-1}\right)-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(-\frac{2 \sqrt{x^{3}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}-2 \left(x^{3}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{4}+1\right) x^{4}+2 \left(x^{3}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}+1\right) x^{3}+\RootOf \left(\textit{\_Z}^{4}+1\right)}{x^{4}+x^{3}-1}\right)$&$206$\\ \hline \end{longtable}"," ",0,"-RootOf(_Z^4+1)*ln(-(RootOf(_Z^4+1)^3*x^4+2*(x^3-1)^(1/4)*RootOf(_Z^4+1)^2*x^3-RootOf(_Z^4+1)^3*x^3+2*(x^3-1)^(1/2)*RootOf(_Z^4+1)*x^2+2*(x^3-1)^(3/4)*x+RootOf(_Z^4+1)^3)/(x^4+x^3-1))-RootOf(_Z^4+1)^3*ln(-(2*(x^3-1)^(1/2)*RootOf(_Z^4+1)^3*x^2-2*(x^3-1)^(1/4)*RootOf(_Z^4+1)^2*x^3+RootOf(_Z^4+1)*x^4+2*(x^3-1)^(3/4)*x-RootOf(_Z^4+1)*x^3+RootOf(_Z^4+1))/(x^4+x^3-1))","C"
1065,0,0,60,0.006000," ","int(x^6/(a*x^4+b)^(3/4),x)","\[\int \frac{x^{6}}{\left(a \,x^{4}+b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(x^6/(a*x^4+b)^(3/4),x)","F"
1066,0,0,66,0.003000," ","int((a*x^4+b*x^2)^(1/4)/x^2,x)","\[\int \frac{\left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}{x^{2}}\, dx\]"," ",0,"int((a*x^4+b*x^2)^(1/4)/x^2,x)","F"
1067,1,6505,31,25.219000," ","int((x^4+2)^(1/4)*(x^8-4)/x^6/(x^8-2*x^4-4),x)","\[\text{output too large to display}\]"," ",0,"result too large to display","B"
1068,1,6507,31,21.347000," ","int((x^4+2)^(1/4)*(x^8-4)/x^6/(x^8-2*x^4-4),x)","\[\text{output too large to display}\]"," ",0,"result too large to display","B"
1069,1,3975,31,20.907000," ","int((x^4-1)^(1/4)*(2*x^8+x^4-1)/x^6/(x^8-x^4+1),x)","\[\text{output too large to display}\]"," ",0,"-1/5*(x^8-2*x^4+1)/x^5/(x^4-1)^(3/4)+(331776*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*ln(-(127401984*RootOf(5308416*_Z^8-2304*_Z^4+1)^10*x^12-254803968*RootOf(5308416*_Z^8-2304*_Z^4+1)^10*x^8-165888*x^12*RootOf(5308416*_Z^8-2304*_Z^4+1)^6-9216*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9+127401984*RootOf(5308416*_Z^8-2304*_Z^4+1)^10*x^4+387072*x^8*RootOf(5308416*_Z^8-2304*_Z^4+1)^6+48*RootOf(5308416*_Z^8-2304*_Z^4+1)^2*x^12-442368*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x^3+2304*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(5308416*_Z^8-2304*_Z^4+1)^4*x^6+18432*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5-4*RootOf(5308416*_Z^8-2304*_Z^4+1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9-276480*x^4*RootOf(5308416*_Z^8-2304*_Z^4+1)^6-120*RootOf(5308416*_Z^8-2304*_Z^4+1)^2*x^8+384*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3-2304*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(5308416*_Z^8-2304*_Z^4+1)^4*x^2-(x^12-3*x^8+3*x^4-1)^(1/2)*x^6-9216*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*(x^12-3*x^8+3*x^4-1)^(1/4)*x+8*RootOf(5308416*_Z^8-2304*_Z^4+1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5+55296*RootOf(5308416*_Z^8-2304*_Z^4+1)^6+96*x^4*RootOf(5308416*_Z^8-2304*_Z^4+1)^2+(x^12-3*x^8+3*x^4-1)^(1/2)*x^2-4*RootOf(5308416*_Z^8-2304*_Z^4+1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x-24*RootOf(5308416*_Z^8-2304*_Z^4+1)^2)/(442368*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x-384*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x+1)/(18432*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x-4*x*RootOf(5308416*_Z^8-2304*_Z^4+1)+1)/(442368*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x-384*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x-1)/(18432*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x-4*x*RootOf(5308416*_Z^8-2304*_Z^4+1)-1)/(110592*x*RootOf(5308416*_Z^8-2304*_Z^4+1)^6+1)^2/(-1+x)^2/(1+x)^2/(110592*x*RootOf(5308416*_Z^8-2304*_Z^4+1)^6-1)^2)-331776*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*ln((-13824*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x^12+2304*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^4*x^9+27648*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x^8-6*RootOf(5308416*_Z^8-2304*_Z^4+1)*x^12+110592*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^6*x^3-576*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x^6-4608*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^4*x^5+(x^12-3*x^8+3*x^4-1)^(1/4)*x^9-13824*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x^4+18*RootOf(5308416*_Z^8-2304*_Z^4+1)*x^8+48*RootOf(5308416*_Z^8-2304*_Z^4+1)^2*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3+576*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x^2+2304*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^4*x-2*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5-18*RootOf(5308416*_Z^8-2304*_Z^4+1)*x^4+(x^12-3*x^8+3*x^4-1)^(1/4)*x+6*RootOf(5308416*_Z^8-2304*_Z^4+1))/(442368*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x+192*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x+1)/(9216*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x-8*x*RootOf(5308416*_Z^8-2304*_Z^4+1)+1)/(9216*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x-8*x*RootOf(5308416*_Z^8-2304*_Z^4+1)-1)/(442368*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x+192*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x-1)/(110592*x*RootOf(5308416*_Z^8-2304*_Z^4+1)^6+1)^2/(-1+x)^2/(1+x)^2/(110592*x*RootOf(5308416*_Z^8-2304*_Z^4+1)^6-1)^2)-6912*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*ln((127401984*RootOf(5308416*_Z^8-2304*_Z^4+1)^10*x^12-254803968*RootOf(5308416*_Z^8-2304*_Z^4+1)^10*x^8-165888*x^12*RootOf(5308416*_Z^8-2304*_Z^4+1)^6-884736*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9+127401984*RootOf(5308416*_Z^8-2304*_Z^4+1)^10*x^4+387072*x^8*RootOf(5308416*_Z^8-2304*_Z^4+1)^6+48*RootOf(5308416*_Z^8-2304*_Z^4+1)^2*x^12+1769472*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5+192*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9-2304*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(5308416*_Z^8-2304*_Z^4+1)^4*x^6-18432*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3-276480*x^4*RootOf(5308416*_Z^8-2304*_Z^4+1)^6-120*RootOf(5308416*_Z^8-2304*_Z^4+1)^2*x^8-884736*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*(x^12-3*x^8+3*x^4-1)^(1/4)*x-384*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5+2304*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(5308416*_Z^8-2304*_Z^4+1)^4*x^2+(x^12-3*x^8+3*x^4-1)^(1/2)*x^6+4*RootOf(5308416*_Z^8-2304*_Z^4+1)*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3+55296*RootOf(5308416*_Z^8-2304*_Z^4+1)^6+96*x^4*RootOf(5308416*_Z^8-2304*_Z^4+1)^2+192*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*(x^12-3*x^8+3*x^4-1)^(1/4)*x-(x^12-3*x^8+3*x^4-1)^(1/2)*x^2-24*RootOf(5308416*_Z^8-2304*_Z^4+1)^2)/(442368*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x-384*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x+1)/(18432*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x-4*x*RootOf(5308416*_Z^8-2304*_Z^4+1)+1)/(442368*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x-384*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x-1)/(18432*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x-4*x*RootOf(5308416*_Z^8-2304*_Z^4+1)-1)/(110592*x*RootOf(5308416*_Z^8-2304*_Z^4+1)^6+1)^2/(-1+x)^2/(1+x)^2/(110592*x*RootOf(5308416*_Z^8-2304*_Z^4+1)^6-1)^2)-144*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*ln(-(127401984*RootOf(5308416*_Z^8-2304*_Z^4+1)^10*x^12-254803968*RootOf(5308416*_Z^8-2304*_Z^4+1)^10*x^8-165888*x^12*RootOf(5308416*_Z^8-2304*_Z^4+1)^6-9216*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9+127401984*RootOf(5308416*_Z^8-2304*_Z^4+1)^10*x^4+387072*x^8*RootOf(5308416*_Z^8-2304*_Z^4+1)^6+48*RootOf(5308416*_Z^8-2304*_Z^4+1)^2*x^12-442368*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x^3+2304*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(5308416*_Z^8-2304*_Z^4+1)^4*x^6+18432*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5-4*RootOf(5308416*_Z^8-2304*_Z^4+1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9-276480*x^4*RootOf(5308416*_Z^8-2304*_Z^4+1)^6-120*RootOf(5308416*_Z^8-2304*_Z^4+1)^2*x^8+384*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3-2304*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(5308416*_Z^8-2304*_Z^4+1)^4*x^2-(x^12-3*x^8+3*x^4-1)^(1/2)*x^6-9216*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*(x^12-3*x^8+3*x^4-1)^(1/4)*x+8*RootOf(5308416*_Z^8-2304*_Z^4+1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5+55296*RootOf(5308416*_Z^8-2304*_Z^4+1)^6+96*x^4*RootOf(5308416*_Z^8-2304*_Z^4+1)^2+(x^12-3*x^8+3*x^4-1)^(1/2)*x^2-4*RootOf(5308416*_Z^8-2304*_Z^4+1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x-24*RootOf(5308416*_Z^8-2304*_Z^4+1)^2)/(442368*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x-384*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x+1)/(18432*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x-4*x*RootOf(5308416*_Z^8-2304*_Z^4+1)+1)/(442368*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x-384*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x-1)/(18432*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x-4*x*RootOf(5308416*_Z^8-2304*_Z^4+1)-1)/(110592*x*RootOf(5308416*_Z^8-2304*_Z^4+1)^6+1)^2/(-1+x)^2/(1+x)^2/(110592*x*RootOf(5308416*_Z^8-2304*_Z^4+1)^6-1)^2)+3*RootOf(5308416*_Z^8-2304*_Z^4+1)*ln(-(-6912*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x^12+110592*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^6*x^9+13824*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x^8-3*RootOf(5308416*_Z^8-2304*_Z^4+1)*x^12-221184*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^6*x^5-24*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^2*x^9+288*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x^6-1152*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^4*x^3-6912*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x^4+9*RootOf(5308416*_Z^8-2304*_Z^4+1)*x^8+110592*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^6*x+48*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^2*x^5-288*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x^2+(x^12-3*x^8+3*x^4-1)^(3/4)*x^3-9*RootOf(5308416*_Z^8-2304*_Z^4+1)*x^4-24*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^2*x+3*RootOf(5308416*_Z^8-2304*_Z^4+1))/(442368*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x+192*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x+1)/(9216*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x-8*x*RootOf(5308416*_Z^8-2304*_Z^4+1)+1)/(9216*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x-8*x*RootOf(5308416*_Z^8-2304*_Z^4+1)-1)/(442368*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x+192*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x-1)/(110592*x*RootOf(5308416*_Z^8-2304*_Z^4+1)^6+1)^2/(-1+x)^2/(1+x)^2/(110592*x*RootOf(5308416*_Z^8-2304*_Z^4+1)^6-1)^2))/(x^4-1)^(3/4)*((x^4-1)^3)^(1/4)","B"
1070,1,3974,31,272.829000," ","int((x^4-1)^(1/4)*(2*x^8+x^4-1)/x^6/(x^8-x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$3974$\\ trager&$\text{Expression too large to display}$&$6331$\\ \hline \end{longtable}"," ",0,"-1/5*(x^8-2*x^4+1)/x^5/(x^4-1)^(3/4)+(-331776*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*ln((-13824*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x^12+2304*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^4*x^9+27648*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x^8-6*RootOf(5308416*_Z^8-2304*_Z^4+1)*x^12+110592*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^6*x^3-576*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x^6-4608*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^4*x^5+(x^12-3*x^8+3*x^4-1)^(1/4)*x^9-13824*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x^4+18*RootOf(5308416*_Z^8-2304*_Z^4+1)*x^8+48*RootOf(5308416*_Z^8-2304*_Z^4+1)^2*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3+576*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x^2+2304*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^4*x-2*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5-18*RootOf(5308416*_Z^8-2304*_Z^4+1)*x^4+(x^12-3*x^8+3*x^4-1)^(1/4)*x+6*RootOf(5308416*_Z^8-2304*_Z^4+1))/(442368*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x+192*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x+1)/(9216*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x-8*x*RootOf(5308416*_Z^8-2304*_Z^4+1)+1)/(9216*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x-8*x*RootOf(5308416*_Z^8-2304*_Z^4+1)-1)/(442368*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x+192*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x-1)/(110592*x*RootOf(5308416*_Z^8-2304*_Z^4+1)^6+1)^2/(-1+x)^2/(1+x)^2/(110592*x*RootOf(5308416*_Z^8-2304*_Z^4+1)^6-1)^2)+331776*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*ln(-(127401984*RootOf(5308416*_Z^8-2304*_Z^4+1)^10*x^12-254803968*RootOf(5308416*_Z^8-2304*_Z^4+1)^10*x^8-165888*x^12*RootOf(5308416*_Z^8-2304*_Z^4+1)^6-9216*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9+127401984*RootOf(5308416*_Z^8-2304*_Z^4+1)^10*x^4+387072*x^8*RootOf(5308416*_Z^8-2304*_Z^4+1)^6+48*RootOf(5308416*_Z^8-2304*_Z^4+1)^2*x^12-442368*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x^3+2304*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(5308416*_Z^8-2304*_Z^4+1)^4*x^6+18432*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5-4*RootOf(5308416*_Z^8-2304*_Z^4+1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9-276480*x^4*RootOf(5308416*_Z^8-2304*_Z^4+1)^6-120*RootOf(5308416*_Z^8-2304*_Z^4+1)^2*x^8+384*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3-2304*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(5308416*_Z^8-2304*_Z^4+1)^4*x^2-(x^12-3*x^8+3*x^4-1)^(1/2)*x^6-9216*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*(x^12-3*x^8+3*x^4-1)^(1/4)*x+8*RootOf(5308416*_Z^8-2304*_Z^4+1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5+55296*RootOf(5308416*_Z^8-2304*_Z^4+1)^6+96*x^4*RootOf(5308416*_Z^8-2304*_Z^4+1)^2+(x^12-3*x^8+3*x^4-1)^(1/2)*x^2-4*RootOf(5308416*_Z^8-2304*_Z^4+1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x-24*RootOf(5308416*_Z^8-2304*_Z^4+1)^2)/(442368*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x-384*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x+1)/(18432*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x-4*x*RootOf(5308416*_Z^8-2304*_Z^4+1)+1)/(442368*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x-384*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x-1)/(18432*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x-4*x*RootOf(5308416*_Z^8-2304*_Z^4+1)-1)/(110592*x*RootOf(5308416*_Z^8-2304*_Z^4+1)^6+1)^2/(-1+x)^2/(1+x)^2/(110592*x*RootOf(5308416*_Z^8-2304*_Z^4+1)^6-1)^2)+6912*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*ln((127401984*RootOf(5308416*_Z^8-2304*_Z^4+1)^10*x^12-254803968*RootOf(5308416*_Z^8-2304*_Z^4+1)^10*x^8-165888*x^12*RootOf(5308416*_Z^8-2304*_Z^4+1)^6+884736*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9+127401984*RootOf(5308416*_Z^8-2304*_Z^4+1)^10*x^4+387072*x^8*RootOf(5308416*_Z^8-2304*_Z^4+1)^6+48*RootOf(5308416*_Z^8-2304*_Z^4+1)^2*x^12-1769472*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5-192*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9-2304*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(5308416*_Z^8-2304*_Z^4+1)^4*x^6+18432*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3-276480*x^4*RootOf(5308416*_Z^8-2304*_Z^4+1)^6-120*RootOf(5308416*_Z^8-2304*_Z^4+1)^2*x^8+884736*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*(x^12-3*x^8+3*x^4-1)^(1/4)*x+384*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5+2304*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(5308416*_Z^8-2304*_Z^4+1)^4*x^2+(x^12-3*x^8+3*x^4-1)^(1/2)*x^6-4*RootOf(5308416*_Z^8-2304*_Z^4+1)*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3+55296*RootOf(5308416*_Z^8-2304*_Z^4+1)^6+96*x^4*RootOf(5308416*_Z^8-2304*_Z^4+1)^2-192*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*(x^12-3*x^8+3*x^4-1)^(1/4)*x-(x^12-3*x^8+3*x^4-1)^(1/2)*x^2-24*RootOf(5308416*_Z^8-2304*_Z^4+1)^2)/(442368*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x-384*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x+1)/(18432*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x-4*x*RootOf(5308416*_Z^8-2304*_Z^4+1)+1)/(442368*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x-384*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x-1)/(18432*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x-4*x*RootOf(5308416*_Z^8-2304*_Z^4+1)-1)/(110592*x*RootOf(5308416*_Z^8-2304*_Z^4+1)^6+1)^2/(-1+x)^2/(1+x)^2/(110592*x*RootOf(5308416*_Z^8-2304*_Z^4+1)^6-1)^2)-144*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*ln(-(127401984*RootOf(5308416*_Z^8-2304*_Z^4+1)^10*x^12-254803968*RootOf(5308416*_Z^8-2304*_Z^4+1)^10*x^8-165888*x^12*RootOf(5308416*_Z^8-2304*_Z^4+1)^6-9216*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9+127401984*RootOf(5308416*_Z^8-2304*_Z^4+1)^10*x^4+387072*x^8*RootOf(5308416*_Z^8-2304*_Z^4+1)^6+48*RootOf(5308416*_Z^8-2304*_Z^4+1)^2*x^12-442368*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x^3+2304*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(5308416*_Z^8-2304*_Z^4+1)^4*x^6+18432*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5-4*RootOf(5308416*_Z^8-2304*_Z^4+1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9-276480*x^4*RootOf(5308416*_Z^8-2304*_Z^4+1)^6-120*RootOf(5308416*_Z^8-2304*_Z^4+1)^2*x^8+384*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3-2304*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(5308416*_Z^8-2304*_Z^4+1)^4*x^2-(x^12-3*x^8+3*x^4-1)^(1/2)*x^6-9216*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*(x^12-3*x^8+3*x^4-1)^(1/4)*x+8*RootOf(5308416*_Z^8-2304*_Z^4+1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5+55296*RootOf(5308416*_Z^8-2304*_Z^4+1)^6+96*x^4*RootOf(5308416*_Z^8-2304*_Z^4+1)^2+(x^12-3*x^8+3*x^4-1)^(1/2)*x^2-4*RootOf(5308416*_Z^8-2304*_Z^4+1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x-24*RootOf(5308416*_Z^8-2304*_Z^4+1)^2)/(442368*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x-384*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x+1)/(18432*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x-4*x*RootOf(5308416*_Z^8-2304*_Z^4+1)+1)/(442368*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x-384*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x-1)/(18432*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x-4*x*RootOf(5308416*_Z^8-2304*_Z^4+1)-1)/(110592*x*RootOf(5308416*_Z^8-2304*_Z^4+1)^6+1)^2/(-1+x)^2/(1+x)^2/(110592*x*RootOf(5308416*_Z^8-2304*_Z^4+1)^6-1)^2)-3*RootOf(5308416*_Z^8-2304*_Z^4+1)*ln((6912*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x^12+110592*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^6*x^9-13824*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x^8+3*RootOf(5308416*_Z^8-2304*_Z^4+1)*x^12-221184*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^6*x^5-24*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^2*x^9-288*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x^6-1152*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^4*x^3+6912*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x^4-9*RootOf(5308416*_Z^8-2304*_Z^4+1)*x^8+110592*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^6*x+48*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^2*x^5+288*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x^2+(x^12-3*x^8+3*x^4-1)^(3/4)*x^3+9*RootOf(5308416*_Z^8-2304*_Z^4+1)*x^4-24*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(5308416*_Z^8-2304*_Z^4+1)^2*x-3*RootOf(5308416*_Z^8-2304*_Z^4+1))/(442368*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x+192*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x+1)/(9216*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x-8*x*RootOf(5308416*_Z^8-2304*_Z^4+1)+1)/(9216*RootOf(5308416*_Z^8-2304*_Z^4+1)^5*x-8*x*RootOf(5308416*_Z^8-2304*_Z^4+1)-1)/(442368*RootOf(5308416*_Z^8-2304*_Z^4+1)^7*x+192*RootOf(5308416*_Z^8-2304*_Z^4+1)^3*x-1)/(110592*x*RootOf(5308416*_Z^8-2304*_Z^4+1)^6+1)^2/(-1+x)^2/(1+x)^2/(110592*x*RootOf(5308416*_Z^8-2304*_Z^4+1)^6-1)^2))/(x^4-1)^(3/4)*((x^4-1)^3)^(1/4)","B"
1071,0,0,69,0.092000," ","int((-2*a*b+(a+b)*x)/(x^2*(-a+x)*(-b+x))^(1/4)/(a*b*d-(a+b)*d*x+(-1+d)*x^2),x)","\[\int \frac{-2 a b +\left(a +b \right) x}{\left(x^{2} \left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{4}} \left(a b d -\left(a +b \right) d x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((-2*a*b+(a+b)*x)/(x^2*(-a+x)*(-b+x))^(1/4)/(a*b*d-(a+b)*d*x+(-1+d)*x^2),x)","F"
1072,1,48,63,1.932000," ","int((x^3+1)^(1/3)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{-\Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[\frac{2}{3}, 1, 1\right], \left[2, 2\right], -x^{3}\right)-3 \left(3+\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)}{9 \Gamma \left(\frac{2}{3}\right)}$&$48$\\ trager&$\left(x^{3}+1\right)^{\frac{1}{3}}+\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+17 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}+15 x^{3}+24 \left(x^{3}+1\right)^{\frac{2}{3}}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+24 \left(x^{3}+1\right)^{\frac{1}{3}}+11 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+20}{x^{3}}\right)}{3}-\frac{\ln \left(\frac{-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}-2 x^{3}-9 \left(x^{3}+1\right)^{\frac{2}{3}}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-9 \left(x^{3}+1\right)^{\frac{1}{3}}+19 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-5}{x^{3}}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{3}-\frac{\ln \left(\frac{-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}-2 x^{3}-9 \left(x^{3}+1\right)^{\frac{2}{3}}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-9 \left(x^{3}+1\right)^{\frac{1}{3}}+19 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-5}{x^{3}}\right)}{3}$&$354$\\ \hline \end{longtable}"," ",0,"-1/9/GAMMA(2/3)*(-GAMMA(2/3)*x^3*hypergeom([2/3,1,1],[2,2],-x^3)-3*(3+1/6*Pi*3^(1/2)-3/2*ln(3)+3*ln(x))*GAMMA(2/3))","C"
1073,0,0,69,0.012000," ","int((3*a*b-2*(a+b)*x+x^2)/(x*(-a+x)*(-b+x))^(1/4)/(-a*b*d+(a+b)*d*x-d*x^2+x^3),x)","\[\int \frac{3 a b -2 \left(a +b \right) x +x^{2}}{\left(x \left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{4}} \left(-a b d +\left(a +b \right) d x -d \,x^{2}+x^{3}\right)}\, dx\]"," ",0,"int((3*a*b-2*(a+b)*x+x^2)/(x*(-a+x)*(-b+x))^(1/4)/(-a*b*d+(a+b)*d*x-d*x^2+x^3),x)","F"
1074,0,0,14,0.033000," ","int(1/(a^3*x^3-b)/(a^3*x^3-b*x^2)^(1/3),x)","\[\int \frac{1}{\left(a^{3} x^{3}-b \right) \left(a^{3} x^{3}-b \,x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(a^3*x^3-b)/(a^3*x^3-b*x^2)^(1/3),x)","F"
1075,0,0,14,0.000000," ","int(1/(a^3*x^3-b)/(a^3*x^3-b*x^2)^(1/3),x)","\[\int \frac{1}{\left(a^{3} x^{3}-b \right) \left(a^{3} x^{3}-b \,x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(a^3*x^3-b)/(a^3*x^3-b*x^2)^(1/3),x)","F"
1076,0,0,69,0.092000," ","int((-2*a*b*x^2+(a+b)*x^3)/(x^2*(-a+x)*(-b+x))^(3/4)/(-a*b+(a+b)*x+(-1+d)*x^2),x)","\[\int \frac{-2 a b \,x^{2}+\left(a +b \right) x^{3}}{\left(x^{2} \left(-a +x \right) \left(-b +x \right)\right)^{\frac{3}{4}} \left(-a b +\left(a +b \right) x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((-2*a*b*x^2+(a+b)*x^3)/(x^2*(-a+x)*(-b+x))^(3/4)/(-a*b+(a+b)*x+(-1+d)*x^2),x)","F"
1077,0,0,61,0.033000," ","int((x^4-1)^(3/4)/(x^4+1),x)","\[\int \frac{\left(x^{4}-1\right)^{\frac{3}{4}}}{x^{4}+1}\, dx\]"," ",0,"int((x^4-1)^(3/4)/(x^4+1),x)","F"
1078,1,265,66,8.607000," ","int((x^4-x^2)^(1/4)/x^4/(x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{2 \left(x^{2}-1\right) \left(x^{4}-x^{2}\right)^{\frac{1}{4}}}{5 x^{3}}-\frac{\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(\frac{-3 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{3}+4 \left(x^{4}-x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}-4 \sqrt{x^{4}-x^{2}}\, \RootOf \left(\textit{\_Z}^{4}-2\right) x +\RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x +4 \left(x^{4}-x^{2}\right)^{\frac{3}{4}}}{x \left(x^{2}+1\right)}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(\frac{-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{3}-4 \left(x^{4}-x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}+4 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \sqrt{x^{4}-x^{2}}\, x +\RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x +4 \left(x^{4}-x^{2}\right)^{\frac{3}{4}}}{x \left(x^{2}+1\right)}\right)}{4}$&$265$\\ risch&$-\frac{2 \left(x^{4}-2 x^{2}+1\right) \left(x^{2} \left(x^{2}-1\right)\right)^{\frac{1}{4}}}{5 x^{3} \left(x^{2}-1\right)}+\frac{\left(-\frac{\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}} x^{4}-3 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{6}-4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}} x^{2}+7 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{4}+2 \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}-5 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}+4 \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)-4 \sqrt{x^{8}-3 x^{6}+3 x^{4}-x^{2}}\, x^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+4 \sqrt{x^{8}-3 x^{6}+3 x^{4}-x^{2}}}{\left(-1+x \right)^{2} \left(1+x \right)^{2} \left(x^{2}+1\right)}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}} x^{4}+3 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{6}-4 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}} x^{2}-7 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{4}+2 \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-4 \left(x^{8}-3 x^{6}+3 x^{4}-x^{2}\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)+5 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}-4 \sqrt{x^{8}-3 x^{6}+3 x^{4}-x^{2}}\, x^{2}-\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+4 \sqrt{x^{8}-3 x^{6}+3 x^{4}-x^{2}}}{\left(-1+x \right)^{2} \left(1+x \right)^{2} \left(x^{2}+1\right)}\right)}{4}\right) \left(x^{2} \left(x^{2}-1\right)\right)^{\frac{1}{4}} \left(x^{2} \left(x^{2}-1\right)^{3}\right)^{\frac{1}{4}}}{x \left(x^{2}-1\right)}$&$632$\\ \hline \end{longtable}"," ",0,"-2/5*(x^2-1)*(x^4-x^2)^(1/4)/x^3-1/4*RootOf(_Z^4-2)*ln((-3*RootOf(_Z^4-2)^3*x^3+4*(x^4-x^2)^(1/4)*RootOf(_Z^4-2)^2*x^2-4*(x^4-x^2)^(1/2)*RootOf(_Z^4-2)*x+RootOf(_Z^4-2)^3*x+4*(x^4-x^2)^(3/4))/x/(x^2+1))+1/4*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln((-3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*x^3-4*(x^4-x^2)^(1/4)*RootOf(_Z^4-2)^2*x^2+4*RootOf(_Z^2+RootOf(_Z^4-2)^2)*(x^4-x^2)^(1/2)*x+RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x+4*(x^4-x^2)^(3/4))/x/(x^2+1))","C"
1079,1,380,73,3.343000," ","int((-x^2+1)^2/(x^2+1)/(x^4+6*x^2+1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right)^{3} \sqrt{x^{4}+6 x^{2}+1}\, x^{4}+\RootOf \left(\textit{\_Z}^{2}+1\right)^{3} x^{6}+\RootOf \left(\textit{\_Z}^{2}+1\right)^{2} \left(x^{4}+6 x^{2}+1\right)^{\frac{1}{4}} x^{5}-\RootOf \left(\textit{\_Z}^{2}+1\right)^{3} \sqrt{x^{4}+6 x^{2}+1}\, x^{2}+5 \RootOf \left(\textit{\_Z}^{2}+1\right)^{3} x^{4}+\left(x^{4}+6 x^{2}+1\right)^{\frac{3}{4}} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+1\right)^{2} \left(x^{4}+6 x^{2}+1\right)^{\frac{1}{4}} x^{3}+\RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+6 x^{2}+1}\, x^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+\left(x^{4}+6 x^{2}+1\right)^{\frac{3}{4}} x -\left(x^{4}+6 x^{2}+1\right)^{\frac{1}{4}} x^{3}+\RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+6 x^{2}+1}-5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-3 \left(x^{4}+6 x^{2}+1\right)^{\frac{1}{4}} x}{\left(\RootOf \left(\textit{\_Z}^{2}+1\right) x -1\right)^{2} \left(\RootOf \left(\textit{\_Z}^{2}+1\right) x +1\right)^{2}}\right)}{2}+\frac{\ln \left(\frac{\left(x^{4}+6 x^{2}+1\right)^{\frac{3}{4}} x +x^{2} \sqrt{x^{4}+6 x^{2}+1}+\left(x^{4}+6 x^{2}+1\right)^{\frac{1}{4}} x^{3}+x^{4}+\sqrt{x^{4}+6 x^{2}+1}+3 \left(x^{4}+6 x^{2}+1\right)^{\frac{1}{4}} x +5 x^{2}}{x^{2}+1}\right)}{2}$&$380$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^2+1)*ln(-(-RootOf(_Z^2+1)^3*(x^4+6*x^2+1)^(1/2)*x^4+RootOf(_Z^2+1)^3*x^6+RootOf(_Z^2+1)^2*(x^4+6*x^2+1)^(1/4)*x^5-RootOf(_Z^2+1)^3*(x^4+6*x^2+1)^(1/2)*x^2+5*RootOf(_Z^2+1)^3*x^4+(x^4+6*x^2+1)^(3/4)*x^3+3*RootOf(_Z^2+1)^2*(x^4+6*x^2+1)^(1/4)*x^3+RootOf(_Z^2+1)*(x^4+6*x^2+1)^(1/2)*x^2-RootOf(_Z^2+1)*x^4+(x^4+6*x^2+1)^(3/4)*x-(x^4+6*x^2+1)^(1/4)*x^3+RootOf(_Z^2+1)*(x^4+6*x^2+1)^(1/2)-5*RootOf(_Z^2+1)*x^2-3*(x^4+6*x^2+1)^(1/4)*x)/(RootOf(_Z^2+1)*x-1)^2/(RootOf(_Z^2+1)*x+1)^2)+1/2*ln(((x^4+6*x^2+1)^(3/4)*x+x^2*(x^4+6*x^2+1)^(1/2)+(x^4+6*x^2+1)^(1/4)*x^3+x^4+(x^4+6*x^2+1)^(1/2)+3*(x^4+6*x^2+1)^(1/4)*x+5*x^2)/(x^2+1))","C"
1080,0,0,63,0.013000," ","int(1/(1+x)/(x^4+6*x^2+1)^(1/4),x)","\[\int \frac{1}{\left(1+x \right) \left(x^{4}+6 x^{2}+1\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(1+x)/(x^4+6*x^2+1)^(1/4),x)","F"
1081,1,70,77,0.223000," ","int((1+x)/(x^4-12*x^3+14*x^2+4*x-7)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(-1+x \right) \sqrt{x^{2}-10 x -7}\, \left(2 \ln \left(-5+x +\sqrt{x^{2}-10 x -7}\right)-\arctan \left(\frac{3+x}{\sqrt{x^{2}-10 x -7}}\right)\right)}{2 \sqrt{x^{4}-12 x^{3}+14 x^{2}+4 x -7}}$&$70$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x +\sqrt{x^{4}-12 x^{3}+14 x^{2}+4 x -7}+3 \RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(-1+x \right)^{2}}\right)}{2}+\ln \left(-\frac{x^{2}+\sqrt{x^{4}-12 x^{3}+14 x^{2}+4 x -7}-6 x +5}{-1+x}\right)$&$102$\\ \hline \end{longtable}"," ",0,"1/2*(-1+x)*(x^2-10*x-7)^(1/2)*(2*ln(-5+x+(x^2-10*x-7)^(1/2))-arctan((3+x)/(x^2-10*x-7)^(1/2)))/(x^4-12*x^3+14*x^2+4*x-7)^(1/2)","A"
1082,1,343,63,2.751000," ","int((x^4+3)/(x^4-1)^(1/3)/(x^4-8*x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \ln \left(\frac{4 \left(x^{4}-1\right)^{\frac{2}{3}} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x +8 \left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{2}+16 x^{3} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+x^{4}+4 \left(x^{4}-1\right)^{\frac{2}{3}} x +8 \left(x^{4}-1\right)^{\frac{1}{3}} x^{2}+8 x^{3}-1}{x^{4}-8 x^{3}-1}\right)-\frac{\ln \left(-\frac{4 \left(x^{4}-1\right)^{\frac{2}{3}} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x +8 \left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{2}+16 x^{3} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)-x^{4}-2 \left(x^{4}-1\right)^{\frac{2}{3}} x -4 \left(x^{4}-1\right)^{\frac{1}{3}} x^{2}+1}{x^{4}-8 x^{3}-1}\right)}{2}-\ln \left(-\frac{4 \left(x^{4}-1\right)^{\frac{2}{3}} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x +8 \left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{2}+16 x^{3} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)-x^{4}-2 \left(x^{4}-1\right)^{\frac{2}{3}} x -4 \left(x^{4}-1\right)^{\frac{1}{3}} x^{2}+1}{x^{4}-8 x^{3}-1}\right) \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)$&$343$\\ \hline \end{longtable}"," ",0,"RootOf(4*_Z^2+2*_Z+1)*ln((4*(x^4-1)^(2/3)*RootOf(4*_Z^2+2*_Z+1)*x+8*(x^4-1)^(1/3)*RootOf(4*_Z^2+2*_Z+1)*x^2+16*x^3*RootOf(4*_Z^2+2*_Z+1)+x^4+4*(x^4-1)^(2/3)*x+8*(x^4-1)^(1/3)*x^2+8*x^3-1)/(x^4-8*x^3-1))-1/2*ln(-(4*(x^4-1)^(2/3)*RootOf(4*_Z^2+2*_Z+1)*x+8*(x^4-1)^(1/3)*RootOf(4*_Z^2+2*_Z+1)*x^2+16*x^3*RootOf(4*_Z^2+2*_Z+1)-x^4-2*(x^4-1)^(2/3)*x-4*(x^4-1)^(1/3)*x^2+1)/(x^4-8*x^3-1))-ln(-(4*(x^4-1)^(2/3)*RootOf(4*_Z^2+2*_Z+1)*x+8*(x^4-1)^(1/3)*RootOf(4*_Z^2+2*_Z+1)*x^2+16*x^3*RootOf(4*_Z^2+2*_Z+1)-x^4-2*(x^4-1)^(2/3)*x-4*(x^4-1)^(1/3)*x^2+1)/(x^4-8*x^3-1))*RootOf(4*_Z^2+2*_Z+1)","C"
1083,1,100,70,2.621000," ","int((-3+2*x)*(3*x^4+2*x^2-2*x)^(1/2)/(x^3+2*x-2)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{x \sqrt{3 x^{4}+2 x^{2}-2 x}}{2 x^{3}+4 x -4}+\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{5 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{3}+4 \sqrt{3 x^{4}+2 x^{2}-2 x}\, x +2 \RootOf \left(\textit{\_Z}^{2}-2\right) x -2 \RootOf \left(\textit{\_Z}^{2}-2\right)}{x^{3}+2 x -2}\right)}{8}$&$100$\\ default&$\text{Expression too large to display}$&$1689$\\ elliptic&$\text{Expression too large to display}$&$1689$\\ risch&$\text{Expression too large to display}$&$1699$\\ \hline \end{longtable}"," ",0,"1/2*x*(3*x^4+2*x^2-2*x)^(1/2)/(x^3+2*x-2)+1/8*RootOf(_Z^2-2)*ln(-(5*RootOf(_Z^2-2)*x^3+4*(3*x^4+2*x^2-2*x)^(1/2)*x+2*RootOf(_Z^2-2)*x-2*RootOf(_Z^2-2))/(x^3+2*x-2))","C"
1084,0,0,61,0.008000," ","int((a*x^4-2*b)/x^4/(a*x^4-b)^(1/4),x)","\[\int \frac{a \,x^{4}-2 b}{x^{4} \left(a \,x^{4}-b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^4-2*b)/x^4/(a*x^4-b)^(1/4),x)","F"
1085,0,0,61,0.014000," ","int((a*x^4-b)^(3/4),x)","\[\int \left(a \,x^{4}-b \right)^{\frac{3}{4}}\, dx\]"," ",0,"int((a*x^4-b)^(3/4),x)","F"
1086,0,0,61,0.004000," ","int((a*x^4-b)^(3/4)/x^4,x)","\[\int \frac{\left(a \,x^{4}-b \right)^{\frac{3}{4}}}{x^{4}}\, dx\]"," ",0,"int((a*x^4-b)^(3/4)/x^4,x)","F"
1087,0,0,14,0.034000," ","int(1/(a*x^3-b*x^2)^(1/3)/(a*x^4+b),x)","\[\int \frac{1}{\left(a \,x^{3}-b \,x^{2}\right)^{\frac{1}{3}} \left(a \,x^{4}+b \right)}\, dx\]"," ",0,"int(1/(a*x^3-b*x^2)^(1/3)/(a*x^4+b),x)","F"
1088,0,0,14,0.001000," ","int(1/(a*x^3-b*x^2)^(1/3)/(a*x^4+b),x)","\[\int \frac{1}{\left(a \,x^{3}-b \,x^{2}\right)^{\frac{1}{3}} \left(a \,x^{4}+b \right)}\, dx\]"," ",0,"int(1/(a*x^3-b*x^2)^(1/3)/(a*x^4+b),x)","F"
1089,0,0,67,0.005000," ","int((a*x^4+b*x^3)^(1/4)/x^2,x)","\[\int \frac{\left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}}{x^{2}}\, dx\]"," ",0,"int((a*x^4+b*x^3)^(1/4)/x^2,x)","F"
1090,1,249,71,10.629000," ","int((x^6+x^4-x^3+1)^(3/4)*(2*x^6+x^3-4)/(x^6-x^3+1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{x \left(x^{6}+x^{4}-x^{3}+1\right)^{\frac{3}{4}}}{x^{6}-x^{3}+1}-\frac{3 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{6}+x^{4}-x^{3}+1}\, x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-2 \left(x^{6}+x^{4}-x^{3}+1\right)^{\frac{3}{4}} x +2 \left(x^{6}+x^{4}-x^{3}+1\right)^{\frac{1}{4}} x^{3}-\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{6}-x^{3}+1}\right)}{4}+\frac{3 \ln \left(-\frac{-x^{6}+2 \left(x^{6}+x^{4}-x^{3}+1\right)^{\frac{3}{4}} x -2 \sqrt{x^{6}+x^{4}-x^{3}+1}\, x^{2}+2 \left(x^{6}+x^{4}-x^{3}+1\right)^{\frac{1}{4}} x^{3}-2 x^{4}+x^{3}-1}{x^{6}-x^{3}+1}\right)}{4}$&$249$\\ risch&$-\frac{x \left(x^{6}+x^{4}-x^{3}+1\right)^{\frac{3}{4}}}{x^{6}-x^{3}+1}+\frac{3 \ln \left(-\frac{-x^{6}+2 \left(x^{6}+x^{4}-x^{3}+1\right)^{\frac{3}{4}} x -2 \sqrt{x^{6}+x^{4}-x^{3}+1}\, x^{2}+2 \left(x^{6}+x^{4}-x^{3}+1\right)^{\frac{1}{4}} x^{3}-2 x^{4}+x^{3}-1}{x^{6}-x^{3}+1}\right)}{4}+\frac{3 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{6}+x^{4}-x^{3}+1}\, x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{6}+x^{4}-x^{3}+1\right)^{\frac{3}{4}} x -2 \left(x^{6}+x^{4}-x^{3}+1\right)^{\frac{1}{4}} x^{3}-\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{6}-x^{3}+1}\right)}{4}$&$250$\\ \hline \end{longtable}"," ",0,"-x*(x^6+x^4-x^3+1)^(3/4)/(x^6-x^3+1)-3/4*RootOf(_Z^2+1)*ln((-RootOf(_Z^2+1)*x^6+2*RootOf(_Z^2+1)*(x^6+x^4-x^3+1)^(1/2)*x^2-2*RootOf(_Z^2+1)*x^4+RootOf(_Z^2+1)*x^3-2*(x^6+x^4-x^3+1)^(3/4)*x+2*(x^6+x^4-x^3+1)^(1/4)*x^3-RootOf(_Z^2+1))/(x^6-x^3+1))+3/4*ln(-(-x^6+2*(x^6+x^4-x^3+1)^(3/4)*x-2*(x^6+x^4-x^3+1)^(1/2)*x^2+2*(x^6+x^4-x^3+1)^(1/4)*x^3-2*x^4+x^3-1)/(x^6-x^3+1))","C"
1091,1,222,61,2.925000," ","int((2*x^4+1)/(x^4+1)^(1/4)/(x^8-x^4-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{x}{3 \left(x^{4}+1\right)^{\frac{1}{4}}}-\frac{5 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-54\right)^{2}\right) \ln \left(-\frac{-2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}-54\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-54\right)^{2}\right) x^{2}-6 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-54\right)^{2} x^{3}+15 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-54\right)^{2}\right) x^{4}+36 \left(x^{4}+1\right)^{\frac{3}{4}} x +6 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-54\right)^{2}\right)}{x^{4}-2}\right)}{72}-\frac{5 \RootOf \left(\textit{\_Z}^{4}-54\right) \ln \left(-\frac{2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}-54\right)^{3} x^{2}+6 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-54\right)^{2} x^{3}+15 \RootOf \left(\textit{\_Z}^{4}-54\right) x^{4}+36 \left(x^{4}+1\right)^{\frac{3}{4}} x +6 \RootOf \left(\textit{\_Z}^{4}-54\right)}{x^{4}-2}\right)}{72}$&$222$\\ risch&$\frac{x}{3 \left(x^{4}+1\right)^{\frac{1}{4}}}+\frac{5 \RootOf \left(\textit{\_Z}^{4}-54\right) \ln \left(-\frac{-2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}-54\right)^{3} x^{2}+6 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-54\right)^{2} x^{3}-15 \RootOf \left(\textit{\_Z}^{4}-54\right) x^{4}+36 \left(x^{4}+1\right)^{\frac{3}{4}} x -6 \RootOf \left(\textit{\_Z}^{4}-54\right)}{x^{4}-2}\right)}{72}-\frac{5 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-54\right)^{2}\right) \ln \left(-\frac{-2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}-54\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-54\right)^{2}\right) x^{2}-6 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-54\right)^{2} x^{3}+15 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-54\right)^{2}\right) x^{4}+36 \left(x^{4}+1\right)^{\frac{3}{4}} x +6 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-54\right)^{2}\right)}{x^{4}-2}\right)}{72}$&$222$\\ \hline \end{longtable}"," ",0,"1/3*x/(x^4+1)^(1/4)-5/72*RootOf(_Z^2+RootOf(_Z^4-54)^2)*ln(-(-2*(x^4+1)^(1/2)*RootOf(_Z^4-54)^2*RootOf(_Z^2+RootOf(_Z^4-54)^2)*x^2-6*(x^4+1)^(1/4)*RootOf(_Z^4-54)^2*x^3+15*RootOf(_Z^2+RootOf(_Z^4-54)^2)*x^4+36*(x^4+1)^(3/4)*x+6*RootOf(_Z^2+RootOf(_Z^4-54)^2))/(x^4-2))-5/72*RootOf(_Z^4-54)*ln(-(2*(x^4+1)^(1/2)*RootOf(_Z^4-54)^3*x^2+6*(x^4+1)^(1/4)*RootOf(_Z^4-54)^2*x^3+15*RootOf(_Z^4-54)*x^4+36*(x^4+1)^(3/4)*x+6*RootOf(_Z^4-54))/(x^4-2))","C"
1092,0,0,14,0.037000," ","int(1/(a*x^4-b*x^2)^(1/4)/(a*x^8+b),x)","\[\int \frac{1}{\left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}} \left(a \,x^{8}+b \right)}\, dx\]"," ",0,"int(1/(a*x^4-b*x^2)^(1/4)/(a*x^8+b),x)","F"
1093,0,0,14,0.001000," ","int(1/(a*x^4-b*x^2)^(1/4)/(a*x^8+b),x)","\[\int \frac{1}{\left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}} \left(a \,x^{8}+b \right)}\, dx\]"," ",0,"int(1/(a*x^4-b*x^2)^(1/4)/(a*x^8+b),x)","F"
1094,1,168,65,0.204000," ","int((a^4*x^4-b^4)*(a^4*x^4+b^4)^(1/2)/(a^8*x^8+b^8),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}+b^{4}}}{x \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}\right)}{2 \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}-\frac{\sqrt{2}\, \ln \left(\frac{\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{2 x}+\frac{\sqrt{2}\, \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}{2}}{\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{2 x}-\frac{\sqrt{2}\, \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}{2}}\right)}{4 \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}\right) \sqrt{2}}{2}$&$168$\\ elliptic&$\frac{\left(\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}+b^{4}}}{x \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}\right)}{2 \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}-\frac{\sqrt{2}\, \ln \left(\frac{\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{2 x}+\frac{\sqrt{2}\, \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}{2}}{\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{2 x}-\frac{\sqrt{2}\, \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}{2}}\right)}{4 \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}\right) \sqrt{2}}{2}$&$168$\\ \hline \end{longtable}"," ",0,"1/2*(1/2*2^(1/2)/(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*arctan((a^4*x^4+b^4)^(1/2)/x/(2^(1/2)*(a^4*b^4)^(1/2))^(1/2))-1/4*2^(1/2)/(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*ln((1/2*(a^4*x^4+b^4)^(1/2)*2^(1/2)/x+1/2*2^(1/2)*(2^(1/2)*(a^4*b^4)^(1/2))^(1/2))/(1/2*(a^4*x^4+b^4)^(1/2)*2^(1/2)/x-1/2*2^(1/2)*(2^(1/2)*(a^4*b^4)^(1/2))^(1/2))))*2^(1/2)","B"
1095,1,168,65,0.165000," ","int((a^8*x^8-b^8)/(a^4*x^4+b^4)^(1/2)/(a^8*x^8+b^8),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}+b^{4}}}{x \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}\right)}{2 \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}-\frac{\sqrt{2}\, \ln \left(\frac{\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{2 x}+\frac{\sqrt{2}\, \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}{2}}{\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{2 x}-\frac{\sqrt{2}\, \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}{2}}\right)}{4 \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}\right) \sqrt{2}}{2}$&$168$\\ default&$\frac{\sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, i\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}+b^{4}}}-\frac{b^{8} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{8} \textit{\_Z}^{8}+b^{8}\right)}{\sum}\frac{-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-a^{4} \underline{\hspace{1.25 ex}}\alpha^{6}+b^{4} x^{2}\right) a^{4}}{b^{4} \sqrt{a^{4} \underline{\hspace{1.25 ex}}\alpha^{4}+b^{4}}\, \sqrt{a^{4} x^{4}+b^{4}}}\right)}{\sqrt{a^{4} \underline{\hspace{1.25 ex}}\alpha^{4}+b^{4}}}+\frac{2 \underline{\hspace{1.25 ex}}\alpha^{7} a^{8} \sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, \frac{i \underline{\hspace{1.25 ex}}\alpha^{6} a^{6}}{b^{6}}, \frac{\sqrt{-\frac{i a^{2}}{b^{2}}}}{\sqrt{\frac{i a^{2}}{b^{2}}}}\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, b^{8} \sqrt{a^{4} x^{4}+b^{4}}}}{\underline{\hspace{1.25 ex}}\alpha^{7}}\right)}{8 a^{8}}$&$287$\\ \hline \end{longtable}"," ",0,"1/2*(1/2*2^(1/2)/(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*arctan((a^4*x^4+b^4)^(1/2)/x/(2^(1/2)*(a^4*b^4)^(1/2))^(1/2))-1/4*2^(1/2)/(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*ln((1/2*(a^4*x^4+b^4)^(1/2)*2^(1/2)/x+1/2*2^(1/2)*(2^(1/2)*(a^4*b^4)^(1/2))^(1/2))/(1/2*(a^4*x^4+b^4)^(1/2)*2^(1/2)/x-1/2*2^(1/2)*(2^(1/2)*(a^4*b^4)^(1/2))^(1/2))))*2^(1/2)","B"
1096,0,0,63,0.027000," ","int((b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2)^(3/2),x)","\[\int \frac{\sqrt{b +\sqrt{a \,x^{2}+b^{2}}}}{\left(a \,x^{2}+b^{2}\right)^{\frac{3}{2}}}\, dx\]"," ",0,"int((b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2)^(3/2),x)","F"
1097,0,0,63,180.000000," ","int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^4+b)^(1/2),x)","\[\int \frac{\sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}{\sqrt{a^{2} x^{4}+b}}\, dx\]"," ",0,"int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^4+b)^(1/2),x)","F"
1098,0,0,14,0.034000," ","int(1/(a*x^3-b*x^2)^(1/3)/(a*x^4-b),x)","\[\int \frac{1}{\left(a \,x^{3}-b \,x^{2}\right)^{\frac{1}{3}} \left(a \,x^{4}-b \right)}\, dx\]"," ",0,"int(1/(a*x^3-b*x^2)^(1/3)/(a*x^4-b),x)","F"
1099,0,0,14,0.002000," ","int(1/(a*x^3-b*x^2)^(1/3)/(a*x^4-b),x)","\[\int \frac{1}{\left(a \,x^{3}-b \,x^{2}\right)^{\frac{1}{3}} \left(a \,x^{4}-b \right)}\, dx\]"," ",0,"int(1/(a*x^3-b*x^2)^(1/3)/(a*x^4-b),x)","F"
1100,0,0,11,0.034000," ","int((a*x^4-b*x^3)^(1/4)/x/(a*x^3+b),x)","\[\int \frac{\left(a \,x^{4}-b \,x^{3}\right)^{\frac{1}{4}}}{x \left(a \,x^{3}+b \right)}\, dx\]"," ",0,"int((a*x^4-b*x^3)^(1/4)/x/(a*x^3+b),x)","F"
1101,0,0,11,0.000000," ","int((a*x^4-b*x^3)^(1/4)/x/(a*x^3+b),x)","\[\int \frac{\left(a \,x^{4}-b \,x^{3}\right)^{\frac{1}{4}}}{x \left(a \,x^{3}+b \right)}\, dx\]"," ",0,"int((a*x^4-b*x^3)^(1/4)/x/(a*x^3+b),x)","F"
1102,0,0,64,0.004000," ","int((a*x^4+b*x^3)^(1/4)/x,x)","\[\int \frac{\left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}}{x}\, dx\]"," ",0,"int((a*x^4+b*x^3)^(1/4)/x,x)","F"
1103,0,0,64,0.010000," ","int((a*x-b)*(a*x^4+b*x^3)^(1/4)/x/(a*x+b),x)","\[\int \frac{\left(a x -b \right) \left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}}{x \left(a x +b \right)}\, dx\]"," ",0,"int((a*x-b)*(a*x^4+b*x^3)^(1/4)/x/(a*x+b),x)","F"
1104,1,511,68,4.338000," ","int((3*x^4-1)/(x^4-x+1)/(x^6+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{-1823 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{5}-1101 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{5}+9494 x^{5}+3646 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+12039 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+x^{2}\right)^{\frac{2}{3}}+12039 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+x^{2}\right)^{\frac{1}{3}} x -1823 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x +14963 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+21912 \left(x^{6}+x^{2}\right)^{\frac{2}{3}}+21912 x \left(x^{6}+x^{2}\right)^{\frac{1}{3}}-1101 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +14241 x^{2}+9494 x}{x \left(x^{4}-x +1\right)}\right)-\ln \left(\frac{1823 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{5}+2545 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{5}-8772 x^{5}-3646 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+12039 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+x^{2}\right)^{\frac{2}{3}}+12039 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+x^{2}\right)^{\frac{1}{3}} x +1823 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x +7671 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-9873 \left(x^{6}+x^{2}\right)^{\frac{2}{3}}-9873 x \left(x^{6}+x^{2}\right)^{\frac{1}{3}}+2545 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x -2924 x^{2}-8772 x}{x \left(x^{4}-x +1\right)}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-\ln \left(\frac{1823 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{5}+2545 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{5}-8772 x^{5}-3646 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+12039 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+x^{2}\right)^{\frac{2}{3}}+12039 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+x^{2}\right)^{\frac{1}{3}} x +1823 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x +7671 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-9873 \left(x^{6}+x^{2}\right)^{\frac{2}{3}}-9873 x \left(x^{6}+x^{2}\right)^{\frac{1}{3}}+2545 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x -2924 x^{2}-8772 x}{x \left(x^{4}-x +1\right)}\right)$&$511$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2+_Z+1)*ln(-(-1823*RootOf(_Z^2+_Z+1)^2*x^5-1101*RootOf(_Z^2+_Z+1)*x^5+9494*x^5+3646*RootOf(_Z^2+_Z+1)^2*x^2+12039*RootOf(_Z^2+_Z+1)*(x^6+x^2)^(2/3)+12039*RootOf(_Z^2+_Z+1)*(x^6+x^2)^(1/3)*x-1823*RootOf(_Z^2+_Z+1)^2*x+14963*RootOf(_Z^2+_Z+1)*x^2+21912*(x^6+x^2)^(2/3)+21912*x*(x^6+x^2)^(1/3)-1101*RootOf(_Z^2+_Z+1)*x+14241*x^2+9494*x)/x/(x^4-x+1))-ln((1823*RootOf(_Z^2+_Z+1)^2*x^5+2545*RootOf(_Z^2+_Z+1)*x^5-8772*x^5-3646*RootOf(_Z^2+_Z+1)^2*x^2+12039*RootOf(_Z^2+_Z+1)*(x^6+x^2)^(2/3)+12039*RootOf(_Z^2+_Z+1)*(x^6+x^2)^(1/3)*x+1823*RootOf(_Z^2+_Z+1)^2*x+7671*RootOf(_Z^2+_Z+1)*x^2-9873*(x^6+x^2)^(2/3)-9873*x*(x^6+x^2)^(1/3)+2545*RootOf(_Z^2+_Z+1)*x-2924*x^2-8772*x)/x/(x^4-x+1))*RootOf(_Z^2+_Z+1)-ln((1823*RootOf(_Z^2+_Z+1)^2*x^5+2545*RootOf(_Z^2+_Z+1)*x^5-8772*x^5-3646*RootOf(_Z^2+_Z+1)^2*x^2+12039*RootOf(_Z^2+_Z+1)*(x^6+x^2)^(2/3)+12039*RootOf(_Z^2+_Z+1)*(x^6+x^2)^(1/3)*x+1823*RootOf(_Z^2+_Z+1)^2*x+7671*RootOf(_Z^2+_Z+1)*x^2-9873*(x^6+x^2)^(2/3)-9873*x*(x^6+x^2)^(1/3)+2545*RootOf(_Z^2+_Z+1)*x-2924*x^2-8772*x)/x/(x^4-x+1))","C"
1105,0,0,14,0.037000," ","int(1/(a*x^4-b*x^2)^(1/4)/(a*x^8-b),x)","\[\int \frac{1}{\left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}} \left(a \,x^{8}-b \right)}\, dx\]"," ",0,"int(1/(a*x^4-b*x^2)^(1/4)/(a*x^8-b),x)","F"
1106,0,0,14,0.002000," ","int(1/(a*x^4-b*x^2)^(1/4)/(a*x^8-b),x)","\[\int \frac{1}{\left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}} \left(a \,x^{8}-b \right)}\, dx\]"," ",0,"int(1/(a*x^4-b*x^2)^(1/4)/(a*x^8-b),x)","F"
1107,0,0,62,0.009000," ","int((a*x^8-b)/x^2/(a*x^4+b)^(3/4),x)","\[\int \frac{a \,x^{8}-b}{x^{2} \left(a \,x^{4}+b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int((a*x^8-b)/x^2/(a*x^4+b)^(3/4),x)","F"
1108,0,0,12,0.023000," ","int(x^5*(5*a*x^2-4*b)/(a*x^2-b)^(1/4)/(a*x^10-b*x^8+b),x)","\[\int \frac{x^{5} \left(5 a \,x^{2}-4 b \right)}{\left(a \,x^{2}-b \right)^{\frac{1}{4}} \left(a \,x^{10}-b \,x^{8}+b \right)}\, dx\]"," ",0,"int(x^5*(5*a*x^2-4*b)/(a*x^2-b)^(1/4)/(a*x^10-b*x^8+b),x)","F"
1109,1,15,69,0.482000," ","int(1/(x^3+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$3 x^{\frac{1}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x \right)$&$15$\\ trager&$\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\frac{-4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}+15 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{2}{3}}+15 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{1}{3}} x +4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x +19 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+9 \left(x^{3}+x^{2}\right)^{\frac{2}{3}}+9 x \left(x^{3}+x^{2}\right)^{\frac{1}{3}}+9 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x +5 x^{2}+2 x}{x}\right)-\ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}+15 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{2}{3}}+15 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{1}{3}} x -4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x +11 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-24 \left(x^{3}+x^{2}\right)^{\frac{2}{3}}-24 x \left(x^{3}+x^{2}\right)^{\frac{1}{3}}+17 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x -20 x^{2}-15 x}{x}\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+\ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}+15 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{2}{3}}+15 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{1}{3}} x -4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x +11 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-24 \left(x^{3}+x^{2}\right)^{\frac{2}{3}}-24 x \left(x^{3}+x^{2}\right)^{\frac{1}{3}}+17 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x -20 x^{2}-15 x}{x}\right)$&$427$\\ \hline \end{longtable}"," ",0,"3*x^(1/3)*hypergeom([1/3,1/3],[4/3],-x)","C"
1110,0,0,71,0.058000," ","int((a-3*b+2*x)/((-a+x)*(-b+x))^(1/4)/(-a^3+b*d-(-3*a^2+d)*x-3*a*x^2+x^3),x)","\[\int \frac{a -3 b +2 x}{\left(\left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{4}} \left(-a^{3}+b d -\left(-3 a^{2}+d \right) x -3 a \,x^{2}+x^{3}\right)}\, dx\]"," ",0,"int((a-3*b+2*x)/((-a+x)*(-b+x))^(1/4)/(-a^3+b*d-(-3*a^2+d)*x-3*a*x^2+x^3),x)","F"
1111,0,0,71,0.058000," ","int((a-3*b+2*x)*(a^2-2*a*x+x^2)/((-a+x)*(-b+x))^(3/4)/(-b+a^3*d+(-3*a^2*d+1)*x+3*a*d*x^2-d*x^3),x)","\[\int \frac{\left(a -3 b +2 x \right) \left(a^{2}-2 a x +x^{2}\right)}{\left(\left(-a +x \right) \left(-b +x \right)\right)^{\frac{3}{4}} \left(-b +a^{3} d +\left(-3 a^{2} d +1\right) x +3 a d \,x^{2}-d \,x^{3}\right)}\, dx\]"," ",0,"int((a-3*b+2*x)*(a^2-2*a*x+x^2)/((-a+x)*(-b+x))^(3/4)/(-b+a^3*d+(-3*a^2*d+1)*x+3*a*d*x^2-d*x^3),x)","F"
1112,0,0,71,0.014000," ","int((-1-2*(-1+k)*x+k*x^2)/((1-x)*x*(-k*x+1))^(1/4)/(-1+(d+3*k)*x-(3*k^2+d)*x^2+k^3*x^3),x)","\[\int \frac{-1-2 \left(-1+k \right) x +k \,x^{2}}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{4}} \left(-1+\left(d +3 k \right) x -\left(3 k^{2}+d \right) x^{2}+k^{3} x^{3}\right)}\, dx\]"," ",0,"int((-1-2*(-1+k)*x+k*x^2)/((1-x)*x*(-k*x+1))^(1/4)/(-1+(d+3*k)*x-(3*k^2+d)*x^2+k^3*x^3),x)","F"
1113,1,74,69,0.429000," ","int((x^4+6*x^2+1)^(1/2)/x/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(\frac{x^{2}+\sqrt{x^{4}+6 x^{2}+1}-1}{x}\right)+\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)-\sqrt{x^{4}+6 x^{2}+1}}{x^{2}+1}\right)$&$74$\\ default&$-\frac{\sqrt{\left(x^{2}+1\right)^{2}+4 x^{2}}}{2}-\ln \left(x^{2}+3+\sqrt{\left(x^{2}+1\right)^{2}+4 x^{2}}\right)+\arctan \left(\frac{4 x^{2}-4}{4 \sqrt{\left(x^{2}+1\right)^{2}+4 x^{2}}}\right)+\frac{\sqrt{x^{4}+6 x^{2}+1}}{2}+\frac{3 \ln \left(x^{2}+3+\sqrt{x^{4}+6 x^{2}+1}\right)}{2}-\frac{\arctanh \left(\frac{6 x^{2}+2}{2 \sqrt{x^{4}+6 x^{2}+1}}\right)}{2}$&$125$\\ elliptic&$-\frac{\sqrt{\left(x^{2}+1\right)^{2}+4 x^{2}}}{2}-\ln \left(x^{2}+3+\sqrt{\left(x^{2}+1\right)^{2}+4 x^{2}}\right)+\arctan \left(\frac{4 x^{2}-4}{4 \sqrt{\left(x^{2}+1\right)^{2}+4 x^{2}}}\right)+\frac{\sqrt{x^{4}+6 x^{2}+1}}{2}+\frac{3 \ln \left(x^{2}+3+\sqrt{x^{4}+6 x^{2}+1}\right)}{2}-\frac{\arctanh \left(\frac{6 x^{2}+2}{2 \sqrt{x^{4}+6 x^{2}+1}}\right)}{2}$&$125$\\ \hline \end{longtable}"," ",0,"ln((x^2+(x^4+6*x^2+1)^(1/2)-1)/x)+RootOf(_Z^2+1)*ln(-(RootOf(_Z^2+1)*x^2-RootOf(_Z^2+1)-(x^4+6*x^2+1)^(1/2))/(x^2+1))","C"
1114,1,326,70,126.116000," ","int((x^2-1)*(2*x^4+2*x^2-1)^(1/4)/x^2/(2*x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(2 x^{4}+2 x^{2}-1\right)^{\frac{1}{4}}}{x}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{4}+4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(2 x^{4}+2 x^{2}-1\right)^{\frac{1}{4}} x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}-4 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \sqrt{2 x^{4}+2 x^{2}-1}\, x^{2}-4 \left(2 x^{4}+2 x^{2}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)}{2 x^{2}-1}\right)}{4}-\frac{\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{4}-4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(2 x^{4}+2 x^{2}-1\right)^{\frac{1}{4}} x^{3}+2 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{2}+4 \RootOf \left(\textit{\_Z}^{4}-2\right) \sqrt{2 x^{4}+2 x^{2}-1}\, x^{2}-4 \left(2 x^{4}+2 x^{2}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}-2\right)^{3}}{2 x^{2}-1}\right)}{4}$&$326$\\ risch&$-\frac{\left(2 x^{4}+2 x^{2}-1\right)^{\frac{1}{4}}}{x}+\frac{\left(\frac{\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(\frac{16 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{12}+8 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} \left(8 x^{12}+24 x^{10}+12 x^{8}-16 x^{6}-6 x^{4}+6 x^{2}-1\right)^{\frac{1}{4}} x^{9}+40 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{10}+16 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} \left(8 x^{12}+24 x^{10}+12 x^{8}-16 x^{6}-6 x^{4}+6 x^{2}-1\right)^{\frac{1}{4}} x^{7}+12 x^{8} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-24 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{6}+8 \sqrt{8 x^{12}+24 x^{10}+12 x^{8}-16 x^{6}-6 x^{4}+6 x^{2}-1}\, x^{6}-8 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} \left(8 x^{12}+24 x^{10}+12 x^{8}-16 x^{6}-6 x^{4}+6 x^{2}-1\right)^{\frac{1}{4}} x^{3}+4 \RootOf \left(\textit{\_Z}^{4}-2\right) \left(8 x^{12}+24 x^{10}+12 x^{8}-16 x^{6}-6 x^{4}+6 x^{2}-1\right)^{\frac{3}{4}} x^{3}-4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{4}+8 \sqrt{8 x^{12}+24 x^{10}+12 x^{8}-16 x^{6}-6 x^{4}+6 x^{2}-1}\, x^{4}+2 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} \left(8 x^{12}+24 x^{10}+12 x^{8}-16 x^{6}-6 x^{4}+6 x^{2}-1\right)^{\frac{1}{4}} x +6 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}-4 \sqrt{8 x^{12}+24 x^{10}+12 x^{8}-16 x^{6}-6 x^{4}+6 x^{2}-1}\, x^{2}-\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}}{\left(2 x^{2}-1\right) \left(2 x^{4}+2 x^{2}-1\right)^{2}}\right)}{4}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(\frac{-16 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{12}+8 \left(8 x^{12}+24 x^{10}+12 x^{8}-16 x^{6}-6 x^{4}+6 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{9}-40 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{10}+16 \left(8 x^{12}+24 x^{10}+12 x^{8}-16 x^{6}-6 x^{4}+6 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{7}-12 x^{8} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+24 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{6}+8 \sqrt{8 x^{12}+24 x^{10}+12 x^{8}-16 x^{6}-6 x^{4}+6 x^{2}-1}\, x^{6}-8 \left(8 x^{12}+24 x^{10}+12 x^{8}-16 x^{6}-6 x^{4}+6 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{3}-4 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \left(8 x^{12}+24 x^{10}+12 x^{8}-16 x^{6}-6 x^{4}+6 x^{2}-1\right)^{\frac{3}{4}} x^{3}+4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{4}+8 \sqrt{8 x^{12}+24 x^{10}+12 x^{8}-16 x^{6}-6 x^{4}+6 x^{2}-1}\, x^{4}+2 \left(8 x^{12}+24 x^{10}+12 x^{8}-16 x^{6}-6 x^{4}+6 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x -6 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}-4 \sqrt{8 x^{12}+24 x^{10}+12 x^{8}-16 x^{6}-6 x^{4}+6 x^{2}-1}\, x^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}}{\left(2 x^{2}-1\right) \left(2 x^{4}+2 x^{2}-1\right)^{2}}\right)}{4}\right) \left(\left(2 x^{4}+2 x^{2}-1\right)^{3}\right)^{\frac{1}{4}}}{\left(2 x^{4}+2 x^{2}-1\right)^{\frac{3}{4}}}$&$1057$\\ \hline \end{longtable}"," ",0,"-(2*x^4+2*x^2-1)^(1/4)/x+1/4*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln(-(4*RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^4+4*RootOf(_Z^4-2)^2*(2*x^4+2*x^2-1)^(1/4)*x^3+2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*x^2-4*RootOf(_Z^2+RootOf(_Z^4-2)^2)*(2*x^4+2*x^2-1)^(1/2)*x^2-4*(2*x^4+2*x^2-1)^(3/4)*x-RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2))/(2*x^2-1))-1/4*RootOf(_Z^4-2)*ln(-(4*RootOf(_Z^4-2)^3*x^4-4*RootOf(_Z^4-2)^2*(2*x^4+2*x^2-1)^(1/4)*x^3+2*RootOf(_Z^4-2)^3*x^2+4*RootOf(_Z^4-2)*(2*x^4+2*x^2-1)^(1/2)*x^2-4*(2*x^4+2*x^2-1)^(3/4)*x-RootOf(_Z^4-2)^3)/(2*x^2-1))","C"
1115,0,0,61,0.033000," ","int(1/(a*x^4+b)^(1/4)/(a*x^4+2*b),x)","\[\int \frac{1}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(a \,x^{4}+2 b \right)}\, dx\]"," ",0,"int(1/(a*x^4+b)^(1/4)/(a*x^4+2*b),x)","F"
1116,0,0,69,0.004000," ","int((a*x^4-b*x^2)^(1/4)/x^2,x)","\[\int \frac{\left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}{x^{2}}\, dx\]"," ",0,"int((a*x^4-b*x^2)^(1/4)/x^2,x)","F"
1117,0,0,14,0.036000," ","int(1/(a*x^4-b*x^2)^(1/4)/(b*x^8+a),x)","\[\int \frac{1}{\left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}} \left(b \,x^{8}+a \right)}\, dx\]"," ",0,"int(1/(a*x^4-b*x^2)^(1/4)/(b*x^8+a),x)","F"
1118,0,0,14,0.001000," ","int(1/(a*x^4-b*x^2)^(1/4)/(b*x^8+a),x)","\[\int \frac{1}{\left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}} \left(b \,x^{8}+a \right)}\, dx\]"," ",0,"int(1/(a*x^4-b*x^2)^(1/4)/(b*x^8+a),x)","F"
1119,1,68,61,0.038000," ","int((-1+x)*(x+(1+x)^(1/2))^(1/2)/(1+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\sqrt{1+x}\, \left(x +\sqrt{1+x}\right)^{\frac{3}{2}}}{2}-\frac{5 \left(x +\sqrt{1+x}\right)^{\frac{3}{2}}}{12}-\frac{23 \left(2 \sqrt{1+x}+1\right) \sqrt{x +\sqrt{1+x}}}{32}+\frac{115 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{64}$&$68$\\ default&$\frac{\sqrt{1+x}\, \left(x +\sqrt{1+x}\right)^{\frac{3}{2}}}{2}-\frac{5 \left(x +\sqrt{1+x}\right)^{\frac{3}{2}}}{12}-\frac{23 \left(2 \sqrt{1+x}+1\right) \sqrt{x +\sqrt{1+x}}}{32}+\frac{115 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{64}$&$68$\\ \hline \end{longtable}"," ",0,"1/2*(1+x)^(1/2)*(x+(1+x)^(1/2))^(3/2)-5/12*(x+(1+x)^(1/2))^(3/2)-23/32*(2*(1+x)^(1/2)+1)*(x+(1+x)^(1/2))^(1/2)+115/64*ln(1/2+(1+x)^(1/2)+(x+(1+x)^(1/2))^(1/2))","A"
1120,1,68,61,0.036000," ","int(x*(x+(1+x)^(1/2))^(1/2)/(1+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\sqrt{1+x}\, \left(x +\sqrt{1+x}\right)^{\frac{3}{2}}}{2}-\frac{5 \left(x +\sqrt{1+x}\right)^{\frac{3}{2}}}{12}-\frac{7 \left(2 \sqrt{1+x}+1\right) \sqrt{x +\sqrt{1+x}}}{32}+\frac{35 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{64}$&$68$\\ default&$\frac{\sqrt{1+x}\, \left(x +\sqrt{1+x}\right)^{\frac{3}{2}}}{2}-\frac{5 \left(x +\sqrt{1+x}\right)^{\frac{3}{2}}}{12}-\frac{7 \left(2 \sqrt{1+x}+1\right) \sqrt{x +\sqrt{1+x}}}{32}+\frac{35 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{64}$&$68$\\ \hline \end{longtable}"," ",0,"1/2*(1+x)^(1/2)*(x+(1+x)^(1/2))^(3/2)-5/12*(x+(1+x)^(1/2))^(3/2)-7/32*(2*(1+x)^(1/2)+1)*(x+(1+x)^(1/2))^(1/2)+35/64*ln(1/2+(1+x)^(1/2)+(x+(1+x)^(1/2))^(1/2))","A"
1121,1,68,61,0.041000," ","int((1+x)^(1/2)*(x+(1+x)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\sqrt{1+x}\, \left(x +\sqrt{1+x}\right)^{\frac{3}{2}}}{2}-\frac{5 \left(x +\sqrt{1+x}\right)^{\frac{3}{2}}}{12}+\frac{9 \left(2 \sqrt{1+x}+1\right) \sqrt{x +\sqrt{1+x}}}{32}-\frac{45 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{64}$&$68$\\ default&$\frac{\sqrt{1+x}\, \left(x +\sqrt{1+x}\right)^{\frac{3}{2}}}{2}-\frac{5 \left(x +\sqrt{1+x}\right)^{\frac{3}{2}}}{12}+\frac{9 \left(2 \sqrt{1+x}+1\right) \sqrt{x +\sqrt{1+x}}}{32}-\frac{45 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{64}$&$68$\\ \hline \end{longtable}"," ",0,"1/2*(1+x)^(1/2)*(x+(1+x)^(1/2))^(3/2)-5/12*(x+(1+x)^(1/2))^(3/2)+9/32*(2*(1+x)^(1/2)+1)*(x+(1+x)^(1/2))^(1/2)-45/64*ln(1/2+(1+x)^(1/2)+(x+(1+x)^(1/2))^(1/2))","A"
1122,0,0,69,0.018000," ","int((1+(x^2+1)^(1/2))/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{1+\sqrt{x^{2}+1}}{\sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((1+(x^2+1)^(1/2))/(x+(x^2+1)^(1/2))^(1/2),x)","F"
1123,1,57,11,1.086000," ","int(((x^2-4*x+1)^(1/2)+(x^2-4*x+1)^(3/2))/((x^2-4*x+1)^(1/2)+(x^2-4*x+1)^(3/2)-(x^2-4*x+1)^(5/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-8 \textit{\_Z}^{3}+17 \textit{\_Z}^{2}-4 \textit{\_Z} -1\right)}{\sum}\frac{\left(\textit{\_R}^{2}-4 \textit{\_R} +2\right) \ln \left(x -\textit{\_R} \right)}{2 \textit{\_R}^{3}-12 \textit{\_R}^{2}+17 \textit{\_R} -2}\right)}{2}$&$57$\\ trager&$-\RootOf \left(4400 \textit{\_Z}^{4}-340 \textit{\_Z}^{2}+1\right) \ln \left(\frac{440 \RootOf \left(4400 \textit{\_Z}^{4}-340 \textit{\_Z}^{2}+1\right)^{3} x +440 \RootOf \left(4400 \textit{\_Z}^{4}-340 \textit{\_Z}^{2}+1\right)^{2} x -122 \RootOf \left(4400 \textit{\_Z}^{4}-340 \textit{\_Z}^{2}+1\right) x -10 x +7}{440 \RootOf \left(4400 \textit{\_Z}^{4}-340 \textit{\_Z}^{2}+1\right)^{3} x -440 \RootOf \left(4400 \textit{\_Z}^{4}-340 \textit{\_Z}^{2}+1\right)^{2} x -122 \RootOf \left(4400 \textit{\_Z}^{4}-340 \textit{\_Z}^{2}+1\right) x +10 x -7}\right)-\frac{\RootOf \left(\textit{\_Z}^{2}+12100 \RootOf \left(4400 \textit{\_Z}^{4}-340 \textit{\_Z}^{2}+1\right)^{2}-935\right) \ln \left(-\frac{20 \RootOf \left(4400 \textit{\_Z}^{4}-340 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+12100 \RootOf \left(4400 \textit{\_Z}^{4}-340 \textit{\_Z}^{2}+1\right)^{2}-935\right) x +2200 \RootOf \left(4400 \textit{\_Z}^{4}-340 \textit{\_Z}^{2}+1\right)^{2} x +4 \RootOf \left(\textit{\_Z}^{2}+12100 \RootOf \left(4400 \textit{\_Z}^{4}-340 \textit{\_Z}^{2}+1\right)^{2}-935\right) x -120 x -35}{20 \RootOf \left(4400 \textit{\_Z}^{4}-340 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+12100 \RootOf \left(4400 \textit{\_Z}^{4}-340 \textit{\_Z}^{2}+1\right)^{2}-935\right) x -2200 \RootOf \left(4400 \textit{\_Z}^{4}-340 \textit{\_Z}^{2}+1\right)^{2} x +4 \RootOf \left(\textit{\_Z}^{2}+12100 \RootOf \left(4400 \textit{\_Z}^{4}-340 \textit{\_Z}^{2}+1\right)^{2}-935\right) x +120 x +35}\right)}{110}$&$345$\\ default&\verb|error in AlgebraicFunction: argument is not an algebraic\|& N/A\\ \hline \end{longtable}"," ",0,"-1/2*sum((_R^2-4*_R+2)/(2*_R^3-12*_R^2+17*_R-2)*ln(x-_R),_R=RootOf(_Z^4-8*_Z^3+17*_Z^2-4*_Z-1))","B"
1124,0,0,73,0.050000," ","int(x^2/(a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x)","\[\int \frac{x^{2}}{\sqrt{a^{2} x^{2}-b x}\, \left(a \,x^{2}+x \sqrt{a^{2} x^{2}-b x}\right)^{\frac{3}{2}}}\, dx\]"," ",0,"int(x^2/(a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x)","F"
1125,1,2553,76,0.323000," ","int((a^2*b-a*(2*a+b)*x+3*a*x^2-x^3)/x/(-b+x)/(x*(-a+x)*(-b+x))^(1/2)/(a+(-b*d-1)*x+d*x^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{2 a b -2 a x -2 b x +2 x^{2}}{b \sqrt{x \left(a b -a x -b x +x^{2}\right)}}-\frac{2 \left(-a x +x^{2}\right)}{b \sqrt{\left(-b +x \right) \left(-a x +x^{2}\right)}}+\frac{2 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}+\frac{b^{3} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) d}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}+\frac{2 b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}-\frac{4 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) a}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}+\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right) d}-\frac{2 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) a}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}+\frac{b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}+\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right) d}-\frac{b^{3} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) d}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}-\frac{2 b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}-\frac{2 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) a}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}+\frac{b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}+\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right) d}+\frac{4 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) a}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}-\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right) d}$&$2553$\\ risch&$\frac{2 \left(a -x \right) \left(b -x \right)}{b \sqrt{x \left(-a +x \right) \left(-b +x \right)}}-\frac{-\frac{2 a \sqrt{-\frac{-a +x}{a}}\, \sqrt{\frac{-b +x}{a -b}}\, \sqrt{\frac{x}{a}}\, \left(\left(a -b \right) \EllipticE \left(\sqrt{-\frac{-a +x}{a}}, \sqrt{\frac{a}{a -b}}\right)+b \EllipticF \left(\sqrt{-\frac{-a +x}{a}}, \sqrt{\frac{a}{a -b}}\right)\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}-b \left(\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b^{2} d}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}+\frac{2 a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}-\frac{4 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}+\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right) d}-\frac{2 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}+\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}+\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right) d}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b^{2} d}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}-\frac{2 a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}-\frac{2 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}+\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right) b}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}+\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right) d}+\frac{4 a^{2} \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}-\frac{a \sqrt{1-\frac{x}{a}}\, \sqrt{-\frac{b}{a -b}+\frac{x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticPi \left(\sqrt{-\frac{-a +x}{a}}, \frac{a}{a +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(a -\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right) d}\right)+\left(a -b \right) b \left(\frac{-2 a x +2 x^{2}}{b \left(a -b \right) \sqrt{\left(-b +x \right) \left(-a x +x^{2}\right)}}-\frac{2 \left(-\frac{1}{b}+\frac{a}{b \left(a -b \right)}\right) a \sqrt{-\frac{-a +x}{a}}\, \sqrt{\frac{-b +x}{a -b}}\, \sqrt{\frac{x}{a}}\, \EllipticF \left(\sqrt{-\frac{-a +x}{a}}, \sqrt{\frac{a}{a -b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}+\frac{2 a \sqrt{-\frac{-a +x}{a}}\, \sqrt{\frac{-b +x}{a -b}}\, \sqrt{\frac{x}{a}}\, \left(\left(a -b \right) \EllipticE \left(\sqrt{-\frac{-a +x}{a}}, \sqrt{\frac{a}{a -b}}\right)+b \EllipticF \left(\sqrt{-\frac{-a +x}{a}}, \sqrt{\frac{a}{a -b}}\right)\right)}{b \left(a -b \right) \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}\right)}{b}$&$2839$\\ default&$-\left(a -b \right) \left(\frac{-2 a x +2 x^{2}}{b \left(a -b \right) \sqrt{\left(-b +x \right) \left(-a x +x^{2}\right)}}+\frac{2 \left(\frac{1}{b}-\frac{a}{b \left(a -b \right)}\right) b \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}+\frac{2 \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \left(\left(-a +b \right) \EllipticE \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)+a \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)\right)}{\left(a -b \right) \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}\right)-a \left(-\frac{2 \left(a b -a x -b x +x^{2}\right)}{a b \sqrt{x \left(a b -a x -b x +x^{2}\right)}}-\frac{2 \left(\frac{a +b}{a b}+\frac{-a -b}{a b}\right) b \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}-\frac{2 \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \left(\left(-a +b \right) \EllipticE \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)+a \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)\right)}{a \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}\right)+\frac{b^{3} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) d}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}+\frac{2 b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}-\frac{4 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) a}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}+\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right) d}-\frac{2 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) a}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}+\frac{b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right)}+\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b -\frac{b d +1+\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}-\frac{1}{2 d}-\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}\right) d}-\frac{b^{3} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) d}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}-\frac{2 b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}-\frac{2 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) a}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}+\frac{b^{2} \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}+\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right) d}+\frac{4 b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right) a}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right)}-\frac{b \sqrt{1-\frac{x}{b}}\, \sqrt{-\frac{a}{-a +b}+\frac{x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, \frac{b}{b +\frac{-b d +\sqrt{b^{2} d^{2}-4 a d +2 b d +1}-1}{2 d}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}\, \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}\, \left(\frac{b}{2}+\frac{\sqrt{b^{2} d^{2}-4 a d +2 b d +1}}{2 d}-\frac{1}{2 d}\right) d}$&$2935$\\ \hline \end{longtable}"," ",0,"2*(a*b-a*x-b*x+x^2)/b/(x*(a*b-a*x-b*x+x^2))^(1/2)-2*(-a*x+x^2)/b/((-b+x)*(-a*x+x^2))^(1/2)+2*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)*EllipticF((-(-b+x)/b)^(1/2),(b/(-a+b))^(1/2))+1/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*b^3*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2/d-1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(b-1/2/d*(b*d+1+(b^2*d^2-4*a*d+2*b*d+1)^(1/2))),(b/(-a+b))^(1/2))*d+2/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*b^2*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2/d-1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(b-1/2/d*(b*d+1+(b^2*d^2-4*a*d+2*b*d+1)^(1/2))),(b/(-a+b))^(1/2))-4/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2/d-1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(b-1/2/d*(b*d+1+(b^2*d^2-4*a*d+2*b*d+1)^(1/2))),(b/(-a+b))^(1/2))*a+1/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2/d-1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(b-1/2/d*(b*d+1+(b^2*d^2-4*a*d+2*b*d+1)^(1/2))),(b/(-a+b))^(1/2))/d-2*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2/d-1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(b-1/2/d*(b*d+1+(b^2*d^2-4*a*d+2*b*d+1)^(1/2))),(b/(-a+b))^(1/2))*a+b^2*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2/d-1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(b-1/2/d*(b*d+1+(b^2*d^2-4*a*d+2*b*d+1)^(1/2))),(b/(-a+b))^(1/2))+b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b-1/2/d-1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2))*EllipticPi((-(-b+x)/b)^(1/2),b/(b-1/2/d*(b*d+1+(b^2*d^2-4*a*d+2*b*d+1)^(1/2))),(b/(-a+b))^(1/2))/d-1/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*b^3*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b+1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-b+x)/b)^(1/2),b/(b+1/2*(-b*d+(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1)/d),(b/(-a+b))^(1/2))*d-2/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*b^2*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b+1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-b+x)/b)^(1/2),b/(b+1/2*(-b*d+(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1)/d),(b/(-a+b))^(1/2))-2*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b+1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-b+x)/b)^(1/2),b/(b+1/2*(-b*d+(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1)/d),(b/(-a+b))^(1/2))*a+b^2*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b+1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-b+x)/b)^(1/2),b/(b+1/2*(-b*d+(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1)/d),(b/(-a+b))^(1/2))+b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b+1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-b+x)/b)^(1/2),b/(b+1/2*(-b*d+(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1)/d),(b/(-a+b))^(1/2))/d+4/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b+1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-b+x)/b)^(1/2),b/(b+1/2*(-b*d+(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1)/d),(b/(-a+b))^(1/2))*a-1/(b^2*d^2-4*a*d+2*b*d+1)^(1/2)*b*(1-x/b)^(1/2)*(-1/(-a+b)*a+1/(-a+b)*x)^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)/(1/2*b+1/2/d*(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1/2/d)*EllipticPi((-(-b+x)/b)^(1/2),b/(b+1/2*(-b*d+(b^2*d^2-4*a*d+2*b*d+1)^(1/2)-1)/d),(b/(-a+b))^(1/2))/d","C"
1126,1,64,65,2.376000," ","int((x^3+1)^(2/3)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\frac{2 \pi  \sqrt{3}\, x^{3} \hypergeom \left(\left[\frac{1}{3}, 1, 1\right], \left[2, 2\right], -x^{3}\right)}{3 \Gamma \left(\frac{2}{3}\right)}-\frac{\left(\frac{3}{2}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)\right) \pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right)}\right)}{9 \pi}$&$64$\\ trager&$\frac{\left(x^{3}+1\right)^{\frac{2}{3}}}{2}+\frac{\ln \left(\frac{-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}-2 x^{3}-9 \left(x^{3}+1\right)^{\frac{2}{3}}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-9 \left(x^{3}+1\right)^{\frac{1}{3}}+19 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-5}{x^{3}}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{3}-\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+17 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}+15 x^{3}+24 \left(x^{3}+1\right)^{\frac{2}{3}}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+24 \left(x^{3}+1\right)^{\frac{1}{3}}+11 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+20}{x^{3}}\right)}{3}-\frac{\ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+17 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}+15 x^{3}+24 \left(x^{3}+1\right)^{\frac{2}{3}}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+24 \left(x^{3}+1\right)^{\frac{1}{3}}+11 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+20}{x^{3}}\right)}{3}$&$357$\\ \hline \end{longtable}"," ",0,"-1/9/Pi*3^(1/2)*GAMMA(2/3)*(-2/3*Pi*3^(1/2)/GAMMA(2/3)*x^3*hypergeom([1/3,1,1],[2,2],-x^3)-(3/2-1/6*Pi*3^(1/2)-3/2*ln(3)+3*ln(x))*Pi*3^(1/2)/GAMMA(2/3))","C"
1127,0,0,66,0.010000," ","int((2*a*x^2-b)*(a*x^4+b*x^2)^(1/4)/(a*x^2+b),x)","\[\int \frac{\left(2 a \,x^{2}-b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}{a \,x^{2}+b}\, dx\]"," ",0,"int((2*a*x^2-b)*(a*x^4+b*x^2)^(1/4)/(a*x^2+b),x)","F"
1128,1,128,70,0.852000," ","int((x^4-1)*(x^4+x^2+1)^(1/2)*(x^8+x^6+3*x^4+x^2+1)/(x^4+1)^3/(x^4-x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(3 \ln \left(-1+\frac{\sqrt{x^{4}+x^{2}+1}\, \sqrt{2}}{2 x}\right)-3 \ln \left(1+\frac{\sqrt{x^{4}+x^{2}+1}\, \sqrt{2}}{2 x}\right)-\frac{8 \left(-\frac{9 \left(x^{4}+x^{2}+1\right)^{\frac{3}{2}} \sqrt{2}}{64 x^{3}}+\frac{7 \sqrt{x^{4}+x^{2}+1}\, \sqrt{2}}{64 x}\right)}{\left(\frac{x^{4}+x^{2}+1}{x^{2}}-1\right)^{2}}+\frac{31 \sqrt{2}\, \arctanh \left(\frac{\sqrt{x^{4}+x^{2}+1}}{x}\right)}{8}\right) \sqrt{2}}{2}$&$128$\\ trager&$\frac{\left(9 x^{4}+2 x^{2}+9\right) x \sqrt{x^{4}+x^{2}+1}}{8 \left(x^{4}+1\right)^{2}}-\frac{3 \RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x^{4}+3 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}+4 \sqrt{x^{4}+x^{2}+1}\, x +\RootOf \left(\textit{\_Z}^{2}-2\right)}{x^{4}-x^{2}+1}\right)}{2}-\frac{31 \ln \left(-\frac{-x^{4}+2 \sqrt{x^{4}+x^{2}+1}\, x -2 x^{2}-1}{x^{4}+1}\right)}{16}$&$135$\\ risch&$\frac{\left(9 x^{4}+2 x^{2}+9\right) x \sqrt{x^{4}+x^{2}+1}}{8 \left(x^{4}+1\right)^{2}}+\frac{17 \sqrt{1-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{-2+2 i \sqrt{3}}}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{4 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}-\frac{31 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2}+1\right) \left(-3 \underline{\hspace{1.25 ex}}\alpha^{2}+5 x^{2}+4\right)}{10 \sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{x^{4}+x^{2}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{\sqrt{2}\, \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{x^{2}+2-i \sqrt{3}\, x^{2}}\, \sqrt{x^{2}+2+i \sqrt{3}\, x^{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , \frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{2}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-1+i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}\right)\right)}{32}+\frac{3 \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}-\textit{\_Z}^{2}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2}+1\right) \left(-3 \underline{\hspace{1.25 ex}}\alpha^{2}+7 x^{2}+8\right) \sqrt{2}}{28 \sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{x^{4}+x^{2}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}}-\frac{2 \left(-\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{x^{2}+2-i \sqrt{3}\, x^{2}}\, \sqrt{x^{2}+2+i \sqrt{3}\, x^{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , \frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{2}-\frac{1}{2}-\frac{i \sqrt{3}}{2}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-1+i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}\right)\right)}{4}$&$468$\\ default&$\frac{17 \sqrt{1-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{-2+2 i \sqrt{3}}}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{4 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}+\frac{3 \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}-\textit{\_Z}^{2}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2}+1\right) \left(-3 \underline{\hspace{1.25 ex}}\alpha^{2}+7 x^{2}+8\right) \sqrt{2}}{28 \sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{x^{4}+x^{2}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}}-\frac{2 \left(-\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{x^{2}+2-i \sqrt{3}\, x^{2}}\, \sqrt{x^{2}+2+i \sqrt{3}\, x^{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , \frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{2}-\frac{1}{2}-\frac{i \sqrt{3}}{2}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-1+i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}\right)\right)}{4}+\frac{x^{3} \sqrt{x^{4}+x^{2}+1}}{4 \left(x^{4}+1\right)^{2}}-\frac{2 \left(-\frac{1}{8} x^{3}-\frac{1}{16} x \right) \sqrt{x^{4}+x^{2}+1}}{x^{4}+1}-\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \left(-\frac{\arctanh \left(\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2}+1\right) \left(-3 \underline{\hspace{1.25 ex}}\alpha^{2}+5 x^{2}+4\right)}{10 \sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{x^{4}+x^{2}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{\sqrt{2}\, \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{x^{2}+2-i \sqrt{3}\, x^{2}}\, \sqrt{x^{2}+2+i \sqrt{3}\, x^{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , \frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{2}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-1+i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}\right)\right)}{32}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2}-3\right) \left(-\frac{\arctanh \left(\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2}+1\right) \left(-3 \underline{\hspace{1.25 ex}}\alpha^{2}+5 x^{2}+4\right)}{10 \sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{x^{4}+x^{2}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{\sqrt{2}\, \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{x^{2}+2-i \sqrt{3}\, x^{2}}\, \sqrt{x^{2}+2+i \sqrt{3}\, x^{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , \frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{2}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-1+i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}\right)\right)}{4}+\frac{\left(-\frac{1}{4} x^{3}+x \right) \sqrt{x^{4}+x^{2}+1}}{x^{4}+1}-\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(3 \underline{\hspace{1.25 ex}}\alpha^{2}+4\right) \left(-\frac{\arctanh \left(\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2}+1\right) \left(-3 \underline{\hspace{1.25 ex}}\alpha^{2}+5 x^{2}+4\right)}{10 \sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{x^{4}+x^{2}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{\sqrt{2}\, \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{x^{2}+2-i \sqrt{3}\, x^{2}}\, \sqrt{x^{2}+2+i \sqrt{3}\, x^{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , \frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{2}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-1+i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}\right)\right)}{16}$&$862$\\ \hline \end{longtable}"," ",0,"1/2*(3*ln(-1+1/2*(x^4+x^2+1)^(1/2)*2^(1/2)/x)-3*ln(1+1/2*(x^4+x^2+1)^(1/2)*2^(1/2)/x)-8*(-9/64*(x^4+x^2+1)^(3/2)*2^(1/2)/x^3+7/64*(x^4+x^2+1)^(1/2)*2^(1/2)/x)/((x^4+x^2+1)/x^2-1)^2+31/8*2^(1/2)*arctanh(1/x*(x^4+x^2+1)^(1/2)))*2^(1/2)","A"
1129,1,103,72,1.941000," ","int((x^6+1)*(x^6+x^3-1)*(x^12+1)^(1/2)/x^7/(x^6-x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{6}+4 x^{3}-1\right) \sqrt{x^{12}+1}}{6 x^{6}}+\ln \left(\frac{-1+x^{6}+\sqrt{x^{12}+1}}{x^{3}}\right)+\frac{2 \RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) x^{6}+2 \RootOf \left(\textit{\_Z}^{2}-3\right) x^{3}-\RootOf \left(\textit{\_Z}^{2}-3\right)-3 \sqrt{x^{12}+1}}{x^{6}-x^{3}-1}\right)}{3}$&$103$\\ risch&$\frac{4 x^{15}-x^{12}+4 x^{3}-1}{6 x^{6} \sqrt{x^{12}+1}}+\frac{\sqrt{x^{12}+1}}{6}-\ln \left(\frac{-x^{6}+\sqrt{x^{12}+1}+1}{x^{3}}\right)-\frac{2 \RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) x^{6}+2 \RootOf \left(\textit{\_Z}^{2}-3\right) x^{3}-\RootOf \left(\textit{\_Z}^{2}-3\right)+3 \sqrt{x^{12}+1}}{x^{6}-x^{3}-1}\right)}{3}$&$122$\\ \hline \end{longtable}"," ",0,"1/6*(x^6+4*x^3-1)*(x^12+1)^(1/2)/x^6+ln((-1+x^6+(x^12+1)^(1/2))/x^3)+2/3*RootOf(_Z^2-3)*ln(-(RootOf(_Z^2-3)*x^6+2*RootOf(_Z^2-3)*x^3-RootOf(_Z^2-3)-3*(x^12+1)^(1/2))/(x^6-x^3-1))","C"
1130,1,41,70,0.056000," ","int((d+c*(a*x+b)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\frac{4 \left(d +c \sqrt{a x +b}\right)^{\frac{5}{2}}}{5}-\frac{4 d \left(d +c \sqrt{a x +b}\right)^{\frac{3}{2}}}{3}}{a \,c^{2}}$&$41$\\ default&$\frac{\frac{4 \left(d +c \sqrt{a x +b}\right)^{\frac{5}{2}}}{5}-\frac{4 d \left(d +c \sqrt{a x +b}\right)^{\frac{3}{2}}}{3}}{a \,c^{2}}$&$41$\\ \hline \end{longtable}"," ",0,"4/a/c^2*(1/5*(d+c*(a*x+b)^(1/2))^(5/2)-1/3*d*(d+c*(a*x+b)^(1/2))^(3/2))","A"
1131,1,62,65,1.879000," ","int((2*x^2+1)/x/(x^2+1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$x^{2} \hypergeom \left(\left[\frac{2}{3}, 1\right], \left[2\right], -x^{2}\right)+\frac{-\frac{2 \Gamma \left(\frac{2}{3}\right) x^{2} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 2\right], -x^{2}\right)}{3}+\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+2 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)}{2 \Gamma \left(\frac{2}{3}\right)}$&$62$\\ trager&$3 \left(x^{2}+1\right)^{\frac{1}{3}}+\frac{\ln \left(\frac{-36 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{2}+90 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}}-18 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{2}-9 \left(x^{2}+1\right)^{\frac{2}{3}}-144 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{1}{3}}+36 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2}+10 x^{2}-15 \left(x^{2}+1\right)^{\frac{1}{3}}+60 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)+25}{x^{2}}\right)}{2}-\frac{\ln \left(-\frac{-180 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{2}+90 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}}-96 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{2}+24 \left(x^{2}+1\right)^{\frac{2}{3}}+54 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{1}{3}}+180 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2}-3 x^{2}-15 \left(x^{2}+1\right)^{\frac{1}{3}}-114 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)-4}{x^{2}}\right)}{2}-3 \ln \left(-\frac{-180 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{2}+90 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}}-96 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{2}+24 \left(x^{2}+1\right)^{\frac{2}{3}}+54 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{1}{3}}+180 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2}-3 x^{2}-15 \left(x^{2}+1\right)^{\frac{1}{3}}-114 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)-4}{x^{2}}\right) \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)$&$426$\\ \hline \end{longtable}"," ",0,"x^2*hypergeom([2/3,1],[2],-x^2)+1/2/GAMMA(2/3)*(-2/3*GAMMA(2/3)*x^2*hypergeom([1,1,5/3],[2,2],-x^2)+(1/6*Pi*3^(1/2)-3/2*ln(3)+2*ln(x))*GAMMA(2/3))","C"
1132,1,232,77,0.093000," ","int(x/((1-x)*x*(-k^2*x+1))^(1/2)/(k^2*x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{4} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}-\frac{\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{4} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}$&$232$\\ elliptic&$-\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{4} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}-\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{4} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}$&$240$\\ \hline \end{longtable}"," ",0,"-1/k^4*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/k)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+1/k),(1/k^2/(1/k^2-1))^(1/2))-1/k^4*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-1/k)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-1/k),(1/k^2/(1/k^2-1))^(1/2))","C"
1133,1,96,57,1.787000," ","int((1+x)/(x^2+2*x-1)/(x^3-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \sqrt{2}\, \EllipticPi \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}+\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \sqrt{2}\, \EllipticPi \left(\sqrt{1+x}, -\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}$&$96$\\ elliptic&$-\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \sqrt{2}\, \EllipticPi \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}+\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \sqrt{2}\, \EllipticPi \left(\sqrt{1+x}, -\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}$&$96$\\ trager&$4 \ln \left(-\frac{-27452160 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{5} x^{2}+45753600 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{5} x +18301440 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{5}-37781952 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{3} x^{2}+54200480 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{3} x +2278872 \sqrt{x^{3}-x}\, \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{2}+16418528 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{3}-12987008 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right) x^{2}+15422072 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right) x +1527689 \sqrt{x^{3}-x}+2435064 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)}{\left(8 x \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{2}-16 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{2}+9 x -4\right)^{2}}\right) \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{3}+3 \ln \left(-\frac{-27452160 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{5} x^{2}+45753600 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{5} x +18301440 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{5}-37781952 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{3} x^{2}+54200480 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{3} x +2278872 \sqrt{x^{3}-x}\, \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{2}+16418528 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{3}-12987008 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right) x^{2}+15422072 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right) x +1527689 \sqrt{x^{3}-x}+2435064 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)}{\left(8 x \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{2}-16 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{2}+9 x -4\right)^{2}}\right) \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)+\frac{\RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right) \ln \left(\frac{8868864 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{5} x^{2}-14781440 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{5} x -5912576 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{5}+3959200 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{3} x^{2}-9431776 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{3} x +2278872 \sqrt{x^{3}-x}\, \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{2}-5472576 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{3}+268344 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right) x^{2}-1475892 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right) x +181465 \sqrt{x^{3}-x}-1207548 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)}{\left(8 x \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{2}-16 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{2}-3 x -8\right)^{2}}\right)}{2}$&$774$\\ \hline \end{longtable}"," ",0,"-1/4*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*2^(1/2)*EllipticPi((1+x)^(1/2),1/2*2^(1/2),1/2*2^(1/2))+1/4*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*2^(1/2)*EllipticPi((1+x)^(1/2),-1/2*2^(1/2),1/2*2^(1/2))","C"
1134,1,222,57,1.606000," ","int((x^2-x)/(x^2+2*x-1)/(x^3-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticF \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}}-\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}}+\frac{3 \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \sqrt{2}\, \EllipticPi \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}-\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}}-\frac{3 \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \sqrt{2}\, \EllipticPi \left(\sqrt{1+x}, -\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}$&$222$\\ elliptic&$\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticF \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}}-\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}}+\frac{3 \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \sqrt{2}\, \EllipticPi \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}-\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}}-\frac{3 \sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \sqrt{2}\, \EllipticPi \left(\sqrt{1+x}, -\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)}{4 \sqrt{x^{3}-x}}$&$222$\\ trager&$4 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{3} \ln \left(\frac{-8868864 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{5} x^{2}+14781440 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{5} x +5912576 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{5}-3959200 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{3} x^{2}+9431776 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{3} x +2278872 \sqrt{x^{3}-x}\, \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{2}+5472576 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{3}-268344 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right) x^{2}+1475892 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right) x +181465 \sqrt{x^{3}-x}+1207548 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)}{\left(8 x \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{2}-16 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{2}-3 x -8\right)^{2}}\right)+3 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right) \ln \left(\frac{-8868864 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{5} x^{2}+14781440 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{5} x +5912576 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{5}-3959200 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{3} x^{2}+9431776 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{3} x +2278872 \sqrt{x^{3}-x}\, \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{2}+5472576 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{3}-268344 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right) x^{2}+1475892 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right) x +181465 \sqrt{x^{3}-x}+1207548 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)}{\left(8 x \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{2}-16 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{2}-3 x -8\right)^{2}}\right)-\frac{\ln \left(-\frac{-27452160 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{5} x^{2}+45753600 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{5} x +18301440 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{5}-37781952 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{3} x^{2}+54200480 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{3} x +2278872 \sqrt{x^{3}-x}\, \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{2}+16418528 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{3}-12987008 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right) x^{2}+15422072 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right) x +1527689 \sqrt{x^{3}-x}+2435064 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)}{\left(8 x \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{2}-16 \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)^{2}+9 x -4\right)^{2}}\right) \RootOf \left(64 \textit{\_Z}^{4}+48 \textit{\_Z}^{2}+1\right)}{2}$&$773$\\ \hline \end{longtable}"," ",0,"(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticF((1+x)^(1/2),1/2*2^(1/2))-(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticPi((1+x)^(1/2),1/2*2^(1/2),1/2*2^(1/2))+3/4*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*2^(1/2)*EllipticPi((1+x)^(1/2),1/2*2^(1/2),1/2*2^(1/2))-(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticPi((1+x)^(1/2),-1/2*2^(1/2),1/2*2^(1/2))-3/4*(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*2^(1/2)*EllipticPi((1+x)^(1/2),-1/2*2^(1/2),1/2*2^(1/2))","C"
1135,1,255,68,1.404000," ","int((x^2+3)/(x^2+1)^(1/3)/(x^3+x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}} x -\left(x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+2 \left(x^{2}+1\right)^{\frac{2}{3}} x +\left(x^{2}+1\right)^{\frac{1}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-x^{3}+x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1}{x^{3}+x^{2}+1}\right)+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}} x +2 \left(x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-\left(x^{2}+1\right)^{\frac{2}{3}} x +\left(x^{2}+1\right)^{\frac{1}{3}} x^{2}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-x^{2}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1}{x^{3}+x^{2}+1}\right)$&$255$\\ \hline \end{longtable}"," ",0,"ln((-RootOf(_Z^2+_Z+1)^2*x^3+RootOf(_Z^2+_Z+1)*(x^2+1)^(2/3)*x-(x^2+1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2-2*RootOf(_Z^2+_Z+1)*x^3+2*(x^2+1)^(2/3)*x+(x^2+1)^(1/3)*x^2+RootOf(_Z^2+_Z+1)*x^2-x^3+x^2+RootOf(_Z^2+_Z+1)+1)/(x^3+x^2+1))+RootOf(_Z^2+_Z+1)*ln(-(-RootOf(_Z^2+_Z+1)^2*x^3+RootOf(_Z^2+_Z+1)*(x^2+1)^(2/3)*x+2*(x^2+1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2-RootOf(_Z^2+_Z+1)*x^3-(x^2+1)^(2/3)*x+(x^2+1)^(1/3)*x^2-RootOf(_Z^2+_Z+1)*x^2-x^2-RootOf(_Z^2+_Z+1)-1)/(x^3+x^2+1))","C"
1136,1,447,70,0.878000," ","int(x/(x^3-1)/(2*x^3-1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(-\frac{-27 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+15 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(2 x^{3}-1\right)^{\frac{2}{3}} x -3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(2 x^{3}-1\right)^{\frac{1}{3}} x^{2}-30 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+4 \left(2 x^{3}-1\right)^{\frac{2}{3}} x -5 \left(2 x^{3}-1\right)^{\frac{1}{3}} x^{2}-3 x^{3}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+1}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right)}{3}-\frac{\ln \left(\frac{-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+15 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(2 x^{3}-1\right)^{\frac{2}{3}} x -12 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(2 x^{3}-1\right)^{\frac{1}{3}} x^{2}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+\left(2 x^{3}-1\right)^{\frac{2}{3}} x -5 \left(2 x^{3}-1\right)^{\frac{1}{3}} x^{2}+6 x^{3}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-3}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right)}{3}-\ln \left(\frac{-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+15 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(2 x^{3}-1\right)^{\frac{2}{3}} x -12 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(2 x^{3}-1\right)^{\frac{1}{3}} x^{2}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+\left(2 x^{3}-1\right)^{\frac{2}{3}} x -5 \left(2 x^{3}-1\right)^{\frac{1}{3}} x^{2}+6 x^{3}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-3}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)$&$447$\\ \hline \end{longtable}"," ",0,"1/3*ln(-(-27*RootOf(9*_Z^2+3*_Z+1)^2*x^3+15*RootOf(9*_Z^2+3*_Z+1)*(2*x^3-1)^(2/3)*x-3*RootOf(9*_Z^2+3*_Z+1)*(2*x^3-1)^(1/3)*x^2-30*RootOf(9*_Z^2+3*_Z+1)*x^3+4*(2*x^3-1)^(2/3)*x-5*(2*x^3-1)^(1/3)*x^2-3*x^3+9*RootOf(9*_Z^2+3*_Z+1)+1)/(-1+x)/(x^2+x+1))-1/3*ln((-9*RootOf(9*_Z^2+3*_Z+1)^2*x^3+15*RootOf(9*_Z^2+3*_Z+1)*(2*x^3-1)^(2/3)*x-12*RootOf(9*_Z^2+3*_Z+1)*(2*x^3-1)^(1/3)*x^2-3*RootOf(9*_Z^2+3*_Z+1)*x^3+(2*x^3-1)^(2/3)*x-5*(2*x^3-1)^(1/3)*x^2+6*x^3-3*RootOf(9*_Z^2+3*_Z+1)-3)/(-1+x)/(x^2+x+1))-ln((-9*RootOf(9*_Z^2+3*_Z+1)^2*x^3+15*RootOf(9*_Z^2+3*_Z+1)*(2*x^3-1)^(2/3)*x-12*RootOf(9*_Z^2+3*_Z+1)*(2*x^3-1)^(1/3)*x^2-3*RootOf(9*_Z^2+3*_Z+1)*x^3+(2*x^3-1)^(2/3)*x-5*(2*x^3-1)^(1/3)*x^2+6*x^3-3*RootOf(9*_Z^2+3*_Z+1)-3)/(-1+x)/(x^2+x+1))*RootOf(9*_Z^2+3*_Z+1)","C"
1137,0,0,73,0.020000," ","int((-1-2*(-1+k)*x+k*x^2)*(k^2*x^2-2*k*x+1)/((1-x)*x*(-k*x+1))^(3/4)/(-d+(3*d*k+1)*x-(3*d*k^2+1)*x^2+d*k^3*x^3),x)","\[\int \frac{\left(-1-2 \left(-1+k \right) x +k \,x^{2}\right) \left(k^{2} x^{2}-2 k x +1\right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{3}{4}} \left(-d +\left(3 d k +1\right) x -\left(3 d \,k^{2}+1\right) x^{2}+d \,k^{3} x^{3}\right)}\, dx\]"," ",0,"int((-1-2*(-1+k)*x+k*x^2)*(k^2*x^2-2*k*x+1)/((1-x)*x*(-k*x+1))^(3/4)/(-d+(3*d*k+1)*x-(3*d*k^2+1)*x^2+d*k^3*x^3),x)","F"
1138,1,119,70,2.660000," ","int((x^4-1)/(x^3-x)^(1/2)/(x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticF \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}}+\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+1\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  -1\right) \sqrt{1+x}\, \sqrt{1-x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{1}{2} \underline{\hspace{1.25 ex}}\alpha^{3}+\frac{1}{2} \underline{\hspace{1.25 ex}}\alpha^{2}-\frac{1}{2} \underline{\hspace{1.25 ex}}\alpha  +\frac{1}{2}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x \left(x^{2}-1\right)}}\right)}{4}$&$119$\\ elliptic&$\frac{\sqrt{1+x}\, \sqrt{2-2 x}\, \sqrt{-x}\, \EllipticF \left(\sqrt{1+x}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{3}-x}}+\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+1\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  -1\right) \sqrt{1+x}\, \sqrt{1-x}\, \sqrt{-x}\, \EllipticPi \left(\sqrt{1+x}, -\frac{1}{2} \underline{\hspace{1.25 ex}}\alpha^{3}+\frac{1}{2} \underline{\hspace{1.25 ex}}\alpha^{2}-\frac{1}{2} \underline{\hspace{1.25 ex}}\alpha  +\frac{1}{2}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x \left(x^{2}-1\right)}}\right)}{4}$&$119$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(-\frac{8 \RootOf \left(\textit{\_Z}^{4}+8\right)^{4} x^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)-12 \RootOf \left(\textit{\_Z}^{4}+8\right)^{4} x \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)-8 \RootOf \left(\textit{\_Z}^{4}+8\right)^{4} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)-50 \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{2}+7 \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x +200 \sqrt{x^{3}-x}\, \RootOf \left(\textit{\_Z}^{4}+8\right)^{2}+50 \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)+78 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{2}+104 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x -56 \sqrt{x^{3}-x}-78 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)}{2 \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-3 \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x -2 \RootOf \left(\textit{\_Z}^{4}+8\right)^{2}+6 x^{2}+8 x -6}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{4}+8\right) \ln \left(-\frac{8 \RootOf \left(\textit{\_Z}^{4}+8\right)^{5} x^{2}-12 \RootOf \left(\textit{\_Z}^{4}+8\right)^{5} x -8 \RootOf \left(\textit{\_Z}^{4}+8\right)^{5}+50 \RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{2}-7 \RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x -50 \RootOf \left(\textit{\_Z}^{4}+8\right)^{3}-200 \sqrt{x^{3}-x}\, \RootOf \left(\textit{\_Z}^{4}+8\right)^{2}+78 \RootOf \left(\textit{\_Z}^{4}+8\right) x^{2}+104 \RootOf \left(\textit{\_Z}^{4}+8\right) x -78 \RootOf \left(\textit{\_Z}^{4}+8\right)-56 \sqrt{x^{3}-x}}{2 \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-3 \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x -2 \RootOf \left(\textit{\_Z}^{4}+8\right)^{2}-6 x^{2}-8 x +6}\right)}{4}$&$476$\\ \hline \end{longtable}"," ",0,"(1+x)^(1/2)*(2-2*x)^(1/2)*(-x)^(1/2)/(x^3-x)^(1/2)*EllipticF((1+x)^(1/2),1/2*2^(1/2))+1/4*2^(1/2)*sum(_alpha*(_alpha^3-_alpha^2+_alpha-1)*(1+x)^(1/2)*(1-x)^(1/2)*(-x)^(1/2)/(x*(x^2-1))^(1/2)*EllipticPi((1+x)^(1/2),-1/2*_alpha^3+1/2*_alpha^2-1/2*_alpha+1/2,1/2*2^(1/2)),_alpha=RootOf(_Z^4+1))","C"
1139,1,307,71,1.700000," ","int((x^2-1)/(x^2+x+1)/(x^4+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x -3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{4}+x^{2}\right)^{\frac{2}{3}}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+2 x^{3}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x +3 \left(x^{4}+x^{2}\right)^{\frac{2}{3}}+3 x \left(x^{4}+x^{2}\right)^{\frac{1}{3}}-x^{2}+2 x}{x \left(x^{2}+x +1\right)}\right)+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x -3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{4}+x^{2}\right)^{\frac{2}{3}}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{4}+x^{2}\right)^{\frac{1}{3}} x +3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-x^{3}+3 x \left(x^{4}+x^{2}\right)^{\frac{1}{3}}-x^{2}-x}{x \left(x^{2}+x +1\right)}\right)$&$307$\\ \hline \end{longtable}"," ",0,"-ln((RootOf(_Z^2-_Z+1)^2*x^3-2*RootOf(_Z^2-_Z+1)^2*x^2-3*RootOf(_Z^2-_Z+1)*x^3+RootOf(_Z^2-_Z+1)^2*x-3*RootOf(_Z^2-_Z+1)*(x^4+x^2)^(2/3)+3*RootOf(_Z^2-_Z+1)*x^2+2*x^3-3*RootOf(_Z^2-_Z+1)*x+3*(x^4+x^2)^(2/3)+3*x*(x^4+x^2)^(1/3)-x^2+2*x)/x/(x^2+x+1))+RootOf(_Z^2-_Z+1)*ln(-(RootOf(_Z^2-_Z+1)^2*x^3-2*RootOf(_Z^2-_Z+1)^2*x^2+RootOf(_Z^2-_Z+1)^2*x-3*RootOf(_Z^2-_Z+1)*(x^4+x^2)^(2/3)-3*RootOf(_Z^2-_Z+1)*(x^4+x^2)^(1/3)*x+3*RootOf(_Z^2-_Z+1)*x^2-x^3+3*x*(x^4+x^2)^(1/3)-x^2-x)/x/(x^2+x+1))","C"
1140,0,0,65,0.009000," ","int((a*x^4-2*b)*(a*x^4+b)^(3/4)/x^8,x)","\[\int \frac{\left(a \,x^{4}-2 b \right) \left(a \,x^{4}+b \right)^{\frac{3}{4}}}{x^{8}}\, dx\]"," ",0,"int((a*x^4-2*b)*(a*x^4+b)^(3/4)/x^8,x)","F"
1141,0,0,69,0.008000," ","int((a*x^4-b)^(3/4)*(2*a*x^4-b)/x^8,x)","\[\int \frac{\left(a \,x^{4}-b \right)^{\frac{3}{4}} \left(2 a \,x^{4}-b \right)}{x^{8}}\, dx\]"," ",0,"int((a*x^4-b)^(3/4)*(2*a*x^4-b)/x^8,x)","F"
1142,1,140,79,0.253000," ","int((p*x^2-q)*(a*p*x^2+a*q+b*x)*(p^2*x^4+q^2)^(1/2)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{p b \sqrt{p^{2} x^{4}+q^{2}}}{2}-\frac{b \,p^{2} q \ln \left(\frac{p^{2} x^{2}}{\sqrt{p^{2}}}+\sqrt{p^{2} x^{4}+q^{2}}\right)}{2 \sqrt{p^{2}}}+\frac{b q \sqrt{p^{2} x^{4}+q^{2}}}{2 x^{2}}-\frac{p b \,q^{2} \ln \left(\frac{2 q^{2}+2 \sqrt{q^{2}}\, \sqrt{p^{2} x^{4}+q^{2}}}{x^{2}}\right)}{2 \sqrt{q^{2}}}+\frac{a \left(p^{2} x^{4}+q^{2}\right)^{\frac{3}{2}}}{3 x^{3}}$&$140$\\ risch&$\frac{\sqrt{p^{2} x^{4}+q^{2}}\, q \left(2 a q +3 b x \right)}{6 x^{3}}+\frac{a \,p^{2} x \sqrt{p^{2} x^{4}+q^{2}}}{3}+\frac{p b \sqrt{p^{2} x^{4}+q^{2}}}{2}-\frac{b \,p^{2} q \ln \left(\frac{p^{2} x^{2}}{\sqrt{p^{2}}}+\sqrt{p^{2} x^{4}+q^{2}}\right)}{2 \sqrt{p^{2}}}-\frac{p b \,q^{2} \ln \left(\frac{2 q^{2}+2 \sqrt{q^{2}}\, \sqrt{p^{2} x^{4}+q^{2}}}{x^{2}}\right)}{2 \sqrt{q^{2}}}$&$149$\\ default&$a \,p^{2} \left(\frac{x \sqrt{p^{2} x^{4}+q^{2}}}{3}+\frac{2 q^{2} \sqrt{1-\frac{i p \,x^{2}}{q}}\, \sqrt{1+\frac{i p \,x^{2}}{q}}\, \EllipticF \left(x \sqrt{\frac{i p}{q}}, i\right)}{3 \sqrt{\frac{i p}{q}}\, \sqrt{p^{2} x^{4}+q^{2}}}\right)-a \,q^{2} \left(-\frac{\sqrt{p^{2} x^{4}+q^{2}}}{3 x^{3}}+\frac{2 p^{2} \sqrt{1-\frac{i p \,x^{2}}{q}}\, \sqrt{1+\frac{i p \,x^{2}}{q}}\, \EllipticF \left(x \sqrt{\frac{i p}{q}}, i\right)}{3 \sqrt{\frac{i p}{q}}\, \sqrt{p^{2} x^{4}+q^{2}}}\right)+p b \left(\frac{\sqrt{p^{2} x^{4}+q^{2}}}{2}-\frac{q^{2} \ln \left(\frac{2 q^{2}+2 \sqrt{q^{2}}\, \sqrt{p^{2} x^{4}+q^{2}}}{x^{2}}\right)}{2 \sqrt{q^{2}}}\right)-q b \left(-\frac{\left(p^{2} x^{4}+q^{2}\right)^{\frac{3}{2}}}{2 q^{2} x^{2}}+\frac{p^{2} x^{2} \sqrt{p^{2} x^{4}+q^{2}}}{2 q^{2}}+\frac{p^{2} \ln \left(\frac{p^{2} x^{2}}{\sqrt{p^{2}}}+\sqrt{p^{2} x^{4}+q^{2}}\right)}{2 \sqrt{p^{2}}}\right)$&$334$\\ \hline \end{longtable}"," ",0,"1/2*p*b*(p^2*x^4+q^2)^(1/2)-1/2*b*p^2*q*ln(p^2*x^2/(p^2)^(1/2)+(p^2*x^4+q^2)^(1/2))/(p^2)^(1/2)+1/2*b*q/x^2*(p^2*x^4+q^2)^(1/2)-1/2*p*b*q^2/(q^2)^(1/2)*ln((2*q^2+2*(q^2)^(1/2)*(p^2*x^4+q^2)^(1/2))/x^2)+1/3*a*(p^2*x^4+q^2)^(3/2)/x^3","A"
1143,1,368,71,3.424000," ","int((2*x^3-1)/(x^3+x+1)/(x^5+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(\frac{-7 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{4}+22 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{4}+14 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}-16 x^{4}+21 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{5}+x^{2}\right)^{\frac{2}{3}}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{5}+x^{2}\right)^{\frac{1}{3}} x -7 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x -23 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-24 \left(x^{5}+x^{2}\right)^{\frac{2}{3}}-21 x \left(x^{5}+x^{2}\right)^{\frac{1}{3}}+22 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x +8 x^{2}-16 x}{x \left(x^{3}+x +1\right)}\right)+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\frac{99 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{4}+257 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{4}-198 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}+158 x^{4}+474 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{5}+x^{2}\right)^{\frac{2}{3}}-297 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{5}+x^{2}\right)^{\frac{1}{3}} x +99 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x -217 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-771 \left(x^{5}+x^{2}\right)^{\frac{2}{3}}-474 x \left(x^{5}+x^{2}\right)^{\frac{1}{3}}+257 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x +158 x^{2}+158 x}{x \left(x^{3}+x +1\right)}\right)$&$368$\\ \hline \end{longtable}"," ",0,"-ln((-7*RootOf(_Z^2-_Z+1)^2*x^4+22*RootOf(_Z^2-_Z+1)*x^4+14*RootOf(_Z^2-_Z+1)^2*x^2-16*x^4+21*RootOf(_Z^2-_Z+1)*(x^5+x^2)^(2/3)-3*RootOf(_Z^2-_Z+1)*(x^5+x^2)^(1/3)*x-7*RootOf(_Z^2-_Z+1)^2*x-23*RootOf(_Z^2-_Z+1)*x^2-24*(x^5+x^2)^(2/3)-21*x*(x^5+x^2)^(1/3)+22*RootOf(_Z^2-_Z+1)*x+8*x^2-16*x)/x/(x^3+x+1))+RootOf(_Z^2-_Z+1)*ln((99*RootOf(_Z^2-_Z+1)^2*x^4+257*RootOf(_Z^2-_Z+1)*x^4-198*RootOf(_Z^2-_Z+1)^2*x^2+158*x^4+474*RootOf(_Z^2-_Z+1)*(x^5+x^2)^(2/3)-297*RootOf(_Z^2-_Z+1)*(x^5+x^2)^(1/3)*x+99*RootOf(_Z^2-_Z+1)^2*x-217*RootOf(_Z^2-_Z+1)*x^2-771*(x^5+x^2)^(2/3)-474*x*(x^5+x^2)^(1/3)+257*RootOf(_Z^2-_Z+1)*x+158*x^2+158*x)/x/(x^3+x+1))","C"
1144,1,539,71,7.682000," ","int((3*x^5+2)/(x^5+x^2-1)/(x^6-x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\frac{62685010802979296884 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{5}-494135918029415995819 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{5}+64534903374029948502 x^{5}-485808833723089550851 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}+433300799797487350553 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-x \right)^{\frac{2}{3}}-433300799797487350553 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-x \right)^{\frac{1}{3}} x +487658726294140202469 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+427751122084335395699 \left(x^{6}-x \right)^{\frac{2}{3}}-427751122084335395699 x \left(x^{6}-x \right)^{\frac{1}{3}}-62685010802979296884 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}-56207819067703503534 x^{2}+494135918029415995819 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-64534903374029948502}{x^{5}+x^{2}-1}\right)-\ln \left(\frac{-11150604486509769179735404 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{5}-167804753076351270129207425 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{5}-624632666348769715120455774 x^{5}+86417184770450711142949381 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}+971392776987982024558606028 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-x \right)^{\frac{2}{3}}-971392776987982024558606028 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-x \right)^{\frac{1}{3}} x +706020234654670274106713818 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+434526704299398906631777541 \left(x^{6}-x \right)^{\frac{2}{3}}-434526704299398906631777541 x \left(x^{6}-x \right)^{\frac{1}{3}}+11150604486509769179735404 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}-92538172792410328165993448 x^{2}+167804753076351270129207425 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+624632666348769715120455774}{x^{5}+x^{2}-1}\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+\ln \left(\frac{-11150604486509769179735404 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{5}-167804753076351270129207425 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{5}-624632666348769715120455774 x^{5}+86417184770450711142949381 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}+971392776987982024558606028 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-x \right)^{\frac{2}{3}}-971392776987982024558606028 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-x \right)^{\frac{1}{3}} x +706020234654670274106713818 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+434526704299398906631777541 \left(x^{6}-x \right)^{\frac{2}{3}}-434526704299398906631777541 x \left(x^{6}-x \right)^{\frac{1}{3}}+11150604486509769179735404 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}-92538172792410328165993448 x^{2}+167804753076351270129207425 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+624632666348769715120455774}{x^{5}+x^{2}-1}\right)$&$539$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2-_Z+1)*ln((62685010802979296884*RootOf(_Z^2-_Z+1)^2*x^5-494135918029415995819*RootOf(_Z^2-_Z+1)*x^5+64534903374029948502*x^5-485808833723089550851*RootOf(_Z^2-_Z+1)^2*x^2+433300799797487350553*RootOf(_Z^2-_Z+1)*(x^6-x)^(2/3)-433300799797487350553*RootOf(_Z^2-_Z+1)*(x^6-x)^(1/3)*x+487658726294140202469*RootOf(_Z^2-_Z+1)*x^2+427751122084335395699*(x^6-x)^(2/3)-427751122084335395699*x*(x^6-x)^(1/3)-62685010802979296884*RootOf(_Z^2-_Z+1)^2-56207819067703503534*x^2+494135918029415995819*RootOf(_Z^2-_Z+1)-64534903374029948502)/(x^5+x^2-1))-ln((-11150604486509769179735404*RootOf(_Z^2-_Z+1)^2*x^5-167804753076351270129207425*RootOf(_Z^2-_Z+1)*x^5-624632666348769715120455774*x^5+86417184770450711142949381*RootOf(_Z^2-_Z+1)^2*x^2+971392776987982024558606028*RootOf(_Z^2-_Z+1)*(x^6-x)^(2/3)-971392776987982024558606028*RootOf(_Z^2-_Z+1)*(x^6-x)^(1/3)*x+706020234654670274106713818*RootOf(_Z^2-_Z+1)*x^2+434526704299398906631777541*(x^6-x)^(2/3)-434526704299398906631777541*x*(x^6-x)^(1/3)+11150604486509769179735404*RootOf(_Z^2-_Z+1)^2-92538172792410328165993448*x^2+167804753076351270129207425*RootOf(_Z^2-_Z+1)+624632666348769715120455774)/(x^5+x^2-1))*RootOf(_Z^2-_Z+1)+ln((-11150604486509769179735404*RootOf(_Z^2-_Z+1)^2*x^5-167804753076351270129207425*RootOf(_Z^2-_Z+1)*x^5-624632666348769715120455774*x^5+86417184770450711142949381*RootOf(_Z^2-_Z+1)^2*x^2+971392776987982024558606028*RootOf(_Z^2-_Z+1)*(x^6-x)^(2/3)-971392776987982024558606028*RootOf(_Z^2-_Z+1)*(x^6-x)^(1/3)*x+706020234654670274106713818*RootOf(_Z^2-_Z+1)*x^2+434526704299398906631777541*(x^6-x)^(2/3)-434526704299398906631777541*x*(x^6-x)^(1/3)+11150604486509769179735404*RootOf(_Z^2-_Z+1)^2-92538172792410328165993448*x^2+167804753076351270129207425*RootOf(_Z^2-_Z+1)+624632666348769715120455774)/(x^5+x^2-1))","C"
1145,1,96,67,1.156000," ","int((x^6-1)^(1/2)*(2*x^6-1)^2/x^4/(4*x^6-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{6}-1}\, \left(x^{6}+2\right)}{6 x^{3}}+\frac{5 \ln \left(-x^{3}+\sqrt{x^{6}-1}\right)}{12}+\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{6}+6 x^{3} \sqrt{x^{6}-1}-\RootOf \left(\textit{\_Z}^{2}+3\right)}{\left(2 x^{3}-1\right) \left(2 x^{3}+1\right)}\right)}{24}$&$96$\\ risch&$\frac{x^{12}+x^{6}-2}{6 x^{3} \sqrt{x^{6}-1}}+\frac{5 \ln \left(x^{3}-\sqrt{x^{6}-1}\right)}{12}-\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{6}+6 x^{3} \sqrt{x^{6}-1}+\RootOf \left(\textit{\_Z}^{2}+3\right)}{\left(2 x^{3}-1\right) \left(2 x^{3}+1\right)}\right)}{24}$&$97$\\ \hline \end{longtable}"," ",0,"1/6*(x^6-1)^(1/2)*(x^6+2)/x^3+5/12*ln(-x^3+(x^6-1)^(1/2))+1/24*RootOf(_Z^2+3)*ln(-(-2*RootOf(_Z^2+3)*x^6+6*x^3*(x^6-1)^(1/2)-RootOf(_Z^2+3))/(2*x^3-1)/(2*x^3+1))","C"
1146,1,1514,11,16.572000," ","int((x^4+1)/(x^4-1)^(1/4)/(x^8+x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1514$\\ \hline \end{longtable}"," ",0,"-1/12*RootOf(_Z^2+RootOf(_Z^8+27)^2)*ln(-36*(-2*RootOf(_Z^2+RootOf(_Z^8+27)^2)*RootOf(_Z^8+27)^8*x^4+6*(x^4-1)^(1/2)*RootOf(_Z^2+RootOf(_Z^8+27)^2)*RootOf(_Z^8+27)^6*x^2-24*(x^4-1)^(1/4)*RootOf(_Z^8+27)^6*x^3-39*RootOf(_Z^2+RootOf(_Z^8+27)^2)*RootOf(_Z^8+27)^4*x^4+54*RootOf(_Z^8+27)^4*(x^4-1)^(3/4)*x+90*(x^4-1)^(1/2)*RootOf(_Z^2+RootOf(_Z^8+27)^2)*RootOf(_Z^8+27)^2*x^2-108*(x^4-1)^(1/4)*RootOf(_Z^8+27)^2*x^3+12*RootOf(_Z^2+RootOf(_Z^8+27)^2)*RootOf(_Z^8+27)^4-135*x^4*RootOf(_Z^2+RootOf(_Z^8+27)^2)+54*(x^4-1)^(3/4)*x+54*RootOf(_Z^2+RootOf(_Z^8+27)^2))/(RootOf(_Z^8+27)^4*x^2+6-3*x^2)/(RootOf(_Z^8+27)^4*x+3*x-6)/(RootOf(_Z^8+27)^4*x+3*x+6))-1/12*RootOf(_Z^8+27)*ln(-36*(-2*RootOf(_Z^8+27)^9*x^4-6*(x^4-1)^(1/2)*RootOf(_Z^8+27)^7*x^2+24*(x^4-1)^(1/4)*RootOf(_Z^8+27)^6*x^3-39*RootOf(_Z^8+27)^5*x^4+54*RootOf(_Z^8+27)^4*(x^4-1)^(3/4)*x-90*(x^4-1)^(1/2)*RootOf(_Z^8+27)^3*x^2+108*(x^4-1)^(1/4)*RootOf(_Z^8+27)^2*x^3+12*RootOf(_Z^8+27)^5-135*RootOf(_Z^8+27)*x^4+54*(x^4-1)^(3/4)*x+54*RootOf(_Z^8+27))/(RootOf(_Z^8+27)^4*x^2+6-3*x^2)/(RootOf(_Z^8+27)^4*x+3*x-6)/(RootOf(_Z^8+27)^4*x+3*x+6))+1/324*RootOf(_Z^8+27)^7*RootOf(_Z^2+RootOf(_Z^8+27)^2)*RootOf(_Z^2-RootOf(_Z^8+27)*RootOf(_Z^2+RootOf(_Z^8+27)^2))*ln(36*(RootOf(_Z^2+RootOf(_Z^8+27)^2)*RootOf(_Z^2-RootOf(_Z^8+27)*RootOf(_Z^2+RootOf(_Z^8+27)^2))*RootOf(_Z^8+27)^11*x^4-12*x^4*RootOf(_Z^8+27)^7*RootOf(_Z^2+RootOf(_Z^8+27)^2)*RootOf(_Z^2-RootOf(_Z^8+27)*RootOf(_Z^2+RootOf(_Z^8+27)^2))-36*(x^4-1)^(1/4)*RootOf(_Z^8+27)^5*RootOf(_Z^2+RootOf(_Z^8+27)^2)*x^3+6*RootOf(_Z^8+27)^7*RootOf(_Z^2+RootOf(_Z^8+27)^2)*RootOf(_Z^2-RootOf(_Z^8+27)*RootOf(_Z^2+RootOf(_Z^8+27)^2))-45*RootOf(_Z^2+RootOf(_Z^8+27)^2)*RootOf(_Z^2-RootOf(_Z^8+27)*RootOf(_Z^2+RootOf(_Z^8+27)^2))*RootOf(_Z^8+27)^3*x^4+108*RootOf(_Z^8+27)^4*(x^4-1)^(3/4)*x+216*(x^4-1)^(1/2)*RootOf(_Z^2-RootOf(_Z^8+27)*RootOf(_Z^2+RootOf(_Z^8+27)^2))*RootOf(_Z^8+27)^2*x^2+324*(x^4-1)^(1/4)*RootOf(_Z^8+27)*RootOf(_Z^2+RootOf(_Z^8+27)^2)*x^3+18*RootOf(_Z^2+RootOf(_Z^8+27)^2)*RootOf(_Z^2-RootOf(_Z^8+27)*RootOf(_Z^2+RootOf(_Z^8+27)^2))*RootOf(_Z^8+27)^3-324*(x^4-1)^(3/4)*x)/(RootOf(_Z^8+27)^4*x^2+3*x^2-6)/(RootOf(_Z^8+27)^4*x-3*x+6)/(RootOf(_Z^8+27)^4*x-3*x-6))-1/12*RootOf(_Z^2-RootOf(_Z^8+27)*RootOf(_Z^2+RootOf(_Z^8+27)^2))*ln(36*(RootOf(_Z^2-RootOf(_Z^8+27)*RootOf(_Z^2+RootOf(_Z^8+27)^2))*RootOf(_Z^8+27)^8*x^4+4*(x^4-1)^(1/2)*RootOf(_Z^8+27)^5*RootOf(_Z^2+RootOf(_Z^8+27)^2)*RootOf(_Z^2-RootOf(_Z^8+27)*RootOf(_Z^2+RootOf(_Z^8+27)^2))*x^2+12*(x^4-1)^(1/4)*RootOf(_Z^8+27)^5*RootOf(_Z^2+RootOf(_Z^8+27)^2)*x^3-30*RootOf(_Z^2-RootOf(_Z^8+27)*RootOf(_Z^2+RootOf(_Z^8+27)^2))*RootOf(_Z^8+27)^4*x^4+48*RootOf(_Z^8+27)^4*(x^4-1)^(3/4)*x+108*(x^4-1)^(1/2)*RootOf(_Z^8+27)*RootOf(_Z^2+RootOf(_Z^8+27)^2)*RootOf(_Z^2-RootOf(_Z^8+27)*RootOf(_Z^2+RootOf(_Z^8+27)^2))*x^2-180*(x^4-1)^(1/4)*RootOf(_Z^8+27)*RootOf(_Z^2+RootOf(_Z^8+27)^2)*x^3+6*RootOf(_Z^2-RootOf(_Z^8+27)*RootOf(_Z^2+RootOf(_Z^8+27)^2))*RootOf(_Z^8+27)^4+225*x^4*RootOf(_Z^2-RootOf(_Z^8+27)*RootOf(_Z^2+RootOf(_Z^8+27)^2))-216*(x^4-1)^(3/4)*x-90*RootOf(_Z^2-RootOf(_Z^8+27)*RootOf(_Z^2+RootOf(_Z^8+27)^2)))/(RootOf(_Z^8+27)^4*x^2+3*x^2-6)/(RootOf(_Z^8+27)^4*x-3*x+6)/(RootOf(_Z^8+27)^4*x-3*x-6))","B"
1147,0,0,11,180.000000," ","int((2*x^4-1)/(x^4-1)^(1/4)/(2*x^8-x^4-2),x)","\[\int \frac{2 x^{4}-1}{\left(x^{4}-1\right)^{\frac{1}{4}} \left(2 x^{8}-x^{4}-2\right)}\, dx\]"," ",0,"int((2*x^4-1)/(x^4-1)^(1/4)/(2*x^8-x^4-2),x)","F"
1148,1,474,32,5.631000," ","int((2*x^8+x^4-1)/(x^4-1)^(1/4)/(x^8-x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}-1}\, x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \left(x^{4}-1\right)^{\frac{3}{4}} x -2 x^{3} \left(x^{4}-1\right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{2}-\frac{\ln \left(2 \left(x^{4}-1\right)^{\frac{3}{4}} x -2 x^{2} \sqrt{x^{4}-1}+2 x^{3} \left(x^{4}-1\right)^{\frac{1}{4}}-2 x^{4}+1\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{2}+3 \RootOf \left(\textit{\_Z}^{2}+1\right)\right) \ln \left(-\frac{-6 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{4}-1\right)^{\frac{1}{4}} x^{7}+5 \RootOf \left(\textit{\_Z}^{2}+3 \RootOf \left(\textit{\_Z}^{2}+1\right)\right) x^{8}+6 \left(x^{4}-1\right)^{\frac{3}{4}} x^{5}+6 \RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{2}+3 \RootOf \left(\textit{\_Z}^{2}+1\right)\right) \sqrt{x^{4}-1}\, x^{2}+12 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{4}-1\right)^{\frac{1}{4}} x^{3}-5 \RootOf \left(\textit{\_Z}^{2}+3 \RootOf \left(\textit{\_Z}^{2}+1\right)\right) x^{4}+6 \left(x^{4}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{2}+3 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{x^{8}-x^{4}+1}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{2}+3 \RootOf \left(\textit{\_Z}^{2}+1\right)\right) \ln \left(-\frac{-5 \RootOf \left(\textit{\_Z}^{2}+3 \RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) x^{8}+6 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{4}-1\right)^{\frac{1}{4}} x^{7}+6 \left(x^{4}-1\right)^{\frac{3}{4}} x^{5}+5 \RootOf \left(\textit{\_Z}^{2}+3 \RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-6 \RootOf \left(\textit{\_Z}^{2}+3 \RootOf \left(\textit{\_Z}^{2}+1\right)\right) \sqrt{x^{4}-1}\, x^{2}-12 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{4}-1\right)^{\frac{1}{4}} x^{3}+6 \left(x^{4}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{2}+3 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{x^{8}-x^{4}+1}\right)}{4}$&$474$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^2+1)*ln(-2*RootOf(_Z^2+1)*(x^4-1)^(1/2)*x^2+2*RootOf(_Z^2+1)*x^4+2*(x^4-1)^(3/4)*x-2*x^3*(x^4-1)^(1/4)-RootOf(_Z^2+1))-1/2*ln(2*(x^4-1)^(3/4)*x-2*x^2*(x^4-1)^(1/2)+2*x^3*(x^4-1)^(1/4)-2*x^4+1)-1/4*RootOf(_Z^2+3*RootOf(_Z^2+1))*ln(-(-6*RootOf(_Z^2+1)*(x^4-1)^(1/4)*x^7+5*RootOf(_Z^2+3*RootOf(_Z^2+1))*x^8+6*(x^4-1)^(3/4)*x^5+6*RootOf(_Z^2+1)*RootOf(_Z^2+3*RootOf(_Z^2+1))*(x^4-1)^(1/2)*x^2+12*RootOf(_Z^2+1)*(x^4-1)^(1/4)*x^3-5*RootOf(_Z^2+3*RootOf(_Z^2+1))*x^4+6*(x^4-1)^(3/4)*x-RootOf(_Z^2+3*RootOf(_Z^2+1)))/(x^8-x^4+1))+1/4*RootOf(_Z^2+1)*RootOf(_Z^2+3*RootOf(_Z^2+1))*ln(-(-5*RootOf(_Z^2+3*RootOf(_Z^2+1))*RootOf(_Z^2+1)*x^8+6*RootOf(_Z^2+1)*(x^4-1)^(1/4)*x^7+6*(x^4-1)^(3/4)*x^5+5*RootOf(_Z^2+3*RootOf(_Z^2+1))*RootOf(_Z^2+1)*x^4-6*RootOf(_Z^2+3*RootOf(_Z^2+1))*(x^4-1)^(1/2)*x^2-12*RootOf(_Z^2+1)*(x^4-1)^(1/4)*x^3+6*(x^4-1)^(3/4)*x+RootOf(_Z^2+1)*RootOf(_Z^2+3*RootOf(_Z^2+1)))/(x^8-x^4+1))","B"
1149,0,0,14,0.035000," ","int(1/(a*x^4+b*x^2)^(1/4)/(a*x^8-2*b),x)","\[\int \frac{1}{\left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}} \left(a \,x^{8}-2 b \right)}\, dx\]"," ",0,"int(1/(a*x^4+b*x^2)^(1/4)/(a*x^8-2*b),x)","F"
1150,0,0,14,0.001000," ","int(1/(a*x^4+b*x^2)^(1/4)/(a*x^8-2*b),x)","\[\int \frac{1}{\left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}} \left(a \,x^{8}-2 b \right)}\, dx\]"," ",0,"int(1/(a*x^4+b*x^2)^(1/4)/(a*x^8-2*b),x)","F"
1151,1,235,77,13.552000," ","int((x^5+4)*(2*x^5+x^4-2)^(1/4)*(2*x^10+x^8-4*x^5+2)/x^10/(x^5-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(2 x^{5}+x^{4}-2\right)^{\frac{1}{4}} \left(10 x^{10}+x^{9}+43 x^{8}-20 x^{5}-x^{4}+10\right)}{45 x^{9}}+\ln \left(-\frac{-x^{5}+\left(2 x^{5}+x^{4}-2\right)^{\frac{3}{4}} x -\sqrt{2 x^{5}+x^{4}-2}\, x^{2}+\left(2 x^{5}+x^{4}-2\right)^{\frac{1}{4}} x^{3}-x^{4}+1}{\left(-1+x \right) \left(x^{4}+x^{3}+x^{2}+x +1\right)}\right)+\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{5}+\RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{2 x^{5}+x^{4}-2}\, x^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-\left(2 x^{5}+x^{4}-2\right)^{\frac{3}{4}} x +\left(2 x^{5}+x^{4}-2\right)^{\frac{1}{4}} x^{3}+\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(-1+x \right) \left(x^{4}+x^{3}+x^{2}+x +1\right)}\right)$&$235$\\ risch&$\frac{\frac{116}{15} x^{13}+\frac{172}{45} x^{12}-\frac{32}{15} x^{9}-\frac{116}{15} x^{8}+\frac{16}{15} x^{4}-\frac{16}{3} x^{10}+\frac{16}{3} x^{5}-\frac{16}{9}+\frac{16}{9} x^{15}+\frac{16}{15} x^{14}}{x^{9} \left(2 x^{5}+x^{4}-2\right)^{\frac{3}{4}}}+\frac{\left(-\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-4 x^{15}-8 x^{14}-4 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(8 x^{15}+12 x^{14}+6 x^{13}+x^{12}-24 x^{10}-24 x^{9}-6 x^{8}+24 x^{5}+12 x^{4}-8\right)^{\frac{1}{4}} x^{11}-5 x^{13}-4 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(8 x^{15}+12 x^{14}+6 x^{13}+x^{12}-24 x^{10}-24 x^{9}-6 x^{8}+24 x^{5}+12 x^{4}-8\right)^{\frac{1}{4}} x^{10}-x^{12}-\RootOf \left(\textit{\_Z}^{2}+1\right) \left(8 x^{15}+12 x^{14}+6 x^{13}+x^{12}-24 x^{10}-24 x^{9}-6 x^{8}+24 x^{5}+12 x^{4}-8\right)^{\frac{1}{4}} x^{9}+12 x^{10}+2 \sqrt{8 x^{15}+12 x^{14}+6 x^{13}+x^{12}-24 x^{10}-24 x^{9}-6 x^{8}+24 x^{5}+12 x^{4}-8}\, x^{7}+16 x^{9}+\sqrt{8 x^{15}+12 x^{14}+6 x^{13}+x^{12}-24 x^{10}-24 x^{9}-6 x^{8}+24 x^{5}+12 x^{4}-8}\, x^{6}+8 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(8 x^{15}+12 x^{14}+6 x^{13}+x^{12}-24 x^{10}-24 x^{9}-6 x^{8}+24 x^{5}+12 x^{4}-8\right)^{\frac{1}{4}} x^{6}+5 x^{8}+\RootOf \left(\textit{\_Z}^{2}+1\right) \left(8 x^{15}+12 x^{14}+6 x^{13}+x^{12}-24 x^{10}-24 x^{9}-6 x^{8}+24 x^{5}+12 x^{4}-8\right)^{\frac{3}{4}} x^{3}+4 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(8 x^{15}+12 x^{14}+6 x^{13}+x^{12}-24 x^{10}-24 x^{9}-6 x^{8}+24 x^{5}+12 x^{4}-8\right)^{\frac{1}{4}} x^{5}-12 x^{5}-2 \sqrt{8 x^{15}+12 x^{14}+6 x^{13}+x^{12}-24 x^{10}-24 x^{9}-6 x^{8}+24 x^{5}+12 x^{4}-8}\, x^{2}-8 x^{4}-4 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(8 x^{15}+12 x^{14}+6 x^{13}+x^{12}-24 x^{10}-24 x^{9}-6 x^{8}+24 x^{5}+12 x^{4}-8\right)^{\frac{1}{4}} x +4}{\left(-1+x \right) \left(x^{4}+x^{3}+x^{2}+x +1\right) \left(2 x^{5}+x^{4}-2\right)^{2}}\right)-\ln \left(-\frac{4 x^{15}+8 x^{14}+5 x^{13}+4 \left(8 x^{15}+12 x^{14}+6 x^{13}+x^{12}-24 x^{10}-24 x^{9}-6 x^{8}+24 x^{5}+12 x^{4}-8\right)^{\frac{1}{4}} x^{11}+x^{12}+4 \left(8 x^{15}+12 x^{14}+6 x^{13}+x^{12}-24 x^{10}-24 x^{9}-6 x^{8}+24 x^{5}+12 x^{4}-8\right)^{\frac{1}{4}} x^{10}+\left(8 x^{15}+12 x^{14}+6 x^{13}+x^{12}-24 x^{10}-24 x^{9}-6 x^{8}+24 x^{5}+12 x^{4}-8\right)^{\frac{1}{4}} x^{9}-12 x^{10}+2 \sqrt{8 x^{15}+12 x^{14}+6 x^{13}+x^{12}-24 x^{10}-24 x^{9}-6 x^{8}+24 x^{5}+12 x^{4}-8}\, x^{7}-16 x^{9}+\sqrt{8 x^{15}+12 x^{14}+6 x^{13}+x^{12}-24 x^{10}-24 x^{9}-6 x^{8}+24 x^{5}+12 x^{4}-8}\, x^{6}-5 x^{8}-8 \left(8 x^{15}+12 x^{14}+6 x^{13}+x^{12}-24 x^{10}-24 x^{9}-6 x^{8}+24 x^{5}+12 x^{4}-8\right)^{\frac{1}{4}} x^{6}+\left(8 x^{15}+12 x^{14}+6 x^{13}+x^{12}-24 x^{10}-24 x^{9}-6 x^{8}+24 x^{5}+12 x^{4}-8\right)^{\frac{3}{4}} x^{3}-4 \left(8 x^{15}+12 x^{14}+6 x^{13}+x^{12}-24 x^{10}-24 x^{9}-6 x^{8}+24 x^{5}+12 x^{4}-8\right)^{\frac{1}{4}} x^{5}+12 x^{5}-2 \sqrt{8 x^{15}+12 x^{14}+6 x^{13}+x^{12}-24 x^{10}-24 x^{9}-6 x^{8}+24 x^{5}+12 x^{4}-8}\, x^{2}+8 x^{4}+4 \left(8 x^{15}+12 x^{14}+6 x^{13}+x^{12}-24 x^{10}-24 x^{9}-6 x^{8}+24 x^{5}+12 x^{4}-8\right)^{\frac{1}{4}} x -4}{\left(-1+x \right) \left(x^{4}+x^{3}+x^{2}+x +1\right) \left(2 x^{5}+x^{4}-2\right)^{2}}\right)\right) \left(\left(2 x^{5}+x^{4}-2\right)^{3}\right)^{\frac{1}{4}}}{\left(2 x^{5}+x^{4}-2\right)^{\frac{3}{4}}}$&$1337$\\ \hline \end{longtable}"," ",0,"4/45*(2*x^5+x^4-2)^(1/4)*(10*x^10+x^9+43*x^8-20*x^5-x^4+10)/x^9+ln(-(-x^5+(2*x^5+x^4-2)^(3/4)*x-(2*x^5+x^4-2)^(1/2)*x^2+(2*x^5+x^4-2)^(1/4)*x^3-x^4+1)/(-1+x)/(x^4+x^3+x^2+x+1))+RootOf(_Z^2+1)*ln((-RootOf(_Z^2+1)*x^5+RootOf(_Z^2+1)*(2*x^5+x^4-2)^(1/2)*x^2-RootOf(_Z^2+1)*x^4-(2*x^5+x^4-2)^(3/4)*x+(2*x^5+x^4-2)^(1/4)*x^3+RootOf(_Z^2+1))/(-1+x)/(x^4+x^3+x^2+x+1))","C"
1152,1,99,61,0.938000," ","int((x^12+1)/(x^4+1)^(1/2)/(x^12-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\ln \left(-1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{12}+\frac{\arctan \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{6}-\frac{\ln \left(1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{12}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{x^{4}+1}}{x}\right)}{3}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{x^{4}+1}}{x}\right)}{3}\right) \sqrt{2}}{2}$&$99$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x +\sqrt{x^{4}+1}}{x^{2}+1}\right)}{12}+\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}-2\right) x +\sqrt{x^{4}+1}}{\left(-1+x \right) \left(1+x \right)}\right)}{12}-\frac{\ln \left(-\frac{x^{4}+2 \sqrt{x^{4}+1}\, x +x^{2}+1}{x^{4}-x^{2}+1}\right)}{6}+\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \RootOf \left(\textit{\_Z}^{2}+2\right) x^{4}-\RootOf \left(\textit{\_Z}^{2}+2\right) \RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}-2\right) \RootOf \left(\textit{\_Z}^{2}+2\right)-4 \sqrt{x^{4}+1}\, x}{\left(x^{2}+x +1\right) \left(x^{2}-x +1\right)}\right)}{12}$&$199$\\ default&$\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{3 \sqrt{x^{4}+1}}+\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{3 \sqrt{x^{4}+1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}-\textit{\_Z}^{2}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}+1\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{x^{4}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{2 \left(-1\right)^{\frac{3}{4}} \left(-\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \underline{\hspace{1.25 ex}}\alpha^{2}-i, i\right)}{\sqrt{x^{4}+1}}\right)\right)}{12}+\frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{\arctanh \left(\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x^{2}-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{6}+\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-\frac{\arctanh \left(\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x^{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{6}+\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{\arctanh \left(\frac{\sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \left(x^{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{6}+\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(\frac{\arctanh \left(\frac{\sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}\, \left(x^{2}-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\sqrt{x^{4}+1}}\right)}{2 \sqrt{\frac{1}{2}-\frac{i \sqrt{3}}{2}}}+\frac{\left(-1\right)^{\frac{3}{4}} \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right), i\right)}{\sqrt{x^{4}+1}}\right)}{6}$&$730$\\ \hline \end{longtable}"," ",0,"1/2*(1/12*ln(-1+1/2*2^(1/2)/x*(x^4+1)^(1/2))+1/6*arctan(1/2*2^(1/2)/x*(x^4+1)^(1/2))-1/12*ln(1+1/2*2^(1/2)/x*(x^4+1)^(1/2))+1/3*2^(1/2)*arctan((x^4+1)^(1/2)/x)-1/3*2^(1/2)*arctanh((x^4+1)^(1/2)/x))*2^(1/2)","A"
1153,0,0,71,180.000000," ","int((-x^6+1)^(1/2)*(2*x^6+1)*(x^12-x^8-2*x^6-x^4+x^2+1)/(x^6-1)/(x^18-3*x^12+2*x^6-1),x)","\[\int \frac{\sqrt{-x^{6}+1}\, \left(2 x^{6}+1\right) \left(x^{12}-x^{8}-2 x^{6}-x^{4}+x^{2}+1\right)}{\left(x^{6}-1\right) \left(x^{18}-3 x^{12}+2 x^{6}-1\right)}\, dx\]"," ",0,"int((-x^6+1)^(1/2)*(2*x^6+1)*(x^12-x^8-2*x^6-x^4+x^2+1)/(x^6-1)/(x^18-3*x^12+2*x^6-1),x)","F"
1154,0,0,64,0.023000," ","int((x^2-(x^2+1)^(1/2))/(1+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{x^{2}-\sqrt{x^{2}+1}}{\sqrt{1+\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^2-(x^2+1)^(1/2))/(1+(x^2+1)^(1/2))^(1/2),x)","F"
1155,1,432,68,1.682000," ","int(1/(-1+x)/(x^2-2*x+2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\frac{-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}-2 x +2\right)^{\frac{2}{3}}+8 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x +9 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-9 \left(x^{2}-2 x +2\right)^{\frac{2}{3}}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}-2 x +2\right)^{\frac{1}{3}}-18 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x -2 x^{2}-9 \left(x^{2}-2 x +2\right)^{\frac{1}{3}}+28 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+4 x -7}{\left(-1+x \right)^{2}}\right)}{2}-\frac{\ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}-2 x +2\right)^{\frac{2}{3}}-8 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x +17 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+24 \left(x^{2}-2 x +2\right)^{\frac{2}{3}}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}-2 x +2\right)^{\frac{1}{3}}-34 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +15 x^{2}+24 \left(x^{2}-2 x +2\right)^{\frac{1}{3}}+28 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-30 x +35}{\left(-1+x \right)^{2}}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{2}-\frac{\ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}-2 x +2\right)^{\frac{2}{3}}-8 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x +17 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+24 \left(x^{2}-2 x +2\right)^{\frac{2}{3}}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}-2 x +2\right)^{\frac{1}{3}}-34 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +15 x^{2}+24 \left(x^{2}-2 x +2\right)^{\frac{1}{3}}+28 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-30 x +35}{\left(-1+x \right)^{2}}\right)}{2}$&$432$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^2+_Z+1)*ln((-4*RootOf(_Z^2+_Z+1)^2*x^2+15*RootOf(_Z^2+_Z+1)*(x^2-2*x+2)^(2/3)+8*RootOf(_Z^2+_Z+1)^2*x+9*RootOf(_Z^2+_Z+1)*x^2-9*(x^2-2*x+2)^(2/3)+15*RootOf(_Z^2+_Z+1)*(x^2-2*x+2)^(1/3)-18*RootOf(_Z^2+_Z+1)*x-2*x^2-9*(x^2-2*x+2)^(1/3)+28*RootOf(_Z^2+_Z+1)+4*x-7)/(-1+x)^2)-1/2*ln(-(4*RootOf(_Z^2+_Z+1)^2*x^2+15*RootOf(_Z^2+_Z+1)*(x^2-2*x+2)^(2/3)-8*RootOf(_Z^2+_Z+1)^2*x+17*RootOf(_Z^2+_Z+1)*x^2+24*(x^2-2*x+2)^(2/3)+15*RootOf(_Z^2+_Z+1)*(x^2-2*x+2)^(1/3)-34*RootOf(_Z^2+_Z+1)*x+15*x^2+24*(x^2-2*x+2)^(1/3)+28*RootOf(_Z^2+_Z+1)-30*x+35)/(-1+x)^2)*RootOf(_Z^2+_Z+1)-1/2*ln(-(4*RootOf(_Z^2+_Z+1)^2*x^2+15*RootOf(_Z^2+_Z+1)*(x^2-2*x+2)^(2/3)-8*RootOf(_Z^2+_Z+1)^2*x+17*RootOf(_Z^2+_Z+1)*x^2+24*(x^2-2*x+2)^(2/3)+15*RootOf(_Z^2+_Z+1)*(x^2-2*x+2)^(1/3)-34*RootOf(_Z^2+_Z+1)*x+15*x^2+24*(x^2-2*x+2)^(1/3)+28*RootOf(_Z^2+_Z+1)-30*x+35)/(-1+x)^2)","C"
1156,1,433,68,1.735000," ","int(1/(1+x)/(x^2+2*x+2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+8 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x -15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+2 x +2\right)^{\frac{2}{3}}-9 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-15 \left(x^{2}+2 x +2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-18 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +9 \left(x^{2}+2 x +2\right)^{\frac{2}{3}}+2 x^{2}-28 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+9 \left(x^{2}+2 x +2\right)^{\frac{1}{3}}+4 x +7}{\left(1+x \right)^{2}}\right)}{2}-\frac{\ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+8 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x +15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+2 x +2\right)^{\frac{2}{3}}+17 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+15 \left(x^{2}+2 x +2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+34 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +24 \left(x^{2}+2 x +2\right)^{\frac{2}{3}}+15 x^{2}+28 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+24 \left(x^{2}+2 x +2\right)^{\frac{1}{3}}+30 x +35}{\left(1+x \right)^{2}}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{2}-\frac{\ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+8 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x +15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+2 x +2\right)^{\frac{2}{3}}+17 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+15 \left(x^{2}+2 x +2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+34 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +24 \left(x^{2}+2 x +2\right)^{\frac{2}{3}}+15 x^{2}+28 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+24 \left(x^{2}+2 x +2\right)^{\frac{1}{3}}+30 x +35}{\left(1+x \right)^{2}}\right)}{2}$&$433$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^2+_Z+1)*ln(-(4*RootOf(_Z^2+_Z+1)^2*x^2+8*RootOf(_Z^2+_Z+1)^2*x-15*RootOf(_Z^2+_Z+1)*(x^2+2*x+2)^(2/3)-9*RootOf(_Z^2+_Z+1)*x^2-15*(x^2+2*x+2)^(1/3)*RootOf(_Z^2+_Z+1)-18*RootOf(_Z^2+_Z+1)*x+9*(x^2+2*x+2)^(2/3)+2*x^2-28*RootOf(_Z^2+_Z+1)+9*(x^2+2*x+2)^(1/3)+4*x+7)/(1+x)^2)-1/2*ln(-(4*RootOf(_Z^2+_Z+1)^2*x^2+8*RootOf(_Z^2+_Z+1)^2*x+15*RootOf(_Z^2+_Z+1)*(x^2+2*x+2)^(2/3)+17*RootOf(_Z^2+_Z+1)*x^2+15*(x^2+2*x+2)^(1/3)*RootOf(_Z^2+_Z+1)+34*RootOf(_Z^2+_Z+1)*x+24*(x^2+2*x+2)^(2/3)+15*x^2+28*RootOf(_Z^2+_Z+1)+24*(x^2+2*x+2)^(1/3)+30*x+35)/(1+x)^2)*RootOf(_Z^2+_Z+1)-1/2*ln(-(4*RootOf(_Z^2+_Z+1)^2*x^2+8*RootOf(_Z^2+_Z+1)^2*x+15*RootOf(_Z^2+_Z+1)*(x^2+2*x+2)^(2/3)+17*RootOf(_Z^2+_Z+1)*x^2+15*(x^2+2*x+2)^(1/3)*RootOf(_Z^2+_Z+1)+34*RootOf(_Z^2+_Z+1)*x+24*(x^2+2*x+2)^(2/3)+15*x^2+28*RootOf(_Z^2+_Z+1)+24*(x^2+2*x+2)^(1/3)+30*x+35)/(1+x)^2)","C"
1157,1,84,67,3.634000," ","int((x^3-1)^(2/3)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}} \left(\frac{2 \pi  \sqrt{3}\, x^{3} \hypergeom \left(\left[\frac{1}{3}, 1, 1\right], \left[2, 2\right], x^{3}\right)}{3 \Gamma \left(\frac{2}{3}\right)}-\frac{\left(\frac{3}{2}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right)}\right)}{9 \pi  \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}}}$&$84$\\ trager&$\frac{\left(x^{3}-1\right)^{\frac{2}{3}}}{2}+\frac{\ln \left(\frac{-211 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-3126 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+5502 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-11543 x^{3}-14247 \left(x^{3}-1\right)^{\frac{2}{3}}+19749 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}}+1688 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+5502 \left(x^{3}-1\right)^{\frac{1}{3}}+15935 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+21437}{x^{3}}\right)}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{-1649 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+9683 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+5502 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1266 x^{3}+19749 \left(x^{3}-1\right)^{\frac{2}{3}}-14247 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}}+13192 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+5502 \left(x^{3}-1\right)^{\frac{1}{3}}-6557 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1055}{x^{3}}\right)}{3}$&$239$\\ \hline \end{longtable}"," ",0,"-1/9/Pi*3^(1/2)*GAMMA(2/3)*signum(x^3-1)^(2/3)/(-signum(x^3-1))^(2/3)*(2/3*Pi*3^(1/2)/GAMMA(2/3)*x^3*hypergeom([1/3,1,1],[2,2],x^3)-(3/2-1/6*Pi*3^(1/2)-3/2*ln(3)+3*ln(x)+I*Pi)*Pi*3^(1/2)/GAMMA(2/3))","C"
1158,1,287,69,1.190000," ","int((x^2+3)/(x^2+1)^(1/3)/(x^3-x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}} x +\left(x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+2 \left(x^{2}+1\right)^{\frac{2}{3}} x +2 \left(x^{2}+1\right)^{\frac{1}{3}} x^{2}+x^{3}+x^{2}+1}{x^{3}-x^{2}-1}\right)-\ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}} x +\left(x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-\left(x^{2}+1\right)^{\frac{2}{3}} x -\left(x^{2}+1\right)^{\frac{1}{3}} x^{2}-x^{2}-1}{x^{3}-x^{2}-1}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-\ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}} x +\left(x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-\left(x^{2}+1\right)^{\frac{2}{3}} x -\left(x^{2}+1\right)^{\frac{1}{3}} x^{2}-x^{2}-1}{x^{3}-x^{2}-1}\right)$&$287$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2+_Z+1)*ln(-(RootOf(_Z^2+_Z+1)*(x^2+1)^(2/3)*x+(x^2+1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2+RootOf(_Z^2+_Z+1)*x^3+2*(x^2+1)^(2/3)*x+2*(x^2+1)^(1/3)*x^2+x^3+x^2+1)/(x^3-x^2-1))-ln((RootOf(_Z^2+_Z+1)*(x^2+1)^(2/3)*x+(x^2+1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2+RootOf(_Z^2+_Z+1)*x^3-(x^2+1)^(2/3)*x-(x^2+1)^(1/3)*x^2-x^2-1)/(x^3-x^2-1))*RootOf(_Z^2+_Z+1)-ln((RootOf(_Z^2+_Z+1)*(x^2+1)^(2/3)*x+(x^2+1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2+RootOf(_Z^2+_Z+1)*x^3-(x^2+1)^(2/3)*x-(x^2+1)^(1/3)*x^2-x^2-1)/(x^3-x^2-1))","C"
1159,0,0,74,0.031000," ","int((-2-(-1+k)*(1+k)*x+2*k^2*x^2)/((-x^2+1)*(-k^2*x^2+1))^(1/4)/(-1+d-(3+d)*x-(d*k^2+3)*x^2+(d*k^2-1)*x^3),x)","\[\int \frac{-2-\left(-1+k \right) \left(1+k \right) x +2 k^{2} x^{2}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{1}{4}} \left(-1+d -\left(3+d \right) x -\left(d \,k^{2}+3\right) x^{2}+\left(d \,k^{2}-1\right) x^{3}\right)}\, dx\]"," ",0,"int((-2-(-1+k)*(1+k)*x+2*k^2*x^2)/((-x^2+1)*(-k^2*x^2+1))^(1/4)/(-1+d-(3+d)*x-(d*k^2+3)*x^2+(d*k^2-1)*x^3),x)","F"
1160,0,0,74,0.030000," ","int((-2+(-1+k)*(1+k)*x+2*k^2*x^2)/((-x^2+1)*(-k^2*x^2+1))^(1/4)/(1-d-(3+d)*x+(d*k^2+3)*x^2+(d*k^2-1)*x^3),x)","\[\int \frac{-2+\left(-1+k \right) \left(1+k \right) x +2 k^{2} x^{2}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{1}{4}} \left(1-d -\left(3+d \right) x +\left(d \,k^{2}+3\right) x^{2}+\left(d \,k^{2}-1\right) x^{3}\right)}\, dx\]"," ",0,"int((-2+(-1+k)*(1+k)*x+2*k^2*x^2)/((-x^2+1)*(-k^2*x^2+1))^(1/4)/(1-d-(3+d)*x+(d*k^2+3)*x^2+(d*k^2-1)*x^3),x)","F"
1161,1,64,64,6.903000," ","int((x^4-1)^(1/4)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}} \left(\Gamma \left(\frac{3}{4}\right) x^{4} \hypergeom \left(\left[\frac{3}{4}, 1, 1\right], \left[2, 2\right], x^{4}\right)-4 \left(4-3 \ln \left(2\right)+\frac{\pi}{2}+4 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{3}{4}\right)\right)}{16 \Gamma \left(\frac{3}{4}\right) \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}}}$&$64$\\ trager&$\left(x^{4}-1\right)^{\frac{1}{4}}+\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{-2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+\RootOf \left(\textit{\_Z}^{4}+1\right) x^{4}+2 \left(x^{4}-1\right)^{\frac{3}{4}}-2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)}{x^{4}}\right)}{4}-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{4}+2 \left(x^{4}-1\right)^{\frac{3}{4}}+2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)+2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{x^{4}}\right)}{4}$&$164$\\ \hline \end{longtable}"," ",0,"-1/16/GAMMA(3/4)*signum(x^4-1)^(1/4)/(-signum(x^4-1))^(1/4)*(GAMMA(3/4)*x^4*hypergeom([3/4,1,1],[2,2],x^4)-4*(4-3*ln(2)+1/2*Pi+4*ln(x)+I*Pi)*GAMMA(3/4))","C"
1162,1,636,70,0.208000," ","int((x^4-x)^(1/2)/(a*x^3-b),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{a \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}-\frac{2 \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}-b \right)}{\sum}\frac{\left(-1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(1-i \sqrt{3}\right) \sqrt{\frac{x \left(-3+i \sqrt{3}\right)}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{\left(-1+x \right) \left(-1-i \sqrt{3}\right)}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\frac{\underline{\hspace{1.25 ex}}\alpha^{2} a \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}\, a -3 \underline{\hspace{1.25 ex}}\alpha^{2} a -i \sqrt{3}\, b +3 b}{6 b}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{b}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(-3+i \sqrt{3}\right) \sqrt{x \left(-1+x \right) \left(i \sqrt{3}+2 x +1\right) \left(1+2 x -i \sqrt{3}\right)}}\right)}{3 a}$&$636$\\ elliptic&$\frac{2 \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{a \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}-\frac{2 \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}-b \right)}{\sum}\frac{\left(-1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(1-i \sqrt{3}\right) \sqrt{\frac{x \left(-3+i \sqrt{3}\right)}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{\left(-1+x \right) \left(-1-i \sqrt{3}\right)}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\frac{\underline{\hspace{1.25 ex}}\alpha^{2} a \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}\, a -3 \underline{\hspace{1.25 ex}}\alpha^{2} a -i \sqrt{3}\, b +3 b}{6 b}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{b}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(-3+i \sqrt{3}\right) \sqrt{x \left(-1+x \right) \left(i \sqrt{3}+2 x +1\right) \left(1+2 x -i \sqrt{3}\right)}}\right)}{3 a}$&$636$\\ \hline \end{longtable}"," ",0,"2/a*(1/2-1/2*I*3^(1/2))*((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2)*(-1+x)^2*((x+1/2+1/2*I*3^(1/2))/(-1/2-1/2*I*3^(1/2))/(-1+x))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2)/(-3/2+1/2*I*3^(1/2))/(x*(-1+x)*(x+1/2+1/2*I*3^(1/2))*(x+1/2-1/2*I*3^(1/2)))^(1/2)*(EllipticF(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-EllipticPi(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),(-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)),((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)))-2/3/a*4^(1/2)*sum(1/_alpha*(-1+x)^2*(_alpha^2+_alpha+1)*(1-I*3^(1/2))*(x/(-1+x)*(-3+I*3^(1/2))/(-1+I*3^(1/2)))^(1/2)*(1/(-1+x)*(I*3^(1/2)+2*x+1)/(-1-I*3^(1/2)))^(1/2)*(1/(-1+x)*(1+2*x-I*3^(1/2))/(-1+I*3^(1/2)))^(1/2)/(-3+I*3^(1/2))/(x*(-1+x)*(I*3^(1/2)+2*x+1)*(1+2*x-I*3^(1/2)))^(1/2)*(EllipticF(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-_alpha^2*a/b*EllipticPi(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),1/6*(I*_alpha^2*3^(1/2)*a-3*_alpha^2*a-I*3^(1/2)*b+3*b)/b,((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))),_alpha=RootOf(_Z^3*a-b))","C"
1163,1,249,68,6.894000," ","int(1/(x^4-1)/(x^4-x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{x}{\left(x^{2} \left(x^{2}-1\right)\right)^{\frac{1}{4}}}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(-\frac{\sqrt{x^{4}-x^{2}}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x +2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \left(x^{4}-x^{2}\right)^{\frac{1}{4}} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{3}-4 \left(x^{4}-x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x}{x \left(x^{2}+1\right)}\right)}{8}+\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(-\frac{\sqrt{x^{4}-x^{2}}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x -2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \left(x^{4}-x^{2}\right)^{\frac{1}{4}} x^{2}+3 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{3}-4 \left(x^{4}-x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}-8\right) x}{x \left(x^{2}+1\right)}\right)}{8}$&$249$\\ trager&$-\frac{\left(x^{4}-x^{2}\right)^{\frac{3}{4}}}{x \left(x^{2}-1\right)}-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(\frac{\sqrt{x^{4}-x^{2}}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x +2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \left(x^{4}-x^{2}\right)^{\frac{1}{4}} x^{2}+3 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{3}+4 \left(x^{4}-x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}-8\right) x}{x \left(x^{2}+1\right)}\right)}{8}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(-\frac{\sqrt{x^{4}-x^{2}}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x +2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \left(x^{4}-x^{2}\right)^{\frac{1}{4}} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{3}-4 \left(x^{4}-x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x}{x \left(x^{2}+1\right)}\right)}{8}$&$257$\\ \hline \end{longtable}"," ",0,"-x/(x^2*(x^2-1))^(1/4)-1/8*RootOf(_Z^2+RootOf(_Z^4-8)^2)*ln(-((x^4-x^2)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x+2*RootOf(_Z^4-8)^2*(x^4-x^2)^(1/4)*x^2-3*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^3-4*(x^4-x^2)^(3/4)+RootOf(_Z^2+RootOf(_Z^4-8)^2)*x)/x/(x^2+1))+1/8*RootOf(_Z^4-8)*ln(-((x^4-x^2)^(1/2)*RootOf(_Z^4-8)^3*x-2*RootOf(_Z^4-8)^2*(x^4-x^2)^(1/4)*x^2+3*RootOf(_Z^4-8)*x^3-4*(x^4-x^2)^(3/4)-RootOf(_Z^4-8)*x)/x/(x^2+1))","C"
1164,1,3910,44,13.648000," ","int((x^4-x^3)^(1/4)/(x^2-2*x-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$3910$\\ \hline \end{longtable}"," ",0,"-ln((2*(x^4-x^3)^(3/4)-2*(x^4-x^3)^(1/2)*x+2*x^2*(x^4-x^3)^(1/4)-2*x^3+x^2)/x^2)+RootOf(_Z^2+1)*ln((2*(x^4-x^3)^(1/2)*RootOf(_Z^2+1)*x-2*RootOf(_Z^2+1)*x^3+2*(x^4-x^3)^(3/4)-2*x^2*(x^4-x^3)^(1/4)+RootOf(_Z^2+1)*x^2)/x^2)-2048/343*ln((-1277952*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)^9*x^3+2555904*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)^9*x^2+3039232*(x^4-x^3)^(1/2)*RootOf(2048*_Z^8-640*_Z^4+1)^7*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*x-1335296*x^3*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)^5*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)+294400*x^2*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)^5*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)-3512320*(x^4-x^3)^(1/4)*RootOf(2048*_Z^8-640*_Z^4+1)^6*x^2-17024*(x^4-x^3)^(1/2)*RootOf(2048*_Z^8-640*_Z^4+1)^3*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*x+2765952*(x^4-x^3)^(3/4)*RootOf(2048*_Z^8-640*_Z^4+1)^4+2680*x^3*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)-600*x^2*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)-85064*(x^4-x^3)^(1/4)*RootOf(2048*_Z^8-640*_Z^4+1)^2*x^2-2401*(x^4-x^3)^(3/4))/(64*x*RootOf(2048*_Z^8-640*_Z^4+1)^4-128*RootOf(2048*_Z^8-640*_Z^4+1)^4-3*x-1)/x^2)*RootOf(2048*_Z^8-640*_Z^4+1)^7*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)+320/343*ln((-1277952*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)^9*x^3+2555904*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)^9*x^2+3039232*(x^4-x^3)^(1/2)*RootOf(2048*_Z^8-640*_Z^4+1)^7*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*x-1335296*x^3*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)^5*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)+294400*x^2*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)^5*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)-3512320*(x^4-x^3)^(1/4)*RootOf(2048*_Z^8-640*_Z^4+1)^6*x^2-17024*(x^4-x^3)^(1/2)*RootOf(2048*_Z^8-640*_Z^4+1)^3*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*x+2765952*(x^4-x^3)^(3/4)*RootOf(2048*_Z^8-640*_Z^4+1)^4+2680*x^3*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)-600*x^2*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)-85064*(x^4-x^3)^(1/4)*RootOf(2048*_Z^8-640*_Z^4+1)^2*x^2-2401*(x^4-x^3)^(3/4))/(64*x*RootOf(2048*_Z^8-640*_Z^4+1)^4-128*RootOf(2048*_Z^8-640*_Z^4+1)^4-3*x-1)/x^2)*RootOf(2048*_Z^8-640*_Z^4+1)^3*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)-1/7*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*ln(-(-1277952*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)^10*x^3+2555904*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)^10*x^2+2134016*x^3*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)^6+7651840*(x^4-x^3)^(1/4)*RootOf(2048*_Z^8-640*_Z^4+1)^6*x^2-1891840*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)^6*x^2+65408*(x^4-x^3)^(1/2)*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)^4*x+395136*(x^4-x^3)^(3/4)*RootOf(2048*_Z^8-640*_Z^4+1)^4-539400*x^3*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)^2-2378264*(x^4-x^3)^(1/4)*RootOf(2048*_Z^8-640*_Z^4+1)^2*x^2+341000*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)^2*x^2-20608*(x^4-x^3)^(1/2)*RootOf(_Z^2+2240*RootOf(2048*_Z^8-640*_Z^4+1)^6-693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*x-123137*(x^4-x^3)^(3/4))/(64*x*RootOf(2048*_Z^8-640*_Z^4+1)^4-128*RootOf(2048*_Z^8-640*_Z^4+1)^4-17*x+41)/x^2)-1/7*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*ln(-(1277952*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)^10*x^3-2555904*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)^10*x^2-2134016*x^3*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)^6+1891840*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)^6*x^2-7651840*(x^4-x^3)^(1/4)*RootOf(2048*_Z^8-640*_Z^4+1)^6*x^2+65408*(x^4-x^3)^(1/2)*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)^4*x+395136*(x^4-x^3)^(3/4)*RootOf(2048*_Z^8-640*_Z^4+1)^4+539400*x^3*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)^2-341000*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*RootOf(2048*_Z^8-640*_Z^4+1)^2*x^2+2378264*(x^4-x^3)^(1/4)*RootOf(2048*_Z^8-640*_Z^4+1)^2*x^2-20608*(x^4-x^3)^(1/2)*RootOf(_Z^2-2240*RootOf(2048*_Z^8-640*_Z^4+1)^6+693*RootOf(2048*_Z^8-640*_Z^4+1)^2)*x-123137*(x^4-x^3)^(3/4))/(64*x*RootOf(2048*_Z^8-640*_Z^4+1)^4-128*RootOf(2048*_Z^8-640*_Z^4+1)^4-17*x+41)/x^2)-RootOf(2048*_Z^8-640*_Z^4+1)*ln((65536*RootOf(2048*_Z^8-640*_Z^4+1)^11*x^3-131072*x^2*RootOf(2048*_Z^8-640*_Z^4+1)^11+76288*RootOf(2048*_Z^8-640*_Z^4+1)^7*x^3+71680*(x^4-x^3)^(1/4)*RootOf(2048*_Z^8-640*_Z^4+1)^6*x^2-30720*RootOf(2048*_Z^8-640*_Z^4+1)^7*x^2+65408*(x^4-x^3)^(1/2)*RootOf(2048*_Z^8-640*_Z^4+1)^5*x+56448*(x^4-x^3)^(3/4)*RootOf(2048*_Z^8-640*_Z^4+1)^4+8040*x^3*RootOf(2048*_Z^8-640*_Z^4+1)^3+1736*(x^4-x^3)^(1/4)*RootOf(2048*_Z^8-640*_Z^4+1)^2*x^2-1800*RootOf(2048*_Z^8-640*_Z^4+1)^3*x^2+168*(x^4-x^3)^(1/2)*RootOf(2048*_Z^8-640*_Z^4+1)*x-49*(x^4-x^3)^(3/4))/(64*x*RootOf(2048*_Z^8-640*_Z^4+1)^4-128*RootOf(2048*_Z^8-640*_Z^4+1)^4-3*x-1)/x^2)","B"
1165,1,5300,44,17.267000," ","int((x^4-x^3)^(1/4)/(x^2-2*x-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$5300$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1166,0,0,66,0.007000," ","int(x^6/(a*x^4-b)^(3/4),x)","\[\int \frac{x^{6}}{\left(a \,x^{4}-b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(x^6/(a*x^4-b)^(3/4),x)","F"
1167,0,0,66,0.009000," ","int((a*x^4-b)*(a*x^4+b)^(1/4)/x^2,x)","\[\int \frac{\left(a \,x^{4}-b \right) \left(a \,x^{4}+b \right)^{\frac{1}{4}}}{x^{2}}\, dx\]"," ",0,"int((a*x^4-b)*(a*x^4+b)^(1/4)/x^2,x)","F"
1168,1,9278,31,274.190000," ","int((x^3-1)^(2/3)*(x^3+2)/x^6/(x^6-2*x^3-4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$9278$\\ trager&$\text{Expression too large to display}$&$10424$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1169,1,7527,31,315.158000," ","int((x^3-1)^(2/3)*(x^3+2)/x^6/(x^6-2*x^3-4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$7527$\\ risch&$\text{Expression too large to display}$&$9274$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1170,1,6935,31,374.270000," ","int((x^3-1)^(2/3)*(x^6-2*x^3+4)/x^6/(x^6+4*x^3-8),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$6935$\\ trager&$\text{Expression too large to display}$&$12165$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1171,1,7149,31,285.048000," ","int((x^3-1)^(2/3)*(x^6-2*x^3+4)/x^6/(x^6+4*x^3-8),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$7149$\\ trager&$\text{Expression too large to display}$&$8785$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1172,1,8190,31,298.780000," ","int((x^3-1)^(2/3)*(x^6-2*x^3+2)/x^6/(x^6+4*x^3-4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$8190$\\ trager&$\text{Expression too large to display}$&$13768$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1173,1,7362,31,278.554000," ","int((x^3-1)^(2/3)*(x^6-2*x^3+2)/x^6/(x^6+4*x^3-4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$7362$\\ trager&$\text{Expression too large to display}$&$8489$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1174,1,3206,11,23.196000," ","int((x^4+2)/(x^4-1)^(1/4)/(x^8-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$3206$\\ \hline \end{longtable}"," ",0,"-134217728/68921*ln(-(26388279066624*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(134217728*_Z^8-950272*_Z^4+1)^11*x^4-561030103040*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(134217728*_Z^8-950272*_Z^4+1)^7*x^4-687865856*(x^4-1)^(1/2)*RootOf(134217728*_Z^8-950272*_Z^4+1)^5*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*x^2-1951260475392*(x^4-1)^(1/4)*RootOf(134217728*_Z^8-950272*_Z^4+1)^6*x^3+132070244352*RootOf(134217728*_Z^8-950272*_Z^4+1)^7*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)+2757033984*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(134217728*_Z^8-950272*_Z^4+1)^3*x^4+2258403328*(x^4-1)^(3/4)*RootOf(134217728*_Z^8-950272*_Z^4+1)^4*x-2728960*(x^4-1)^(1/2)*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(134217728*_Z^8-950272*_Z^4+1)*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*x^2+13779789056*(x^4-1)^(1/4)*RootOf(134217728*_Z^8-950272*_Z^4+1)^2*x^3-1018363904*RootOf(134217728*_Z^8-950272*_Z^4+1)^3*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)-10820597*(x^4-1)^(3/4)*x)/(8192*x^4*RootOf(134217728*_Z^8-950272*_Z^4+1)^4-29*x^4-41))*RootOf(134217728*_Z^8-950272*_Z^4+1)^7*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)+475136/68921*ln(-(26388279066624*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(134217728*_Z^8-950272*_Z^4+1)^11*x^4-561030103040*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(134217728*_Z^8-950272*_Z^4+1)^7*x^4-687865856*(x^4-1)^(1/2)*RootOf(134217728*_Z^8-950272*_Z^4+1)^5*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*x^2-1951260475392*(x^4-1)^(1/4)*RootOf(134217728*_Z^8-950272*_Z^4+1)^6*x^3+132070244352*RootOf(134217728*_Z^8-950272*_Z^4+1)^7*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)+2757033984*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(134217728*_Z^8-950272*_Z^4+1)^3*x^4+2258403328*(x^4-1)^(3/4)*RootOf(134217728*_Z^8-950272*_Z^4+1)^4*x-2728960*(x^4-1)^(1/2)*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(134217728*_Z^8-950272*_Z^4+1)*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*x^2+13779789056*(x^4-1)^(1/4)*RootOf(134217728*_Z^8-950272*_Z^4+1)^2*x^3-1018363904*RootOf(134217728*_Z^8-950272*_Z^4+1)^3*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)-10820597*(x^4-1)^(3/4)*x)/(8192*x^4*RootOf(134217728*_Z^8-950272*_Z^4+1)^4-29*x^4-41))*RootOf(134217728*_Z^8-950272*_Z^4+1)^3*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)-1/41*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*ln((2684354560*RootOf(134217728*_Z^8-950272*_Z^4+1)^8*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*x^4-687865856*(x^4-1)^(1/2)*RootOf(134217728*_Z^8-950272*_Z^4+1)^6*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*x^2-8813281280*(x^4-1)^(1/4)*RootOf(134217728*_Z^8-950272*_Z^4+1)^6*x^3+15925248*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(134217728*_Z^8-950272*_Z^4+1)^4*x^4+55083008*(x^4-1)^(3/4)*RootOf(134217728*_Z^8-950272*_Z^4+1)^4*x+7599104*(x^4-1)^(1/2)*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(134217728*_Z^8-950272*_Z^4+1)^2*x^2+66486912*(x^4-1)^(1/4)*RootOf(134217728*_Z^8-950272*_Z^4+1)^2*x^3-13434880*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(134217728*_Z^8-950272*_Z^4+1)^4-9328*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*x^4-126075*(x^4-1)^(3/4)*x+7216*RootOf(_Z^2-19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6+137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2))/(8192*x^4*RootOf(134217728*_Z^8-950272*_Z^4+1)^4-29*x^4+41))+1/41*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*ln((-5905580032*RootOf(134217728*_Z^8-950272*_Z^4+1)^8*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*x^4+1375731712*(x^4-1)^(1/2)*RootOf(134217728*_Z^8-950272*_Z^4+1)^6*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*x^2-5287968768*(x^4-1)^(1/4)*RootOf(134217728*_Z^8-950272*_Z^4+1)^6*x^3-38797312*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(134217728*_Z^8-950272*_Z^4+1)^4*x^4+82624512*(x^4-1)^(3/4)*RootOf(134217728*_Z^8-950272*_Z^4+1)^4*x-3148800*(x^4-1)^(1/2)*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(134217728*_Z^8-950272*_Z^4+1)^2*x^2+27541504*(x^4-1)^(1/4)*RootOf(134217728*_Z^8-950272*_Z^4+1)^2*x^3+29556736*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*RootOf(134217728*_Z^8-950272*_Z^4+1)^4-3816*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2)*x^4+52111*(x^4-1)^(3/4)*x+2952*RootOf(_Z^2+19480576*RootOf(134217728*_Z^8-950272*_Z^4+1)^6-137883*RootOf(134217728*_Z^8-950272*_Z^4+1)^2))/(8192*x^4*RootOf(134217728*_Z^8-950272*_Z^4+1)^4-29*x^4+41))+RootOf(134217728*_Z^8-950272*_Z^4+1)*ln(-(2684354560*x^4*RootOf(134217728*_Z^8-950272*_Z^4+1)^9-31641829376*(x^4-1)^(1/2)*RootOf(134217728*_Z^8-950272*_Z^4+1)^7*x^2+1160773632*(x^4-1)^(1/4)*RootOf(134217728*_Z^8-950272*_Z^4+1)^6*x^3-53936128*RootOf(134217728*_Z^8-950272*_Z^4+1)^5*x^4+1343488*(x^4-1)^(3/4)*RootOf(134217728*_Z^8-950272*_Z^4+1)^4*x+223900672*(x^4-1)^(1/2)*RootOf(134217728*_Z^8-950272*_Z^4+1)^3*x^2-8197376*(x^4-1)^(1/4)*RootOf(134217728*_Z^8-950272*_Z^4+1)^2*x^3+13434880*RootOf(134217728*_Z^8-950272*_Z^4+1)^5+237984*RootOf(134217728*_Z^8-950272*_Z^4+1)*x^4-6437*(x^4-1)^(3/4)*x-87904*RootOf(134217728*_Z^8-950272*_Z^4+1))/(8192*x^4*RootOf(134217728*_Z^8-950272*_Z^4+1)^4-29*x^4-41))","B"
1175,0,0,66,0.009000," ","int((a*x^8-b)/x^6/(a*x^4+b)^(3/4),x)","\[\int \frac{a \,x^{8}-b}{x^{6} \left(a \,x^{4}+b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int((a*x^8-b)/x^6/(a*x^4+b)^(3/4),x)","F"
1176,1,76,65,0.106000," ","int(x^(1/2)/(-1+x)/(-x^(1/2)+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$2 \ln \left(-\frac{1}{2}+\sqrt{x}+\sqrt{-\sqrt{x}+x}\right)+\frac{\sqrt{2}\, \arctanh \left(\frac{\left(1-3 \sqrt{x}\right) \sqrt{2}}{4 \sqrt{\left(1+\sqrt{x}\right)^{2}-3 \sqrt{x}-1}}\right)}{2}-\frac{2 \sqrt{\left(-1+\sqrt{x}\right)^{2}+\sqrt{x}-1}}{-1+\sqrt{x}}$&$76$\\ default&$\frac{\sqrt{-\sqrt{x}+x}\, \left(2 \sqrt{2}\, \sqrt{x}\, \arctanh \left(\frac{\left(-1+3 \sqrt{x}\right) \sqrt{2}}{4 \sqrt{-\sqrt{x}+x}}\right)-\sqrt{2}\, x \arctanh \left(\frac{\left(-1+3 \sqrt{x}\right) \sqrt{2}}{4 \sqrt{-\sqrt{x}+x}}\right)-4 \left(-\sqrt{x}+x \right)^{\frac{3}{2}}-\sqrt{2}\, \arctanh \left(\frac{\left(-1+3 \sqrt{x}\right) \sqrt{2}}{4 \sqrt{-\sqrt{x}+x}}\right)-8 \sqrt{x}\, \sqrt{-\sqrt{x}+x}-8 \sqrt{x}\, \ln \left(-\frac{1}{2}+\sqrt{x}+\sqrt{-\sqrt{x}+x}\right)+4 x \sqrt{-\sqrt{x}+x}+4 x \ln \left(-\frac{1}{2}+\sqrt{x}+\sqrt{-\sqrt{x}+x}\right)+4 \sqrt{-\sqrt{x}+x}+4 \ln \left(-\frac{1}{2}+\sqrt{x}+\sqrt{-\sqrt{x}+x}\right)\right)}{2 \sqrt{\sqrt{x}\, \left(-1+\sqrt{x}\right)}\, \left(-1+\sqrt{x}\right)^{2}}$&$219$\\ \hline \end{longtable}"," ",0,"2*ln(-1/2+x^(1/2)+(-x^(1/2)+x)^(1/2))+1/2*2^(1/2)*arctanh(1/4*(1-3*x^(1/2))*2^(1/2)/((1+x^(1/2))^2-3*x^(1/2)-1)^(1/2))-2/(-1+x^(1/2))*((-1+x^(1/2))^2+x^(1/2)-1)^(1/2)","A"
1177,1,55,68,1.958000," ","int(1/x^3/(x^2+1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\frac{5 \Gamma \left(\frac{2}{3}\right) x^{2} \hypergeom \left(\left[1, 1, \frac{8}{3}\right], \left[2, 3\right], -x^{2}\right)}{9}-\frac{2 \left(\frac{1}{2}+\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+2 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)}{3}-\frac{\Gamma \left(\frac{2}{3}\right)}{x^{2}}}{2 \Gamma \left(\frac{2}{3}\right)}$&$55$\\ risch&$-\frac{\left(x^{2}+1\right)^{\frac{1}{3}}}{2 x^{2}}-\frac{-\frac{2 \Gamma \left(\frac{2}{3}\right) x^{2} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 2\right], -x^{2}\right)}{3}+\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+2 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)}{3 \Gamma \left(\frac{2}{3}\right)}$&$59$\\ trager&$-\frac{\left(x^{2}+1\right)^{\frac{1}{3}}}{2 x^{2}}-\frac{\ln \left(-\frac{36 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{2}+90 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}}-18 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}+9 \left(x^{2}+1\right)^{\frac{2}{3}}-144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{1}{3}}-36 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2}-10 x^{2}+15 \left(x^{2}+1\right)^{\frac{1}{3}}+60 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)-25}{x^{2}}\right)}{3}+\frac{\ln \left(\frac{180 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{2}+90 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}}-96 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}-24 \left(x^{2}+1\right)^{\frac{2}{3}}+54 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{1}{3}}-180 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2}+3 x^{2}+15 \left(x^{2}+1\right)^{\frac{1}{3}}-114 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)+4}{x^{2}}\right)}{3}-2 \ln \left(\frac{180 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{2}+90 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}}-96 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}-24 \left(x^{2}+1\right)^{\frac{2}{3}}+54 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{1}{3}}-180 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2}+3 x^{2}+15 \left(x^{2}+1\right)^{\frac{1}{3}}-114 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)+4}{x^{2}}\right) \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)$&$428$\\ \hline \end{longtable}"," ",0,"1/2/GAMMA(2/3)*(5/9*GAMMA(2/3)*x^2*hypergeom([1,1,8/3],[2,3],-x^2)-2/3*(1/2+1/6*Pi*3^(1/2)-3/2*ln(3)+2*ln(x))*GAMMA(2/3)-GAMMA(2/3)/x^2)","C"
1178,1,76,68,1.704000," ","int((x^2+1)^(2/3)/x^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(\frac{\pi  \sqrt{3}\, x^{2} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 3\right], -x^{2}\right)}{9 \Gamma \left(\frac{2}{3}\right)}-\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+2 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}+\frac{\pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right) x^{2}}\right)}{6 \pi}$&$76$\\ risch&$-\frac{\left(x^{2}+1\right)^{\frac{2}{3}}}{2 x^{2}}+\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\frac{2 \pi  \sqrt{3}\, x^{2} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], -x^{2}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+2 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{6 \pi}$&$76$\\ trager&$-\frac{\left(x^{2}+1\right)^{\frac{2}{3}}}{2 x^{2}}+\RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(\frac{-36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}+45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}}+27 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}-9 \left(x^{2}+1\right)^{\frac{2}{3}}+45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{1}{3}}+36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-2 x^{2}-9 \left(x^{2}+1\right)^{\frac{1}{3}}+57 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-5}{x^{2}}\right)-\frac{\ln \left(-\frac{36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}+45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}}+51 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+24 \left(x^{2}+1\right)^{\frac{2}{3}}+45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{1}{3}}-36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+15 x^{2}+24 \left(x^{2}+1\right)^{\frac{1}{3}}+33 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+20}{x^{2}}\right)}{3}-\ln \left(-\frac{36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}+45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}}+51 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+24 \left(x^{2}+1\right)^{\frac{2}{3}}+45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{1}{3}}-36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+15 x^{2}+24 \left(x^{2}+1\right)^{\frac{1}{3}}+33 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+20}{x^{2}}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)$&$439$\\ \hline \end{longtable}"," ",0,"-1/6/Pi*3^(1/2)*GAMMA(2/3)*(1/9*Pi*3^(1/2)/GAMMA(2/3)*x^2*hypergeom([1,1,4/3],[2,3],-x^2)-2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)-1+2*ln(x))*Pi*3^(1/2)/GAMMA(2/3)+Pi*3^(1/2)/GAMMA(2/3)/x^2)","C"
1179,1,64,65,1.512000," ","int((x^2+1)^(2/3)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\frac{2 \pi  \sqrt{3}\, x^{2} \hypergeom \left(\left[\frac{1}{3}, 1, 1\right], \left[2, 2\right], -x^{2}\right)}{3 \Gamma \left(\frac{2}{3}\right)}-\frac{\left(\frac{3}{2}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+2 \ln \left(x \right)\right) \pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right)}\right)}{6 \pi}$&$64$\\ trager&$\frac{3 \left(x^{2}+1\right)^{\frac{2}{3}}}{4}+\frac{3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(\frac{-36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}+45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}}+27 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}-9 \left(x^{2}+1\right)^{\frac{2}{3}}+45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{1}{3}}+36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-2 x^{2}-9 \left(x^{2}+1\right)^{\frac{1}{3}}+57 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-5}{x^{2}}\right)}{2}-\frac{\ln \left(-\frac{36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}+45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}}+51 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+24 \left(x^{2}+1\right)^{\frac{2}{3}}+45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{1}{3}}-36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+15 x^{2}+24 \left(x^{2}+1\right)^{\frac{1}{3}}+33 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+20}{x^{2}}\right)}{2}-\frac{3 \ln \left(-\frac{36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}+45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}}+51 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+24 \left(x^{2}+1\right)^{\frac{2}{3}}+45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{1}{3}}-36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+15 x^{2}+24 \left(x^{2}+1\right)^{\frac{1}{3}}+33 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+20}{x^{2}}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{2}$&$437$\\ \hline \end{longtable}"," ",0,"-1/6/Pi*3^(1/2)*GAMMA(2/3)*(-2/3*Pi*3^(1/2)/GAMMA(2/3)*x^2*hypergeom([1/3,1,1],[2,2],-x^2)-(3/2-1/6*Pi*3^(1/2)-3/2*ln(3)+2*ln(x))*Pi*3^(1/2)/GAMMA(2/3))","C"
1180,1,129,75,6.748000," ","int((3+4*x)*(-2*x^4+2*x^2+x)^(1/2)/(1+2*x)/(x^3+2*x+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{3}+4 \sqrt{-2 x^{4}+2 x^{2}+x}\, x -2 \RootOf \left(\textit{\_Z}^{2}+2\right) x -\RootOf \left(\textit{\_Z}^{2}+2\right)}{1+2 x}\right)+\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(-\frac{-5 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{3}+6 \sqrt{-2 x^{4}+2 x^{2}+x}\, x +2 \RootOf \left(\textit{\_Z}^{2}+3\right) x +\RootOf \left(\textit{\_Z}^{2}+3\right)}{x^{3}+2 x +1}\right)$&$129$\\ default&$\text{Expression too large to display}$&$6278$\\ elliptic&$\text{Expression too large to display}$&$414320$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2+2)*ln(-(4*RootOf(_Z^2+2)*x^3+4*(-2*x^4+2*x^2+x)^(1/2)*x-2*RootOf(_Z^2+2)*x-RootOf(_Z^2+2))/(1+2*x))+RootOf(_Z^2+3)*ln(-(-5*RootOf(_Z^2+3)*x^3+6*(-2*x^4+2*x^2+x)^(1/2)*x+2*RootOf(_Z^2+3)*x+RootOf(_Z^2+3))/(x^3+2*x+1))","C"
1181,1,64,65,5.168000," ","int((x^4+1)^(2/3)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\frac{2 \pi  \sqrt{3}\, x^{4} \hypergeom \left(\left[\frac{1}{3}, 1, 1\right], \left[2, 2\right], -x^{4}\right)}{3 \Gamma \left(\frac{2}{3}\right)}-\frac{\left(\frac{3}{2}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)\right) \pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right)}\right)}{12 \pi}$&$64$\\ trager&$\frac{3 \left(x^{4}+1\right)^{\frac{2}{3}}}{8}+\frac{\ln \left(\frac{-333 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}-393 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}-60 x^{4}+351 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}}-48 \left(x^{4}+1\right)^{\frac{2}{3}}+144 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{1}{3}}+333 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+165 \left(x^{4}+1\right)^{\frac{1}{3}}-384 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-80}{x^{4}}\right)}{4}-\frac{\ln \left(-\frac{-153 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}+162 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}-40 x^{4}+351 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}}+165 \left(x^{4}+1\right)^{\frac{2}{3}}-495 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{1}{3}}+153 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-48 \left(x^{4}+1\right)^{\frac{1}{3}}+195 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-100}{x^{4}}\right)}{4}-\frac{3 \ln \left(-\frac{-153 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}+162 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}-40 x^{4}+351 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}}+165 \left(x^{4}+1\right)^{\frac{2}{3}}-495 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{1}{3}}+153 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-48 \left(x^{4}+1\right)^{\frac{1}{3}}+195 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-100}{x^{4}}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{4}$&$426$\\ \hline \end{longtable}"," ",0,"-1/12/Pi*3^(1/2)*GAMMA(2/3)*(-2/3*Pi*3^(1/2)/GAMMA(2/3)*x^4*hypergeom([1/3,1,1],[2,2],-x^4)-(3/2-1/6*Pi*3^(1/2)-3/2*ln(3)+4*ln(x))*Pi*3^(1/2)/GAMMA(2/3))","C"
1182,1,593,71,8.989000," ","int((x^4-1)^(1/3)*(x^4+3)/x^2/(x^4-x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(x^{4}-1\right)^{\frac{1}{3}}}{x}-6 \ln \left(\frac{1149120 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{4}-2154600 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{3}-160116 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{4}-4118136 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}} x +2586522 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{1}{3}} x^{2}+1524150 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{3}-340561 x^{4}-255269 \left(x^{4}-1\right)^{\frac{2}{3}} x +686356 \left(x^{4}-1\right)^{\frac{1}{3}} x^{2}-118456 x^{3}-1149120 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2}+160116 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)+340561}{x^{4}-x^{3}-1}\right) \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)+\ln \left(\frac{4264416 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{4}-7995780 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{3}-1524150 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{4}+4118136 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}} x -1531614 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{1}{3}} x^{2}-1684266 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{3}+59850 x^{4}+431087 \left(x^{4}-1\right)^{\frac{2}{3}} x -686356 \left(x^{4}-1\right)^{\frac{1}{3}} x^{2}+91770 x^{3}-4264416 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2}+1524150 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)-59850}{x^{4}-x^{3}-1}\right)-\ln \left(\frac{1149120 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{4}-2154600 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{3}-160116 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{4}-4118136 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}} x +2586522 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{1}{3}} x^{2}+1524150 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{3}-340561 x^{4}-255269 \left(x^{4}-1\right)^{\frac{2}{3}} x +686356 \left(x^{4}-1\right)^{\frac{1}{3}} x^{2}-118456 x^{3}-1149120 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2}+160116 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)+340561}{x^{4}-x^{3}-1}\right)$&$593$\\ risch&$\frac{3 \left(x^{4}-1\right)^{\frac{1}{3}}}{x}+\frac{\left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{7}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{8}-x^{7} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+x^{8}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{8}-2 x^{4}+1\right)^{\frac{1}{3}} x^{5}+2 \left(x^{8}-2 x^{4}+1\right)^{\frac{1}{3}} x^{5}+\left(x^{8}-2 x^{4}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}+2 \left(x^{8}-2 x^{4}+1\right)^{\frac{2}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-2 x^{4}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{8}-2 x^{4}+1\right)^{\frac{1}{3}} x -2 \left(x^{8}-2 x^{4}+1\right)^{\frac{1}{3}} x +\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1}{\left(x^{4}-x^{3}-1\right) \left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)-\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{7}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{8}+x^{7} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{8}-2 x^{4}+1\right)^{\frac{1}{3}} x^{5}-\left(x^{8}-2 x^{4}+1\right)^{\frac{1}{3}} x^{5}+\left(x^{8}-2 x^{4}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}-\left(x^{8}-2 x^{4}+1\right)^{\frac{2}{3}} x^{2}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{8}-2 x^{4}+1\right)^{\frac{1}{3}} x +\left(x^{8}-2 x^{4}+1\right)^{\frac{1}{3}} x +\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{\left(x^{4}-x^{3}-1\right) \left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{7}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{8}+x^{7} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{8}-2 x^{4}+1\right)^{\frac{1}{3}} x^{5}-\left(x^{8}-2 x^{4}+1\right)^{\frac{1}{3}} x^{5}+\left(x^{8}-2 x^{4}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}-\left(x^{8}-2 x^{4}+1\right)^{\frac{2}{3}} x^{2}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{8}-2 x^{4}+1\right)^{\frac{1}{3}} x +\left(x^{8}-2 x^{4}+1\right)^{\frac{1}{3}} x +\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{\left(x^{4}-x^{3}-1\right) \left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)\right) \left(\left(x^{4}-1\right)^{2}\right)^{\frac{1}{3}}}{\left(x^{4}-1\right)^{\frac{2}{3}}}$&$747$\\ \hline \end{longtable}"," ",0,"3*(x^4-1)^(1/3)/x-6*ln((1149120*RootOf(36*_Z^2+6*_Z+1)^2*x^4-2154600*RootOf(36*_Z^2+6*_Z+1)^2*x^3-160116*RootOf(36*_Z^2+6*_Z+1)*x^4-4118136*RootOf(36*_Z^2+6*_Z+1)*(x^4-1)^(2/3)*x+2586522*RootOf(36*_Z^2+6*_Z+1)*(x^4-1)^(1/3)*x^2+1524150*RootOf(36*_Z^2+6*_Z+1)*x^3-340561*x^4-255269*(x^4-1)^(2/3)*x+686356*(x^4-1)^(1/3)*x^2-118456*x^3-1149120*RootOf(36*_Z^2+6*_Z+1)^2+160116*RootOf(36*_Z^2+6*_Z+1)+340561)/(x^4-x^3-1))*RootOf(36*_Z^2+6*_Z+1)+ln((4264416*RootOf(36*_Z^2+6*_Z+1)^2*x^4-7995780*RootOf(36*_Z^2+6*_Z+1)^2*x^3-1524150*RootOf(36*_Z^2+6*_Z+1)*x^4+4118136*RootOf(36*_Z^2+6*_Z+1)*(x^4-1)^(2/3)*x-1531614*RootOf(36*_Z^2+6*_Z+1)*(x^4-1)^(1/3)*x^2-1684266*RootOf(36*_Z^2+6*_Z+1)*x^3+59850*x^4+431087*(x^4-1)^(2/3)*x-686356*(x^4-1)^(1/3)*x^2+91770*x^3-4264416*RootOf(36*_Z^2+6*_Z+1)^2+1524150*RootOf(36*_Z^2+6*_Z+1)-59850)/(x^4-x^3-1))-ln((1149120*RootOf(36*_Z^2+6*_Z+1)^2*x^4-2154600*RootOf(36*_Z^2+6*_Z+1)^2*x^3-160116*RootOf(36*_Z^2+6*_Z+1)*x^4-4118136*RootOf(36*_Z^2+6*_Z+1)*(x^4-1)^(2/3)*x+2586522*RootOf(36*_Z^2+6*_Z+1)*(x^4-1)^(1/3)*x^2+1524150*RootOf(36*_Z^2+6*_Z+1)*x^3-340561*x^4-255269*(x^4-1)^(2/3)*x+686356*(x^4-1)^(1/3)*x^2-118456*x^3-1149120*RootOf(36*_Z^2+6*_Z+1)^2+160116*RootOf(36*_Z^2+6*_Z+1)+340561)/(x^4-x^3-1))","C"
1183,1,205,70,1.674000," ","int(x^2*(x^3+4)/(x^3+1)^(3/4)/(x^4+x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{-2 \sqrt{x^{3}+1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}-2 \left(x^{3}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{4}+1\right) x^{4}+2 \left(x^{3}+1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}+1\right) x^{3}+\RootOf \left(\textit{\_Z}^{4}+1\right)}{x^{4}+x^{3}+1}\right)-\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{4}+2 \left(x^{3}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{3}+2 \sqrt{x^{3}+1}\, \RootOf \left(\textit{\_Z}^{4}+1\right) x^{2}+2 \left(x^{3}+1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{x^{4}+x^{3}+1}\right)$&$205$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^4+1)^3*ln((-2*(x^3+1)^(1/2)*RootOf(_Z^4+1)^3*x^2-2*(x^3+1)^(1/4)*RootOf(_Z^4+1)^2*x^3-RootOf(_Z^4+1)*x^4+2*(x^3+1)^(3/4)*x+RootOf(_Z^4+1)*x^3+RootOf(_Z^4+1))/(x^4+x^3+1))-RootOf(_Z^4+1)*ln((RootOf(_Z^4+1)^3*x^4+2*(x^3+1)^(1/4)*RootOf(_Z^4+1)^2*x^3-RootOf(_Z^4+1)^3*x^3+2*(x^3+1)^(1/2)*RootOf(_Z^4+1)*x^2+2*(x^3+1)^(3/4)*x-RootOf(_Z^4+1)^3)/(x^4+x^3+1))","C"
1184,0,0,63,0.037000," ","int(x^2/(a*x^4-b)^(3/4)/(a*x^4+b),x)","\[\int \frac{x^{2}}{\left(a \,x^{4}-b \right)^{\frac{3}{4}} \left(a \,x^{4}+b \right)}\, dx\]"," ",0,"int(x^2/(a*x^4-b)^(3/4)/(a*x^4+b),x)","F"
1185,0,0,63,0.036000," ","int(1/(a*x^4-b)^(1/4)/(a*x^4+b),x)","\[\int \frac{1}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(a \,x^{4}+b \right)}\, dx\]"," ",0,"int(1/(a*x^4-b)^(1/4)/(a*x^4+b),x)","F"
1186,1,246,75,0.112000," ","int((-a^2*b+a*(2*a+b)*x-3*a*x^2+x^3)/(x*(-a+x)*(-b+x))^(1/2)/(-a^2+2*a*x+(b^2*d-1)*x^2-2*b*d*x^3+d*x^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(d \,\textit{\_Z}^{4}-2 b d \,\textit{\_Z}^{3}+\left(b^{2} d -1\right) \textit{\_Z}^{2}+2 a \textit{\_Z} -a^{2}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{3}+3 \underline{\hspace{1.25 ex}}\alpha^{2} a -2 \underline{\hspace{1.25 ex}}\alpha  \,a^{2}-\underline{\hspace{1.25 ex}}\alpha  a b +a^{2} b \right) \left(d \,\underline{\hspace{1.25 ex}}\alpha^{3}-b d \,\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +2 a -b \right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, -\frac{\left(d \,\underline{\hspace{1.25 ex}}\alpha^{3}-b d \,\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +2 a -b \right) b}{a^{2}-2 a b +b^{2}}, \sqrt{\frac{b}{-a +b}}\right)}{\left(-2 d \,\underline{\hspace{1.25 ex}}\alpha^{3}+3 b d \,\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  \,b^{2} d +\underline{\hspace{1.25 ex}}\alpha  -a \right) \left(a^{2}-2 a b +b^{2}\right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}\right)$&$246$\\ elliptic&$b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(d \,\textit{\_Z}^{4}-2 b d \,\textit{\_Z}^{3}+\left(b^{2} d -1\right) \textit{\_Z}^{2}+2 a \textit{\_Z} -a^{2}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{3}+3 \underline{\hspace{1.25 ex}}\alpha^{2} a -2 \underline{\hspace{1.25 ex}}\alpha  \,a^{2}-\underline{\hspace{1.25 ex}}\alpha  a b +a^{2} b \right) \left(d \,\underline{\hspace{1.25 ex}}\alpha^{3}-b d \,\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +2 a -b \right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, -\frac{\left(d \,\underline{\hspace{1.25 ex}}\alpha^{3}-b d \,\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +2 a -b \right) b}{a^{2}-2 a b +b^{2}}, \sqrt{\frac{b}{-a +b}}\right)}{\left(-2 d \,\underline{\hspace{1.25 ex}}\alpha^{3}+3 b d \,\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  \,b^{2} d +\underline{\hspace{1.25 ex}}\alpha  -a \right) \left(a^{2}-2 a b +b^{2}\right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}\right)$&$246$\\ \hline \end{longtable}"," ",0,"b*sum((-_alpha^3+3*_alpha^2*a-2*_alpha*a^2-_alpha*a*b+a^2*b)/(-2*_alpha^3*d+3*_alpha^2*b*d-_alpha*b^2*d+_alpha-a)*(_alpha^3*d-_alpha^2*b*d-_alpha+2*a-b)/(a^2-2*a*b+b^2)*(-(-b+x)/b)^(1/2)*((-a+x)/(-a+b))^(1/2)*(x/b)^(1/2)/(x*(a*b-a*x-b*x+x^2))^(1/2)*EllipticPi((-(-b+x)/b)^(1/2),-(_alpha^3*d-_alpha^2*b*d-_alpha+2*a-b)*b/(a^2-2*a*b+b^2),(b/(-a+b))^(1/2)),_alpha=RootOf(d*_Z^4-2*b*d*_Z^3+(b^2*d-1)*_Z^2+2*a*_Z-a^2))","C"
1187,1,87,83,0.168000," ","int((k^2*x^4+1)/((-x^2+1)*(-k^2*x^2+1))^(1/2)/(k^2*x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)}}{x \left(-1+k \right)}\right)}{-2+2 k}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)}}{x \left(1+k \right)}\right)}{2+2 k}\right) \sqrt{2}}{2}$&$87$\\ default&$\frac{\sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticF \left(x , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}-\frac{\sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticPi \left(x , -k , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}-\frac{\sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticPi \left(x , k , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}$&$155$\\ \hline \end{longtable}"," ",0,"1/2*(1/2*2^(1/2)/(-1+k)*arctan(((-x^2+1)*(-k^2*x^2+1))^(1/2)/x/(-1+k))+1/2*2^(1/2)/(1+k)*arctan(((-x^2+1)*(-k^2*x^2+1))^(1/2)/x/(1+k)))*2^(1/2)","A"
1188,0,0,11,0.048000," ","int(x*(k*x-1)*(-1+(-1+2*k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(-1+(4-c)*x+(c*k+b+2*c-6)*x^2+(-2*b*k-2*c*k-c+4)*x^3+(b*k^2+c*k-1)*x^4),x)","\[\int \frac{x \left(k x -1\right) \left(-1+\left(-1+2 k \right) x \right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(-1+\left(4-c \right) x +\left(c k +b +2 c -6\right) x^{2}+\left(-2 b k -2 c k -c +4\right) x^{3}+\left(b \,k^{2}+c k -1\right) x^{4}\right)}\, dx\]"," ",0,"int(x*(k*x-1)*(-1+(-1+2*k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(-1+(4-c)*x+(c*k+b+2*c-6)*x^2+(-2*b*k-2*c*k-c+4)*x^3+(b*k^2+c*k-1)*x^4),x)","F"
1189,1,64,65,6.248000," ","int((x^5+1)^(2/3)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\frac{2 \pi  \sqrt{3}\, x^{5} \hypergeom \left(\left[\frac{1}{3}, 1, 1\right], \left[2, 2\right], -x^{5}\right)}{3 \Gamma \left(\frac{2}{3}\right)}-\frac{\left(\frac{3}{2}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+5 \ln \left(x \right)\right) \pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right)}\right)}{15 \pi}$&$64$\\ trager&$\frac{3 \left(x^{5}+1\right)^{\frac{2}{3}}}{10}+\frac{3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(\frac{-132201 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{5}+126582 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{5}-25632 x^{5}+137820 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}+1\right)^{\frac{2}{3}}-78769 \left(x^{5}+1\right)^{\frac{2}{3}}+137820 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}+1\right)^{\frac{1}{3}}+132201 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-78769 \left(x^{5}+1\right)^{\frac{1}{3}}+181887 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-64080}{x^{5}}\right)}{5}-\frac{\ln \left(-\frac{132201 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{5}+214716 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{5}+82515 x^{5}+137820 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}+1\right)^{\frac{2}{3}}+124709 \left(x^{5}+1\right)^{\frac{2}{3}}+137820 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}+1\right)^{\frac{1}{3}}-132201 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+124709 \left(x^{5}+1\right)^{\frac{1}{3}}+93753 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+110020}{x^{5}}\right)}{5}-\frac{3 \ln \left(-\frac{132201 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{5}+214716 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{5}+82515 x^{5}+137820 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}+1\right)^{\frac{2}{3}}+124709 \left(x^{5}+1\right)^{\frac{2}{3}}+137820 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}+1\right)^{\frac{1}{3}}-132201 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+124709 \left(x^{5}+1\right)^{\frac{1}{3}}+93753 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+110020}{x^{5}}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{5}$&$437$\\ \hline \end{longtable}"," ",0,"-1/15/Pi*3^(1/2)*GAMMA(2/3)*(-2/3*Pi*3^(1/2)/GAMMA(2/3)*x^5*hypergeom([1/3,1,1],[2,2],-x^5)-(3/2-1/6*Pi*3^(1/2)-3/2*ln(3)+5*ln(x))*Pi*3^(1/2)/GAMMA(2/3))","C"
1190,1,64,65,8.215000," ","int((x^6+1)^(2/3)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\frac{2 \pi  \sqrt{3}\, x^{6} \hypergeom \left(\left[\frac{1}{3}, 1, 1\right], \left[2, 2\right], -x^{6}\right)}{3 \Gamma \left(\frac{2}{3}\right)}-\frac{\left(\frac{3}{2}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+6 \ln \left(x \right)\right) \pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right)}\right)}{18 \pi}$&$64$\\ trager&$\frac{\left(x^{6}+1\right)^{\frac{2}{3}}}{4}+\frac{\ln \left(\frac{184653895 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}-538491663 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+338367746 x^{6}+1600004967 \left(x^{6}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+569431707 \left(x^{6}+1\right)^{\frac{2}{3}}-1030573260 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}}-184653895 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-1600004967 \left(x^{6}+1\right)^{\frac{1}{3}}-754085602 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+845919365}{x^{6}}\right)}{6}+\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{-169183873 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}-322897724 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+553961685 x^{6}+1600004967 \left(x^{6}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1030573260 \left(x^{6}+1\right)^{\frac{2}{3}}-569431707 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}}+169183873 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-1600004967 \left(x^{6}+1\right)^{\frac{1}{3}}-861389387 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+738615580}{x^{6}}\right)}{6}$&$239$\\ \hline \end{longtable}"," ",0,"-1/18/Pi*3^(1/2)*GAMMA(2/3)*(-2/3*Pi*3^(1/2)/GAMMA(2/3)*x^6*hypergeom([1/3,1,1],[2,2],-x^6)-(3/2-1/6*Pi*3^(1/2)-3/2*ln(3)+6*ln(x))*Pi*3^(1/2)/GAMMA(2/3))","C"
1191,1,173,79,1.084000," ","int((2*x^4-x^2+1)*(-x^6-x^4-x^2+1)^(1/2)/(x^2-1)/(x^2+1)/(x^6+x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x^{6}+\RootOf \left(\textit{\_Z}^{2}+2\right) x^{4}+3 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{2}-4 \sqrt{-x^{6}-x^{4}-x^{2}+1}\, x -\RootOf \left(\textit{\_Z}^{2}+2\right)}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)^{2}}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-2 \sqrt{-x^{6}-x^{4}-x^{2}+1}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{6}+x^{4}-1}\right)}{2}$&$173$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^2+2)*ln((RootOf(_Z^2+2)*x^6+RootOf(_Z^2+2)*x^4+3*RootOf(_Z^2+2)*x^2-4*(-x^6-x^4-x^2+1)^(1/2)*x-RootOf(_Z^2+2))/(-1+x)/(1+x)/(x^2+1)^2)-1/2*RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)*x^6+RootOf(_Z^2+1)*x^4+2*RootOf(_Z^2+1)*x^2-2*(-x^6-x^4-x^2+1)^(1/2)*x-RootOf(_Z^2+1))/(x^6+x^4-1))","C"
1192,1,606,71,197.674000," ","int((x^8-1)^(1/3)*(5*x^8+3)/x^2/(x^8-x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(x^{8}-1\right)^{\frac{1}{3}}}{x}-6 \ln \left(\frac{5141860766708129562144283736588098527161696987675808 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{8}-31108581467491893886477983948838281630881262490114194 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{8}+20147370141885701559053156928011918590840844728896840 x^{8}-163896811938821629793349044103745640553279091482166380 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{3}+88061685794919605613792863040370530405109906887374910 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{8}-1\right)^{\frac{2}{3}} x +88061685794919605613792863040370530405109906887374910 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{8}-1\right)^{\frac{1}{3}} x^{2}+92711108733725916128403386928015888364971603628407342 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{3}+45336674395944826278015303299258325827740741623155051 \left(x^{8}-1\right)^{\frac{2}{3}} x +45336674395944826278015303299258325827740741623155051 \left(x^{8}-1\right)^{\frac{1}{3}} x^{2}+20779444499278194156984236361047586625063302602744584 x^{3}-5141860766708129562144283736588098527161696987675808 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2}+31108581467491893886477983948838281630881262490114194 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)-20147370141885701559053156928011918590840844728896840}{x^{8}-x^{3}-1}\right) \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)+6 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \ln \left(\frac{13140237860954654571358816426666205541798616800476611104 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{8}+72969596556035543676622386529356559272725556718096737834 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{8}+5325987117630295715001316896928139382907509781721573335 x^{8}-418845081817929614462062273599985301644830910515191978940 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{3}+111793230762796870634677068939366581324372951945784600474 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{8}-1\right)^{\frac{2}{3}} x +111793230762796870634677068939366581324372951945784600474 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{8}-1\right)^{\frac{1}{3}} x^{2}-28793839786067833023729227118876493965524653724764698666 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{3}+16757573329138738851585113739228332287150734968044551246 \left(x^{8}-1\right)^{\frac{2}{3}} x +16757573329138738851585113739228332287150734968044551246 \left(x^{8}-1\right)^{\frac{1}{3}} x^{2}+162007212703583139619811920819106901381217027580884360 x^{3}-13140237860954654571358816426666205541798616800476611104 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2}-72969596556035543676622386529356559272725556718096737834 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)-5325987117630295715001316896928139382907509781721573335}{x^{8}-x^{3}-1}\right)-\ln \left(\frac{5141860766708129562144283736588098527161696987675808 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{8}-31108581467491893886477983948838281630881262490114194 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{8}+20147370141885701559053156928011918590840844728896840 x^{8}-163896811938821629793349044103745640553279091482166380 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{3}+88061685794919605613792863040370530405109906887374910 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{8}-1\right)^{\frac{2}{3}} x +88061685794919605613792863040370530405109906887374910 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{8}-1\right)^{\frac{1}{3}} x^{2}+92711108733725916128403386928015888364971603628407342 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{3}+45336674395944826278015303299258325827740741623155051 \left(x^{8}-1\right)^{\frac{2}{3}} x +45336674395944826278015303299258325827740741623155051 \left(x^{8}-1\right)^{\frac{1}{3}} x^{2}+20779444499278194156984236361047586625063302602744584 x^{3}-5141860766708129562144283736588098527161696987675808 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2}+31108581467491893886477983948838281630881262490114194 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)-20147370141885701559053156928011918590840844728896840}{x^{8}-x^{3}-1}\right)$&$606$\\ risch&$\frac{3 \left(x^{8}-1\right)^{\frac{1}{3}}}{x}+\frac{\left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\frac{-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{16}-x^{16}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{11}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{11}-3 \left(x^{16}-2 x^{8}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{9}-3 \left(x^{16}-2 x^{8}+1\right)^{\frac{1}{3}} x^{9}+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{8}+2 x^{8}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-3 \left(x^{16}-2 x^{8}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-3 \left(x^{16}-2 x^{8}+1\right)^{\frac{2}{3}} x^{2}+3 \left(x^{16}-2 x^{8}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +3 \left(x^{16}-2 x^{8}+1\right)^{\frac{1}{3}} x -2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right) \left(x^{4}+1\right) \left(x^{8}-x^{3}-1\right)}\right)-\ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{16}+x^{16}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{11}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{11}+3 \left(x^{16}-2 x^{8}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{9}+x^{11}-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{8}-2 x^{8}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \left(x^{16}-2 x^{8}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-3 \left(x^{16}-2 x^{8}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x -x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right) \left(x^{4}+1\right) \left(x^{8}-x^{3}-1\right)}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-\ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{16}+x^{16}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{11}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{11}+3 \left(x^{16}-2 x^{8}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{9}+x^{11}-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{8}-2 x^{8}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \left(x^{16}-2 x^{8}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-3 \left(x^{16}-2 x^{8}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x -x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right) \left(x^{4}+1\right) \left(x^{8}-x^{3}-1\right)}\right)\right) \left(\left(x^{8}-1\right)^{2}\right)^{\frac{1}{3}}}{\left(x^{8}-1\right)^{\frac{2}{3}}}$&$726$\\ \hline \end{longtable}"," ",0,"3*(x^8-1)^(1/3)/x-6*ln((5141860766708129562144283736588098527161696987675808*RootOf(36*_Z^2+6*_Z+1)^2*x^8-31108581467491893886477983948838281630881262490114194*RootOf(36*_Z^2+6*_Z+1)*x^8+20147370141885701559053156928011918590840844728896840*x^8-163896811938821629793349044103745640553279091482166380*RootOf(36*_Z^2+6*_Z+1)^2*x^3+88061685794919605613792863040370530405109906887374910*RootOf(36*_Z^2+6*_Z+1)*(x^8-1)^(2/3)*x+88061685794919605613792863040370530405109906887374910*RootOf(36*_Z^2+6*_Z+1)*(x^8-1)^(1/3)*x^2+92711108733725916128403386928015888364971603628407342*RootOf(36*_Z^2+6*_Z+1)*x^3+45336674395944826278015303299258325827740741623155051*(x^8-1)^(2/3)*x+45336674395944826278015303299258325827740741623155051*(x^8-1)^(1/3)*x^2+20779444499278194156984236361047586625063302602744584*x^3-5141860766708129562144283736588098527161696987675808*RootOf(36*_Z^2+6*_Z+1)^2+31108581467491893886477983948838281630881262490114194*RootOf(36*_Z^2+6*_Z+1)-20147370141885701559053156928011918590840844728896840)/(x^8-x^3-1))*RootOf(36*_Z^2+6*_Z+1)+6*RootOf(36*_Z^2+6*_Z+1)*ln((13140237860954654571358816426666205541798616800476611104*RootOf(36*_Z^2+6*_Z+1)^2*x^8+72969596556035543676622386529356559272725556718096737834*RootOf(36*_Z^2+6*_Z+1)*x^8+5325987117630295715001316896928139382907509781721573335*x^8-418845081817929614462062273599985301644830910515191978940*RootOf(36*_Z^2+6*_Z+1)^2*x^3+111793230762796870634677068939366581324372951945784600474*RootOf(36*_Z^2+6*_Z+1)*(x^8-1)^(2/3)*x+111793230762796870634677068939366581324372951945784600474*RootOf(36*_Z^2+6*_Z+1)*(x^8-1)^(1/3)*x^2-28793839786067833023729227118876493965524653724764698666*RootOf(36*_Z^2+6*_Z+1)*x^3+16757573329138738851585113739228332287150734968044551246*(x^8-1)^(2/3)*x+16757573329138738851585113739228332287150734968044551246*(x^8-1)^(1/3)*x^2+162007212703583139619811920819106901381217027580884360*x^3-13140237860954654571358816426666205541798616800476611104*RootOf(36*_Z^2+6*_Z+1)^2-72969596556035543676622386529356559272725556718096737834*RootOf(36*_Z^2+6*_Z+1)-5325987117630295715001316896928139382907509781721573335)/(x^8-x^3-1))-ln((5141860766708129562144283736588098527161696987675808*RootOf(36*_Z^2+6*_Z+1)^2*x^8-31108581467491893886477983948838281630881262490114194*RootOf(36*_Z^2+6*_Z+1)*x^8+20147370141885701559053156928011918590840844728896840*x^8-163896811938821629793349044103745640553279091482166380*RootOf(36*_Z^2+6*_Z+1)^2*x^3+88061685794919605613792863040370530405109906887374910*RootOf(36*_Z^2+6*_Z+1)*(x^8-1)^(2/3)*x+88061685794919605613792863040370530405109906887374910*RootOf(36*_Z^2+6*_Z+1)*(x^8-1)^(1/3)*x^2+92711108733725916128403386928015888364971603628407342*RootOf(36*_Z^2+6*_Z+1)*x^3+45336674395944826278015303299258325827740741623155051*(x^8-1)^(2/3)*x+45336674395944826278015303299258325827740741623155051*(x^8-1)^(1/3)*x^2+20779444499278194156984236361047586625063302602744584*x^3-5141860766708129562144283736588098527161696987675808*RootOf(36*_Z^2+6*_Z+1)^2+31108581467491893886477983948838281630881262490114194*RootOf(36*_Z^2+6*_Z+1)-20147370141885701559053156928011918590840844728896840)/(x^8-x^3-1))","C"
1193,1,50,69,1.070000," ","int((x^8+2)*(x^16-2*x^8+4)^(1/2)/x^9,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{8}-2\right) \sqrt{x^{16}-2 x^{8}+4}}{8 x^{8}}-\frac{\ln \left(\frac{2-x^{8}+\sqrt{x^{16}-2 x^{8}+4}}{x^{4}}\right)}{4}$&$50$\\ risch&$\frac{x^{24}-4 x^{16}+8 x^{8}-8}{8 x^{8} \sqrt{x^{16}-2 x^{8}+4}}+\frac{\ln \left(\frac{x^{8}+\sqrt{x^{16}-2 x^{8}+4}-2}{x^{4}}\right)}{4}$&$58$\\ \hline \end{longtable}"," ",0,"1/8*(x^8-2)*(x^16-2*x^8+4)^(1/2)/x^8-1/4*ln((2-x^8+(x^16-2*x^8+4)^(1/2))/x^4)","A"
1194,1,127,65,0.033000," ","int((x+(1+x)^(1/2))^(1/2)/(1-(1+x)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\left(2 \sqrt{1+x}+1\right) \sqrt{x +\sqrt{1+x}}}{2}+\frac{5 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{4}-2 \sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}-3 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}\right)+2 \arctanh \left(\frac{-1+3 \sqrt{1+x}}{2 \sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}}\right)$&$127$\\ default&$-\frac{\left(2 \sqrt{1+x}+1\right) \sqrt{x +\sqrt{1+x}}}{2}+\frac{5 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{4}-2 \sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}-3 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}\right)+2 \arctanh \left(\frac{-1+3 \sqrt{1+x}}{2 \sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}}\right)$&$127$\\ \hline \end{longtable}"," ",0,"-1/2*(2*(1+x)^(1/2)+1)*(x+(1+x)^(1/2))^(1/2)+5/4*ln(1/2+(1+x)^(1/2)+(x+(1+x)^(1/2))^(1/2))-2*((-1+(1+x)^(1/2))^2+3*(1+x)^(1/2)-2)^(1/2)-3*ln(1/2+(1+x)^(1/2)+((-1+(1+x)^(1/2))^2+3*(1+x)^(1/2)-2)^(1/2))+2*arctanh(1/2*(-1+3*(1+x)^(1/2))/((-1+(1+x)^(1/2))^2+3*(1+x)^(1/2)-2)^(1/2))","A"
1195,1,60,71,0.063000," ","int((c+(a*x+b)^(1/2))^(1/2)/(d-(a*x+b)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{-\frac{4 \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}-4 d \sqrt{c +\sqrt{a x +b}}+4 d \sqrt{c +d}\, \arctanh \left(\frac{\sqrt{c +\sqrt{a x +b}}}{\sqrt{c +d}}\right)}{a}$&$60$\\ default&$-\frac{2 \left(\frac{2 \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}+2 d \sqrt{c +\sqrt{a x +b}}-2 d \sqrt{c +d}\, \arctanh \left(\frac{\sqrt{c +\sqrt{a x +b}}}{\sqrt{c +d}}\right)\right)}{a}$&$60$\\ \hline \end{longtable}"," ",0,"2/a*(-2/3*(c+(a*x+b)^(1/2))^(3/2)-2*d*(c+(a*x+b)^(1/2))^(1/2)+2*d*(c+d)^(1/2)*arctanh((c+(a*x+b)^(1/2))^(1/2)/(c+d)^(1/2)))","A"
1196,1,153,73,0.047000," ","int((a*x^2+b^2)*(b+(a*x^2+b^2)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\left(b^{2}\right)^{\frac{1}{4}} a \sqrt{2}\, x^{3} \hypergeom \left(\left[-\frac{1}{4}, \frac{1}{4}, \frac{3}{2}\right], \left[\frac{1}{2}, \frac{5}{2}\right], -\frac{x^{2} a}{b^{2}}\right)}{3}-\frac{b^{2} \left(b^{2}\right)^{\frac{1}{4}} \left(-\frac{32 \sqrt{\pi}\, \sqrt{2}\, x^{3} \sqrt{\frac{a}{b^{2}}}\, a \cosh \left(\frac{3 \arcsinh \left(\frac{x \sqrt{a}}{b}\right)}{2}\right)}{3 b^{2}}-\frac{8 \sqrt{\pi}\, \sqrt{2}\, \sqrt{\frac{a}{b^{2}}}\, \left(-\frac{4 x^{4} a^{2}}{3 b^{4}}-\frac{2 x^{2} a}{3 b^{2}}+\frac{2}{3}\right) \sinh \left(\frac{3 \arcsinh \left(\frac{x \sqrt{a}}{b}\right)}{2}\right) b}{\sqrt{a}\, \sqrt{\frac{x^{2} a}{b^{2}}+1}}\right)}{8 \sqrt{\pi}\, \sqrt{\frac{a}{b^{2}}}}$&$153$\\ \hline \end{longtable}"," ",0,"1/3*(b^2)^(1/4)*a*2^(1/2)*x^3*hypergeom([-1/4,1/4,3/2],[1/2,5/2],-x^2*a/b^2)-1/8*b^2*(b^2)^(1/4)/Pi^(1/2)/(a/b^2)^(1/2)*(-32/3*Pi^(1/2)*2^(1/2)*x^3*(a/b^2)^(1/2)*a/b^2*cosh(3/2*arcsinh(x*a^(1/2)/b))-8*Pi^(1/2)*2^(1/2)*(a/b^2)^(1/2)*(-4/3*x^4*a^2/b^4-2/3*x^2*a/b^2+2/3)*sinh(3/2*arcsinh(x*a^(1/2)/b))/a^(1/2)*b/(x^2*a/b^2+1)^(1/2))","C"
1197,0,0,24,0.040000," ","int(1/(x+(x+(x^2+1)^(1/2))^(1/2)),x)","\[\int \frac{1}{x +\sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int(1/(x+(x+(x^2+1)^(1/2))^(1/2)),x)","F"
1198,0,0,24,0.001000," ","int(1/(x+(x+(x^2+1)^(1/2))^(1/2)),x)","\[\int \frac{1}{x +\sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int(1/(x+(x+(x^2+1)^(1/2))^(1/2)),x)","F"
1199,1,346,70,1.964000," ","int(1/(-2+x)/(x^2-4*x-4)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\ln \left(-\frac{4 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x^{2}+48 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{2}-4 x -4\right)^{\frac{2}{3}}-16 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x +9 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x^{2}-9 \left(x^{2}-4 x -4\right)^{\frac{2}{3}}+60 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{2}-4 x -4\right)^{\frac{1}{3}}-36 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x +2 x^{2}-48 \left(x^{2}-4 x -4\right)^{\frac{1}{3}}-28 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)-8 x -56}{\left(-2+x \right)^{2}}\right)}{4}+\frac{\RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \ln \left(\frac{-32 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x^{2}+96 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{2}-4 x -4\right)^{\frac{2}{3}}+128 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x +20 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x^{2}-30 \left(x^{2}-4 x -4\right)^{\frac{2}{3}}+72 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{2}-4 x -4\right)^{\frac{1}{3}}-80 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x +3 x^{2}-96 \left(x^{2}-4 x -4\right)^{\frac{1}{3}}-224 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)-12 x -28}{\left(-2+x \right)^{2}}\right)}{2}$&$346$\\ \hline \end{longtable}"," ",0,"-1/4*ln(-(4*RootOf(4*_Z^2-2*_Z+1)^2*x^2+48*RootOf(4*_Z^2-2*_Z+1)*(x^2-4*x-4)^(2/3)-16*RootOf(4*_Z^2-2*_Z+1)^2*x+9*RootOf(4*_Z^2-2*_Z+1)*x^2-9*(x^2-4*x-4)^(2/3)+60*RootOf(4*_Z^2-2*_Z+1)*(x^2-4*x-4)^(1/3)-36*RootOf(4*_Z^2-2*_Z+1)*x+2*x^2-48*(x^2-4*x-4)^(1/3)-28*RootOf(4*_Z^2-2*_Z+1)-8*x-56)/(-2+x)^2)+1/2*RootOf(4*_Z^2-2*_Z+1)*ln((-32*RootOf(4*_Z^2-2*_Z+1)^2*x^2+96*RootOf(4*_Z^2-2*_Z+1)*(x^2-4*x-4)^(2/3)+128*RootOf(4*_Z^2-2*_Z+1)^2*x+20*RootOf(4*_Z^2-2*_Z+1)*x^2-30*(x^2-4*x-4)^(2/3)+72*RootOf(4*_Z^2-2*_Z+1)*(x^2-4*x-4)^(1/3)-80*RootOf(4*_Z^2-2*_Z+1)*x+3*x^2-96*(x^2-4*x-4)^(1/3)-224*RootOf(4*_Z^2-2*_Z+1)-12*x-28)/(-2+x)^2)","C"
1200,1,315,70,0.166000," ","int((k*x^2-1)/(b*x+a)/((1-x)*x*(-k*x+1))^(1/2)/(a*k*x+b),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 \sqrt{-\left(x -\frac{1}{k}\right) k}\, \sqrt{\frac{-1+x}{\frac{1}{k}-1}}\, \sqrt{k x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k}\right) k}, \sqrt{\frac{1}{k \left(\frac{1}{k}-1\right)}}\right)}{a b k \sqrt{k \,x^{3}-k \,x^{2}-x^{2}+x}}+\frac{2 \sqrt{-\left(x -\frac{1}{k}\right) k}\, \sqrt{\frac{-1+x}{\frac{1}{k}-1}}\, \sqrt{k x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k}\right) k}, \frac{1}{k \left(\frac{1}{k}+\frac{b}{a k}\right)}, \sqrt{\frac{1}{k \left(\frac{1}{k}-1\right)}}\right)}{a^{2} k^{2} \sqrt{k \,x^{3}-k \,x^{2}-x^{2}+x}\, \left(\frac{1}{k}+\frac{b}{a k}\right)}+\frac{2 \sqrt{-\left(x -\frac{1}{k}\right) k}\, \sqrt{\frac{-1+x}{\frac{1}{k}-1}}\, \sqrt{k x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k}\right) k}, \frac{1}{k \left(\frac{1}{k}+\frac{a}{b}\right)}, \sqrt{\frac{1}{k \left(\frac{1}{k}-1\right)}}\right)}{b^{2} k \sqrt{k \,x^{3}-k \,x^{2}-x^{2}+x}\, \left(\frac{1}{k}+\frac{a}{b}\right)}$&$315$\\ elliptic&$-\frac{2 \sqrt{-k x +1}\, \sqrt{-\frac{1}{\frac{1}{k}-1}+\frac{x}{\frac{1}{k}-1}}\, \sqrt{k x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k}\right) k}, \sqrt{\frac{1}{k \left(\frac{1}{k}-1\right)}}\right)}{a b k \sqrt{k \,x^{3}-k \,x^{2}-x^{2}+x}}+\frac{2 \sqrt{-k x +1}\, \sqrt{-\frac{1}{\frac{1}{k}-1}+\frac{x}{\frac{1}{k}-1}}\, \sqrt{k x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k}\right) k}, \frac{1}{k \left(\frac{1}{k}+\frac{a}{b}\right)}, \sqrt{\frac{1}{k \left(\frac{1}{k}-1\right)}}\right)}{\left(-a^{2} k +b^{2}\right) k \sqrt{k \,x^{3}-k \,x^{2}-x^{2}+x}\, \left(\frac{1}{k}+\frac{a}{b}\right)}-\frac{2 \sqrt{-k x +1}\, \sqrt{-\frac{1}{\frac{1}{k}-1}+\frac{x}{\frac{1}{k}-1}}\, \sqrt{k x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k}\right) k}, \frac{1}{k \left(\frac{1}{k}+\frac{a}{b}\right)}, \sqrt{\frac{1}{k \left(\frac{1}{k}-1\right)}}\right) a^{2}}{\left(-a^{2} k +b^{2}\right) \sqrt{k \,x^{3}-k \,x^{2}-x^{2}+x}\, \left(\frac{1}{k}+\frac{a}{b}\right) b^{2}}+\frac{2 \sqrt{-k x +1}\, \sqrt{-\frac{1}{\frac{1}{k}-1}+\frac{x}{\frac{1}{k}-1}}\, \sqrt{k x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k}\right) k}, \frac{1}{k \left(\frac{1}{k}+\frac{b}{a k}\right)}, \sqrt{\frac{1}{k \left(\frac{1}{k}-1\right)}}\right)}{\left(a^{2} k -b^{2}\right) k \sqrt{k \,x^{3}-k \,x^{2}-x^{2}+x}\, \left(\frac{1}{k}+\frac{b}{a k}\right)}-\frac{2 \sqrt{-k x +1}\, \sqrt{-\frac{1}{\frac{1}{k}-1}+\frac{x}{\frac{1}{k}-1}}\, \sqrt{k x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k}\right) k}, \frac{1}{k \left(\frac{1}{k}+\frac{b}{a k}\right)}, \sqrt{\frac{1}{k \left(\frac{1}{k}-1\right)}}\right) b^{2}}{\left(a^{2} k -b^{2}\right) k^{2} \sqrt{k \,x^{3}-k \,x^{2}-x^{2}+x}\, \left(\frac{1}{k}+\frac{b}{a k}\right) a^{2}}$&$608$\\ \hline \end{longtable}"," ",0,"-2/a/b/k*(-(x-1/k)*k)^(1/2)*((-1+x)/(1/k-1))^(1/2)*(k*x)^(1/2)/(k*x^3-k*x^2-x^2+x)^(1/2)*EllipticF((-(x-1/k)*k)^(1/2),(1/k/(1/k-1))^(1/2))+2/a^2/k^2*(-(x-1/k)*k)^(1/2)*((-1+x)/(1/k-1))^(1/2)*(k*x)^(1/2)/(k*x^3-k*x^2-x^2+x)^(1/2)/(1/k+b/a/k)*EllipticPi((-(x-1/k)*k)^(1/2),1/k/(1/k+b/a/k),(1/k/(1/k-1))^(1/2))+2/b^2/k*(-(x-1/k)*k)^(1/2)*((-1+x)/(1/k-1))^(1/2)*(k*x)^(1/2)/(k*x^3-k*x^2-x^2+x)^(1/2)/(1/k+a/b)*EllipticPi((-(x-1/k)*k)^(1/2),1/k/(1/k+a/b),(1/k/(1/k-1))^(1/2))","C"
1201,1,358,76,0.112000," ","int(x*(-b+x)*(a*b-2*a*x+x^2)/(x*(-a+x)*(-b+x))^(1/2)/(-a^2+2*a*x+(b^2*d-1)*x^2-2*b*d*x^3+d*x^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 b \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)}{d \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}-\frac{b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(d \,\textit{\_Z}^{4}-2 b d \,\textit{\_Z}^{3}+\left(b^{2} d -1\right) \textit{\_Z}^{2}+2 a \textit{\_Z} -a^{2}\right)}{\sum}\frac{\left(-2 \underline{\hspace{1.25 ex}}\alpha^{3} a d +\underline{\hspace{1.25 ex}}\alpha^{3} b d +3 \underline{\hspace{1.25 ex}}\alpha^{2} a b d -\underline{\hspace{1.25 ex}}\alpha^{2} b^{2} d -\underline{\hspace{1.25 ex}}\alpha  a \,b^{2} d +\underline{\hspace{1.25 ex}}\alpha^{2}-2 \underline{\hspace{1.25 ex}}\alpha  a +a^{2}\right) \left(d \,\underline{\hspace{1.25 ex}}\alpha^{3}-b d \,\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +2 a -b \right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, -\frac{\left(d \,\underline{\hspace{1.25 ex}}\alpha^{3}-b d \,\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +2 a -b \right) b}{a^{2}-2 a b +b^{2}}, \sqrt{\frac{b}{-a +b}}\right)}{\left(-2 d \,\underline{\hspace{1.25 ex}}\alpha^{3}+3 b d \,\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  \,b^{2} d +\underline{\hspace{1.25 ex}}\alpha  -a \right) \left(a^{2}-2 a b +b^{2}\right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}\right)}{d}$&$358$\\ elliptic&$-\frac{2 b \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)}{d \sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}-\frac{b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(d \,\textit{\_Z}^{4}-2 b d \,\textit{\_Z}^{3}+\left(b^{2} d -1\right) \textit{\_Z}^{2}+2 a \textit{\_Z} -a^{2}\right)}{\sum}\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{3} a d -\underline{\hspace{1.25 ex}}\alpha^{3} b d -3 \underline{\hspace{1.25 ex}}\alpha^{2} a b d +\underline{\hspace{1.25 ex}}\alpha^{2} b^{2} d +\underline{\hspace{1.25 ex}}\alpha  a \,b^{2} d -\underline{\hspace{1.25 ex}}\alpha^{2}+2 \underline{\hspace{1.25 ex}}\alpha  a -a^{2}\right) \left(d \,\underline{\hspace{1.25 ex}}\alpha^{3}-b d \,\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +2 a -b \right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, -\frac{\left(d \,\underline{\hspace{1.25 ex}}\alpha^{3}-b d \,\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +2 a -b \right) b}{a^{2}-2 a b +b^{2}}, \sqrt{\frac{b}{-a +b}}\right)}{\left(2 d \,\underline{\hspace{1.25 ex}}\alpha^{3}-3 b d \,\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  \,b^{2} d -\underline{\hspace{1.25 ex}}\alpha  +a \right) \left(a^{2}-2 a b +b^{2}\right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}\right)}{d}$&$360$\\ \hline \end{longtable}"," ",0,"-2/d*b*(-(-b+x)/b)^(1/2)*((-a+x)/(-a+b))^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)*EllipticF((-(-b+x)/b)^(1/2),(b/(-a+b))^(1/2))-1/d*b*sum((-2*_alpha^3*a*d+_alpha^3*b*d+3*_alpha^2*a*b*d-_alpha^2*b^2*d-_alpha*a*b^2*d+_alpha^2-2*_alpha*a+a^2)/(-2*_alpha^3*d+3*_alpha^2*b*d-_alpha*b^2*d+_alpha-a)*(_alpha^3*d-_alpha^2*b*d-_alpha+2*a-b)/(a^2-2*a*b+b^2)*(-(-b+x)/b)^(1/2)*((-a+x)/(-a+b))^(1/2)*(x/b)^(1/2)/(x*(a*b-a*x-b*x+x^2))^(1/2)*EllipticPi((-(-b+x)/b)^(1/2),-(_alpha^3*d-_alpha^2*b*d-_alpha+2*a-b)*b/(a^2-2*a*b+b^2),(b/(-a+b))^(1/2)),_alpha=RootOf(d*_Z^4-2*b*d*_Z^3+(b^2*d-1)*_Z^2+2*a*_Z-a^2))","C"
1202,1,601,70,5.417000," ","int((x^4+1)/(x^4-x^2-1)/(x^5-x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\ln \left(-\frac{8793584675980112 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{4}+19508929144777782 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{4}-32975942534925420 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{2}-3267606844103087 x^{4}+41156279639771682 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{5}-x \right)^{\frac{2}{3}}+41156279639771682 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{5}-x \right)^{\frac{1}{3}} x +9556171565521246 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{2}+2090065390295748 \left(x^{5}-x \right)^{\frac{2}{3}}+2090065390295748 x \left(x^{5}-x \right)^{\frac{1}{3}}-8793584675980112 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}-687917230337492 x^{2}-19508929144777782 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+3267606844103087}{x^{4}-x^{2}-1}\right)}{2}-\ln \left(-\frac{8793584675980112 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{4}+19508929144777782 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{4}-32975942534925420 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{2}-3267606844103087 x^{4}+41156279639771682 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{5}-x \right)^{\frac{2}{3}}+41156279639771682 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{5}-x \right)^{\frac{1}{3}} x +9556171565521246 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{2}+2090065390295748 \left(x^{5}-x \right)^{\frac{2}{3}}+2090065390295748 x \left(x^{5}-x \right)^{\frac{1}{3}}-8793584675980112 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}-687917230337492 x^{2}-19508929144777782 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+3267606844103087}{x^{4}-x^{2}-1}\right) \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+\RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \ln \left(\frac{-8793584675980112 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{4}+10715344468797670 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{4}+32975942534925420 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{2}+10823675247496950 x^{4}+41156279639771682 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{5}-x \right)^{\frac{2}{3}}+41156279639771682 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{5}-x \right)^{\frac{1}{3}} x +42532114100446666 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{2}+18488074429590093 \left(x^{5}-x \right)^{\frac{2}{3}}+18488074429590093 x \left(x^{5}-x \right)^{\frac{1}{3}}+8793584675980112 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}+13709988646829470 x^{2}-10715344468797670 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)-10823675247496950}{x^{4}-x^{2}-1}\right)$&$601$\\ \hline \end{longtable}"," ",0,"-1/2*ln(-(8793584675980112*RootOf(4*_Z^2+2*_Z+1)^2*x^4+19508929144777782*RootOf(4*_Z^2+2*_Z+1)*x^4-32975942534925420*RootOf(4*_Z^2+2*_Z+1)^2*x^2-3267606844103087*x^4+41156279639771682*RootOf(4*_Z^2+2*_Z+1)*(x^5-x)^(2/3)+41156279639771682*RootOf(4*_Z^2+2*_Z+1)*(x^5-x)^(1/3)*x+9556171565521246*RootOf(4*_Z^2+2*_Z+1)*x^2+2090065390295748*(x^5-x)^(2/3)+2090065390295748*x*(x^5-x)^(1/3)-8793584675980112*RootOf(4*_Z^2+2*_Z+1)^2-687917230337492*x^2-19508929144777782*RootOf(4*_Z^2+2*_Z+1)+3267606844103087)/(x^4-x^2-1))-ln(-(8793584675980112*RootOf(4*_Z^2+2*_Z+1)^2*x^4+19508929144777782*RootOf(4*_Z^2+2*_Z+1)*x^4-32975942534925420*RootOf(4*_Z^2+2*_Z+1)^2*x^2-3267606844103087*x^4+41156279639771682*RootOf(4*_Z^2+2*_Z+1)*(x^5-x)^(2/3)+41156279639771682*RootOf(4*_Z^2+2*_Z+1)*(x^5-x)^(1/3)*x+9556171565521246*RootOf(4*_Z^2+2*_Z+1)*x^2+2090065390295748*(x^5-x)^(2/3)+2090065390295748*x*(x^5-x)^(1/3)-8793584675980112*RootOf(4*_Z^2+2*_Z+1)^2-687917230337492*x^2-19508929144777782*RootOf(4*_Z^2+2*_Z+1)+3267606844103087)/(x^4-x^2-1))*RootOf(4*_Z^2+2*_Z+1)+RootOf(4*_Z^2+2*_Z+1)*ln((-8793584675980112*RootOf(4*_Z^2+2*_Z+1)^2*x^4+10715344468797670*RootOf(4*_Z^2+2*_Z+1)*x^4+32975942534925420*RootOf(4*_Z^2+2*_Z+1)^2*x^2+10823675247496950*x^4+41156279639771682*RootOf(4*_Z^2+2*_Z+1)*(x^5-x)^(2/3)+41156279639771682*RootOf(4*_Z^2+2*_Z+1)*(x^5-x)^(1/3)*x+42532114100446666*RootOf(4*_Z^2+2*_Z+1)*x^2+18488074429590093*(x^5-x)^(2/3)+18488074429590093*x*(x^5-x)^(1/3)+8793584675980112*RootOf(4*_Z^2+2*_Z+1)^2+13709988646829470*x^2-10715344468797670*RootOf(4*_Z^2+2*_Z+1)-10823675247496950)/(x^4-x^2-1))","C"
1203,1,33,70,3.183000," ","int(x^3/(x^6-1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{2}{3}} x^{4} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], x^{6}\right)}{4 \mathrm{signum}\left(x^{6}-1\right)^{\frac{2}{3}}}$&$33$\\ trager&$-\frac{\ln \left(-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}+x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}-3 x^{4} \left(x^{6}-1\right)^{\frac{1}{3}}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-1\right)}{6}+\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}-2 x^{6}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}+3 x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+1\right)}{6}$&$195$\\ \hline \end{longtable}"," ",0,"1/4/signum(x^6-1)^(2/3)*(-signum(x^6-1))^(2/3)*x^4*hypergeom([2/3,2/3],[5/3],x^6)","C"
1204,1,33,70,3.494000," ","int(x/(x^6-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} x^{2} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{6}\right)}{2 \mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}}}$&$33$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}-4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}+4 x^{6}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}+3 x^{4} \left(x^{6}-1\right)^{\frac{1}{3}}+3 x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-2\right)}{6}-\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}+x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-1\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)}{6}+\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}+x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-1\right)}{6}$&$314$\\ \hline \end{longtable}"," ",0,"1/2/signum(x^6-1)^(1/3)*(-signum(x^6-1))^(1/3)*x^2*hypergeom([1/3,1/3],[4/3],x^6)","C"
1205,1,17,70,3.122000," ","int(x^3/(x^6+1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{x^{4} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], -x^{6}\right)}{4}$&$17$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}} x^{4}+x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+1\right)}{6}-\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}-4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}} x^{4}+4 x^{6}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x^{2}+3 x^{4} \left(x^{6}+1\right)^{\frac{1}{3}}+3 x^{2} \left(x^{6}+1\right)^{\frac{2}{3}}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+2\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)}{6}+\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}-4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}} x^{4}+4 x^{6}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x^{2}+3 x^{4} \left(x^{6}+1\right)^{\frac{1}{3}}+3 x^{2} \left(x^{6}+1\right)^{\frac{2}{3}}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+2\right)}{6}$&$340$\\ \hline \end{longtable}"," ",0,"1/4*x^4*hypergeom([2/3,2/3],[5/3],-x^6)","C"
1206,1,17,70,3.712000," ","int(x/(x^6+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{x^{2} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{6}\right)}{2}$&$17$\\ trager&$-\frac{\ln \left(-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}+5 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}-2 x^{6}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x^{2}-3 x^{4} \left(x^{6}+1\right)^{\frac{1}{3}}+3 x^{2} \left(x^{6}+1\right)^{\frac{2}{3}}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-1\right)}{6}+\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}} x^{4}-2 x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x^{2}+3 x^{4} \left(x^{6}+1\right)^{\frac{1}{3}}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-2\right)}{6}$&$209$\\ \hline \end{longtable}"," ",0,"1/2*x^2*hypergeom([1/3,1/3],[4/3],-x^6)","C"
1207,0,0,68,0.011000," ","int((a*x^8-b)/x^2/(a*x^4-b)^(3/4),x)","\[\int \frac{a \,x^{8}-b}{x^{2} \left(a \,x^{4}-b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int((a*x^8-b)/x^2/(a*x^4-b)^(3/4),x)","F"
1208,0,0,72,0.010000," ","int((2*a*x^8-3*b)/x^8/(a*x^4-b)^(1/4),x)","\[\int \frac{2 a \,x^{8}-3 b}{x^{8} \left(a \,x^{4}-b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((2*a*x^8-3*b)/x^8/(a*x^4-b)^(1/4),x)","F"
1209,0,0,34,0.013000," ","int((a^2*x^8-b^2)/x^2/(a*x^4+b)^(3/4)/(a^2*x^8+b^2),x)","\[\int \frac{a^{2} x^{8}-b^{2}}{x^{2} \left(a \,x^{4}+b \right)^{\frac{3}{4}} \left(a^{2} x^{8}+b^{2}\right)}\, dx\]"," ",0,"int((a^2*x^8-b^2)/x^2/(a*x^4+b)^(3/4)/(a^2*x^8+b^2),x)","F"
1210,0,0,74,0.035000," ","int((a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2)/x/(-a/b^2+a^2*x^2/b^2)^(1/2),x)","\[\int \frac{\sqrt{a \,x^{2}+b x \sqrt{-\frac{a}{b^{2}}+\frac{a^{2} x^{2}}{b^{2}}}}}{x \sqrt{-\frac{a}{b^{2}}+\frac{a^{2} x^{2}}{b^{2}}}}\, dx\]"," ",0,"int((a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2)/x/(-a/b^2+a^2*x^2/b^2)^(1/2),x)","F"
1211,1,84,67,1.867000," ","int((x^2-1)^(2/3)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \mathrm{signum}\left(x^{2}-1\right)^{\frac{2}{3}} \left(\frac{2 \pi  \sqrt{3}\, x^{2} \hypergeom \left(\left[\frac{1}{3}, 1, 1\right], \left[2, 2\right], x^{2}\right)}{3 \Gamma \left(\frac{2}{3}\right)}-\frac{\left(\frac{3}{2}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+2 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right)}\right)}{6 \pi  \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{2}{3}}}$&$84$\\ trager&$\frac{3 \left(x^{2}-1\right)^{\frac{2}{3}}}{4}-\frac{\ln \left(\frac{-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}+45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{2}{3}}-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}-9 \left(x^{2}-1\right)^{\frac{2}{3}}-45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{1}{3}}+36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+10 x^{2}+9 \left(x^{2}-1\right)^{\frac{1}{3}}+57 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-5}{x^{2}}\right)}{2}-\frac{3 \ln \left(\frac{-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}+45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{2}{3}}-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}-9 \left(x^{2}-1\right)^{\frac{2}{3}}-45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{1}{3}}+36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+10 x^{2}+9 \left(x^{2}-1\right)^{\frac{1}{3}}+57 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-5}{x^{2}}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{2}+\frac{3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(-\frac{9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}+45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{2}{3}}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+24 \left(x^{2}-1\right)^{\frac{2}{3}}-45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{1}{3}}-36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-12 x^{2}-24 \left(x^{2}-1\right)^{\frac{1}{3}}+33 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+20}{x^{2}}\right)}{2}$&$436$\\ \hline \end{longtable}"," ",0,"-1/6/Pi*3^(1/2)*GAMMA(2/3)*signum(x^2-1)^(2/3)/(-signum(x^2-1))^(2/3)*(2/3*Pi*3^(1/2)/GAMMA(2/3)*x^2*hypergeom([1/3,1,1],[2,2],x^2)-(3/2-1/6*Pi*3^(1/2)-3/2*ln(3)+2*ln(x)+I*Pi)*Pi*3^(1/2)/GAMMA(2/3))","C"
1212,1,334,73,2.086000," ","int((-3+x)/(x^2-1)^(1/3)/(x^2+x+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}-6 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x -\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+3 \left(x^{2}-1\right)^{\frac{2}{3}}+3 x \left(x^{2}-1\right)^{\frac{1}{3}}-5 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +3 \left(x^{2}-1\right)^{\frac{1}{3}}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-x +1}{x^{2}+x +2}\right)-\ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}-6 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x -3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+3 \left(x^{2}-1\right)^{\frac{2}{3}}+3 x \left(x^{2}-1\right)^{\frac{1}{3}}-7 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x -x^{2}+3 \left(x^{2}-1\right)^{\frac{1}{3}}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2 x -1}{x^{2}+x +2}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-\ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}-6 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x -3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+3 \left(x^{2}-1\right)^{\frac{2}{3}}+3 x \left(x^{2}-1\right)^{\frac{1}{3}}-7 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x -x^{2}+3 \left(x^{2}-1\right)^{\frac{1}{3}}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2 x -1}{x^{2}+x +2}\right)$&$334$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2+_Z+1)*ln(-(-2*RootOf(_Z^2+_Z+1)^2*x^2-6*RootOf(_Z^2+_Z+1)^2*x-RootOf(_Z^2+_Z+1)*x^2+3*(x^2-1)^(2/3)+3*x*(x^2-1)^(1/3)-5*RootOf(_Z^2+_Z+1)*x+3*(x^2-1)^(1/3)+2*RootOf(_Z^2+_Z+1)-x+1)/(x^2+x+2))-ln(-(-2*RootOf(_Z^2+_Z+1)^2*x^2-6*RootOf(_Z^2+_Z+1)^2*x-3*RootOf(_Z^2+_Z+1)*x^2+3*(x^2-1)^(2/3)+3*x*(x^2-1)^(1/3)-7*RootOf(_Z^2+_Z+1)*x-x^2+3*(x^2-1)^(1/3)-2*RootOf(_Z^2+_Z+1)-2*x-1)/(x^2+x+2))*RootOf(_Z^2+_Z+1)-ln(-(-2*RootOf(_Z^2+_Z+1)^2*x^2-6*RootOf(_Z^2+_Z+1)^2*x-3*RootOf(_Z^2+_Z+1)*x^2+3*(x^2-1)^(2/3)+3*x*(x^2-1)^(1/3)-7*RootOf(_Z^2+_Z+1)*x-x^2+3*(x^2-1)^(1/3)-2*RootOf(_Z^2+_Z+1)-2*x-1)/(x^2+x+2))","C"
1213,1,1516,69,1.176000," ","int((x^2+2)/(x^2-2*x-2)/(x^3-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{3 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}+\frac{\sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}+\frac{3 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}-\frac{\sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}$&$1516$\\ elliptic&$-\frac{3 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}+\frac{3 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}+\frac{\sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}+\frac{3 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}-\frac{\sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}$&$1725$\\ \hline \end{longtable}"," ",0,"2*(-3/2-1/2*I*3^(1/2))*((-1+x)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((-1+x)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))+3*(-1/(-3/2-1/2*I*3^(1/2))+1/(-3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)*EllipticPi(((-1+x)/(-3/2-1/2*I*3^(1/2)))^(1/2),-1/3*(3/2+1/2*I*3^(1/2))*3^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))+I*(-1/(-3/2-1/2*I*3^(1/2))+1/(-3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)*EllipticPi(((-1+x)/(-3/2-1/2*I*3^(1/2)))^(1/2),-1/3*(3/2+1/2*I*3^(1/2))*3^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))+I*(-1/(-3/2-1/2*I*3^(1/2))+1/(-3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)*EllipticPi(((-1+x)/(-3/2-1/2*I*3^(1/2)))^(1/2),-1/3*(3/2+1/2*I*3^(1/2))*3^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)+(-1/(-3/2-1/2*I*3^(1/2))+1/(-3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)*EllipticPi(((-1+x)/(-3/2-1/2*I*3^(1/2)))^(1/2),-1/3*(3/2+1/2*I*3^(1/2))*3^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)+3*(-1/(-3/2-1/2*I*3^(1/2))+1/(-3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)*EllipticPi(((-1+x)/(-3/2-1/2*I*3^(1/2)))^(1/2),1/3*(3/2+1/2*I*3^(1/2))*3^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-I*(-1/(-3/2-1/2*I*3^(1/2))+1/(-3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)*EllipticPi(((-1+x)/(-3/2-1/2*I*3^(1/2)))^(1/2),1/3*(3/2+1/2*I*3^(1/2))*3^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))+I*(-1/(-3/2-1/2*I*3^(1/2))+1/(-3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)*EllipticPi(((-1+x)/(-3/2-1/2*I*3^(1/2)))^(1/2),1/3*(3/2+1/2*I*3^(1/2))*3^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)-(-1/(-3/2-1/2*I*3^(1/2))+1/(-3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)*EllipticPi(((-1+x)/(-3/2-1/2*I*3^(1/2)))^(1/2),1/3*(3/2+1/2*I*3^(1/2))*3^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)","C"
1214,1,65,70,2.397000," ","int((x^3-1)*(x^3+1)^(1/3)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{-\Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[\frac{2}{3}, 1, 1\right], \left[2, 2\right], -x^{3}\right)-3 \left(3+\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{x^{3} \hypergeom \left(\left[-\frac{1}{3}, 1\right], \left[2\right], -x^{3}\right)}{3}$&$65$\\ trager&$\left(\frac{x^{3}}{4}-\frac{3}{4}\right) \left(x^{3}+1\right)^{\frac{1}{3}}+\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\frac{-4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+17 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+15 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}-15 x^{3}-24 \left(x^{3}+1\right)^{\frac{2}{3}}+15 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}-24 \left(x^{3}+1\right)^{\frac{1}{3}}+11 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-20}{x^{3}}\right)}{3}-\frac{\ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+15 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}+2 x^{3}+9 \left(x^{3}+1\right)^{\frac{2}{3}}+15 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}+9 \left(x^{3}+1\right)^{\frac{1}{3}}+19 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+5}{x^{3}}\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)}{3}+\frac{\ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+15 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}+2 x^{3}+9 \left(x^{3}+1\right)^{\frac{2}{3}}+15 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}+9 \left(x^{3}+1\right)^{\frac{1}{3}}+19 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+5}{x^{3}}\right)}{3}$&$403$\\ \hline \end{longtable}"," ",0,"1/9/GAMMA(2/3)*(-GAMMA(2/3)*x^3*hypergeom([2/3,1,1],[2,2],-x^3)-3*(3+1/6*Pi*3^(1/2)-3/2*ln(3)+3*ln(x))*GAMMA(2/3))+1/3*x^3*hypergeom([-1/3,1],[2],-x^3)","C"
1215,0,0,77,0.012000," ","int((-a*b+2*(a-b)*x+x^2)/(x*(-a+x)*(-b+x))^(1/4)/(-a^3+(3*a^2+b*d)*x-(3*a+d)*x^2+x^3),x)","\[\int \frac{-a b +2 \left(a -b \right) x +x^{2}}{\left(x \left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{4}} \left(-a^{3}+\left(3 a^{2}+b d \right) x -\left(3 a +d \right) x^{2}+x^{3}\right)}\, dx\]"," ",0,"int((-a*b+2*(a-b)*x+x^2)/(x*(-a+x)*(-b+x))^(1/4)/(-a^3+(3*a^2+b*d)*x-(3*a+d)*x^2+x^3),x)","F"
1216,0,0,73,0.020000," ","int((x^2-2*x+1)*(-1+2*(-1+k)*x+k*x^2)/((1-x)*x*(-k*x+1))^(3/4)/(-d+(1+3*d)*x-(3*d+k)*x^2+d*x^3),x)","\[\int \frac{\left(x^{2}-2 x +1\right) \left(-1+2 \left(-1+k \right) x +k \,x^{2}\right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{3}{4}} \left(-d +\left(1+3 d \right) x -\left(3 d +k \right) x^{2}+d \,x^{3}\right)}\, dx\]"," ",0,"int((x^2-2*x+1)*(-1+2*(-1+k)*x+k*x^2)/((1-x)*x*(-k*x+1))^(3/4)/(-d+(1+3*d)*x-(3*d+k)*x^2+d*x^3),x)","F"
1217,1,133,73,0.811000," ","int(x^2/(x^3+x^2+x)^(1/2)/(x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) x^{2}+4 \RootOf \left(\textit{\_Z}^{2}-3\right) x +6 \sqrt{x^{3}+x^{2}+x}+\RootOf \left(\textit{\_Z}^{2}-3\right)}{\left(-1+x \right)^{2}}\right)}{24}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \sqrt{x^{3}+x^{2}+x}-\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(1+x \right)^{2}}\right)}{8}+\frac{\ln \left(\frac{x^{2}+2 \sqrt{x^{3}+x^{2}+x}+2 x +1}{x^{2}+1}\right)}{4}$&$133$\\ default&$-\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{1}{2}-i-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{12 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{1}{2}-i-\frac{i \sqrt{3}}{2}\right)}+\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{1}{2}-i-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{4 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{1}{2}-i-\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{1}{2}+i-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{12 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{1}{2}+i-\frac{i \sqrt{3}}{2}\right)}-\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{1}{2}+i-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{4 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{1}{2}+i-\frac{i \sqrt{3}}{2}\right)}-\frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{6 \sqrt{x^{3}+x^{2}+x}\, \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}+\frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{6 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}$&$960$\\ elliptic&$-\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}-i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{12 \sqrt{x^{3}+x^{2}+x}}-\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}-i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{6 \sqrt{x^{3}+x^{2}+x}}+\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}-i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{4 \sqrt{x^{3}+x^{2}+x}}+\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}+i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{12 \sqrt{x^{3}+x^{2}+x}}-\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}+i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{6 \sqrt{x^{3}+x^{2}+x}}-\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}+i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{4 \sqrt{x^{3}+x^{2}+x}}-\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{12 \sqrt{x^{3}+x^{2}+x}\, \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{4 \sqrt{x^{3}+x^{2}+x}\, \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}+\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{12 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{4 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}$&$1500$\\ \hline \end{longtable}"," ",0,"-1/24*RootOf(_Z^2-3)*ln((RootOf(_Z^2-3)*x^2+4*RootOf(_Z^2-3)*x+6*(x^3+x^2+x)^(1/2)+RootOf(_Z^2-3))/(-1+x)^2)+1/8*RootOf(_Z^2+1)*ln((-RootOf(_Z^2+1)*x^2+2*(x^3+x^2+x)^(1/2)-RootOf(_Z^2+1))/(1+x)^2)+1/4*ln((x^2+2*(x^3+x^2+x)^(1/2)+2*x+1)/(x^2+1))","C"
1218,1,133,73,0.745000," ","int((x^3+x^2+x)^(1/2)/(x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \sqrt{x^{3}+x^{2}+x}+\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(1+x \right)^{2}}\right)}{8}+\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}-3\right) x^{2}-4 \RootOf \left(\textit{\_Z}^{2}-3\right) x +6 \sqrt{x^{3}+x^{2}+x}-\RootOf \left(\textit{\_Z}^{2}-3\right)}{\left(-1+x \right)^{2}}\right)}{8}+\frac{\ln \left(\frac{x^{2}+2 \sqrt{x^{3}+x^{2}+x}+2 x +1}{x^{2}+1}\right)}{4}$&$133$\\ elliptic&$-\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}-i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{12 \sqrt{x^{3}+x^{2}+x}}-\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}-i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{6 \sqrt{x^{3}+x^{2}+x}}+\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}-i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{4 \sqrt{x^{3}+x^{2}+x}}+\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}+i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{12 \sqrt{x^{3}+x^{2}+x}}-\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}+i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{6 \sqrt{x^{3}+x^{2}+x}}-\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}+i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{4 \sqrt{x^{3}+x^{2}+x}}+\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{12 \sqrt{x^{3}+x^{2}+x}\, \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{4 \sqrt{x^{3}+x^{2}+x}\, \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}+\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{4 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}+\frac{3 i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{4 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}$&$1500$\\ default&$\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{6 \sqrt{x^{3}+x^{2}+x}}+\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{1}{2}+i-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{12 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{1}{2}+i-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{1}{2}-i-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{12 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{1}{2}-i-\frac{i \sqrt{3}}{2}\right)}-\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticE \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{2 \sqrt{x^{3}+x^{2}+x}}-\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{2 \sqrt{x^{3}+x^{2}+x}}+\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{1}{2}-i-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{4 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{1}{2}-i-\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticE \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{2 \sqrt{x^{3}+x^{2}+x}}-\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{1}{2}+i-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{4 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{1}{2}+i-\frac{i \sqrt{3}}{2}\right)}+\frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}}+\frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \left(-i \sqrt{3}\, \EllipticE \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)+\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticF \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)\right)}{3 \sqrt{x^{3}+x^{2}+x}}+\frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{6 \sqrt{x^{3}+x^{2}+x}\, \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}+\frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{2 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}$&$1788$\\ \hline \end{longtable}"," ",0,"1/8*RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)*x^2+2*(x^3+x^2+x)^(1/2)+RootOf(_Z^2+1))/(1+x)^2)+1/8*RootOf(_Z^2-3)*ln((-RootOf(_Z^2-3)*x^2-4*RootOf(_Z^2-3)*x+6*(x^3+x^2+x)^(1/2)-RootOf(_Z^2-3))/(-1+x)^2)+1/4*ln((x^2+2*(x^3+x^2+x)^(1/2)+2*x+1)/(x^2+1))","C"
1219,1,84,67,4.048000," ","int((x^4-1)^(2/3)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \mathrm{signum}\left(x^{4}-1\right)^{\frac{2}{3}} \left(\frac{2 \pi  \sqrt{3}\, x^{4} \hypergeom \left(\left[\frac{1}{3}, 1, 1\right], \left[2, 2\right], x^{4}\right)}{3 \Gamma \left(\frac{2}{3}\right)}-\frac{\left(\frac{3}{2}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right)}\right)}{12 \pi  \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{2}{3}}}$&$84$\\ trager&$\frac{3 \left(x^{4}-1\right)^{\frac{2}{3}}}{8}-\frac{\ln \left(-\frac{-117171 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}+440973 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}+493850 x^{4}+560547 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}}-666879 \left(x^{4}-1\right)^{\frac{2}{3}}-560547 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{1}{3}}+1874736 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+666879 \left(x^{4}-1\right)^{\frac{1}{3}}+1185459 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-458575}{x^{4}}\right)}{4}-\frac{3 \ln \left(-\frac{-117171 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}+440973 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}+493850 x^{4}+560547 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}}-666879 \left(x^{4}-1\right)^{\frac{2}{3}}-560547 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{1}{3}}+1874736 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+666879 \left(x^{4}-1\right)^{\frac{1}{3}}+1185459 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-458575}{x^{4}}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{4}+\frac{3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(\frac{117171 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}+519087 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}-333840 x^{4}+560547 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}}+853728 \left(x^{4}-1\right)^{\frac{2}{3}}-560547 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{1}{3}}-1874736 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-853728 \left(x^{4}-1\right)^{\frac{1}{3}}-64365 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+645424}{x^{4}}\right)}{4}$&$437$\\ \hline \end{longtable}"," ",0,"-1/12/Pi*3^(1/2)*GAMMA(2/3)*signum(x^4-1)^(2/3)/(-signum(x^4-1))^(2/3)*(2/3*Pi*3^(1/2)/GAMMA(2/3)*x^4*hypergeom([1/3,1,1],[2,2],x^4)-(3/2-1/6*Pi*3^(1/2)-3/2*ln(3)+4*ln(x)+I*Pi)*Pi*3^(1/2)/GAMMA(2/3))","C"
1220,1,136,73,0.845000," ","int((x^4-x^2+1)/(x^3+x^2+x)^(1/2)/(x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) x^{2}+4 \RootOf \left(\textit{\_Z}^{2}-3\right) x +\RootOf \left(\textit{\_Z}^{2}-3\right)-6 \sqrt{x^{3}+x^{2}+x}}{\left(-1+x \right)^{2}}\right)}{24}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \sqrt{x^{3}+x^{2}+x}-\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(1+x \right)^{2}}\right)}{8}+\frac{3 \ln \left(\frac{-x^{2}+2 \sqrt{x^{3}+x^{2}+x}-2 x -1}{x^{2}+1}\right)}{4}$&$136$\\ default&$\frac{2 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}}+\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{1}{2}-i-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{4 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{1}{2}-i-\frac{i \sqrt{3}}{2}\right)}-\frac{3 \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{1}{2}-i-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{4 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{1}{2}-i-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{1}{2}+i-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{4 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{1}{2}+i-\frac{i \sqrt{3}}{2}\right)}+\frac{3 \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{1}{2}+i-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{4 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{1}{2}+i-\frac{i \sqrt{3}}{2}\right)}-\frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{6 \sqrt{x^{3}+x^{2}+x}\, \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}+\frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{6 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}$&$1080$\\ elliptic&$\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}}+\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{\sqrt{x^{3}+x^{2}+x}}+\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}-i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{4 \sqrt{x^{3}+x^{2}+x}}+\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}-i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{2 \sqrt{x^{3}+x^{2}+x}}-\frac{3 \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}-i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{4 \sqrt{x^{3}+x^{2}+x}}-\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}+i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{4 \sqrt{x^{3}+x^{2}+x}}+\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}+i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{2 \sqrt{x^{3}+x^{2}+x}}+\frac{3 \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}+i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{4 \sqrt{x^{3}+x^{2}+x}}-\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{12 \sqrt{x^{3}+x^{2}+x}\, \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{4 \sqrt{x^{3}+x^{2}+x}\, \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}+\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{12 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{4 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}$&$1764$\\ \hline \end{longtable}"," ",0,"1/24*RootOf(_Z^2-3)*ln(-(RootOf(_Z^2-3)*x^2+4*RootOf(_Z^2-3)*x+RootOf(_Z^2-3)-6*(x^3+x^2+x)^(1/2))/(-1+x)^2)+1/8*RootOf(_Z^2+1)*ln((-RootOf(_Z^2+1)*x^2+2*(x^3+x^2+x)^(1/2)-RootOf(_Z^2+1))/(1+x)^2)+3/4*ln((-x^2+2*(x^3+x^2+x)^(1/2)-2*x-1)/(x^2+1))","C"
1221,1,94,77,1.113000," ","int((x^2-x+1)/(x^2-1)/(x^4-x^3+x^2-x+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\ln \left(-\frac{3 x^{2}+2 \sqrt{x^{4}-x^{3}+x^{2}-x +1}-4 x +3}{\left(-1+x \right)^{2}}\right)}{4}-\frac{3 \RootOf \left(\textit{\_Z}^{2}-5\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-5\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}-5\right)-2 \sqrt{x^{4}-x^{3}+x^{2}-x +1}}{\left(1+x \right)^{2}}\right)}{20}$&$94$\\ default&$\text{Expression too large to display}$&$2852$\\ elliptic&$\text{Expression too large to display}$&$101423$\\ \hline \end{longtable}"," ",0,"-1/4*ln(-(3*x^2+2*(x^4-x^3+x^2-x+1)^(1/2)-4*x+3)/(-1+x)^2)-3/20*RootOf(_Z^2-5)*ln((RootOf(_Z^2-5)*x^2+RootOf(_Z^2-5)-2*(x^4-x^3+x^2-x+1)^(1/2))/(1+x)^2)","C"
1222,1,209,77,0.803000," ","int((-1+x)^2*(2*x^3-2*x^2+x)/(-1+2*x)/((1-2*x)/(2*x^2+1))^(1/2)/(2*x^4-4*x^3+3*x^2+4*x-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(2 x^{2}+1\right) \left(-1+x \right) \sqrt{-\frac{-1+2 x}{2 x^{2}+1}}}{3 \left(-1+2 x \right)}+\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(\frac{-2 \RootOf \left(\textit{\_Z}^{2}-3\right) x^{4}+12 \sqrt{-\frac{-1+2 x}{2 x^{2}+1}}\, x^{3}+4 \RootOf \left(\textit{\_Z}^{2}-3\right) x^{3}-12 \sqrt{-\frac{-1+2 x}{2 x^{2}+1}}\, x^{2}-3 \RootOf \left(\textit{\_Z}^{2}-3\right) x^{2}+6 \sqrt{-\frac{-1+2 x}{2 x^{2}+1}}\, x +8 \RootOf \left(\textit{\_Z}^{2}-3\right) x -6 \sqrt{-\frac{-1+2 x}{2 x^{2}+1}}-4 \RootOf \left(\textit{\_Z}^{2}-3\right)}{2 x^{4}-4 x^{3}+3 x^{2}+4 x -2}\right)}{6}$&$209$\\ default&$\frac{i \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(2 \textit{\_Z}^{4}-4 \textit{\_Z}^{3}+3 \textit{\_Z}^{2}+4 \textit{\_Z} -2\right)}{\sum}\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{3}-2 \underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  -1\right) \sqrt{-i \left(2 x +i \sqrt{2}\right)}\, \sqrt{-\frac{-1+2 x}{1+i \sqrt{2}}}\, \sqrt{-i \left(i \sqrt{2}-2 x \right)}\, \left(-2 \underline{\hspace{1.25 ex}}\alpha^{3}+6 \underline{\hspace{1.25 ex}}\alpha^{2}-6 \underline{\hspace{1.25 ex}}\alpha  -4+i \sqrt{2}\, \left(2 \underline{\hspace{1.25 ex}}\alpha^{3}-3 \underline{\hspace{1.25 ex}}\alpha^{2}+7\right)\right) \EllipticPi \left(\frac{\sqrt{-i \left(2 x +i \sqrt{2}\right) \sqrt{2}}}{2}, \frac{4 \underline{\hspace{1.25 ex}}\alpha^{3}}{9}-\frac{2 \underline{\hspace{1.25 ex}}\alpha^{2}}{3}+\frac{2 i \sqrt{2}\, \underline{\hspace{1.25 ex}}\alpha^{3}}{9}-\frac{2 i \sqrt{2}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{3}+\frac{14}{9}+\frac{2 i \underline{\hspace{1.25 ex}}\alpha  \sqrt{2}}{3}+\frac{4 i \sqrt{2}}{9}, \sqrt{2}\, \sqrt{\frac{i \sqrt{2}}{1+i \sqrt{2}}}\right)}{\sqrt{-4 x^{3}+2 x^{2}-2 x +1}}\right) \sqrt{-\left(-1+2 x \right) \left(2 x^{2}+1\right)}-9 \sqrt{-4 x^{3}+2 x^{2}-2 x +1}\, \sqrt{-\left(-1+2 x \right) \left(2 x^{2}+1\right)}-18 x^{2}-9}{54 \sqrt{-\frac{-1+2 x}{2 x^{2}+1}}\, \left(2 x^{2}+1\right)}$&$314$\\ \hline \end{longtable}"," ",0,"-1/3*(2*x^2+1)*(-1+x)/(-1+2*x)*(-(-1+2*x)/(2*x^2+1))^(1/2)+1/6*RootOf(_Z^2-3)*ln((-2*RootOf(_Z^2-3)*x^4+12*(-(-1+2*x)/(2*x^2+1))^(1/2)*x^3+4*RootOf(_Z^2-3)*x^3-12*(-(-1+2*x)/(2*x^2+1))^(1/2)*x^2-3*RootOf(_Z^2-3)*x^2+6*(-(-1+2*x)/(2*x^2+1))^(1/2)*x+8*RootOf(_Z^2-3)*x-6*(-(-1+2*x)/(2*x^2+1))^(1/2)-4*RootOf(_Z^2-3))/(2*x^4-4*x^3+3*x^2+4*x-2))","C"
1223,1,84,67,6.369000," ","int((x^5-1)^(2/3)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \mathrm{signum}\left(x^{5}-1\right)^{\frac{2}{3}} \left(\frac{2 \pi  \sqrt{3}\, x^{5} \hypergeom \left(\left[\frac{1}{3}, 1, 1\right], \left[2, 2\right], x^{5}\right)}{3 \Gamma \left(\frac{2}{3}\right)}-\frac{\left(\frac{3}{2}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+5 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right)}\right)}{15 \pi  \left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{2}{3}}}$&$84$\\ trager&$\frac{3 \left(x^{5}-1\right)^{\frac{2}{3}}}{10}-\frac{\ln \left(-\frac{5742104900265 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{5}-65560760325012 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{5}+81397113223620 x^{5}+377226895287639 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{2}{3}}-58267503137446 \left(x^{5}-1\right)^{\frac{2}{3}}-377226895287639 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{1}{3}}-183747356808480 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+58267503137446 \left(x^{5}-1\right)^{\frac{1}{3}}+315977776351479 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-78683876116166}{x^{5}}\right)}{5}-\frac{3 \ln \left(-\frac{5742104900265 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{5}-65560760325012 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{5}+81397113223620 x^{5}+377226895287639 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{2}{3}}-58267503137446 \left(x^{5}-1\right)^{\frac{2}{3}}-377226895287639 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{1}{3}}-183747356808480 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+58267503137446 \left(x^{5}-1\right)^{\frac{1}{3}}+315977776351479 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-78683876116166}{x^{5}}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{5}+\frac{3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(\frac{198940836807275869130067 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{5}+1958108662877424349459590 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{5}-1008670947132405081583613 x^{5}+1200531403057974808044627 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{2}{3}}+2692149319313648931779319 \left(x^{5}-1\right)^{\frac{2}{3}}-1200531403057974808044627 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{1}{3}}-6366106777832827812162144 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-2692149319313648931779319 \left(x^{5}-1\right)^{\frac{1}{3}}-921504189552967796009421 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+1984804121776668063761303}{x^{5}}\right)}{5}$&$437$\\ \hline \end{longtable}"," ",0,"-1/15/Pi*3^(1/2)*GAMMA(2/3)*signum(x^5-1)^(2/3)/(-signum(x^5-1))^(2/3)*(2/3*Pi*3^(1/2)/GAMMA(2/3)*x^5*hypergeom([1/3,1,1],[2,2],x^5)-(3/2-1/6*Pi*3^(1/2)-3/2*ln(3)+5*ln(x)+I*Pi)*Pi*3^(1/2)/GAMMA(2/3))","C"
1224,1,84,67,8.294000," ","int((x^6-1)^(2/3)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \mathrm{signum}\left(x^{6}-1\right)^{\frac{2}{3}} \left(\frac{2 \pi  \sqrt{3}\, x^{6} \hypergeom \left(\left[\frac{1}{3}, 1, 1\right], \left[2, 2\right], x^{6}\right)}{3 \Gamma \left(\frac{2}{3}\right)}-\frac{\left(\frac{3}{2}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+6 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right)}\right)}{18 \pi  \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{2}{3}}}$&$84$\\ trager&$\frac{\left(x^{6}-1\right)^{\frac{2}{3}}}{4}+\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\frac{-1505024575790858565046 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}-94448748446849318458973 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+23171389162410581752275 x^{6}+68267310132857019576606 \left(x^{6}-1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-142296551347461340528569 \left(x^{6}-1\right)^{\frac{2}{3}}-68267310132857019576606 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}}+96321572850614948162944 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+142296551347461340528569 \left(x^{6}-1\right)^{\frac{1}{3}}+164588882983471967739550 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-45974978496846392365625}{x^{6}}\right)}{6}-\frac{\ln \left(-\frac{1505024575790858565046 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}-91438699295267601328881 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-116115113033469041646202 x^{6}+68267310132857019576606 \left(x^{6}-1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+210563861480318360105175 \left(x^{6}-1\right)^{\frac{2}{3}}-68267310132857019576606 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}}-96321572850614948162944 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-210563861480318360105175 \left(x^{6}-1\right)^{\frac{1}{3}}-28054262717757928586338 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+114242288629703411942231}{x^{6}}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{6}-\frac{\ln \left(-\frac{1505024575790858565046 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}-91438699295267601328881 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-116115113033469041646202 x^{6}+68267310132857019576606 \left(x^{6}-1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+210563861480318360105175 \left(x^{6}-1\right)^{\frac{2}{3}}-68267310132857019576606 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}}-96321572850614948162944 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-210563861480318360105175 \left(x^{6}-1\right)^{\frac{1}{3}}-28054262717757928586338 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+114242288629703411942231}{x^{6}}\right)}{6}$&$357$\\ \hline \end{longtable}"," ",0,"-1/18/Pi*3^(1/2)*GAMMA(2/3)*signum(x^6-1)^(2/3)/(-signum(x^6-1))^(2/3)*(2/3*Pi*3^(1/2)/GAMMA(2/3)*x^6*hypergeom([1/3,1,1],[2,2],x^6)-(3/2-1/6*Pi*3^(1/2)-3/2*ln(3)+6*ln(x)+I*Pi)*Pi*3^(1/2)/GAMMA(2/3))","C"
1225,0,0,65,180.000000," ","int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x)","\[\int \sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}\, dx\]"," ",0,"int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x)","F"
1226,1,96,70,2.034000," ","int((x^2-1)^(2/3)/x^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{\left(x^{2}-1\right)^{\frac{2}{3}}}{2 x^{2}}+\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}} \left(\frac{2 \pi  \sqrt{3}\, x^{2} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], x^{2}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+2 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{6 \pi  \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}}}$&$96$\\ meijerg&$\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \mathrm{signum}\left(x^{2}-1\right)^{\frac{2}{3}} \left(-\frac{\pi  \sqrt{3}\, x^{2} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 3\right], x^{2}\right)}{9 \Gamma \left(\frac{2}{3}\right)}-\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+2 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}-\frac{\pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right) x^{2}}\right)}{6 \pi  \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{2}{3}}}$&$97$\\ trager&$-\frac{\left(x^{2}-1\right)^{\frac{2}{3}}}{2 x^{2}}-\frac{\ln \left(\frac{-576 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)^{2} x^{2}+180 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{2}{3}}+204 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) x^{2}-24 \left(x^{2}-1\right)^{\frac{2}{3}}-108 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{1}{3}}+2304 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)^{2}-15 x^{2}-15 \left(x^{2}-1\right)^{\frac{1}{3}}-480 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)+25}{x^{2}}\right)}{3}+4 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) \ln \left(-\frac{-720 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)^{2} x^{2}+180 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{2}{3}}-72 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) x^{2}+9 \left(x^{2}-1\right)^{\frac{2}{3}}+288 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{1}{3}}+2880 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)^{2}+8 x^{2}-15 \left(x^{2}-1\right)^{\frac{1}{3}}-132 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)-4}{x^{2}}\right)$&$294$\\ \hline \end{longtable}"," ",0,"-1/2*(x^2-1)^(2/3)/x^2+1/6/Pi*3^(1/2)*GAMMA(2/3)/signum(x^2-1)^(1/3)*(-signum(x^2-1))^(1/3)*(2/9*Pi*3^(1/2)/GAMMA(2/3)*x^2*hypergeom([1,1,4/3],[2,2],x^2)+2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)+2*ln(x)+I*Pi)*Pi*3^(1/2)/GAMMA(2/3))","C"
1227,1,76,73,2.700000," ","int((x^2+x-2)/x^2/(x^2-1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{2 \left(x^{2}-1\right)^{\frac{1}{4}}}{x}+\frac{\left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{3}{4}} \left(\frac{3 \Gamma \left(\frac{3}{4}\right) x^{2} \hypergeom \left(\left[1, 1, \frac{7}{4}\right], \left[2, 2\right], x^{2}\right)}{4}+\left(-3 \ln \left(2\right)+\frac{\pi}{2}+2 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{3}{4}\right)\right)}{2 \Gamma \left(\frac{3}{4}\right) \mathrm{signum}\left(x^{2}-1\right)^{\frac{3}{4}}}$&$76$\\ meijerg&$\frac{\left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{3}{4}} x \hypergeom \left(\left[\frac{1}{2}, \frac{3}{4}\right], \left[\frac{3}{2}\right], x^{2}\right)}{\mathrm{signum}\left(x^{2}-1\right)^{\frac{3}{4}}}+\frac{\left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{3}{4}} \left(\frac{3 \Gamma \left(\frac{3}{4}\right) x^{2} \hypergeom \left(\left[1, 1, \frac{7}{4}\right], \left[2, 2\right], x^{2}\right)}{4}+\left(-3 \ln \left(2\right)+\frac{\pi}{2}+2 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{3}{4}\right)\right)}{2 \Gamma \left(\frac{3}{4}\right) \mathrm{signum}\left(x^{2}-1\right)^{\frac{3}{4}}}+\frac{2 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{3}{4}} \hypergeom \left(\left[-\frac{1}{2}, \frac{3}{4}\right], \left[\frac{1}{2}\right], x^{2}\right)}{\mathrm{signum}\left(x^{2}-1\right)^{\frac{3}{4}} x}$&$125$\\ trager&$-\frac{2 \left(x^{2}-1\right)^{\frac{1}{4}}}{x}-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(-\frac{-2 \sqrt{x^{2}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+2 \left(x^{2}-1\right)^{\frac{3}{4}}-2 \left(x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+\RootOf \left(\textit{\_Z}^{4}+1\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)}{x^{2}}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}+2 \left(x^{2}-1\right)^{\frac{3}{4}}-2 \sqrt{x^{2}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)+2 \left(x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{x^{2}}\right)}{2}$&$170$\\ \hline \end{longtable}"," ",0,"-2*(x^2-1)^(1/4)/x+1/2/GAMMA(3/4)/signum(x^2-1)^(3/4)*(-signum(x^2-1))^(3/4)*(3/4*GAMMA(3/4)*x^2*hypergeom([1,1,7/4],[2,2],x^2)+(-3*ln(2)+1/2*Pi+2*ln(x)+I*Pi)*GAMMA(3/4))","C"
1228,1,55,68,2.233000," ","int((x^3+1)^(1/3)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\frac{\Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 3\right], -x^{3}\right)}{3}-\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+3 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)+\frac{3 \Gamma \left(\frac{2}{3}\right)}{x^{3}}}{9 \Gamma \left(\frac{2}{3}\right)}$&$55$\\ risch&$-\frac{\left(x^{3}+1\right)^{\frac{1}{3}}}{3 x^{3}}+\frac{-\frac{2 \Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 2\right], -x^{3}\right)}{3}+\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)}{9 \Gamma \left(\frac{2}{3}\right)}$&$59$\\ trager&$-\frac{\left(x^{3}+1\right)^{\frac{1}{3}}}{3 x^{3}}+\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+17 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}+15 x^{3}+24 \left(x^{3}+1\right)^{\frac{2}{3}}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+24 \left(x^{3}+1\right)^{\frac{1}{3}}+11 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+20}{x^{3}}\right)}{9}-\frac{\ln \left(\frac{-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}-2 x^{3}-9 \left(x^{3}+1\right)^{\frac{2}{3}}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-9 \left(x^{3}+1\right)^{\frac{1}{3}}+19 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-5}{x^{3}}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{9}-\frac{\ln \left(\frac{-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}-2 x^{3}-9 \left(x^{3}+1\right)^{\frac{2}{3}}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-9 \left(x^{3}+1\right)^{\frac{1}{3}}+19 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-5}{x^{3}}\right)}{9}$&$359$\\ \hline \end{longtable}"," ",0,"-1/9/GAMMA(2/3)*(1/3*GAMMA(2/3)*x^3*hypergeom([1,1,5/3],[2,3],-x^3)-(1/6*Pi*3^(1/2)-3/2*ln(3)-1+3*ln(x))*GAMMA(2/3)+3*GAMMA(2/3)/x^3)","C"
1229,1,76,68,3.149000," ","int((x^3+1)^(2/3)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(\frac{\pi  \sqrt{3}\, x^{3} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 3\right], -x^{3}\right)}{9 \Gamma \left(\frac{2}{3}\right)}-\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+3 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}+\frac{\pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right) x^{3}}\right)}{9 \pi}$&$76$\\ risch&$-\frac{\left(x^{3}+1\right)^{\frac{2}{3}}}{3 x^{3}}+\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\frac{2 \pi  \sqrt{3}\, x^{3} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], -x^{3}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{9 \pi}$&$76$\\ trager&$-\frac{\left(x^{3}+1\right)^{\frac{2}{3}}}{3 x^{3}}+\frac{2 \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}+10 x^{3}-9 \left(x^{3}+1\right)^{\frac{2}{3}}-24 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-15 \left(x^{3}+1\right)^{\frac{1}{3}}+10 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+25}{x^{3}}\right)}{9}+\frac{2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{-5 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-16 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}-3 x^{3}+24 \left(x^{3}+1\right)^{\frac{2}{3}}+9 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}+5 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-15 \left(x^{3}+1\right)^{\frac{1}{3}}-19 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-4}{x^{3}}\right)}{9}$&$240$\\ \hline \end{longtable}"," ",0,"-1/9/Pi*3^(1/2)*GAMMA(2/3)*(1/9*Pi*3^(1/2)/GAMMA(2/3)*x^3*hypergeom([1,1,4/3],[2,3],-x^3)-2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)-1+3*ln(x))*Pi*3^(1/2)/GAMMA(2/3)+Pi*3^(1/2)/GAMMA(2/3)/x^3)","C"
1230,0,0,78,0.033000," ","int((-2*k-(-1+k)*(1+k)*x+2*k*x^2)/((-x^2+1)*(-k^2*x^2+1))^(1/4)/(-1+d+(3+d)*k*x-(3*k^2+d)*x^2+k*(k^2-d)*x^3),x)","\[\int \frac{-2 k -\left(-1+k \right) \left(1+k \right) x +2 k \,x^{2}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{1}{4}} \left(-1+d +\left(3+d \right) k x -\left(3 k^{2}+d \right) x^{2}+k \left(k^{2}-d \right) x^{3}\right)}\, dx\]"," ",0,"int((-2*k-(-1+k)*(1+k)*x+2*k*x^2)/((-x^2+1)*(-k^2*x^2+1))^(1/4)/(-1+d+(3+d)*k*x-(3*k^2+d)*x^2+k*(k^2-d)*x^3),x)","F"
1231,0,0,78,0.033000," ","int((-2*k+(-1+k)*(1+k)*x+2*k*x^2)/((-x^2+1)*(-k^2*x^2+1))^(1/4)/(1-d+(3+d)*k*x+(3*k^2+d)*x^2+k*(k^2-d)*x^3),x)","\[\int \frac{-2 k +\left(-1+k \right) \left(1+k \right) x +2 k \,x^{2}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{1}{4}} \left(1-d +\left(3+d \right) k x +\left(3 k^{2}+d \right) x^{2}+k \left(k^{2}-d \right) x^{3}\right)}\, dx\]"," ",0,"int((-2*k+(-1+k)*(1+k)*x+2*k*x^2)/((-x^2+1)*(-k^2*x^2+1))^(1/4)/(1-d+(3+d)*k*x+(3*k^2+d)*x^2+k*(k^2-d)*x^3),x)","F"
1232,1,55,72,0.533000," ","int((x^2+1)*(-2*x^4+1)^(1/2)/x^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\frac{\sqrt{2}\, \arcsin \left(\sqrt{2}\, x^{2}\right)}{2}-\frac{\sqrt{-2 x^{4}+1}}{4 x^{4}}+\frac{\arctanh \left(\frac{1}{\sqrt{-2 x^{4}+1}}\right)}{2}-\frac{\sqrt{-2 x^{4}+1}}{2 x^{2}}$&$55$\\ risch&$\frac{4 x^{6}+2 x^{4}-2 x^{2}-1}{4 x^{4} \sqrt{-2 x^{4}+1}}-\frac{\sqrt{2}\, \arcsin \left(\sqrt{2}\, x^{2}\right)}{2}+\frac{\arctanh \left(\frac{1}{\sqrt{-2 x^{4}+1}}\right)}{2}$&$58$\\ trager&$-\frac{\left(2 x^{2}+1\right) \sqrt{-2 x^{4}+1}}{4 x^{4}}+\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(-\RootOf \left(\textit{\_Z}^{2}+2\right) x^{2}-\sqrt{-2 x^{4}+1}\right)}{2}-\frac{\ln \left(\frac{\sqrt{-2 x^{4}+1}-1}{x^{2}}\right)}{2}$&$73$\\ default&$-\frac{\left(-2 x^{4}+1\right)^{\frac{3}{2}}}{4 x^{4}}-\frac{\sqrt{-2 x^{4}+1}}{2}+\frac{\arctanh \left(\frac{1}{\sqrt{-2 x^{4}+1}}\right)}{2}-\frac{\left(-2 x^{4}+1\right)^{\frac{3}{2}}}{2 x^{2}}-x^{2} \sqrt{-2 x^{4}+1}-\frac{\sqrt{2}\, \arcsin \left(\sqrt{2}\, x^{2}\right)}{2}$&$80$\\ meijerg&$\frac{\frac{\sqrt{\pi}\, \left(-8 x^{4}+8\right)}{8 x^{4}}-\frac{\sqrt{\pi}\, \sqrt{-2 x^{4}+1}}{x^{4}}+2 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{-2 x^{4}+1}}{2}\right)-\left(-\ln \left(2\right)-1+4 \ln \left(x \right)+i \pi \right) \sqrt{\pi}-\frac{\sqrt{\pi}}{x^{4}}}{4 \sqrt{\pi}}-\frac{i \sqrt{2}\, \left(-\frac{2 i \sqrt{\pi}\, \sqrt{2}\, \sqrt{-2 x^{4}+1}}{x^{2}}-4 i \sqrt{\pi}\, \arcsin \left(\sqrt{2}\, x^{2}\right)\right)}{8 \sqrt{\pi}}$&$131$\\ \hline \end{longtable}"," ",0,"-1/2*2^(1/2)*arcsin(2^(1/2)*x^2)-1/4/x^4*(-2*x^4+1)^(1/2)+1/2*arctanh(1/(-2*x^4+1)^(1/2))-1/2/x^2*(-2*x^4+1)^(1/2)","A"
1233,1,76,68,4.585000," ","int((x^4+1)^(2/3)/x^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(\frac{\pi  \sqrt{3}\, x^{4} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 3\right], -x^{4}\right)}{9 \Gamma \left(\frac{2}{3}\right)}-\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+4 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}+\frac{\pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right) x^{4}}\right)}{12 \pi}$&$76$\\ risch&$-\frac{\left(x^{4}+1\right)^{\frac{2}{3}}}{4 x^{4}}+\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\frac{2 \pi  \sqrt{3}\, x^{4} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], -x^{4}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{12 \pi}$&$76$\\ trager&$-\frac{\left(x^{4}+1\right)^{\frac{2}{3}}}{4 x^{4}}+\frac{\ln \left(\frac{-333 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}-393 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}-60 x^{4}+351 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}}-48 \left(x^{4}+1\right)^{\frac{2}{3}}+144 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{1}{3}}+333 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+165 \left(x^{4}+1\right)^{\frac{1}{3}}-384 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-80}{x^{4}}\right)}{6}-\frac{\ln \left(-\frac{-153 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}+162 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}-40 x^{4}+351 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}}+165 \left(x^{4}+1\right)^{\frac{2}{3}}-495 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{1}{3}}+153 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-48 \left(x^{4}+1\right)^{\frac{1}{3}}+195 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-100}{x^{4}}\right)}{6}-\frac{\ln \left(-\frac{-153 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}+162 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}-40 x^{4}+351 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}}+165 \left(x^{4}+1\right)^{\frac{2}{3}}-495 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{1}{3}}+153 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-48 \left(x^{4}+1\right)^{\frac{1}{3}}+195 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-100}{x^{4}}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{2}$&$429$\\ \hline \end{longtable}"," ",0,"-1/12/Pi*3^(1/2)*GAMMA(2/3)*(1/9*Pi*3^(1/2)/GAMMA(2/3)*x^4*hypergeom([1,1,4/3],[2,3],-x^4)-2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)-1+4*ln(x))*Pi*3^(1/2)/GAMMA(2/3)+Pi*3^(1/2)/GAMMA(2/3)/x^4)","C"
1234,1,267,72,7.229000," ","int((x^4-3)*(x^4+1)^(2/3)/x^3/(x^4-x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 \left(x^{4}+1\right)^{\frac{2}{3}}}{2 x^{2}}+\ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x -\left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+x^{4}-2 \left(x^{4}+1\right)^{\frac{2}{3}} x +x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}+x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1}{x^{4}-x^{3}+1}\right)+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x +2 \left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-x^{4}+\left(x^{4}+1\right)^{\frac{2}{3}} x +x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1}{x^{4}-x^{3}+1}\right)$&$267$\\ trager&$\frac{3 \left(x^{4}+1\right)^{\frac{2}{3}}}{2 x^{2}}-3 \ln \left(\frac{10305 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}-20610 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+17859 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}+9621 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x +9621 \left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}-11673 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+7554 x^{4}+11217 \left(x^{4}+1\right)^{\frac{2}{3}} x +11217 x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}+2518 x^{3}+10305 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+17859 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+7554}{x^{4}-x^{3}+1}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(-\frac{-10305 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}+20610 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+10989 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}+9621 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x +9621 \left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+2067 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}-2746 x^{4}-8010 \left(x^{4}+1\right)^{\frac{2}{3}} x -8010 x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}-4119 x^{3}-10305 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+10989 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-2746}{x^{4}-x^{3}+1}\right)-\ln \left(\frac{10305 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}-20610 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+17859 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}+9621 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x +9621 \left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}-11673 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+7554 x^{4}+11217 \left(x^{4}+1\right)^{\frac{2}{3}} x +11217 x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}+2518 x^{3}+10305 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+17859 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+7554}{x^{4}-x^{3}+1}\right)$&$607$\\ \hline \end{longtable}"," ",0,"3/2*(x^4+1)^(2/3)/x^2+ln((RootOf(_Z^2+_Z+1)^2*x^3+RootOf(_Z^2+_Z+1)*x^4-RootOf(_Z^2+_Z+1)*(x^4+1)^(2/3)*x-(x^4+1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2+2*RootOf(_Z^2+_Z+1)*x^3+x^4-2*(x^4+1)^(2/3)*x+x^2*(x^4+1)^(1/3)+x^3+RootOf(_Z^2+_Z+1)+1)/(x^4-x^3+1))+RootOf(_Z^2+_Z+1)*ln(-(RootOf(_Z^2+_Z+1)^2*x^3-RootOf(_Z^2+_Z+1)*x^4-RootOf(_Z^2+_Z+1)*(x^4+1)^(2/3)*x+2*(x^4+1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2+RootOf(_Z^2+_Z+1)*x^3-x^4+(x^4+1)^(2/3)*x+x^2*(x^4+1)^(1/3)-RootOf(_Z^2+_Z+1)-1)/(x^4-x^3+1))","C"
1235,1,402,74,9.647000," ","int((x^4-1)^(1/3)*(x^4+3)/x^2/(x^4+x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(x^{4}-1\right)^{\frac{1}{3}}}{x}-\ln \left(-\frac{10242144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{4}-19204020 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{3}-108450 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{4}+4707432 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}} x +4619142 \left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}+4710954 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{3}-233639 x^{4}-769857 \left(x^{4}-1\right)^{\frac{2}{3}} x +14715 \left(x^{4}-1\right)^{\frac{1}{3}} x^{2}-267016 x^{3}-10242144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2}+108450 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)+233639}{x^{4}+x^{3}-1}\right)+6 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \ln \left(\frac{629568 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{4}-1180440 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{3}+1405356 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{4}+4707432 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}} x +88290 \left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}-2912118 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{3}-500655 x^{4}-14715 \left(x^{4}-1\right)^{\frac{2}{3}} x +769857 \left(x^{4}-1\right)^{\frac{1}{3}} x^{2}+233639 x^{3}-629568 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2}-1405356 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)+500655}{x^{4}+x^{3}-1}\right)$&$402$\\ risch&$\frac{3 \left(x^{4}-1\right)^{\frac{1}{3}}}{x}+\frac{\left(-\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{7}-x^{8}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{8}-2 x^{4}+1\right)^{\frac{1}{3}} x^{5}-2 \left(x^{8}-2 x^{4}+1\right)^{\frac{1}{3}} x^{5}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{8}-2 x^{4}+1\right)^{\frac{2}{3}} x^{2}-\left(x^{8}-2 x^{4}+1\right)^{\frac{2}{3}} x^{2}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+2 x^{4}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{8}-2 x^{4}+1\right)^{\frac{1}{3}} x +2 \left(x^{8}-2 x^{4}+1\right)^{\frac{1}{3}} x -1}{\left(x^{4}+x^{3}-1\right) \left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{7}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{8}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{7}+x^{8}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{8}-2 x^{4}+1\right)^{\frac{1}{3}} x^{5}-x^{7}-\left(x^{8}-2 x^{4}+1\right)^{\frac{1}{3}} x^{5}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{8}-2 x^{4}+1\right)^{\frac{2}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{4}-2 \left(x^{8}-2 x^{4}+1\right)^{\frac{2}{3}} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-2 x^{4}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{8}-2 x^{4}+1\right)^{\frac{1}{3}} x +x^{3}+\left(x^{8}-2 x^{4}+1\right)^{\frac{1}{3}} x -\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+1}{\left(x^{4}+x^{3}-1\right) \left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)\right) \left(\left(x^{4}-1\right)^{2}\right)^{\frac{1}{3}}}{\left(x^{4}-1\right)^{\frac{2}{3}}}$&$505$\\ \hline \end{longtable}"," ",0,"3*(x^4-1)^(1/3)/x-ln(-(10242144*RootOf(36*_Z^2-6*_Z+1)^2*x^4-19204020*RootOf(36*_Z^2-6*_Z+1)^2*x^3-108450*RootOf(36*_Z^2-6*_Z+1)*x^4+4707432*RootOf(36*_Z^2-6*_Z+1)*(x^4-1)^(2/3)*x+4619142*(x^4-1)^(1/3)*RootOf(36*_Z^2-6*_Z+1)*x^2+4710954*RootOf(36*_Z^2-6*_Z+1)*x^3-233639*x^4-769857*(x^4-1)^(2/3)*x+14715*(x^4-1)^(1/3)*x^2-267016*x^3-10242144*RootOf(36*_Z^2-6*_Z+1)^2+108450*RootOf(36*_Z^2-6*_Z+1)+233639)/(x^4+x^3-1))+6*RootOf(36*_Z^2-6*_Z+1)*ln((629568*RootOf(36*_Z^2-6*_Z+1)^2*x^4-1180440*RootOf(36*_Z^2-6*_Z+1)^2*x^3+1405356*RootOf(36*_Z^2-6*_Z+1)*x^4+4707432*RootOf(36*_Z^2-6*_Z+1)*(x^4-1)^(2/3)*x+88290*(x^4-1)^(1/3)*RootOf(36*_Z^2-6*_Z+1)*x^2-2912118*RootOf(36*_Z^2-6*_Z+1)*x^3-500655*x^4-14715*(x^4-1)^(2/3)*x+769857*(x^4-1)^(1/3)*x^2+233639*x^3-629568*RootOf(36*_Z^2-6*_Z+1)^2-1405356*RootOf(36*_Z^2-6*_Z+1)+500655)/(x^4+x^3-1))","C"
1236,1,267,72,8.830000," ","int((x^4-1)^(2/3)*(x^4+3)/x^3/(x^4+x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 \left(x^{4}-1\right)^{\frac{2}{3}}}{2 x^{2}}+\ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}} x -\left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+x^{4}+2 \left(x^{4}-1\right)^{\frac{2}{3}} x +\left(x^{4}-1\right)^{\frac{1}{3}} x^{2}-x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1}{x^{4}+x^{3}-1}\right)+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}} x +2 \left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-x^{4}-\left(x^{4}-1\right)^{\frac{2}{3}} x +\left(x^{4}-1\right)^{\frac{1}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1}{x^{4}+x^{3}-1}\right)$&$267$\\ trager&$\frac{3 \left(x^{4}-1\right)^{\frac{2}{3}}}{2 x^{2}}+12 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \ln \left(-\frac{-38450304 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{4}+72094320 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{3}-9421908 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{4}+9414864 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}} x -9414864 \left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{2}+9205008 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{3}-533445 x^{4}+14715 \left(x^{4}-1\right)^{\frac{2}{3}} x -14715 \left(x^{4}-1\right)^{\frac{1}{3}} x^{2}+248941 x^{3}+38450304 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}+9421908 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)+533445}{x^{4}+x^{3}-1}\right)-12 \ln \left(\frac{38450304 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{4}-72094320 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{3}-3013524 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{4}+9414864 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}} x -9414864 \left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{2}-2810712 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{3}+15302 x^{4}+769857 \left(x^{4}-1\right)^{\frac{2}{3}} x -769857 \left(x^{4}-1\right)^{\frac{1}{3}} x^{2}+17488 x^{3}-38450304 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}+3013524 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)-15302}{x^{4}+x^{3}-1}\right) \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)-\ln \left(\frac{38450304 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{4}-72094320 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{3}-3013524 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{4}+9414864 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}} x -9414864 \left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{2}-2810712 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{3}+15302 x^{4}+769857 \left(x^{4}-1\right)^{\frac{2}{3}} x -769857 \left(x^{4}-1\right)^{\frac{1}{3}} x^{2}+17488 x^{3}-38450304 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}+3013524 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)-15302}{x^{4}+x^{3}-1}\right)$&$601$\\ \hline \end{longtable}"," ",0,"3/2*(x^4-1)^(2/3)/x^2+ln((-RootOf(_Z^2+_Z+1)^2*x^3+RootOf(_Z^2+_Z+1)*x^4+RootOf(_Z^2+_Z+1)*(x^4-1)^(2/3)*x-(x^4-1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2-2*RootOf(_Z^2+_Z+1)*x^3+x^4+2*(x^4-1)^(2/3)*x+(x^4-1)^(1/3)*x^2-x^3-RootOf(_Z^2+_Z+1)-1)/(x^4+x^3-1))+RootOf(_Z^2+_Z+1)*ln(-(-RootOf(_Z^2+_Z+1)^2*x^3-RootOf(_Z^2+_Z+1)*x^4+RootOf(_Z^2+_Z+1)*(x^4-1)^(2/3)*x+2*(x^4-1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2-RootOf(_Z^2+_Z+1)*x^3-x^4-(x^4-1)^(2/3)*x+(x^4-1)^(1/3)*x^2+RootOf(_Z^2+_Z+1)+1)/(x^4+x^3-1))","C"
1237,1,477,74,8.084000," ","int((x^4-3)*(x^4+1)^(1/3)/x^2/(x^4+x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 \left(x^{4}+1\right)^{\frac{1}{3}}}{x}+\frac{\left(-\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{7}-x^{8}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{8}+2 x^{4}+1\right)^{\frac{1}{3}} x^{5}-2 \left(x^{8}+2 x^{4}+1\right)^{\frac{1}{3}} x^{5}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{8}+2 x^{4}+1\right)^{\frac{2}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-\left(x^{8}+2 x^{4}+1\right)^{\frac{2}{3}} x^{2}-2 x^{4}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{8}+2 x^{4}+1\right)^{\frac{1}{3}} x -2 \left(x^{8}+2 x^{4}+1\right)^{\frac{1}{3}} x -1}{\left(x^{4}+x^{3}+1\right) \left(x^{4}+1\right)}\right)+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{7}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{8}-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{7}-x^{8}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{8}+2 x^{4}+1\right)^{\frac{1}{3}} x^{5}+x^{7}+\left(x^{8}+2 x^{4}+1\right)^{\frac{1}{3}} x^{5}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{8}+2 x^{4}+1\right)^{\frac{2}{3}} x^{2}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+2 \left(x^{8}+2 x^{4}+1\right)^{\frac{2}{3}} x^{2}-2 x^{4}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{8}+2 x^{4}+1\right)^{\frac{1}{3}} x +x^{3}+\left(x^{8}+2 x^{4}+1\right)^{\frac{1}{3}} x +\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-1}{\left(x^{4}+x^{3}+1\right) \left(x^{4}+1\right)}\right)\right) \left(\left(x^{4}+1\right)^{2}\right)^{\frac{1}{3}}}{\left(x^{4}+1\right)^{\frac{2}{3}}}$&$477$\\ trager&$\frac{3 \left(x^{4}+1\right)^{\frac{1}{3}}}{x}-3 \ln \left(\frac{81 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{4}-162 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{3}-39 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{4}-45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x +45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{1}{3}} x^{2}-3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{3}-10 x^{4}+42 \left(x^{4}+1\right)^{\frac{2}{3}} x -42 x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}+5 x^{3}+81 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}-39 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-10}{x^{4}+x^{3}+1}\right) \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)+3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \ln \left(\frac{81 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{4}-162 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{3}-15 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{4}+45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x -45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{1}{3}} x^{2}+111 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{3}-14 x^{4}+27 \left(x^{4}+1\right)^{\frac{2}{3}} x -27 x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}-14 x^{3}+81 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}-15 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-14}{x^{4}+x^{3}+1}\right)+\ln \left(\frac{81 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{4}-162 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{3}-39 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{4}-45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x +45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{1}{3}} x^{2}-3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{3}-10 x^{4}+42 \left(x^{4}+1\right)^{\frac{2}{3}} x -42 x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}+5 x^{3}+81 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}-39 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-10}{x^{4}+x^{3}+1}\right)$&$598$\\ \hline \end{longtable}"," ",0,"3*(x^4+1)^(1/3)/x+(-ln(-(RootOf(_Z^2-_Z+1)*x^7-x^8+RootOf(_Z^2-_Z+1)*(x^8+2*x^4+1)^(1/3)*x^5-2*(x^8+2*x^4+1)^(1/3)*x^5+2*RootOf(_Z^2-_Z+1)*(x^8+2*x^4+1)^(2/3)*x^2+RootOf(_Z^2-_Z+1)*x^3-(x^8+2*x^4+1)^(2/3)*x^2-2*x^4+RootOf(_Z^2-_Z+1)*(x^8+2*x^4+1)^(1/3)*x-2*(x^8+2*x^4+1)^(1/3)*x-1)/(x^4+x^3+1)/(x^4+1))+RootOf(_Z^2-_Z+1)*ln((RootOf(_Z^2-_Z+1)^2*x^7+RootOf(_Z^2-_Z+1)*x^8-2*RootOf(_Z^2-_Z+1)*x^7-x^8+RootOf(_Z^2-_Z+1)*(x^8+2*x^4+1)^(1/3)*x^5+x^7+(x^8+2*x^4+1)^(1/3)*x^5+RootOf(_Z^2-_Z+1)^2*x^3-RootOf(_Z^2-_Z+1)*(x^8+2*x^4+1)^(2/3)*x^2+2*RootOf(_Z^2-_Z+1)*x^4-2*RootOf(_Z^2-_Z+1)*x^3+2*(x^8+2*x^4+1)^(2/3)*x^2-2*x^4+RootOf(_Z^2-_Z+1)*(x^8+2*x^4+1)^(1/3)*x+x^3+(x^8+2*x^4+1)^(1/3)*x+RootOf(_Z^2-_Z+1)-1)/(x^4+x^3+1)/(x^4+1)))/(x^4+1)^(2/3)*((x^4+1)^2)^(1/3)","C"
1238,1,314,74,11.158000," ","int((4+3*x)*(x^4-x-1)*(2*x^4-x-1)^(1/4)/x^6/(x^4+x+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{4 \left(2 x^{4}-x -1\right)^{\frac{1}{4}} \left(12 x^{4}-x -1\right)}{5 x^{5}}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) \ln \left(-\frac{-5 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) x^{4}+6 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} \left(2 x^{4}-x -1\right)^{\frac{1}{4}} x^{3}+6 \sqrt{2 x^{4}-x -1}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) x^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) x -6 \left(2 x^{4}-x -1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}-3\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right)}{x^{4}+x +1}\right)-2 \RootOf \left(\textit{\_Z}^{4}-3\right) \ln \left(-\frac{5 \RootOf \left(\textit{\_Z}^{4}-3\right)^{3} x^{4}-6 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} \left(2 x^{4}-x -1\right)^{\frac{1}{4}} x^{3}+6 \RootOf \left(\textit{\_Z}^{4}-3\right) \sqrt{2 x^{4}-x -1}\, x^{2}-\RootOf \left(\textit{\_Z}^{4}-3\right)^{3} x -6 \left(2 x^{4}-x -1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}-3\right)^{3}}{x^{4}+x +1}\right)$&$314$\\ risch&$-\frac{4 \left(24 x^{8}-14 x^{5}-14 x^{4}+x^{2}+2 x +1\right)}{5 x^{5} \left(2 x^{4}-x -1\right)^{\frac{3}{4}}}+\frac{\left(-2 \RootOf \left(\textit{\_Z}^{4}-3\right) \ln \left(\frac{-20 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{12}+8 \left(8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-3\right)^{3} x^{9}+24 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{9}-8 \left(8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-3\right)^{3} x^{6}+24 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{8}-8 \left(8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-3\right)^{3} x^{5}-9 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{6}-12 \sqrt{8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1}\, x^{6}+2 \left(8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-3\right)^{3} x^{3}-18 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{5}+6 \left(8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{4}-3\right) x^{3}+4 \left(8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-3\right)^{3} x^{2}-9 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{4}+2 \left(8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-3\right)^{3} x +\RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{3}+6 \sqrt{8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1}\, x^{3}+3 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{2}+6 \sqrt{8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1}\, x^{2}+3 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x +\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}}{\left(2 x^{3}+2 x^{2}+2 x +1\right)^{2} \left(x^{4}+x +1\right) \left(-1+x \right)^{2}}\right)-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) \ln \left(-\frac{-20 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{12}+8 \left(8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{9}+24 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{9}-8 \left(8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{6}+24 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{8}-8 \left(8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{5}-9 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{6}+12 \sqrt{8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1}\, x^{6}+2 \left(8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{3}-18 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{5}-6 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) \left(8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right)^{\frac{3}{4}} x^{3}+4 \left(8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{2}-9 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{4}+2 \left(8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x +\RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{3}-6 \sqrt{8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1}\, x^{3}+3 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x^{2}-6 \sqrt{8 x^{12}-12 x^{9}-12 x^{8}+6 x^{6}+12 x^{5}+6 x^{4}-x^{3}-3 x^{2}-3 x -1}\, x^{2}+3 \RootOf \left(\textit{\_Z}^{4}-3\right)^{2} x +\RootOf \left(\textit{\_Z}^{4}-3\right)^{2}}{\left(2 x^{3}+2 x^{2}+2 x +1\right)^{2} \left(x^{4}+x +1\right) \left(-1+x \right)^{2}}\right)\right) \left(\left(2 x^{4}-x -1\right)^{3}\right)^{\frac{1}{4}}}{\left(2 x^{4}-x -1\right)^{\frac{3}{4}}}$&$1633$\\ \hline \end{longtable}"," ",0,"-4/5*(2*x^4-x-1)^(1/4)*(12*x^4-x-1)/x^5-2*RootOf(_Z^2+RootOf(_Z^4-3)^2)*ln(-(-5*RootOf(_Z^4-3)^2*RootOf(_Z^2+RootOf(_Z^4-3)^2)*x^4+6*RootOf(_Z^4-3)^2*(2*x^4-x-1)^(1/4)*x^3+6*(2*x^4-x-1)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-3)^2)*x^2+RootOf(_Z^4-3)^2*RootOf(_Z^2+RootOf(_Z^4-3)^2)*x-6*(2*x^4-x-1)^(3/4)*x+RootOf(_Z^4-3)^2*RootOf(_Z^2+RootOf(_Z^4-3)^2))/(x^4+x+1))-2*RootOf(_Z^4-3)*ln(-(5*RootOf(_Z^4-3)^3*x^4-6*RootOf(_Z^4-3)^2*(2*x^4-x-1)^(1/4)*x^3+6*RootOf(_Z^4-3)*(2*x^4-x-1)^(1/2)*x^2-RootOf(_Z^4-3)^3*x-6*(2*x^4-x-1)^(3/4)*x-RootOf(_Z^4-3)^3)/(x^4+x+1))","C"
1239,1,86,66,1.301000," ","int((3*x^4+1)^(1/2)/(3*x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(-\frac{3^{\frac{3}{4}} \ln \left(\frac{\frac{\sqrt{3 x^{4}+1}\, \sqrt{2}}{2 x}+3^{\frac{1}{4}}}{\frac{\sqrt{3 x^{4}+1}\, \sqrt{2}}{2 x}-3^{\frac{1}{4}}}\right)}{12}+\frac{3^{\frac{3}{4}} \arctan \left(\frac{\sqrt{3 x^{4}+1}\, \sqrt{2}\, 3^{\frac{3}{4}}}{6 x}\right)}{6}\right) \sqrt{2}}{2}$&$86$\\ elliptic&$\frac{\left(-\frac{3^{\frac{3}{4}} \ln \left(\frac{\frac{\sqrt{3 x^{4}+1}\, \sqrt{2}}{2 x}+3^{\frac{1}{4}}}{\frac{\sqrt{3 x^{4}+1}\, \sqrt{2}}{2 x}-3^{\frac{1}{4}}}\right)}{12}+\frac{3^{\frac{3}{4}} \arctan \left(\frac{\sqrt{3 x^{4}+1}\, \sqrt{2}\, 3^{\frac{3}{4}}}{6 x}\right)}{6}\right) \sqrt{2}}{2}$&$86$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-108\right)^{2}\right) \ln \left(\frac{x \RootOf \left(\textit{\_Z}^{4}-108\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-108\right)^{2}\right)+18 \sqrt{3 x^{4}+1}}{\RootOf \left(\textit{\_Z}^{4}-108\right)^{2} x^{2}+6}\right)}{12}-\frac{\RootOf \left(\textit{\_Z}^{4}-108\right) \ln \left(\frac{x \RootOf \left(\textit{\_Z}^{4}-108\right)^{3}+18 \sqrt{3 x^{4}+1}}{\RootOf \left(\textit{\_Z}^{4}-108\right)^{2} x^{2}-6}\right)}{12}$&$118$\\ \hline \end{longtable}"," ",0,"1/2*(-1/12*3^(3/4)*ln((1/2*(3*x^4+1)^(1/2)*2^(1/2)/x+3^(1/4))/(1/2*(3*x^4+1)^(1/2)*2^(1/2)/x-3^(1/4)))+1/6*3^(3/4)*arctan(1/6*(3*x^4+1)^(1/2)*2^(1/2)/x*3^(3/4)))*2^(1/2)","A"
1240,0,0,70,0.008000," ","int((a*x^2+b)*(a*x^4-b*x^2)^(1/4)/(a*x^2-b),x)","\[\int \frac{\left(a \,x^{2}+b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}{a \,x^{2}-b}\, dx\]"," ",0,"int((a*x^2+b)*(a*x^4-b*x^2)^(1/4)/(a*x^2-b),x)","F"
1241,0,0,76,0.038000," ","int((2*a*x^2-b)/(a*x^2+b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{2 a \,x^{2}-b}{\left(a \,x^{2}+b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((2*a*x^2-b)/(a*x^2+b)/(a*x^4+b*x^2)^(1/4),x)","F"
1242,1,76,68,5.845000," ","int((x^5+1)^(2/3)/x^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(\frac{\pi  \sqrt{3}\, x^{5} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 3\right], -x^{5}\right)}{9 \Gamma \left(\frac{2}{3}\right)}-\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+5 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}+\frac{\pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right) x^{5}}\right)}{15 \pi}$&$76$\\ risch&$-\frac{\left(x^{5}+1\right)^{\frac{2}{3}}}{5 x^{5}}+\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\frac{2 \pi  \sqrt{3}\, x^{5} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], -x^{5}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+5 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{15 \pi}$&$76$\\ trager&$-\frac{\left(x^{5}+1\right)^{\frac{2}{3}}}{5 x^{5}}+\frac{2 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(\frac{-132201 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{5}+126582 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{5}-25632 x^{5}+137820 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}+1\right)^{\frac{2}{3}}-78769 \left(x^{5}+1\right)^{\frac{2}{3}}+137820 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}+1\right)^{\frac{1}{3}}+132201 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-78769 \left(x^{5}+1\right)^{\frac{1}{3}}+181887 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-64080}{x^{5}}\right)}{5}-\frac{2 \ln \left(-\frac{132201 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{5}+214716 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{5}+82515 x^{5}+137820 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}+1\right)^{\frac{2}{3}}+124709 \left(x^{5}+1\right)^{\frac{2}{3}}+137820 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}+1\right)^{\frac{1}{3}}-132201 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+124709 \left(x^{5}+1\right)^{\frac{1}{3}}+93753 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+110020}{x^{5}}\right)}{15}-\frac{2 \ln \left(-\frac{132201 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{5}+214716 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{5}+82515 x^{5}+137820 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}+1\right)^{\frac{2}{3}}+124709 \left(x^{5}+1\right)^{\frac{2}{3}}+137820 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}+1\right)^{\frac{1}{3}}-132201 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+124709 \left(x^{5}+1\right)^{\frac{1}{3}}+93753 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+110020}{x^{5}}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{5}$&$440$\\ \hline \end{longtable}"," ",0,"-1/15/Pi*3^(1/2)*GAMMA(2/3)*(1/9*Pi*3^(1/2)/GAMMA(2/3)*x^5*hypergeom([1,1,4/3],[2,3],-x^5)-2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)-1+5*ln(x))*Pi*3^(1/2)/GAMMA(2/3)+Pi*3^(1/2)/GAMMA(2/3)/x^5)","C"
1243,1,289,72,10.578000," ","int((x^5+1)^(2/3)*(2*x^5-3)/x^3/(x^5-x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 \left(x^{5}+1\right)^{\frac{2}{3}}}{2 x^{2}}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{5}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+x^{5}+3 \left(x^{5}+1\right)^{\frac{2}{3}} x +3 \left(x^{5}+1\right)^{\frac{1}{3}} x^{2}+x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1}{x^{5}-x^{3}+1}\right)-\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{5}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+2 x^{5}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 \left(x^{5}+1\right)^{\frac{2}{3}} x +3 \left(x^{5}+1\right)^{\frac{1}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+2}{x^{5}-x^{3}+1}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{5}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+2 x^{5}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 \left(x^{5}+1\right)^{\frac{2}{3}} x +3 \left(x^{5}+1\right)^{\frac{1}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+2}{x^{5}-x^{3}+1}\right)$&$289$\\ trager&$\frac{3 \left(x^{5}+1\right)^{\frac{2}{3}}}{2 x^{2}}-3 \ln \left(\frac{970550226 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{5}-471795651 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{5}-1941100452 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}-116825222 x^{5}+552672423 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}+1\right)^{\frac{2}{3}} x +916632378 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}+1\right)^{\frac{1}{3}} x^{2}-1321025892 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}-305544126 \left(x^{5}+1\right)^{\frac{2}{3}} x +489768267 \left(x^{5}+1\right)^{\frac{1}{3}} x^{2}-175237833 x^{3}+970550226 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-471795651 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-116825222}{x^{5}-x^{3}+1}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+\ln \left(-\frac{444836727 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{5}+269598894 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{5}-889673454 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}-175237833 x^{5}+552672423 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}+1\right)^{\frac{2}{3}} x -1469304801 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}+1\right)^{\frac{1}{3}} x^{2}+498754575 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+489768267 \left(x^{5}+1\right)^{\frac{2}{3}} x -305544126 \left(x^{5}+1\right)^{\frac{1}{3}} x^{2}-58412611 x^{3}+444836727 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+269598894 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-175237833}{x^{5}-x^{3}+1}\right)-\ln \left(\frac{970550226 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{5}-471795651 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{5}-1941100452 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}-116825222 x^{5}+552672423 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}+1\right)^{\frac{2}{3}} x +916632378 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{5}+1\right)^{\frac{1}{3}} x^{2}-1321025892 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}-305544126 \left(x^{5}+1\right)^{\frac{2}{3}} x +489768267 \left(x^{5}+1\right)^{\frac{1}{3}} x^{2}-175237833 x^{3}+970550226 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-471795651 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-116825222}{x^{5}-x^{3}+1}\right)$&$594$\\ \hline \end{longtable}"," ",0,"3/2*(x^5+1)^(2/3)/x^2+RootOf(_Z^2+_Z+1)*ln(-(-RootOf(_Z^2+_Z+1)*x^5-RootOf(_Z^2+_Z+1)^2*x^3+x^5+3*(x^5+1)^(2/3)*x+3*(x^5+1)^(1/3)*x^2+x^3-RootOf(_Z^2+_Z+1)+1)/(x^5-x^3+1))-ln(-(RootOf(_Z^2+_Z+1)*x^5-RootOf(_Z^2+_Z+1)^2*x^3+2*x^5-2*RootOf(_Z^2+_Z+1)*x^3+3*(x^5+1)^(2/3)*x+3*(x^5+1)^(1/3)*x^2+RootOf(_Z^2+_Z+1)+2)/(x^5-x^3+1))*RootOf(_Z^2+_Z+1)-ln(-(RootOf(_Z^2+_Z+1)*x^5-RootOf(_Z^2+_Z+1)^2*x^3+2*x^5-2*RootOf(_Z^2+_Z+1)*x^3+3*(x^5+1)^(2/3)*x+3*(x^5+1)^(1/3)*x^2+RootOf(_Z^2+_Z+1)+2)/(x^5-x^3+1))","C"
1244,1,220,72,16.826000," ","int((x^5-1)^(2/3)*(2*x^5+3)/x^3/(x^5-x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 \left(x^{5}-1\right)^{\frac{2}{3}}}{2 x^{2}}+\ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{5}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-2 x^{5}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{1}{3}} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 \left(x^{5}-1\right)^{\frac{2}{3}} x -2 x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+2}{x^{5}-x^{3}-1}\right)+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{5}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-x^{5}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{1}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 \left(x^{5}-1\right)^{\frac{2}{3}} x +2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1}{x^{5}-x^{3}-1}\right)$&$220$\\ trager&$\frac{3 \left(x^{5}-1\right)^{\frac{2}{3}}}{2 x^{2}}+12 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \ln \left(\frac{407978262043934802048 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{5}-129590444982696930036 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{5}-1580915765420247357936 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{3}-695089578528133787 x^{5}-205927896932357002488 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{2}{3}} x -205927896932357002488 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{1}{3}} x^{2}-174082243897686118776 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{3}+6575842216196707137 \left(x^{5}-1\right)^{\frac{2}{3}} x +6575842216196707137 \left(x^{5}-1\right)^{\frac{1}{3}} x^{2}-874467534277329603 x^{3}-407978262043934802048 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}+129590444982696930036 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)+695089578528133787}{x^{5}-x^{3}-1}\right)-12 \ln \left(\frac{407978262043934802048 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{5}+197586821990019397044 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{5}-1580915765420247357936 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{3}+12937296545335046508 x^{5}+205927896932357002488 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{2}{3}} x +205927896932357002488 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{1}{3}} x^{2}-89403717005688440880 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{3}+23736500293893124011 \left(x^{5}-1\right)^{\frac{2}{3}} x +23736500293893124011 \left(x^{5}-1\right)^{\frac{1}{3}} x^{2}+2653804419555906976 x^{3}-407978262043934802048 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}-197586821990019397044 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)-12937296545335046508}{x^{5}-x^{3}-1}\right) \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)-\ln \left(\frac{407978262043934802048 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{5}+197586821990019397044 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{5}-1580915765420247357936 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{3}+12937296545335046508 x^{5}+205927896932357002488 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{2}{3}} x +205927896932357002488 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{1}{3}} x^{2}-89403717005688440880 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{3}+23736500293893124011 \left(x^{5}-1\right)^{\frac{2}{3}} x +23736500293893124011 \left(x^{5}-1\right)^{\frac{1}{3}} x^{2}+2653804419555906976 x^{3}-407978262043934802048 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}-197586821990019397044 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)-12937296545335046508}{x^{5}-x^{3}-1}\right)$&$606$\\ \hline \end{longtable}"," ",0,"3/2*(x^5-1)^(2/3)/x^2+ln(-(-RootOf(_Z^2+_Z+1)*x^5-RootOf(_Z^2+_Z+1)^2*x^3-2*x^5+3*RootOf(_Z^2+_Z+1)*(x^5-1)^(1/3)*x^2-3*RootOf(_Z^2+_Z+1)*x^3+3*(x^5-1)^(2/3)*x-2*x^3+RootOf(_Z^2+_Z+1)+2)/(x^5-x^3-1))+RootOf(_Z^2+_Z+1)*ln(-(-2*RootOf(_Z^2+_Z+1)*x^5+2*RootOf(_Z^2+_Z+1)^2*x^3-x^5+3*RootOf(_Z^2+_Z+1)*(x^5-1)^(1/3)*x^2+RootOf(_Z^2+_Z+1)*x^3+3*(x^5-1)^(2/3)*x+2*RootOf(_Z^2+_Z+1)+1)/(x^5-x^3-1))","C"
1245,1,64,66,11.705000," ","int((x^6-1)^(1/4)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{4}} \left(\Gamma \left(\frac{3}{4}\right) x^{6} \hypergeom \left(\left[\frac{3}{4}, 1, 1\right], \left[2, 2\right], x^{6}\right)-4 \left(4-3 \ln \left(2\right)+\frac{\pi}{2}+6 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{3}{4}\right)\right)}{24 \Gamma \left(\frac{3}{4}\right) \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{4}}}$&$64$\\ trager&$\frac{2 \left(x^{6}-1\right)^{\frac{1}{4}}}{3}-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{6}+2 \left(x^{6}-1\right)^{\frac{3}{4}}+2 \sqrt{x^{6}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)+2 \left(x^{6}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{x^{6}}\right)}{6}+\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) x^{6}-2 \sqrt{x^{6}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+2 \left(x^{6}-1\right)^{\frac{3}{4}}-2 \left(x^{6}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)}{x^{6}}\right)}{6}$&$168$\\ \hline \end{longtable}"," ",0,"-1/24/GAMMA(3/4)*signum(x^6-1)^(1/4)/(-signum(x^6-1))^(1/4)*(GAMMA(3/4)*x^6*hypergeom([3/4,1,1],[2,2],x^6)-4*(4-3*ln(2)+1/2*Pi+6*ln(x)+I*Pi)*GAMMA(3/4))","C"
1246,1,76,68,7.637000," ","int(1/x^7/(x^6+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{\left(x^{6}+1\right)^{\frac{2}{3}}}{6 x^{6}}-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\frac{2 \pi  \sqrt{3}\, x^{6} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], -x^{6}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+6 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{36 \pi}$&$76$\\ meijerg&$\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(\frac{4 \pi  \sqrt{3}\, x^{6} \hypergeom \left(\left[1, 1, \frac{7}{3}\right], \left[2, 3\right], -x^{6}\right)}{27 \Gamma \left(\frac{2}{3}\right)}-\frac{2 \left(2-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+6 \ln \left(x \right)\right) \pi  \sqrt{3}}{9 \Gamma \left(\frac{2}{3}\right)}-\frac{2 \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right) x^{6}}\right)}{12 \pi}$&$77$\\ trager&$-\frac{\left(x^{6}+1\right)^{\frac{2}{3}}}{6 x^{6}}-\frac{\ln \left(\frac{738615580 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x^{6}+1076983326 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x^{6}+338367746 x^{6}-3200009934 \left(x^{6}+1\right)^{\frac{2}{3}} \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)-738615580 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2}+2061146520 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}}+569431707 \left(x^{6}+1\right)^{\frac{2}{3}}+1508171204 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)-1600004967 \left(x^{6}+1\right)^{\frac{1}{3}}+845919365}{x^{6}}\right)}{18}+\frac{\RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \ln \left(\frac{676735492 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x^{6}-645795448 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x^{6}-553961685 x^{6}+3200009934 \left(x^{6}+1\right)^{\frac{2}{3}} \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)-676735492 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2}-1138863414 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}}-1030573260 \left(x^{6}+1\right)^{\frac{2}{3}}-1722778774 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)+1600004967 \left(x^{6}+1\right)^{\frac{1}{3}}-738615580}{x^{6}}\right)}{9}$&$293$\\ \hline \end{longtable}"," ",0,"-1/6*(x^6+1)^(2/3)/x^6-1/36/Pi*3^(1/2)*GAMMA(2/3)*(-2/9*Pi*3^(1/2)/GAMMA(2/3)*x^6*hypergeom([1,1,4/3],[2,2],-x^6)+2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)+6*ln(x))*Pi*3^(1/2)/GAMMA(2/3))","C"
1247,1,76,68,6.645000," ","int((x^6+1)^(2/3)/x^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(\frac{\pi  \sqrt{3}\, x^{6} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 3\right], -x^{6}\right)}{9 \Gamma \left(\frac{2}{3}\right)}-\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+6 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}+\frac{\pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right) x^{6}}\right)}{18 \pi}$&$76$\\ risch&$-\frac{\left(x^{6}+1\right)^{\frac{2}{3}}}{6 x^{6}}+\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\frac{2 \pi  \sqrt{3}\, x^{6} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], -x^{6}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+6 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{18 \pi}$&$76$\\ trager&$-\frac{\left(x^{6}+1\right)^{\frac{2}{3}}}{6 x^{6}}+\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\frac{-143971236 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}+255097463 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+65690018 x^{6}+608729953 \left(x^{6}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+20253809 \left(x^{6}+1\right)^{\frac{2}{3}}+608729953 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}}+143971236 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+20253809 \left(x^{6}+1\right)^{\frac{1}{3}}+752701189 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+164225045}{x^{6}}\right)}{9}-\frac{\ln \left(-\frac{353837768 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}+1230697177 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+507551619 x^{6}+1600004967 \left(x^{6}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1030573260 \left(x^{6}+1\right)^{\frac{2}{3}}+1600004967 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}}-353837768 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+1030573260 \left(x^{6}+1\right)^{\frac{1}{3}}+1246167199 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+676735492}{x^{6}}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{9}-\frac{\ln \left(-\frac{353837768 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}+1230697177 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+507551619 x^{6}+1600004967 \left(x^{6}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1030573260 \left(x^{6}+1\right)^{\frac{2}{3}}+1600004967 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}}-353837768 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+1030573260 \left(x^{6}+1\right)^{\frac{1}{3}}+1246167199 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+676735492}{x^{6}}\right)}{9}$&$360$\\ \hline \end{longtable}"," ",0,"-1/18/Pi*3^(1/2)*GAMMA(2/3)*(1/9*Pi*3^(1/2)/GAMMA(2/3)*x^6*hypergeom([1,1,4/3],[2,3],-x^6)-2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)-1+6*ln(x))*Pi*3^(1/2)/GAMMA(2/3)+Pi*3^(1/2)/GAMMA(2/3)/x^6)","C"
1248,0,0,78,0.018000," ","int(((k^2-3)*x+2*k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/4)/(-1+d+(-d*k^2+3)*x^2-3*x^4+x^6),x)","\[\int \frac{\left(k^{2}-3\right) x +2 k^{2} x^{3}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{1}{4}} \left(-1+d +\left(-d \,k^{2}+3\right) x^{2}-3 x^{4}+x^{6}\right)}\, dx\]"," ",0,"int(((k^2-3)*x+2*k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/4)/(-1+d+(-d*k^2+3)*x^2-3*x^4+x^6),x)","F"
1249,1,264,72,59.829000," ","int((x^7-1)^(2/3)*(4*x^7+3)/x^3/(x^7+x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 \left(x^{7}-1\right)^{\frac{2}{3}}}{2 x^{2}}+\ln \left(\frac{-x^{7} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-x^{7}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-\left(x^{7}-1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{7}-1\right)^{\frac{1}{3}} x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-2 \left(x^{7}-1\right)^{\frac{2}{3}} x -\left(x^{7}-1\right)^{\frac{1}{3}} x^{2}+x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1}{x^{7}+x^{3}-1}\right)+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{x^{7} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+x^{7}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-\left(x^{7}-1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{7}-1\right)^{\frac{1}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+\left(x^{7}-1\right)^{\frac{2}{3}} x -\left(x^{7}-1\right)^{\frac{1}{3}} x^{2}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1}{x^{7}+x^{3}-1}\right)$&$264$\\ trager&$\frac{3 \left(x^{7}-1\right)^{\frac{2}{3}}}{2 x^{2}}-12 \ln \left(-\frac{66066186469498767988246012779075919590528 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{7}-16844938467913844130160220890990438495796 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{7}-80634406416788660822330883626933520827419 x^{7}-1048800710203292941813405452867830223499632 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{3}-928417484526511344275296327342965046304892 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{7}-1\right)^{\frac{2}{3}} x +928417484526511344275296327342965046304892 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{7}-1\right)^{\frac{1}{3}} x^{2}-1038167997717157830888927503704530996724868 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{3}+82955737212302297388569874434225445140826 \left(x^{7}-1\right)^{\frac{2}{3}} x -82955737212302297388569874434225445140826 \left(x^{7}-1\right)^{\frac{1}{3}} x^{2}-5420800431380750307383588815256035013608 x^{3}-66066186469498767988246012779075919590528 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}+16844938467913844130160220890990438495796 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)+80634406416788660822330883626933520827419}{x^{7}+x^{3}-1}\right) \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)+12 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \ln \left(-\frac{198198559408496303964738038337227758771584 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{7}+83567908638490916384603669062509275282652 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{7}-236315605748606297101364137058488871200172 x^{7}-3146402130609878825440216358603490670498896 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{3}+2785252453579534032825888982028895138914676 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{7}-1\right)^{\frac{2}{3}} x -2785252453579534032825888982028895138914676 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{7}-1\right)^{\frac{1}{3}} x^{2}+2590103638049827021760079784679677878424788 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{3}+480971582768534728234533705138417596998701 \left(x^{7}-1\right)^{\frac{2}{3}} x -480971582768534728234533705138417596998701 \left(x^{7}-1\right)^{\frac{1}{3}} x^{2}+221429583339245270512301829212284847817484 x^{3}-198198559408496303964738038337227758771584 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}-83567908638490916384603669062509275282652 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)+236315605748606297101364137058488871200172}{x^{7}+x^{3}-1}\right)-\ln \left(-\frac{66066186469498767988246012779075919590528 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{7}-16844938467913844130160220890990438495796 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{7}-80634406416788660822330883626933520827419 x^{7}-1048800710203292941813405452867830223499632 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{3}-928417484526511344275296327342965046304892 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{7}-1\right)^{\frac{2}{3}} x +928417484526511344275296327342965046304892 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{7}-1\right)^{\frac{1}{3}} x^{2}-1038167997717157830888927503704530996724868 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{3}+82955737212302297388569874434225445140826 \left(x^{7}-1\right)^{\frac{2}{3}} x -82955737212302297388569874434225445140826 \left(x^{7}-1\right)^{\frac{1}{3}} x^{2}-5420800431380750307383588815256035013608 x^{3}-66066186469498767988246012779075919590528 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}+16844938467913844130160220890990438495796 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)+80634406416788660822330883626933520827419}{x^{7}+x^{3}-1}\right)$&$603$\\ \hline \end{longtable}"," ",0,"3/2*(x^7-1)^(2/3)/x^2+ln((-x^7*RootOf(_Z^2+_Z+1)-x^7+RootOf(_Z^2+_Z+1)^2*x^3-(x^7-1)^(2/3)*RootOf(_Z^2+_Z+1)*x+RootOf(_Z^2+_Z+1)*(x^7-1)^(1/3)*x^2+2*RootOf(_Z^2+_Z+1)*x^3-2*(x^7-1)^(2/3)*x-(x^7-1)^(1/3)*x^2+x^3+RootOf(_Z^2+_Z+1)+1)/(x^7+x^3-1))+RootOf(_Z^2+_Z+1)*ln(-(x^7*RootOf(_Z^2+_Z+1)+x^7+RootOf(_Z^2+_Z+1)^2*x^3-(x^7-1)^(2/3)*RootOf(_Z^2+_Z+1)*x-2*RootOf(_Z^2+_Z+1)*(x^7-1)^(1/3)*x^2+RootOf(_Z^2+_Z+1)*x^3+(x^7-1)^(2/3)*x-(x^7-1)^(1/3)*x^2-RootOf(_Z^2+_Z+1)-1)/(x^7+x^3-1))","C"
1250,0,0,76,0.046000," ","int(x/(a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x)","\[\int \frac{x}{\sqrt{a^{2} x^{2}-b x}\, \left(a \,x^{2}+x \sqrt{a^{2} x^{2}-b x}\right)^{\frac{3}{2}}}\, dx\]"," ",0,"int(x/(a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x)","F"
1251,1,564,77,0.197000," ","int((-(a*b)^(1/2)+x)/(x*(a+x)*(b+x))^(1/2)/((a*b)^(1/2)+x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 b \sqrt{\frac{b +x}{b}}\, \sqrt{\frac{a +x}{a -b}}\, \sqrt{-\frac{x}{b}}\, \EllipticF \left(\sqrt{\frac{b +x}{b}}, \sqrt{-\frac{b}{a -b}}\right)}{\sqrt{a b x +a \,x^{2}+b \,x^{2}+x^{3}}}-2 \sqrt{a b}\, \left(\frac{b \sqrt{1+\frac{x}{b}}\, \sqrt{\frac{a}{a -b}+\frac{x}{a -b}}\, \sqrt{-\frac{x}{b}}\, \EllipticPi \left(\sqrt{\frac{b +x}{b}}, -\frac{b}{-b -\sqrt{a b}}, \sqrt{-\frac{b}{a -b}}\right)}{\sqrt{a b x +a \,x^{2}+b \,x^{2}+x^{3}}\, \left(-b -\sqrt{a b}\right)}+\frac{b \sqrt{1+\frac{x}{b}}\, \sqrt{\frac{a}{a -b}+\frac{x}{a -b}}\, \sqrt{-\frac{x}{b}}\, \EllipticPi \left(\sqrt{\frac{b +x}{b}}, -\frac{b}{-b +\sqrt{a b}}, \sqrt{-\frac{b}{a -b}}\right)}{\sqrt{a b x +a \,x^{2}+b \,x^{2}+x^{3}}\, \left(-b +\sqrt{a b}\right)}-\frac{a \,b^{2} \sqrt{1+\frac{x}{b}}\, \sqrt{\frac{a}{a -b}+\frac{x}{a -b}}\, \sqrt{-\frac{x}{b}}\, \EllipticPi \left(\sqrt{\frac{b +x}{b}}, -\frac{b}{-b -\sqrt{a b}}, \sqrt{-\frac{b}{a -b}}\right)}{\sqrt{a b}\, \sqrt{a^{2} b^{2} x +a^{2} b \,x^{2}+a \,b^{2} x^{2}+a b \,x^{3}}\, \left(-b -\sqrt{a b}\right)}+\frac{a \,b^{2} \sqrt{1+\frac{x}{b}}\, \sqrt{\frac{a}{a -b}+\frac{x}{a -b}}\, \sqrt{-\frac{x}{b}}\, \EllipticPi \left(\sqrt{\frac{b +x}{b}}, -\frac{b}{-b +\sqrt{a b}}, \sqrt{-\frac{b}{a -b}}\right)}{\sqrt{a b}\, \sqrt{a^{2} b^{2} x +a^{2} b \,x^{2}+a \,b^{2} x^{2}+a b \,x^{3}}\, \left(-b +\sqrt{a b}\right)}\right)$&$564$\\ elliptic&$\frac{2 b \sqrt{1+\frac{x}{b}}\, \sqrt{\frac{a}{a -b}+\frac{x}{a -b}}\, \sqrt{-\frac{x}{b}}\, \EllipticF \left(\sqrt{\frac{b +x}{b}}, \sqrt{-\frac{b}{a -b}}\right)}{\sqrt{a b x +a \,x^{2}+b \,x^{2}+x^{3}}}+\frac{2 a \,b^{2} \sqrt{1+\frac{x}{b}}\, \sqrt{\frac{a}{a -b}+\frac{x}{a -b}}\, \sqrt{-\frac{x}{b}}\, \EllipticPi \left(\sqrt{\frac{b +x}{b}}, -\frac{b}{-b -\sqrt{a b}}, \sqrt{-\frac{b}{a -b}}\right)}{\sqrt{a b}\, \sqrt{a b x +a \,x^{2}+b \,x^{2}+x^{3}}\, \left(-b -\sqrt{a b}\right)}-\frac{2 a \,b^{2} \sqrt{1+\frac{x}{b}}\, \sqrt{\frac{a}{a -b}+\frac{x}{a -b}}\, \sqrt{-\frac{x}{b}}\, \EllipticPi \left(\sqrt{\frac{b +x}{b}}, -\frac{b}{-b +\sqrt{a b}}, \sqrt{-\frac{b}{a -b}}\right)}{\sqrt{a b}\, \sqrt{a b x +a \,x^{2}+b \,x^{2}+x^{3}}\, \left(-b +\sqrt{a b}\right)}-\frac{2 a \,b^{2} \sqrt{1+\frac{x}{b}}\, \sqrt{\frac{a}{a -b}+\frac{x}{a -b}}\, \sqrt{-\frac{x}{b}}\, \EllipticPi \left(\sqrt{\frac{b +x}{b}}, -\frac{b}{-b -\sqrt{a b}}, \sqrt{-\frac{b}{a -b}}\right)}{\sqrt{a^{2} b^{2} x +a^{2} b \,x^{2}+a \,b^{2} x^{2}+a b \,x^{3}}\, \left(-b -\sqrt{a b}\right)}-\frac{2 a \,b^{2} \sqrt{1+\frac{x}{b}}\, \sqrt{\frac{a}{a -b}+\frac{x}{a -b}}\, \sqrt{-\frac{x}{b}}\, \EllipticPi \left(\sqrt{\frac{b +x}{b}}, -\frac{b}{-b +\sqrt{a b}}, \sqrt{-\frac{b}{a -b}}\right)}{\sqrt{a^{2} b^{2} x +a^{2} b \,x^{2}+a \,b^{2} x^{2}+a b \,x^{3}}\, \left(-b +\sqrt{a b}\right)}$&$573$\\ \hline \end{longtable}"," ",0,"2*b*((b+x)/b)^(1/2)*((a+x)/(a-b))^(1/2)*(-x/b)^(1/2)/(a*b*x+a*x^2+b*x^2+x^3)^(1/2)*EllipticF(((b+x)/b)^(1/2),(-b/(a-b))^(1/2))-2*(a*b)^(1/2)*(b*(1+x/b)^(1/2)*(a/(a-b)+1/(a-b)*x)^(1/2)*(-x/b)^(1/2)/(a*b*x+a*x^2+b*x^2+x^3)^(1/2)/(-b-(a*b)^(1/2))*EllipticPi(((b+x)/b)^(1/2),-b/(-b-(a*b)^(1/2)),(-b/(a-b))^(1/2))+b*(1+x/b)^(1/2)*(a/(a-b)+1/(a-b)*x)^(1/2)*(-x/b)^(1/2)/(a*b*x+a*x^2+b*x^2+x^3)^(1/2)/(-b+(a*b)^(1/2))*EllipticPi(((b+x)/b)^(1/2),-b/(-b+(a*b)^(1/2)),(-b/(a-b))^(1/2))-a*b^2/(a*b)^(1/2)*(1+x/b)^(1/2)*(a/(a-b)+1/(a-b)*x)^(1/2)*(-x/b)^(1/2)/(a^2*b^2*x+a^2*b*x^2+a*b^2*x^2+a*b*x^3)^(1/2)/(-b-(a*b)^(1/2))*EllipticPi(((b+x)/b)^(1/2),-b/(-b-(a*b)^(1/2)),(-b/(a-b))^(1/2))+a*b^2/(a*b)^(1/2)*(1+x/b)^(1/2)*(a/(a-b)+1/(a-b)*x)^(1/2)*(-x/b)^(1/2)/(a^2*b^2*x+a^2*b*x^2+a*b^2*x^2+a*b*x^3)^(1/2)/(-b+(a*b)^(1/2))*EllipticPi(((b+x)/b)^(1/2),-b/(-b+(a*b)^(1/2)),(-b/(a-b))^(1/2)))","C"
1252,1,27,77,0.606000," ","int(1/(x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{3}} x^{\frac{1}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x\right)}{\mathrm{signum}\left(-1+x \right)^{\frac{1}{3}}}$&$27$\\ trager&$-\ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{2}+48 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}-30 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}-x^{2}\right)^{\frac{1}{3}} x +2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x -16 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-36 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+96 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}+18 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x -64 x^{2}+16 x}{x}\right)+\frac{\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{2}+24 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}-9 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}-x^{2}\right)^{\frac{1}{3}} x -4 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x -19 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-30 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+48 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}+10 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x -10 x^{2}+6 x}{x}\right)}{2}$&$300$\\ \hline \end{longtable}"," ",0,"3/signum(-1+x)^(1/3)*(-signum(-1+x))^(1/3)*x^(1/3)*hypergeom([1/3,1/3],[4/3],x)","C"
1253,1,233,79,4.825000," ","int((-x^2+3)/(-x^2+1)/(x^4-6*x^2+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(-\frac{\left(x^{4}-6 x^{2}+1\right)^{\frac{3}{4}} x +\sqrt{x^{4}-6 x^{2}+1}\, x^{2}+\left(x^{4}-6 x^{2}+1\right)^{\frac{1}{4}} x^{3}+x^{4}-\sqrt{x^{4}-6 x^{2}+1}-3 \left(x^{4}-6 x^{2}+1\right)^{\frac{1}{4}} x -5 x^{2}}{\left(1+x \right) \left(-1+x \right)}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}-6 x^{2}+1}\, x^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-\left(x^{4}-6 x^{2}+1\right)^{\frac{3}{4}} x +\left(x^{4}-6 x^{2}+1\right)^{\frac{1}{4}} x^{3}-\RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}-6 x^{2}+1}+5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-3 \left(x^{4}-6 x^{2}+1\right)^{\frac{1}{4}} x}{\left(1+x \right) \left(-1+x \right)}\right)}{2}$&$233$\\ \hline \end{longtable}"," ",0,"1/2*ln(-((x^4-6*x^2+1)^(3/4)*x+(x^4-6*x^2+1)^(1/2)*x^2+(x^4-6*x^2+1)^(1/4)*x^3+x^4-(x^4-6*x^2+1)^(1/2)-3*(x^4-6*x^2+1)^(1/4)*x-5*x^2)/(1+x)/(-1+x))+1/2*RootOf(_Z^2+1)*ln(-(RootOf(_Z^2+1)*(x^4-6*x^2+1)^(1/2)*x^2-RootOf(_Z^2+1)*x^4-(x^4-6*x^2+1)^(3/4)*x+(x^4-6*x^2+1)^(1/4)*x^3-RootOf(_Z^2+1)*(x^4-6*x^2+1)^(1/2)+5*RootOf(_Z^2+1)*x^2-3*(x^4-6*x^2+1)^(1/4)*x)/(1+x)/(-1+x))","C"
1254,1,227,79,5.144000," ","int((x^4-3)/(x^4+1)/(-3*x^5+4*x^4-3*x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(-\frac{3 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{4}+4 \RootOf \left(\textit{\_Z}^{2}+2\right) \sqrt{-3 x^{5}+4 x^{4}-3 x}\, x -8 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{3}-4 \left(-3 x^{5}+4 x^{4}-3 x \right)^{\frac{3}{4}}+8 \left(-3 x^{5}+4 x^{4}-3 x \right)^{\frac{1}{4}} x^{2}+3 \RootOf \left(\textit{\_Z}^{2}+2\right)}{x^{4}+1}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{3 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{4}-4 \RootOf \left(\textit{\_Z}^{2}-2\right) \sqrt{-3 x^{5}+4 x^{4}-3 x}\, x -8 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{3}+4 \left(-3 x^{5}+4 x^{4}-3 x \right)^{\frac{3}{4}}+8 \left(-3 x^{5}+4 x^{4}-3 x \right)^{\frac{1}{4}} x^{2}+3 \RootOf \left(\textit{\_Z}^{2}-2\right)}{x^{4}+1}\right)}{2}$&$227$\\ \hline \end{longtable}"," ",0,"-1/2*RootOf(_Z^2+2)*ln(-(3*RootOf(_Z^2+2)*x^4+4*RootOf(_Z^2+2)*(-3*x^5+4*x^4-3*x)^(1/2)*x-8*RootOf(_Z^2+2)*x^3-4*(-3*x^5+4*x^4-3*x)^(3/4)+8*(-3*x^5+4*x^4-3*x)^(1/4)*x^2+3*RootOf(_Z^2+2))/(x^4+1))+1/2*RootOf(_Z^2-2)*ln((3*RootOf(_Z^2-2)*x^4-4*RootOf(_Z^2-2)*(-3*x^5+4*x^4-3*x)^(1/2)*x-8*RootOf(_Z^2-2)*x^3+4*(-3*x^5+4*x^4-3*x)^(3/4)+8*(-3*x^5+4*x^4-3*x)^(1/4)*x^2+3*RootOf(_Z^2-2))/(x^4+1))","C"
1255,1,599,74,28.268000," ","int((x^6-1)^(1/3)*(x^6+1)/x^2/(x^6+x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{6}-1\right)^{\frac{1}{3}}}{x}+\frac{\ln \left(\frac{942898597041750773061343380768 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{6}-1211814230256347664106488816042 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{6}-33783984098747171016688237221 x^{6}-7425326451703787337858079123548 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{3}+694810793316614380319244932460 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x -694810793316614380319244932460 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{2}+877700737851189734699326533804 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{3}+295728634269156474191717482137 x \left(x^{6}-1\right)^{\frac{2}{3}}-295728634269156474191717482137 x^{2} \left(x^{6}-1\right)^{\frac{1}{3}}+29493954371922133427267508685 x^{3}-942898597041750773061343380768 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2}+1211814230256347664106488816042 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)+33783984098747171016688237221}{x^{6}+x^{3}-1}\right)}{3}-2 \ln \left(\frac{942898597041750773061343380768 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{6}-1211814230256347664106488816042 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{6}-33783984098747171016688237221 x^{6}-7425326451703787337858079123548 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{3}+694810793316614380319244932460 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x -694810793316614380319244932460 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{2}+877700737851189734699326533804 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{3}+295728634269156474191717482137 x \left(x^{6}-1\right)^{\frac{2}{3}}-295728634269156474191717482137 x^{2} \left(x^{6}-1\right)^{\frac{1}{3}}+29493954371922133427267508685 x^{3}-942898597041750773061343380768 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2}+1211814230256347664106488816042 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)+33783984098747171016688237221}{x^{6}+x^{3}-1}\right) \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)+2 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \ln \left(\frac{942898597041750773061343380768 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{6}+897514697909097406419374355786 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{6}-209561394779200926893843501540 x^{6}-7425326451703787337858079123548 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{3}-694810793316614380319244932460 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x +694810793316614380319244932460 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{2}+1597408079383406044586699840712 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{3}+411530433155258870911591637547 x \left(x^{6}-1\right)^{\frac{2}{3}}-411530433155258870911591637547 x^{2} \left(x^{6}-1\right)^{\frac{1}{3}}-30481657422429225730013600224 x^{3}-942898597041750773061343380768 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2}-897514697909097406419374355786 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)+209561394779200926893843501540}{x^{6}+x^{3}-1}\right)$&$599$\\ risch&$\frac{\left(x^{6}-1\right)^{\frac{1}{3}}}{x}+\frac{\left(\frac{\ln \left(-\frac{6 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{12}-x^{12}+18 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{9}-9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{9}-9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{12}-2 x^{6}+1\right)^{\frac{1}{3}} x^{7}+x^{9}-12 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{6}+2 x^{6}+9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{12}-2 x^{6}+1\right)^{\frac{2}{3}} x^{2}-18 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{3}+9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{12}-2 x^{6}+1\right)^{\frac{1}{3}} x -x^{3}+6 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-1}{\left(-1+x \right) \left(x^{2}+x +1\right) \left(1+x \right) \left(x^{2}-x +1\right) \left(x^{6}+x^{3}-1\right)}\right)}{3}-\ln \left(-\frac{6 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{12}-x^{12}+18 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{9}-9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{9}-9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{12}-2 x^{6}+1\right)^{\frac{1}{3}} x^{7}+x^{9}-12 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{6}+2 x^{6}+9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{12}-2 x^{6}+1\right)^{\frac{2}{3}} x^{2}-18 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{3}+9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{12}-2 x^{6}+1\right)^{\frac{1}{3}} x -x^{3}+6 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-1}{\left(-1+x \right) \left(x^{2}+x +1\right) \left(1+x \right) \left(x^{2}-x +1\right) \left(x^{6}+x^{3}-1\right)}\right) \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)+\RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \ln \left(\frac{6 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{12}-x^{12}-18 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{9}+3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{9}-9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{12}-2 x^{6}+1\right)^{\frac{1}{3}} x^{7}+3 \left(x^{12}-2 x^{6}+1\right)^{\frac{1}{3}} x^{7}-12 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{6}+2 x^{6}+9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{12}-2 x^{6}+1\right)^{\frac{2}{3}} x^{2}+18 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{3}-3 \left(x^{12}-2 x^{6}+1\right)^{\frac{2}{3}} x^{2}-3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{3}+9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{12}-2 x^{6}+1\right)^{\frac{1}{3}} x -3 \left(x^{12}-2 x^{6}+1\right)^{\frac{1}{3}} x +6 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-1}{\left(-1+x \right) \left(x^{2}+x +1\right) \left(1+x \right) \left(x^{2}-x +1\right) \left(x^{6}+x^{3}-1\right)}\right)\right) \left(\left(x^{6}-1\right)^{2}\right)^{\frac{1}{3}}}{\left(x^{6}-1\right)^{\frac{2}{3}}}$&$866$\\ \hline \end{longtable}"," ",0,"(x^6-1)^(1/3)/x+1/3*ln((942898597041750773061343380768*RootOf(36*_Z^2-6*_Z+1)^2*x^6-1211814230256347664106488816042*RootOf(36*_Z^2-6*_Z+1)*x^6-33783984098747171016688237221*x^6-7425326451703787337858079123548*RootOf(36*_Z^2-6*_Z+1)^2*x^3+694810793316614380319244932460*RootOf(36*_Z^2-6*_Z+1)*(x^6-1)^(2/3)*x-694810793316614380319244932460*RootOf(36*_Z^2-6*_Z+1)*(x^6-1)^(1/3)*x^2+877700737851189734699326533804*RootOf(36*_Z^2-6*_Z+1)*x^3+295728634269156474191717482137*x*(x^6-1)^(2/3)-295728634269156474191717482137*x^2*(x^6-1)^(1/3)+29493954371922133427267508685*x^3-942898597041750773061343380768*RootOf(36*_Z^2-6*_Z+1)^2+1211814230256347664106488816042*RootOf(36*_Z^2-6*_Z+1)+33783984098747171016688237221)/(x^6+x^3-1))-2*ln((942898597041750773061343380768*RootOf(36*_Z^2-6*_Z+1)^2*x^6-1211814230256347664106488816042*RootOf(36*_Z^2-6*_Z+1)*x^6-33783984098747171016688237221*x^6-7425326451703787337858079123548*RootOf(36*_Z^2-6*_Z+1)^2*x^3+694810793316614380319244932460*RootOf(36*_Z^2-6*_Z+1)*(x^6-1)^(2/3)*x-694810793316614380319244932460*RootOf(36*_Z^2-6*_Z+1)*(x^6-1)^(1/3)*x^2+877700737851189734699326533804*RootOf(36*_Z^2-6*_Z+1)*x^3+295728634269156474191717482137*x*(x^6-1)^(2/3)-295728634269156474191717482137*x^2*(x^6-1)^(1/3)+29493954371922133427267508685*x^3-942898597041750773061343380768*RootOf(36*_Z^2-6*_Z+1)^2+1211814230256347664106488816042*RootOf(36*_Z^2-6*_Z+1)+33783984098747171016688237221)/(x^6+x^3-1))*RootOf(36*_Z^2-6*_Z+1)+2*RootOf(36*_Z^2-6*_Z+1)*ln((942898597041750773061343380768*RootOf(36*_Z^2-6*_Z+1)^2*x^6+897514697909097406419374355786*RootOf(36*_Z^2-6*_Z+1)*x^6-209561394779200926893843501540*x^6-7425326451703787337858079123548*RootOf(36*_Z^2-6*_Z+1)^2*x^3-694810793316614380319244932460*RootOf(36*_Z^2-6*_Z+1)*(x^6-1)^(2/3)*x+694810793316614380319244932460*RootOf(36*_Z^2-6*_Z+1)*(x^6-1)^(1/3)*x^2+1597408079383406044586699840712*RootOf(36*_Z^2-6*_Z+1)*x^3+411530433155258870911591637547*x*(x^6-1)^(2/3)-411530433155258870911591637547*x^2*(x^6-1)^(1/3)-30481657422429225730013600224*x^3-942898597041750773061343380768*RootOf(36*_Z^2-6*_Z+1)^2-897514697909097406419374355786*RootOf(36*_Z^2-6*_Z+1)+209561394779200926893843501540)/(x^6+x^3-1))","C"
1256,1,126,63,1.402000," ","int((x^4-1)*(x^4+1)^(1/2)/(x^8+x^6+3*x^4+x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(-\frac{\sqrt{2}\, \ln \left(\frac{x^{4}+1}{x^{2}}+\frac{\sqrt{x^{4}+1}}{x}+1\right)}{4}+\frac{\sqrt{6}\, \arctan \left(\frac{\left(\frac{2 \sqrt{2}\, \sqrt{x^{4}+1}}{x}+\sqrt{2}\right) \sqrt{6}}{6}\right)}{6}+\frac{\sqrt{2}\, \ln \left(\frac{x^{4}+1}{x^{2}}-\frac{\sqrt{x^{4}+1}}{x}+1\right)}{4}+\frac{\sqrt{6}\, \arctan \left(\frac{\left(\frac{2 \sqrt{2}\, \sqrt{x^{4}+1}}{x}-\sqrt{2}\right) \sqrt{6}}{6}\right)}{6}\right) \sqrt{2}}{2}$&$126$\\ elliptic&$\frac{\left(-\frac{\sqrt{2}\, \ln \left(\frac{x^{4}+1}{x^{2}}+\frac{\sqrt{x^{4}+1}}{x}+1\right)}{4}+\frac{\sqrt{6}\, \arctan \left(\frac{\left(\frac{2 \sqrt{2}\, \sqrt{x^{4}+1}}{x}+\sqrt{2}\right) \sqrt{6}}{6}\right)}{6}+\frac{\sqrt{2}\, \ln \left(\frac{x^{4}+1}{x^{2}}-\frac{\sqrt{x^{4}+1}}{x}+1\right)}{4}+\frac{\sqrt{6}\, \arctan \left(\frac{\left(\frac{2 \sqrt{2}\, \sqrt{x^{4}+1}}{x}-\sqrt{2}\right) \sqrt{6}}{6}\right)}{6}\right) \sqrt{2}}{2}$&$126$\\ trager&$\RootOf \left(12 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \ln \left(\frac{x^{4}+12 \sqrt{x^{4}+1}\, \RootOf \left(12 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x +6 \RootOf \left(12 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{2}+4 \sqrt{x^{4}+1}\, x +x^{2}+1}{-x^{4}+6 \RootOf \left(12 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{2}+x^{2}-1}\right)-\frac{\ln \left(-\frac{-x^{4}+12 \sqrt{x^{4}+1}\, \RootOf \left(12 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x +6 \RootOf \left(12 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{2}+2 \sqrt{x^{4}+1}\, x +2 x^{2}-1}{x^{4}+6 \RootOf \left(12 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{2}+2 x^{2}+1}\right)}{2}-\ln \left(-\frac{-x^{4}+12 \sqrt{x^{4}+1}\, \RootOf \left(12 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x +6 \RootOf \left(12 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{2}+2 \sqrt{x^{4}+1}\, x +2 x^{2}-1}{x^{4}+6 \RootOf \left(12 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{2}+2 x^{2}+1}\right) \RootOf \left(12 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)$&$294$\\ \hline \end{longtable}"," ",0,"1/2*(-1/4*2^(1/2)*ln(1/x^2*(x^4+1)+(x^4+1)^(1/2)/x+1)+1/6*6^(1/2)*arctan(1/6*(2*2^(1/2)/x*(x^4+1)^(1/2)+2^(1/2))*6^(1/2))+1/4*2^(1/2)*ln(1/x^2*(x^4+1)-(x^4+1)^(1/2)/x+1)+1/6*6^(1/2)*arctan(1/6*(2*2^(1/2)/x*(x^4+1)^(1/2)-2^(1/2))*6^(1/2)))*2^(1/2)","A"
1257,0,0,67,0.016000," ","int((2*x^8-1)/(x^4+1)^(1/4)/(x^8-1),x)","\[\int \frac{2 x^{8}-1}{\left(x^{4}+1\right)^{\frac{1}{4}} \left(x^{8}-1\right)}\, dx\]"," ",0,"int((2*x^8-1)/(x^4+1)^(1/4)/(x^8-1),x)","F"
1258,0,0,71,0.021000," ","int((a*x^8+b*x^5)^(1/4),x)","\[\int \left(a \,x^{8}+b \,x^{5}\right)^{\frac{1}{4}}\, dx\]"," ",0,"int((a*x^8+b*x^5)^(1/4),x)","F"
1259,0,0,75,0.020000," ","int((x-(x^2+1)^(1/2))^(1/2)/(1-(x^2+1)^(1/2)),x)","\[\int \frac{\sqrt{x -\sqrt{x^{2}+1}}}{1-\sqrt{x^{2}+1}}\, dx\]"," ",0,"int((x-(x^2+1)^(1/2))^(1/2)/(1-(x^2+1)^(1/2)),x)","F"
1260,1,315,76,2.600000," ","int((-1+x)*(3+x)/(x^2-1)^(2/3)/(x^2-x+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{1}{3}} x -3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x -3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+3 \left(x^{2}-1\right)^{\frac{2}{3}}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{1}{3}}+3 x \left(x^{2}-1\right)^{\frac{1}{3}}+8 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x +2 x^{2}-3 \left(x^{2}-1\right)^{\frac{1}{3}}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-4 x +2}{x^{2}-x +2}\right)+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{1}{3}} x -3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x -2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+3 \left(x^{2}-1\right)^{\frac{2}{3}}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{1}{3}}+3 x \left(x^{2}-1\right)^{\frac{1}{3}}+7 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x -3 \left(x^{2}-1\right)^{\frac{1}{3}}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-2 x -2}{x^{2}-x +2}\right)$&$315$\\ \hline \end{longtable}"," ",0,"-ln(-(RootOf(_Z^2-_Z+1)^2*x^2-3*RootOf(_Z^2-_Z+1)*(x^2-1)^(1/3)*x-3*RootOf(_Z^2-_Z+1)^2*x-3*RootOf(_Z^2-_Z+1)*x^2+3*(x^2-1)^(2/3)+3*RootOf(_Z^2-_Z+1)*(x^2-1)^(1/3)+3*x*(x^2-1)^(1/3)+8*RootOf(_Z^2-_Z+1)*x+2*x^2-3*(x^2-1)^(1/3)-RootOf(_Z^2-_Z+1)-4*x+2)/(x^2-x+2))+RootOf(_Z^2-_Z+1)*ln(-(RootOf(_Z^2-_Z+1)^2*x^2-3*RootOf(_Z^2-_Z+1)*(x^2-1)^(1/3)*x-3*RootOf(_Z^2-_Z+1)^2*x-2*RootOf(_Z^2-_Z+1)*x^2+3*(x^2-1)^(2/3)+3*RootOf(_Z^2-_Z+1)*(x^2-1)^(1/3)+3*x*(x^2-1)^(1/3)+7*RootOf(_Z^2-_Z+1)*x-3*(x^2-1)^(1/3)+RootOf(_Z^2-_Z+1)-2*x-2)/(x^2-x+2))","C"
1261,1,75,70,3.207000," ","int((x^3-1)^(1/3)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \left(-\frac{\Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 3\right], x^{3}\right)}{3}-\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+3 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{2}{3}\right)-\frac{3 \Gamma \left(\frac{2}{3}\right)}{x^{3}}\right)}{9 \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}}}$&$75$\\ risch&$-\frac{\left(x^{3}-1\right)^{\frac{1}{3}}}{3 x^{3}}+\frac{\left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} \left(\frac{2 \Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 2\right], x^{3}\right)}{3}+\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{2}{3}\right)\right)}{9 \Gamma \left(\frac{2}{3}\right) \mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}}}$&$79$\\ trager&$-\frac{\left(x^{3}-1\right)^{\frac{1}{3}}}{3 x^{3}}+\frac{\ln \left(\frac{-13504 \RootOf \left(64 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2} x^{3}-25008 \RootOf \left(64 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) x^{3}+44016 \RootOf \left(64 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}-11543 x^{3}-14247 \left(x^{3}-1\right)^{\frac{2}{3}}+157992 \RootOf \left(64 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}}+108032 \RootOf \left(64 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2}+5502 \left(x^{3}-1\right)^{\frac{1}{3}}+127480 \RootOf \left(64 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)+21437}{x^{3}}\right)}{9}-\frac{\ln \left(-\frac{-105536 \RootOf \left(64 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2} x^{3}+77464 \RootOf \left(64 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) x^{3}+44016 \RootOf \left(64 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}+1266 x^{3}+19749 \left(x^{3}-1\right)^{\frac{2}{3}}-113976 \RootOf \left(64 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}}+844288 \RootOf \left(64 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2}+5502 \left(x^{3}-1\right)^{\frac{1}{3}}-52456 \RootOf \left(64 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)-1055}{x^{3}}\right)}{9}-\frac{8 \ln \left(-\frac{-105536 \RootOf \left(64 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2} x^{3}+77464 \RootOf \left(64 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) x^{3}+44016 \RootOf \left(64 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}+1266 x^{3}+19749 \left(x^{3}-1\right)^{\frac{2}{3}}-113976 \RootOf \left(64 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}}+844288 \RootOf \left(64 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)^{2}+5502 \left(x^{3}-1\right)^{\frac{1}{3}}-52456 \RootOf \left(64 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)-1055}{x^{3}}\right) \RootOf \left(64 \textit{\_Z}^{2}+8 \textit{\_Z} +1\right)}{9}$&$429$\\ \hline \end{longtable}"," ",0,"1/9/GAMMA(2/3)*signum(x^3-1)^(1/3)/(-signum(x^3-1))^(1/3)*(-1/3*GAMMA(2/3)*x^3*hypergeom([1,1,5/3],[2,3],x^3)-(1/6*Pi*3^(1/2)-3/2*ln(3)-1+3*ln(x)+I*Pi)*GAMMA(2/3)-3*GAMMA(2/3)/x^3)","C"
1262,1,96,70,3.231000," ","int((x^3-1)^(2/3)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{\left(x^{3}-1\right)^{\frac{2}{3}}}{3 x^{3}}+\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} \left(\frac{2 \pi  \sqrt{3}\, x^{3} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], x^{3}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{9 \pi  \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}}}$&$96$\\ meijerg&$\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}} \left(-\frac{\pi  \sqrt{3}\, x^{3} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 3\right], x^{3}\right)}{9 \Gamma \left(\frac{2}{3}\right)}-\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+3 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}-\frac{\pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right) x^{3}}\right)}{9 \pi  \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}}}$&$97$\\ trager&$-\frac{\left(x^{3}-1\right)^{\frac{2}{3}}}{3 x^{3}}+\frac{2 \ln \left(\frac{-92032 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{2} x^{3}-55832 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) x^{3}+44016 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}+9894 x^{3}-19749 \left(x^{3}-1\right)^{\frac{2}{3}}-44016 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}}+736256 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{2}+19749 \left(x^{3}-1\right)^{\frac{1}{3}}-48016 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)-8245}{x^{3}}\right)}{9}-\frac{16 \ln \left(\frac{-92032 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{2} x^{3}-55832 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) x^{3}+44016 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}+9894 x^{3}-19749 \left(x^{3}-1\right)^{\frac{2}{3}}-44016 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}}+736256 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{2}+19749 \left(x^{3}-1\right)^{\frac{1}{3}}-48016 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)-8245}{x^{3}}\right) \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)}{9}+\frac{16 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) \ln \left(-\frac{92032 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{2} x^{3}-78840 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) x^{3}+44016 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}-1477 x^{3}+14247 \left(x^{3}-1\right)^{\frac{2}{3}}-44016 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}}-736256 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{2}-14247 \left(x^{3}-1\right)^{\frac{1}{3}}+136048 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)+2743}{x^{3}}\right)}{9}$&$439$\\ \hline \end{longtable}"," ",0,"-1/3*(x^3-1)^(2/3)/x^3+1/9/Pi*3^(1/2)*GAMMA(2/3)/signum(x^3-1)^(1/3)*(-signum(x^3-1))^(1/3)*(2/9*Pi*3^(1/2)/GAMMA(2/3)*x^3*hypergeom([1,1,4/3],[2,2],x^3)+2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)+3*ln(x)+I*Pi)*Pi*3^(1/2)/GAMMA(2/3))","C"
1263,1,17,74,2.251000," ","int((x^3+1)^(1/3)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\hypergeom \left(\left[-\frac{1}{3}, -\frac{1}{3}\right], \left[\frac{2}{3}\right], -x^{3}\right)}{x}$&$17$\\ risch&$-\frac{\left(x^{3}+1\right)^{\frac{1}{3}}}{x}+\frac{x^{2} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], -x^{3}\right)}{2}$&$30$\\ trager&$-\frac{\left(x^{3}+1\right)^{\frac{1}{3}}}{x}+\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x -3 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-5 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-54 x \left(x^{3}+1\right)^{\frac{2}{3}}-54 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}-52 x^{3}-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}+19 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-39\right)}{3}-\frac{\ln \left(2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +3 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-57 x \left(x^{3}+1\right)^{\frac{2}{3}}-57 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}-55 x^{3}-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}-15 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-22\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)}{3}+\frac{\ln \left(2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +3 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-57 x \left(x^{3}+1\right)^{\frac{2}{3}}-57 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}-55 x^{3}-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}-15 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-22\right)}{3}$&$408$\\ \hline \end{longtable}"," ",0,"-1/x*hypergeom([-1/3,-1/3],[2/3],-x^3)","C"
1264,1,816,76,3.559000," ","int((-1+x)/(1+x)/(x^3+2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(-\frac{23 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+80 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{2}{3}} x +80 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{1}{3}} x^{2}-46 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}+57 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+160 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{2}{3}}-x \left(x^{3}+2\right)^{\frac{2}{3}}+320 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{1}{3}} x -\left(x^{3}+2\right)^{\frac{1}{3}} x^{2}-92 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x +208 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+22 x^{3}-2 \left(x^{3}+2\right)^{\frac{2}{3}}+320 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{1}{3}}-4 x \left(x^{3}+2\right)^{\frac{1}{3}}+416 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x +110 x^{2}-4 \left(x^{3}+2\right)^{\frac{1}{3}}+322 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+220 x +154}{\left(1+x \right)^{2}}\right)-\ln \left(\frac{-1239 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+4504 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{2}{3}} x +4504 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{1}{3}} x^{2}+2478 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}+5743 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+9008 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{2}{3}}-4839 x \left(x^{3}+2\right)^{\frac{2}{3}}+18016 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{1}{3}} x -4839 \left(x^{3}+2\right)^{\frac{1}{3}} x^{2}+4956 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x +5860 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-6078 x^{3}-9678 \left(x^{3}+2\right)^{\frac{2}{3}}+18016 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{1}{3}}-19356 x \left(x^{3}+2\right)^{\frac{1}{3}}+11720 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x -16208 x^{2}-19356 \left(x^{3}+2\right)^{\frac{1}{3}}+17346 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-32416 x -28364}{\left(1+x \right)^{2}}\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+\ln \left(\frac{-1239 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+4504 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{2}{3}} x +4504 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{1}{3}} x^{2}+2478 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}+5743 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+9008 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{2}{3}}-4839 x \left(x^{3}+2\right)^{\frac{2}{3}}+18016 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{1}{3}} x -4839 \left(x^{3}+2\right)^{\frac{1}{3}} x^{2}+4956 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x +5860 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-6078 x^{3}-9678 \left(x^{3}+2\right)^{\frac{2}{3}}+18016 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{1}{3}}-19356 x \left(x^{3}+2\right)^{\frac{1}{3}}+11720 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x -16208 x^{2}-19356 \left(x^{3}+2\right)^{\frac{1}{3}}+17346 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-32416 x -28364}{\left(1+x \right)^{2}}\right)$&$816$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2-_Z+1)*ln(-(23*RootOf(_Z^2-_Z+1)^2*x^3+80*RootOf(_Z^2-_Z+1)*(x^3+2)^(2/3)*x+80*RootOf(_Z^2-_Z+1)*(x^3+2)^(1/3)*x^2-46*RootOf(_Z^2-_Z+1)^2*x^2+57*RootOf(_Z^2-_Z+1)*x^3+160*RootOf(_Z^2-_Z+1)*(x^3+2)^(2/3)-x*(x^3+2)^(2/3)+320*RootOf(_Z^2-_Z+1)*(x^3+2)^(1/3)*x-(x^3+2)^(1/3)*x^2-92*RootOf(_Z^2-_Z+1)^2*x+208*RootOf(_Z^2-_Z+1)*x^2+22*x^3-2*(x^3+2)^(2/3)+320*RootOf(_Z^2-_Z+1)*(x^3+2)^(1/3)-4*x*(x^3+2)^(1/3)+416*RootOf(_Z^2-_Z+1)*x+110*x^2-4*(x^3+2)^(1/3)+322*RootOf(_Z^2-_Z+1)+220*x+154)/(1+x)^2)-ln((-1239*RootOf(_Z^2-_Z+1)^2*x^3+4504*RootOf(_Z^2-_Z+1)*(x^3+2)^(2/3)*x+4504*RootOf(_Z^2-_Z+1)*(x^3+2)^(1/3)*x^2+2478*RootOf(_Z^2-_Z+1)^2*x^2+5743*RootOf(_Z^2-_Z+1)*x^3+9008*RootOf(_Z^2-_Z+1)*(x^3+2)^(2/3)-4839*x*(x^3+2)^(2/3)+18016*RootOf(_Z^2-_Z+1)*(x^3+2)^(1/3)*x-4839*(x^3+2)^(1/3)*x^2+4956*RootOf(_Z^2-_Z+1)^2*x+5860*RootOf(_Z^2-_Z+1)*x^2-6078*x^3-9678*(x^3+2)^(2/3)+18016*RootOf(_Z^2-_Z+1)*(x^3+2)^(1/3)-19356*x*(x^3+2)^(1/3)+11720*RootOf(_Z^2-_Z+1)*x-16208*x^2-19356*(x^3+2)^(1/3)+17346*RootOf(_Z^2-_Z+1)-32416*x-28364)/(1+x)^2)*RootOf(_Z^2-_Z+1)+ln((-1239*RootOf(_Z^2-_Z+1)^2*x^3+4504*RootOf(_Z^2-_Z+1)*(x^3+2)^(2/3)*x+4504*RootOf(_Z^2-_Z+1)*(x^3+2)^(1/3)*x^2+2478*RootOf(_Z^2-_Z+1)^2*x^2+5743*RootOf(_Z^2-_Z+1)*x^3+9008*RootOf(_Z^2-_Z+1)*(x^3+2)^(2/3)-4839*x*(x^3+2)^(2/3)+18016*RootOf(_Z^2-_Z+1)*(x^3+2)^(1/3)*x-4839*(x^3+2)^(1/3)*x^2+4956*RootOf(_Z^2-_Z+1)^2*x+5860*RootOf(_Z^2-_Z+1)*x^2-6078*x^3-9678*(x^3+2)^(2/3)+18016*RootOf(_Z^2-_Z+1)*(x^3+2)^(1/3)-19356*x*(x^3+2)^(1/3)+11720*RootOf(_Z^2-_Z+1)*x-16208*x^2-19356*(x^3+2)^(1/3)+17346*RootOf(_Z^2-_Z+1)-32416*x-28364)/(1+x)^2)","C"
1265,0,0,72,0.005000," ","int(1/x^7/(a*x^3+b)^(3/4),x)","\[\int \frac{1}{x^{7} \left(a \,x^{3}+b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x^7/(a*x^3+b)^(3/4),x)","F"
1266,0,0,76,0.040000," ","int((x^2+2*x+1)*(-2-(-1+k)*(1+k)*x+2*k^2*x^2)/((-x^2+1)*(-k^2*x^2+1))^(3/4)/(1-d-(1+3*d)*x-(k^2+3*d)*x^2+(k^2-d)*x^3),x)","\[\int \frac{\left(x^{2}+2 x +1\right) \left(-2-\left(-1+k \right) \left(1+k \right) x +2 k^{2} x^{2}\right)}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{3}{4}} \left(1-d -\left(1+3 d \right) x -\left(k^{2}+3 d \right) x^{2}+\left(k^{2}-d \right) x^{3}\right)}\, dx\]"," ",0,"int((x^2+2*x+1)*(-2-(-1+k)*(1+k)*x+2*k^2*x^2)/((-x^2+1)*(-k^2*x^2+1))^(3/4)/(1-d-(1+3*d)*x-(k^2+3*d)*x^2+(k^2-d)*x^3),x)","F"
1267,1,96,70,4.365000," ","int(1/x^5/(x^4-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(x^{4}-1\right)^{\frac{2}{3}}}{4 x^{4}}+\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{3}} \left(\frac{2 \pi  \sqrt{3}\, x^{4} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], x^{4}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{24 \pi  \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{3}}}$&$96$\\ meijerg&$-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{3}} \left(-\frac{4 \pi  \sqrt{3}\, x^{4} \hypergeom \left(\left[1, 1, \frac{7}{3}\right], \left[2, 3\right], x^{4}\right)}{27 \Gamma \left(\frac{2}{3}\right)}-\frac{2 \left(2-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right) x^{4}}\right)}{8 \pi  \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{3}}}$&$97$\\ trager&$\frac{\left(x^{4}-1\right)^{\frac{2}{3}}}{4 x^{4}}+\frac{\ln \left(\frac{6749049600 \RootOf \left(518400 \textit{\_Z}^{2}-720 \textit{\_Z} +1\right)^{2} x^{4}+105833520 \RootOf \left(518400 \textit{\_Z}^{2}-720 \textit{\_Z} +1\right) x^{4}-493850 x^{4}+134531280 \RootOf \left(518400 \textit{\_Z}^{2}-720 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}}+666879 \left(x^{4}-1\right)^{\frac{2}{3}}-134531280 \RootOf \left(518400 \textit{\_Z}^{2}-720 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{1}{3}}-107984793600 \RootOf \left(518400 \textit{\_Z}^{2}-720 \textit{\_Z} +1\right)^{2}-666879 \left(x^{4}-1\right)^{\frac{1}{3}}+284510160 \RootOf \left(518400 \textit{\_Z}^{2}-720 \textit{\_Z} +1\right)+458575}{x^{4}}\right)}{12}-60 \ln \left(\frac{6749049600 \RootOf \left(518400 \textit{\_Z}^{2}-720 \textit{\_Z} +1\right)^{2} x^{4}+105833520 \RootOf \left(518400 \textit{\_Z}^{2}-720 \textit{\_Z} +1\right) x^{4}-493850 x^{4}+134531280 \RootOf \left(518400 \textit{\_Z}^{2}-720 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}}+666879 \left(x^{4}-1\right)^{\frac{2}{3}}-134531280 \RootOf \left(518400 \textit{\_Z}^{2}-720 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{1}{3}}-107984793600 \RootOf \left(518400 \textit{\_Z}^{2}-720 \textit{\_Z} +1\right)^{2}-666879 \left(x^{4}-1\right)^{\frac{1}{3}}+284510160 \RootOf \left(518400 \textit{\_Z}^{2}-720 \textit{\_Z} +1\right)+458575}{x^{4}}\right) \RootOf \left(518400 \textit{\_Z}^{2}-720 \textit{\_Z} +1\right)+60 \RootOf \left(518400 \textit{\_Z}^{2}-720 \textit{\_Z} +1\right) \ln \left(-\frac{-421815600 \RootOf \left(518400 \textit{\_Z}^{2}-720 \textit{\_Z} +1\right)^{2} x^{4}+7786305 \RootOf \left(518400 \textit{\_Z}^{2}-720 \textit{\_Z} +1\right) x^{4}+20865 x^{4}+8408205 \RootOf \left(518400 \textit{\_Z}^{2}-720 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}}-53358 \left(x^{4}-1\right)^{\frac{2}{3}}-8408205 \RootOf \left(518400 \textit{\_Z}^{2}-720 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{1}{3}}+6749049600 \RootOf \left(518400 \textit{\_Z}^{2}-720 \textit{\_Z} +1\right)^{2}+53358 \left(x^{4}-1\right)^{\frac{1}{3}}-965475 \RootOf \left(518400 \textit{\_Z}^{2}-720 \textit{\_Z} +1\right)-40339}{x^{4}}\right)$&$439$\\ \hline \end{longtable}"," ",0,"1/4*(x^4-1)^(2/3)/x^4+1/24/Pi*3^(1/2)*GAMMA(2/3)/signum(x^4-1)^(1/3)*(-signum(x^4-1))^(1/3)*(2/9*Pi*3^(1/2)/GAMMA(2/3)*x^4*hypergeom([1,1,4/3],[2,2],x^4)+2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)+4*ln(x)+I*Pi)*Pi*3^(1/2)/GAMMA(2/3))","C"
1268,1,357,80,0.120000," ","int(x*(-b+x)*(a*b-2*a*x+x^2)/(x*(-a+x)*(-b+x))^(1/2)/(-a^2*d+2*a*d*x+(b^2-d)*x^2-2*b*x^3+x^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 b \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}-\frac{b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}-2 b \,\textit{\_Z}^{3}+\left(b^{2}-d \right) \textit{\_Z}^{2}+2 a d \textit{\_Z} -a^{2} d \right)}{\sum}\frac{\left(-2 \underline{\hspace{1.25 ex}}\alpha^{3} a +\underline{\hspace{1.25 ex}}\alpha^{3} b +3 \underline{\hspace{1.25 ex}}\alpha^{2} a b -\underline{\hspace{1.25 ex}}\alpha^{2} b^{2}-\underline{\hspace{1.25 ex}}\alpha  a \,b^{2}+\underline{\hspace{1.25 ex}}\alpha^{2} d -2 \underline{\hspace{1.25 ex}}\alpha  a d +a^{2} d \right) \left(\underline{\hspace{1.25 ex}}\alpha^{3}-b \,\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  d +2 a d -b d \right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, -\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{3}-b \,\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  d +2 a d -b d \right) b}{d \left(a^{2}-2 a b +b^{2}\right)}, \sqrt{\frac{b}{-a +b}}\right)}{\left(-2 \underline{\hspace{1.25 ex}}\alpha^{3}+3 b \,\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  \,b^{2}+\underline{\hspace{1.25 ex}}\alpha  d -a d \right) \left(a^{2}-2 a b +b^{2}\right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}\right)}{d}$&$357$\\ elliptic&$-\frac{2 b \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticF \left(\sqrt{-\frac{-b +x}{b}}, \sqrt{\frac{b}{-a +b}}\right)}{\sqrt{a b x -a \,x^{2}-b \,x^{2}+x^{3}}}+\frac{b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}-2 b \,\textit{\_Z}^{3}+\left(b^{2}-d \right) \textit{\_Z}^{2}+2 a d \textit{\_Z} -a^{2} d \right)}{\sum}\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{3} a -\underline{\hspace{1.25 ex}}\alpha^{3} b -3 \underline{\hspace{1.25 ex}}\alpha^{2} a b +\underline{\hspace{1.25 ex}}\alpha^{2} b^{2}+\underline{\hspace{1.25 ex}}\alpha  a \,b^{2}-\underline{\hspace{1.25 ex}}\alpha^{2} d +2 \underline{\hspace{1.25 ex}}\alpha  a d -a^{2} d \right) \left(\underline{\hspace{1.25 ex}}\alpha^{3}-b \,\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  d +2 a d -b d \right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, -\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{3}-b \,\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  d +2 a d -b d \right) b}{d \left(a^{2}-2 a b +b^{2}\right)}, \sqrt{\frac{b}{-a +b}}\right)}{\left(-2 \underline{\hspace{1.25 ex}}\alpha^{3}+3 b \,\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  \,b^{2}+\underline{\hspace{1.25 ex}}\alpha  d -a d \right) \left(a^{2}-2 a b +b^{2}\right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}\right)}{d}$&$357$\\ \hline \end{longtable}"," ",0,"-2*b*(-(-b+x)/b)^(1/2)*((-a+x)/(-a+b))^(1/2)*(x/b)^(1/2)/(a*b*x-a*x^2-b*x^2+x^3)^(1/2)*EllipticF((-(-b+x)/b)^(1/2),(b/(-a+b))^(1/2))-b/d*sum((-2*_alpha^3*a+_alpha^3*b+3*_alpha^2*a*b-_alpha^2*b^2-_alpha*a*b^2+_alpha^2*d-2*_alpha*a*d+a^2*d)/(-2*_alpha^3+3*_alpha^2*b-_alpha*b^2+_alpha*d-a*d)*(_alpha^3-_alpha^2*b-_alpha*d+2*a*d-b*d)/(a^2-2*a*b+b^2)*(-(-b+x)/b)^(1/2)*((-a+x)/(-a+b))^(1/2)*(x/b)^(1/2)/(x*(a*b-a*x-b*x+x^2))^(1/2)*EllipticPi((-(-b+x)/b)^(1/2),-(_alpha^3-_alpha^2*b-_alpha*d+2*a*d-b*d)*b/d/(a^2-2*a*b+b^2),(b/(-a+b))^(1/2)),_alpha=RootOf(_Z^4-2*b*_Z^3+(b^2-d)*_Z^2+2*a*d*_Z-a^2*d))","C"
1269,0,0,72,0.007000," ","int(1/x^9/(a*x^4+b)^(3/4),x)","\[\int \frac{1}{x^{9} \left(a \,x^{4}+b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x^9/(a*x^4+b)^(3/4),x)","F"
1270,0,0,72,0.006000," ","int(x^4*(a*x^4+b)^(3/4),x)","\[\int x^{4} \left(a \,x^{4}+b \right)^{\frac{3}{4}}\, dx\]"," ",0,"int(x^4*(a*x^4+b)^(3/4),x)","F"
1271,0,0,11,0.093000," ","int((a*x^4-b*x^3)^(1/4)/x/(c*x+x^2+d),x)","\[\int \frac{\left(a \,x^{4}-b \,x^{3}\right)^{\frac{1}{4}}}{x \left(c x +x^{2}+d \right)}\, dx\]"," ",0,"int((a*x^4-b*x^3)^(1/4)/x/(c*x+x^2+d),x)","F"
1272,0,0,11,0.001000," ","int((a*x^4-b*x^3)^(1/4)/x/(c*x+x^2+d),x)","\[\int \frac{\left(a \,x^{4}-b \,x^{3}\right)^{\frac{1}{4}}}{x \left(c x +x^{2}+d \right)}\, dx\]"," ",0,"int((a*x^4-b*x^3)^(1/4)/x/(c*x+x^2+d),x)","F"
1273,1,96,70,6.720000," ","int((x^5-1)^(2/3)/x^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{\left(x^{5}-1\right)^{\frac{2}{3}}}{5 x^{5}}+\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{1}{3}} \left(\frac{2 \pi  \sqrt{3}\, x^{5} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], x^{5}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+5 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{15 \pi  \mathrm{signum}\left(x^{5}-1\right)^{\frac{1}{3}}}$&$96$\\ meijerg&$\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \mathrm{signum}\left(x^{5}-1\right)^{\frac{2}{3}} \left(-\frac{\pi  \sqrt{3}\, x^{5} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 3\right], x^{5}\right)}{9 \Gamma \left(\frac{2}{3}\right)}-\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+5 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}-\frac{\pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right) x^{5}}\right)}{15 \pi  \left(-\mathrm{signum}\left(x^{5}-1\right)\right)^{\frac{2}{3}}}$&$97$\\ trager&$-\frac{\left(x^{5}-1\right)^{\frac{2}{3}}}{5 x^{5}}-\frac{2 \ln \left(\frac{30885108600167424 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x^{5}+9590347318616160 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{5}-19140349667550 x^{5}+12071260649204448 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{2}{3}}+58267503137446 \left(x^{5}-1\right)^{\frac{2}{3}}-5593680301194816 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{1}{3}}-988323475205357568 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2}+184009801566659 \left(x^{5}-1\right)^{\frac{1}{3}}-7369904750343456 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)+18502338011965}{x^{5}}\right)}{15}+\frac{2 \ln \left(-\frac{25005193182296064 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x^{5}-8013344512846944 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{5}-19778361323135 x^{5}+12071260649204448 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{2}{3}}-184009801566659 \left(x^{5}-1\right)^{\frac{2}{3}}+17664940950399264 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{1}{3}}-800166181833474048 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2}-58267503137446 \left(x^{5}-1\right)^{\frac{1}{3}}+13928744695293504 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)+38918710990685}{x^{5}}\right)}{15}-\frac{64 \ln \left(-\frac{25005193182296064 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x^{5}-8013344512846944 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{5}-19778361323135 x^{5}+12071260649204448 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{2}{3}}-184009801566659 \left(x^{5}-1\right)^{\frac{2}{3}}+17664940950399264 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{1}{3}}-800166181833474048 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2}-58267503137446 \left(x^{5}-1\right)^{\frac{1}{3}}+13928744695293504 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)+38918710990685}{x^{5}}\right) \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)}{5}$&$429$\\ \hline \end{longtable}"," ",0,"-1/5*(x^5-1)^(2/3)/x^5+1/15/Pi*3^(1/2)*GAMMA(2/3)/signum(x^5-1)^(1/3)*(-signum(x^5-1))^(1/3)*(2/9*Pi*3^(1/2)/GAMMA(2/3)*x^5*hypergeom([1,1,4/3],[2,2],x^5)+2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)+5*ln(x)+I*Pi)*Pi*3^(1/2)/GAMMA(2/3))","C"
1274,0,0,72,0.006000," ","int(1/x^11/(a*x^5+b)^(3/4),x)","\[\int \frac{1}{x^{11} \left(a \,x^{5}+b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x^11/(a*x^5+b)^(3/4),x)","F"
1275,1,96,70,8.638000," ","int(1/x^7/(x^6-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(x^{6}-1\right)^{\frac{2}{3}}}{6 x^{6}}+\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} \left(\frac{2 \pi  \sqrt{3}\, x^{6} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], x^{6}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+6 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{36 \pi  \mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}}}$&$96$\\ meijerg&$-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} \left(-\frac{4 \pi  \sqrt{3}\, x^{6} \hypergeom \left(\left[1, 1, \frac{7}{3}\right], \left[2, 3\right], x^{6}\right)}{27 \Gamma \left(\frac{2}{3}\right)}-\frac{2 \left(2-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+6 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right) x^{6}}\right)}{12 \pi  \mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}}}$&$97$\\ trager&$\frac{\left(x^{6}-1\right)^{\frac{2}{3}}}{6 x^{6}}+224 \RootOf \left(16257024 \textit{\_Z}^{2}-4032 \textit{\_Z} +1\right) \ln \left(-\frac{24467220649221806672558383104 \RootOf \left(16257024 \textit{\_Z}^{2}-4032 \textit{\_Z} +1\right)^{2} x^{6}-380817353737696452026579136 \RootOf \left(16257024 \textit{\_Z}^{2}-4032 \textit{\_Z} +1\right) x^{6}-23171389162410581752275 x^{6}+275253794455679502932875392 \left(x^{6}-1\right)^{\frac{2}{3}} \RootOf \left(16257024 \textit{\_Z}^{2}-4032 \textit{\_Z} +1\right)+142296551347461340528569 \left(x^{6}-1\right)^{\frac{2}{3}}-275253794455679502932875392 \RootOf \left(16257024 \textit{\_Z}^{2}-4032 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}}-1565902121550195627043736518656 \RootOf \left(16257024 \textit{\_Z}^{2}-4032 \textit{\_Z} +1\right)^{2}-142296551347461340528569 \left(x^{6}-1\right)^{\frac{1}{3}}+663622376189358973925865600 \RootOf \left(16257024 \textit{\_Z}^{2}-4032 \textit{\_Z} +1\right)+45974978496846392365625}{x^{6}}\right)+\frac{\ln \left(\frac{-24467220649221806672558383104 \RootOf \left(16257024 \textit{\_Z}^{2}-4032 \textit{\_Z} +1\right)^{2} x^{6}-368680835558518968558048192 \RootOf \left(16257024 \textit{\_Z}^{2}-4032 \textit{\_Z} +1\right) x^{6}+116115113033469041646202 x^{6}+275253794455679502932875392 \left(x^{6}-1\right)^{\frac{2}{3}} \RootOf \left(16257024 \textit{\_Z}^{2}-4032 \textit{\_Z} +1\right)-210563861480318360105175 \left(x^{6}-1\right)^{\frac{2}{3}}-275253794455679502932875392 \RootOf \left(16257024 \textit{\_Z}^{2}-4032 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}}+1565902121550195627043736518656 \RootOf \left(16257024 \textit{\_Z}^{2}-4032 \textit{\_Z} +1\right)^{2}+210563861480318360105175 \left(x^{6}-1\right)^{\frac{1}{3}}-113114787277999968060114816 \RootOf \left(16257024 \textit{\_Z}^{2}-4032 \textit{\_Z} +1\right)-114242288629703411942231}{x^{6}}\right)}{18}-224 \ln \left(\frac{-24467220649221806672558383104 \RootOf \left(16257024 \textit{\_Z}^{2}-4032 \textit{\_Z} +1\right)^{2} x^{6}-368680835558518968558048192 \RootOf \left(16257024 \textit{\_Z}^{2}-4032 \textit{\_Z} +1\right) x^{6}+116115113033469041646202 x^{6}+275253794455679502932875392 \left(x^{6}-1\right)^{\frac{2}{3}} \RootOf \left(16257024 \textit{\_Z}^{2}-4032 \textit{\_Z} +1\right)-210563861480318360105175 \left(x^{6}-1\right)^{\frac{2}{3}}-275253794455679502932875392 \RootOf \left(16257024 \textit{\_Z}^{2}-4032 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}}+1565902121550195627043736518656 \RootOf \left(16257024 \textit{\_Z}^{2}-4032 \textit{\_Z} +1\right)^{2}+210563861480318360105175 \left(x^{6}-1\right)^{\frac{1}{3}}-113114787277999968060114816 \RootOf \left(16257024 \textit{\_Z}^{2}-4032 \textit{\_Z} +1\right)-114242288629703411942231}{x^{6}}\right) \RootOf \left(16257024 \textit{\_Z}^{2}-4032 \textit{\_Z} +1\right)$&$439$\\ \hline \end{longtable}"," ",0,"1/6*(x^6-1)^(2/3)/x^6+1/36/Pi*3^(1/2)*GAMMA(2/3)/signum(x^6-1)^(1/3)*(-signum(x^6-1))^(1/3)*(2/9*Pi*3^(1/2)/GAMMA(2/3)*x^6*hypergeom([1,1,4/3],[2,2],x^6)+2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)+6*ln(x)+I*Pi)*Pi*3^(1/2)/GAMMA(2/3))","C"
1276,1,96,70,8.691000," ","int((x^6-1)^(2/3)/x^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{\left(x^{6}-1\right)^{\frac{2}{3}}}{6 x^{6}}+\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} \left(\frac{2 \pi  \sqrt{3}\, x^{6} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], x^{6}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+6 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{18 \pi  \mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}}}$&$96$\\ meijerg&$\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \mathrm{signum}\left(x^{6}-1\right)^{\frac{2}{3}} \left(-\frac{\pi  \sqrt{3}\, x^{6} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 3\right], x^{6}\right)}{9 \Gamma \left(\frac{2}{3}\right)}-\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+6 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}-\frac{\pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right) x^{6}}\right)}{18 \pi  \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{2}{3}}}$&$97$\\ trager&$-\frac{\left(x^{6}-1\right)^{\frac{2}{3}}}{6 x^{6}}+\frac{\ln \left(\frac{-6164580662439356682428416 \RootOf \left(4096 \textit{\_Z}^{2}-64 \textit{\_Z} +1\right)^{2} x^{6}-5852076754897126485048384 \RootOf \left(4096 \textit{\_Z}^{2}-64 \textit{\_Z} +1\right) x^{6}+116115113033469041646202 x^{6}+4369107848502849252902784 \left(x^{6}-1\right)^{\frac{2}{3}} \RootOf \left(4096 \textit{\_Z}^{2}-64 \textit{\_Z} +1\right)-210563861480318360105175 \left(x^{6}-1\right)^{\frac{2}{3}}-4369107848502849252902784 \RootOf \left(4096 \textit{\_Z}^{2}-64 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}}+394533162396118827675418624 \RootOf \left(4096 \textit{\_Z}^{2}-64 \textit{\_Z} +1\right)^{2}+210563861480318360105175 \left(x^{6}-1\right)^{\frac{1}{3}}-1795472813936507429525632 \RootOf \left(4096 \textit{\_Z}^{2}-64 \textit{\_Z} +1\right)-114242288629703411942231}{x^{6}}\right)}{9}-\frac{64 \ln \left(\frac{-6164580662439356682428416 \RootOf \left(4096 \textit{\_Z}^{2}-64 \textit{\_Z} +1\right)^{2} x^{6}-5852076754897126485048384 \RootOf \left(4096 \textit{\_Z}^{2}-64 \textit{\_Z} +1\right) x^{6}+116115113033469041646202 x^{6}+4369107848502849252902784 \left(x^{6}-1\right)^{\frac{2}{3}} \RootOf \left(4096 \textit{\_Z}^{2}-64 \textit{\_Z} +1\right)-210563861480318360105175 \left(x^{6}-1\right)^{\frac{2}{3}}-4369107848502849252902784 \RootOf \left(4096 \textit{\_Z}^{2}-64 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}}+394533162396118827675418624 \RootOf \left(4096 \textit{\_Z}^{2}-64 \textit{\_Z} +1\right)^{2}+210563861480318360105175 \left(x^{6}-1\right)^{\frac{1}{3}}-1795472813936507429525632 \RootOf \left(4096 \textit{\_Z}^{2}-64 \textit{\_Z} +1\right)-114242288629703411942231}{x^{6}}\right) \RootOf \left(4096 \textit{\_Z}^{2}-64 \textit{\_Z} +1\right)}{9}+\frac{64 \RootOf \left(4096 \textit{\_Z}^{2}-64 \textit{\_Z} +1\right) \ln \left(-\frac{6164580662439356682428416 \RootOf \left(4096 \textit{\_Z}^{2}-64 \textit{\_Z} +1\right)^{2} x^{6}-6044719900598356381374272 \RootOf \left(4096 \textit{\_Z}^{2}-64 \textit{\_Z} +1\right) x^{6}-23171389162410581752275 x^{6}+4369107848502849252902784 \left(x^{6}-1\right)^{\frac{2}{3}} \RootOf \left(4096 \textit{\_Z}^{2}-64 \textit{\_Z} +1\right)+142296551347461340528569 \left(x^{6}-1\right)^{\frac{2}{3}}-4369107848502849252902784 \RootOf \left(4096 \textit{\_Z}^{2}-64 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}}-394533162396118827675418624 \RootOf \left(4096 \textit{\_Z}^{2}-64 \textit{\_Z} +1\right)^{2}-142296551347461340528569 \left(x^{6}-1\right)^{\frac{1}{3}}+10533688510942205935331200 \RootOf \left(4096 \textit{\_Z}^{2}-64 \textit{\_Z} +1\right)+45974978496846392365625}{x^{6}}\right)}{9}$&$439$\\ \hline \end{longtable}"," ",0,"-1/6*(x^6-1)^(2/3)/x^6+1/18/Pi*3^(1/2)*GAMMA(2/3)/signum(x^6-1)^(1/3)*(-signum(x^6-1))^(1/3)*(2/9*Pi*3^(1/2)/GAMMA(2/3)*x^6*hypergeom([1,1,4/3],[2,2],x^6)+2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)+6*ln(x)+I*Pi)*Pi*3^(1/2)/GAMMA(2/3))","C"
1277,1,729,74,8.984000," ","int((2*x^6+x^4-1)*(x^7+x^5+x)^(1/3)/(x^6+x^4+1)/(x^6+x^4-x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(\frac{20906848965368 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{6}-23910827812306 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{6}+20906848965368 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{4}-11174168453619 x^{6}-23910827812306 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{4}-62720546896104 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{2}-11174168453619 x^{4}+35926743200058 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{7}+x^{5}+x \right)^{\frac{2}{3}}+31239270484854 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{7}+x^{5}+x \right)^{\frac{1}{3}} x -64162034837974 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{2}+33583006842456 \left(x^{7}+x^{5}+x \right)^{\frac{2}{3}}-17963371600029 x \left(x^{7}+x^{5}+x \right)^{\frac{1}{3}}+20906848965368 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}-14898891271492 x^{2}-23910827812306 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)-11174168453619}{x^{6}+x^{4}-x^{2}+1}\right)}{2}-\frac{\ln \left(-\frac{14898891271492 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{6}+40251207025668 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{6}+14898891271492 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{4}+20906848965368 x^{6}+40251207025668 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{4}-44696673814476 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{2}+20906848965368 x^{4}+35926743200058 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{7}+x^{5}+x \right)^{\frac{2}{3}}-67166013684912 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{7}+x^{5}+x \right)^{\frac{1}{3}} x -23910827812306 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{2}-15619635242427 \left(x^{7}+x^{5}+x \right)^{\frac{2}{3}}-17963371600029 x \left(x^{7}+x^{5}+x \right)^{\frac{1}{3}}+14898891271492 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}+5226712241342 x^{2}+40251207025668 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+20906848965368}{x^{6}+x^{4}-x^{2}+1}\right)}{2}-\ln \left(-\frac{14898891271492 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{6}+40251207025668 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{6}+14898891271492 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{4}+20906848965368 x^{6}+40251207025668 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{4}-44696673814476 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{2}+20906848965368 x^{4}+35926743200058 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{7}+x^{5}+x \right)^{\frac{2}{3}}-67166013684912 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{7}+x^{5}+x \right)^{\frac{1}{3}} x -23910827812306 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{2}-15619635242427 \left(x^{7}+x^{5}+x \right)^{\frac{2}{3}}-17963371600029 x \left(x^{7}+x^{5}+x \right)^{\frac{1}{3}}+14898891271492 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}+5226712241342 x^{2}+40251207025668 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+20906848965368}{x^{6}+x^{4}-x^{2}+1}\right) \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)$&$729$\\ \hline \end{longtable}"," ",0,"1/2*ln((20906848965368*RootOf(4*_Z^2+2*_Z+1)^2*x^6-23910827812306*RootOf(4*_Z^2+2*_Z+1)*x^6+20906848965368*RootOf(4*_Z^2+2*_Z+1)^2*x^4-11174168453619*x^6-23910827812306*RootOf(4*_Z^2+2*_Z+1)*x^4-62720546896104*RootOf(4*_Z^2+2*_Z+1)^2*x^2-11174168453619*x^4+35926743200058*RootOf(4*_Z^2+2*_Z+1)*(x^7+x^5+x)^(2/3)+31239270484854*RootOf(4*_Z^2+2*_Z+1)*(x^7+x^5+x)^(1/3)*x-64162034837974*RootOf(4*_Z^2+2*_Z+1)*x^2+33583006842456*(x^7+x^5+x)^(2/3)-17963371600029*x*(x^7+x^5+x)^(1/3)+20906848965368*RootOf(4*_Z^2+2*_Z+1)^2-14898891271492*x^2-23910827812306*RootOf(4*_Z^2+2*_Z+1)-11174168453619)/(x^6+x^4-x^2+1))-1/2*ln(-(14898891271492*RootOf(4*_Z^2+2*_Z+1)^2*x^6+40251207025668*RootOf(4*_Z^2+2*_Z+1)*x^6+14898891271492*RootOf(4*_Z^2+2*_Z+1)^2*x^4+20906848965368*x^6+40251207025668*RootOf(4*_Z^2+2*_Z+1)*x^4-44696673814476*RootOf(4*_Z^2+2*_Z+1)^2*x^2+20906848965368*x^4+35926743200058*RootOf(4*_Z^2+2*_Z+1)*(x^7+x^5+x)^(2/3)-67166013684912*RootOf(4*_Z^2+2*_Z+1)*(x^7+x^5+x)^(1/3)*x-23910827812306*RootOf(4*_Z^2+2*_Z+1)*x^2-15619635242427*(x^7+x^5+x)^(2/3)-17963371600029*x*(x^7+x^5+x)^(1/3)+14898891271492*RootOf(4*_Z^2+2*_Z+1)^2+5226712241342*x^2+40251207025668*RootOf(4*_Z^2+2*_Z+1)+20906848965368)/(x^6+x^4-x^2+1))-ln(-(14898891271492*RootOf(4*_Z^2+2*_Z+1)^2*x^6+40251207025668*RootOf(4*_Z^2+2*_Z+1)*x^6+14898891271492*RootOf(4*_Z^2+2*_Z+1)^2*x^4+20906848965368*x^6+40251207025668*RootOf(4*_Z^2+2*_Z+1)*x^4-44696673814476*RootOf(4*_Z^2+2*_Z+1)^2*x^2+20906848965368*x^4+35926743200058*RootOf(4*_Z^2+2*_Z+1)*(x^7+x^5+x)^(2/3)-67166013684912*RootOf(4*_Z^2+2*_Z+1)*(x^7+x^5+x)^(1/3)*x-23910827812306*RootOf(4*_Z^2+2*_Z+1)*x^2-15619635242427*(x^7+x^5+x)^(2/3)-17963371600029*x*(x^7+x^5+x)^(1/3)+14898891271492*RootOf(4*_Z^2+2*_Z+1)^2+5226712241342*x^2+40251207025668*RootOf(4*_Z^2+2*_Z+1)+20906848965368)/(x^6+x^4-x^2+1))*RootOf(4*_Z^2+2*_Z+1)","C"
1278,1,97,68,0.044000," ","int((1+(1+x)^(1/2))^(1/2)/(x-(1+x)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$4 \sqrt{1+\sqrt{1+x}}-\ln \left(\sqrt{1+x}+\sqrt{1+\sqrt{1+x}}\right)-\frac{6 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}+1\right) \sqrt{5}}{5}\right)}{5}+\ln \left(\sqrt{1+x}-\sqrt{1+\sqrt{1+x}}\right)-\frac{6 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}-1\right) \sqrt{5}}{5}\right)}{5}$&$97$\\ default&$4 \sqrt{1+\sqrt{1+x}}-\ln \left(\sqrt{1+x}+\sqrt{1+\sqrt{1+x}}\right)-\frac{6 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}+1\right) \sqrt{5}}{5}\right)}{5}+\ln \left(\sqrt{1+x}-\sqrt{1+\sqrt{1+x}}\right)-\frac{6 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}-1\right) \sqrt{5}}{5}\right)}{5}$&$97$\\ \hline \end{longtable}"," ",0,"4*(1+(1+x)^(1/2))^(1/2)-ln((1+x)^(1/2)+(1+(1+x)^(1/2))^(1/2))-6/5*5^(1/2)*arctanh(1/5*(2*(1+(1+x)^(1/2))^(1/2)+1)*5^(1/2))+ln((1+x)^(1/2)-(1+(1+x)^(1/2))^(1/2))-6/5*5^(1/2)*arctanh(1/5*(2*(1+(1+x)^(1/2))^(1/2)-1)*5^(1/2))","A"
1279,1,71,69,2.612000," ","int(1/x^3/(x^2-1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{3}{4}} \left(-\frac{21 \Gamma \left(\frac{3}{4}\right) x^{2} \hypergeom \left(\left[1, 1, \frac{11}{4}\right], \left[2, 3\right], x^{2}\right)}{32}-\frac{3 \left(\frac{1}{3}-3 \ln \left(2\right)+\frac{\pi}{2}+2 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{3}{4}\right)}{4}+\frac{\Gamma \left(\frac{3}{4}\right)}{x^{2}}\right)}{2 \Gamma \left(\frac{3}{4}\right) \mathrm{signum}\left(x^{2}-1\right)^{\frac{3}{4}}}$&$71$\\ risch&$\frac{\left(x^{2}-1\right)^{\frac{1}{4}}}{2 x^{2}}+\frac{3 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{3}{4}} \left(\frac{3 \Gamma \left(\frac{3}{4}\right) x^{2} \hypergeom \left(\left[1, 1, \frac{7}{4}\right], \left[2, 2\right], x^{2}\right)}{4}+\left(-3 \ln \left(2\right)+\frac{\pi}{2}+2 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{3}{4}\right)\right)}{8 \Gamma \left(\frac{3}{4}\right) \mathrm{signum}\left(x^{2}-1\right)^{\frac{3}{4}}}$&$76$\\ trager&$\frac{\left(x^{2}-1\right)^{\frac{1}{4}}}{2 x^{2}}+\frac{3 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(-\frac{2 \sqrt{x^{2}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+2 \left(x^{2}-1\right)^{\frac{3}{4}}-2 \left(x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-\RootOf \left(\textit{\_Z}^{4}+1\right) x^{2}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)}{x^{2}}\right)}{8}-\frac{3 \RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}+2 \left(x^{2}-1\right)^{\frac{3}{4}}-2 \sqrt{x^{2}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)+2 \left(x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{x^{2}}\right)}{8}$&$171$\\ \hline \end{longtable}"," ",0,"-1/2/GAMMA(3/4)/signum(x^2-1)^(3/4)*(-signum(x^2-1))^(3/4)*(-21/32*GAMMA(3/4)*x^2*hypergeom([1,1,11/4],[2,3],x^2)-3/4*(1/3-3*ln(2)+1/2*Pi+2*ln(x)+I*Pi)*GAMMA(3/4)+GAMMA(3/4)/x^2)","C"
1280,1,33,74,2.897000," ","int((x^3-1)^(2/3)/x^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}} \hypergeom \left(\left[-\frac{2}{3}, -\frac{2}{3}\right], \left[\frac{1}{3}\right], x^{3}\right)}{2 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} x^{2}}$&$33$\\ risch&$-\frac{\left(x^{3}-1\right)^{\frac{2}{3}}}{2 x^{2}}+\frac{\left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{3}\right)}{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}}}$&$43$\\ trager&$-\frac{\left(x^{3}-1\right)^{\frac{2}{3}}}{2 x^{2}}+\frac{4 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) \ln \left(182271728 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)^{2} x^{3}+775851456 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +775851456 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) x^{2}+730283524 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) x^{3}-1508552373 x \left(x^{3}-1\right)^{\frac{2}{3}}-1508552373 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-1497160390 x^{3}-1458173824 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)^{2}+1858712316 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)+476369215\right)}{3}+\frac{\ln \left(182271728 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)^{2} x^{3}-775851456 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -775851456 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) x^{2}-821419388 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) x^{3}-1314589509 x \left(x^{3}-1\right)^{\frac{2}{3}}-1314589509 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-1303197526 x^{3}-1458173824 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)^{2}-1129625404 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)+849911430\right)}{3}-\frac{4 \ln \left(182271728 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)^{2} x^{3}-775851456 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -775851456 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) x^{2}-821419388 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) x^{3}-1314589509 x \left(x^{3}-1\right)^{\frac{2}{3}}-1314589509 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-1303197526 x^{3}-1458173824 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)^{2}-1129625404 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)+849911430\right) \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)}{3}$&$450$\\ \hline \end{longtable}"," ",0,"-1/2*signum(x^3-1)^(2/3)/(-signum(x^3-1))^(2/3)/x^2*hypergeom([-2/3,-2/3],[1/3],x^3)","C"
1281,1,1500,73,1.122000," ","int((x^2+2)/(x^2+2*x-2)/(x^3+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{\sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}-\frac{3 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}-\frac{3 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}-\frac{\sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}$&$1500$\\ elliptic&$\frac{3 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}-\frac{3 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}+\frac{\sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}-\frac{3 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}-\frac{\sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}$&$1705$\\ \hline \end{longtable}"," ",0,"2*(3/2-1/2*I*3^(1/2))*((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+(1/(3/2-1/2*I*3^(1/2))+1/(3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2),-1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)-3*(1/(3/2-1/2*I*3^(1/2))+1/(3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2),-1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))-I*(1/(3/2-1/2*I*3^(1/2))+1/(3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2),-1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+I*(1/(3/2-1/2*I*3^(1/2))+1/(3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2),-1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)-3*(1/(3/2-1/2*I*3^(1/2))+1/(3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2),1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+I*(1/(3/2-1/2*I*3^(1/2))+1/(3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2),1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+I*(1/(3/2-1/2*I*3^(1/2))+1/(3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2),1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)-(1/(3/2-1/2*I*3^(1/2))+1/(3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2),1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)","C"
1282,1,17,74,3.345000," ","int((x^3+1)^(2/3)/x^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\hypergeom \left(\left[-\frac{2}{3}, -\frac{2}{3}\right], \left[\frac{1}{3}\right], -x^{3}\right)}{2 x^{2}}$&$17$\\ risch&$-\frac{\left(x^{3}+1\right)^{\frac{2}{3}}}{2 x^{2}}+x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{3}\right)$&$27$\\ trager&$-\frac{\left(x^{3}+1\right)^{\frac{2}{3}}}{2 x^{2}}-\frac{\ln \left(317 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-555 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +2358 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-2120 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-1803 x \left(x^{3}+1\right)^{\frac{2}{3}}-555 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}+2675 x^{3}-317 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}-99 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+1070\right)}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(-535 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+555 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +1803 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-1823 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-2358 x \left(x^{3}+1\right)^{\frac{2}{3}}+555 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}+1268 x^{3}+535 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}-1922 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+951\right)}{3}$&$275$\\ \hline \end{longtable}"," ",0,"-1/2/x^2*hypergeom([-2/3,-2/3],[1/3],-x^3)","C"
1283,0,0,81,0.015000," ","int((2*a*b*x+(-3*a+b)*x^2)/(x^2*(-a+x)*(-b+x))^(1/4)/(a^3-3*a^2*x+(-b*d+3*a)*x^2+(-1+d)*x^3),x)","\[\int \frac{2 a b x +\left(-3 a +b \right) x^{2}}{\left(x^{2} \left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{4}} \left(a^{3}-3 a^{2} x +\left(-b d +3 a \right) x^{2}+\left(-1+d \right) x^{3}\right)}\, dx\]"," ",0,"int((2*a*b*x+(-3*a+b)*x^2)/(x^2*(-a+x)*(-b+x))^(1/4)/(a^3-3*a^2*x+(-b*d+3*a)*x^2+(-1+d)*x^3),x)","F"
1284,1,72,69,7.887000," ","int((x^4-1)^(1/4)/x^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}} \left(-\frac{3 \Gamma \left(\frac{3}{4}\right) x^{4} \hypergeom \left(\left[1, 1, \frac{7}{4}\right], \left[2, 3\right], x^{4}\right)}{8}-\left(-3 \ln \left(2\right)+\frac{\pi}{2}-1+4 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{3}{4}\right)-\frac{4 \Gamma \left(\frac{3}{4}\right)}{x^{4}}\right)}{16 \Gamma \left(\frac{3}{4}\right) \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}}}$&$72$\\ risch&$-\frac{\left(x^{4}-1\right)^{\frac{1}{4}}}{4 x^{4}}+\frac{\left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{3}{4}} \left(\frac{3 \Gamma \left(\frac{3}{4}\right) x^{4} \hypergeom \left(\left[1, 1, \frac{7}{4}\right], \left[2, 2\right], x^{4}\right)}{4}+\left(-3 \ln \left(2\right)+\frac{\pi}{2}+4 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{3}{4}\right)\right)}{16 \Gamma \left(\frac{3}{4}\right) \mathrm{signum}\left(x^{4}-1\right)^{\frac{3}{4}}}$&$76$\\ trager&$-\frac{\left(x^{4}-1\right)^{\frac{1}{4}}}{4 x^{4}}+\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}-\RootOf \left(\textit{\_Z}^{4}+1\right) x^{4}+2 \left(x^{4}-1\right)^{\frac{3}{4}}-2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)}{x^{4}}\right)}{16}-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{4}+2 \left(x^{4}-1\right)^{\frac{3}{4}}-2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)+2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{x^{4}}\right)}{16}$&$169$\\ \hline \end{longtable}"," ",0,"1/16/GAMMA(3/4)*signum(x^4-1)^(1/4)/(-signum(x^4-1))^(1/4)*(-3/8*GAMMA(3/4)*x^4*hypergeom([1,1,7/4],[2,3],x^4)-(-3*ln(2)+1/2*Pi-1+4*ln(x)+I*Pi)*GAMMA(3/4)-4*GAMMA(3/4)/x^4)","C"
1285,1,581,79,2.517000," ","int((x^2+1)/(x^2+x-1)/(x^4-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \ln \left(\frac{494 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{3}-741 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{2}-2222 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{3}+1356 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{4}-x^{2}\right)^{\frac{2}{3}}-1356 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{4}-x^{2}\right)^{\frac{1}{3}} x -494 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x +1604 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}+2220 x^{3}+1980 \left(x^{4}-x^{2}\right)^{\frac{2}{3}}-1980 x \left(x^{4}-x^{2}\right)^{\frac{1}{3}}+2222 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x -740 x^{2}-2220 x}{x \left(x^{2}+x -1\right)}\right)}{2}-\frac{\ln \left(-\frac{-494 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{3}+741 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{2}-246 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{3}+1356 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{4}-x^{2}\right)^{\frac{2}{3}}-1356 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{4}-x^{2}\right)^{\frac{1}{3}} x +494 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x -1360 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}+248 x^{3}-4692 \left(x^{4}-x^{2}\right)^{\frac{2}{3}}+4692 x \left(x^{4}-x^{2}\right)^{\frac{1}{3}}+246 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x +496 x^{2}-248 x}{x \left(x^{2}+x -1\right)}\right) \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)}{2}+\ln \left(-\frac{-494 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{3}+741 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{2}-246 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{3}+1356 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{4}-x^{2}\right)^{\frac{2}{3}}-1356 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{4}-x^{2}\right)^{\frac{1}{3}} x +494 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x -1360 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}+248 x^{3}-4692 \left(x^{4}-x^{2}\right)^{\frac{2}{3}}+4692 x \left(x^{4}-x^{2}\right)^{\frac{1}{3}}+246 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x +496 x^{2}-248 x}{x \left(x^{2}+x -1\right)}\right)$&$581$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^2-2*_Z+4)*ln((494*RootOf(_Z^2-2*_Z+4)^2*x^3-741*RootOf(_Z^2-2*_Z+4)^2*x^2-2222*RootOf(_Z^2-2*_Z+4)*x^3+1356*RootOf(_Z^2-2*_Z+4)*(x^4-x^2)^(2/3)-1356*RootOf(_Z^2-2*_Z+4)*(x^4-x^2)^(1/3)*x-494*RootOf(_Z^2-2*_Z+4)^2*x+1604*RootOf(_Z^2-2*_Z+4)*x^2+2220*x^3+1980*(x^4-x^2)^(2/3)-1980*x*(x^4-x^2)^(1/3)+2222*RootOf(_Z^2-2*_Z+4)*x-740*x^2-2220*x)/x/(x^2+x-1))-1/2*ln(-(-494*RootOf(_Z^2-2*_Z+4)^2*x^3+741*RootOf(_Z^2-2*_Z+4)^2*x^2-246*RootOf(_Z^2-2*_Z+4)*x^3+1356*RootOf(_Z^2-2*_Z+4)*(x^4-x^2)^(2/3)-1356*RootOf(_Z^2-2*_Z+4)*(x^4-x^2)^(1/3)*x+494*RootOf(_Z^2-2*_Z+4)^2*x-1360*RootOf(_Z^2-2*_Z+4)*x^2+248*x^3-4692*(x^4-x^2)^(2/3)+4692*x*(x^4-x^2)^(1/3)+246*RootOf(_Z^2-2*_Z+4)*x+496*x^2-248*x)/x/(x^2+x-1))*RootOf(_Z^2-2*_Z+4)+ln(-(-494*RootOf(_Z^2-2*_Z+4)^2*x^3+741*RootOf(_Z^2-2*_Z+4)^2*x^2-246*RootOf(_Z^2-2*_Z+4)*x^3+1356*RootOf(_Z^2-2*_Z+4)*(x^4-x^2)^(2/3)-1356*RootOf(_Z^2-2*_Z+4)*(x^4-x^2)^(1/3)*x+494*RootOf(_Z^2-2*_Z+4)^2*x-1360*RootOf(_Z^2-2*_Z+4)*x^2+248*x^3-4692*(x^4-x^2)^(2/3)+4692*x*(x^4-x^2)^(1/3)+246*RootOf(_Z^2-2*_Z+4)*x+496*x^2-248*x)/x/(x^2+x-1))","C"
1286,1,420,81,2.699000," ","int((-1+2*x)*(x^2-x+2)*(x^4-2*x^3+x^2-2)^(1/2)/(2*x^2-2*x+3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\left(\frac{1}{4}-\frac{1}{4} x +\frac{1}{4} x^{2}\right) \sqrt{x^{4}-2 x^{3}+x^{2}-2}-\frac{\ln \left(-\frac{-1+14 x +26 x^{2} \sqrt{x^{4}-2 x^{3}+x^{2}-2}-2 x \sqrt{x^{4}-2 x^{3}+x^{2}-2}-2 \sqrt{x^{4}-2 x^{3}+x^{2}-2}+360 x^{9}+368 x^{10}+624 x^{7}-176 x^{5}-152 x^{6}-12 x^{2}-60 x^{3}-784 x^{8}+186 x^{4}-864 x^{11}+872 x^{12}+8 x^{16}-64 x^{15}+240 x^{14}-560 x^{13}+8 \sqrt{x^{4}-2 x^{3}+x^{2}-2}\, x^{14}-56 \sqrt{x^{4}-2 x^{3}+x^{2}-2}\, x^{13}+184 \sqrt{x^{4}-2 x^{3}+x^{2}-2}\, x^{12}-376 \sqrt{x^{4}-2 x^{3}+x^{2}-2}\, x^{11}+504 \sqrt{x^{4}-2 x^{3}+x^{2}-2}\, x^{10}-408 \sqrt{x^{4}-2 x^{3}+x^{2}-2}\, x^{9}+96 \sqrt{x^{4}-2 x^{3}+x^{2}-2}\, x^{8}+216 \sqrt{x^{4}-2 x^{3}+x^{2}-2}\, x^{7}-300 \sqrt{x^{4}-2 x^{3}+x^{2}-2}\, x^{6}+164 \sqrt{x^{4}-2 x^{3}+x^{2}-2}\, x^{5}-4 \sqrt{x^{4}-2 x^{3}+x^{2}-2}\, x^{4}-52 \sqrt{x^{4}-2 x^{3}+x^{2}-2}\, x^{3}}{2 x^{2}-2 x +3}\right)}{8}$&$420$\\ risch&$\text{Expression too large to display}$&$3445$\\ default&$\text{Expression too large to display}$&$3475$\\ elliptic&$\text{Expression too large to display}$&$3475$\\ \hline \end{longtable}"," ",0,"(1/4-1/4*x+1/4*x^2)*(x^4-2*x^3+x^2-2)^(1/2)-1/8*ln(-(-1+14*x+26*x^2*(x^4-2*x^3+x^2-2)^(1/2)-2*x*(x^4-2*x^3+x^2-2)^(1/2)-2*(x^4-2*x^3+x^2-2)^(1/2)+360*x^9+368*x^10+624*x^7-176*x^5-152*x^6-12*x^2-60*x^3-784*x^8+186*x^4-864*x^11+872*x^12+8*x^16-64*x^15+240*x^14-560*x^13+8*(x^4-2*x^3+x^2-2)^(1/2)*x^14-56*(x^4-2*x^3+x^2-2)^(1/2)*x^13+184*(x^4-2*x^3+x^2-2)^(1/2)*x^12-376*(x^4-2*x^3+x^2-2)^(1/2)*x^11+504*(x^4-2*x^3+x^2-2)^(1/2)*x^10-408*(x^4-2*x^3+x^2-2)^(1/2)*x^9+96*(x^4-2*x^3+x^2-2)^(1/2)*x^8+216*(x^4-2*x^3+x^2-2)^(1/2)*x^7-300*(x^4-2*x^3+x^2-2)^(1/2)*x^6+164*(x^4-2*x^3+x^2-2)^(1/2)*x^5-4*(x^4-2*x^3+x^2-2)^(1/2)*x^4-52*(x^4-2*x^3+x^2-2)^(1/2)*x^3)/(2*x^2-2*x+3))","B"
1287,1,387,77,1.509000," ","int((x^4-x^3)^(1/4)/x/(1+x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \sqrt{x^{4}-x^{3}}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}-2 x^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}}{x^{2}}\right)+\ln \left(\frac{2 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}+2 \sqrt{x^{4}-x^{3}}\, x +2 x^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}+2 x^{3}-x^{2}}{x^{2}}\right)-\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(\frac{3 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{3}+4 \left(x^{4}-x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}-\RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{2}+4 \sqrt{x^{4}-x^{3}}\, \RootOf \left(\textit{\_Z}^{4}-2\right) x +4 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(1+x \right)}\right)-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(\frac{-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}-4 \left(x^{4}-x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}+4 \sqrt{x^{4}-x^{3}}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x +4 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(1+x \right)}\right)$&$387$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2+1)*ln((2*(x^4-x^3)^(1/2)*RootOf(_Z^2+1)*x-2*RootOf(_Z^2+1)*x^3+2*(x^4-x^3)^(3/4)-2*x^2*(x^4-x^3)^(1/4)+RootOf(_Z^2+1)*x^2)/x^2)+ln((2*(x^4-x^3)^(3/4)+2*(x^4-x^3)^(1/2)*x+2*x^2*(x^4-x^3)^(1/4)+2*x^3-x^2)/x^2)-RootOf(_Z^4-2)*ln((3*RootOf(_Z^4-2)^3*x^3+4*(x^4-x^3)^(1/4)*RootOf(_Z^4-2)^2*x^2-RootOf(_Z^4-2)^3*x^2+4*(x^4-x^3)^(1/2)*RootOf(_Z^4-2)*x+4*(x^4-x^3)^(3/4))/x^2/(1+x))-RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln((-3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*x^3+RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*x^2-4*(x^4-x^3)^(1/4)*RootOf(_Z^4-2)^2*x^2+4*(x^4-x^3)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x+4*(x^4-x^3)^(3/4))/x^2/(1+x))","C"
1288,1,582,79,4.315000," ","int((2*x^3+1)/(x^3+x-1)/(x^5-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \ln \left(-\frac{3175724374 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{4}-28078997418 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{4}-11115035309 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{2}+40942487600 x^{4}-3175724374 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x +35847343722 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{5}-x^{2}\right)^{\frac{2}{3}}-35847343722 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{5}-x^{2}\right)^{\frac{1}{3}} x +36349865670 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}+28078997418 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x -13024082868 \left(x^{5}-x^{2}\right)^{\frac{2}{3}}+13024082868 x \left(x^{5}-x^{2}\right)^{\frac{1}{3}}-29244634000 x^{2}-40942487600 x}{x \left(x^{3}+x -1\right)}\right)}{2}-\frac{\ln \left(-\frac{3175724374 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{4}+15376099922 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{4}-11115035309 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{2}-2512609740 x^{4}-3175724374 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x -35847343722 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{5}-x^{2}\right)^{\frac{2}{3}}+35847343722 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{5}-x^{2}\right)^{\frac{1}{3}} x +8110275566 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-15376099922 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x +58670604576 \left(x^{5}-x^{2}\right)^{\frac{2}{3}}-58670604576 x \left(x^{5}-x^{2}\right)^{\frac{1}{3}}-1005043896 x^{2}+2512609740 x}{x \left(x^{3}+x -1\right)}\right) \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)}{2}+\ln \left(-\frac{3175724374 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{4}+15376099922 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{4}-11115035309 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{2}-2512609740 x^{4}-3175724374 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x -35847343722 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{5}-x^{2}\right)^{\frac{2}{3}}+35847343722 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{5}-x^{2}\right)^{\frac{1}{3}} x +8110275566 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-15376099922 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x +58670604576 \left(x^{5}-x^{2}\right)^{\frac{2}{3}}-58670604576 x \left(x^{5}-x^{2}\right)^{\frac{1}{3}}-1005043896 x^{2}+2512609740 x}{x \left(x^{3}+x -1\right)}\right)$&$582$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^2-2*_Z+4)*ln(-(3175724374*RootOf(_Z^2-2*_Z+4)^2*x^4-28078997418*RootOf(_Z^2-2*_Z+4)*x^4-11115035309*RootOf(_Z^2-2*_Z+4)^2*x^2+40942487600*x^4-3175724374*RootOf(_Z^2-2*_Z+4)^2*x+35847343722*RootOf(_Z^2-2*_Z+4)*(x^5-x^2)^(2/3)-35847343722*RootOf(_Z^2-2*_Z+4)*(x^5-x^2)^(1/3)*x+36349865670*RootOf(_Z^2-2*_Z+4)*x^2+28078997418*RootOf(_Z^2-2*_Z+4)*x-13024082868*(x^5-x^2)^(2/3)+13024082868*x*(x^5-x^2)^(1/3)-29244634000*x^2-40942487600*x)/x/(x^3+x-1))-1/2*ln(-(3175724374*RootOf(_Z^2-2*_Z+4)^2*x^4+15376099922*RootOf(_Z^2-2*_Z+4)*x^4-11115035309*RootOf(_Z^2-2*_Z+4)^2*x^2-2512609740*x^4-3175724374*RootOf(_Z^2-2*_Z+4)^2*x-35847343722*RootOf(_Z^2-2*_Z+4)*(x^5-x^2)^(2/3)+35847343722*RootOf(_Z^2-2*_Z+4)*(x^5-x^2)^(1/3)*x+8110275566*RootOf(_Z^2-2*_Z+4)*x^2-15376099922*RootOf(_Z^2-2*_Z+4)*x+58670604576*(x^5-x^2)^(2/3)-58670604576*x*(x^5-x^2)^(1/3)-1005043896*x^2+2512609740*x)/x/(x^3+x-1))*RootOf(_Z^2-2*_Z+4)+ln(-(3175724374*RootOf(_Z^2-2*_Z+4)^2*x^4+15376099922*RootOf(_Z^2-2*_Z+4)*x^4-11115035309*RootOf(_Z^2-2*_Z+4)^2*x^2-2512609740*x^4-3175724374*RootOf(_Z^2-2*_Z+4)^2*x-35847343722*RootOf(_Z^2-2*_Z+4)*(x^5-x^2)^(2/3)+35847343722*RootOf(_Z^2-2*_Z+4)*(x^5-x^2)^(1/3)*x+8110275566*RootOf(_Z^2-2*_Z+4)*x^2-15376099922*RootOf(_Z^2-2*_Z+4)*x+58670604576*(x^5-x^2)^(2/3)-58670604576*x*(x^5-x^2)^(1/3)-1005043896*x^2+2512609740*x)/x/(x^3+x-1))","C"
1289,1,72,69,12.135000," ","int((x^6-1)^(1/4)/x^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{4}} \left(-\frac{3 \Gamma \left(\frac{3}{4}\right) x^{6} \hypergeom \left(\left[1, 1, \frac{7}{4}\right], \left[2, 3\right], x^{6}\right)}{8}-\left(-3 \ln \left(2\right)+\frac{\pi}{2}-1+6 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{3}{4}\right)-\frac{4 \Gamma \left(\frac{3}{4}\right)}{x^{6}}\right)}{24 \Gamma \left(\frac{3}{4}\right) \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{4}}}$&$72$\\ risch&$-\frac{\left(x^{6}-1\right)^{\frac{1}{4}}}{6 x^{6}}+\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{3}{4}} \left(\frac{3 \Gamma \left(\frac{3}{4}\right) x^{6} \hypergeom \left(\left[1, 1, \frac{7}{4}\right], \left[2, 2\right], x^{6}\right)}{4}+\left(-3 \ln \left(2\right)+\frac{\pi}{2}+6 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{3}{4}\right)\right)}{24 \Gamma \left(\frac{3}{4}\right) \mathrm{signum}\left(x^{6}-1\right)^{\frac{3}{4}}}$&$76$\\ trager&$-\frac{\left(x^{6}-1\right)^{\frac{1}{4}}}{6 x^{6}}+\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{6}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}-2 \left(x^{6}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-2 \sqrt{x^{6}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)-2 \left(x^{6}-1\right)^{\frac{3}{4}}}{x^{6}}\right)}{24}-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}+1\right) x^{6}+2 \sqrt{x^{6}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+2 \left(x^{6}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-2 \left(x^{6}-1\right)^{\frac{3}{4}}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)}{x^{6}}\right)}{24}$&$169$\\ \hline \end{longtable}"," ",0,"1/24/GAMMA(3/4)*signum(x^6-1)^(1/4)/(-signum(x^6-1))^(1/4)*(-3/8*GAMMA(3/4)*x^6*hypergeom([1,1,7/4],[2,3],x^6)-(-3*ln(2)+1/2*Pi-1+6*ln(x)+I*Pi)*GAMMA(3/4)-4*GAMMA(3/4)/x^6)","C"
1290,1,386,79,6.368000," ","int((3*x^4+1)/(x^4+x-1)/(x^6-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(-\frac{-680618 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{5}+11776766 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{5}-23512440 x^{5}+5104635 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{2}+10436076 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}-x^{2}\right)^{\frac{2}{3}}-10374438 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}-x^{2}\right)^{\frac{1}{3}} x +680618 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x -20604254 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-41621028 \left(x^{6}-x^{2}\right)^{\frac{2}{3}}-20872152 x \left(x^{6}-x^{2}\right)^{\frac{1}{3}}-11776766 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x +20377448 x^{2}+23512440 x}{x \left(x^{4}+x -1\right)}\right)+\frac{\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \ln \left(\frac{-391874 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{5}-4413744 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{5}+8848034 x^{5}+2939055 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{2}+5218038 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}-x^{2}\right)^{\frac{2}{3}}+10405257 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}-x^{2}\right)^{\frac{1}{3}} x +391874 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x -5888383 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}+10374438 \left(x^{6}-x^{2}\right)^{\frac{2}{3}}-10436076 x \left(x^{6}-x^{2}\right)^{\frac{1}{3}}+4413744 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x +1361236 x^{2}-8848034 x}{x \left(x^{4}+x -1\right)}\right)}{2}$&$386$\\ \hline \end{longtable}"," ",0,"-ln(-(-680618*RootOf(_Z^2-2*_Z+4)^2*x^5+11776766*RootOf(_Z^2-2*_Z+4)*x^5-23512440*x^5+5104635*RootOf(_Z^2-2*_Z+4)^2*x^2+10436076*RootOf(_Z^2-2*_Z+4)*(x^6-x^2)^(2/3)-10374438*RootOf(_Z^2-2*_Z+4)*(x^6-x^2)^(1/3)*x+680618*RootOf(_Z^2-2*_Z+4)^2*x-20604254*RootOf(_Z^2-2*_Z+4)*x^2-41621028*(x^6-x^2)^(2/3)-20872152*x*(x^6-x^2)^(1/3)-11776766*RootOf(_Z^2-2*_Z+4)*x+20377448*x^2+23512440*x)/x/(x^4+x-1))+1/2*RootOf(_Z^2-2*_Z+4)*ln((-391874*RootOf(_Z^2-2*_Z+4)^2*x^5-4413744*RootOf(_Z^2-2*_Z+4)*x^5+8848034*x^5+2939055*RootOf(_Z^2-2*_Z+4)^2*x^2+5218038*RootOf(_Z^2-2*_Z+4)*(x^6-x^2)^(2/3)+10405257*RootOf(_Z^2-2*_Z+4)*(x^6-x^2)^(1/3)*x+391874*RootOf(_Z^2-2*_Z+4)^2*x-5888383*RootOf(_Z^2-2*_Z+4)*x^2+10374438*(x^6-x^2)^(2/3)-10436076*x*(x^6-x^2)^(1/3)+4413744*RootOf(_Z^2-2*_Z+4)*x+1361236*x^2-8848034*x)/x/(x^4+x-1))","C"
1291,1,674,66,5.046000," ","int((x^3+2)*(x^3-x^2-1)^(1/2)/(x^6+x^5-x^4-2*x^3-x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-5 \ln \left(-\frac{175 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right)^{5} x^{2}-35 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right)^{3} x^{3}+230 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right)^{3} x^{2}-30 \sqrt{x^{3}-x^{2}-1}\, \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right)^{2} x -18 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right) x^{3}+35 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right)^{3}+72 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right) x^{2}-16 \sqrt{x^{3}-x^{2}-1}\, x +18 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right)}{5 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right)^{2} x^{2}+x^{3}+2 x^{2}-1}\right) \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right)^{3}+\RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right) \ln \left(\frac{75 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right)^{5} x^{2}+15 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right)^{3} x^{3}-5 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right)^{3} x^{2}-30 \sqrt{x^{3}-x^{2}-1}\, \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right)^{2} x +2 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right) x^{3}-15 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right)^{3}-2 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right) x^{2}-2 \sqrt{x^{3}-x^{2}-1}\, x -2 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right)}{5 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right)^{2} x^{2}-x^{3}+x^{2}+1}\right)-3 \ln \left(-\frac{175 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right)^{5} x^{2}-35 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right)^{3} x^{3}+230 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right)^{3} x^{2}-30 \sqrt{x^{3}-x^{2}-1}\, \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right)^{2} x -18 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right) x^{3}+35 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right)^{3}+72 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right) x^{2}-16 \sqrt{x^{3}-x^{2}-1}\, x +18 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right)}{5 \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right)^{2} x^{2}+x^{3}+2 x^{2}-1}\right) \RootOf \left(25 \textit{\_Z}^{4}+15 \textit{\_Z}^{2}+1\right)$&$674$\\ default&$\text{Expression too large to display}$&$2877$\\ elliptic&$\text{Expression too large to display}$&$2877$\\ \hline \end{longtable}"," ",0,"-5*ln(-(175*RootOf(25*_Z^4+15*_Z^2+1)^5*x^2-35*RootOf(25*_Z^4+15*_Z^2+1)^3*x^3+230*RootOf(25*_Z^4+15*_Z^2+1)^3*x^2-30*(x^3-x^2-1)^(1/2)*RootOf(25*_Z^4+15*_Z^2+1)^2*x-18*RootOf(25*_Z^4+15*_Z^2+1)*x^3+35*RootOf(25*_Z^4+15*_Z^2+1)^3+72*RootOf(25*_Z^4+15*_Z^2+1)*x^2-16*(x^3-x^2-1)^(1/2)*x+18*RootOf(25*_Z^4+15*_Z^2+1))/(5*RootOf(25*_Z^4+15*_Z^2+1)^2*x^2+x^3+2*x^2-1))*RootOf(25*_Z^4+15*_Z^2+1)^3+RootOf(25*_Z^4+15*_Z^2+1)*ln((75*RootOf(25*_Z^4+15*_Z^2+1)^5*x^2+15*RootOf(25*_Z^4+15*_Z^2+1)^3*x^3-5*RootOf(25*_Z^4+15*_Z^2+1)^3*x^2-30*(x^3-x^2-1)^(1/2)*RootOf(25*_Z^4+15*_Z^2+1)^2*x+2*RootOf(25*_Z^4+15*_Z^2+1)*x^3-15*RootOf(25*_Z^4+15*_Z^2+1)^3-2*RootOf(25*_Z^4+15*_Z^2+1)*x^2-2*(x^3-x^2-1)^(1/2)*x-2*RootOf(25*_Z^4+15*_Z^2+1))/(5*RootOf(25*_Z^4+15*_Z^2+1)^2*x^2-x^3+x^2+1))-3*ln(-(175*RootOf(25*_Z^4+15*_Z^2+1)^5*x^2-35*RootOf(25*_Z^4+15*_Z^2+1)^3*x^3+230*RootOf(25*_Z^4+15*_Z^2+1)^3*x^2-30*(x^3-x^2-1)^(1/2)*RootOf(25*_Z^4+15*_Z^2+1)^2*x-18*RootOf(25*_Z^4+15*_Z^2+1)*x^3+35*RootOf(25*_Z^4+15*_Z^2+1)^3+72*RootOf(25*_Z^4+15*_Z^2+1)*x^2-16*(x^3-x^2-1)^(1/2)*x+18*RootOf(25*_Z^4+15*_Z^2+1))/(5*RootOf(25*_Z^4+15*_Z^2+1)^2*x^2+x^3+2*x^2-1))*RootOf(25*_Z^4+15*_Z^2+1)","C"
1292,1,209,66,1.850000," ","int((x^4+1)*(x^4-x^2-1)^(1/2)/(x^8+x^6-3*x^4-x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(\frac{4 \arctan \left(\frac{4 \sqrt{x^{4}-x^{2}-1}\, \sqrt{2}}{x \left(2 \sqrt{10}+2 \sqrt{2}\right)}\right)}{2 \sqrt{10}+2 \sqrt{2}}+\frac{12 \sqrt{5}\, \arctan \left(\frac{4 \sqrt{x^{4}-x^{2}-1}\, \sqrt{2}}{x \left(2 \sqrt{10}+2 \sqrt{2}\right)}\right)}{5 \left(2 \sqrt{10}+2 \sqrt{2}\right)}-\frac{12 \sqrt{5}\, \arctan \left(\frac{4 \sqrt{x^{4}-x^{2}-1}\, \sqrt{2}}{x \left(2 \sqrt{10}-2 \sqrt{2}\right)}\right)}{5 \left(2 \sqrt{10}-2 \sqrt{2}\right)}+\frac{4 \arctan \left(\frac{4 \sqrt{x^{4}-x^{2}-1}\, \sqrt{2}}{x \left(2 \sqrt{10}-2 \sqrt{2}\right)}\right)}{2 \sqrt{10}-2 \sqrt{2}}\right) \sqrt{2}}{2}$&$209$\\ elliptic&$\frac{\left(\frac{4 \arctan \left(\frac{4 \sqrt{x^{4}-x^{2}-1}\, \sqrt{2}}{x \left(2 \sqrt{10}+2 \sqrt{2}\right)}\right)}{2 \sqrt{10}+2 \sqrt{2}}+\frac{12 \sqrt{5}\, \arctan \left(\frac{4 \sqrt{x^{4}-x^{2}-1}\, \sqrt{2}}{x \left(2 \sqrt{10}+2 \sqrt{2}\right)}\right)}{5 \left(2 \sqrt{10}+2 \sqrt{2}\right)}-\frac{12 \sqrt{5}\, \arctan \left(\frac{4 \sqrt{x^{4}-x^{2}-1}\, \sqrt{2}}{x \left(2 \sqrt{10}-2 \sqrt{2}\right)}\right)}{5 \left(2 \sqrt{10}-2 \sqrt{2}\right)}+\frac{4 \arctan \left(\frac{4 \sqrt{x^{4}-x^{2}-1}\, \sqrt{2}}{x \left(2 \sqrt{10}-2 \sqrt{2}\right)}\right)}{2 \sqrt{10}-2 \sqrt{2}}\right) \sqrt{2}}{2}$&$209$\\ trager&$-20 \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right)^{3} \ln \left(\frac{-1400 x^{2} \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right)^{5}+70 \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right)^{3} x^{4}-460 \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right)^{3} x^{2}+9 \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right) x^{4}+30 \sqrt{x^{4}-x^{2}-1}\, \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right)^{2} x -70 \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right)^{3}-36 \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right) x^{2}+4 x \sqrt{x^{4}-x^{2}-1}-9 \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right)}{20 x^{2} \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right)^{2}+x^{4}+2 x^{2}-1}\right)-\RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right) \ln \left(-\frac{1200 x^{2} \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right)^{5}+60 \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right)^{3} x^{4}-20 \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right)^{3} x^{2}+2 \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right) x^{4}+60 \sqrt{x^{4}-x^{2}-1}\, \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right)^{2} x -60 \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right)^{3}-2 \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right) x^{2}+x \sqrt{x^{4}-x^{2}-1}-2 \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right)}{20 x^{2} \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right)^{2}-x^{4}+x^{2}+1}\right)-3 \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right) \ln \left(\frac{-1400 x^{2} \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right)^{5}+70 \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right)^{3} x^{4}-460 \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right)^{3} x^{2}+9 \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right) x^{4}+30 \sqrt{x^{4}-x^{2}-1}\, \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right)^{2} x -70 \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right)^{3}-36 \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right) x^{2}+4 x \sqrt{x^{4}-x^{2}-1}-9 \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right)}{20 x^{2} \RootOf \left(400 \textit{\_Z}^{4}+60 \textit{\_Z}^{2}+1\right)^{2}+x^{4}+2 x^{2}-1}\right)$&$673$\\ \hline \end{longtable}"," ",0,"1/2*(4/(2*10^(1/2)+2*2^(1/2))*arctan(4*(x^4-x^2-1)^(1/2)*2^(1/2)/x/(2*10^(1/2)+2*2^(1/2)))+12/5*5^(1/2)/(2*10^(1/2)+2*2^(1/2))*arctan(4*(x^4-x^2-1)^(1/2)*2^(1/2)/x/(2*10^(1/2)+2*2^(1/2)))-12/5*5^(1/2)/(2*10^(1/2)-2*2^(1/2))*arctan(4*(x^4-x^2-1)^(1/2)*2^(1/2)/x/(2*10^(1/2)-2*2^(1/2)))+4/(2*10^(1/2)-2*2^(1/2))*arctan(4*(x^4-x^2-1)^(1/2)*2^(1/2)/x/(2*10^(1/2)-2*2^(1/2))))*2^(1/2)","B"
1293,1,98,71,0.044000," ","int(x^2*(x+(1+x)^(1/2))^(1/2)/(1+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\left(1+x \right)^{\frac{3}{2}} \left(x +\sqrt{1+x}\right)^{\frac{3}{2}}}{3}-\frac{3 \left(1+x \right) \left(x +\sqrt{1+x}\right)^{\frac{3}{2}}}{10}-\frac{39 \sqrt{1+x}\, \left(x +\sqrt{1+x}\right)^{\frac{3}{2}}}{80}+\frac{33 \left(x +\sqrt{1+x}\right)^{\frac{3}{2}}}{160}+\frac{77 \left(2 \sqrt{1+x}+1\right) \sqrt{x +\sqrt{1+x}}}{256}-\frac{385 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{512}$&$98$\\ default&$\frac{\left(1+x \right)^{\frac{3}{2}} \left(x +\sqrt{1+x}\right)^{\frac{3}{2}}}{3}-\frac{3 \left(1+x \right) \left(x +\sqrt{1+x}\right)^{\frac{3}{2}}}{10}-\frac{39 \sqrt{1+x}\, \left(x +\sqrt{1+x}\right)^{\frac{3}{2}}}{80}+\frac{33 \left(x +\sqrt{1+x}\right)^{\frac{3}{2}}}{160}+\frac{77 \left(2 \sqrt{1+x}+1\right) \sqrt{x +\sqrt{1+x}}}{256}-\frac{385 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{512}$&$98$\\ \hline \end{longtable}"," ",0,"1/3*(1+x)^(3/2)*(x+(1+x)^(1/2))^(3/2)-3/10*(1+x)*(x+(1+x)^(1/2))^(3/2)-39/80*(1+x)^(1/2)*(x+(1+x)^(1/2))^(3/2)+33/160*(x+(1+x)^(1/2))^(3/2)+77/256*(2*(1+x)^(1/2)+1)*(x+(1+x)^(1/2))^(1/2)-385/512*ln(1/2+(1+x)^(1/2)+(x+(1+x)^(1/2))^(1/2))","A"
1294,1,30,72,2.061000," ","int((x^3-1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}} x \hypergeom \left(\left[-\frac{2}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{3}\right)}{\left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}}}$&$30$\\ risch&$\frac{x \left(x^{3}-1\right)^{\frac{2}{3}}}{3}-\frac{2 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{3}\right)}{3 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}}}$&$42$\\ trager&$\frac{x \left(x^{3}-1\right)^{\frac{2}{3}}}{3}+\frac{2 \ln \left(-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -5 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}-1\right)^{\frac{2}{3}}-3 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-2 x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1\right)}{9}+\frac{2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-2 x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+2\right)}{9}$&$192$\\ \hline \end{longtable}"," ",0,"signum(x^3-1)^(2/3)/(-signum(x^3-1))^(2/3)*x*hypergeom([-2/3,1/3],[4/3],x^3)","C"
1295,1,14,72,1.645000," ","int((x^3+1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$x \hypergeom \left(\left[-\frac{2}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{3}\right)$&$14$\\ risch&$\frac{x \left(x^{3}+1\right)^{\frac{2}{3}}}{3}+\frac{2 x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{3}\right)}{3}$&$26$\\ trager&$\frac{x \left(x^{3}+1\right)^{\frac{2}{3}}}{3}+\frac{2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x -3 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}+1\right)^{\frac{2}{3}}+3 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}+4 x^{3}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+2\right)}{9}-\frac{2 \ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +3 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+x^{3}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+1\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)}{9}+\frac{2 \ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +3 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+x^{3}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+1\right)}{9}$&$314$\\ \hline \end{longtable}"," ",0,"x*hypergeom([-2/3,1/3],[4/3],-x^3)","C"
1296,1,29,72,1.765000," ","int((x^3-1)/(x^3+2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x \left(x^{3}+2\right)^{\frac{2}{3}}}{3}-\frac{5 \,2^{\frac{2}{3}} x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -\frac{x^{3}}{2}\right)}{6}$&$29$\\ meijerg&$-\frac{2^{\frac{2}{3}} x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -\frac{x^{3}}{2}\right)}{2}+\frac{2^{\frac{2}{3}} x^{4} \hypergeom \left(\left[\frac{1}{3}, \frac{4}{3}\right], \left[\frac{7}{3}\right], -\frac{x^{3}}{2}\right)}{8}$&$38$\\ trager&$\frac{x \left(x^{3}+2\right)^{\frac{2}{3}}}{3}+\frac{10 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \ln \left(4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{3}+6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{2}{3}} x +6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{1}{3}} x^{2}+8 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}+2\right)^{\frac{2}{3}}+3 \left(x^{3}+2\right)^{\frac{1}{3}} x^{2}+4 x^{3}+4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+4\right)}{9}-\frac{5 \ln \left(4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{3}-6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{2}{3}} x -6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{1}{3}} x^{2}-4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{3}+x^{3}-4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+2\right)}{9}-\frac{10 \ln \left(4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{3}-6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{2}{3}} x -6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{1}{3}} x^{2}-4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{3}+x^{3}-4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+2\right) \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)}{9}$&$355$\\ \hline \end{longtable}"," ",0,"1/3*x*(x^3+2)^(2/3)-5/6*2^(2/3)*x*hypergeom([1/3,1/3],[4/3],-1/2*x^3)","C"
1297,1,17,72,4.245000," ","int((x^3+x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 x^{\frac{4}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], -x^{2}\right)}{4}$&$17$\\ trager&$\frac{x \left(x^{3}+x \right)^{\frac{1}{3}}}{2}-\frac{\ln \left(-36 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}-72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}+27 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x +57 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}+36 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}+15 \left(x^{3}+x \right)^{\frac{2}{3}}-24 x \left(x^{3}+x \right)^{\frac{1}{3}}+5 x^{2}+27 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)+2\right)}{6}+\frac{\ln \left(-9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}+72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}-45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x -24 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}+9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}-9 \left(x^{3}+x \right)^{\frac{2}{3}}+24 x \left(x^{3}+x \right)^{\frac{1}{3}}-16 x^{2}+3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-12\right)}{6}-\frac{\ln \left(-9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}+72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}-45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x -24 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}+9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}-9 \left(x^{3}+x \right)^{\frac{2}{3}}+24 x \left(x^{3}+x \right)^{\frac{1}{3}}-16 x^{2}+3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-12\right) \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)}{2}$&$419$\\ risch&$\frac{x \left(x \left(x^{2}+1\right)\right)^{\frac{1}{3}}}{2}+\frac{\left(\frac{\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{4}+11 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{4}+15 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-40 x^{4}+15 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}-48 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}+28 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-48 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}+15 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}-2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2}-70 x^{2}-48 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}+17 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)-30}{x^{2}+1}\right)}{12}-\frac{\ln \left(\frac{-2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{4}+19 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{4}+15 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}+10 x^{4}+15 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}+18 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}+28 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}+18 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}+15 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}+2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2}+14 x^{2}+18 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}+9 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)+4}{x^{2}+1}\right) \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)}{12}+\frac{\ln \left(\frac{-2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{4}+19 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{4}+15 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}+10 x^{4}+15 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}+18 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}+28 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}+18 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}+15 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}+2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2}+14 x^{2}+18 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}+9 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)+4}{x^{2}+1}\right)}{6}\right) \left(x \left(x^{2}+1\right)\right)^{\frac{1}{3}} \left(x^{2} \left(x^{2}+1\right)^{2}\right)^{\frac{1}{3}}}{x \left(x^{2}+1\right)}$&$727$\\ \hline \end{longtable}"," ",0,"3/4*x^(4/3)*hypergeom([-1/3,2/3],[5/3],-x^2)","C"
1298,0,0,78,0.043000," ","int((-2*k+(-1+k)*(1+k)*x+2*k*x^2)*(k^2*x^2+2*k*x+1)/((-x^2+1)*(-k^2*x^2+1))^(3/4)/(-1+d+(1+3*d)*k*x+(3*d*k^2+1)*x^2+k*(d*k^2-1)*x^3),x)","\[\int \frac{\left(-2 k +\left(-1+k \right) \left(1+k \right) x +2 k \,x^{2}\right) \left(k^{2} x^{2}+2 k x +1\right)}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{3}{4}} \left(-1+d +\left(1+3 d \right) k x +\left(3 d \,k^{2}+1\right) x^{2}+k \left(d \,k^{2}-1\right) x^{3}\right)}\, dx\]"," ",0,"int((-2*k+(-1+k)*(1+k)*x+2*k*x^2)*(k^2*x^2+2*k*x+1)/((-x^2+1)*(-k^2*x^2+1))^(3/4)/(-1+d+(1+3*d)*k*x+(3*d*k^2+1)*x^2+k*(d*k^2-1)*x^3),x)","F"
1299,1,241,68,11.227000," ","int((x^4-1)^(3/4)*(x^4+4)/x^8/(x^4-4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{4}-1\right)^{\frac{3}{4}} \left(x^{4}+6\right)}{42 x^{7}}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-108\right)^{2}\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-108\right)^{2}\right) \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}-108\right)^{2} x^{2}-6 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-108\right)^{2} x^{3}-21 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-108\right)^{2}\right) x^{4}+72 \left(x^{4}-1\right)^{\frac{3}{4}} x +12 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-108\right)^{2}\right)}{\left(x^{2}-2\right) \left(x^{2}+2\right)}\right)}{32}-\frac{\RootOf \left(\textit{\_Z}^{4}-108\right) \ln \left(\frac{2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}-108\right)^{3} x^{2}+6 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-108\right)^{2} x^{3}+21 \RootOf \left(\textit{\_Z}^{4}-108\right) x^{4}+72 \left(x^{4}-1\right)^{\frac{3}{4}} x -12 \RootOf \left(\textit{\_Z}^{4}-108\right)}{\left(x^{2}-2\right) \left(x^{2}+2\right)}\right)}{32}$&$241$\\ risch&$\frac{x^{8}+5 x^{4}-6}{42 x^{7} \left(x^{4}-1\right)^{\frac{1}{4}}}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-108\right)^{2}\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-108\right)^{2}\right) \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}-108\right)^{2} x^{2}-6 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-108\right)^{2} x^{3}-21 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-108\right)^{2}\right) x^{4}+72 \left(x^{4}-1\right)^{\frac{3}{4}} x +12 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-108\right)^{2}\right)}{\left(x^{2}-2\right) \left(x^{2}+2\right)}\right)}{32}-\frac{\RootOf \left(\textit{\_Z}^{4}-108\right) \ln \left(\frac{2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}-108\right)^{3} x^{2}+6 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-108\right)^{2} x^{3}+21 \RootOf \left(\textit{\_Z}^{4}-108\right) x^{4}+72 \left(x^{4}-1\right)^{\frac{3}{4}} x -12 \RootOf \left(\textit{\_Z}^{4}-108\right)}{\left(x^{2}-2\right) \left(x^{2}+2\right)}\right)}{32}$&$246$\\ \hline \end{longtable}"," ",0,"1/42*(x^4-1)^(3/4)*(x^4+6)/x^7+1/32*RootOf(_Z^2+RootOf(_Z^4-108)^2)*ln((2*RootOf(_Z^2+RootOf(_Z^4-108)^2)*(x^4-1)^(1/2)*RootOf(_Z^4-108)^2*x^2-6*(x^4-1)^(1/4)*RootOf(_Z^4-108)^2*x^3-21*RootOf(_Z^2+RootOf(_Z^4-108)^2)*x^4+72*(x^4-1)^(3/4)*x+12*RootOf(_Z^2+RootOf(_Z^4-108)^2))/(x^2-2)/(x^2+2))-1/32*RootOf(_Z^4-108)*ln((2*(x^4-1)^(1/2)*RootOf(_Z^4-108)^3*x^2+6*(x^4-1)^(1/4)*RootOf(_Z^4-108)^2*x^3+21*RootOf(_Z^4-108)*x^4+72*(x^4-1)^(3/4)*x-12*RootOf(_Z^4-108))/(x^2-2)/(x^2+2))","C"
1300,0,0,77,0.023000," ","int((a*x^3+4*b)/(a*x^3+b)^(1/4)/(a*x^3+x^4+b),x)","\[\int \frac{a \,x^{3}+4 b}{\left(a \,x^{3}+b \right)^{\frac{1}{4}} \left(a \,x^{3}+x^{4}+b \right)}\, dx\]"," ",0,"int((a*x^3+4*b)/(a*x^3+b)^(1/4)/(a*x^3+x^4+b),x)","F"
1301,1,251,82,0.103000," ","int((-a^2*b+a*(2*a+b)*x-3*a*x^2+x^3)/(x*(-a+x)*(-b+x))^(1/2)/(-a^2*d+2*a*d*x+(b^2-d)*x^2-2*b*x^3+x^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}-2 b \,\textit{\_Z}^{3}+\left(b^{2}-d \right) \textit{\_Z}^{2}+2 a d \textit{\_Z} -a^{2} d \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{3}+3 \underline{\hspace{1.25 ex}}\alpha^{2} a -2 \underline{\hspace{1.25 ex}}\alpha  \,a^{2}-\underline{\hspace{1.25 ex}}\alpha  a b +a^{2} b \right) \left(\underline{\hspace{1.25 ex}}\alpha^{3}-b \,\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  d +2 a d -b d \right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, -\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{3}-b \,\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  d +2 a d -b d \right) b}{d \left(a^{2}-2 a b +b^{2}\right)}, \sqrt{\frac{b}{-a +b}}\right)}{\left(-2 \underline{\hspace{1.25 ex}}\alpha^{3}+3 b \,\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  \,b^{2}+\underline{\hspace{1.25 ex}}\alpha  d -a d \right) \left(a^{2}-2 a b +b^{2}\right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}\right)}{d}$&$251$\\ elliptic&$\frac{b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}-2 b \,\textit{\_Z}^{3}+\left(b^{2}-d \right) \textit{\_Z}^{2}+2 a d \textit{\_Z} -a^{2} d \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{3}+3 \underline{\hspace{1.25 ex}}\alpha^{2} a -2 \underline{\hspace{1.25 ex}}\alpha  \,a^{2}-\underline{\hspace{1.25 ex}}\alpha  a b +a^{2} b \right) \left(\underline{\hspace{1.25 ex}}\alpha^{3}-b \,\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  d +2 a d -b d \right) \sqrt{-\frac{-b +x}{b}}\, \sqrt{\frac{-a +x}{-a +b}}\, \sqrt{\frac{x}{b}}\, \EllipticPi \left(\sqrt{-\frac{-b +x}{b}}, -\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{3}-b \,\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  d +2 a d -b d \right) b}{d \left(a^{2}-2 a b +b^{2}\right)}, \sqrt{\frac{b}{-a +b}}\right)}{\left(-2 \underline{\hspace{1.25 ex}}\alpha^{3}+3 b \,\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  \,b^{2}+\underline{\hspace{1.25 ex}}\alpha  d -a d \right) \left(a^{2}-2 a b +b^{2}\right) \sqrt{x \left(a b -a x -b x +x^{2}\right)}}\right)}{d}$&$251$\\ \hline \end{longtable}"," ",0,"b/d*sum((-_alpha^3+3*_alpha^2*a-2*_alpha*a^2-_alpha*a*b+a^2*b)/(-2*_alpha^3+3*_alpha^2*b-_alpha*b^2+_alpha*d-a*d)*(_alpha^3-_alpha^2*b-_alpha*d+2*a*d-b*d)/(a^2-2*a*b+b^2)*(-(-b+x)/b)^(1/2)*((-a+x)/(-a+b))^(1/2)*(x/b)^(1/2)/(x*(a*b-a*x-b*x+x^2))^(1/2)*EllipticPi((-(-b+x)/b)^(1/2),-(_alpha^3-_alpha^2*b-_alpha*d+2*a*d-b*d)*b/d/(a^2-2*a*b+b^2),(b/(-a+b))^(1/2)),_alpha=RootOf(_Z^4-2*b*_Z^3+(b^2-d)*_Z^2+2*a*d*_Z-a^2*d))","C"
1302,0,0,78,0.010000," ","int((a*x^4-2*b)/x^4/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{a \,x^{4}-2 b}{x^{4} \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^4-2*b)/x^4/(a*x^4+b*x^2)^(1/4),x)","F"
1303,0,0,78,0.009000," ","int((a*x^4+2*b)/x^4/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{a \,x^{4}+2 b}{x^{4} \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^4+2*b)/x^4/(a*x^4+b*x^2)^(1/4),x)","F"
1304,1,2813,82,0.165000," ","int((-1+x)/(1+x)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$2813$\\ elliptic&$\text{Expression too large to display}$&$2813$\\ \hline \end{longtable}"," ",0,"2*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))^2*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2)*EllipticF(((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2),((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2))-4*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))^2*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)+1)*(EllipticF(((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2),((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2))+(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1)+1)*EllipticPi(((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2),(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)+1)*(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1)+1)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)),((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)))","C"
1305,1,2813,82,0.154000," ","int((1+x)/(-1+x)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$2813$\\ elliptic&$\text{Expression too large to display}$&$2813$\\ \hline \end{longtable}"," ",0,"2*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))^2*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2)*EllipticF(((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2),((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2))+4*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))^2*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-1)*(EllipticF(((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2),((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2))+(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1)-1)*EllipticPi(((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2),(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-1)*(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1)-1)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)),((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)))","C"
1306,1,93,86,0.117000," ","int(x^2/((-x^2+1)*(-k^2*x^2+1))^(1/2)/(k^2*x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)}}{x \left(1+k \right)}\right)}{4 k \left(1+k \right)}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)}}{x \left(-1+k \right)}\right)}{4 k \left(-1+k \right)}\right) \sqrt{2}}{2}$&$93$\\ default&$\frac{\sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticPi \left(x , -k , k\right)}{2 k \sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}-\frac{\sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticPi \left(x , k , k\right)}{2 k \sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}$&$112$\\ \hline \end{longtable}"," ",0,"1/2*(-1/4/k*2^(1/2)/(1+k)*arctan(((-x^2+1)*(-k^2*x^2+1))^(1/2)/x/(1+k))+1/4/k*2^(1/2)/(-1+k)*arctan(((-x^2+1)*(-k^2*x^2+1))^(1/2)/x/(-1+k)))*2^(1/2)","A"
1307,1,406,74,23.352000," ","int((x^6-1)^(2/3)*(x^6+1)/x^3/(x^6-x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{6}-1\right)^{\frac{2}{3}}}{2 x^{2}}+\frac{\ln \left(\frac{27960018709626208768001196672 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{6}-9793442531921313212690595108 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{6}-5614428583490269128672312324 x^{6}-220185147338306394048009423792 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{3}-45456256378905085721353124616 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x +127282845030980663272778333724 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{2}-88051906839210946445401966260 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{3}+6818882387672964795952100759 x \left(x^{6}-1\right)^{\frac{2}{3}}+3788021364908757143446093718 x^{2} \left(x^{6}-1\right)^{\frac{1}{3}}-6327371895679509652948161508 x^{3}-27960018709626208768001196672 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}+9793442531921313212690595108 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)+5614428583490269128672312324}{x^{6}-x^{3}-1}\right)}{3}+4 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \ln \left(-\frac{102663836955250635495722282496 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{6}+78258464307289633232711371152 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{6}+1723230319777309741777851531 x^{6}-808477716022598754528812974656 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{3}-45456256378905085721353124616 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x -81826588652075577551425209108 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{2}-9793442531921313212690595108 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{3}-10606903752581721939398194477 x \left(x^{6}-1\right)^{\frac{2}{3}}+3788021364908757143446093718 x^{2} \left(x^{6}-1\right)^{\frac{1}{3}}+194166796594626449777786088 x^{3}-102663836955250635495722282496 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}-78258464307289633232711371152 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)-1723230319777309741777851531}{x^{6}-x^{3}-1}\right)$&$406$\\ risch&$\frac{\left(x^{6}-1\right)^{\frac{2}{3}}}{2 x^{2}}+\frac{\ln \left(\frac{-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}-2 x^{6}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x -9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{2}+6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+3 x \left(x^{6}-1\right)^{\frac{2}{3}}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+2}{x^{6}-x^{3}-1}\right)}{3}-\frac{\ln \left(-\frac{-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}-2 x^{6}-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x -9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+3 x^{2} \left(x^{6}-1\right)^{\frac{1}{3}}-2 x^{3}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+2}{x^{6}-x^{3}-1}\right)}{3}-\ln \left(-\frac{-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}-2 x^{6}-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x -9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+3 x^{2} \left(x^{6}-1\right)^{\frac{1}{3}}-2 x^{3}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+2}{x^{6}-x^{3}-1}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)$&$415$\\ \hline \end{longtable}"," ",0,"1/2*(x^6-1)^(2/3)/x^2+1/3*ln((27960018709626208768001196672*RootOf(144*_Z^2+12*_Z+1)^2*x^6-9793442531921313212690595108*RootOf(144*_Z^2+12*_Z+1)*x^6-5614428583490269128672312324*x^6-220185147338306394048009423792*RootOf(144*_Z^2+12*_Z+1)^2*x^3-45456256378905085721353124616*RootOf(144*_Z^2+12*_Z+1)*(x^6-1)^(2/3)*x+127282845030980663272778333724*RootOf(144*_Z^2+12*_Z+1)*(x^6-1)^(1/3)*x^2-88051906839210946445401966260*RootOf(144*_Z^2+12*_Z+1)*x^3+6818882387672964795952100759*x*(x^6-1)^(2/3)+3788021364908757143446093718*x^2*(x^6-1)^(1/3)-6327371895679509652948161508*x^3-27960018709626208768001196672*RootOf(144*_Z^2+12*_Z+1)^2+9793442531921313212690595108*RootOf(144*_Z^2+12*_Z+1)+5614428583490269128672312324)/(x^6-x^3-1))+4*RootOf(144*_Z^2+12*_Z+1)*ln(-(102663836955250635495722282496*RootOf(144*_Z^2+12*_Z+1)^2*x^6+78258464307289633232711371152*RootOf(144*_Z^2+12*_Z+1)*x^6+1723230319777309741777851531*x^6-808477716022598754528812974656*RootOf(144*_Z^2+12*_Z+1)^2*x^3-45456256378905085721353124616*RootOf(144*_Z^2+12*_Z+1)*(x^6-1)^(2/3)*x-81826588652075577551425209108*RootOf(144*_Z^2+12*_Z+1)*(x^6-1)^(1/3)*x^2-9793442531921313212690595108*RootOf(144*_Z^2+12*_Z+1)*x^3-10606903752581721939398194477*x*(x^6-1)^(2/3)+3788021364908757143446093718*x^2*(x^6-1)^(1/3)+194166796594626449777786088*x^3-102663836955250635495722282496*RootOf(144*_Z^2+12*_Z+1)^2-78258464307289633232711371152*RootOf(144*_Z^2+12*_Z+1)-1723230319777309741777851531)/(x^6-x^3-1))","C"
1308,1,405,74,8.517000," ","int((x^6-1)*(x^6+1)^(2/3)/x^3/(x^6-x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{6}+1\right)^{\frac{2}{3}}}{2 x^{2}}+\frac{\ln \left(-\frac{6624 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{6}-2763 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}-1102 x^{6}-13248 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+4428 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x +6057 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}} x^{2}-9930 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+3495 x \left(x^{6}+1\right)^{\frac{2}{3}}-1476 x^{2} \left(x^{6}+1\right)^{\frac{1}{3}}-1653 x^{3}+6624 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-2763 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-1102}{x^{6}-x^{3}+1}\right)}{3}+\RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(\frac{4959 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{6}+7167 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}+2208 x^{6}-9918 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+4428 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x -10485 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}} x^{2}-2763 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}-2019 x \left(x^{6}+1\right)^{\frac{2}{3}}-1476 x^{2} \left(x^{6}+1\right)^{\frac{1}{3}}+736 x^{3}+4959 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+7167 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+2208}{x^{6}-x^{3}+1}\right)$&$405$\\ risch&$\frac{\left(x^{6}+1\right)^{\frac{2}{3}}}{2 x^{2}}+\frac{\ln \left(\frac{-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}-2 x^{6}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x -9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}} x^{2}+6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+3 x \left(x^{6}+1\right)^{\frac{2}{3}}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-2}{x^{6}-x^{3}+1}\right)}{3}-\frac{\ln \left(\frac{3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}+2 x^{6}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x +9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}-3 x^{2} \left(x^{6}+1\right)^{\frac{1}{3}}+2 x^{3}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+2}{x^{6}-x^{3}+1}\right)}{3}-\ln \left(\frac{3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}+2 x^{6}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x +9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}-3 x^{2} \left(x^{6}+1\right)^{\frac{1}{3}}+2 x^{3}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+2}{x^{6}-x^{3}+1}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)$&$413$\\ \hline \end{longtable}"," ",0,"1/2*(x^6+1)^(2/3)/x^2+1/3*ln(-(6624*RootOf(9*_Z^2+3*_Z+1)^2*x^6-2763*RootOf(9*_Z^2+3*_Z+1)*x^6-1102*x^6-13248*RootOf(9*_Z^2+3*_Z+1)^2*x^3+4428*RootOf(9*_Z^2+3*_Z+1)*(x^6+1)^(2/3)*x+6057*RootOf(9*_Z^2+3*_Z+1)*(x^6+1)^(1/3)*x^2-9930*RootOf(9*_Z^2+3*_Z+1)*x^3+3495*x*(x^6+1)^(2/3)-1476*x^2*(x^6+1)^(1/3)-1653*x^3+6624*RootOf(9*_Z^2+3*_Z+1)^2-2763*RootOf(9*_Z^2+3*_Z+1)-1102)/(x^6-x^3+1))+RootOf(9*_Z^2+3*_Z+1)*ln((4959*RootOf(9*_Z^2+3*_Z+1)^2*x^6+7167*RootOf(9*_Z^2+3*_Z+1)*x^6+2208*x^6-9918*RootOf(9*_Z^2+3*_Z+1)^2*x^3+4428*RootOf(9*_Z^2+3*_Z+1)*(x^6+1)^(2/3)*x-10485*RootOf(9*_Z^2+3*_Z+1)*(x^6+1)^(1/3)*x^2-2763*RootOf(9*_Z^2+3*_Z+1)*x^3-2019*x*(x^6+1)^(2/3)-1476*x^2*(x^6+1)^(1/3)+736*x^3+4959*RootOf(9*_Z^2+3*_Z+1)^2+7167*RootOf(9*_Z^2+3*_Z+1)+2208)/(x^6-x^3+1))","C"
1309,0,0,40,180.000000," ","int((x^8-1)/(x^4-x^2)^(1/4)/(x^8+1),x)","\[\int \frac{x^{8}-1}{\left(x^{4}-x^{2}\right)^{\frac{1}{4}} \left(x^{8}+1\right)}\, dx\]"," ",0,"int((x^8-1)/(x^4-x^2)^(1/4)/(x^8+1),x)","F"
1310,0,0,40,180.000000," ","int((x^8-1)/(x^4-x^2)^(1/4)/(x^8+1),x)","\[\int \frac{x^{8}-1}{\left(x^{4}-x^{2}\right)^{\frac{1}{4}} \left(x^{8}+1\right)}\, dx\]"," ",0,"int((x^8-1)/(x^4-x^2)^(1/4)/(x^8+1),x)","F"
1311,1,287,77,30.332000," ","int((x^8+3*x^4+1)/x^2/(x^4+1)^(3/4)/(3*x^8+3*x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(x^{4}+1\right)^{\frac{1}{4}}}{x}+\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(\frac{12 \RootOf \left(\textit{\_Z}^{2}-3\right) \sqrt{x^{4}+1}\, x^{6}+9 \RootOf \left(\textit{\_Z}^{2}-3\right) x^{8}+18 \left(x^{4}+1\right)^{\frac{3}{4}} x^{5}+18 \left(x^{4}+1\right)^{\frac{1}{4}} x^{7}+6 \RootOf \left(\textit{\_Z}^{2}-3\right) \sqrt{x^{4}+1}\, x^{2}+9 \RootOf \left(\textit{\_Z}^{2}-3\right) x^{4}+6 \left(x^{4}+1\right)^{\frac{3}{4}} x +12 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{2}-3\right)}{3 x^{8}+3 x^{4}+1}\right)}{6}-\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(-\frac{12 \RootOf \left(\textit{\_Z}^{2}+3\right) \sqrt{x^{4}+1}\, x^{6}-9 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{8}-18 \left(x^{4}+1\right)^{\frac{3}{4}} x^{5}+18 \left(x^{4}+1\right)^{\frac{1}{4}} x^{7}+6 \RootOf \left(\textit{\_Z}^{2}+3\right) \sqrt{x^{4}+1}\, x^{2}-9 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{4}-6 \left(x^{4}+1\right)^{\frac{3}{4}} x +12 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+3\right)}{3 x^{8}+3 x^{4}+1}\right)}{6}$&$287$\\ risch&$-\frac{\left(x^{4}+1\right)^{\frac{1}{4}}}{x}+\frac{\left(-\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(\frac{-9 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{16}-18 \left(x^{12}+3 x^{8}+3 x^{4}+1\right)^{\frac{1}{4}} x^{13}+12 \sqrt{x^{12}+3 x^{8}+3 x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}+3\right) x^{10}-27 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{12}+18 \left(x^{12}+3 x^{8}+3 x^{4}+1\right)^{\frac{3}{4}} x^{7}-42 \left(x^{12}+3 x^{8}+3 x^{4}+1\right)^{\frac{1}{4}} x^{9}+18 \sqrt{x^{12}+3 x^{8}+3 x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}+3\right) x^{6}-28 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{8}+12 \left(x^{12}+3 x^{8}+3 x^{4}+1\right)^{\frac{3}{4}} x^{3}-30 \left(x^{12}+3 x^{8}+3 x^{4}+1\right)^{\frac{1}{4}} x^{5}+6 \sqrt{x^{12}+3 x^{8}+3 x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}+3\right) x^{2}-11 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{4}-6 \left(x^{12}+3 x^{8}+3 x^{4}+1\right)^{\frac{1}{4}} x -\RootOf \left(\textit{\_Z}^{2}+3\right)}{\left(x^{4}+1\right)^{2} \left(3 x^{8}+3 x^{4}+1\right)}\right)}{6}+\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(\frac{9 \RootOf \left(\textit{\_Z}^{2}-3\right) x^{16}+18 \left(x^{12}+3 x^{8}+3 x^{4}+1\right)^{\frac{1}{4}} x^{13}+12 \sqrt{x^{12}+3 x^{8}+3 x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}-3\right) x^{10}+27 \RootOf \left(\textit{\_Z}^{2}-3\right) x^{12}+18 \left(x^{12}+3 x^{8}+3 x^{4}+1\right)^{\frac{3}{4}} x^{7}+42 \left(x^{12}+3 x^{8}+3 x^{4}+1\right)^{\frac{1}{4}} x^{9}+18 \sqrt{x^{12}+3 x^{8}+3 x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}-3\right) x^{6}+28 \RootOf \left(\textit{\_Z}^{2}-3\right) x^{8}+12 \left(x^{12}+3 x^{8}+3 x^{4}+1\right)^{\frac{3}{4}} x^{3}+30 \left(x^{12}+3 x^{8}+3 x^{4}+1\right)^{\frac{1}{4}} x^{5}+6 \sqrt{x^{12}+3 x^{8}+3 x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}-3\right) x^{2}+11 \RootOf \left(\textit{\_Z}^{2}-3\right) x^{4}+6 \left(x^{12}+3 x^{8}+3 x^{4}+1\right)^{\frac{1}{4}} x +\RootOf \left(\textit{\_Z}^{2}-3\right)}{\left(x^{4}+1\right)^{2} \left(3 x^{8}+3 x^{4}+1\right)}\right)}{6}\right) \left(\left(x^{4}+1\right)^{3}\right)^{\frac{1}{4}}}{\left(x^{4}+1\right)^{\frac{3}{4}}}$&$626$\\ \hline \end{longtable}"," ",0,"-(x^4+1)^(1/4)/x+1/6*RootOf(_Z^2-3)*ln((12*RootOf(_Z^2-3)*(x^4+1)^(1/2)*x^6+9*RootOf(_Z^2-3)*x^8+18*(x^4+1)^(3/4)*x^5+18*(x^4+1)^(1/4)*x^7+6*RootOf(_Z^2-3)*(x^4+1)^(1/2)*x^2+9*RootOf(_Z^2-3)*x^4+6*(x^4+1)^(3/4)*x+12*x^3*(x^4+1)^(1/4)+RootOf(_Z^2-3))/(3*x^8+3*x^4+1))-1/6*RootOf(_Z^2+3)*ln(-(12*RootOf(_Z^2+3)*(x^4+1)^(1/2)*x^6-9*RootOf(_Z^2+3)*x^8-18*(x^4+1)^(3/4)*x^5+18*(x^4+1)^(1/4)*x^7+6*RootOf(_Z^2+3)*(x^4+1)^(1/2)*x^2-9*RootOf(_Z^2+3)*x^4-6*(x^4+1)^(3/4)*x+12*x^3*(x^4+1)^(1/4)-RootOf(_Z^2+3))/(3*x^8+3*x^4+1))","C"
1312,0,0,13,0.023000," ","int((c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2)/(a^2*x^2+b),x)","\[\int \frac{\sqrt{c +\sqrt{a x +\sqrt{a^{2} x^{2}+b}}}}{a^{2} x^{2}+b}\, dx\]"," ",0,"int((c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2)/(a^2*x^2+b),x)","F"
1313,0,0,13,0.002000," ","int((c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2)/(a^2*x^2+b),x)","\[\int \frac{\sqrt{c +\sqrt{a x +\sqrt{a^{2} x^{2}+b}}}}{a^{2} x^{2}+b}\, dx\]"," ",0,"int((c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2)/(a^2*x^2+b),x)","F"
1314,1,90,73,3.346000," ","int((-1+x)/x^4/(x^3+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(\frac{4 \pi  \sqrt{3}\, x^{3} \hypergeom \left(\left[1, 1, \frac{7}{3}\right], \left[2, 3\right], -x^{3}\right)}{27 \Gamma \left(\frac{2}{3}\right)}-\frac{2 \left(2-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)\right) \pi  \sqrt{3}}{9 \Gamma \left(\frac{2}{3}\right)}-\frac{2 \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right) x^{3}}\right)}{6 \pi}-\frac{\left(x^{3}+1\right)^{\frac{2}{3}}}{2 x^{2}}$&$90$\\ risch&$-\frac{3 x^{4}-2 x^{3}+3 x -2}{6 x^{3} \left(x^{3}+1\right)^{\frac{1}{3}}}+\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\frac{2 \pi  \sqrt{3}\, x^{3} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], -x^{3}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{18 \pi}$&$91$\\ trager&$-\frac{\left(-2+3 x \right) \left(x^{3}+1\right)^{\frac{2}{3}}}{6 x^{3}}-\frac{\ln \left(-\frac{16 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{3}+34 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{3}+30 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}+15 x^{3}-16 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}+30 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}+24 \left(x^{3}+1\right)^{\frac{2}{3}}+22 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+24 \left(x^{3}+1\right)^{\frac{1}{3}}+20}{x^{3}}\right)}{9}-\frac{2 \ln \left(-\frac{16 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{3}+34 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{3}+30 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}+15 x^{3}-16 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}+30 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}+24 \left(x^{3}+1\right)^{\frac{2}{3}}+22 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+24 \left(x^{3}+1\right)^{\frac{1}{3}}+20}{x^{3}}\right) \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)}{9}+\frac{2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \ln \left(-\frac{16 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{3}-18 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{3}-30 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}+2 x^{3}-16 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}-30 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}+9 \left(x^{3}+1\right)^{\frac{2}{3}}-38 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+9 \left(x^{3}+1\right)^{\frac{1}{3}}+5}{x^{3}}\right)}{9}$&$446$\\ \hline \end{longtable}"," ",0,"-1/6/Pi*3^(1/2)*GAMMA(2/3)*(4/27*Pi*3^(1/2)/GAMMA(2/3)*x^3*hypergeom([1,1,7/3],[2,3],-x^3)-2/9*(2-1/6*Pi*3^(1/2)-3/2*ln(3)+3*ln(x))*Pi*3^(1/2)/GAMMA(2/3)-2/3*Pi*3^(1/2)/GAMMA(2/3)/x^3)-1/2*(x^3+1)^(2/3)/x^2","C"
1315,1,389,79,6.976000," ","int((3+2*x)*(x^3+x+1)^(1/3)/x^2/(1+x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{3 \left(x^{3}+x +1\right)^{\frac{1}{3}}}{x}-\ln \left(\frac{18990 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right)^{2} x^{3}-37665 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) \left(x^{3}+x +1\right)^{\frac{2}{3}} x +3357 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) \left(x^{3}+x +1\right)^{\frac{1}{3}} x^{2}+21648 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) x^{3}-9495 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right)^{2} x +2238 \left(x^{3}+x +1\right)^{\frac{2}{3}} x +22872 \left(x^{3}+x +1\right)^{\frac{1}{3}} x^{2}-16670 x^{3}-9495 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right)^{2}+30321 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) x +30321 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right)-13336 x -13336}{1+x}\right)+\frac{3 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) \ln \left(-\frac{7974 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right)^{2} x^{3}-75330 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) \left(x^{3}+x +1\right)^{\frac{2}{3}} x +68616 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) \left(x^{3}+x +1\right)^{\frac{1}{3}} x^{2}+1398 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) x^{3}-3987 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right)^{2} x +45744 \left(x^{3}+x +1\right)^{\frac{2}{3}} x +4476 \left(x^{3}+x +1\right)^{\frac{1}{3}} x^{2}-46676 x^{3}-3987 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right)^{2}-17976 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) x -17976 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right)-20004 x -20004}{1+x}\right)}{2}$&$389$\\ risch&$-\frac{3 \left(x^{3}+x +1\right)^{\frac{1}{3}}}{x}+\frac{\left(-\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{6}+4 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{6}+\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{4}+4 x^{6}+\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{3}-6 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+2 x^{3}+x^{2}+2 x +1\right)^{\frac{2}{3}} x^{2}+6 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{4}-12 \left(x^{6}+2 x^{4}+2 x^{3}+x^{2}+2 x +1\right)^{\frac{1}{3}} x^{4}+6 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{3}+12 x^{2} \left(x^{6}+2 x^{4}+2 x^{3}+x^{2}+2 x +1\right)^{\frac{2}{3}}+8 x^{4}+2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-12 \left(x^{6}+2 x^{4}+2 x^{3}+x^{2}+2 x +1\right)^{\frac{1}{3}} x^{2}+8 x^{3}+4 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x -12 \left(x^{6}+2 x^{4}+2 x^{3}+x^{2}+2 x +1\right)^{\frac{1}{3}} x +4 x^{2}+2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)+8 x +4}{\left(1+x \right) \left(x^{3}+x +1\right)}\right)+\frac{\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{6}-2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{6}+\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{4}-6 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+2 x^{3}+x^{2}+2 x +1\right)^{\frac{1}{3}} x^{4}-8 x^{6}+\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{3}+6 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+2 x^{3}+x^{2}+2 x +1\right)^{\frac{2}{3}} x^{2}-4 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{4}+12 \left(x^{6}+2 x^{4}+2 x^{3}+x^{2}+2 x +1\right)^{\frac{1}{3}} x^{4}-6 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+2 x^{3}+x^{2}+2 x +1\right)^{\frac{1}{3}} x^{2}-4 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{3}-12 x^{4}-6 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+2 x^{3}+x^{2}+2 x +1\right)^{\frac{1}{3}} x -2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}+12 \left(x^{6}+2 x^{4}+2 x^{3}+x^{2}+2 x +1\right)^{\frac{1}{3}} x^{2}-12 x^{3}-4 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x +12 \left(x^{6}+2 x^{4}+2 x^{3}+x^{2}+2 x +1\right)^{\frac{1}{3}} x -4 x^{2}-2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)-8 x -4}{\left(1+x \right) \left(x^{3}+x +1\right)}\right)}{2}\right) \left(\left(x^{3}+x +1\right)^{2}\right)^{\frac{1}{3}}}{\left(x^{3}+x +1\right)^{\frac{2}{3}}}$&$753$\\ \hline \end{longtable}"," ",0,"-3*(x^3+x+1)^(1/3)/x-ln((18990*RootOf(9*_Z^2-6*_Z+4)^2*x^3-37665*RootOf(9*_Z^2-6*_Z+4)*(x^3+x+1)^(2/3)*x+3357*RootOf(9*_Z^2-6*_Z+4)*(x^3+x+1)^(1/3)*x^2+21648*RootOf(9*_Z^2-6*_Z+4)*x^3-9495*RootOf(9*_Z^2-6*_Z+4)^2*x+2238*(x^3+x+1)^(2/3)*x+22872*(x^3+x+1)^(1/3)*x^2-16670*x^3-9495*RootOf(9*_Z^2-6*_Z+4)^2+30321*RootOf(9*_Z^2-6*_Z+4)*x+30321*RootOf(9*_Z^2-6*_Z+4)-13336*x-13336)/(1+x))+3/2*RootOf(9*_Z^2-6*_Z+4)*ln(-(7974*RootOf(9*_Z^2-6*_Z+4)^2*x^3-75330*RootOf(9*_Z^2-6*_Z+4)*(x^3+x+1)^(2/3)*x+68616*RootOf(9*_Z^2-6*_Z+4)*(x^3+x+1)^(1/3)*x^2+1398*RootOf(9*_Z^2-6*_Z+4)*x^3-3987*RootOf(9*_Z^2-6*_Z+4)^2*x+45744*(x^3+x+1)^(2/3)*x+4476*(x^3+x+1)^(1/3)*x^2-46676*x^3-3987*RootOf(9*_Z^2-6*_Z+4)^2-17976*RootOf(9*_Z^2-6*_Z+4)*x-17976*RootOf(9*_Z^2-6*_Z+4)-20004*x-20004)/(1+x))","C"
1316,0,0,83,0.023000," ","int((a^2-2*a*x+x^2)*(-a*b+2*(a-b)*x+x^2)/(x*(-a+x)*(-b+x))^(3/4)/(-a^3*d+(3*a^2*d+b)*x-(3*a*d+1)*x^2+d*x^3),x)","\[\int \frac{\left(a^{2}-2 a x +x^{2}\right) \left(-a b +2 \left(a -b \right) x +x^{2}\right)}{\left(x \left(-a +x \right) \left(-b +x \right)\right)^{\frac{3}{4}} \left(-a^{3} d +\left(3 a^{2} d +b \right) x -\left(3 a d +1\right) x^{2}+d \,x^{3}\right)}\, dx\]"," ",0,"int((a^2-2*a*x+x^2)*(-a*b+2*(a-b)*x+x^2)/(x*(-a+x)*(-b+x))^(3/4)/(-a^3*d+(3*a^2*d+b)*x-(3*a*d+1)*x^2+d*x^3),x)","F"
1317,1,233,83,3.922000," ","int((x^2+1)^2/(-x^2+1)/(x^4-6*x^2+1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}-6 x^{2}+1}\, x^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-\left(x^{4}-6 x^{2}+1\right)^{\frac{3}{4}} x +\left(x^{4}-6 x^{2}+1\right)^{\frac{1}{4}} x^{3}-\RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}-6 x^{2}+1}+5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-3 \left(x^{4}-6 x^{2}+1\right)^{\frac{1}{4}} x}{\left(1+x \right) \left(-1+x \right)}\right)}{2}+\frac{\ln \left(-\frac{\left(x^{4}-6 x^{2}+1\right)^{\frac{3}{4}} x -\sqrt{x^{4}-6 x^{2}+1}\, x^{2}+\left(x^{4}-6 x^{2}+1\right)^{\frac{1}{4}} x^{3}-x^{4}+\sqrt{x^{4}-6 x^{2}+1}-3 \left(x^{4}-6 x^{2}+1\right)^{\frac{1}{4}} x +5 x^{2}}{\left(1+x \right) \left(-1+x \right)}\right)}{2}$&$233$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)*(x^4-6*x^2+1)^(1/2)*x^2-RootOf(_Z^2+1)*x^4-(x^4-6*x^2+1)^(3/4)*x+(x^4-6*x^2+1)^(1/4)*x^3-RootOf(_Z^2+1)*(x^4-6*x^2+1)^(1/2)+5*RootOf(_Z^2+1)*x^2-3*(x^4-6*x^2+1)^(1/4)*x)/(1+x)/(-1+x))+1/2*ln(-((x^4-6*x^2+1)^(3/4)*x-(x^4-6*x^2+1)^(1/2)*x^2+(x^4-6*x^2+1)^(1/4)*x^3-x^4+(x^4-6*x^2+1)^(1/2)-3*(x^4-6*x^2+1)^(1/4)*x+5*x^2)/(1+x)/(-1+x))","C"
1318,1,221,77,8.279000," ","int((x^3-4)*(x^4-x^3+1)/x^2/(x^3-1)^(3/4)/(x^4+x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{3}-1\right)^{\frac{1}{4}}}{x}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{-2 \sqrt{x^{3}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}-2 \left(x^{3}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{4}+1\right) x^{4}+2 \left(x^{3}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}+1\right) x^{3}-\RootOf \left(\textit{\_Z}^{4}+1\right)}{x^{4}+x^{3}-1}\right)+2 \RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{4}+2 \left(x^{3}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{3}-2 \sqrt{x^{3}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right) x^{2}+2 \left(x^{3}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{x^{4}+x^{3}-1}\right)$&$221$\\ risch&$\frac{4 \left(x^{3}-1\right)^{\frac{1}{4}}}{x}+\frac{\left(-2 \RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{10}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{9}-3 x^{6}+3 x^{3}-1\right)^{\frac{1}{4}} x^{7}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{9}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{7}-4 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{9}-3 x^{6}+3 x^{3}-1\right)^{\frac{1}{4}} x^{4}-3 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{6}-2 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{9}-3 x^{6}+3 x^{3}-1\right)^{\frac{3}{4}} x^{3}-2 \sqrt{x^{9}-3 x^{6}+3 x^{3}-1}\, x^{5}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{4}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{9}-3 x^{6}+3 x^{3}-1\right)^{\frac{1}{4}} x +3 x^{3} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+2 \sqrt{x^{9}-3 x^{6}+3 x^{3}-1}\, x^{2}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{2}}{\left(-1+x \right)^{2} \left(x^{2}+x +1\right)^{2} \left(x^{4}+x^{3}-1\right)}\right)-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{10}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{9}+2 \left(x^{9}-3 x^{6}+3 x^{3}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{3}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{7}-2 \left(x^{9}-3 x^{6}+3 x^{3}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right) x^{7}-3 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{6}+2 \sqrt{x^{9}-3 x^{6}+3 x^{3}-1}\, x^{5}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{4}+4 \left(x^{9}-3 x^{6}+3 x^{3}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right) x^{4}+3 x^{3} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-2 \sqrt{x^{9}-3 x^{6}+3 x^{3}-1}\, x^{2}-2 \left(x^{9}-3 x^{6}+3 x^{3}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right) x -\RootOf \left(\textit{\_Z}^{4}+1\right)^{2}}{\left(-1+x \right)^{2} \left(x^{2}+x +1\right)^{2} \left(x^{4}+x^{3}-1\right)}\right)\right) \left(\left(x^{3}-1\right)^{3}\right)^{\frac{1}{4}}}{\left(x^{3}-1\right)^{\frac{3}{4}}}$&$593$\\ \hline \end{longtable}"," ",0,"4*(x^3-1)^(1/4)/x+2*RootOf(_Z^4+1)^3*ln((-2*(x^3-1)^(1/2)*RootOf(_Z^4+1)^3*x^2-2*(x^3-1)^(1/4)*RootOf(_Z^4+1)^2*x^3-RootOf(_Z^4+1)*x^4+2*(x^3-1)^(3/4)*x+RootOf(_Z^4+1)*x^3-RootOf(_Z^4+1))/(x^4+x^3-1))+2*RootOf(_Z^4+1)*ln(-(-RootOf(_Z^4+1)^3*x^4+2*(x^3-1)^(1/4)*RootOf(_Z^4+1)^2*x^3+RootOf(_Z^4+1)^3*x^3-2*(x^3-1)^(1/2)*RootOf(_Z^4+1)*x^2+2*(x^3-1)^(3/4)*x-RootOf(_Z^4+1)^3)/(x^4+x^3-1))","C"
1319,1,277,79,24.689000," ","int((x^4-1)*(x^4+3)*(x^4-x^3-1)/x^6/(x^4-2*x^3-1)/(x^5-x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(3 x^{4}+7 x^{3}-3\right) \left(x^{5}-x \right)^{\frac{3}{4}}}{21 x^{6}}-\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(-\frac{\sqrt{x^{5}-x}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x +2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \left(x^{5}-x \right)^{\frac{1}{4}} x^{2}+x^{4} \RootOf \left(\textit{\_Z}^{4}-8\right)+2 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{3}+4 \left(x^{5}-x \right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}-8\right)}{x^{4}-2 x^{3}-1}\right)-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(\frac{\sqrt{x^{5}-x}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x +2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \left(x^{5}-x \right)^{\frac{1}{4}} x^{2}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{3}-4 \left(x^{5}-x \right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right)}{x^{4}-2 x^{3}-1}\right)$&$277$\\ risch&$\frac{\frac{4}{7} x^{8}-\frac{8}{7} x^{4}+\frac{4}{7}+\frac{4}{3} x^{7}-\frac{4}{3} x^{3}}{x^{5} \left(x \left(x^{4}-1\right)\right)^{\frac{1}{4}}}+\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(\frac{\sqrt{x^{5}-x}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x -2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \left(x^{5}-x \right)^{\frac{1}{4}} x^{2}+x^{4} \RootOf \left(\textit{\_Z}^{4}-8\right)+2 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{3}-4 \left(x^{5}-x \right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}-8\right)}{x^{4}-2 x^{3}-1}\right)+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(-\frac{\sqrt{x^{5}-x}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x -2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \left(x^{5}-x \right)^{\frac{1}{4}} x^{2}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{3}+4 \left(x^{5}-x \right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right)}{x^{4}-2 x^{3}-1}\right)$&$285$\\ \hline \end{longtable}"," ",0,"4/21*(3*x^4+7*x^3-3)*(x^5-x)^(3/4)/x^6-RootOf(_Z^4-8)*ln(-((x^5-x)^(1/2)*RootOf(_Z^4-8)^3*x+2*RootOf(_Z^4-8)^2*(x^5-x)^(1/4)*x^2+x^4*RootOf(_Z^4-8)+2*RootOf(_Z^4-8)*x^3+4*(x^5-x)^(3/4)-RootOf(_Z^4-8))/(x^4-2*x^3-1))-RootOf(_Z^2+RootOf(_Z^4-8)^2)*ln(((x^5-x)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x+2*RootOf(_Z^4-8)^2*(x^5-x)^(1/4)*x^2-RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^4-2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^3-4*(x^5-x)^(3/4)+RootOf(_Z^2+RootOf(_Z^4-8)^2))/(x^4-2*x^3-1))","C"
1320,0,0,81,0.020000," ","int((a*x^5+4*b)*(a*x^5+c*x^4-b)/x^2/(a*x^5-b)^(3/4)/(a*x^5-c*x^4-b),x)","\[\int \frac{\left(a \,x^{5}+4 b \right) \left(a \,x^{5}+c \,x^{4}-b \right)}{x^{2} \left(a \,x^{5}-b \right)^{\frac{3}{4}} \left(a \,x^{5}-c \,x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^5+4*b)*(a*x^5+c*x^4-b)/x^2/(a*x^5-b)^(3/4)/(a*x^5-c*x^4-b),x)","F"
1321,1,216,75,31.985000," ","int((x^6-2)*(x^6-x^4+1)/x^4/(x^6+1)^(1/4)/(x^6+x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{6}+1\right)^{\frac{3}{4}}}{3 x^{3}}+\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(-\frac{-2 \sqrt{x^{6}+1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}+\RootOf \left(\textit{\_Z}^{4}+1\right) x^{6}-2 \left(x^{6}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{4}+1\right) x^{4}+2 \left(x^{6}+1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}+1\right)}{x^{6}+x^{4}+1}\right)+\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{6}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{4}+2 \left(x^{6}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}-2 \sqrt{x^{6}+1}\, \RootOf \left(\textit{\_Z}^{4}+1\right) x^{2}+2 \left(x^{6}+1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{x^{6}+x^{4}+1}\right)$&$216$\\ risch&$\frac{2 \left(x^{6}+1\right)^{\frac{3}{4}}}{3 x^{3}}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{6}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{4}+2 \left(x^{6}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}-2 \sqrt{x^{6}+1}\, \RootOf \left(\textit{\_Z}^{4}+1\right) x^{2}+2 \left(x^{6}+1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{x^{6}+x^{4}+1}\right)-\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{2 \sqrt{x^{6}+1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}-\RootOf \left(\textit{\_Z}^{4}+1\right) x^{6}-2 \left(x^{6}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{4}+1\right) x^{4}+2 \left(x^{6}+1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}+1\right)}{x^{6}+x^{4}+1}\right)$&$217$\\ \hline \end{longtable}"," ",0,"2/3*(x^6+1)^(3/4)/x^3+RootOf(_Z^4+1)*ln(-(-2*(x^6+1)^(1/2)*RootOf(_Z^4+1)^3*x^2+RootOf(_Z^4+1)*x^6-2*(x^6+1)^(1/4)*RootOf(_Z^4+1)^2*x^3-RootOf(_Z^4+1)*x^4+2*(x^6+1)^(3/4)*x+RootOf(_Z^4+1))/(x^6+x^4+1))+RootOf(_Z^4+1)^3*ln(-(RootOf(_Z^4+1)^3*x^6-RootOf(_Z^4+1)^3*x^4+2*(x^6+1)^(1/4)*RootOf(_Z^4+1)^2*x^3-2*(x^6+1)^(1/2)*RootOf(_Z^4+1)*x^2+2*(x^6+1)^(3/4)*x+RootOf(_Z^4+1)^3)/(x^6+x^4+1))","C"
1322,0,0,84,0.039000," ","int(x^4*(a*x^6+2*b)/(a*x^6-b)^(1/4)/(a*x^6-x^4-b)^2,x)","\[\int \frac{x^{4} \left(a \,x^{6}+2 b \right)}{\left(a \,x^{6}-b \right)^{\frac{1}{4}} \left(a \,x^{6}-x^{4}-b \right)^{2}}\, dx\]"," ",0,"int(x^4*(a*x^6+2*b)/(a*x^6-b)^(1/4)/(a*x^6-x^4-b)^2,x)","F"
1323,0,0,81,0.016000," ","int((a*x^6+2*b)*(a*x^6-x^4-b)/x^4/(a*x^6-b)^(1/4)/(a*x^6-2*x^4-b),x)","\[\int \frac{\left(a \,x^{6}+2 b \right) \left(a \,x^{6}-x^{4}-b \right)}{x^{4} \left(a \,x^{6}-b \right)^{\frac{1}{4}} \left(a \,x^{6}-2 x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^6+2*b)*(a*x^6-x^4-b)/x^4/(a*x^6-b)^(1/4)/(a*x^6-2*x^4-b),x)","F"
1324,1,195,87,1.261000," ","int((-x^8-2*x^3-2*x^2-1)^(1/2)*(3*x^8+x^3-1)/(x^8+2*x^3+1)/(x^8+2*x^3+x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{8}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \sqrt{-x^{8}-2 x^{3}-2 x^{2}-1}\, x +\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{8}+2 x^{3}+x^{2}+1}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x^{8}+2 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{3}+4 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{2}+4 \sqrt{-x^{8}-2 x^{3}-2 x^{2}-1}\, x +\RootOf \left(\textit{\_Z}^{2}+2\right)}{\left(1+x \right) \left(x^{7}-x^{6}+x^{5}-x^{4}+x^{3}+x^{2}-x +1\right)}\right)}{2}$&$195$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^2+1)*ln(-(RootOf(_Z^2+1)*x^8+2*RootOf(_Z^2+1)*x^3+3*RootOf(_Z^2+1)*x^2+2*(-x^8-2*x^3-2*x^2-1)^(1/2)*x+RootOf(_Z^2+1))/(x^8+2*x^3+x^2+1))-1/2*RootOf(_Z^2+2)*ln(-(RootOf(_Z^2+2)*x^8+2*RootOf(_Z^2+2)*x^3+4*RootOf(_Z^2+2)*x^2+4*(-x^8-2*x^3-2*x^2-1)^(1/2)*x+RootOf(_Z^2+2))/(1+x)/(x^7-x^6+x^5-x^4+x^3+x^2-x+1))","C"
1325,1,578,67,4.143000," ","int((x^6+1)*(x^6-x^2-2)^(1/2)/(x^12-4*x^6-3*x^4+4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right) \ln \left(-\frac{-384 \RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right)^{3} x^{6}-73728 \RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right)^{5} x^{2}+4 \RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right) x^{6}+1152 \RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right)^{3} x^{2}+192 \sqrt{x^{6}-x^{2}-2}\, \RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right)^{2} x +768 \RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right)^{3}-4 \RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right) x^{2}-\sqrt{x^{6}-x^{2}-2}\, x -8 \RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right)}{-x^{6}+192 x^{2} \RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right)^{2}+x^{2}+2}\right)+\frac{\RootOf \left(\textit{\_Z}^{2}+576 \RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right)^{2}+6\right) \ln \left(\frac{-48 \RootOf \left(\textit{\_Z}^{2}+576 \RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right)^{2}+6\right) \RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right)^{2} x^{6}+9216 \RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right)^{4} \RootOf \left(\textit{\_Z}^{2}+576 \RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right)^{2}+6\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}+576 \RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right)^{2}+6\right) x^{6}+336 \RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+576 \RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right)^{2}+6\right) x^{2}+576 \sqrt{x^{6}-x^{2}-2}\, \RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right)^{2} x +96 \RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+576 \RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right)^{2}+6\right)+3 \RootOf \left(\textit{\_Z}^{2}+576 \RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right)^{2}+6\right) x^{2}+9 \sqrt{x^{6}-x^{2}-2}\, x +2 \RootOf \left(\textit{\_Z}^{2}+576 \RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right)^{2}+6\right)}{x^{6}+192 x^{2} \RootOf \left(18432 \textit{\_Z}^{4}+192 \textit{\_Z}^{2}-1\right)^{2}+x^{2}-2}\right)}{24}$&$578$\\ \hline \end{longtable}"," ",0,"RootOf(18432*_Z^4+192*_Z^2-1)*ln(-(-384*RootOf(18432*_Z^4+192*_Z^2-1)^3*x^6-73728*RootOf(18432*_Z^4+192*_Z^2-1)^5*x^2+4*RootOf(18432*_Z^4+192*_Z^2-1)*x^6+1152*RootOf(18432*_Z^4+192*_Z^2-1)^3*x^2+192*(x^6-x^2-2)^(1/2)*RootOf(18432*_Z^4+192*_Z^2-1)^2*x+768*RootOf(18432*_Z^4+192*_Z^2-1)^3-4*RootOf(18432*_Z^4+192*_Z^2-1)*x^2-(x^6-x^2-2)^(1/2)*x-8*RootOf(18432*_Z^4+192*_Z^2-1))/(-x^6+192*x^2*RootOf(18432*_Z^4+192*_Z^2-1)^2+x^2+2))+1/24*RootOf(_Z^2+576*RootOf(18432*_Z^4+192*_Z^2-1)^2+6)*ln((-48*RootOf(_Z^2+576*RootOf(18432*_Z^4+192*_Z^2-1)^2+6)*RootOf(18432*_Z^4+192*_Z^2-1)^2*x^6+9216*RootOf(18432*_Z^4+192*_Z^2-1)^4*RootOf(_Z^2+576*RootOf(18432*_Z^4+192*_Z^2-1)^2+6)*x^2-RootOf(_Z^2+576*RootOf(18432*_Z^4+192*_Z^2-1)^2+6)*x^6+336*RootOf(18432*_Z^4+192*_Z^2-1)^2*RootOf(_Z^2+576*RootOf(18432*_Z^4+192*_Z^2-1)^2+6)*x^2+576*(x^6-x^2-2)^(1/2)*RootOf(18432*_Z^4+192*_Z^2-1)^2*x+96*RootOf(18432*_Z^4+192*_Z^2-1)^2*RootOf(_Z^2+576*RootOf(18432*_Z^4+192*_Z^2-1)^2+6)+3*RootOf(_Z^2+576*RootOf(18432*_Z^4+192*_Z^2-1)^2+6)*x^2+9*(x^6-x^2-2)^(1/2)*x+2*RootOf(_Z^2+576*RootOf(18432*_Z^4+192*_Z^2-1)^2+6))/(x^6+192*x^2*RootOf(18432*_Z^4+192*_Z^2-1)^2+x^2-2))","C"
1326,1,33,74,1.677000," ","int(x*(x^3-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} x^{2} \hypergeom \left(\left[-\frac{1}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], x^{3}\right)}{2 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}}}$&$33$\\ risch&$\frac{x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}}{3}-\frac{\left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} x^{2} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], x^{3}\right)}{6 \mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}}}$&$46$\\ trager&$\frac{x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1\right)}{9}-\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}-1\right)^{\frac{2}{3}}+3 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}+4 x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{9}-\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}-1\right)^{\frac{2}{3}}+3 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}+4 x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2\right)}{9}$&$308$\\ \hline \end{longtable}"," ",0,"1/2*signum(x^3-1)^(1/3)/(-signum(x^3-1))^(1/3)*x^2*hypergeom([-1/3,2/3],[5/3],x^3)","C"
1327,1,17,74,1.490000," ","int(x*(x^3+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{x^{2} \hypergeom \left(\left[-\frac{1}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], -x^{3}\right)}{2}$&$17$\\ risch&$\frac{x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}}{3}+\frac{x^{2} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], -x^{3}\right)}{6}$&$30$\\ trager&$\frac{x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}}{3}+\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +3 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+x^{3}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+1\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)}{9}-\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x -3 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}+1\right)^{\frac{2}{3}}+3 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}+4 x^{3}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+2\right)}{9}+\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x -3 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}+1\right)^{\frac{2}{3}}+3 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}+4 x^{3}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+2\right)}{9}$&$342$\\ \hline \end{longtable}"," ",0,"1/2*x^2*hypergeom([-1/3,2/3],[5/3],-x^3)","C"
1328,1,17,74,4.102000," ","int((x^3+x)^(1/3)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{3 \hypergeom \left(\left[-\frac{1}{3}, -\frac{1}{3}\right], \left[\frac{2}{3}\right], -x^{2}\right)}{2 x^{\frac{2}{3}}}$&$17$\\ trager&$-\frac{3 \left(x^{3}+x \right)^{\frac{1}{3}}}{2 x}+\frac{\ln \left(45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}-72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}-72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x -87 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}+15 \left(x^{3}+x \right)^{\frac{2}{3}}+15 x \left(x^{3}+x \right)^{\frac{1}{3}}-45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}+20 x^{2}-18 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)+8\right)}{2}-\frac{3 \ln \left(45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}-72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}-72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x -87 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}+15 \left(x^{3}+x \right)^{\frac{2}{3}}+15 x \left(x^{3}+x \right)^{\frac{1}{3}}-45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}+20 x^{2}-18 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)+8\right) \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)}{2}+\frac{3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \ln \left(45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}+72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}+72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x +57 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}-9 \left(x^{3}+x \right)^{\frac{2}{3}}-9 x \left(x^{3}+x \right)^{\frac{1}{3}}-45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}-4 x^{2}+48 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-3\right)}{2}$&$432$\\ risch&$-\frac{3 \left(x \left(x^{2}+1\right)\right)^{\frac{1}{3}}}{2 x}+\frac{\left(-\frac{\ln \left(-\frac{-5 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{4}-38 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{4}+18 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}+16 x^{4}+30 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}+60 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}-70 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-96 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}+18 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}+5 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2}+28 x^{2}+60 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}-32 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)+12}{x^{2}+1}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{4}+20 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{4}-48 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-100 x^{4}+30 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}+60 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}+14 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}+36 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}-48 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}+\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2}-140 x^{2}+60 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}-6 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)-40}{x^{2}+1}\right)}{4}\right) \left(x \left(x^{2}+1\right)\right)^{\frac{1}{3}} \left(x^{2} \left(x^{2}+1\right)^{2}\right)^{\frac{1}{3}}}{x \left(x^{2}+1\right)}$&$498$\\ \hline \end{longtable}"," ",0,"-3/2/x^(2/3)*hypergeom([-1/3,-1/3],[2/3],-x^2)","C"
1329,0,0,82,0.017000," ","int((-1+x)*(k*x-1)*(3-2*(1+k)*x+k*x^2)/x/((1-x)*x*(-k*x+1))^(3/4)/(-1+(1+k)*x-k*x^2+d*x^3),x)","\[\int \frac{\left(-1+x \right) \left(k x -1\right) \left(3-2 \left(1+k \right) x +k \,x^{2}\right)}{x \left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{3}{4}} \left(-1+\left(1+k \right) x -k \,x^{2}+d \,x^{3}\right)}\, dx\]"," ",0,"int((-1+x)*(k*x-1)*(3-2*(1+k)*x+k*x^2)/x/((1-x)*x*(-k*x+1))^(3/4)/(-1+(1+k)*x-k*x^2+d*x^3),x)","F"
1330,0,0,80,0.043000," ","int((x^2-2*x+1)*(-2+(-1+k)*(1+k)*x+2*k^2*x^2)/((-x^2+1)*(-k^2*x^2+1))^(3/4)/(-1+d-(1+3*d)*x+(k^2+3*d)*x^2+(k^2-d)*x^3),x)","\[\int \frac{\left(x^{2}-2 x +1\right) \left(-2+\left(-1+k \right) \left(1+k \right) x +2 k^{2} x^{2}\right)}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{3}{4}} \left(-1+d -\left(1+3 d \right) x +\left(k^{2}+3 d \right) x^{2}+\left(k^{2}-d \right) x^{3}\right)}\, dx\]"," ",0,"int((x^2-2*x+1)*(-2+(-1+k)*(1+k)*x+2*k^2*x^2)/((-x^2+1)*(-k^2*x^2+1))^(3/4)/(-1+d-(1+3*d)*x+(k^2+3*d)*x^2+(k^2-d)*x^3),x)","F"
1331,0,0,82,0.039000," ","int(x^2/(a*x^2-b)/(a*x^4-b*x^2)^(1/4),x)","\[\int \frac{x^{2}}{\left(a \,x^{2}-b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(x^2/(a*x^2-b)/(a*x^4-b*x^2)^(1/4),x)","F"
1332,0,0,80,0.018000," ","int((p*x^5+q)^(1/2)*(3*p*x^5-2*q)*(a*p*x^5+b*x^2+a*q)/x^4/(c*p*x^5+d*x^2+c*q),x)","\[\int \frac{\sqrt{p \,x^{5}+q}\, \left(3 p \,x^{5}-2 q \right) \left(a p \,x^{5}+b \,x^{2}+a q \right)}{x^{4} \left(c p \,x^{5}+d \,x^{2}+c q \right)}\, dx\]"," ",0,"int((p*x^5+q)^(1/2)*(3*p*x^5-2*q)*(a*p*x^5+b*x^2+a*q)/x^4/(c*p*x^5+d*x^2+c*q),x)","F"
1333,1,17,78,4.635000," ","int(x/(x^6+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 x^{\frac{4}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{4}\right)}{4}$&$17$\\ trager&$-\frac{\ln \left(11 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{4}-215 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{4}+789 \left(x^{6}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+800 x^{4}-585 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+x^{2}\right)^{\frac{2}{3}}-585 x^{2} \left(x^{6}+x^{2}\right)^{\frac{1}{3}}-204 \left(x^{6}+x^{2}\right)^{\frac{2}{3}}-11 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}+138 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+320\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(-160 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{4}-629 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{4}+204 \left(x^{6}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+44 x^{4}+585 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+x^{2}\right)^{\frac{2}{3}}+585 x^{2} \left(x^{6}+x^{2}\right)^{\frac{1}{3}}-789 \left(x^{6}+x^{2}\right)^{\frac{2}{3}}+160 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}-491 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+33\right)}{4}$&$275$\\ \hline \end{longtable}"," ",0,"3/4*x^(4/3)*hypergeom([1/3,1/3],[4/3],-x^4)","C"
1334,1,239,80,5.226000," ","int((x^4-1)/(x^4+x^2+1)/(x^6+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(-\frac{2 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x -\RootOf \left(\textit{\_Z}^{4}+1\right) x^{5}-2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{4}+1\right) x^{3}+2 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}+1\right) x}{\left(x^{2}+x +1\right) x \left(x^{2}-x +1\right)}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{5}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{3}+2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}-2 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}+1\right) x +\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x +2 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{\left(x^{2}+x +1\right) x \left(x^{2}-x +1\right)}\right)}{2}$&$239$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^4+1)*ln(-(2*(x^6+x^2)^(1/2)*RootOf(_Z^4+1)^3*x-RootOf(_Z^4+1)*x^5-2*(x^6+x^2)^(1/4)*RootOf(_Z^4+1)^2*x^2+RootOf(_Z^4+1)*x^3+2*(x^6+x^2)^(3/4)-RootOf(_Z^4+1)*x)/(x^2+x+1)/x/(x^2-x+1))-1/2*RootOf(_Z^4+1)^3*ln(-(RootOf(_Z^4+1)^3*x^5-RootOf(_Z^4+1)^3*x^3+2*(x^6+x^2)^(1/4)*RootOf(_Z^4+1)^2*x^2-2*(x^6+x^2)^(1/2)*RootOf(_Z^4+1)*x+RootOf(_Z^4+1)^3*x+2*(x^6+x^2)^(3/4))/(x^2+x+1)/x/(x^2-x+1))","C"
1335,1,238,80,5.002000," ","int((x^4-1)/(x^4+x^2+1)/(x^6+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{5}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{3}+2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}-2 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}+1\right) x +\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x +2 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{\left(x^{2}+x +1\right) x \left(x^{2}-x +1\right)}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(-\frac{-2 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x +\RootOf \left(\textit{\_Z}^{4}+1\right) x^{5}-2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}-\RootOf \left(\textit{\_Z}^{4}+1\right) x^{3}+2 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}+1\right) x}{\left(x^{2}+x +1\right) x \left(x^{2}-x +1\right)}\right)}{2}$&$238$\\ \hline \end{longtable}"," ",0,"-1/2*RootOf(_Z^4+1)^3*ln(-(RootOf(_Z^4+1)^3*x^5-RootOf(_Z^4+1)^3*x^3+2*(x^6+x^2)^(1/4)*RootOf(_Z^4+1)^2*x^2-2*(x^6+x^2)^(1/2)*RootOf(_Z^4+1)*x+RootOf(_Z^4+1)^3*x+2*(x^6+x^2)^(3/4))/(x^2+x+1)/x/(x^2-x+1))-1/2*RootOf(_Z^4+1)*ln(-(-2*(x^6+x^2)^(1/2)*RootOf(_Z^4+1)^3*x+RootOf(_Z^4+1)*x^5-2*(x^6+x^2)^(1/4)*RootOf(_Z^4+1)^2*x^2-RootOf(_Z^4+1)*x^3+2*(x^6+x^2)^(3/4)+RootOf(_Z^4+1)*x)/(x^2+x+1)/x/(x^2-x+1))","C"
1336,0,0,77,0.030000," ","int(x^2*(a*x^6+2*b)/(a*x^6-b)^(3/4)/(a*x^6-2*c*x^4-b),x)","\[\int \frac{x^{2} \left(a \,x^{6}+2 b \right)}{\left(a \,x^{6}-b \right)^{\frac{3}{4}} \left(a \,x^{6}-2 c \,x^{4}-b \right)}\, dx\]"," ",0,"int(x^2*(a*x^6+2*b)/(a*x^6-b)^(3/4)/(a*x^6-2*c*x^4-b),x)","F"
1337,0,0,14,0.024000," ","int(1/(a*x^4+b)^(1/4)/(x^8-2*a*x^4-2*b),x)","\[\int \frac{1}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(x^{8}-2 a \,x^{4}-2 b \right)}\, dx\]"," ",0,"int(1/(a*x^4+b)^(1/4)/(x^8-2*a*x^4-2*b),x)","F"
1338,0,0,14,0.001000," ","int(1/(a*x^4+b)^(1/4)/(x^8-2*a*x^4-2*b),x)","\[\int \frac{1}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(x^{8}-2 a \,x^{4}-2 b \right)}\, dx\]"," ",0,"int(1/(a*x^4+b)^(1/4)/(x^8-2*a*x^4-2*b),x)","F"
1339,0,0,11,0.022000," ","int((a*x^4-2*b)/(a*x^4+b)^(1/4)/(2*x^8-a*x^4-b),x)","\[\int \frac{a \,x^{4}-2 b}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(2 x^{8}-a \,x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^4-2*b)/(a*x^4+b)^(1/4)/(2*x^8-a*x^4-b),x)","F"
1340,1,333,89,0.110000," ","int((k^2*x^2+b*x+1)/((1-x)*x*(-k^2*x+1))^(1/2)/(k^2*x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}-\frac{\left(b -2 k \right) \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{4} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}-\frac{\left(b +2 k \right) \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{4} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}$&$333$\\ elliptic&$-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}-\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{k^{4} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{3} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}-\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{k^{4} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}+\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{3} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}$&$575$\\ \hline \end{longtable}"," ",0,"-2/k^2*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticF((-(x-1/k^2)*k^2)^(1/2),(1/k^2/(1/k^2-1))^(1/2))-(b-2*k)/k^4*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/k)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+1/k),(1/k^2/(1/k^2-1))^(1/2))-(b+2*k)/k^4*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-1/k)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-1/k),(1/k^2/(1/k^2-1))^(1/2))","C"
1341,1,81,75,2.981000," ","int((x^3-1)^(1/3)/x^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \left(\frac{5 \Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{8}{3}\right], \left[2, 4\right], x^{3}\right)}{27}+\frac{\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{2}{3}\right)}{3}+\frac{3 \Gamma \left(\frac{2}{3}\right)}{2 x^{6}}-\frac{\Gamma \left(\frac{2}{3}\right)}{x^{3}}\right)}{9 \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}}}$&$81$\\ risch&$\frac{x^{6}-4 x^{3}+3}{18 x^{6} \left(x^{3}-1\right)^{\frac{2}{3}}}+\frac{\left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} \left(\frac{2 \Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 2\right], x^{3}\right)}{3}+\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{2}{3}\right)\right)}{27 \Gamma \left(\frac{2}{3}\right) \mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}}}$&$89$\\ trager&$\frac{\left(x^{3}-3\right) \left(x^{3}-1\right)^{\frac{1}{3}}}{18 x^{6}}-\frac{\ln \left(\frac{-5890048 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)^{2} x^{3}-630720 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right) x^{3}+352128 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}+1477 x^{3}-14247 \left(x^{3}-1\right)^{\frac{2}{3}}-352128 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)+47120384 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)^{2}+14247 \left(x^{3}-1\right)^{\frac{1}{3}}+1088384 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)-2743}{x^{3}}\right)}{27}-\frac{64 \ln \left(\frac{-5890048 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)^{2} x^{3}-630720 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right) x^{3}+352128 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}+1477 x^{3}-14247 \left(x^{3}-1\right)^{\frac{2}{3}}-352128 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)+47120384 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)^{2}+14247 \left(x^{3}-1\right)^{\frac{1}{3}}+1088384 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)-2743}{x^{3}}\right) \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)}{27}+\frac{64 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right) \ln \left(-\frac{5890048 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)^{2} x^{3}-446656 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right) x^{3}+352128 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}-9894 x^{3}+19749 \left(x^{3}-1\right)^{\frac{2}{3}}-352128 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)-47120384 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)^{2}-19749 \left(x^{3}-1\right)^{\frac{1}{3}}-384128 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)+8245}{x^{3}}\right)}{27}$&$444$\\ \hline \end{longtable}"," ",0,"-1/9/GAMMA(2/3)*signum(x^3-1)^(1/3)/(-signum(x^3-1))^(1/3)*(5/27*GAMMA(2/3)*x^3*hypergeom([1,1,8/3],[2,4],x^3)+1/3*(1/6*Pi*3^(1/2)-3/2*ln(3)+3*ln(x)+I*Pi)*GAMMA(2/3)+3/2*GAMMA(2/3)/x^6-GAMMA(2/3)/x^3)","C"
1342,1,60,75,2.175000," ","int((x^3+1)^(1/3)/x^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{-\frac{5 \Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{8}{3}\right], \left[2, 4\right], -x^{3}\right)}{27}+\frac{\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)}{3}+\frac{3 \Gamma \left(\frac{2}{3}\right)}{2 x^{6}}+\frac{\Gamma \left(\frac{2}{3}\right)}{x^{3}}}{9 \Gamma \left(\frac{2}{3}\right)}$&$60$\\ risch&$-\frac{x^{6}+4 x^{3}+3}{18 x^{6} \left(x^{3}+1\right)^{\frac{2}{3}}}-\frac{-\frac{2 \Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 2\right], -x^{3}\right)}{3}+\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)}{27 \Gamma \left(\frac{2}{3}\right)}$&$69$\\ trager&$-\frac{\left(x^{3}+3\right) \left(x^{3}+1\right)^{\frac{1}{3}}}{18 x^{6}}+\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\frac{-4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+17 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+15 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}-15 x^{3}-24 \left(x^{3}+1\right)^{\frac{2}{3}}+15 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}-24 \left(x^{3}+1\right)^{\frac{1}{3}}+11 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-20}{x^{3}}\right)}{27}-\frac{\ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+15 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}+2 x^{3}+9 \left(x^{3}+1\right)^{\frac{2}{3}}+15 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}+9 \left(x^{3}+1\right)^{\frac{1}{3}}+19 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+5}{x^{3}}\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)}{27}+\frac{\ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+15 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}+2 x^{3}+9 \left(x^{3}+1\right)^{\frac{2}{3}}+15 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}+9 \left(x^{3}+1\right)^{\frac{1}{3}}+19 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+5}{x^{3}}\right)}{27}$&$405$\\ \hline \end{longtable}"," ",0,"-1/9/GAMMA(2/3)*(-5/27*GAMMA(2/3)*x^3*hypergeom([1,1,8/3],[2,4],-x^3)+1/3*(1/6*Pi*3^(1/2)-3/2*ln(3)+3*ln(x))*GAMMA(2/3)+3/2*GAMMA(2/3)/x^6+GAMMA(2/3)/x^3)","C"
1343,1,71,75,2.190000," ","int((x^3-1)*(x^3+1)^(1/3)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 x^{6}+4 x^{3}+1}{3 x^{3} \left(x^{3}+1\right)^{\frac{2}{3}}}+\frac{-\frac{4 \Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 2\right], -x^{3}\right)}{27}+\frac{2 \left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)}{9}}{\Gamma \left(\frac{2}{3}\right)}$&$71$\\ meijerg&$\frac{\frac{\Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 3\right], -x^{3}\right)}{3}-\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+3 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)+\frac{3 \Gamma \left(\frac{2}{3}\right)}{x^{3}}}{9 \Gamma \left(\frac{2}{3}\right)}-\frac{-\Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[\frac{2}{3}, 1, 1\right], \left[2, 2\right], -x^{3}\right)-3 \left(3+\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)}{9 \Gamma \left(\frac{2}{3}\right)}$&$103$\\ trager&$\frac{\left(x^{3}+1\right)^{\frac{1}{3}} \left(3 x^{3}+1\right)}{3 x^{3}}+\frac{2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+17 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}+15 x^{3}-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}+24 \left(x^{3}+1\right)^{\frac{2}{3}}+11 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+24 \left(x^{3}+1\right)^{\frac{1}{3}}+20}{x^{3}}\right)}{9}-\frac{2 \ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-9 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}+2 x^{3}-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}+9 \left(x^{3}+1\right)^{\frac{2}{3}}-19 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+9 \left(x^{3}+1\right)^{\frac{1}{3}}+5}{x^{3}}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{9}-\frac{2 \ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-9 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}+2 x^{3}-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}+9 \left(x^{3}+1\right)^{\frac{2}{3}}-19 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+9 \left(x^{3}+1\right)^{\frac{1}{3}}+5}{x^{3}}\right)}{9}$&$368$\\ \hline \end{longtable}"," ",0,"1/3*(3*x^6+4*x^3+1)/x^3/(x^3+1)^(2/3)+2/9/GAMMA(2/3)*(-2/3*GAMMA(2/3)*x^3*hypergeom([1,1,5/3],[2,2],-x^3)+(1/6*Pi*3^(1/2)-3/2*ln(3)+3*ln(x))*GAMMA(2/3))","C"
1344,1,193132,11,194.570000," ","int((1+x)/(x^3-x-1)/(x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$193132$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1345,1,190624,11,163.861000," ","int((1+x)/(x^3-x-1)/(x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$190624$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1346,1,654,77,2.801000," ","int((x^2-1)/(x^2+1)/(x^3-x^2-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right) \ln \left(-\frac{-325 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{5} x^{2}+325 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{5}-90 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{3} x^{2}-520 x \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{3}+80 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{2} \sqrt{x^{3}-x^{2}-x}+90 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{3}+31 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right) x^{2}-248 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right) x +192 \sqrt{x^{3}-x^{2}-x}-31 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)}{\left(5 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{2} x -5 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{2}-x -3\right)^{2}}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{2}+10\right) \ln \left(\frac{65 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{2}+10\right) \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{4} x^{2}-65 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{2}+10\right) \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{4}+34 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{2}+10\right) x^{2}-104 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{2}+10\right) x +80 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{2} \sqrt{x^{3}-x^{2}-x}-34 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{2}+10\right)-3 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{2}+10\right) x^{2}+8 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{2}+10\right) x -160 \sqrt{x^{3}-x^{2}-x}+3 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{2}+10\right)}{\left(5 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{2} x -5 \RootOf \left(5 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+1\right)^{2}+3 x +1\right)^{2}}\right)}{10}$&$654$\\ default&$\frac{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \sqrt{-5 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{5}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}}+\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}-i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}-i-\frac{\sqrt{5}}{2}\right)}-\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}-i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}-i-\frac{\sqrt{5}}{2}\right)}-\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}+i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}+i-\frac{\sqrt{5}}{2}\right)}+\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}+i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}+i-\frac{\sqrt{5}}{2}\right)}$&$735$\\ elliptic&$\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{5 \sqrt{x^{3}-x^{2}-x}}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}}+\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}-i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}-i-\frac{\sqrt{5}}{2}\right)}-\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}-i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}-i-\frac{\sqrt{5}}{2}\right)}-\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}+i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}+i-\frac{\sqrt{5}}{2}\right)}+\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}+i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}+i-\frac{\sqrt{5}}{2}\right)}$&$873$\\ \hline \end{longtable}"," ",0,"-1/2*RootOf(5*_Z^4+2*_Z^2+1)*ln(-(-325*RootOf(5*_Z^4+2*_Z^2+1)^5*x^2+325*RootOf(5*_Z^4+2*_Z^2+1)^5-90*RootOf(5*_Z^4+2*_Z^2+1)^3*x^2-520*x*RootOf(5*_Z^4+2*_Z^2+1)^3+80*RootOf(5*_Z^4+2*_Z^2+1)^2*(x^3-x^2-x)^(1/2)+90*RootOf(5*_Z^4+2*_Z^2+1)^3+31*RootOf(5*_Z^4+2*_Z^2+1)*x^2-248*RootOf(5*_Z^4+2*_Z^2+1)*x+192*(x^3-x^2-x)^(1/2)-31*RootOf(5*_Z^4+2*_Z^2+1))/(5*RootOf(5*_Z^4+2*_Z^2+1)^2*x-5*RootOf(5*_Z^4+2*_Z^2+1)^2-x-3)^2)-1/10*RootOf(_Z^2+25*RootOf(5*_Z^4+2*_Z^2+1)^2+10)*ln((65*RootOf(_Z^2+25*RootOf(5*_Z^4+2*_Z^2+1)^2+10)*RootOf(5*_Z^4+2*_Z^2+1)^4*x^2-65*RootOf(_Z^2+25*RootOf(5*_Z^4+2*_Z^2+1)^2+10)*RootOf(5*_Z^4+2*_Z^2+1)^4+34*RootOf(5*_Z^4+2*_Z^2+1)^2*RootOf(_Z^2+25*RootOf(5*_Z^4+2*_Z^2+1)^2+10)*x^2-104*RootOf(5*_Z^4+2*_Z^2+1)^2*RootOf(_Z^2+25*RootOf(5*_Z^4+2*_Z^2+1)^2+10)*x+80*RootOf(5*_Z^4+2*_Z^2+1)^2*(x^3-x^2-x)^(1/2)-34*RootOf(5*_Z^4+2*_Z^2+1)^2*RootOf(_Z^2+25*RootOf(5*_Z^4+2*_Z^2+1)^2+10)-3*RootOf(_Z^2+25*RootOf(5*_Z^4+2*_Z^2+1)^2+10)*x^2+8*RootOf(_Z^2+25*RootOf(5*_Z^4+2*_Z^2+1)^2+10)*x-160*(x^3-x^2-x)^(1/2)+3*RootOf(_Z^2+25*RootOf(5*_Z^4+2*_Z^2+1)^2+10))/(5*RootOf(5*_Z^4+2*_Z^2+1)^2*x-5*RootOf(5*_Z^4+2*_Z^2+1)^2+3*x+1)^2)","C"
1347,1,15,79,0.954000," ","int((x^3+x^2)^(1/3)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 x^{\frac{2}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], -x \right)}{2}$&$15$\\ trager&$\left(x^{3}+x^{2}\right)^{\frac{1}{3}}-\frac{\ln \left(-\frac{9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}+45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{2}{3}}-72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{1}{3}} x -9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x +24 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}-24 \left(x^{3}+x^{2}\right)^{\frac{2}{3}}+9 x \left(x^{3}+x^{2}\right)^{\frac{1}{3}}-3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x +16 x^{2}+12 x}{x}\right)}{3}+\RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \ln \left(\frac{45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}+45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{2}{3}}+27 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{1}{3}} x -45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x -87 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}+9 \left(x^{3}+x^{2}\right)^{\frac{2}{3}}-24 x \left(x^{3}+x^{2}\right)^{\frac{1}{3}}-18 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x +20 x^{2}+8 x}{x}\right)$&$318$\\ risch&$\left(x^{2} \left(1+x \right)\right)^{\frac{1}{3}}+\frac{\left(-\frac{\ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{2}+48 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{2}{3}}-30 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}} x -16 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-36 \left(x^{3}+2 x^{2}+x \right)^{\frac{2}{3}}-30 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}}+96 \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}} x +\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2}-14 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x -64 x^{2}+96 \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}}+2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)-112 x -48}{1+x}\right)}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{2}+24 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{2}{3}}-9 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}} x -19 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-30 \left(x^{3}+2 x^{2}+x \right)^{\frac{2}{3}}-9 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}}+48 \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}} x -2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2}-28 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x -10 x^{2}+48 \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}}-9 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)-14 x -4}{1+x}\right)}{6}\right) \left(x^{2} \left(1+x \right)\right)^{\frac{1}{3}} \left(\left(1+x \right)^{2} x \right)^{\frac{1}{3}}}{x \left(1+x \right)}$&$443$\\ \hline \end{longtable}"," ",0,"3/2*x^(2/3)*hypergeom([-1/3,2/3],[5/3],-x)","C"
1348,1,258,79,4.267000," ","int((x^3+1)^(2/3)*(x^3+2)/x^6/(2*x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{11 x^{6}+7 x^{3}-4}{10 x^{5} \left(x^{3}+1\right)^{\frac{1}{3}}}+\ln \left(-\frac{3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +6 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}-x \left(x^{3}+1\right)^{\frac{2}{3}}+x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}-1}{2 x^{3}+1}\right)+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(\frac{9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x -3 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+2 x \left(x^{3}+1\right)^{\frac{2}{3}}+x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{2 x^{3}+1}\right)$&$258$\\ trager&$\frac{\left(x^{3}+1\right)^{\frac{2}{3}} \left(11 x^{3}-4\right)}{10 x^{5}}+\ln \left(\frac{-18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +63 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+21 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}-15 x \left(x^{3}+1\right)^{\frac{2}{3}}+6 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}-5 x^{3}+18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-10}{2 x^{3}+1}\right)+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(-\frac{45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x -45 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+24 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+21 x \left(x^{3}+1\right)^{\frac{2}{3}}+6 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}-4 x^{3}-45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+21 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-2}{2 x^{3}+1}\right)$&$327$\\ \hline \end{longtable}"," ",0,"1/10*(11*x^6+7*x^3-4)/x^5/(x^3+1)^(1/3)+ln(-(3*RootOf(9*_Z^2+3*_Z+1)*(x^3+1)^(2/3)*x+6*(x^3+1)^(1/3)*RootOf(9*_Z^2+3*_Z+1)*x^2+3*RootOf(9*_Z^2+3*_Z+1)*x^3-x*(x^3+1)^(2/3)+x^2*(x^3+1)^(1/3)-1)/(2*x^3+1))+3*RootOf(9*_Z^2+3*_Z+1)*ln((9*RootOf(9*_Z^2+3*_Z+1)^2*x^3+3*RootOf(9*_Z^2+3*_Z+1)*(x^3+1)^(2/3)*x-3*(x^3+1)^(1/3)*RootOf(9*_Z^2+3*_Z+1)*x^2+3*RootOf(9*_Z^2+3*_Z+1)*x^3+2*x*(x^3+1)^(2/3)+x^2*(x^3+1)^(1/3)+3*RootOf(9*_Z^2+3*_Z+1))/(2*x^3+1))","C"
1349,1,69,75,3.913000," ","int((x^4-3)*(x^4+1)^(1/3)/x^9,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{x^{8}-2 x^{4}-3}{8 x^{8} \left(x^{4}+1\right)^{\frac{2}{3}}}+\frac{-\frac{2 \Gamma \left(\frac{2}{3}\right) x^{4} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 2\right], -x^{4}\right)}{3}+\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)}{6 \Gamma \left(\frac{2}{3}\right)}$&$69$\\ meijerg&$\frac{-\frac{5 \Gamma \left(\frac{2}{3}\right) x^{4} \hypergeom \left(\left[1, 1, \frac{8}{3}\right], \left[2, 4\right], -x^{4}\right)}{27}+\frac{\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)}{3}+\frac{3 \Gamma \left(\frac{2}{3}\right)}{2 x^{8}}+\frac{\Gamma \left(\frac{2}{3}\right)}{x^{4}}}{4 \Gamma \left(\frac{2}{3}\right)}-\frac{\frac{\Gamma \left(\frac{2}{3}\right) x^{4} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 3\right], -x^{4}\right)}{3}-\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+4 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)+\frac{3 \Gamma \left(\frac{2}{3}\right)}{x^{4}}}{12 \Gamma \left(\frac{2}{3}\right)}$&$115$\\ trager&$-\frac{\left(x^{4}-3\right) \left(x^{4}+1\right)^{\frac{1}{3}}}{8 x^{8}}+\frac{\ln \left(-\frac{333 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}+393 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}+60 x^{4}-351 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}}-333 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-144 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{1}{3}}+48 \left(x^{4}+1\right)^{\frac{2}{3}}+384 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-165 \left(x^{4}+1\right)^{\frac{1}{3}}+80}{x^{4}}\right)}{6}+\frac{\RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(\frac{153 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}-162 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}+40 x^{4}-351 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}}-153 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+495 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{1}{3}}-165 \left(x^{4}+1\right)^{\frac{2}{3}}-195 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+48 \left(x^{4}+1\right)^{\frac{1}{3}}+100}{x^{4}}\right)}{2}$&$299$\\ \hline \end{longtable}"," ",0,"-1/8*(x^8-2*x^4-3)/x^8/(x^4+1)^(2/3)+1/6/GAMMA(2/3)*(-2/3*GAMMA(2/3)*x^4*hypergeom([1,1,5/3],[2,2],-x^4)+(1/6*Pi*3^(1/2)-3/2*ln(3)+4*ln(x))*GAMMA(2/3))","C"
1350,0,0,77,0.009000," ","int((a*x^3-b)/x^3/(a*x^4+b*x)^(1/4),x)","\[\int \frac{a \,x^{3}-b}{x^{3} \left(a \,x^{4}+b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^3-b)/x^3/(a*x^4+b*x)^(1/4),x)","F"
1351,0,0,77,0.008000," ","int((a*x^3+b)/x^3/(a*x^4+b*x)^(1/4),x)","\[\int \frac{a \,x^{3}+b}{x^{3} \left(a \,x^{4}+b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^3+b)/x^3/(a*x^4+b*x)^(1/4),x)","F"
1352,1,86,75,6.661000," ","int(1/x^13/(x^6+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{4 x^{12}+x^{6}-3}{36 x^{12} \left(x^{6}+1\right)^{\frac{1}{3}}}+\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\frac{2 \pi  \sqrt{3}\, x^{6} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], -x^{6}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+6 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{54 \pi}$&$86$\\ meijerg&$\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\frac{28 \pi  \sqrt{3}\, x^{6} \hypergeom \left(\left[1, 1, \frac{10}{3}\right], \left[2, 4\right], -x^{6}\right)}{243 \Gamma \left(\frac{2}{3}\right)}+\frac{4 \left(\frac{9}{4}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+6 \ln \left(x \right)\right) \pi  \sqrt{3}}{27 \Gamma \left(\frac{2}{3}\right)}-\frac{\pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right) x^{12}}+\frac{2 \pi  \sqrt{3}}{9 \Gamma \left(\frac{2}{3}\right) x^{6}}\right)}{12 \pi}$&$90$\\ trager&$\frac{\left(x^{6}+1\right)^{\frac{2}{3}} \left(4 x^{6}-3\right)}{36 x^{12}}-\frac{\ln \left(-\frac{5670704 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{6}+10826002 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{6}+3479919 x^{6}+11856814 \left(x^{6}+1\right)^{\frac{2}{3}} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)-5670704 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}+11856814 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}}+6057568 \left(x^{6}+1\right)^{\frac{2}{3}}+9021462 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+6057568 \left(x^{6}+1\right)^{\frac{1}{3}}+4639892}{x^{6}}\right)}{27}-\frac{2 \ln \left(-\frac{5670704 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{6}+10826002 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{6}+3479919 x^{6}+11856814 \left(x^{6}+1\right)^{\frac{2}{3}} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)-5670704 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}+11856814 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}}+6057568 \left(x^{6}+1\right)^{\frac{2}{3}}+9021462 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+6057568 \left(x^{6}+1\right)^{\frac{1}{3}}+4639892}{x^{6}}\right) \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)}{27}+\frac{2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \ln \left(-\frac{1415351072 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{6}-1046043282 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{6}-369307790 x^{6}-3200009934 \left(x^{6}+1\right)^{\frac{2}{3}} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)-1415351072 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}-3200009934 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}}-569431707 \left(x^{6}+1\right)^{\frac{2}{3}}-3907685470 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)-569431707 \left(x^{6}+1\right)^{\frac{1}{3}}-923269475}{x^{6}}\right)}{27}$&$448$\\ \hline \end{longtable}"," ",0,"1/36*(4*x^12+x^6-3)/x^12/(x^6+1)^(1/3)+1/54/Pi*3^(1/2)*GAMMA(2/3)*(-2/9*Pi*3^(1/2)/GAMMA(2/3)*x^6*hypergeom([1,1,4/3],[2,2],-x^6)+2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)+6*ln(x))*Pi*3^(1/2)/GAMMA(2/3))","C"
1353,1,436,83,2.059000," ","int((5*x^8-3)/(x^8+1)/(x^8-x^3+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{8}+x^{8}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-3 \left(x^{8}-x^{3}+1\right)^{\frac{2}{3}} x +3 \left(x^{8}-x^{3}+1\right)^{\frac{1}{3}} x^{2}-2 x^{3}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+1}{x^{8}+1}\right)-\ln \left(\frac{-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{8}+x^{8}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+3 \left(x^{8}-x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x -3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{8}-x^{3}+1\right)^{\frac{1}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-3 \left(x^{8}-x^{3}+1\right)^{\frac{2}{3}} x +3 \left(x^{8}-x^{3}+1\right)^{\frac{1}{3}} x^{2}-x^{3}-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+1}{x^{8}+1}\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+\ln \left(\frac{-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{8}+x^{8}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+3 \left(x^{8}-x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x -3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{8}-x^{3}+1\right)^{\frac{1}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-3 \left(x^{8}-x^{3}+1\right)^{\frac{2}{3}} x +3 \left(x^{8}-x^{3}+1\right)^{\frac{1}{3}} x^{2}-x^{3}-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+1}{x^{8}+1}\right)$&$436$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2-_Z+1)*ln(-(RootOf(_Z^2-_Z+1)*x^8+x^8+RootOf(_Z^2-_Z+1)^2*x^3-RootOf(_Z^2-_Z+1)*x^3-3*(x^8-x^3+1)^(2/3)*x+3*(x^8-x^3+1)^(1/3)*x^2-2*x^3+RootOf(_Z^2-_Z+1)+1)/(x^8+1))-ln((-2*RootOf(_Z^2-_Z+1)*x^8+x^8+2*RootOf(_Z^2-_Z+1)^2*x^3+3*(x^8-x^3+1)^(2/3)*RootOf(_Z^2-_Z+1)*x-3*RootOf(_Z^2-_Z+1)*(x^8-x^3+1)^(1/3)*x^2+RootOf(_Z^2-_Z+1)*x^3-3*(x^8-x^3+1)^(2/3)*x+3*(x^8-x^3+1)^(1/3)*x^2-x^3-2*RootOf(_Z^2-_Z+1)+1)/(x^8+1))*RootOf(_Z^2-_Z+1)+ln((-2*RootOf(_Z^2-_Z+1)*x^8+x^8+2*RootOf(_Z^2-_Z+1)^2*x^3+3*(x^8-x^3+1)^(2/3)*RootOf(_Z^2-_Z+1)*x-3*RootOf(_Z^2-_Z+1)*(x^8-x^3+1)^(1/3)*x^2+RootOf(_Z^2-_Z+1)*x^3-3*(x^8-x^3+1)^(2/3)*x+3*(x^8-x^3+1)^(1/3)*x^2-x^3-2*RootOf(_Z^2-_Z+1)+1)/(x^8+1))","C"
1354,1,125,71,0.036000," ","int((x+(1+x)^(1/2))^(1/2)/(1+(1+x)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\left(2 \sqrt{1+x}+1\right) \sqrt{x +\sqrt{1+x}}}{2}-\frac{5 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{4}-2 \sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}+\ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}\right)+2 \arctan \left(\frac{-3-\sqrt{1+x}}{2 \sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}}\right)$&$125$\\ default&$\frac{\left(2 \sqrt{1+x}+1\right) \sqrt{x +\sqrt{1+x}}}{2}-\frac{5 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{4}-2 \sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}+\ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}\right)+2 \arctan \left(\frac{-3-\sqrt{1+x}}{2 \sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}}\right)$&$125$\\ \hline \end{longtable}"," ",0,"1/2*(2*(1+x)^(1/2)+1)*(x+(1+x)^(1/2))^(1/2)-5/4*ln(1/2+(1+x)^(1/2)+(x+(1+x)^(1/2))^(1/2))-2*((1+(1+x)^(1/2))^2-(1+x)^(1/2)-2)^(1/2)+ln(1/2+(1+x)^(1/2)+((1+(1+x)^(1/2))^2-(1+x)^(1/2)-2)^(1/2))+2*arctan(1/2*(-3-(1+x)^(1/2))/((1+(1+x)^(1/2))^2-(1+x)^(1/2)-2)^(1/2))","A"
1355,0,0,71,0.024000," ","int((x+(x^2+1)^(1/2))/(1+(x+(x^2+1)^(1/2))^(1/2)),x)","\[\int \frac{x +\sqrt{x^{2}+1}}{1+\sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x+(x^2+1)^(1/2))/(1+(x+(x^2+1)^(1/2))^(1/2)),x)","F"
1356,0,0,72,0.048000," ","int(x^2/(a*x^2-2*b)/(a*x^2-b)^(3/4),x)","\[\int \frac{x^{2}}{\left(a \,x^{2}-2 b \right) \left(a \,x^{2}-b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(x^2/(a*x^2-2*b)/(a*x^2-b)^(3/4),x)","F"
1357,0,0,82,0.040000," ","int((-2*k-(-1+k)*(1+k)*x+2*k*x^2)*(k^2*x^2-2*k*x+1)/((-x^2+1)*(-k^2*x^2+1))^(3/4)/(1-d+(1+3*d)*k*x-(3*d*k^2+1)*x^2+k*(d*k^2-1)*x^3),x)","\[\int \frac{\left(-2 k -\left(-1+k \right) \left(1+k \right) x +2 k \,x^{2}\right) \left(k^{2} x^{2}-2 k x +1\right)}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{3}{4}} \left(1-d +\left(1+3 d \right) k x -\left(3 d \,k^{2}+1\right) x^{2}+k \left(d \,k^{2}-1\right) x^{3}\right)}\, dx\]"," ",0,"int((-2*k-(-1+k)*(1+k)*x+2*k*x^2)*(k^2*x^2-2*k*x+1)/((-x^2+1)*(-k^2*x^2+1))^(3/4)/(1-d+(1+3*d)*k*x-(3*d*k^2+1)*x^2+k*(d*k^2-1)*x^3),x)","F"
1358,1,117,88,0.898000," ","int((x^2-1)*(x^2+1)*(x^4+3*x^2+1)^(1/2)/x^2/(x^2+x+1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{2}+2 x +1\right) \sqrt{x^{4}+3 x^{2}+1}}{x \left(x^{2}+x +1\right)}-\frac{3 \RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}-2\right) x +\RootOf \left(\textit{\_Z}^{2}-2\right)-2 \sqrt{x^{4}+3 x^{2}+1}}{x^{2}+x +1}\right)}{2}-2 \ln \left(\frac{1+x^{2}+\sqrt{x^{4}+3 x^{2}+1}}{x}\right)$&$117$\\ risch&$\frac{\left(x^{2}+2 x +1\right) \sqrt{x^{4}+3 x^{2}+1}}{x \left(x^{2}+x +1\right)}+\frac{3 \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{3}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{3}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticF \left(x \left(\frac{i \sqrt{5}}{2}-\frac{i}{2}\right), \frac{3}{2}+\frac{\sqrt{5}}{2}\right)}{\left(\frac{i \sqrt{5}}{2}-\frac{i}{2}\right) \sqrt{x^{4}+3 x^{2}+1}}-\ln \left(\frac{3}{2}+x^{2}+\sqrt{x^{4}+3 x^{2}+1}\right)-\arctanh \left(\frac{3 x^{2}+2}{2 \sqrt{x^{4}+3 x^{2}+1}}\right)-\frac{3 \arctanh \left(\frac{\left(-2+i \sqrt{3}\right) \left(7 x^{2}+\frac{11}{2}-\frac{5 i \sqrt{3}}{2}\right)}{14 \sqrt{-1-i \sqrt{3}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{4 \sqrt{-1-i \sqrt{3}}}-\frac{3 \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{3}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{3}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, x , -\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{5}}{2}+\frac{3}{4}-\frac{3 i \sqrt{3}}{4}, \frac{\sqrt{-\frac{3}{2}-\frac{\sqrt{5}}{2}}}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}}\right)}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, \sqrt{x^{4}+3 x^{2}+1}}+\frac{3 i \sqrt{3}\, \arctanh \left(\frac{\left(-2+i \sqrt{3}\right) \left(7 x^{2}+\frac{11}{2}-\frac{5 i \sqrt{3}}{2}\right)}{14 \sqrt{-1-i \sqrt{3}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{4 \sqrt{-1-i \sqrt{3}}}-\frac{3 \arctanh \left(\frac{\left(-2-i \sqrt{3}\right) \left(7 x^{2}+\frac{11}{2}+\frac{5 i \sqrt{3}}{2}\right)}{14 \sqrt{-1+i \sqrt{3}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{4 \sqrt{-1+i \sqrt{3}}}-\frac{3 \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{3}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{3}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, x , -\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{5}}{2}+\frac{3}{4}+\frac{3 i \sqrt{3}}{4}, \frac{\sqrt{-\frac{3}{2}-\frac{\sqrt{5}}{2}}}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}}\right)}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, \sqrt{x^{4}+3 x^{2}+1}}-\frac{3 i \sqrt{3}\, \arctanh \left(\frac{\left(-2-i \sqrt{3}\right) \left(7 x^{2}+\frac{11}{2}+\frac{5 i \sqrt{3}}{2}\right)}{14 \sqrt{-1+i \sqrt{3}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{4 \sqrt{-1+i \sqrt{3}}}$&$608$\\ elliptic&$-\ln \left(\frac{3}{2}+x^{2}+\sqrt{x^{4}+3 x^{2}+1}\right)+\frac{\sqrt{-\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}+5}\, \left(-\frac{3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}+5}\, \sqrt{2}}{4}\right) \left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}+\frac{2 \sqrt{6}\, \arctan \left(\frac{2 \sqrt{6}\, \sqrt{-\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}+5}\, \left(x^{2}-1\right)}{3 \left(\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}-5\right) \left(-x^{2}-1\right)}\right) \left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}-9 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}+5}\, \sqrt{2}}{4}\right)+6 \sqrt{6}\, \arctan \left(\frac{2 \sqrt{6}\, \sqrt{-\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}+5}\, \left(x^{2}-1\right)}{3 \left(\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}-5\right) \left(-x^{2}-1\right)}\right)+12 \sqrt{-\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}+5}\right)}{6 \sqrt{-\frac{\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}-5}{\left(\frac{x^{2}-1}{-x^{2}-1}+1\right)^{2}}}\, \left(\frac{x^{2}-1}{-x^{2}-1}+1\right) \left(\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}+3\right)}-\arctanh \left(\frac{3 x^{2}+2}{2 \sqrt{x^{4}+3 x^{2}+1}}\right)+\frac{\sqrt{-\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}+5}\, \left(6 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}+5}\, \sqrt{2}}{4}\right)-\sqrt{6}\, \arctan \left(\frac{2 \sqrt{6}\, \sqrt{-\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}+5}\, \left(x^{2}-1\right)}{3 \left(\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}-5\right) \left(-x^{2}-1\right)}\right)\right)}{3 \left(\frac{x^{2}-1}{-x^{2}-1}+1\right) \sqrt{-\frac{\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}-5}{\left(\frac{x^{2}-1}{-x^{2}-1}+1\right)^{2}}}}+\frac{\left(\frac{\sqrt{x^{4}+3 x^{2}+1}\, \sqrt{2}}{x}-\frac{1}{2 \left(-1+\frac{\sqrt{x^{4}+3 x^{2}+1}\, \sqrt{2}}{2 x}\right)}+\frac{3 \ln \left(-1+\frac{\sqrt{x^{4}+3 x^{2}+1}\, \sqrt{2}}{2 x}\right)}{2}-\frac{1}{2 \left(1+\frac{\sqrt{x^{4}+3 x^{2}+1}\, \sqrt{2}}{2 x}\right)}-\frac{3 \ln \left(1+\frac{\sqrt{x^{4}+3 x^{2}+1}\, \sqrt{2}}{2 x}\right)}{2}\right) \sqrt{2}}{2}$&$725$\\ default&$\frac{\sqrt{x^{4}+3 x^{2}+1}}{x}+\frac{3 \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{3}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{3}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticF \left(x \left(\frac{i \sqrt{5}}{2}-\frac{i}{2}\right), \frac{3}{2}+\frac{\sqrt{5}}{2}\right)}{\left(\frac{i \sqrt{5}}{2}-\frac{i}{2}\right) \sqrt{x^{4}+3 x^{2}+1}}+\frac{3 \ln \left(\frac{3}{2}+x^{2}+\sqrt{x^{4}+3 x^{2}+1}\right)}{2}-\arctanh \left(\frac{3 x^{2}+2}{2 \sqrt{x^{4}+3 x^{2}+1}}\right)-\frac{5 \ln \left(2 x^{2}+3+2 \sqrt{x^{4}+3 x^{2}+1}\right)}{2}+\frac{4 i \sqrt{3}\, \left(\frac{\arctanh \left(\frac{\left(-2+i \sqrt{3}\right) \left(7 x^{2}+\frac{11}{2}-\frac{5 i \sqrt{3}}{2}\right)}{14 \sqrt{-1-i \sqrt{3}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{2 \sqrt{-1-i \sqrt{3}}}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{3}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{3}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, x , -\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{5}}{2}+\frac{3}{4}-\frac{3 i \sqrt{3}}{4}, \frac{\sqrt{-\frac{3}{2}-\frac{\sqrt{5}}{2}}}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}}\right)}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{3}-\frac{4 i \sqrt{3}\, \left(\frac{\arctanh \left(\frac{\left(-2-i \sqrt{3}\right) \left(7 x^{2}+\frac{11}{2}+\frac{5 i \sqrt{3}}{2}\right)}{14 \sqrt{-1+i \sqrt{3}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{2 \sqrt{-1+i \sqrt{3}}}-\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{3}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{3}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, x , -\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{5}}{2}+\frac{3}{4}+\frac{3 i \sqrt{3}}{4}, \frac{\sqrt{-\frac{3}{2}-\frac{\sqrt{5}}{2}}}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}}\right)}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{3}+\frac{\sqrt{x^{4}+3 x^{2}+1}}{x^{2}+x +1}-\left(\frac{3}{2}-\frac{i \sqrt{3}}{6}\right) \left(\frac{\arctanh \left(\frac{\left(-2+i \sqrt{3}\right) \left(7 x^{2}+\frac{11}{2}-\frac{5 i \sqrt{3}}{2}\right)}{14 \sqrt{-1-i \sqrt{3}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{2 \sqrt{-1-i \sqrt{3}}}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{3}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{3}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, x , -\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{5}}{2}+\frac{3}{4}-\frac{3 i \sqrt{3}}{4}, \frac{\sqrt{-\frac{3}{2}-\frac{\sqrt{5}}{2}}}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}}\right)}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)-\left(\frac{3}{2}+\frac{i \sqrt{3}}{6}\right) \left(\frac{\arctanh \left(\frac{\left(-2-i \sqrt{3}\right) \left(7 x^{2}+\frac{11}{2}+\frac{5 i \sqrt{3}}{2}\right)}{14 \sqrt{-1+i \sqrt{3}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{2 \sqrt{-1+i \sqrt{3}}}-\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{3}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{3}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, x , -\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{5}}{2}+\frac{3}{4}+\frac{3 i \sqrt{3}}{4}, \frac{\sqrt{-\frac{3}{2}-\frac{\sqrt{5}}{2}}}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}}\right)}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)$&$911$\\ \hline \end{longtable}"," ",0,"(x^2+2*x+1)*(x^4+3*x^2+1)^(1/2)/x/(x^2+x+1)-3/2*RootOf(_Z^2-2)*ln(-(RootOf(_Z^2-2)*x^2-RootOf(_Z^2-2)*x+RootOf(_Z^2-2)-2*(x^4+3*x^2+1)^(1/2))/(x^2+x+1))-2*ln((1+x^2+(x^4+3*x^2+1)^(1/2))/x)","C"
1359,1,88,80,0.638000," ","int((x^2+2)*(2*x^2+x-4)*(2*x^4-7*x^2+8)^(1/2)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{2 x^{4}-7 x^{2}+8}\, \left(4 x^{4}+3 x^{3}-14 x^{2}-6 x +16\right)}{6 x^{3}}-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}+\sqrt{2 x^{4}-7 x^{2}+8}+2 \RootOf \left(\textit{\_Z}^{2}-2\right)}{x}\right)}{4}$&$88$\\ elliptic&$\frac{\sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{15}\, \left(x^{2}-\frac{7}{4}\right)}{15}\right)}{8}+\frac{\sqrt{2 x^{4}-7 x^{2}+8}}{2}-\frac{\sqrt{2 x^{4}-7 x^{2}+8}}{x^{2}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(-7 x^{2}+16\right) \sqrt{2}}{8 \sqrt{2 x^{4}-7 x^{2}+8}}\right)}{8}+\frac{\left(2 x^{4}-7 x^{2}+8\right)^{\frac{3}{2}}}{3 x^{3}}$&$104$\\ risch&$-\frac{14 x^{6}+6 x^{5}-65 x^{4}-21 x^{3}+112 x^{2}+24 x -64}{3 x^{3} \sqrt{2 x^{4}-7 x^{2}+8}}+\frac{2 x \sqrt{2 x^{4}-7 x^{2}+8}}{3}+\frac{\sqrt{2 x^{4}-7 x^{2}+8}}{2}+\frac{\sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{15}\, \left(x^{2}-\frac{7}{4}\right)}{15}\right)}{8}-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(-7 x^{2}+16\right) \sqrt{2}}{8 \sqrt{2 x^{4}-7 x^{2}+8}}\right)}{8}$&$132$\\ default&$\frac{2 x \sqrt{2 x^{4}-7 x^{2}+8}}{3}+\frac{8 \sqrt{2 x^{4}-7 x^{2}+8}}{3 x^{3}}-\frac{7 \sqrt{2 x^{4}-7 x^{2}+8}}{3 x}+\frac{\sqrt{2 x^{4}-7 x^{2}+8}}{16}+\frac{\sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{15}\, \left(x^{2}-\frac{7}{4}\right)}{15}\right)}{8}-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(-7 x^{2}+16\right) \sqrt{2}}{8 \sqrt{2 x^{4}-7 x^{2}+8}}\right)}{8}-\frac{\left(2 x^{4}-7 x^{2}+8\right)^{\frac{3}{2}}}{8 x^{2}}+\frac{\left(4 x^{2}-7\right) \sqrt{2 x^{4}-7 x^{2}+8}}{16}$&$163$\\ \hline \end{longtable}"," ",0,"1/6*(2*x^4-7*x^2+8)^(1/2)*(4*x^4+3*x^3-14*x^2-6*x+16)/x^3-1/4*RootOf(_Z^2-2)*ln((-RootOf(_Z^2-2)*x^2+(2*x^4-7*x^2+8)^(1/2)+2*RootOf(_Z^2-2))/x)","C"
1360,0,0,78,0.006000," ","int(x^4*(a*x^4-b)^(3/4),x)","\[\int x^{4} \left(a \,x^{4}-b \right)^{\frac{3}{4}}\, dx\]"," ",0,"int(x^4*(a*x^4-b)^(3/4),x)","F"
1361,0,0,78,0.009000," ","int((a*x^2-2*b)*(a*x^4+b*x^2)^(1/4)/x^2,x)","\[\int \frac{\left(a \,x^{2}-2 b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}{x^{2}}\, dx\]"," ",0,"int((a*x^2-2*b)*(a*x^4+b*x^2)^(1/4)/x^2,x)","F"
1362,0,0,78,0.010000," ","int((a*x^2+2*b)*(a*x^4+b*x^2)^(1/4)/x^2,x)","\[\int \frac{\left(a \,x^{2}+2 b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}{x^{2}}\, dx\]"," ",0,"int((a*x^2+2*b)*(a*x^4+b*x^2)^(1/4)/x^2,x)","F"
1363,0,0,86,0.020000," ","int(((-3*k^2+1)*x+2*k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/4)/(-1+d+(3*k^2-d)*x^2-3*k^4*x^4+k^6*x^6),x)","\[\int \frac{\left(-3 k^{2}+1\right) x +2 k^{2} x^{3}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{1}{4}} \left(-1+d +\left(3 k^{2}-d \right) x^{2}-3 k^{4} x^{4}+k^{6} x^{6}\right)}\, dx\]"," ",0,"int(((-3*k^2+1)*x+2*k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/4)/(-1+d+(3*k^2-d)*x^2-3*k^4*x^4+k^6*x^6),x)","F"
1364,0,0,11,0.028000," ","int((a*x^4-b)/(a*x^4+b)^(1/4)/(x^8-a*x^4+b),x)","\[\int \frac{a \,x^{4}-b}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(x^{8}-a \,x^{4}+b \right)}\, dx\]"," ",0,"int((a*x^4-b)/(a*x^4+b)^(1/4)/(x^8-a*x^4+b),x)","F"
1365,0,0,11,0.001000," ","int((a*x^4-b)/(a*x^4+b)^(1/4)/(x^8-a*x^4+b),x)","\[\int \frac{a \,x^{4}-b}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(x^{8}-a \,x^{4}+b \right)}\, dx\]"," ",0,"int((a*x^4-b)/(a*x^4+b)^(1/4)/(x^8-a*x^4+b),x)","F"
1366,0,0,24,180.000000," ","int((x^5+4)*(x^10+x^9+x^8-2*x^5-x^4+1)/x^2/(x^5-1)^(3/4)/(x^10-x^9-x^8-2*x^5+x^4+1),x)","\[\int \frac{\left(x^{5}+4\right) \left(x^{10}+x^{9}+x^{8}-2 x^{5}-x^{4}+1\right)}{x^{2} \left(x^{5}-1\right)^{\frac{3}{4}} \left(x^{10}-x^{9}-x^{8}-2 x^{5}+x^{4}+1\right)}\, dx\]"," ",0,"int((x^5+4)*(x^10+x^9+x^8-2*x^5-x^4+1)/x^2/(x^5-1)^(3/4)/(x^10-x^9-x^8-2*x^5+x^4+1),x)","F"
1367,0,0,24,180.000000," ","int((x^5+4)*(x^10+x^9+x^8-2*x^5-x^4+1)/x^2/(x^5-1)^(3/4)/(x^10-x^9-x^8-2*x^5+x^4+1),x)","\[\int \frac{\left(x^{5}+4\right) \left(x^{10}+x^{9}+x^{8}-2 x^{5}-x^{4}+1\right)}{x^{2} \left(x^{5}-1\right)^{\frac{3}{4}} \left(x^{10}-x^{9}-x^{8}-2 x^{5}+x^{4}+1\right)}\, dx\]"," ",0,"int((x^5+4)*(x^10+x^9+x^8-2*x^5-x^4+1)/x^2/(x^5-1)^(3/4)/(x^10-x^9-x^8-2*x^5+x^4+1),x)","F"
1368,0,0,76,180.000000," ","int(1/(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x)","\[\int \frac{1}{\sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}\, dx\]"," ",0,"int(1/(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x)","F"
1369,0,0,83,0.023000," ","int((2*a*x^2-3*b)*(a^2*x^2+b^2)^(3/4)/x,x)","\[\int \frac{\left(2 a \,x^{2}-3 b \right) \left(a^{2} x^{2}+b^{2}\right)^{\frac{3}{4}}}{x}\, dx\]"," ",0,"int((2*a*x^2-3*b)*(a^2*x^2+b^2)^(3/4)/x,x)","F"
1370,1,702,75,1.016000," ","int((-1+x)/(x^2-2*x-2)/(x^3-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}-1}}+\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}-1}}-\frac{\sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}-1}}-\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}-1}}$&$702$\\ elliptic&$\frac{\sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}-1}}+\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}-1}}-\frac{\sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}-1}}-\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}-1}}$&$702$\\ \hline \end{longtable}"," ",0,"1/2*(-1/(-3/2-1/2*I*3^(1/2))+1/(-3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)*EllipticPi(((-1+x)/(-3/2-1/2*I*3^(1/2)))^(1/2),-1/3*(3/2+1/2*I*3^(1/2))*3^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)+1/2*I*(-1/(-3/2-1/2*I*3^(1/2))+1/(-3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)*EllipticPi(((-1+x)/(-3/2-1/2*I*3^(1/2)))^(1/2),-1/3*(3/2+1/2*I*3^(1/2))*3^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-1/2*(-1/(-3/2-1/2*I*3^(1/2))+1/(-3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)*EllipticPi(((-1+x)/(-3/2-1/2*I*3^(1/2)))^(1/2),1/3*(3/2+1/2*I*3^(1/2))*3^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)-1/2*I*(-1/(-3/2-1/2*I*3^(1/2))+1/(-3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)*EllipticPi(((-1+x)/(-3/2-1/2*I*3^(1/2)))^(1/2),1/3*(3/2+1/2*I*3^(1/2))*3^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))","C"
1371,1,592,75,3.086000," ","int((x^2-x+3)/(x^2-2*x-2)/(x^3-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)^{2}+30\right) \ln \left(-\frac{3888 \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)^{2}+30\right) \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)^{4} x^{2}+7776 x \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)^{4} \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)^{2}+30\right)+8280 \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)^{2} \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)^{2}+30\right) x^{2}+10512 \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)^{2} \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)^{2}+30\right) x +44352 \sqrt{x^{3}-1}\, \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)^{2}+6048 \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)^{2} \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)^{2}+30\right)+4147 \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)^{2}+30\right) x^{2}+286 \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)^{2}+30\right) x +44352 \sqrt{x^{3}-1}+8008 \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)^{2}+30\right)}{\left(36 x \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)^{2}+29 x +28\right)^{2}}\right)}{12}+\frac{\RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right) \ln \left(\frac{3888 x^{2} \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)^{5}+7776 x \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)^{5}-1800 \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)^{3} x^{2}+2448 \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)^{3} x -6048 \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)^{3}+7392 \sqrt{x^{3}-1}\, \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)^{2}-53 \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right) x^{2}-3074 \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right) x +2968 \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)-1232 \sqrt{x^{3}-1}}{\left(36 x \RootOf \left(432 \textit{\_Z}^{4}+360 \textit{\_Z}^{2}-121\right)^{2}+x -28\right)^{2}}\right)}{2}$&$592$\\ default&$\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{3 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}-1}}+\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}+\frac{\sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}-1}}+\frac{3 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}-1}}+\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}-\frac{\sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}-1}}$&$1517$\\ elliptic&$-\frac{3 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}+\frac{3 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}-1}}+\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}+\frac{\sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}-1}}+\frac{3 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}-1}}+\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}-\frac{\sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}-1}}$&$1726$\\ \hline \end{longtable}"," ",0,"-1/12*RootOf(_Z^2+36*RootOf(432*_Z^4+360*_Z^2-121)^2+30)*ln(-(3888*RootOf(_Z^2+36*RootOf(432*_Z^4+360*_Z^2-121)^2+30)*RootOf(432*_Z^4+360*_Z^2-121)^4*x^2+7776*x*RootOf(432*_Z^4+360*_Z^2-121)^4*RootOf(_Z^2+36*RootOf(432*_Z^4+360*_Z^2-121)^2+30)+8280*RootOf(432*_Z^4+360*_Z^2-121)^2*RootOf(_Z^2+36*RootOf(432*_Z^4+360*_Z^2-121)^2+30)*x^2+10512*RootOf(432*_Z^4+360*_Z^2-121)^2*RootOf(_Z^2+36*RootOf(432*_Z^4+360*_Z^2-121)^2+30)*x+44352*(x^3-1)^(1/2)*RootOf(432*_Z^4+360*_Z^2-121)^2+6048*RootOf(432*_Z^4+360*_Z^2-121)^2*RootOf(_Z^2+36*RootOf(432*_Z^4+360*_Z^2-121)^2+30)+4147*RootOf(_Z^2+36*RootOf(432*_Z^4+360*_Z^2-121)^2+30)*x^2+286*RootOf(_Z^2+36*RootOf(432*_Z^4+360*_Z^2-121)^2+30)*x+44352*(x^3-1)^(1/2)+8008*RootOf(_Z^2+36*RootOf(432*_Z^4+360*_Z^2-121)^2+30))/(36*x*RootOf(432*_Z^4+360*_Z^2-121)^2+29*x+28)^2)+1/2*RootOf(432*_Z^4+360*_Z^2-121)*ln((3888*x^2*RootOf(432*_Z^4+360*_Z^2-121)^5+7776*x*RootOf(432*_Z^4+360*_Z^2-121)^5-1800*RootOf(432*_Z^4+360*_Z^2-121)^3*x^2+2448*RootOf(432*_Z^4+360*_Z^2-121)^3*x-6048*RootOf(432*_Z^4+360*_Z^2-121)^3+7392*(x^3-1)^(1/2)*RootOf(432*_Z^4+360*_Z^2-121)^2-53*RootOf(432*_Z^4+360*_Z^2-121)*x^2-3074*RootOf(432*_Z^4+360*_Z^2-121)*x+2968*RootOf(432*_Z^4+360*_Z^2-121)-1232*(x^3-1)^(1/2))/(36*x*RootOf(432*_Z^4+360*_Z^2-121)^2+x-28)^2)","C"
1372,1,584,75,2.779000," ","int((x^2+2*x)/(x^2-2*x-2)/(x^3-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right) \ln \left(\frac{243 \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)^{5} x^{2}+486 \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)^{5} x -306 x^{2} \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)^{3}-396 x \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)^{3}-216 \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)^{3}+48 \sqrt{x^{3}-1}\, \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)^{2}+95 \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right) x^{2}+38 \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right) x +152 \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)-32 \sqrt{x^{3}-1}}{\left(9 \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)^{2} x -5 x -4\right)^{2}}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{2}+9 \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)^{2}-6\right) \ln \left(\frac{243 \RootOf \left(\textit{\_Z}^{2}+9 \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)^{2}-6\right) \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)^{4} x^{2}+486 \RootOf \left(\textit{\_Z}^{2}+9 \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)^{2}-6\right) \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)^{4} x -18 \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+9 \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)^{2}-6\right) x^{2}-252 \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+9 \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)^{2}-6\right) x +216 \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+9 \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)^{2}-6\right)-144 \sqrt{x^{3}-1}\, \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)^{2}-\RootOf \left(\textit{\_Z}^{2}+9 \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)^{2}-6\right) x^{2}-10 \RootOf \left(\textit{\_Z}^{2}+9 \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)^{2}-6\right) x +8 \RootOf \left(\textit{\_Z}^{2}+9 \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)^{2}-6\right)}{\left(9 \RootOf \left(27 \textit{\_Z}^{4}-18 \textit{\_Z}^{2}-1\right)^{2} x -x +4\right)^{2}}\right)}{6}$&$584$\\ default&$\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{3 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{2 i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}+\frac{2 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}+\frac{3 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{2 i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}-\frac{2 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}$&$1517$\\ elliptic&$-\frac{3 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}+\frac{3 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{2 i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}+\frac{2 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}-\frac{2 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}+\frac{3 \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{2 i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{i \sqrt{-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{-1+x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}-1}}$&$1726$\\ \hline \end{longtable}"," ",0,"-1/2*RootOf(27*_Z^4-18*_Z^2-1)*ln((243*RootOf(27*_Z^4-18*_Z^2-1)^5*x^2+486*RootOf(27*_Z^4-18*_Z^2-1)^5*x-306*x^2*RootOf(27*_Z^4-18*_Z^2-1)^3-396*x*RootOf(27*_Z^4-18*_Z^2-1)^3-216*RootOf(27*_Z^4-18*_Z^2-1)^3+48*(x^3-1)^(1/2)*RootOf(27*_Z^4-18*_Z^2-1)^2+95*RootOf(27*_Z^4-18*_Z^2-1)*x^2+38*RootOf(27*_Z^4-18*_Z^2-1)*x+152*RootOf(27*_Z^4-18*_Z^2-1)-32*(x^3-1)^(1/2))/(9*RootOf(27*_Z^4-18*_Z^2-1)^2*x-5*x-4)^2)-1/6*RootOf(_Z^2+9*RootOf(27*_Z^4-18*_Z^2-1)^2-6)*ln((243*RootOf(_Z^2+9*RootOf(27*_Z^4-18*_Z^2-1)^2-6)*RootOf(27*_Z^4-18*_Z^2-1)^4*x^2+486*RootOf(_Z^2+9*RootOf(27*_Z^4-18*_Z^2-1)^2-6)*RootOf(27*_Z^4-18*_Z^2-1)^4*x-18*RootOf(27*_Z^4-18*_Z^2-1)^2*RootOf(_Z^2+9*RootOf(27*_Z^4-18*_Z^2-1)^2-6)*x^2-252*RootOf(27*_Z^4-18*_Z^2-1)^2*RootOf(_Z^2+9*RootOf(27*_Z^4-18*_Z^2-1)^2-6)*x+216*RootOf(27*_Z^4-18*_Z^2-1)^2*RootOf(_Z^2+9*RootOf(27*_Z^4-18*_Z^2-1)^2-6)-144*(x^3-1)^(1/2)*RootOf(27*_Z^4-18*_Z^2-1)^2-RootOf(_Z^2+9*RootOf(27*_Z^4-18*_Z^2-1)^2-6)*x^2-10*RootOf(_Z^2+9*RootOf(27*_Z^4-18*_Z^2-1)^2-6)*x+8*RootOf(_Z^2+9*RootOf(27*_Z^4-18*_Z^2-1)^2-6))/(9*RootOf(27*_Z^4-18*_Z^2-1)^2*x-x+4)^2)","C"
1373,1,91,77,3.002000," ","int((x^3-1)^(1/3)*(x^3+1)/x^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{5 x^{6}-2 x^{3}-3}{18 x^{6} \left(x^{3}-1\right)^{\frac{2}{3}}}+\frac{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} \left(\frac{2 \Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 2\right], x^{3}\right)}{3}+\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{2}{3}\right)\right)}{27 \Gamma \left(\frac{2}{3}\right) \mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}}}$&$91$\\ meijerg&$\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \left(-\frac{\Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 3\right], x^{3}\right)}{3}-\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+3 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{2}{3}\right)-\frac{3 \Gamma \left(\frac{2}{3}\right)}{x^{3}}\right)}{9 \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}}}-\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \left(\frac{5 \Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{8}{3}\right], \left[2, 4\right], x^{3}\right)}{27}+\frac{\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{2}{3}\right)}{3}+\frac{3 \Gamma \left(\frac{2}{3}\right)}{2 x^{6}}-\frac{\Gamma \left(\frac{2}{3}\right)}{x^{3}}\right)}{9 \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}}}$&$156$\\ trager&$-\frac{\left(5 x^{3}+3\right) \left(x^{3}-1\right)^{\frac{1}{3}}}{18 x^{6}}+\frac{4 \ln \left(-\frac{32768 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)^{2} x^{3}+4416 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right) x^{3}+2496 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}+91 x^{3}-262144 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)^{2}-6720 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)+144 \left(x^{3}-1\right)^{\frac{2}{3}}-13312 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)+39 \left(x^{3}-1\right)^{\frac{1}{3}}-169}{x^{3}}\right)}{27}-\frac{4 \ln \left(\frac{6754304 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)^{2} x^{3}-619712 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right) x^{3}-352128 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}-1266 x^{3}-54034432 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)^{2}+911808 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)-19749 \left(x^{3}-1\right)^{\frac{2}{3}}+419648 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)-5502 \left(x^{3}-1\right)^{\frac{1}{3}}+1055}{x^{3}}\right)}{27}-\frac{256 \ln \left(\frac{6754304 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)^{2} x^{3}-619712 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right) x^{3}-352128 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}-1266 x^{3}-54034432 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)^{2}+911808 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)-19749 \left(x^{3}-1\right)^{\frac{2}{3}}+419648 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)-5502 \left(x^{3}-1\right)^{\frac{1}{3}}+1055}{x^{3}}\right) \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)}{27}$&$435$\\ \hline \end{longtable}"," ",0,"-1/18*(5*x^6-2*x^3-3)/x^6/(x^3-1)^(2/3)+4/27/GAMMA(2/3)/signum(x^3-1)^(2/3)*(-signum(x^3-1))^(2/3)*(2/3*GAMMA(2/3)*x^3*hypergeom([1,1,5/3],[2,2],x^3)+(1/6*Pi*3^(1/2)-3/2*ln(3)+3*ln(x)+I*Pi)*GAMMA(2/3))","C"
1374,1,91,77,3.058000," ","int((x^3-1)^(1/3)*(2*x^3-1)/x^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{13 x^{6}-16 x^{3}+3}{18 x^{6} \left(x^{3}-1\right)^{\frac{2}{3}}}+\frac{5 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} \left(\frac{2 \Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 2\right], x^{3}\right)}{3}+\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{2}{3}\right)\right)}{27 \Gamma \left(\frac{2}{3}\right) \mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}}}$&$91$\\ meijerg&$\frac{2 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \left(-\frac{\Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 3\right], x^{3}\right)}{3}-\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+3 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{2}{3}\right)-\frac{3 \Gamma \left(\frac{2}{3}\right)}{x^{3}}\right)}{9 \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}}}+\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \left(\frac{5 \Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{8}{3}\right], \left[2, 4\right], x^{3}\right)}{27}+\frac{\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{2}{3}\right)}{3}+\frac{3 \Gamma \left(\frac{2}{3}\right)}{2 x^{6}}-\frac{\Gamma \left(\frac{2}{3}\right)}{x^{3}}\right)}{9 \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}}}$&$156$\\ trager&$-\frac{\left(13 x^{3}-3\right) \left(x^{3}-1\right)^{\frac{1}{3}}}{18 x^{6}}+\frac{5 \ln \left(-\frac{864256 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)^{2} x^{3}-173056 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right) x^{3}+352128 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}+8628 x^{3}-6914048 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)^{2}+1263936 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)+19749 \left(x^{3}-1\right)^{\frac{2}{3}}+803776 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)+14247 \left(x^{3}-1\right)^{\frac{1}{3}}-7190}{x^{3}}\right)}{27}+\frac{320 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right) \ln \left(\frac{6754304 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)^{2} x^{3}+830784 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right) x^{3}+352128 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}+10066 x^{3}-54034432 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)^{2}-911808 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)-14247 \left(x^{3}-1\right)^{\frac{2}{3}}-2108224 \RootOf \left(4096 \textit{\_Z}^{2}+64 \textit{\_Z} +1\right)-19749 \left(x^{3}-1\right)^{\frac{1}{3}}-18694}{x^{3}}\right)}{27}$&$301$\\ \hline \end{longtable}"," ",0,"-1/18*(13*x^6-16*x^3+3)/x^6/(x^3-1)^(2/3)+5/27/GAMMA(2/3)/signum(x^3-1)^(2/3)*(-signum(x^3-1))^(2/3)*(2/3*GAMMA(2/3)*x^3*hypergeom([1,1,5/3],[2,2],x^3)+(1/6*Pi*3^(1/2)-3/2*ln(3)+3*ln(x)+I*Pi)*GAMMA(2/3))","C"
1375,0,0,87,0.020000," ","int((a^2-2*a*x+x^2)*(-2*a*b*x+(3*a-b)*x^2)/(x^2*(-a+x)*(-b+x))^(3/4)/(a^3*d-3*a^2*d*x+(3*a*d-b)*x^2+(1-d)*x^3),x)","\[\int \frac{\left(a^{2}-2 a x +x^{2}\right) \left(-2 a b x +\left(3 a -b \right) x^{2}\right)}{\left(x^{2} \left(-a +x \right) \left(-b +x \right)\right)^{\frac{3}{4}} \left(a^{3} d -3 a^{2} d x +\left(3 a d -b \right) x^{2}+\left(1-d \right) x^{3}\right)}\, dx\]"," ",0,"int((a^2-2*a*x+x^2)*(-2*a*b*x+(3*a-b)*x^2)/(x^2*(-a+x)*(-b+x))^(3/4)/(a^3*d-3*a^2*d*x+(3*a*d-b)*x^2+(1-d)*x^3),x)","F"
1376,1,841,77,4.237000," ","int((x^2+1)/((2*x^2-x-2)/(x^2+x-1))^(1/2)/(x^4-x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2}+10\right) \ln \left(-\frac{-1620 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2}+10\right) \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{4} x +260 \sqrt{-\frac{-2 x^{2}+x +2}{x^{2}+x -1}}\, \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2} x^{2}+459 \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2}+10\right) x^{2}+260 \sqrt{-\frac{-2 x^{2}+x +2}{x^{2}+x -1}}\, \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2} x -207 \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2}+10\right) x -260 \sqrt{-\frac{-2 x^{2}+x +2}{x^{2}+x -1}}\, \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2}+265 \sqrt{-\frac{-2 x^{2}+x +2}{x^{2}+x -1}}\, x^{2}-459 \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2}+10\right)+51 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2}+10\right) x^{2}+265 \sqrt{-\frac{-2 x^{2}+x +2}{x^{2}+x -1}}\, x -3 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2}+10\right) x -265 \sqrt{-\frac{-2 x^{2}+x +2}{x^{2}+x -1}}-51 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2}+10\right)}{3 x^{2}+20 \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2} x +x -3}\right)}{10}-\RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right) \ln \left(\frac{-16200 \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{5} x +260 \sqrt{-\frac{-2 x^{2}+x +2}{x^{2}+x -1}}\, \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2} x^{2}-4590 \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{3} x^{2}+260 \sqrt{-\frac{-2 x^{2}+x +2}{x^{2}+x -1}}\, \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2} x -1170 \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{3} x -260 \sqrt{-\frac{-2 x^{2}+x +2}{x^{2}+x -1}}\, \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2}-239 \sqrt{-\frac{-2 x^{2}+x +2}{x^{2}+x -1}}\, x^{2}+4590 \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{3}+51 \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right) x^{2}-239 \sqrt{-\frac{-2 x^{2}+x +2}{x^{2}+x -1}}\, x +15 \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right) x +239 \sqrt{-\frac{-2 x^{2}+x +2}{x^{2}+x -1}}-51 \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)}{20 \RootOf \left(40 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)^{2} x -3 x^{2}+x +3}\right)$&$841$\\ default&$\text{Expression too large to display}$&$7672$\\ \hline \end{longtable}"," ",0,"1/10*RootOf(_Z^2+100*RootOf(40*_Z^4+4*_Z^2+1)^2+10)*ln(-(-1620*RootOf(_Z^2+100*RootOf(40*_Z^4+4*_Z^2+1)^2+10)*RootOf(40*_Z^4+4*_Z^2+1)^4*x+260*(-(-2*x^2+x+2)/(x^2+x-1))^(1/2)*RootOf(40*_Z^4+4*_Z^2+1)^2*x^2+459*RootOf(40*_Z^4+4*_Z^2+1)^2*RootOf(_Z^2+100*RootOf(40*_Z^4+4*_Z^2+1)^2+10)*x^2+260*(-(-2*x^2+x+2)/(x^2+x-1))^(1/2)*RootOf(40*_Z^4+4*_Z^2+1)^2*x-207*RootOf(40*_Z^4+4*_Z^2+1)^2*RootOf(_Z^2+100*RootOf(40*_Z^4+4*_Z^2+1)^2+10)*x-260*(-(-2*x^2+x+2)/(x^2+x-1))^(1/2)*RootOf(40*_Z^4+4*_Z^2+1)^2+265*(-(-2*x^2+x+2)/(x^2+x-1))^(1/2)*x^2-459*RootOf(40*_Z^4+4*_Z^2+1)^2*RootOf(_Z^2+100*RootOf(40*_Z^4+4*_Z^2+1)^2+10)+51*RootOf(_Z^2+100*RootOf(40*_Z^4+4*_Z^2+1)^2+10)*x^2+265*(-(-2*x^2+x+2)/(x^2+x-1))^(1/2)*x-3*RootOf(_Z^2+100*RootOf(40*_Z^4+4*_Z^2+1)^2+10)*x-265*(-(-2*x^2+x+2)/(x^2+x-1))^(1/2)-51*RootOf(_Z^2+100*RootOf(40*_Z^4+4*_Z^2+1)^2+10))/(3*x^2+20*RootOf(40*_Z^4+4*_Z^2+1)^2*x+x-3))-RootOf(40*_Z^4+4*_Z^2+1)*ln((-16200*RootOf(40*_Z^4+4*_Z^2+1)^5*x+260*(-(-2*x^2+x+2)/(x^2+x-1))^(1/2)*RootOf(40*_Z^4+4*_Z^2+1)^2*x^2-4590*RootOf(40*_Z^4+4*_Z^2+1)^3*x^2+260*(-(-2*x^2+x+2)/(x^2+x-1))^(1/2)*RootOf(40*_Z^4+4*_Z^2+1)^2*x-1170*RootOf(40*_Z^4+4*_Z^2+1)^3*x-260*(-(-2*x^2+x+2)/(x^2+x-1))^(1/2)*RootOf(40*_Z^4+4*_Z^2+1)^2-239*(-(-2*x^2+x+2)/(x^2+x-1))^(1/2)*x^2+4590*RootOf(40*_Z^4+4*_Z^2+1)^3+51*RootOf(40*_Z^4+4*_Z^2+1)*x^2-239*(-(-2*x^2+x+2)/(x^2+x-1))^(1/2)*x+15*RootOf(40*_Z^4+4*_Z^2+1)*x+239*(-(-2*x^2+x+2)/(x^2+x-1))^(1/2)-51*RootOf(40*_Z^4+4*_Z^2+1))/(20*RootOf(40*_Z^4+4*_Z^2+1)^2*x-3*x^2+x+3))","C"
1377,0,0,48,0.014000," ","int((a*x^4-2*b)/x^4/(a*x^4+b)/(a*x^4-b*x^2)^(1/4),x)","\[\int \frac{a \,x^{4}-2 b}{x^{4} \left(a \,x^{4}+b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^4-2*b)/x^4/(a*x^4+b)/(a*x^4-b*x^2)^(1/4),x)","F"
1378,0,0,48,0.001000," ","int((a*x^4-2*b)/x^4/(a*x^4+b)/(a*x^4-b*x^2)^(1/4),x)","\[\int \frac{a \,x^{4}-2 b}{x^{4} \left(a \,x^{4}+b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^4-2*b)/x^4/(a*x^4+b)/(a*x^4-b*x^2)^(1/4),x)","F"
1379,0,0,79,0.020000," ","int((a*x^4+b*x^3)^(1/4),x)","\[\int \left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}\, dx\]"," ",0,"int((a*x^4+b*x^3)^(1/4),x)","F"
1380,1,108,77,8.235000," ","int(1/x^13/(x^6-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{4 x^{12}-x^{6}-3}{36 x^{12} \left(x^{6}-1\right)^{\frac{1}{3}}}+\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} \left(\frac{2 \pi  \sqrt{3}\, x^{6} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], x^{6}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+6 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{54 \pi  \mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}}}$&$108$\\ meijerg&$\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} \left(\frac{28 \pi  \sqrt{3}\, x^{6} \hypergeom \left(\left[1, 1, \frac{10}{3}\right], \left[2, 4\right], x^{6}\right)}{243 \Gamma \left(\frac{2}{3}\right)}+\frac{4 \left(\frac{9}{4}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+6 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{27 \Gamma \left(\frac{2}{3}\right)}-\frac{\pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right) x^{12}}-\frac{2 \pi  \sqrt{3}}{9 \Gamma \left(\frac{2}{3}\right) x^{6}}\right)}{12 \pi  \mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}}}$&$110$\\ trager&$\frac{\left(x^{6}-1\right)^{\frac{2}{3}} \left(4 x^{6}+3\right)}{36 x^{12}}+\frac{\ln \left(-\frac{100217735779212520130799137193984 \RootOf \left(66588770304 \textit{\_Z}^{2}-258048 \textit{\_Z} +1\right)^{2} x^{6}+23595573475745213987715084288 \RootOf \left(66588770304 \textit{\_Z}^{2}-258048 \textit{\_Z} +1\right) x^{6}-116115113033469041646202 x^{6}-17616242845163488187704025088 \left(x^{6}-1\right)^{\frac{2}{3}} \RootOf \left(66588770304 \textit{\_Z}^{2}-258048 \textit{\_Z} +1\right)-6413935089869601288371144780414976 \RootOf \left(66588770304 \textit{\_Z}^{2}-258048 \textit{\_Z} +1\right)^{2}+17616242845163488187704025088 \RootOf \left(66588770304 \textit{\_Z}^{2}-258048 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}}+210563861480318360105175 \left(x^{6}-1\right)^{\frac{2}{3}}+7239346385791997955847348224 \RootOf \left(66588770304 \textit{\_Z}^{2}-258048 \textit{\_Z} +1\right)-210563861480318360105175 \left(x^{6}-1\right)^{\frac{1}{3}}+114242288629703411942231}{x^{6}}\right)}{27}-\frac{28672 \ln \left(-\frac{100217735779212520130799137193984 \RootOf \left(66588770304 \textit{\_Z}^{2}-258048 \textit{\_Z} +1\right)^{2} x^{6}+23595573475745213987715084288 \RootOf \left(66588770304 \textit{\_Z}^{2}-258048 \textit{\_Z} +1\right) x^{6}-116115113033469041646202 x^{6}-17616242845163488187704025088 \left(x^{6}-1\right)^{\frac{2}{3}} \RootOf \left(66588770304 \textit{\_Z}^{2}-258048 \textit{\_Z} +1\right)-6413935089869601288371144780414976 \RootOf \left(66588770304 \textit{\_Z}^{2}-258048 \textit{\_Z} +1\right)^{2}+17616242845163488187704025088 \RootOf \left(66588770304 \textit{\_Z}^{2}-258048 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}}+210563861480318360105175 \left(x^{6}-1\right)^{\frac{2}{3}}+7239346385791997955847348224 \RootOf \left(66588770304 \textit{\_Z}^{2}-258048 \textit{\_Z} +1\right)-210563861480318360105175 \left(x^{6}-1\right)^{\frac{1}{3}}+114242288629703411942231}{x^{6}}\right) \RootOf \left(66588770304 \textit{\_Z}^{2}-258048 \textit{\_Z} +1\right)}{3}+\frac{28672 \RootOf \left(66588770304 \textit{\_Z}^{2}-258048 \textit{\_Z} +1\right) \ln \left(-\frac{100217735779212520130799137193984 \RootOf \left(66588770304 \textit{\_Z}^{2}-258048 \textit{\_Z} +1\right)^{2} x^{6}-24372310639212572929701064704 \RootOf \left(66588770304 \textit{\_Z}^{2}-258048 \textit{\_Z} +1\right) x^{6}-23171389162410581752275 x^{6}+17616242845163488187704025088 \left(x^{6}-1\right)^{\frac{2}{3}} \RootOf \left(66588770304 \textit{\_Z}^{2}-258048 \textit{\_Z} +1\right)-6413935089869601288371144780414976 \RootOf \left(66588770304 \textit{\_Z}^{2}-258048 \textit{\_Z} +1\right)^{2}-17616242845163488187704025088 \RootOf \left(66588770304 \textit{\_Z}^{2}-258048 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}}+142296551347461340528569 \left(x^{6}-1\right)^{\frac{2}{3}}+42471832076118974331255398400 \RootOf \left(66588770304 \textit{\_Z}^{2}-258048 \textit{\_Z} +1\right)-142296551347461340528569 \left(x^{6}-1\right)^{\frac{1}{3}}+45974978496846392365625}{x^{6}}\right)}{3}$&$448$\\ \hline \end{longtable}"," ",0,"1/36*(4*x^12-x^6-3)/x^12/(x^6-1)^(1/3)+1/54/Pi*3^(1/2)*GAMMA(2/3)/signum(x^6-1)^(1/3)*(-signum(x^6-1))^(1/3)*(2/9*Pi*3^(1/2)/GAMMA(2/3)*x^6*hypergeom([1,1,4/3],[2,2],x^6)+2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)+6*ln(x)+I*Pi)*Pi*3^(1/2)/GAMMA(2/3))","C"
1381,0,0,11,0.023000," ","int((2*a*x^4+b)/(a*x^4+b)^(1/4)/(x^8-a*x^4-2*b),x)","\[\int \frac{2 a \,x^{4}+b}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(x^{8}-a \,x^{4}-2 b \right)}\, dx\]"," ",0,"int((2*a*x^4+b)/(a*x^4+b)^(1/4)/(x^8-a*x^4-2*b),x)","F"
1382,0,0,11,0.025000," ","int((a*x^4+2*b)/(a*x^4+b*x^2)^(1/4)/(2*x^8-a*x^4-b),x)","\[\int \frac{a \,x^{4}+2 b}{\left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}} \left(2 x^{8}-a \,x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^4+2*b)/(a*x^4+b*x^2)^(1/4)/(2*x^8-a*x^4-b),x)","F"
1383,0,0,11,0.001000," ","int((a*x^4+2*b)/(a*x^4+b*x^2)^(1/4)/(2*x^8-a*x^4-b),x)","\[\int \frac{a \,x^{4}+2 b}{\left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}} \left(2 x^{8}-a \,x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^4+2*b)/(a*x^4+b*x^2)^(1/4)/(2*x^8-a*x^4-b),x)","F"
1384,1,867,83,0.082000," ","int((2*x^2-1)*(4*x^4-4*x^2+4*x-1)/((-2*x^2+1)/(2*x^2+1))^(1/2)/(2*x^2+1)/(8*x^8-32*x^7+56*x^6-64*x^5+46*x^4-40*x^3+32*x^2-8*x-1),x)","\[\frac{\left(2 x^{2}-1\right) \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(8 \textit{\_Z}^{8}-32 \textit{\_Z}^{7}+56 \textit{\_Z}^{6}-64 \textit{\_Z}^{5}+46 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+32 \textit{\_Z}^{2}-8 \textit{\_Z} -1\right)}{\sum}\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{3}-2 \underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  -1\right) \left(8 \sqrt{2}\, \sqrt{-4 \underline{\hspace{1.25 ex}}\alpha^{4}+1}\, \sqrt{-2 x^{2}+1}\, \sqrt{2 x^{2}+1}\, \EllipticPi \left(\sqrt{2}\, x , -32 \underline{\hspace{1.25 ex}}\alpha^{7}+132 \underline{\hspace{1.25 ex}}\alpha^{6}-240 \underline{\hspace{1.25 ex}}\alpha^{5}+284 \underline{\hspace{1.25 ex}}\alpha^{4}-216 \underline{\hspace{1.25 ex}}\alpha^{3}+183 \underline{\hspace{1.25 ex}}\alpha^{2}-148 \underline{\hspace{1.25 ex}}\alpha  +48, \frac{\sqrt{-2}\, \sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha^{7}-32 \sqrt{2}\, \sqrt{-4 \underline{\hspace{1.25 ex}}\alpha^{4}+1}\, \sqrt{-2 x^{2}+1}\, \sqrt{2 x^{2}+1}\, \EllipticPi \left(\sqrt{2}\, x , -32 \underline{\hspace{1.25 ex}}\alpha^{7}+132 \underline{\hspace{1.25 ex}}\alpha^{6}-240 \underline{\hspace{1.25 ex}}\alpha^{5}+284 \underline{\hspace{1.25 ex}}\alpha^{4}-216 \underline{\hspace{1.25 ex}}\alpha^{3}+183 \underline{\hspace{1.25 ex}}\alpha^{2}-148 \underline{\hspace{1.25 ex}}\alpha  +48, \frac{\sqrt{-2}\, \sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha^{6}+56 \sqrt{2}\, \sqrt{-4 \underline{\hspace{1.25 ex}}\alpha^{4}+1}\, \sqrt{-2 x^{2}+1}\, \sqrt{2 x^{2}+1}\, \EllipticPi \left(\sqrt{2}\, x , -32 \underline{\hspace{1.25 ex}}\alpha^{7}+132 \underline{\hspace{1.25 ex}}\alpha^{6}-240 \underline{\hspace{1.25 ex}}\alpha^{5}+284 \underline{\hspace{1.25 ex}}\alpha^{4}-216 \underline{\hspace{1.25 ex}}\alpha^{3}+183 \underline{\hspace{1.25 ex}}\alpha^{2}-148 \underline{\hspace{1.25 ex}}\alpha  +48, \frac{\sqrt{-2}\, \sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha^{5}-64 \sqrt{2}\, \sqrt{-4 \underline{\hspace{1.25 ex}}\alpha^{4}+1}\, \sqrt{-2 x^{2}+1}\, \sqrt{2 x^{2}+1}\, \EllipticPi \left(\sqrt{2}\, x , -32 \underline{\hspace{1.25 ex}}\alpha^{7}+132 \underline{\hspace{1.25 ex}}\alpha^{6}-240 \underline{\hspace{1.25 ex}}\alpha^{5}+284 \underline{\hspace{1.25 ex}}\alpha^{4}-216 \underline{\hspace{1.25 ex}}\alpha^{3}+183 \underline{\hspace{1.25 ex}}\alpha^{2}-148 \underline{\hspace{1.25 ex}}\alpha  +48, \frac{\sqrt{-2}\, \sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha^{4}+46 \sqrt{2}\, \sqrt{-4 \underline{\hspace{1.25 ex}}\alpha^{4}+1}\, \sqrt{-2 x^{2}+1}\, \sqrt{2 x^{2}+1}\, \EllipticPi \left(\sqrt{2}\, x , -32 \underline{\hspace{1.25 ex}}\alpha^{7}+132 \underline{\hspace{1.25 ex}}\alpha^{6}-240 \underline{\hspace{1.25 ex}}\alpha^{5}+284 \underline{\hspace{1.25 ex}}\alpha^{4}-216 \underline{\hspace{1.25 ex}}\alpha^{3}+183 \underline{\hspace{1.25 ex}}\alpha^{2}-148 \underline{\hspace{1.25 ex}}\alpha  +48, \frac{\sqrt{-2}\, \sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha^{3}-40 \sqrt{2}\, \sqrt{-4 \underline{\hspace{1.25 ex}}\alpha^{4}+1}\, \sqrt{-2 x^{2}+1}\, \sqrt{2 x^{2}+1}\, \EllipticPi \left(\sqrt{2}\, x , -32 \underline{\hspace{1.25 ex}}\alpha^{7}+132 \underline{\hspace{1.25 ex}}\alpha^{6}-240 \underline{\hspace{1.25 ex}}\alpha^{5}+284 \underline{\hspace{1.25 ex}}\alpha^{4}-216 \underline{\hspace{1.25 ex}}\alpha^{3}+183 \underline{\hspace{1.25 ex}}\alpha^{2}-148 \underline{\hspace{1.25 ex}}\alpha  +48, \frac{\sqrt{-2}\, \sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha^{2}+32 \sqrt{2}\, \sqrt{-4 \underline{\hspace{1.25 ex}}\alpha^{4}+1}\, \sqrt{-2 x^{2}+1}\, \sqrt{2 x^{2}+1}\, \EllipticPi \left(\sqrt{2}\, x , -32 \underline{\hspace{1.25 ex}}\alpha^{7}+132 \underline{\hspace{1.25 ex}}\alpha^{6}-240 \underline{\hspace{1.25 ex}}\alpha^{5}+284 \underline{\hspace{1.25 ex}}\alpha^{4}-216 \underline{\hspace{1.25 ex}}\alpha^{3}+183 \underline{\hspace{1.25 ex}}\alpha^{2}-148 \underline{\hspace{1.25 ex}}\alpha  +48, \frac{\sqrt{-2}\, \sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha  -8 \sqrt{2}\, \sqrt{-2 x^{2}+1}\, \sqrt{2 x^{2}+1}\, \EllipticPi \left(\sqrt{2}\, x , -32 \underline{\hspace{1.25 ex}}\alpha^{7}+132 \underline{\hspace{1.25 ex}}\alpha^{6}-240 \underline{\hspace{1.25 ex}}\alpha^{5}+284 \underline{\hspace{1.25 ex}}\alpha^{4}-216 \underline{\hspace{1.25 ex}}\alpha^{3}+183 \underline{\hspace{1.25 ex}}\alpha^{2}-148 \underline{\hspace{1.25 ex}}\alpha  +48, \frac{\sqrt{-2}\, \sqrt{2}}{2}\right) \sqrt{-4 \underline{\hspace{1.25 ex}}\alpha^{4}+1}-\arctanh \left(\frac{2 \underline{\hspace{1.25 ex}}\alpha^{2} \left(32 \underline{\hspace{1.25 ex}}\alpha^{7}-132 \underline{\hspace{1.25 ex}}\alpha^{6}+240 \underline{\hspace{1.25 ex}}\alpha^{5}-284 \underline{\hspace{1.25 ex}}\alpha^{4}+216 \underline{\hspace{1.25 ex}}\alpha^{3}-183 \underline{\hspace{1.25 ex}}\alpha^{2}+2 x^{2}+148 \underline{\hspace{1.25 ex}}\alpha  -48\right)}{\sqrt{-4 \underline{\hspace{1.25 ex}}\alpha^{4}+1}\, \sqrt{-4 x^{4}+1}}\right) \sqrt{-4 x^{4}+1}\right)}{\sqrt{-4 \underline{\hspace{1.25 ex}}\alpha^{4}+1}\, \sqrt{-4 x^{4}+1}}\right)}{24 \sqrt{-\frac{2 x^{2}-1}{2 x^{2}+1}}\, \sqrt{-\left(2 x^{2}+1\right) \left(2 x^{2}-1\right)}}\]"," ",0,"1/24*(2*x^2-1)*sum((2*_alpha^3-2*_alpha^2+_alpha-1)*(8*2^(1/2)*(-4*_alpha^4+1)^(1/2)*(-2*x^2+1)^(1/2)*(2*x^2+1)^(1/2)*EllipticPi(2^(1/2)*x,-32*_alpha^7+132*_alpha^6-240*_alpha^5+284*_alpha^4-216*_alpha^3+183*_alpha^2-148*_alpha+48,1/2*(-2)^(1/2)*2^(1/2))*_alpha^7-32*2^(1/2)*(-4*_alpha^4+1)^(1/2)*(-2*x^2+1)^(1/2)*(2*x^2+1)^(1/2)*EllipticPi(2^(1/2)*x,-32*_alpha^7+132*_alpha^6-240*_alpha^5+284*_alpha^4-216*_alpha^3+183*_alpha^2-148*_alpha+48,1/2*(-2)^(1/2)*2^(1/2))*_alpha^6+56*2^(1/2)*(-4*_alpha^4+1)^(1/2)*(-2*x^2+1)^(1/2)*(2*x^2+1)^(1/2)*EllipticPi(2^(1/2)*x,-32*_alpha^7+132*_alpha^6-240*_alpha^5+284*_alpha^4-216*_alpha^3+183*_alpha^2-148*_alpha+48,1/2*(-2)^(1/2)*2^(1/2))*_alpha^5-64*2^(1/2)*(-4*_alpha^4+1)^(1/2)*(-2*x^2+1)^(1/2)*(2*x^2+1)^(1/2)*EllipticPi(2^(1/2)*x,-32*_alpha^7+132*_alpha^6-240*_alpha^5+284*_alpha^4-216*_alpha^3+183*_alpha^2-148*_alpha+48,1/2*(-2)^(1/2)*2^(1/2))*_alpha^4+46*2^(1/2)*(-4*_alpha^4+1)^(1/2)*(-2*x^2+1)^(1/2)*(2*x^2+1)^(1/2)*EllipticPi(2^(1/2)*x,-32*_alpha^7+132*_alpha^6-240*_alpha^5+284*_alpha^4-216*_alpha^3+183*_alpha^2-148*_alpha+48,1/2*(-2)^(1/2)*2^(1/2))*_alpha^3-40*2^(1/2)*(-4*_alpha^4+1)^(1/2)*(-2*x^2+1)^(1/2)*(2*x^2+1)^(1/2)*EllipticPi(2^(1/2)*x,-32*_alpha^7+132*_alpha^6-240*_alpha^5+284*_alpha^4-216*_alpha^3+183*_alpha^2-148*_alpha+48,1/2*(-2)^(1/2)*2^(1/2))*_alpha^2+32*2^(1/2)*(-4*_alpha^4+1)^(1/2)*(-2*x^2+1)^(1/2)*(2*x^2+1)^(1/2)*EllipticPi(2^(1/2)*x,-32*_alpha^7+132*_alpha^6-240*_alpha^5+284*_alpha^4-216*_alpha^3+183*_alpha^2-148*_alpha+48,1/2*(-2)^(1/2)*2^(1/2))*_alpha-8*2^(1/2)*(-2*x^2+1)^(1/2)*(2*x^2+1)^(1/2)*EllipticPi(2^(1/2)*x,-32*_alpha^7+132*_alpha^6-240*_alpha^5+284*_alpha^4-216*_alpha^3+183*_alpha^2-148*_alpha+48,1/2*(-2)^(1/2)*2^(1/2))*(-4*_alpha^4+1)^(1/2)-arctanh(2*_alpha^2*(32*_alpha^7-132*_alpha^6+240*_alpha^5-284*_alpha^4+216*_alpha^3-183*_alpha^2+2*x^2+148*_alpha-48)/(-4*_alpha^4+1)^(1/2)/(-4*x^4+1)^(1/2))*(-4*x^4+1)^(1/2))/(-4*_alpha^4+1)^(1/2)/(-4*x^4+1)^(1/2),_alpha=RootOf(8*_Z^8-32*_Z^7+56*_Z^6-64*_Z^5+46*_Z^4-40*_Z^3+32*_Z^2-8*_Z-1))/(-(2*x^2-1)/(2*x^2+1))^(1/2)/(-(2*x^2+1)*(2*x^2-1))^(1/2)","C"
1385,0,0,22,0.056000," ","int((x^2+1)^(1/2)/(x^2+(x+(x^2+1)^(1/2))^(1/2)),x)","\[\int \frac{\sqrt{x^{2}+1}}{x^{2}+\sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^2+1)^(1/2)/(x^2+(x+(x^2+1)^(1/2))^(1/2)),x)","F"
1386,0,0,22,0.000000," ","int((x^2+1)^(1/2)/(x^2+(x+(x^2+1)^(1/2))^(1/2)),x)","\[\int \frac{\sqrt{x^{2}+1}}{x^{2}+\sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^2+1)^(1/2)/(x^2+(x+(x^2+1)^(1/2))^(1/2)),x)","F"
1387,1,4734,94,0.429000," ","int((k*x^2+1)/(c*k*x+k*x^2-1)/((-x^2+1)*(-k^2*x^2+1))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\text{Expression too large to display}$&$4734$\\ default&$\text{Expression too large to display}$&$11680$\\ \hline \end{longtable}"," ",0,"1/4*c^3*k^2/(c^2*k^3*(c^2*k+4))^(1/2)*2^(1/2)/((k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3+2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)^(1/2)*ln(((k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3+2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2+(-k^2-1+c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)+2*k)*(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)+2*k)/k^2)+1/2*2^(1/2)*((k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3+2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)^(1/2)*(4*k^2*(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)+2*k)/k^2)^2+4*(-k^2-1+c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)+2*k)*(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)+2*k)/k^2)+2*(k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3+2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)^(1/2))/(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)+2*k)/k^2))+1/4*c*2^(1/2)/((k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3+2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)^(1/2)*ln(((k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3+2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2+(-k^2-1+c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)+2*k)*(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)+2*k)/k^2)+1/2*2^(1/2)*((k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3+2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)^(1/2)*(4*k^2*(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)+2*k)/k^2)^2+4*(-k^2-1+c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)+2*k)*(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)+2*k)/k^2)+2*(k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3+2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)^(1/2))/(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)+2*k)/k^2))+c*k/(c^2*k^3*(c^2*k+4))^(1/2)*2^(1/2)/((k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3+2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)^(1/2)*ln(((k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3+2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2+(-k^2-1+c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)+2*k)*(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)+2*k)/k^2)+1/2*2^(1/2)*((k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3+2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)^(1/2)*(4*k^2*(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)+2*k)/k^2)^2+4*(-k^2-1+c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)+2*k)*(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)+2*k)/k^2)+2*(k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3+2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)^(1/2))/(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)+2*k)/k^2))-1/4*c^3*k^2/(c^2*k^3*(c^2*k+4))^(1/2)*2^(1/2)/((k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3-2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)^(1/2)*ln(((k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3-2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2+(-k^2-1+c^2*k^2-(c^2*k^3*(c^2*k+4))^(1/2)+2*k)*(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)+1/2*2^(1/2)*((k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3-2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)^(1/2)*(4*k^2*(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)^2+4*(-k^2-1+c^2*k^2-(c^2*k^3*(c^2*k+4))^(1/2)+2*k)*(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)+2*(k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3-2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)^(1/2))/(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2))+1/4*c*2^(1/2)/((k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3-2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)^(1/2)*ln(((k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3-2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2+(-k^2-1+c^2*k^2-(c^2*k^3*(c^2*k+4))^(1/2)+2*k)*(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)+1/2*2^(1/2)*((k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3-2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)^(1/2)*(4*k^2*(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)^2+4*(-k^2-1+c^2*k^2-(c^2*k^3*(c^2*k+4))^(1/2)+2*k)*(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)+2*(k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3-2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)^(1/2))/(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2))-c*k/(c^2*k^3*(c^2*k+4))^(1/2)*2^(1/2)/((k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3-2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)^(1/2)*ln(((k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3-2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2+(-k^2-1+c^2*k^2-(c^2*k^3*(c^2*k+4))^(1/2)+2*k)*(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)+1/2*2^(1/2)*((k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3-2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)^(1/2)*(4*k^2*(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)^2+4*(-k^2-1+c^2*k^2-(c^2*k^3*(c^2*k+4))^(1/2)+2*k)*(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)+2*(k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k+4))^(1/2)*c^2*k^2+4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)*k^2-2*k^3-2*(c^2*k^3*(c^2*k+4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2)^(1/2))/(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k+4))^(1/2)-2*k)/k^2))-1/(2*c^2*k^2-2*k^2+4*k-2)^(1/2)*arctanh(((-x^2+1)*(-k^2*x^2+1))^(1/2)*2^(1/2)/x/(2*c^2*k^2-2*k^2+4*k-2)^(1/2))*2^(1/2)","B"
1388,1,4734,94,0.405000," ","int((k*x^2-1)/(c*k*x+k*x^2+1)/((-x^2+1)*(-k^2*x^2+1))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\text{Expression too large to display}$&$4734$\\ default&$\text{Expression too large to display}$&$11374$\\ \hline \end{longtable}"," ",0,"-1/4*c^3*k^2/(c^2*k^3*(c^2*k-4))^(1/2)*2^(1/2)/((k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3+2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)^(1/2)*ln(((k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3+2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2+(-k^2-1+c^2*k^2-(c^2*k^3*(c^2*k-4))^(1/2)-2*k)*(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)+1/2*2^(1/2)*((k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3+2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)^(1/2)*(4*k^2*(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)^2+4*(-k^2-1+c^2*k^2-(c^2*k^3*(c^2*k-4))^(1/2)-2*k)*(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)+2*(k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3+2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)^(1/2))/(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2))+1/4*c*2^(1/2)/((k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3+2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)^(1/2)*ln(((k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3+2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2+(-k^2-1+c^2*k^2-(c^2*k^3*(c^2*k-4))^(1/2)-2*k)*(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)+1/2*2^(1/2)*((k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3+2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)^(1/2)*(4*k^2*(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)^2+4*(-k^2-1+c^2*k^2-(c^2*k^3*(c^2*k-4))^(1/2)-2*k)*(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)+2*(k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3+2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)^(1/2))/(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2))+c*k/(c^2*k^3*(c^2*k-4))^(1/2)*2^(1/2)/((k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3+2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)^(1/2)*ln(((k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3+2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2+(-k^2-1+c^2*k^2-(c^2*k^3*(c^2*k-4))^(1/2)-2*k)*(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)+1/2*2^(1/2)*((k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3+2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)^(1/2)*(4*k^2*(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)^2+4*(-k^2-1+c^2*k^2-(c^2*k^3*(c^2*k-4))^(1/2)-2*k)*(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)+2*(k^4*c^4-c^2*k^4-(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3+2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)^(1/2))/(x^2+1/2*(-c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2))+1/4*c^3*k^2/(c^2*k^3*(c^2*k-4))^(1/2)*2^(1/2)/((k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3-2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)^(1/2)*ln(((k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3-2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2+(-k^2-1+c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)-2*k)*(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)-2*k)/k^2)+1/2*2^(1/2)*((k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3-2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)^(1/2)*(4*k^2*(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)-2*k)/k^2)^2+4*(-k^2-1+c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)-2*k)*(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)-2*k)/k^2)+2*(k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3-2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)^(1/2))/(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)-2*k)/k^2))+1/4*c*2^(1/2)/((k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3-2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)^(1/2)*ln(((k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3-2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2+(-k^2-1+c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)-2*k)*(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)-2*k)/k^2)+1/2*2^(1/2)*((k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3-2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)^(1/2)*(4*k^2*(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)-2*k)/k^2)^2+4*(-k^2-1+c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)-2*k)*(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)-2*k)/k^2)+2*(k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3-2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)^(1/2))/(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)-2*k)/k^2))-c*k/(c^2*k^3*(c^2*k-4))^(1/2)*2^(1/2)/((k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3-2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)^(1/2)*ln(((k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3-2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2+(-k^2-1+c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)-2*k)*(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)-2*k)/k^2)+1/2*2^(1/2)*((k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3-2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)^(1/2)*(4*k^2*(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)-2*k)/k^2)^2+4*(-k^2-1+c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)-2*k)*(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)-2*k)/k^2)+2*(k^4*c^4-c^2*k^4+(c^2*k^3*(c^2*k-4))^(1/2)*c^2*k^2-4*c^2*k^3-c^2*k^2-(c^2*k^3*(c^2*k-4))^(1/2)*k^2+2*k^3-2*(c^2*k^3*(c^2*k-4))^(1/2)*k+4*k^2-(c^2*k^3*(c^2*k-4))^(1/2)+2*k)/k^2)^(1/2))/(x^2-1/2*(c^2*k^2+(c^2*k^3*(c^2*k-4))^(1/2)-2*k)/k^2))-1/(2*c^2*k^2-2*k^2-4*k-2)^(1/2)*arctanh(((-x^2+1)*(-k^2*x^2+1))^(1/2)*2^(1/2)/x/(2*c^2*k^2-2*k^2-4*k-2)^(1/2))*2^(1/2)","B"
1389,1,17,78,3.950000," ","int(x^2*(x^3+x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 x^{\frac{10}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{5}{3}\right], \left[\frac{8}{3}\right], -x^{2}\right)}{10}$&$17$\\ trager&$\frac{x \left(3 x^{2}+1\right) \left(x^{3}+x \right)^{\frac{1}{3}}}{12}+\frac{\ln \left(-36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}+72 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}-27 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x -57 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+15 \left(x^{3}+x \right)^{\frac{2}{3}}-24 x \left(x^{3}+x \right)^{\frac{1}{3}}+36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+5 x^{2}-27 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+2\right)}{18}-\frac{\ln \left(-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}-72 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}+45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x +24 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}-9 \left(x^{3}+x \right)^{\frac{2}{3}}+24 x \left(x^{3}+x \right)^{\frac{1}{3}}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-16 x^{2}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-12\right)}{18}-\frac{\ln \left(-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}-72 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}+45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x +24 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}-9 \left(x^{3}+x \right)^{\frac{2}{3}}+24 x \left(x^{3}+x \right)^{\frac{1}{3}}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-16 x^{2}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-12\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{6}$&$426$\\ risch&$\frac{x \left(3 x^{2}+1\right) \left(x \left(x^{2}+1\right)\right)^{\frac{1}{3}}}{12}+\frac{\left(\frac{\ln \left(\frac{5 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)^{2} x^{4}-38 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) x^{4}+18 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}-16 x^{4}+30 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}-70 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) x^{2}-60 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}-5 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)^{2}+18 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}+96 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}-28 x^{2}-32 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)-60 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}-12}{x^{2}+1}\right)}{18}+\frac{\RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)^{2} x^{4}+20 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) x^{4}-48 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}+100 x^{4}+30 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}+14 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) x^{2}-60 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}-\RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)^{2}-48 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}-36 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}+140 x^{2}-6 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)-60 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}+40}{x^{2}+1}\right)}{36}\right) \left(x \left(x^{2}+1\right)\right)^{\frac{1}{3}} \left(x^{2} \left(x^{2}+1\right)^{2}\right)^{\frac{1}{3}}}{x \left(x^{2}+1\right)}$&$504$\\ \hline \end{longtable}"," ",0,"3/10*x^(10/3)*hypergeom([-1/3,5/3],[8/3],-x^2)","C"
1390,1,772,81,3.229000," ","int((x^2+2*x+6)/(x^2+2)^(1/3)/(x^3-2*x^2+3*x+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{188 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+573 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+2\right)^{\frac{2}{3}} x -573 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+2\right)^{\frac{1}{3}} x^{2}-470 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+676 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-573 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+2\right)^{\frac{2}{3}}+891 \left(x^{2}+2\right)^{\frac{2}{3}} x +1146 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+2\right)^{\frac{1}{3}} x -891 \left(x^{2}+2\right)^{\frac{1}{3}} x^{2}+564 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x -2019 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+591 x^{3}-891 \left(x^{2}+2\right)^{\frac{2}{3}}-573 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+2\right)^{\frac{1}{3}}+1782 \left(x^{2}+2\right)^{\frac{1}{3}} x +2028 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x -2167 x^{2}-891 \left(x^{2}+2\right)^{\frac{1}{3}}-658 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1773 x -1379}{x^{3}-2 x^{2}+3 x +1}\right)-\ln \left(\frac{-188 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+573 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+2\right)^{\frac{2}{3}} x -573 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+2\right)^{\frac{1}{3}} x^{2}+470 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+300 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-573 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+2\right)^{\frac{2}{3}}-318 \left(x^{2}+2\right)^{\frac{2}{3}} x +1146 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+2\right)^{\frac{1}{3}} x +318 \left(x^{2}+2\right)^{\frac{1}{3}} x^{2}-564 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x -1079 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-103 x^{3}+318 \left(x^{2}+2\right)^{\frac{2}{3}}-573 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+2\right)^{\frac{1}{3}}-636 \left(x^{2}+2\right)^{\frac{1}{3}} x +900 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +618 x^{2}+318 \left(x^{2}+2\right)^{\frac{1}{3}}-658 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-309 x +721}{x^{3}-2 x^{2}+3 x +1}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-\ln \left(\frac{-188 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+573 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+2\right)^{\frac{2}{3}} x -573 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+2\right)^{\frac{1}{3}} x^{2}+470 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+300 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-573 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+2\right)^{\frac{2}{3}}-318 \left(x^{2}+2\right)^{\frac{2}{3}} x +1146 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+2\right)^{\frac{1}{3}} x +318 \left(x^{2}+2\right)^{\frac{1}{3}} x^{2}-564 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x -1079 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-103 x^{3}+318 \left(x^{2}+2\right)^{\frac{2}{3}}-573 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+2\right)^{\frac{1}{3}}-636 \left(x^{2}+2\right)^{\frac{1}{3}} x +900 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +618 x^{2}+318 \left(x^{2}+2\right)^{\frac{1}{3}}-658 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-309 x +721}{x^{3}-2 x^{2}+3 x +1}\right)$&$772$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2+_Z+1)*ln(-(188*RootOf(_Z^2+_Z+1)^2*x^3+573*RootOf(_Z^2+_Z+1)*(x^2+2)^(2/3)*x-573*RootOf(_Z^2+_Z+1)*(x^2+2)^(1/3)*x^2-470*RootOf(_Z^2+_Z+1)^2*x^2+676*RootOf(_Z^2+_Z+1)*x^3-573*RootOf(_Z^2+_Z+1)*(x^2+2)^(2/3)+891*(x^2+2)^(2/3)*x+1146*RootOf(_Z^2+_Z+1)*(x^2+2)^(1/3)*x-891*(x^2+2)^(1/3)*x^2+564*RootOf(_Z^2+_Z+1)^2*x-2019*RootOf(_Z^2+_Z+1)*x^2+591*x^3-891*(x^2+2)^(2/3)-573*RootOf(_Z^2+_Z+1)*(x^2+2)^(1/3)+1782*(x^2+2)^(1/3)*x+2028*RootOf(_Z^2+_Z+1)*x-2167*x^2-891*(x^2+2)^(1/3)-658*RootOf(_Z^2+_Z+1)+1773*x-1379)/(x^3-2*x^2+3*x+1))-ln((-188*RootOf(_Z^2+_Z+1)^2*x^3+573*RootOf(_Z^2+_Z+1)*(x^2+2)^(2/3)*x-573*RootOf(_Z^2+_Z+1)*(x^2+2)^(1/3)*x^2+470*RootOf(_Z^2+_Z+1)^2*x^2+300*RootOf(_Z^2+_Z+1)*x^3-573*RootOf(_Z^2+_Z+1)*(x^2+2)^(2/3)-318*(x^2+2)^(2/3)*x+1146*RootOf(_Z^2+_Z+1)*(x^2+2)^(1/3)*x+318*(x^2+2)^(1/3)*x^2-564*RootOf(_Z^2+_Z+1)^2*x-1079*RootOf(_Z^2+_Z+1)*x^2-103*x^3+318*(x^2+2)^(2/3)-573*RootOf(_Z^2+_Z+1)*(x^2+2)^(1/3)-636*(x^2+2)^(1/3)*x+900*RootOf(_Z^2+_Z+1)*x+618*x^2+318*(x^2+2)^(1/3)-658*RootOf(_Z^2+_Z+1)-309*x+721)/(x^3-2*x^2+3*x+1))*RootOf(_Z^2+_Z+1)-ln((-188*RootOf(_Z^2+_Z+1)^2*x^3+573*RootOf(_Z^2+_Z+1)*(x^2+2)^(2/3)*x-573*RootOf(_Z^2+_Z+1)*(x^2+2)^(1/3)*x^2+470*RootOf(_Z^2+_Z+1)^2*x^2+300*RootOf(_Z^2+_Z+1)*x^3-573*RootOf(_Z^2+_Z+1)*(x^2+2)^(2/3)-318*(x^2+2)^(2/3)*x+1146*RootOf(_Z^2+_Z+1)*(x^2+2)^(1/3)*x+318*(x^2+2)^(1/3)*x^2-564*RootOf(_Z^2+_Z+1)^2*x-1079*RootOf(_Z^2+_Z+1)*x^2-103*x^3+318*(x^2+2)^(2/3)-573*RootOf(_Z^2+_Z+1)*(x^2+2)^(1/3)-636*(x^2+2)^(1/3)*x+900*RootOf(_Z^2+_Z+1)*x+618*x^2+318*(x^2+2)^(1/3)-658*RootOf(_Z^2+_Z+1)-309*x+721)/(x^3-2*x^2+3*x+1))","C"
1391,1,15,84,0.907000," ","int((x^3+x^2)^(1/3)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{3 \hypergeom \left(\left[-\frac{1}{3}, -\frac{1}{3}\right], \left[\frac{2}{3}\right], -x \right)}{x^{\frac{1}{3}}}$&$15$\\ risch&$-\frac{3 \left(x^{2} \left(1+x \right)\right)^{\frac{1}{3}}}{x}+\frac{\left(-\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{2}-48 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{2}{3}}+30 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}} x +16 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2}+30 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}}+14 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x +36 \left(x^{3}+2 x^{2}+x \right)^{\frac{2}{3}}-96 \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}} x +64 x^{2}-2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)-96 \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}}+112 x +48}{1+x}\right)+\frac{\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{2}+24 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{2}{3}}-9 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}} x -19 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-30 \left(x^{3}+2 x^{2}+x \right)^{\frac{2}{3}}-9 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}}+48 \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}} x -2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2}-28 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x -10 x^{2}+48 \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}}-9 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)-14 x -4}{1+x}\right)}{2}\right) \left(x^{2} \left(1+x \right)\right)^{\frac{1}{3}} \left(\left(1+x \right)^{2} x \right)^{\frac{1}{3}}}{x \left(1+x \right)}$&$450$\\ trager&$-\frac{3 \left(x^{3}+x^{2}\right)^{\frac{1}{3}}}{x}-3 \ln \left(-\frac{-45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}+45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{2}{3}}+27 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{1}{3}} x +45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x -57 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}-24 \left(x^{3}+x^{2}\right)^{\frac{2}{3}}+15 x \left(x^{3}+x^{2}\right)^{\frac{1}{3}}-48 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x +4 x^{2}+3 x}{x}\right) \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-\ln \left(\frac{-9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}+45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{2}{3}}-72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{1}{3}} x +9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x +30 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}+9 \left(x^{3}+x^{2}\right)^{\frac{2}{3}}+15 x \left(x^{3}+x^{2}\right)^{\frac{1}{3}}-9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x -25 x^{2}-10 x}{x}\right)+\ln \left(-\frac{-45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}+45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{2}{3}}+27 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{1}{3}} x +45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x -57 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}-24 \left(x^{3}+x^{2}\right)^{\frac{2}{3}}+15 x \left(x^{3}+x^{2}\right)^{\frac{1}{3}}-48 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x +4 x^{2}+3 x}{x}\right)$&$471$\\ \hline \end{longtable}"," ",0,"-3/x^(1/3)*hypergeom([-1/3,-1/3],[2/3],-x)","C"
1392,1,74,78,3.986000," ","int((x^4+1)^(1/3)*(x^4+3)/x^13,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x^{12}-5 x^{8}-15 x^{4}-9}{36 x^{12} \left(x^{4}+1\right)^{\frac{2}{3}}}+\frac{-\frac{2 \Gamma \left(\frac{2}{3}\right) x^{4} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 2\right], -x^{4}\right)}{3}+\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)}{54 \Gamma \left(\frac{2}{3}\right)}$&$74$\\ meijerg&$-\frac{-\frac{5 \Gamma \left(\frac{2}{3}\right) x^{4} \hypergeom \left(\left[1, 1, \frac{8}{3}\right], \left[2, 4\right], -x^{4}\right)}{27}+\frac{\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)}{3}+\frac{3 \Gamma \left(\frac{2}{3}\right)}{2 x^{8}}+\frac{\Gamma \left(\frac{2}{3}\right)}{x^{4}}}{12 \Gamma \left(\frac{2}{3}\right)}-\frac{\frac{10 \Gamma \left(\frac{2}{3}\right) x^{4} \hypergeom \left(\left[1, 1, \frac{11}{3}\right], \left[2, 5\right], -x^{4}\right)}{81}-\frac{5 \left(\frac{4}{15}+\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)}{27}+\frac{\Gamma \left(\frac{2}{3}\right)}{x^{12}}+\frac{\Gamma \left(\frac{2}{3}\right)}{2 x^{8}}-\frac{\Gamma \left(\frac{2}{3}\right)}{3 x^{4}}}{4 \Gamma \left(\frac{2}{3}\right)}$&$128$\\ trager&$\frac{\left(x^{4}+1\right)^{\frac{1}{3}} \left(x^{8}-6 x^{4}-9\right)}{36 x^{12}}+\frac{\RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(\frac{180 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}+129 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}-51 x^{4}+351 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}}-180 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+351 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{1}{3}}-48 \left(x^{4}+1\right)^{\frac{2}{3}}+291 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-48 \left(x^{4}+1\right)^{\frac{1}{3}}-68}{x^{4}}\right)}{18}-\frac{\ln \left(\frac{180 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}-74 x^{4}-351 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}}-180 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-351 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{1}{3}}-165 \left(x^{4}+1\right)^{\frac{2}{3}}-411 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-165 \left(x^{4}+1\right)^{\frac{1}{3}}-185}{x^{4}}\right)}{54}-\frac{\ln \left(\frac{180 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}-74 x^{4}-351 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}}-180 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-351 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{1}{3}}-165 \left(x^{4}+1\right)^{\frac{2}{3}}-411 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-165 \left(x^{4}+1\right)^{\frac{1}{3}}-185}{x^{4}}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{18}$&$448$\\ \hline \end{longtable}"," ",0,"1/36*(x^12-5*x^8-15*x^4-9)/x^12/(x^4+1)^(2/3)+1/54/GAMMA(2/3)*(-2/3*GAMMA(2/3)*x^4*hypergeom([1,1,5/3],[2,2],-x^4)+(1/6*Pi*3^(1/2)-3/2*ln(3)+4*ln(x))*GAMMA(2/3))","C"
1393,1,321,84,8.556000," ","int((x^4-1)^(2/3)*(x^4+3)*(x^4+x^3-1)/x^6/(x^4-x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\frac{3}{5} x^{8}-\frac{6}{5} x^{4}+\frac{3}{5}+3 x^{7}-3 x^{3}}{x^{5} \left(x^{4}-1\right)^{\frac{1}{3}}}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}} x +\left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+x^{4}+2 \left(x^{4}-1\right)^{\frac{2}{3}} x +2 \left(x^{4}-1\right)^{\frac{1}{3}} x^{2}+x^{3}-1}{x^{4}-x^{3}-1}\right)-2 \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}} x +\left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-x^{4}-\left(x^{4}-1\right)^{\frac{2}{3}} x -\left(x^{4}-1\right)^{\frac{1}{3}} x^{2}+1}{x^{4}-x^{3}-1}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2 \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}} x +\left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-x^{4}-\left(x^{4}-1\right)^{\frac{2}{3}} x -\left(x^{4}-1\right)^{\frac{1}{3}} x^{2}+1}{x^{4}-x^{3}-1}\right)$&$321$\\ trager&$\frac{3 \left(x^{4}-1\right)^{\frac{2}{3}} \left(x^{4}+5 x^{3}-1\right)}{5 x^{5}}+2 \ln \left(\frac{1091690496 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2} x^{4}-2046919680 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2} x^{3}-24386400 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) x^{4}+65890176 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}} x -24505824 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{1}{3}} x^{2}-26948256 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) x^{3}+59850 x^{4}+431087 \left(x^{4}-1\right)^{\frac{2}{3}} x -686356 \left(x^{4}-1\right)^{\frac{1}{3}} x^{2}+91770 x^{3}-1091690496 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2}+24386400 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)-59850}{x^{4}-x^{3}-1}\right)+192 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) \ln \left(\frac{294174720 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2} x^{4}-551577600 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2} x^{3}-2561856 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) x^{4}-65890176 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{2}{3}} x +41384352 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) \left(x^{4}-1\right)^{\frac{1}{3}} x^{2}+24386400 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) x^{3}-340561 x^{4}-255269 \left(x^{4}-1\right)^{\frac{2}{3}} x +686356 \left(x^{4}-1\right)^{\frac{1}{3}} x^{2}-118456 x^{3}-294174720 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2}+2561856 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)+340561}{x^{4}-x^{3}-1}\right)$&$415$\\ \hline \end{longtable}"," ",0,"3/5*(x^8+5*x^7-2*x^4-5*x^3+1)/x^5/(x^4-1)^(1/3)+2*RootOf(_Z^2+_Z+1)*ln((RootOf(_Z^2+_Z+1)*(x^4-1)^(2/3)*x+(x^4-1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2+RootOf(_Z^2+_Z+1)*x^3+x^4+2*(x^4-1)^(2/3)*x+2*(x^4-1)^(1/3)*x^2+x^3-1)/(x^4-x^3-1))-2*ln(-(RootOf(_Z^2+_Z+1)*(x^4-1)^(2/3)*x+(x^4-1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2+RootOf(_Z^2+_Z+1)*x^3-x^4-(x^4-1)^(2/3)*x-(x^4-1)^(1/3)*x^2+1)/(x^4-x^3-1))*RootOf(_Z^2+_Z+1)-2*ln(-(RootOf(_Z^2+_Z+1)*(x^4-1)^(2/3)*x+(x^4-1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2+RootOf(_Z^2+_Z+1)*x^3-x^4-(x^4-1)^(2/3)*x-(x^4-1)^(1/3)*x^2+1)/(x^4-x^3-1))","C"
1394,1,320,84,6.290000," ","int((x^4-3)*(x^4+1)^(2/3)*(x^4+x^3+1)/x^6/(x^4-x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\frac{3}{5} x^{8}+\frac{6}{5} x^{4}+\frac{3}{5}+3 x^{7}+3 x^{3}}{x^{5} \left(x^{4}+1\right)^{\frac{1}{3}}}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x +\left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+x^{4}+2 \left(x^{4}+1\right)^{\frac{2}{3}} x +2 x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}+x^{3}+1}{x^{4}-x^{3}+1}\right)-2 \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x +\left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-x^{4}-\left(x^{4}+1\right)^{\frac{2}{3}} x -x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}-1}{x^{4}-x^{3}+1}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2 \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x +\left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-x^{4}-\left(x^{4}+1\right)^{\frac{2}{3}} x -x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}-1}{x^{4}-x^{3}+1}\right)$&$320$\\ trager&$\frac{3 \left(x^{4}+1\right)^{\frac{2}{3}} \left(x^{4}+5 x^{3}+1\right)}{5 x^{5}}-6 \ln \left(\frac{10305 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}-20610 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+17859 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}+9621 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x +9621 \left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}-11673 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+7554 x^{4}+11217 \left(x^{4}+1\right)^{\frac{2}{3}} x +11217 x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}+2518 x^{3}+10305 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+17859 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+7554}{x^{4}-x^{3}+1}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(-\frac{-10305 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}+20610 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+10989 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}+9621 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x +9621 \left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+2067 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}-2746 x^{4}-8010 \left(x^{4}+1\right)^{\frac{2}{3}} x -8010 x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}-4119 x^{3}-10305 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+10989 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-2746}{x^{4}-x^{3}+1}\right)-2 \ln \left(\frac{10305 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}-20610 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+17859 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}+9621 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x +9621 \left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}-11673 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+7554 x^{4}+11217 \left(x^{4}+1\right)^{\frac{2}{3}} x +11217 x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}+2518 x^{3}+10305 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+17859 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+7554}{x^{4}-x^{3}+1}\right)$&$617$\\ \hline \end{longtable}"," ",0,"3/5*(x^8+5*x^7+2*x^4+5*x^3+1)/x^5/(x^4+1)^(1/3)+2*RootOf(_Z^2+_Z+1)*ln(-(RootOf(_Z^2+_Z+1)*(x^4+1)^(2/3)*x+(x^4+1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2+RootOf(_Z^2+_Z+1)*x^3+x^4+2*(x^4+1)^(2/3)*x+2*x^2*(x^4+1)^(1/3)+x^3+1)/(x^4-x^3+1))-2*ln((RootOf(_Z^2+_Z+1)*(x^4+1)^(2/3)*x+(x^4+1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2+RootOf(_Z^2+_Z+1)*x^3-x^4-(x^4+1)^(2/3)*x-x^2*(x^4+1)^(1/3)-1)/(x^4-x^3+1))*RootOf(_Z^2+_Z+1)-2*ln((RootOf(_Z^2+_Z+1)*(x^4+1)^(2/3)*x+(x^4+1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2+RootOf(_Z^2+_Z+1)*x^3-x^4-(x^4+1)^(2/3)*x-x^2*(x^4+1)^(1/3)-1)/(x^4-x^3+1))","C"
1395,0,0,11,0.024000," ","int((a*x^2-b)/(x^4+a*x^2+b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{a \,x^{2}-b}{\left(x^{4}+a \,x^{2}+b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2-b)/(x^4+a*x^2+b)/(a*x^4+b*x^2)^(1/4),x)","F"
1396,0,0,11,0.000000," ","int((a*x^2-b)/(x^4+a*x^2+b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{a \,x^{2}-b}{\left(x^{4}+a \,x^{2}+b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2-b)/(x^4+a*x^2+b)/(a*x^4+b*x^2)^(1/4),x)","F"
1397,1,6585,24,141.110000," ","int((x^3-1)*(x^3+1)^(2/3)/x^3/(x^6-x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$6585$\\ trager&$\text{Expression too large to display}$&$11049$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1398,1,11328,24,176.616000," ","int((x^3-1)*(x^3+1)^(2/3)/x^3/(x^6-x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$11328$\\ trager&$\text{Expression too large to display}$&$15352$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1399,1,632,84,35.092000," ","int((2*x^7+1)^(1/3)*(8*x^7-3)/x^2/(2*x^7+x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(2 x^{7}+1\right)^{\frac{1}{3}}}{x}+3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \ln \left(\frac{-88928146808112798 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{7}-55447617558383298 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{7}+2558542431350156 x^{7}+133392220212169197 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{3}+66431161712710197 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(2 x^{7}+1\right)^{\frac{2}{3}} x -66431161712710197 \left(2 x^{7}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}-20578078271889984 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{3}-20401446009640383 \left(2 x^{7}+1\right)^{\frac{2}{3}} x +20401446009640383 \left(2 x^{7}+1\right)^{\frac{1}{3}} x^{2}+639635607837539 x^{3}-44464073404056399 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}-27723808779191649 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)+1279271215675078}{2 x^{7}+x^{3}+1}\right)-3 \ln \left(-\frac{88928146808112798 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{7}-114733048763791830 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{7}+25804901955679032 x^{7}-133392220212169197 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{3}+66431161712710197 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(2 x^{7}+1\right)^{\frac{2}{3}} x -66431161712710197 \left(2 x^{7}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}+68350068536222814 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{3}-1742274561263016 \left(2 x^{7}+1\right)^{\frac{2}{3}} x +1742274561263016 \left(2 x^{7}+1\right)^{\frac{1}{3}} x^{2}-8601633985226344 x^{3}+44464073404056399 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}-57366524381895915 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)+12902450977839516}{2 x^{7}+x^{3}+1}\right) \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)+\ln \left(-\frac{88928146808112798 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{7}-114733048763791830 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{7}+25804901955679032 x^{7}-133392220212169197 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{3}+66431161712710197 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(2 x^{7}+1\right)^{\frac{2}{3}} x -66431161712710197 \left(2 x^{7}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}+68350068536222814 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{3}-1742274561263016 \left(2 x^{7}+1\right)^{\frac{2}{3}} x +1742274561263016 \left(2 x^{7}+1\right)^{\frac{1}{3}} x^{2}-8601633985226344 x^{3}+44464073404056399 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}-57366524381895915 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)+12902450977839516}{2 x^{7}+x^{3}+1}\right)$&$632$\\ risch&$\frac{3 \left(2 x^{7}+1\right)^{\frac{1}{3}}}{x}+\frac{\left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(-\frac{8 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{14}-4 x^{14}-4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{10}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{10}-6 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(4 x^{14}+4 x^{7}+1\right)^{\frac{1}{3}} x^{8}+6 \left(4 x^{14}+4 x^{7}+1\right)^{\frac{1}{3}} x^{8}+8 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{7}-4 x^{7}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(4 x^{14}+4 x^{7}+1\right)^{\frac{2}{3}} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-3 \left(4 x^{14}+4 x^{7}+1\right)^{\frac{2}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(4 x^{14}+4 x^{7}+1\right)^{\frac{1}{3}} x +3 \left(4 x^{14}+4 x^{7}+1\right)^{\frac{1}{3}} x +2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-1}{\left(2 x^{7}+1\right) \left(2 x^{7}+x^{3}+1\right)}\right)-\ln \left(\frac{8 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{14}-4 x^{14}+4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{10}-6 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{10}-6 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(4 x^{14}+4 x^{7}+1\right)^{\frac{1}{3}} x^{8}+2 x^{10}+8 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{7}-4 x^{7}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(4 x^{14}+4 x^{7}+1\right)^{\frac{2}{3}} x^{2}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(4 x^{14}+4 x^{7}+1\right)^{\frac{1}{3}} x +x^{3}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-1}{\left(2 x^{7}+1\right) \left(2 x^{7}+x^{3}+1\right)}\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+\ln \left(\frac{8 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{14}-4 x^{14}+4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{10}-6 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{10}-6 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(4 x^{14}+4 x^{7}+1\right)^{\frac{1}{3}} x^{8}+2 x^{10}+8 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{7}-4 x^{7}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(4 x^{14}+4 x^{7}+1\right)^{\frac{2}{3}} x^{2}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(4 x^{14}+4 x^{7}+1\right)^{\frac{1}{3}} x +x^{3}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-1}{\left(2 x^{7}+1\right) \left(2 x^{7}+x^{3}+1\right)}\right)\right) \left(\left(2 x^{7}+1\right)^{2}\right)^{\frac{1}{3}}}{\left(2 x^{7}+1\right)^{\frac{2}{3}}}$&$778$\\ \hline \end{longtable}"," ",0,"3*(2*x^7+1)^(1/3)/x+3*RootOf(9*_Z^2-3*_Z+1)*ln((-88928146808112798*RootOf(9*_Z^2-3*_Z+1)^2*x^7-55447617558383298*RootOf(9*_Z^2-3*_Z+1)*x^7+2558542431350156*x^7+133392220212169197*RootOf(9*_Z^2-3*_Z+1)^2*x^3+66431161712710197*RootOf(9*_Z^2-3*_Z+1)*(2*x^7+1)^(2/3)*x-66431161712710197*(2*x^7+1)^(1/3)*RootOf(9*_Z^2-3*_Z+1)*x^2-20578078271889984*RootOf(9*_Z^2-3*_Z+1)*x^3-20401446009640383*(2*x^7+1)^(2/3)*x+20401446009640383*(2*x^7+1)^(1/3)*x^2+639635607837539*x^3-44464073404056399*RootOf(9*_Z^2-3*_Z+1)^2-27723808779191649*RootOf(9*_Z^2-3*_Z+1)+1279271215675078)/(2*x^7+x^3+1))-3*ln(-(88928146808112798*RootOf(9*_Z^2-3*_Z+1)^2*x^7-114733048763791830*RootOf(9*_Z^2-3*_Z+1)*x^7+25804901955679032*x^7-133392220212169197*RootOf(9*_Z^2-3*_Z+1)^2*x^3+66431161712710197*RootOf(9*_Z^2-3*_Z+1)*(2*x^7+1)^(2/3)*x-66431161712710197*(2*x^7+1)^(1/3)*RootOf(9*_Z^2-3*_Z+1)*x^2+68350068536222814*RootOf(9*_Z^2-3*_Z+1)*x^3-1742274561263016*(2*x^7+1)^(2/3)*x+1742274561263016*(2*x^7+1)^(1/3)*x^2-8601633985226344*x^3+44464073404056399*RootOf(9*_Z^2-3*_Z+1)^2-57366524381895915*RootOf(9*_Z^2-3*_Z+1)+12902450977839516)/(2*x^7+x^3+1))*RootOf(9*_Z^2-3*_Z+1)+ln(-(88928146808112798*RootOf(9*_Z^2-3*_Z+1)^2*x^7-114733048763791830*RootOf(9*_Z^2-3*_Z+1)*x^7+25804901955679032*x^7-133392220212169197*RootOf(9*_Z^2-3*_Z+1)^2*x^3+66431161712710197*RootOf(9*_Z^2-3*_Z+1)*(2*x^7+1)^(2/3)*x-66431161712710197*(2*x^7+1)^(1/3)*RootOf(9*_Z^2-3*_Z+1)*x^2+68350068536222814*RootOf(9*_Z^2-3*_Z+1)*x^3-1742274561263016*(2*x^7+1)^(2/3)*x+1742274561263016*(2*x^7+1)^(1/3)*x^2-8601633985226344*x^3+44464073404056399*RootOf(9*_Z^2-3*_Z+1)^2-57366524381895915*RootOf(9*_Z^2-3*_Z+1)+12902450977839516)/(2*x^7+x^3+1))","C"
1400,0,0,11,0.025000," ","int((2*a*x^4-b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x)","\[\int \frac{2 a \,x^{4}-b}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(x^{8}+a \,x^{4}-b \right)}\, dx\]"," ",0,"int((2*a*x^4-b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x)","F"
1401,0,0,11,0.000000," ","int((2*a*x^4-b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x)","\[\int \frac{2 a \,x^{4}-b}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(x^{8}+a \,x^{4}-b \right)}\, dx\]"," ",0,"int((2*a*x^4-b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x)","F"
1402,1,124,84,1.593000," ","int((3*x^4-1)*(x^8+x^5+2*x^4+x+1)^(1/2)/x^2/(4*x^4+x+4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{8}+x^{5}+2 x^{4}+x +1}}{4 x}+\frac{\ln \left(-\frac{2 x^{4}+2 \sqrt{x^{8}+x^{5}+2 x^{4}+x +1}+x +2}{x}\right)}{16}-\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{4}-\RootOf \left(\textit{\_Z}^{2}+3\right) x +2 \RootOf \left(\textit{\_Z}^{2}+3\right)-6 \sqrt{x^{8}+x^{5}+2 x^{4}+x +1}}{4 x^{4}+x +4}\right)}{16}$&$124$\\ risch&$\frac{\sqrt{x^{8}+x^{5}+2 x^{4}+x +1}}{4 x}-\frac{\ln \left(-\frac{-2 x^{4}+2 \sqrt{x^{8}+x^{5}+2 x^{4}+x +1}-x -2}{x}\right)}{16}+\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+3\right) x^{4}-\RootOf \left(\textit{\_Z}^{2}+3\right) x +2 \RootOf \left(\textit{\_Z}^{2}+3\right)+6 \sqrt{x^{8}+x^{5}+2 x^{4}+x +1}}{4 x^{4}+x +4}\right)}{16}$&$127$\\ \hline \end{longtable}"," ",0,"1/4*(x^8+x^5+2*x^4+x+1)^(1/2)/x+1/16*ln(-(2*x^4+2*(x^8+x^5+2*x^4+x+1)^(1/2)+x+2)/x)-1/16*RootOf(_Z^2+3)*ln((2*RootOf(_Z^2+3)*x^4-RootOf(_Z^2+3)*x+2*RootOf(_Z^2+3)-6*(x^8+x^5+2*x^4+x+1)^(1/2))/(4*x^4+x+4))","C"
1403,0,0,80,0.011000," ","int((a*x^8+c*x^4-b)/x^2/(a*x^4-b)^(3/4),x)","\[\int \frac{a \,x^{8}+c \,x^{4}-b}{x^{2} \left(a \,x^{4}-b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int((a*x^8+c*x^4-b)/x^2/(a*x^4-b)^(3/4),x)","F"
1404,0,0,72,0.013000," ","int(1/(1+x)/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{1}{\left(1+x \right) \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int(1/(1+x)/(x+(x^2+1)^(1/2))^(1/2),x)","F"
1405,0,0,80,180.000000," ","int(1/x/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{1}{x \sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int(1/x/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","F"
1406,1,88,91,0.361000," ","int((-3+x)^6*(x^2-x-1)^(3/2)/(-1+x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\sqrt{x^{2}-x -1}\, \left(1146880 x^{8}-23296000 x^{7}+199009280 x^{6}-910869760 x^{5}+2304529024 x^{4}-2700564848 x^{3}-508033624 x^{2}+4423205098 x -1245336401\right)}{10321920}-\frac{19451047 \ln \left(x -\frac{1}{2}+\sqrt{x^{2}-x -1}\right)}{65536}+64 \arctan \left(\frac{-3+x}{2 \sqrt{\left(-1+x \right)^{2}-2+x}}\right)$&$88$\\ trager&$\left(\frac{1}{9} x^{8}-\frac{325}{144} x^{7}+\frac{38869}{2016} x^{6}-\frac{711617}{8064} x^{5}+\frac{2572019}{11520} x^{4}-\frac{168785303}{645120} x^{3}-\frac{9072029}{184320} x^{2}+\frac{2211602549}{5160960} x -\frac{1245336401}{10321920}\right) \sqrt{x^{2}-x -1}+\frac{19451047 \ln \left(1-2 x +2 \sqrt{x^{2}-x -1}\right)}{65536}+64 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x -3 \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \sqrt{x^{2}-x -1}}{-1+x}\right)$&$117$\\ default&$8 \left(-1+2 x \right) \sqrt{\left(-1+x \right)^{2}-2+x}+\frac{x^{4} \left(x^{2}-x -1\right)^{\frac{5}{2}}}{9}-\frac{293 x^{3} \left(x^{2}-x -1\right)^{\frac{5}{2}}}{144}+\frac{30889 x^{2} \left(x^{2}-x -1\right)^{\frac{5}{2}}}{2016}-\frac{482705 x \left(x^{2}-x -1\right)^{\frac{5}{2}}}{8064}-\frac{213909 \left(-1+2 x \right) \left(x^{2}-x -1\right)^{\frac{3}{2}}}{4096}+\frac{3208635 \sqrt{x^{2}-x -1}\, \left(-1+2 x \right)}{32768}+64 \arctan \left(\frac{-3+x}{2 \sqrt{\left(-1+x \right)^{2}-2+x}}\right)+\frac{64 \left(\left(-1+x \right)^{2}-2+x \right)^{\frac{3}{2}}}{3}-64 \sqrt{\left(-1+x \right)^{2}-2+x}-52 \ln \left(-\frac{1}{2}+x +\sqrt{\left(-1+x \right)^{2}-2+x}\right)-\frac{16043175 \ln \left(x -\frac{1}{2}+\sqrt{x^{2}-x -1}\right)}{65536}+\frac{9904793 \left(x^{2}-x -1\right)^{\frac{5}{2}}}{80640}$&$197$\\ \hline \end{longtable}"," ",0,"1/10321920*(x^2-x-1)^(1/2)*(1146880*x^8-23296000*x^7+199009280*x^6-910869760*x^5+2304529024*x^4-2700564848*x^3-508033624*x^2+4423205098*x-1245336401)-19451047/65536*ln(x-1/2+(x^2-x-1)^(1/2))+64*arctan(1/2*(-3+x)/((-1+x)^2-2+x)^(1/2))","A"
1407,1,30,81,2.123000," ","int((x^3-1)*(x^3+1)^(1/3)/x^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\left(x^{3}+1\right)^{\frac{4}{3}}}{4 x^{4}}-\frac{\hypergeom \left(\left[-\frac{1}{3}, -\frac{1}{3}\right], \left[\frac{2}{3}\right], -x^{3}\right)}{x}$&$30$\\ risch&$-\frac{3 x^{6}+2 x^{3}-1}{4 x^{4} \left(x^{3}+1\right)^{\frac{2}{3}}}+\frac{x^{2} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], -x^{3}\right)}{2}$&$42$\\ trager&$-\frac{\left(3 x^{3}-1\right) \left(x^{3}+1\right)^{\frac{1}{3}}}{4 x^{4}}-\frac{\ln \left(317 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+555 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x -2358 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+1486 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-2358 x \left(x^{3}+1\right)^{\frac{2}{3}}+1803 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}+872 x^{3}-317 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}+733 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+654\right)}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(-535 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-555 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x -1803 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+2893 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-1803 x \left(x^{3}+1\right)^{\frac{2}{3}}+2358 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}-1090 x^{3}+535 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}+852 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-436\right)}{3}$&$282$\\ \hline \end{longtable}"," ",0,"1/4*(x^3+1)^(4/3)/x^4-1/x*hypergeom([-1/3,-1/3],[2/3],-x^3)","C"
1408,1,33,79,2.166000," ","int((x^3-1)*(x^3+1)^(1/3)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\hypergeom \left(\left[-\frac{1}{3}, -\frac{1}{3}\right], \left[\frac{2}{3}\right], -x^{3}\right)}{x}+\frac{x^{2} \hypergeom \left(\left[-\frac{1}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], -x^{3}\right)}{2}$&$33$\\ risch&$\frac{x^{6}+4 x^{3}+3}{3 x \left(x^{3}+1\right)^{\frac{2}{3}}}-\frac{x^{2} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], -x^{3}\right)}{3}$&$40$\\ trager&$\frac{\left(x^{3}+1\right)^{\frac{1}{3}} \left(x^{3}+3\right)}{3 x}+\frac{2 \ln \left(317 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-555 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +2358 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}-1486 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-2358 x \left(x^{3}+1\right)^{\frac{2}{3}}+1803 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}+872 x^{3}-317 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-733 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+654\right)}{9}+\frac{2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-535 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+555 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +1803 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}-2893 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-1803 x \left(x^{3}+1\right)^{\frac{2}{3}}+2358 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}-1090 x^{3}+535 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-852 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-436\right)}{9}$&$254$\\ \hline \end{longtable}"," ",0,"1/x*hypergeom([-1/3,-1/3],[2/3],-x^3)+1/2*x^2*hypergeom([-1/3,2/3],[5/3],-x^3)","C"
1409,1,58,81,2.600000," ","int((x^3-1)^(1/3)*(x^3+1)/x^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{3 x^{6}-2 x^{3}-1}{4 x^{4} \left(x^{3}-1\right)^{\frac{2}{3}}}+\frac{\left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} x^{2} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], x^{3}\right)}{2 \mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}}}$&$58$\\ meijerg&$-\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{1}{3}, -\frac{1}{3}\right], \left[\frac{2}{3}\right], x^{3}\right)}{\left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x}-\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \left(-x^{3}+1\right)^{\frac{4}{3}}}{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x^{4}}$&$66$\\ trager&$-\frac{\left(3 x^{3}+1\right) \left(x^{3}-1\right)^{\frac{1}{3}}}{4 x^{4}}-\frac{\ln \left(-17421502720 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)^{2} x^{3}+3103405824 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +21033432144 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-23047994048 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right) x^{3}-1508552373 x \left(x^{3}-1\right)^{\frac{2}{3}}+193962864 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}+1246536764 x^{3}+139372021760 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)^{2}+369329904 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)-396625334\right)}{3}+\frac{\ln \left(14505155072 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)^{2} x^{3}-3103405824 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +24136837968 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-21940004336 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right) x^{3}-1314589509 x \left(x^{3}-1\right)^{\frac{2}{3}}-193962864 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}+1565213135 x^{3}-116041240576 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)^{2}+22309334240 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)-1020791175\right)}{3}-\frac{16 \ln \left(14505155072 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)^{2} x^{3}-3103405824 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +24136837968 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-21940004336 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right) x^{3}-1314589509 x \left(x^{3}-1\right)^{\frac{2}{3}}-193962864 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}+1565213135 x^{3}-116041240576 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)^{2}+22309334240 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)-1020791175\right) \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)}{3}$&$446$\\ \hline \end{longtable}"," ",0,"-1/4*(3*x^6-2*x^3-1)/x^4/(x^3-1)^(2/3)+1/2/signum(x^3-1)^(2/3)*(-signum(x^3-1))^(2/3)*x^2*hypergeom([2/3,2/3],[5/3],x^3)","C"
1410,1,620,77,1.016000," ","int(x/(x^2+1)/(x^3-x^2-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}-i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{10 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}-i-\frac{\sqrt{5}}{2}\right)}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}-i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{10 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}-i-\frac{\sqrt{5}}{2}\right)}+\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}+i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{10 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}+i-\frac{\sqrt{5}}{2}\right)}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}+i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{10 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}+i-\frac{\sqrt{5}}{2}\right)}$&$620$\\ elliptic&$\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}-i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{10 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}-i-\frac{\sqrt{5}}{2}\right)}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}-i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{10 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}-i-\frac{\sqrt{5}}{2}\right)}+\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}+i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{10 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}+i-\frac{\sqrt{5}}{2}\right)}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}+i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{10 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}+i-\frac{\sqrt{5}}{2}\right)}$&$620$\\ \hline \end{longtable}"," ",0,"1/10*(x/(1/2*5^(1/2)-1/2)-1/2/(1/2*5^(1/2)-1/2)+1/2/(1/2*5^(1/2)-1/2)*5^(1/2))^(1/2)*(-5*x*5^(1/2)+5/2*5^(1/2)+25/2)^(1/2)*(-x/(1/2*5^(1/2)-1/2))^(1/2)/(x^3-x^2-x)^(1/2)/(1/2-I-1/2*5^(1/2))*EllipticPi(((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2),(1/2-1/2*5^(1/2))/(1/2-I-1/2*5^(1/2)),1/5*5^(1/2)*((1/2*5^(1/2)-1/2)*5^(1/2))^(1/2))*5^(1/2)-1/10*(x/(1/2*5^(1/2)-1/2)-1/2/(1/2*5^(1/2)-1/2)+1/2/(1/2*5^(1/2)-1/2)*5^(1/2))^(1/2)*(-5*x*5^(1/2)+5/2*5^(1/2)+25/2)^(1/2)*(-x/(1/2*5^(1/2)-1/2))^(1/2)/(x^3-x^2-x)^(1/2)/(1/2-I-1/2*5^(1/2))*EllipticPi(((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2),(1/2-1/2*5^(1/2))/(1/2-I-1/2*5^(1/2)),1/5*5^(1/2)*((1/2*5^(1/2)-1/2)*5^(1/2))^(1/2))+1/10*(x/(1/2*5^(1/2)-1/2)-1/2/(1/2*5^(1/2)-1/2)+1/2/(1/2*5^(1/2)-1/2)*5^(1/2))^(1/2)*(-5*x*5^(1/2)+5/2*5^(1/2)+25/2)^(1/2)*(-x/(1/2*5^(1/2)-1/2))^(1/2)/(x^3-x^2-x)^(1/2)/(1/2+I-1/2*5^(1/2))*EllipticPi(((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2),(1/2-1/2*5^(1/2))/(1/2+I-1/2*5^(1/2)),1/5*5^(1/2)*((1/2*5^(1/2)-1/2)*5^(1/2))^(1/2))*5^(1/2)-1/10*(x/(1/2*5^(1/2)-1/2)-1/2/(1/2*5^(1/2)-1/2)+1/2/(1/2*5^(1/2)-1/2)*5^(1/2))^(1/2)*(-5*x*5^(1/2)+5/2*5^(1/2)+25/2)^(1/2)*(-x/(1/2*5^(1/2)-1/2))^(1/2)/(x^3-x^2-x)^(1/2)/(1/2+I-1/2*5^(1/2))*EllipticPi(((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2),(1/2-1/2*5^(1/2))/(1/2+I-1/2*5^(1/2)),1/5*5^(1/2)*((1/2*5^(1/2)-1/2)*5^(1/2))^(1/2))","C"
1411,1,1353,77,1.228000," ","int((x^2+x-1)/(x^2+1)/(x^3-x^2-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \sqrt{-5 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{5}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}}+\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}-i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{10 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}-i-\frac{\sqrt{5}}{2}\right)}+\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}-i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}-i-\frac{\sqrt{5}}{2}\right)}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}-i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{10 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}-i-\frac{\sqrt{5}}{2}\right)}-\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}-i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}-i-\frac{\sqrt{5}}{2}\right)}+\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}+i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{10 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}+i-\frac{\sqrt{5}}{2}\right)}-\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}+i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}+i-\frac{\sqrt{5}}{2}\right)}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}+i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{10 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}+i-\frac{\sqrt{5}}{2}\right)}+\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}+i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}+i-\frac{\sqrt{5}}{2}\right)}$&$1353$\\ elliptic&$\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{5 \sqrt{x^{3}-x^{2}-x}}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}}+\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}-i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{10 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}-i-\frac{\sqrt{5}}{2}\right)}+\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}-i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}-i-\frac{\sqrt{5}}{2}\right)}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}-i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{10 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}-i-\frac{\sqrt{5}}{2}\right)}-\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}-i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}-i-\frac{\sqrt{5}}{2}\right)}+\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}+i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{10 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}+i-\frac{\sqrt{5}}{2}\right)}-\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}+i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}+i-\frac{\sqrt{5}}{2}\right)}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}+i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{10 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}+i-\frac{\sqrt{5}}{2}\right)}+\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}+i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}+i-\frac{\sqrt{5}}{2}\right)}$&$1491$\\ \hline \end{longtable}"," ",0,"2/5*(1/2*5^(1/2)-1/2)*((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2)*(-5*(x-1/2-1/2*5^(1/2))*5^(1/2))^(1/2)*(-x/(1/2*5^(1/2)-1/2))^(1/2)/(x^3-x^2-x)^(1/2)*EllipticF(((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2),1/5*5^(1/2)*((1/2*5^(1/2)-1/2)*5^(1/2))^(1/2))+1/10*(x/(1/2*5^(1/2)-1/2)-1/2/(1/2*5^(1/2)-1/2)+1/2/(1/2*5^(1/2)-1/2)*5^(1/2))^(1/2)*(-5*x*5^(1/2)+5/2*5^(1/2)+25/2)^(1/2)*(-x/(1/2*5^(1/2)-1/2))^(1/2)/(x^3-x^2-x)^(1/2)/(1/2-I-1/2*5^(1/2))*EllipticPi(((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2),(1/2-1/2*5^(1/2))/(1/2-I-1/2*5^(1/2)),1/5*5^(1/2)*((1/2*5^(1/2)-1/2)*5^(1/2))^(1/2))*5^(1/2)+1/5*I*(x/(1/2*5^(1/2)-1/2)-1/2/(1/2*5^(1/2)-1/2)+1/2/(1/2*5^(1/2)-1/2)*5^(1/2))^(1/2)*(-5*x*5^(1/2)+5/2*5^(1/2)+25/2)^(1/2)*(-x/(1/2*5^(1/2)-1/2))^(1/2)/(x^3-x^2-x)^(1/2)/(1/2-I-1/2*5^(1/2))*EllipticPi(((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2),(1/2-1/2*5^(1/2))/(1/2-I-1/2*5^(1/2)),1/5*5^(1/2)*((1/2*5^(1/2)-1/2)*5^(1/2))^(1/2))*5^(1/2)-1/10*(x/(1/2*5^(1/2)-1/2)-1/2/(1/2*5^(1/2)-1/2)+1/2/(1/2*5^(1/2)-1/2)*5^(1/2))^(1/2)*(-5*x*5^(1/2)+5/2*5^(1/2)+25/2)^(1/2)*(-x/(1/2*5^(1/2)-1/2))^(1/2)/(x^3-x^2-x)^(1/2)/(1/2-I-1/2*5^(1/2))*EllipticPi(((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2),(1/2-1/2*5^(1/2))/(1/2-I-1/2*5^(1/2)),1/5*5^(1/2)*((1/2*5^(1/2)-1/2)*5^(1/2))^(1/2))-1/5*I*(x/(1/2*5^(1/2)-1/2)-1/2/(1/2*5^(1/2)-1/2)+1/2/(1/2*5^(1/2)-1/2)*5^(1/2))^(1/2)*(-5*x*5^(1/2)+5/2*5^(1/2)+25/2)^(1/2)*(-x/(1/2*5^(1/2)-1/2))^(1/2)/(x^3-x^2-x)^(1/2)/(1/2-I-1/2*5^(1/2))*EllipticPi(((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2),(1/2-1/2*5^(1/2))/(1/2-I-1/2*5^(1/2)),1/5*5^(1/2)*((1/2*5^(1/2)-1/2)*5^(1/2))^(1/2))+1/10*(x/(1/2*5^(1/2)-1/2)-1/2/(1/2*5^(1/2)-1/2)+1/2/(1/2*5^(1/2)-1/2)*5^(1/2))^(1/2)*(-5*x*5^(1/2)+5/2*5^(1/2)+25/2)^(1/2)*(-x/(1/2*5^(1/2)-1/2))^(1/2)/(x^3-x^2-x)^(1/2)/(1/2+I-1/2*5^(1/2))*EllipticPi(((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2),(1/2-1/2*5^(1/2))/(1/2+I-1/2*5^(1/2)),1/5*5^(1/2)*((1/2*5^(1/2)-1/2)*5^(1/2))^(1/2))*5^(1/2)-1/5*I*(x/(1/2*5^(1/2)-1/2)-1/2/(1/2*5^(1/2)-1/2)+1/2/(1/2*5^(1/2)-1/2)*5^(1/2))^(1/2)*(-5*x*5^(1/2)+5/2*5^(1/2)+25/2)^(1/2)*(-x/(1/2*5^(1/2)-1/2))^(1/2)/(x^3-x^2-x)^(1/2)/(1/2+I-1/2*5^(1/2))*EllipticPi(((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2),(1/2-1/2*5^(1/2))/(1/2+I-1/2*5^(1/2)),1/5*5^(1/2)*((1/2*5^(1/2)-1/2)*5^(1/2))^(1/2))*5^(1/2)-1/10*(x/(1/2*5^(1/2)-1/2)-1/2/(1/2*5^(1/2)-1/2)+1/2/(1/2*5^(1/2)-1/2)*5^(1/2))^(1/2)*(-5*x*5^(1/2)+5/2*5^(1/2)+25/2)^(1/2)*(-x/(1/2*5^(1/2)-1/2))^(1/2)/(x^3-x^2-x)^(1/2)/(1/2+I-1/2*5^(1/2))*EllipticPi(((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2),(1/2-1/2*5^(1/2))/(1/2+I-1/2*5^(1/2)),1/5*5^(1/2)*((1/2*5^(1/2)-1/2)*5^(1/2))^(1/2))+1/5*I*(x/(1/2*5^(1/2)-1/2)-1/2/(1/2*5^(1/2)-1/2)+1/2/(1/2*5^(1/2)-1/2)*5^(1/2))^(1/2)*(-5*x*5^(1/2)+5/2*5^(1/2)+25/2)^(1/2)*(-x/(1/2*5^(1/2)-1/2))^(1/2)/(x^3-x^2-x)^(1/2)/(1/2+I-1/2*5^(1/2))*EllipticPi(((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2),(1/2-1/2*5^(1/2))/(1/2+I-1/2*5^(1/2)),1/5*5^(1/2)*((1/2*5^(1/2)-1/2)*5^(1/2))^(1/2))","C"
1412,1,15,83,0.529000," ","int(x/(x^3+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 x^{\frac{4}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{4}{3}\right], \left[\frac{7}{3}\right], -x \right)}{4}$&$15$\\ risch&$\frac{x \left(1+x \right)}{\left(x^{2} \left(1+x \right)\right)^{\frac{1}{3}}}-x^{\frac{1}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x \right)$&$30$\\ trager&$\frac{\left(x^{3}+x^{2}\right)^{\frac{2}{3}}}{x}+\frac{\ln \left(-\frac{36 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{2}+90 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{2}{3}}-144 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{1}{3}} x -36 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x +60 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{2}-9 \left(x^{3}+x^{2}\right)^{\frac{2}{3}}-15 x \left(x^{3}+x^{2}\right)^{\frac{1}{3}}-18 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x +25 x^{2}+10 x}{x}\right)}{3}+2 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \ln \left(\frac{180 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{2}+90 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{2}{3}}+54 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{1}{3}} x -180 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x -114 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{2}+24 \left(x^{3}+x^{2}\right)^{\frac{2}{3}}-15 x \left(x^{3}+x^{2}\right)^{\frac{1}{3}}-96 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x -4 x^{2}-3 x}{x}\right)$&$323$\\ \hline \end{longtable}"," ",0,"3/4*x^(4/3)*hypergeom([1/3,4/3],[7/3],-x)","C"
1413,1,2059,61,8.667000," ","int(1/x^6/(x^3+1)/(x^3+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$2059$\\ trager&$\text{Expression too large to display}$&$2821$\\ \hline \end{longtable}"," ",0,"1/52360*(109573*x^6+19071*x^5-6357*x^4+20985*x^3-900*x^2+660*x-9240)/x^5/(x^2*(1+x))^(1/3)+1/3*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*ln(-(-6*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^6*x^2+6*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^6*x-39*(x^3+x^2)^(1/3)*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)^2*RootOf(3*_Z^6+3*_Z^3+1)^3*x-10*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x^2+24*(x^3+x^2)^(2/3)*RootOf(3*_Z^6+3*_Z^3+1)^3+17*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x-15*(x^3+x^2)^(1/3)*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)^2*x+4*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*x^2+13*(x^3+x^2)^(2/3)+10*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*x)/(3*x*RootOf(3*_Z^6+3*_Z^3+1)^3-3*RootOf(3*_Z^6+3*_Z^3+1)^3+2*x-1)/x)-RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*ln((21*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^6*x^2-21*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^6*x+3*(x^3+x^2)^(1/3)*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)^2*RootOf(3*_Z^6+3*_Z^3+1)^3*x+89*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x^2+21*(x^3+x^2)^(2/3)*RootOf(3*_Z^6+3*_Z^3+1)^3+2*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x+24*(x^3+x^2)^(1/3)*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)^2*x+44*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*x^2-(x^3+x^2)^(2/3)+8*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*x)/(3*x*RootOf(3*_Z^6+3*_Z^3+1)^3-3*RootOf(3*_Z^6+3*_Z^3+1)^3+2*x-1)/x)-2/3*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*ln((21*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^6*x^2-21*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^6*x+3*(x^3+x^2)^(1/3)*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)^2*RootOf(3*_Z^6+3*_Z^3+1)^3*x+89*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x^2+21*(x^3+x^2)^(2/3)*RootOf(3*_Z^6+3*_Z^3+1)^3+2*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x+24*(x^3+x^2)^(1/3)*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)^2*x+44*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*x^2-(x^3+x^2)^(2/3)+8*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*x)/(3*x*RootOf(3*_Z^6+3*_Z^3+1)^3-3*RootOf(3*_Z^6+3*_Z^3+1)^3+2*x-1)/x)+1/3*RootOf(3*_Z^6+3*_Z^3+1)*ln((6*RootOf(3*_Z^6+3*_Z^3+1)^7*x^2-6*RootOf(3*_Z^6+3*_Z^3+1)^7*x-39*(x^3+x^2)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^5*x+2*RootOf(3*_Z^6+3*_Z^3+1)^4*x^2+24*(x^3+x^2)^(2/3)*RootOf(3*_Z^6+3*_Z^3+1)^3+5*RootOf(3*_Z^6+3*_Z^3+1)^4*x-24*(x^3+x^2)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^2*x-8*RootOf(3*_Z^6+3*_Z^3+1)*x^2+11*(x^3+x^2)^(2/3)+RootOf(3*_Z^6+3*_Z^3+1)*x)/(3*x*RootOf(3*_Z^6+3*_Z^3+1)^3-3*RootOf(3*_Z^6+3*_Z^3+1)^3+x-2)/x)+RootOf(3*_Z^6+3*_Z^3+1)^4*ln(-(-21*RootOf(3*_Z^6+3*_Z^3+1)^7*x^2+21*RootOf(3*_Z^6+3*_Z^3+1)^7*x+3*(x^3+x^2)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^5*x+47*RootOf(3*_Z^6+3*_Z^3+1)^4*x^2+21*(x^3+x^2)^(2/3)*RootOf(3*_Z^6+3*_Z^3+1)^3+44*RootOf(3*_Z^6+3*_Z^3+1)^4*x-21*(x^3+x^2)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^2*x+24*RootOf(3*_Z^6+3*_Z^3+1)*x^2+22*(x^3+x^2)^(2/3)+15*RootOf(3*_Z^6+3*_Z^3+1)*x)/(3*x*RootOf(3*_Z^6+3*_Z^3+1)^3-3*RootOf(3*_Z^6+3*_Z^3+1)^3+x-2)/x)+1/3*RootOf(3*_Z^6+3*_Z^3+1)*ln(-(-21*RootOf(3*_Z^6+3*_Z^3+1)^7*x^2+21*RootOf(3*_Z^6+3*_Z^3+1)^7*x+3*(x^3+x^2)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^5*x+47*RootOf(3*_Z^6+3*_Z^3+1)^4*x^2+21*(x^3+x^2)^(2/3)*RootOf(3*_Z^6+3*_Z^3+1)^3+44*RootOf(3*_Z^6+3*_Z^3+1)^4*x-21*(x^3+x^2)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^2*x+24*RootOf(3*_Z^6+3*_Z^3+1)*x^2+22*(x^3+x^2)^(2/3)+15*RootOf(3*_Z^6+3*_Z^3+1)*x)/(3*x*RootOf(3*_Z^6+3*_Z^3+1)^3-3*RootOf(3*_Z^6+3*_Z^3+1)^3+x-2)/x)","B"
1414,1,2059,61,8.181000," ","int(1/x^6/(x^3+1)/(x^3+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$2059$\\ trager&$\text{Expression too large to display}$&$2119$\\ \hline \end{longtable}"," ",0,"1/52360*(109573*x^6+19071*x^5-6357*x^4+20985*x^3-900*x^2+660*x-9240)/x^5/(x^2*(1+x))^(1/3)+1/3*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*ln((-6*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^6*x^2+6*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^6*x-69*(x^3+x^2)^(1/3)*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)^2*RootOf(3*_Z^6+3*_Z^3+1)^3*x-31*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x^2+21*(x^3+x^2)^(2/3)*RootOf(3*_Z^6+3*_Z^3+1)^3+5*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x-45*(x^3+x^2)^(1/3)*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)^2*x-33*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*x^2-(x^3+x^2)^(2/3)-6*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*x)/(3*x*RootOf(3*_Z^6+3*_Z^3+1)^3-3*RootOf(3*_Z^6+3*_Z^3+1)^3+2*x-1)/x)+RootOf(3*_Z^6+3*_Z^3+1)^3*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*ln(-(-24*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^6*x^2+24*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^6*x+6*(x^3+x^2)^(1/3)*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)^2*RootOf(3*_Z^6+3*_Z^3+1)^3*x+2*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x^2+24*(x^3+x^2)^(2/3)*RootOf(3*_Z^6+3*_Z^3+1)^3+26*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x-9*(x^3+x^2)^(1/3)*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)^2*x+2*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*x^2+13*(x^3+x^2)^(2/3)+5*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*x)/(3*x*RootOf(3*_Z^6+3*_Z^3+1)^3-3*RootOf(3*_Z^6+3*_Z^3+1)^3+2*x-1)/x)+1/3*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*ln(-(-24*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^6*x^2+24*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^6*x+6*(x^3+x^2)^(1/3)*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)^2*RootOf(3*_Z^6+3*_Z^3+1)^3*x+2*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x^2+24*(x^3+x^2)^(2/3)*RootOf(3*_Z^6+3*_Z^3+1)^3+26*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*RootOf(3*_Z^6+3*_Z^3+1)^3*x-9*(x^3+x^2)^(1/3)*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)^2*x+2*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*x^2+13*(x^3+x^2)^(2/3)+5*RootOf(RootOf(3*_Z^6+3*_Z^3+1)^3+_Z^3+1)*x)/(3*x*RootOf(3*_Z^6+3*_Z^3+1)^3-3*RootOf(3*_Z^6+3*_Z^3+1)^3+2*x-1)/x)+1/3*RootOf(3*_Z^6+3*_Z^3+1)*ln((6*RootOf(3*_Z^6+3*_Z^3+1)^7*x^2-6*RootOf(3*_Z^6+3*_Z^3+1)^7*x-39*(x^3+x^2)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^5*x+2*RootOf(3*_Z^6+3*_Z^3+1)^4*x^2+24*(x^3+x^2)^(2/3)*RootOf(3*_Z^6+3*_Z^3+1)^3+5*RootOf(3*_Z^6+3*_Z^3+1)^4*x-24*(x^3+x^2)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^2*x-8*RootOf(3*_Z^6+3*_Z^3+1)*x^2+11*(x^3+x^2)^(2/3)+RootOf(3*_Z^6+3*_Z^3+1)*x)/(3*x*RootOf(3*_Z^6+3*_Z^3+1)^3-3*RootOf(3*_Z^6+3*_Z^3+1)^3+x-2)/x)+RootOf(3*_Z^6+3*_Z^3+1)^4*ln(-(-21*RootOf(3*_Z^6+3*_Z^3+1)^7*x^2+21*RootOf(3*_Z^6+3*_Z^3+1)^7*x+3*(x^3+x^2)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^5*x+47*RootOf(3*_Z^6+3*_Z^3+1)^4*x^2+21*(x^3+x^2)^(2/3)*RootOf(3*_Z^6+3*_Z^3+1)^3+44*RootOf(3*_Z^6+3*_Z^3+1)^4*x-21*(x^3+x^2)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^2*x+24*RootOf(3*_Z^6+3*_Z^3+1)*x^2+22*(x^3+x^2)^(2/3)+15*RootOf(3*_Z^6+3*_Z^3+1)*x)/(3*x*RootOf(3*_Z^6+3*_Z^3+1)^3-3*RootOf(3*_Z^6+3*_Z^3+1)^3+x-2)/x)+1/3*RootOf(3*_Z^6+3*_Z^3+1)*ln(-(-21*RootOf(3*_Z^6+3*_Z^3+1)^7*x^2+21*RootOf(3*_Z^6+3*_Z^3+1)^7*x+3*(x^3+x^2)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^5*x+47*RootOf(3*_Z^6+3*_Z^3+1)^4*x^2+21*(x^3+x^2)^(2/3)*RootOf(3*_Z^6+3*_Z^3+1)^3+44*RootOf(3*_Z^6+3*_Z^3+1)^4*x-21*(x^3+x^2)^(1/3)*RootOf(3*_Z^6+3*_Z^3+1)^2*x+24*RootOf(3*_Z^6+3*_Z^3+1)*x^2+22*(x^3+x^2)^(2/3)+15*RootOf(3*_Z^6+3*_Z^3+1)*x)/(3*x*RootOf(3*_Z^6+3*_Z^3+1)^3-3*RootOf(3*_Z^6+3*_Z^3+1)^3+x-2)/x)","B"
1415,1,57,81,2.454000," ","int((x^3-1)^(1/3)*(2*x^3-1)/x^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{9 x^{6}-10 x^{3}+1}{4 x^{4} \left(x^{3}-1\right)^{\frac{2}{3}}}+\frac{\left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} x^{2} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], x^{3}\right)}{\mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}}}$&$57$\\ meijerg&$-\frac{2 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{1}{3}, -\frac{1}{3}\right], \left[\frac{2}{3}\right], x^{3}\right)}{\left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x}+\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \left(-x^{3}+1\right)^{\frac{4}{3}}}{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x^{4}}$&$66$\\ trager&$-\frac{\left(9 x^{3}-1\right) \left(x^{3}-1\right)^{\frac{1}{3}}}{4 x^{4}}+\frac{2 \ln \left(2916347648 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)^{2} x^{3}+3103405824 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +3103405824 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+2921134096 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right) x^{3}-1508552373 x \left(x^{3}-1\right)^{\frac{2}{3}}-1508552373 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-1497160390 x^{3}-23330781184 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)^{2}+7434849264 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)+476369215\right)}{3}-\frac{32 \ln \left(2916347648 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)^{2} x^{3}+3103405824 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +3103405824 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+2921134096 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right) x^{3}-1508552373 x \left(x^{3}-1\right)^{\frac{2}{3}}-1508552373 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-1497160390 x^{3}-23330781184 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)^{2}+7434849264 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)+476369215\right) \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)}{3}+\frac{32 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right) \ln \left(2916347648 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)^{2} x^{3}-3103405824 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -3103405824 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-3285677552 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right) x^{3}-1314589509 x \left(x^{3}-1\right)^{\frac{2}{3}}-1314589509 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-1303197526 x^{3}-23330781184 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)^{2}-4518501616 \RootOf \left(256 \textit{\_Z}^{2}-16 \textit{\_Z} +1\right)+849911430\right)}{3}$&$457$\\ \hline \end{longtable}"," ",0,"-1/4*(9*x^6-10*x^3+1)/x^4/(x^3-1)^(2/3)+1/signum(x^3-1)^(2/3)*(-signum(x^3-1))^(2/3)*x^2*hypergeom([2/3,2/3],[5/3],x^3)","C"
1416,1,400,82,3.934000," ","int((x^3-1)^(2/3)*(3*x^3-1)/x^6/(2*x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{7 x^{6}-9 x^{3}+2}{10 x^{5} \left(x^{3}-1\right)^{\frac{1}{3}}}+\RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(-\frac{-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}-1\right)^{\frac{2}{3}}-3 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+1}{2 x^{3}-1}\right)-\frac{\ln \left(-\frac{-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+2 x \left(x^{3}-1\right)^{\frac{2}{3}}-2 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-x^{3}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+1}{2 x^{3}-1}\right)}{3}-\ln \left(-\frac{-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+2 x \left(x^{3}-1\right)^{\frac{2}{3}}-2 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-x^{3}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+1}{2 x^{3}-1}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)$&$400$\\ trager&$\frac{\left(x^{3}-1\right)^{\frac{2}{3}} \left(7 x^{3}-2\right)}{10 x^{5}}+32 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) \ln \left(-\frac{-374952960 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2} x^{3}+10252800 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -10252800 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) x^{2}-34273056 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) x^{3}-421089 x \left(x^{3}-1\right)^{\frac{2}{3}}+421089 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-252248 x^{3}+2999623680 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2}+51556128 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)+220717}{2 x^{3}-1}\right)-\frac{\ln \left(\frac{374952960 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2} x^{3}+10252800 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -10252800 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) x^{2}-26461536 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) x^{3}+527889 x \left(x^{3}-1\right)^{\frac{2}{3}}-527889 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-64078 x^{3}-2999623680 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2}-10936032 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)-9154}{2 x^{3}-1}\right)}{3}-32 \ln \left(\frac{374952960 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2} x^{3}+10252800 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -10252800 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) x^{2}-26461536 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) x^{3}+527889 x \left(x^{3}-1\right)^{\frac{2}{3}}-527889 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-64078 x^{3}-2999623680 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2}-10936032 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)-9154}{2 x^{3}-1}\right) \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)$&$488$\\ \hline \end{longtable}"," ",0,"1/10*(7*x^6-9*x^3+2)/x^5/(x^3-1)^(1/3)+RootOf(9*_Z^2+3*_Z+1)*ln(-(-9*RootOf(9*_Z^2+3*_Z+1)^2*x^3+3*RootOf(9*_Z^2+3*_Z+1)*x^3+3*x*(x^3-1)^(2/3)-3*x^2*(x^3-1)^(1/3)-3*RootOf(9*_Z^2+3*_Z+1)+1)/(2*x^3-1))-1/3*ln(-(-9*RootOf(9*_Z^2+3*_Z+1)^2*x^3+3*RootOf(9*_Z^2+3*_Z+1)*(x^3-1)^(2/3)*x-3*RootOf(9*_Z^2+3*_Z+1)*(x^3-1)^(1/3)*x^2-6*RootOf(9*_Z^2+3*_Z+1)*x^3+2*x*(x^3-1)^(2/3)-2*x^2*(x^3-1)^(1/3)-x^3+3*RootOf(9*_Z^2+3*_Z+1)+1)/(2*x^3-1))-ln(-(-9*RootOf(9*_Z^2+3*_Z+1)^2*x^3+3*RootOf(9*_Z^2+3*_Z+1)*(x^3-1)^(2/3)*x-3*RootOf(9*_Z^2+3*_Z+1)*(x^3-1)^(1/3)*x^2-6*RootOf(9*_Z^2+3*_Z+1)*x^3+2*x*(x^3-1)^(2/3)-2*x^2*(x^3-1)^(1/3)-x^3+3*RootOf(9*_Z^2+3*_Z+1)+1)/(2*x^3-1))*RootOf(9*_Z^2+3*_Z+1)","C"
1417,1,267,81,6.699000," ","int(x^4/(x^4-1)^2/(x^4+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{x \left(13 x^{4}+2 x^{2}+5\right)}{80 \left(x^{2}-1\right) \left(x^{2} \left(x^{2}+1\right)\right)^{\frac{1}{4}} \left(x^{2}+1\right)}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(\frac{\sqrt{x^{4}+x^{2}}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x -2 \left(x^{4}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{3}+4 \left(x^{4}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x}{\left(1+x \right) x \left(-1+x \right)}\right)}{128}-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(\frac{\sqrt{x^{4}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x +2 \left(x^{4}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+3 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{3}+4 \left(x^{4}+x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}-8\right) x}{x \left(-1+x \right) \left(1+x \right)}\right)}{128}$&$267$\\ trager&$-\frac{\left(13 x^{4}+2 x^{2}+5\right) \left(x^{4}+x^{2}\right)^{\frac{3}{4}}}{80 \left(x^{2}-1\right) \left(x^{2}+1\right)^{2} x}+\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(-\frac{\sqrt{x^{4}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x -2 \left(x^{4}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+3 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{3}-4 \left(x^{4}+x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}-8\right) x}{\left(1+x \right) x \left(-1+x \right)}\right)}{128}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(\frac{\sqrt{x^{4}+x^{2}}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x -2 \left(x^{4}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{3}+4 \left(x^{4}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x}{\left(1+x \right) x \left(-1+x \right)}\right)}{128}$&$268$\\ \hline \end{longtable}"," ",0,"-1/80*x*(13*x^4+2*x^2+5)/(x^2-1)/(x^2*(x^2+1))^(1/4)/(x^2+1)+1/128*RootOf(_Z^2+RootOf(_Z^4-8)^2)*ln(((x^4+x^2)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x-2*(x^4+x^2)^(1/4)*RootOf(_Z^4-8)^2*x^2-3*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^3+4*(x^4+x^2)^(3/4)-RootOf(_Z^2+RootOf(_Z^4-8)^2)*x)/(1+x)/x/(-1+x))-1/128*RootOf(_Z^4-8)*ln(((x^4+x^2)^(1/2)*RootOf(_Z^4-8)^3*x+2*(x^4+x^2)^(1/4)*RootOf(_Z^4-8)^2*x^2+3*RootOf(_Z^4-8)*x^3+4*(x^4+x^2)^(3/4)+RootOf(_Z^4-8)*x)/x/(-1+x)/(1+x))","C"
1418,1,439,83,3.464000," ","int((x^2+1)*(x^4+x^3)^(1/4)/x^2/(x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{4}+x^{3}\right)^{\frac{1}{4}}}{x}-\ln \left(\frac{2 \left(x^{4}+x^{3}\right)^{\frac{3}{4}}-2 \sqrt{x^{4}+x^{3}}\, x +2 x^{2} \left(x^{4}+x^{3}\right)^{\frac{1}{4}}-2 x^{3}-x^{2}}{x^{2}}\right)+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(\frac{3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}-4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(x^{4}+x^{3}\right)^{\frac{1}{4}} x^{2}-4 \sqrt{x^{4}+x^{3}}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x +4 \left(x^{4}+x^{3}\right)^{\frac{3}{4}}}{\left(-1+x \right) x^{2}}\right)-\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(\frac{3 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{3}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{2}+4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(x^{4}+x^{3}\right)^{\frac{1}{4}} x^{2}+4 \sqrt{x^{4}+x^{3}}\, \RootOf \left(\textit{\_Z}^{4}-2\right) x +4 \left(x^{4}+x^{3}\right)^{\frac{3}{4}}}{\left(-1+x \right) x^{2}}\right)+\frac{\RootOf \left(\textit{\_Z}^{4}-2\right)^{3} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(\frac{2 \sqrt{x^{4}+x^{3}}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x -2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{3}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{2}+4 \left(x^{4}+x^{3}\right)^{\frac{3}{4}}-4 x^{2} \left(x^{4}+x^{3}\right)^{\frac{1}{4}}}{x^{2}}\right)}{2}$&$439$\\ risch&$\frac{4 \left(x^{3} \left(1+x \right)\right)^{\frac{1}{4}}}{x}+\frac{\left(-\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{3}{4}}+2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x^{2}-5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-4 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x -4 \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(1+x \right)^{2}}\right)+\ln \left(\frac{2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{3}{4}}+2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, x +2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x^{2}+2 x^{3}+2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}+4 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x +5 x^{2}+2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}}+4 x +1}{\left(1+x \right)^{2}}\right)-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(-\frac{2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x +2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)+2 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x^{2}+4 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x -3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{3}+2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-4 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{3}{4}}-7 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{2}-5 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)}{\left(-1+x \right) \left(1+x \right)^{2}}\right)-\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(\frac{2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x +2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}+2 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x^{2}+4 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x +3 \RootOf \left(\textit{\_Z}^{4}-2\right) x^{3}+2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+7 \RootOf \left(\textit{\_Z}^{4}-2\right) x^{2}+4 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{3}{4}}+5 \RootOf \left(\textit{\_Z}^{4}-2\right) x +\RootOf \left(\textit{\_Z}^{4}-2\right)}{\left(-1+x \right) \left(1+x \right)^{2}}\right)\right) \left(x^{3} \left(1+x \right)\right)^{\frac{1}{4}} \left(\left(1+x \right)^{3} x \right)^{\frac{1}{4}}}{x \left(1+x \right)}$&$869$\\ \hline \end{longtable}"," ",0,"4*(x^4+x^3)^(1/4)/x-ln((2*(x^4+x^3)^(3/4)-2*(x^4+x^3)^(1/2)*x+2*x^2*(x^4+x^3)^(1/4)-2*x^3-x^2)/x^2)+RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln((3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*x^3+RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*x^2-4*RootOf(_Z^4-2)^2*(x^4+x^3)^(1/4)*x^2-4*(x^4+x^3)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x+4*(x^4+x^3)^(3/4))/(-1+x)/x^2)-RootOf(_Z^4-2)*ln((3*RootOf(_Z^4-2)^3*x^3+RootOf(_Z^4-2)^3*x^2+4*RootOf(_Z^4-2)^2*(x^4+x^3)^(1/4)*x^2+4*(x^4+x^3)^(1/2)*RootOf(_Z^4-2)*x+4*(x^4+x^3)^(3/4))/(-1+x)/x^2)+1/2*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln((2*(x^4+x^3)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^3*x-2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^3*x^3-RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^3*x^2+4*(x^4+x^3)^(3/4)-4*x^2*(x^4+x^3)^(1/4))/x^2)","C"
1419,1,222,82,7.104000," ","int((x^3+4)*(x^4-x^3-1)/x^2/(x^3+1)^(3/4)/(x^4+x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{3}+1\right)^{\frac{1}{4}}}{x}+2 \RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{4}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{3}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} \left(x^{3}+1\right)^{\frac{1}{4}} x^{3}+2 \RootOf \left(\textit{\_Z}^{4}+1\right) \sqrt{x^{3}+1}\, x^{2}-2 \left(x^{3}+1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{x^{4}+x^{3}+1}\right)+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \sqrt{x^{3}+1}\, x^{2}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} \left(x^{3}+1\right)^{\frac{1}{4}} x^{3}+\RootOf \left(\textit{\_Z}^{4}+1\right) x^{4}-\RootOf \left(\textit{\_Z}^{4}+1\right) x^{3}-2 \left(x^{3}+1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}+1\right)}{x^{4}+x^{3}+1}\right)$&$222$\\ risch&$\frac{4 \left(x^{3}+1\right)^{\frac{1}{4}}}{x}+\frac{\left(2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{10}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{9}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{9}+3 x^{6}+3 x^{3}+1\right)^{\frac{3}{4}} x^{3}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{7}-2 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{9}+3 x^{6}+3 x^{3}+1\right)^{\frac{1}{4}} x^{7}-3 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{6}-2 \sqrt{x^{9}+3 x^{6}+3 x^{3}+1}\, x^{5}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{4}-4 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{9}+3 x^{6}+3 x^{3}+1\right)^{\frac{1}{4}} x^{4}-3 x^{3} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-2 \sqrt{x^{9}+3 x^{6}+3 x^{3}+1}\, x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{9}+3 x^{6}+3 x^{3}+1\right)^{\frac{1}{4}} x -\RootOf \left(\textit{\_Z}^{4}+1\right)^{2}}{\left(x^{4}+x^{3}+1\right) \left(1+x \right)^{2} \left(x^{2}-x +1\right)^{2}}\right)+2 \RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{10}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{9}+3 x^{6}+3 x^{3}+1\right)^{\frac{1}{4}} x^{7}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{9}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{7}+4 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{9}+3 x^{6}+3 x^{3}+1\right)^{\frac{1}{4}} x^{4}-3 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{6}-2 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{9}+3 x^{6}+3 x^{3}+1\right)^{\frac{3}{4}} x^{3}+2 \sqrt{x^{9}+3 x^{6}+3 x^{3}+1}\, x^{5}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{4}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{9}+3 x^{6}+3 x^{3}+1\right)^{\frac{1}{4}} x -3 x^{3} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+2 \sqrt{x^{9}+3 x^{6}+3 x^{3}+1}\, x^{2}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{2}}{\left(x^{4}+x^{3}+1\right) \left(1+x \right)^{2} \left(x^{2}-x +1\right)^{2}}\right)\right) \left(\left(x^{3}+1\right)^{3}\right)^{\frac{1}{4}}}{\left(x^{3}+1\right)^{\frac{3}{4}}}$&$595$\\ \hline \end{longtable}"," ",0,"4*(x^3+1)^(1/4)/x+2*RootOf(_Z^4+1)*ln(-(RootOf(_Z^4+1)^3*x^4-RootOf(_Z^4+1)^3*x^3-2*RootOf(_Z^4+1)^2*(x^3+1)^(1/4)*x^3+2*RootOf(_Z^4+1)*(x^3+1)^(1/2)*x^2-2*(x^3+1)^(3/4)*x-RootOf(_Z^4+1)^3)/(x^4+x^3+1))+2*RootOf(_Z^4+1)^3*ln(-(2*RootOf(_Z^4+1)^3*(x^3+1)^(1/2)*x^2+2*RootOf(_Z^4+1)^2*(x^3+1)^(1/4)*x^3+RootOf(_Z^4+1)*x^4-RootOf(_Z^4+1)*x^3-2*(x^3+1)^(3/4)*x-RootOf(_Z^4+1))/(x^4+x^3+1))","C"
1420,1,291,81,3.048000," ","int((2*x^4+x^2+1)/(x^2+1)^(1/4)/(x^4+3*x^2+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 x}{\left(x^{2}+1\right)^{\frac{1}{4}}}+\frac{7 \ln \left(\frac{8 \left(x^{2}+1\right)^{\frac{3}{4}} \RootOf \left(32 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)-2 \left(x^{2}+1\right)^{\frac{3}{4}}+x \sqrt{x^{2}+1}+8 \left(x^{2}+1\right)^{\frac{1}{4}} \RootOf \left(32 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)-8 \RootOf \left(32 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) x +x}{x^{2}+2}\right)}{2}-14 \ln \left(\frac{8 \left(x^{2}+1\right)^{\frac{3}{4}} \RootOf \left(32 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)-2 \left(x^{2}+1\right)^{\frac{3}{4}}+x \sqrt{x^{2}+1}+8 \left(x^{2}+1\right)^{\frac{1}{4}} \RootOf \left(32 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)-8 \RootOf \left(32 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) x +x}{x^{2}+2}\right) \RootOf \left(32 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)+14 \RootOf \left(32 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) \ln \left(-\frac{8 \left(x^{2}+1\right)^{\frac{3}{4}} \RootOf \left(32 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)-x \sqrt{x^{2}+1}+8 \left(x^{2}+1\right)^{\frac{1}{4}} \RootOf \left(32 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)-8 \RootOf \left(32 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) x -2 \left(x^{2}+1\right)^{\frac{1}{4}}+x}{x^{2}+2}\right)$&$291$\\ risch&$\frac{4 x}{\left(x^{2}+1\right)^{\frac{1}{4}}}+7 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) \ln \left(-\frac{4 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{3}{4}}-x \sqrt{x^{2}+1}+4 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{1}{4}}+4 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) x +2 \left(x^{2}+1\right)^{\frac{1}{4}}+x}{x^{2}+2}\right)-\frac{7 \ln \left(\frac{4 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{3}{4}}+2 \left(x^{2}+1\right)^{\frac{3}{4}}+x \sqrt{x^{2}+1}+4 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{1}{4}}+4 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) x +x}{x^{2}+2}\right)}{2}-7 \ln \left(\frac{4 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{3}{4}}+2 \left(x^{2}+1\right)^{\frac{3}{4}}+x \sqrt{x^{2}+1}+4 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{1}{4}}+4 \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) x +x}{x^{2}+2}\right) \RootOf \left(8 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right)$&$291$\\ \hline \end{longtable}"," ",0,"4*x/(x^2+1)^(1/4)+7/2*ln((8*(x^2+1)^(3/4)*RootOf(32*_Z^2-8*_Z+1)-2*(x^2+1)^(3/4)+x*(x^2+1)^(1/2)+8*(x^2+1)^(1/4)*RootOf(32*_Z^2-8*_Z+1)-8*RootOf(32*_Z^2-8*_Z+1)*x+x)/(x^2+2))-14*ln((8*(x^2+1)^(3/4)*RootOf(32*_Z^2-8*_Z+1)-2*(x^2+1)^(3/4)+x*(x^2+1)^(1/2)+8*(x^2+1)^(1/4)*RootOf(32*_Z^2-8*_Z+1)-8*RootOf(32*_Z^2-8*_Z+1)*x+x)/(x^2+2))*RootOf(32*_Z^2-8*_Z+1)+14*RootOf(32*_Z^2-8*_Z+1)*ln(-(8*(x^2+1)^(3/4)*RootOf(32*_Z^2-8*_Z+1)-x*(x^2+1)^(1/2)+8*(x^2+1)^(1/4)*RootOf(32*_Z^2-8*_Z+1)-8*RootOf(32*_Z^2-8*_Z+1)*x-2*(x^2+1)^(1/4)+x)/(x^2+2))","C"
1421,0,0,81,0.009000," ","int((a*x^2-b)*(a*x^4-b*x^2)^(1/4)/x^2,x)","\[\int \frac{\left(a \,x^{2}-b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}{x^{2}}\, dx\]"," ",0,"int((a*x^2-b)*(a*x^4-b*x^2)^(1/4)/x^2,x)","F"
1422,0,0,47,0.012000," ","int((a*x^4+b)/x^4/(a*x^4+2*b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{a \,x^{4}+b}{x^{4} \left(a \,x^{4}+2 b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^4+b)/x^4/(a*x^4+2*b)/(a*x^4+b*x^2)^(1/4),x)","F"
1423,0,0,47,0.001000," ","int((a*x^4+b)/x^4/(a*x^4+2*b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{a \,x^{4}+b}{x^{4} \left(a \,x^{4}+2 b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^4+b)/x^4/(a*x^4+2*b)/(a*x^4+b*x^2)^(1/4),x)","F"
1424,1,3402,87,0.217000," ","int((-x^4+1)/x^2/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$3402$\\ risch&$\text{Expression too large to display}$&$3402$\\ elliptic&$\text{Expression too large to display}$&$3402$\\ \hline \end{longtable}"," ",0,"-(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2)/a/x+b/a*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))^2*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2)*(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)*EllipticF(((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2),((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2))+(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*EllipticPi(((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2),(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)),((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)))-b/a*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))^2*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2)/RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)*(EllipticF(((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2),((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2))+(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1)*EllipticPi(((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2),RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)*(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)),((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)))","C"
1425,0,0,84,0.025000," ","int((x^2-1)/(x^2+1)/(x^6+x^2)^(1/4),x)","\[\int \frac{x^{2}-1}{\left(x^{2}+1\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((x^2-1)/(x^2+1)/(x^6+x^2)^(1/4),x)","F"
1426,0,0,84,0.002000," ","int((x^2-1)/(x^2+1)/(x^6+x^2)^(1/4),x)","\[\int \frac{x^{2}-1}{\left(x^{2}+1\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((x^2-1)/(x^2+1)/(x^6+x^2)^(1/4),x)","F"
1427,1,64,89,0.795000," ","int((x^4-x^3)^(1/4)*(x^8-1)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{4 \mathrm{signum}\left(-1+x \right)^{\frac{1}{4}} x^{\frac{23}{4}} \hypergeom \left(\left[-\frac{1}{4}, \frac{23}{4}\right], \left[\frac{27}{4}\right], x\right)}{23 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{4}}}+\frac{4 \mathrm{signum}\left(-1+x \right)^{\frac{1}{4}} \left(-\frac{4}{5} x^{2}-\frac{1}{5} x +1\right) \left(1-x \right)^{\frac{1}{4}}}{9 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{4}} x^{\frac{9}{4}}}$&$64$\\ trager&$\frac{\left(x^{4}-x^{3}\right)^{\frac{1}{4}} \left(122880 x^{8}-6144 x^{7}-7296 x^{6}-9120 x^{5}-12540 x^{4}-21945 x^{3}-262144 x^{2}-65536 x +327680\right)}{737280 x^{3}}-\frac{1463 \ln \left(\frac{2 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}+2 \sqrt{x^{4}-x^{3}}\, x +2 x^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}+2 x^{3}-x^{2}}{x^{2}}\right)}{65536}-\frac{1463 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \sqrt{x^{4}-x^{3}}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}-2 x^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}}{x^{2}}\right)}{65536}$&$203$\\ risch&$\frac{\left(122880 x^{9}-129024 x^{8}-1152 x^{7}-1824 x^{6}-3420 x^{5}-9405 x^{4}-240199 x^{3}+196608 x^{2}+393216 x -327680\right) \left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}}}{737280 x^{3} \left(-1+x \right)}+\frac{\left(-\frac{1463 \ln \left(\frac{2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{3}{4}}+2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, x +2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x^{2}+2 x^{3}-2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}-4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x -5 x^{2}+2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}}+4 x -1}{\left(-1+x \right)^{2}}\right)}{65536}+\frac{1463 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{3}{4}}-2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x^{2}+5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x -4 \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(-1+x \right)^{2}}\right)}{65536}\right) \left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}} \left(x \left(-1+x \right)^{3}\right)^{\frac{1}{4}}}{x \left(-1+x \right)}$&$445$\\ \hline \end{longtable}"," ",0,"4/23*signum(-1+x)^(1/4)/(-signum(-1+x))^(1/4)*x^(23/4)*hypergeom([-1/4,23/4],[27/4],x)+4/9*signum(-1+x)^(1/4)/(-signum(-1+x))^(1/4)/x^(9/4)*(-4/5*x^2-1/5*x+1)*(1-x)^(1/4)","C"
1428,1,3136,24,352.092000," ","int((x^4+1)^(1/4)*(x^4+2)/x^2/(x^8+2*x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$3136$\\ risch&$\text{Expression too large to display}$&$5218$\\ \hline \end{longtable}"," ",0,"2*(x^4+1)^(1/4)/x+RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*ln(-(20272245637120*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^10*x^4-20272245637120*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^10+9924432101376*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6*x^4+162133966848*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6*(x^4+1)^(1/4)*x^3-4381999104*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4*(x^4+1)^(1/2)*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*x^2+924327936*(x^4+1)^(3/4)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4*x+14205776297984*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)-3557860034560*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2*x^4-39861820544*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2*(x^4+1)^(1/4)*x^3+604506280*(x^4+1)^(1/2)*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*x^2+9167333*(x^4+1)^(3/4)*x-2243593677312*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2))/(8192*x^4*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4-8192*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4+408*x^4+985))-134217728/1393*ln(-(13056700579840*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^9*x^4+60300046976942080*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^7*(x^4+1)^(1/2)*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*x^2-13056700579840*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^9-15812597383168*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^5*x^4+14074076969566208*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6*(x^4+1)^(1/4)*x^3-14500861407133696*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^3*(x^4+1)^(1/2)*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*x^2-1287588814848*(x^4+1)^(3/4)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4*x+271107227648*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^5+3048798796800*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)*x^4-3384492771480576*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2*(x^4+1)^(1/4)*x^3+322407541799*(x^4+1)^(3/4)*x+690677563904*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2))/(8192*x^4*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4-8192*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4-2378*x^4+985))*RootOf(134217728*_Z^8-32276480*_Z^4+1)^7*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)+32276480/1393*ln(-(13056700579840*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^9*x^4+60300046976942080*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^7*(x^4+1)^(1/2)*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*x^2-13056700579840*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^9-15812597383168*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^5*x^4+14074076969566208*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6*(x^4+1)^(1/4)*x^3-14500861407133696*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^3*(x^4+1)^(1/2)*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*x^2-1287588814848*(x^4+1)^(3/4)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4*x+271107227648*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^5+3048798796800*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)*x^4-3384492771480576*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2*(x^4+1)^(1/4)*x^3+322407541799*(x^4+1)^(3/4)*x+690677563904*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2))/(8192*x^4*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4-8192*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4-2378*x^4+985))*RootOf(134217728*_Z^8-32276480*_Z^4+1)^3*RootOf(RootOf(134217728*_Z^8-32276480*_Z^4+1)^2+_Z^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)+RootOf(134217728*_Z^8-32276480*_Z^4+1)*ln((20272245637120*RootOf(134217728*_Z^8-32276480*_Z^4+1)^11*x^4-20272245637120*RootOf(134217728*_Z^8-32276480*_Z^4+1)^11+9924432101376*RootOf(134217728*_Z^8-32276480*_Z^4+1)^7*x^4+162133966848*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6*(x^4+1)^(1/4)*x^3+4381999104*RootOf(134217728*_Z^8-32276480*_Z^4+1)^5*(x^4+1)^(1/2)*x^2-924327936*(x^4+1)^(3/4)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4*x+14205776297984*RootOf(134217728*_Z^8-32276480*_Z^4+1)^7-3557860034560*RootOf(134217728*_Z^8-32276480*_Z^4+1)^3*x^4-39861820544*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2*(x^4+1)^(1/4)*x^3-604506280*RootOf(134217728*_Z^8-32276480*_Z^4+1)*(x^4+1)^(1/2)*x^2-9167333*(x^4+1)^(3/4)*x-2243593677312*RootOf(134217728*_Z^8-32276480*_Z^4+1)^3)/(8192*x^4*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4-8192*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4+408*x^4+985))-1/1393*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*ln((7627861917696*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^10*x^4-7627861917696*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^10-9242836729856*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6*x^4-8244637831528448*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6*(x^4+1)^(1/4)*x^3-9676914688*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4*(x^4+1)^(1/2)*x^2-604054011904*(x^4+1)^(3/4)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4*x+163334586368*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+1785944985600*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2*x^4+1982589963786880*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2*(x^4+1)^(1/4)*x^3+263176704*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*(x^4+1)^(1/2)*x^2+188861960721*(x^4+1)^(3/4)*x+404589549568*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)/(8192*x^4*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4-8192*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4-2378*x^4+985))","B"
1429,1,3651,24,371.218000," ","int((x^4+1)^(1/4)*(x^4+2)/x^2/(x^8+2*x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$3651$\\ risch&$\text{Expression too large to display}$&$5731$\\ \hline \end{longtable}"," ",0,"2*(x^4+1)^(1/4)/x-RootOf(134217728*_Z^8-32276480*_Z^4+1)*ln(-(20272245637120*RootOf(134217728*_Z^8-32276480*_Z^4+1)^11*x^4-20272245637120*RootOf(134217728*_Z^8-32276480*_Z^4+1)^11+9924432101376*RootOf(134217728*_Z^8-32276480*_Z^4+1)^7*x^4-162133966848*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6*(x^4+1)^(1/4)*x^3+4381999104*RootOf(134217728*_Z^8-32276480*_Z^4+1)^5*(x^4+1)^(1/2)*x^2+924327936*(x^4+1)^(3/4)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4*x+14205776297984*RootOf(134217728*_Z^8-32276480*_Z^4+1)^7-3557860034560*RootOf(134217728*_Z^8-32276480*_Z^4+1)^3*x^4+39861820544*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2*(x^4+1)^(1/4)*x^3-604506280*RootOf(134217728*_Z^8-32276480*_Z^4+1)*(x^4+1)^(1/2)*x^2+9167333*(x^4+1)^(3/4)*x-2243593677312*RootOf(134217728*_Z^8-32276480*_Z^4+1)^3)/(8192*x^4*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4-8192*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4+408*x^4+985))+134217728/2703045457*ln((7627861917696*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^9*x^4+86751896928256*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^7*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*(x^4+1)^(1/2)*x^2-7627861917696*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^9+5574162907136*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^5*x^4+1094058556944023552*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6*(x^4+1)^(1/4)*x^3-23910925860864*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^3*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*(x^4+1)^(1/2)*x^2+841447238582272*(x^4+1)^(3/4)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4*x+3505339236352*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^5+4359946240*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)*x^4-264088838610719360*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2*(x^4+1)^(1/4)*x^3+60734728373333*(x^4+1)^(3/4)*x+2749390848*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2))/(8192*x^4*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4-8192*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4+408*x^4+985))*RootOf(134217728*_Z^8-32276480*_Z^4+1)^7*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)-16138240/2703045457*ln((7627861917696*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^9*x^4+86751896928256*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^7*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*(x^4+1)^(1/2)*x^2-7627861917696*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^9+5574162907136*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^5*x^4+1094058556944023552*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6*(x^4+1)^(1/4)*x^3-23910925860864*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^3*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*(x^4+1)^(1/2)*x^2+841447238582272*(x^4+1)^(3/4)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4*x+3505339236352*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^5+4359946240*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)*x^4-264088838610719360*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2*(x^4+1)^(1/4)*x^3+60734728373333*(x^4+1)^(3/4)*x+2749390848*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2))/(8192*x^4*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4-8192*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4+408*x^4+985))*RootOf(134217728*_Z^8-32276480*_Z^4+1)^3*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)-1/1393*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*ln(-(7627861917696*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^10*x^4-7627861917696*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^10-9242836729856*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6*x^4-8244637831528448*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6*(x^4+1)^(1/4)*x^3+9676914688*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*(x^4+1)^(1/2)*x^2+604054011904*(x^4+1)^(3/4)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4*x+163334586368*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+1785944985600*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2*x^4+1982589963786880*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2*(x^4+1)^(1/4)*x^3-263176704*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*(x^4+1)^(1/2)*x^2-188861960721*(x^4+1)^(3/4)*x+404589549568*RootOf(_Z^2-22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)/(8192*x^4*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4-8192*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4-2378*x^4+985))+1/1393*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*ln(-(7627861917696*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^10*x^4-7627861917696*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^10-9242836729856*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6*x^4+8244637831528448*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6*(x^4+1)^(1/4)*x^3-9676914688*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4*(x^4+1)^(1/2)*x^2+604054011904*(x^4+1)^(3/4)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4*x+163334586368*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6+1785944985600*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2*x^4-1982589963786880*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2*(x^4+1)^(1/4)*x^3+263176704*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*(x^4+1)^(1/2)*x^2-188861960721*(x^4+1)^(3/4)*x+404589549568*RootOf(_Z^2+22480568320*RootOf(134217728*_Z^8-32276480*_Z^4+1)^6-5406092307*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)*RootOf(134217728*_Z^8-32276480*_Z^4+1)^2)/(8192*x^4*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4-8192*RootOf(134217728*_Z^8-32276480*_Z^4+1)^4-2378*x^4+985))","B"
1430,0,0,11,0.039000," ","int((2*a*x^4-b)/(a*x^4-b)^(1/4)/(a*x^8-b),x)","\[\int \frac{2 a \,x^{4}-b}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(a \,x^{8}-b \right)}\, dx\]"," ",0,"int((2*a*x^4-b)/(a*x^4-b)^(1/4)/(a*x^8-b),x)","F"
1431,1,187,77,2.418000," ","int((2*x^6+1)^(1/2)*(4*x^6-1)/(8*x^12+8*x^6+x^4+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{6}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{2}-4 \sqrt{2 x^{6}+1}\, x +2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right)}{-4 x^{6}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{2}-2}\right)}{8}+\frac{\RootOf \left(\textit{\_Z}^{4}+2\right) \ln \left(\frac{-4 \RootOf \left(\textit{\_Z}^{4}+2\right) x^{6}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{3} x^{2}+4 \sqrt{2 x^{6}+1}\, x -2 \RootOf \left(\textit{\_Z}^{4}+2\right)}{4 x^{6}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{2}+2}\right)}{8}$&$187$\\ \hline \end{longtable}"," ",0,"1/8*RootOf(_Z^2+RootOf(_Z^4+2)^2)*ln(-(4*RootOf(_Z^2+RootOf(_Z^4+2)^2)*x^6+RootOf(_Z^4+2)^2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*x^2-4*(2*x^6+1)^(1/2)*x+2*RootOf(_Z^2+RootOf(_Z^4+2)^2))/(-4*x^6+RootOf(_Z^4+2)^2*x^2-2))+1/8*RootOf(_Z^4+2)*ln((-4*RootOf(_Z^4+2)*x^6+RootOf(_Z^4+2)^3*x^2+4*(2*x^6+1)^(1/2)*x-2*RootOf(_Z^4+2))/(4*x^6+RootOf(_Z^4+2)^2*x^2+2))","C"
1432,1,85,44,0.065000," ","int((x^2-1)*(1+(1+x)^(1/2))^(1/2)/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{5}{2}}}{5}-\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}-\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+4 \textit{\_Z}^{4}+1\right)}{\sum}\frac{\left(\textit{\_R}^{4}-\textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+2 \textit{\_R}^{3}}\right)$&$85$\\ default&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{5}{2}}}{5}-\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}-\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+4 \textit{\_Z}^{4}+1\right)}{\sum}\frac{\left(\textit{\_R}^{4}-\textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+2 \textit{\_R}^{3}}\right)$&$85$\\ \hline \end{longtable}"," ",0,"4/5*(1+(1+x)^(1/2))^(5/2)-4/3*(1+(1+x)^(1/2))^(3/2)-sum((_R^4-_R^2)/(_R^7-3*_R^5+2*_R^3)*ln((1+(1+x)^(1/2))^(1/2)-_R),_R=RootOf(_Z^8-4*_Z^6+4*_Z^4+1))","A"
1433,1,85,44,0.068000," ","int((x^2-1)*(1+(1+x)^(1/2))^(1/2)/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{5}{2}}}{5}-\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}-\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+4 \textit{\_Z}^{4}+1\right)}{\sum}\frac{\left(\textit{\_R}^{4}-\textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+2 \textit{\_R}^{3}}\right)$&$85$\\ default&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{5}{2}}}{5}-\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}-\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+4 \textit{\_Z}^{4}+1\right)}{\sum}\frac{\left(\textit{\_R}^{4}-\textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+2 \textit{\_R}^{3}}\right)$&$85$\\ \hline \end{longtable}"," ",0,"4/5*(1+(1+x)^(1/2))^(5/2)-4/3*(1+(1+x)^(1/2))^(3/2)-sum((_R^4-_R^2)/(_R^7-3*_R^5+2*_R^3)*ln((1+(1+x)^(1/2))^(1/2)-_R),_R=RootOf(_Z^8-4*_Z^6+4*_Z^4+1))","A"
1434,1,62,81,0.079000," ","int(x^2*(x^2+(x^4+1)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\frac{5 \sqrt{\pi}\, \sqrt{2}\, \hypergeom \left(\left[1, 1, \frac{7}{4}, \frac{9}{4}\right], \left[2, \frac{5}{2}, 3\right], -\frac{1}{x^{4}}\right)}{32 x^{4}}-\frac{\left(1-4 \ln \left(2\right)-4 \ln \left(x \right)\right) \sqrt{\pi}\, \sqrt{2}}{2}+4 \sqrt{\pi}\, \sqrt{2}\, x^{4}}{16 \sqrt{\pi}}$&$62$\\ \hline \end{longtable}"," ",0,"1/16/Pi^(1/2)*(5/32*Pi^(1/2)*2^(1/2)/x^4*hypergeom([1,1,7/4,9/4],[2,5/2,3],-1/x^4)-1/2*(1-4*ln(2)-4*ln(x))*Pi^(1/2)*2^(1/2)+4*Pi^(1/2)*2^(1/2)*x^4)","C"
1435,0,0,81,0.017000," ","int((x^4-1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2),x)","\[\int \frac{\left(x^{4}-1\right) \sqrt{x^{2}+\sqrt{x^{4}+1}}}{\sqrt{x^{4}+1}}\, dx\]"," ",0,"int((x^4-1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2),x)","F"
1436,0,0,81,0.014000," ","int((x^4+1)^(1/2)*(x^2+(x^4+1)^(1/2))^(1/2),x)","\[\int \sqrt{x^{4}+1}\, \sqrt{x^{2}+\sqrt{x^{4}+1}}\, dx\]"," ",0,"int((x^4+1)^(1/2)*(x^2+(x^4+1)^(1/2))^(1/2),x)","F"
1437,1,33,80,1.776000," ","int(x^3*(x^3-1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}} x^{4} \hypergeom \left(\left[-\frac{2}{3}, \frac{4}{3}\right], \left[\frac{7}{3}\right], x^{3}\right)}{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}}}$&$33$\\ risch&$\frac{x \left(3 x^{3}-2\right) \left(x^{3}-1\right)^{\frac{2}{3}}}{18}-\frac{\left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{3}\right)}{9 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}}}$&$49$\\ trager&$\frac{x \left(3 x^{3}-2\right) \left(x^{3}-1\right)^{\frac{2}{3}}}{18}+\frac{\ln \left(-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -5 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}-1\right)^{\frac{2}{3}}-3 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-2 x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1\right)}{27}+\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-2 x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+2\right)}{27}$&$199$\\ \hline \end{longtable}"," ",0,"1/4*signum(x^3-1)^(2/3)/(-signum(x^3-1))^(2/3)*x^4*hypergeom([-2/3,4/3],[7/3],x^3)","C"
1438,1,17,80,1.615000," ","int(x^4*(x^3+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{x^{5} \hypergeom \left(\left[-\frac{1}{3}, \frac{5}{3}\right], \left[\frac{8}{3}\right], -x^{3}\right)}{5}$&$17$\\ risch&$\frac{x^{2} \left(3 x^{3}+1\right) \left(x^{3}+1\right)^{\frac{1}{3}}}{18}-\frac{x^{2} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], -x^{3}\right)}{18}$&$37$\\ trager&$\frac{x^{2} \left(3 x^{3}+1\right) \left(x^{3}+1\right)^{\frac{1}{3}}}{18}+\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x -3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1\right)}{27}-\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}+1\right)^{\frac{2}{3}}+3 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}+4 x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+2\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{27}-\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}+1\right)^{\frac{2}{3}}+3 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}+4 x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+2\right)}{27}$&$313$\\ \hline \end{longtable}"," ",0,"1/5*x^5*hypergeom([-1/3,5/3],[8/3],-x^3)","C"
1439,1,17,80,1.917000," ","int(x^3*(x^3+1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{x^{4} \hypergeom \left(\left[-\frac{2}{3}, \frac{4}{3}\right], \left[\frac{7}{3}\right], -x^{3}\right)}{4}$&$17$\\ risch&$\frac{x \left(3 x^{3}+2\right) \left(x^{3}+1\right)^{\frac{2}{3}}}{18}-\frac{x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{3}\right)}{9}$&$33$\\ trager&$\frac{x \left(3 x^{3}+2\right) \left(x^{3}+1\right)^{\frac{2}{3}}}{18}+\frac{\ln \left(-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x -5 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}+1\right)^{\frac{2}{3}}-3 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}-2 x^{3}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1\right)}{27}+\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}+1\right)^{\frac{2}{3}}-x^{3}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1\right)}{27}$&$184$\\ \hline \end{longtable}"," ",0,"1/4*x^4*hypergeom([-2/3,4/3],[7/3],-x^3)","C"
1440,1,338,82,4.879000," ","int((x^3-2)^(2/3)*(x^3+4)/x^6/(x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{3}-2\right)^{\frac{2}{3}} \left(21 x^{3}+8\right)}{10 x^{5}}+\frac{5 \ln \left(-\frac{86436864 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2} x^{3}+1075968 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) \left(x^{3}-2\right)^{\frac{2}{3}} x +6592608 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) \left(x^{3}-2\right)^{\frac{1}{3}} x^{2}+3456576 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) x^{3}-57465 \left(x^{3}-2\right)^{\frac{2}{3}} x +11208 \left(x^{3}-2\right)^{\frac{1}{3}} x^{2}-6040 x^{3}-691494912 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2}-4242624 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)+9060}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right)}{3}+160 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) \ln \left(-\frac{13916160 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2} x^{3}-1075968 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) \left(x^{3}-2\right)^{\frac{2}{3}} x +5516640 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) \left(x^{3}-2\right)^{\frac{1}{3}} x^{2}-1335264 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) x^{3}-68673 \left(x^{3}-2\right)^{\frac{2}{3}} x -11208 \left(x^{3}-2\right)^{\frac{1}{3}} x^{2}+28137 x^{3}-111329280 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2}+6913152 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)+18758}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right)$&$338$\\ risch&$\frac{21 x^{6}-34 x^{3}-16}{10 x^{5} \left(x^{3}-2\right)^{\frac{1}{3}}}-\frac{5 \ln \left(-\frac{-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-2\right)^{\frac{2}{3}} x -3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-2\right)^{\frac{1}{3}} x^{2}-6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+2 \left(x^{3}-2\right)^{\frac{2}{3}} x -2 \left(x^{3}-2\right)^{\frac{1}{3}} x^{2}-x^{3}+6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+2}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right)}{3}-5 \ln \left(-\frac{-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-2\right)^{\frac{2}{3}} x -3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-2\right)^{\frac{1}{3}} x^{2}-6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+2 \left(x^{3}-2\right)^{\frac{2}{3}} x -2 \left(x^{3}-2\right)^{\frac{1}{3}} x^{2}-x^{3}+6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+2}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+5 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(\frac{9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-2\right)^{\frac{2}{3}} x -3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-2\right)^{\frac{1}{3}} x^{2}-\left(x^{3}-2\right)^{\frac{2}{3}} x +\left(x^{3}-2\right)^{\frac{1}{3}} x^{2}+6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right)$&$438$\\ \hline \end{longtable}"," ",0,"1/10*(x^3-2)^(2/3)*(21*x^3+8)/x^5+5/3*ln(-(86436864*RootOf(9216*_Z^2+96*_Z+1)^2*x^3+1075968*RootOf(9216*_Z^2+96*_Z+1)*(x^3-2)^(2/3)*x+6592608*RootOf(9216*_Z^2+96*_Z+1)*(x^3-2)^(1/3)*x^2+3456576*RootOf(9216*_Z^2+96*_Z+1)*x^3-57465*(x^3-2)^(2/3)*x+11208*(x^3-2)^(1/3)*x^2-6040*x^3-691494912*RootOf(9216*_Z^2+96*_Z+1)^2-4242624*RootOf(9216*_Z^2+96*_Z+1)+9060)/(-1+x)/(x^2+x+1))+160*RootOf(9216*_Z^2+96*_Z+1)*ln(-(13916160*RootOf(9216*_Z^2+96*_Z+1)^2*x^3-1075968*RootOf(9216*_Z^2+96*_Z+1)*(x^3-2)^(2/3)*x+5516640*RootOf(9216*_Z^2+96*_Z+1)*(x^3-2)^(1/3)*x^2-1335264*RootOf(9216*_Z^2+96*_Z+1)*x^3-68673*(x^3-2)^(2/3)*x-11208*(x^3-2)^(1/3)*x^2+28137*x^3-111329280*RootOf(9216*_Z^2+96*_Z+1)^2+6913152*RootOf(9216*_Z^2+96*_Z+1)+18758)/(-1+x)/(x^2+x+1))","C"
1441,0,0,85,0.022000," ","int((a*x^2+3*b)/(a*x^2+x^3+b)/(a*x^3+b*x)^(1/4),x)","\[\int \frac{a \,x^{2}+3 b}{\left(a \,x^{2}+x^{3}+b \right) \left(a \,x^{3}+b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2+3*b)/(a*x^2+x^3+b)/(a*x^3+b*x)^(1/4),x)","F"
1442,1,76,80,4.133000," ","int((x^4-3)*(x^4+1)^(1/3)/x^13,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{4 x^{12}+7 x^{8}-6 x^{4}-9}{36 x^{12} \left(x^{4}+1\right)^{\frac{2}{3}}}-\frac{2 \left(-\frac{2 \Gamma \left(\frac{2}{3}\right) x^{4} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 2\right], -x^{4}\right)}{3}+\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)\right)}{27 \Gamma \left(\frac{2}{3}\right)}$&$76$\\ meijerg&$\frac{\frac{10 \Gamma \left(\frac{2}{3}\right) x^{4} \hypergeom \left(\left[1, 1, \frac{11}{3}\right], \left[2, 5\right], -x^{4}\right)}{81}-\frac{5 \left(\frac{4}{15}+\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)}{27}+\frac{\Gamma \left(\frac{2}{3}\right)}{x^{12}}+\frac{\Gamma \left(\frac{2}{3}\right)}{2 x^{8}}-\frac{\Gamma \left(\frac{2}{3}\right)}{3 x^{4}}}{4 \Gamma \left(\frac{2}{3}\right)}-\frac{-\frac{5 \Gamma \left(\frac{2}{3}\right) x^{4} \hypergeom \left(\left[1, 1, \frac{8}{3}\right], \left[2, 4\right], -x^{4}\right)}{27}+\frac{\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)}{3}+\frac{3 \Gamma \left(\frac{2}{3}\right)}{2 x^{8}}+\frac{\Gamma \left(\frac{2}{3}\right)}{x^{4}}}{12 \Gamma \left(\frac{2}{3}\right)}$&$128$\\ trager&$-\frac{\left(4 x^{8}+3 x^{4}-9\right) \left(x^{4}+1\right)^{\frac{1}{3}}}{36 x^{12}}+\frac{2 \ln \left(\frac{180 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{4}+9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{4}-74 x^{4}+351 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}}-180 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}+351 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{1}{3}}-165 \left(x^{4}+1\right)^{\frac{2}{3}}+411 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-165 \left(x^{4}+1\right)^{\frac{1}{3}}-185}{x^{4}}\right)}{27}-\frac{2 \ln \left(\frac{180 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{4}+9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{4}-74 x^{4}+351 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}}-180 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}+351 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{1}{3}}-165 \left(x^{4}+1\right)^{\frac{2}{3}}+411 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-165 \left(x^{4}+1\right)^{\frac{1}{3}}-185}{x^{4}}\right) \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)}{9}+\frac{2 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \ln \left(\frac{180 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{4}-129 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{4}-51 x^{4}-351 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}}-180 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}-351 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{1}{3}}-48 \left(x^{4}+1\right)^{\frac{2}{3}}-291 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-48 \left(x^{4}+1\right)^{\frac{1}{3}}-68}{x^{4}}\right)}{9}$&$450$\\ \hline \end{longtable}"," ",0,"-1/36*(4*x^12+7*x^8-6*x^4-9)/x^12/(x^4+1)^(2/3)-2/27/GAMMA(2/3)*(-2/3*GAMMA(2/3)*x^4*hypergeom([1,1,5/3],[2,2],-x^4)+(1/6*Pi*3^(1/2)-3/2*ln(3)+4*ln(x))*GAMMA(2/3))","C"
1443,0,0,86,0.021000," ","int((a*x^2-2*b)/(a*x^2-b)^(1/4)/(x^4+a*x^2-b),x)","\[\int \frac{a \,x^{2}-2 b}{\left(a \,x^{2}-b \right)^{\frac{1}{4}} \left(x^{4}+a \,x^{2}-b \right)}\, dx\]"," ",0,"int((a*x^2-2*b)/(a*x^2-b)^(1/4)/(x^4+a*x^2-b),x)","F"
1444,0,0,85,0.021000," ","int((a*x^3-4*b)/(a*x^3-b)^(1/4)/(a*x^3+x^4-b),x)","\[\int \frac{a \,x^{3}-4 b}{\left(a \,x^{3}-b \right)^{\frac{1}{4}} \left(a \,x^{3}+x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^3-4*b)/(a*x^3-b)^(1/4)/(a*x^3+x^4-b),x)","F"
1445,0,0,11,0.024000," ","int((a*x^2+b)/(x^4-a*x^2+b)/(a*x^4-b*x^2)^(1/4),x)","\[\int \frac{a \,x^{2}+b}{\left(x^{4}-a \,x^{2}+b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2+b)/(x^4-a*x^2+b)/(a*x^4-b*x^2)^(1/4),x)","F"
1446,0,0,11,0.001000," ","int((a*x^2+b)/(x^4-a*x^2+b)/(a*x^4-b*x^2)^(1/4),x)","\[\int \frac{a \,x^{2}+b}{\left(x^{4}-a \,x^{2}+b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2+b)/(x^4-a*x^2+b)/(a*x^4-b*x^2)^(1/4),x)","F"
1447,0,0,47,0.012000," ","int((a*x^4+b)/x^4/(a*x^4-2*b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{a \,x^{4}+b}{x^{4} \left(a \,x^{4}-2 b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^4+b)/x^4/(a*x^4-2*b)/(a*x^4+b*x^2)^(1/4),x)","F"
1448,0,0,47,0.002000," ","int((a*x^4+b)/x^4/(a*x^4-2*b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{a \,x^{4}+b}{x^{4} \left(a \,x^{4}-2 b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^4+b)/x^4/(a*x^4-2*b)/(a*x^4+b*x^2)^(1/4),x)","F"
1449,1,416,84,6.961000," ","int((x^3-1)*(x^3+1)^3*(x^6+1)^(2/3)/x^6/(x^6-x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{6}+1\right)^{\frac{2}{3}} \left(2 x^{6}+15 x^{3}+2\right)}{10 x^{5}}+\ln \left(-\frac{6624 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{6}-2763 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}-1102 x^{6}-13248 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+4428 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x +6057 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}} x^{2}-9930 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+3495 x \left(x^{6}+1\right)^{\frac{2}{3}}-1476 x^{2} \left(x^{6}+1\right)^{\frac{1}{3}}-1653 x^{3}+6624 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-2763 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-1102}{x^{6}-x^{3}+1}\right)+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(\frac{4959 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{6}+7167 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}+2208 x^{6}-9918 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+4428 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x -10485 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}} x^{2}-2763 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}-2019 x \left(x^{6}+1\right)^{\frac{2}{3}}-1476 x^{2} \left(x^{6}+1\right)^{\frac{1}{3}}+736 x^{3}+4959 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+7167 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+2208}{x^{6}-x^{3}+1}\right)$&$416$\\ risch&$\frac{2 x^{12}+15 x^{9}+4 x^{6}+15 x^{3}+2}{10 x^{5} \left(x^{6}+1\right)^{\frac{1}{3}}}-3 \ln \left(-\frac{-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}-2 x^{6}-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x -9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+3 x^{2} \left(x^{6}+1\right)^{\frac{1}{3}}-2 x^{3}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-2}{x^{6}-x^{3}+1}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+\ln \left(\frac{-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}-2 x^{6}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x -9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}} x^{2}+6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+3 x \left(x^{6}+1\right)^{\frac{2}{3}}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-2}{x^{6}-x^{3}+1}\right)-\ln \left(-\frac{-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}-2 x^{6}-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x -9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+3 x^{2} \left(x^{6}+1\right)^{\frac{1}{3}}-2 x^{3}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-2}{x^{6}-x^{3}+1}\right)$&$435$\\ \hline \end{longtable}"," ",0,"1/10*(x^6+1)^(2/3)*(2*x^6+15*x^3+2)/x^5+ln(-(6624*RootOf(9*_Z^2+3*_Z+1)^2*x^6-2763*RootOf(9*_Z^2+3*_Z+1)*x^6-1102*x^6-13248*RootOf(9*_Z^2+3*_Z+1)^2*x^3+4428*RootOf(9*_Z^2+3*_Z+1)*(x^6+1)^(2/3)*x+6057*RootOf(9*_Z^2+3*_Z+1)*(x^6+1)^(1/3)*x^2-9930*RootOf(9*_Z^2+3*_Z+1)*x^3+3495*x*(x^6+1)^(2/3)-1476*x^2*(x^6+1)^(1/3)-1653*x^3+6624*RootOf(9*_Z^2+3*_Z+1)^2-2763*RootOf(9*_Z^2+3*_Z+1)-1102)/(x^6-x^3+1))+3*RootOf(9*_Z^2+3*_Z+1)*ln((4959*RootOf(9*_Z^2+3*_Z+1)^2*x^6+7167*RootOf(9*_Z^2+3*_Z+1)*x^6+2208*x^6-9918*RootOf(9*_Z^2+3*_Z+1)^2*x^3+4428*RootOf(9*_Z^2+3*_Z+1)*(x^6+1)^(2/3)*x-10485*RootOf(9*_Z^2+3*_Z+1)*(x^6+1)^(1/3)*x^2-2763*RootOf(9*_Z^2+3*_Z+1)*x^3-2019*x*(x^6+1)^(2/3)-1476*x^2*(x^6+1)^(1/3)+736*x^3+4959*RootOf(9*_Z^2+3*_Z+1)^2+7167*RootOf(9*_Z^2+3*_Z+1)+2208)/(x^6-x^3+1))","C"
1450,1,490,84,21.090000," ","int((x^6-1)^(2/3)*(x^6+1)*(2*x^6+x^3-2)/x^6/(x^6-x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{4 x^{12}+15 x^{9}-8 x^{6}-15 x^{3}+4}{10 x^{5} \left(x^{6}-1\right)^{\frac{1}{3}}}-3 \ln \left(\frac{6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}+x^{6}-18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x +9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{2}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+3 x \left(x^{6}-1\right)^{\frac{2}{3}}+3 x^{2} \left(x^{6}-1\right)^{\frac{1}{3}}-6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-1}{x^{6}-x^{3}-1}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(-\frac{6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}+x^{6}+18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x +9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{2}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+x^{3}-6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-1}{x^{6}-x^{3}-1}\right)-\ln \left(\frac{6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}+x^{6}-18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x +9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{2}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+3 x \left(x^{6}-1\right)^{\frac{2}{3}}+3 x^{2} \left(x^{6}-1\right)^{\frac{1}{3}}-6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-1}{x^{6}-x^{3}-1}\right)$&$490$\\ trager&$\frac{\left(x^{6}-1\right)^{\frac{2}{3}} \left(4 x^{6}+15 x^{3}-4\right)}{10 x^{5}}-96 \ln \left(-\frac{6570485565136040671726226079744 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2} x^{6}-489182598517982885200727925888 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) x^{6}-4085365060307585836672246881 x^{6}-51742573825446320289844030377984 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2} x^{3}+363650051031240685770824996928 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x +654612709216604620411401672864 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{2}-999622747774761167003559205344 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) x^{3}-6818882387672964795952100759 x \left(x^{6}-1\right)^{\frac{2}{3}}+10606903752581721939398194477 x^{2} \left(x^{6}-1\right)^{\frac{1}{3}}-4604141575902199911170309977 x^{3}-6570485565136040671726226079744 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2}+489182598517982885200727925888 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)+4085365060307585836672246881}{x^{6}-x^{3}-1}\right) \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)+\ln \left(\frac{1789441197416077361152076587008 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2} x^{6}+115627565201538784058859689760 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) x^{6}-4604141575902199911170309977 x^{6}-14091849429651609219072603122688 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2} x^{3}+363650051031240685770824996928 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x -1018262760247845306182226669792 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{2}+410835058262612379499203165024 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) x^{3}+10606903752581721939398194477 x \left(x^{6}-1\right)^{\frac{2}{3}}-6818882387672964795952100759 x^{2} \left(x^{6}-1\right)^{\frac{1}{3}}-518776515594614074498063096 x^{3}-1789441197416077361152076587008 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2}-115627565201538784058859689760 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)+4604141575902199911170309977}{x^{6}-x^{3}-1}\right)-\ln \left(-\frac{6570485565136040671726226079744 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2} x^{6}-489182598517982885200727925888 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) x^{6}-4085365060307585836672246881 x^{6}-51742573825446320289844030377984 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2} x^{3}+363650051031240685770824996928 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x +654612709216604620411401672864 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{2}-999622747774761167003559205344 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right) x^{3}-6818882387672964795952100759 x \left(x^{6}-1\right)^{\frac{2}{3}}+10606903752581721939398194477 x^{2} \left(x^{6}-1\right)^{\frac{1}{3}}-4604141575902199911170309977 x^{3}-6570485565136040671726226079744 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)^{2}+489182598517982885200727925888 \RootOf \left(9216 \textit{\_Z}^{2}+96 \textit{\_Z} +1\right)+4085365060307585836672246881}{x^{6}-x^{3}-1}\right)$&$607$\\ \hline \end{longtable}"," ",0,"1/10*(4*x^12+15*x^9-8*x^6-15*x^3+4)/x^5/(x^6-1)^(1/3)-3*ln((6*RootOf(9*_Z^2+3*_Z+1)*x^6+x^6-18*RootOf(9*_Z^2+3*_Z+1)^2*x^3+9*RootOf(9*_Z^2+3*_Z+1)*(x^6-1)^(2/3)*x+9*RootOf(9*_Z^2+3*_Z+1)*(x^6-1)^(1/3)*x^2-3*RootOf(9*_Z^2+3*_Z+1)*x^3+3*x*(x^6-1)^(2/3)+3*x^2*(x^6-1)^(1/3)-6*RootOf(9*_Z^2+3*_Z+1)-1)/(x^6-x^3-1))*RootOf(9*_Z^2+3*_Z+1)+3*RootOf(9*_Z^2+3*_Z+1)*ln(-(6*RootOf(9*_Z^2+3*_Z+1)*x^6+x^6+18*RootOf(9*_Z^2+3*_Z+1)^2*x^3+9*RootOf(9*_Z^2+3*_Z+1)*(x^6-1)^(2/3)*x+9*RootOf(9*_Z^2+3*_Z+1)*(x^6-1)^(1/3)*x^2+9*RootOf(9*_Z^2+3*_Z+1)*x^3+x^3-6*RootOf(9*_Z^2+3*_Z+1)-1)/(x^6-x^3-1))-ln((6*RootOf(9*_Z^2+3*_Z+1)*x^6+x^6-18*RootOf(9*_Z^2+3*_Z+1)^2*x^3+9*RootOf(9*_Z^2+3*_Z+1)*(x^6-1)^(2/3)*x+9*RootOf(9*_Z^2+3*_Z+1)*(x^6-1)^(1/3)*x^2-3*RootOf(9*_Z^2+3*_Z+1)*x^3+3*x*(x^6-1)^(2/3)+3*x^2*(x^6-1)^(1/3)-6*RootOf(9*_Z^2+3*_Z+1)-1)/(x^6-x^3-1))","C"
1451,0,0,14,0.024000," ","int(1/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x)","\[\int \frac{1}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(x^{8}+a \,x^{4}-b \right)}\, dx\]"," ",0,"int(1/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x)","F"
1452,0,0,14,0.001000," ","int(1/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x)","\[\int \frac{1}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(x^{8}+a \,x^{4}-b \right)}\, dx\]"," ",0,"int(1/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x)","F"
1453,0,0,11,0.027000," ","int((a*x^4-b)/(a*x^4-b*x^2)^(1/4)/(2*x^8+2*a*x^4-b),x)","\[\int \frac{a \,x^{4}-b}{\left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}} \left(2 x^{8}+2 a \,x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^4-b)/(a*x^4-b*x^2)^(1/4)/(2*x^8+2*a*x^4-b),x)","F"
1454,0,0,11,0.002000," ","int((a*x^4-b)/(a*x^4-b*x^2)^(1/4)/(2*x^8+2*a*x^4-b),x)","\[\int \frac{a \,x^{4}-b}{\left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}} \left(2 x^{8}+2 a \,x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^4-b)/(a*x^4-b*x^2)^(1/4)/(2*x^8+2*a*x^4-b),x)","F"
1455,0,0,88,0.021000," ","int((c*x^2-x*(a*x^2-b*x)^(1/2))^(1/2)/x^3,x)","\[\int \frac{\sqrt{c \,x^{2}-x \sqrt{a \,x^{2}-b x}}}{x^{3}}\, dx\]"," ",0,"int((c*x^2-x*(a*x^2-b*x)^(1/2))^(1/2)/x^3,x)","F"
1456,0,0,26,0.042000," ","int(x/(x+(x+(x^2+1)^(1/2))^(1/2)),x)","\[\int \frac{x}{x +\sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int(x/(x+(x+(x^2+1)^(1/2))^(1/2)),x)","F"
1457,0,0,26,0.000000," ","int(x/(x+(x+(x^2+1)^(1/2))^(1/2)),x)","\[\int \frac{x}{x +\sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int(x/(x+(x+(x^2+1)^(1/2))^(1/2)),x)","F"
1458,1,694,79,0.939000," ","int((1+x)/(x^2+2*x-2)/(x^3+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}}+\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}}+\frac{\sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}}-\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}}$&$694$\\ elliptic&$-\frac{\sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}}+\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}}+\frac{\sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}}-\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}}$&$694$\\ \hline \end{longtable}"," ",0,"-1/2*(1/(3/2-1/2*I*3^(1/2))+1/(3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2),-1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)+1/2*I*(1/(3/2-1/2*I*3^(1/2))+1/(3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2),-1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+1/2*(1/(3/2-1/2*I*3^(1/2))+1/(3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2),1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)-1/2*I*(1/(3/2-1/2*I*3^(1/2))+1/(3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2),1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","C"
1459,1,593,79,2.825000," ","int((x^2+x+3)/(x^2+2*x-2)/(x^3+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right) \ln \left(\frac{3888 \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)^{5} x^{2}-7776 x \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)^{5}+1800 \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)^{3} x^{2}+2448 \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)^{3} x +6048 \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)^{3}-7392 \sqrt{x^{3}+1}\, \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)^{2}-53 \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right) x^{2}+3074 \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right) x +2968 \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)-1232 \sqrt{x^{3}+1}}{\left(36 \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)^{2} x -x -28\right)^{2}}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)^{2}-30\right) \ln \left(\frac{3888 \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)^{2}-30\right) \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)^{4} x^{2}-7776 \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)^{4} x \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)^{2}-30\right)-8280 \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)^{2} \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)^{2}-30\right) x^{2}+10512 \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)^{2} \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)^{2}-30\right) x -6048 \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)^{2} \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)^{2}-30\right)+4147 \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)^{2}-30\right) x^{2}+44352 \sqrt{x^{3}+1}\, \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)^{2}-286 \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)^{2}-30\right) x +8008 \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)^{2}-30\right)-44352 \sqrt{x^{3}+1}}{\left(36 \RootOf \left(432 \textit{\_Z}^{4}-360 \textit{\_Z}^{2}-121\right)^{2} x -29 x +28\right)^{2}}\right)}{12}$&$593$\\ default&$\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{3 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}}+\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}+\frac{\sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}}-\frac{3 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}}+\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}-\frac{\sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}}$&$1501$\\ elliptic&$\frac{3 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}-\frac{3 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}}+\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}+\frac{\sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}}-\frac{3 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}}+\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}-\frac{\sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}}$&$1706$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(432*_Z^4-360*_Z^2-121)*ln((3888*RootOf(432*_Z^4-360*_Z^2-121)^5*x^2-7776*x*RootOf(432*_Z^4-360*_Z^2-121)^5+1800*RootOf(432*_Z^4-360*_Z^2-121)^3*x^2+2448*RootOf(432*_Z^4-360*_Z^2-121)^3*x+6048*RootOf(432*_Z^4-360*_Z^2-121)^3-7392*(x^3+1)^(1/2)*RootOf(432*_Z^4-360*_Z^2-121)^2-53*RootOf(432*_Z^4-360*_Z^2-121)*x^2+3074*RootOf(432*_Z^4-360*_Z^2-121)*x+2968*RootOf(432*_Z^4-360*_Z^2-121)-1232*(x^3+1)^(1/2))/(36*RootOf(432*_Z^4-360*_Z^2-121)^2*x-x-28)^2)+1/12*RootOf(_Z^2+36*RootOf(432*_Z^4-360*_Z^2-121)^2-30)*ln((3888*RootOf(_Z^2+36*RootOf(432*_Z^4-360*_Z^2-121)^2-30)*RootOf(432*_Z^4-360*_Z^2-121)^4*x^2-7776*RootOf(432*_Z^4-360*_Z^2-121)^4*x*RootOf(_Z^2+36*RootOf(432*_Z^4-360*_Z^2-121)^2-30)-8280*RootOf(432*_Z^4-360*_Z^2-121)^2*RootOf(_Z^2+36*RootOf(432*_Z^4-360*_Z^2-121)^2-30)*x^2+10512*RootOf(432*_Z^4-360*_Z^2-121)^2*RootOf(_Z^2+36*RootOf(432*_Z^4-360*_Z^2-121)^2-30)*x-6048*RootOf(432*_Z^4-360*_Z^2-121)^2*RootOf(_Z^2+36*RootOf(432*_Z^4-360*_Z^2-121)^2-30)+4147*RootOf(_Z^2+36*RootOf(432*_Z^4-360*_Z^2-121)^2-30)*x^2+44352*(x^3+1)^(1/2)*RootOf(432*_Z^4-360*_Z^2-121)^2-286*RootOf(_Z^2+36*RootOf(432*_Z^4-360*_Z^2-121)^2-30)*x+8008*RootOf(_Z^2+36*RootOf(432*_Z^4-360*_Z^2-121)^2-30)-44352*(x^3+1)^(1/2))/(36*RootOf(432*_Z^4-360*_Z^2-121)^2*x-29*x+28)^2)","C"
1460,1,1501,79,1.129000," ","int((2*x^2-x+3)/(x^2+2*x-2)/(x^3+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{4 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{5 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}}-\frac{6 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{5 i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}}+\frac{2 i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}-\frac{6 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{5 i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}}+\frac{2 i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}-\frac{5 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}}$&$1501$\\ elliptic&$\frac{6 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{2 i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}+\frac{5 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}}-\frac{6 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{5 i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}}+\frac{2 i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}-\frac{6 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{5 i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}}+\frac{2 i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}-\frac{5 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}}$&$1706$\\ \hline \end{longtable}"," ",0,"4*(3/2-1/2*I*3^(1/2))*((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+5/2*(1/(3/2-1/2*I*3^(1/2))+1/(3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2),-1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)-6*(1/(3/2-1/2*I*3^(1/2))+1/(3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2),-1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))-5/2*I*(1/(3/2-1/2*I*3^(1/2))+1/(3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2),-1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+2*I*(1/(3/2-1/2*I*3^(1/2))+1/(3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2),-1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)-6*(1/(3/2-1/2*I*3^(1/2))+1/(3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2),1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+5/2*I*(1/(3/2-1/2*I*3^(1/2))+1/(3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2),1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+2*I*(1/(3/2-1/2*I*3^(1/2))+1/(3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2),1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)-5/2*(1/(3/2-1/2*I*3^(1/2))+1/(3/2-1/2*I*3^(1/2))*x)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((1+x)/(3/2-1/2*I*3^(1/2)))^(1/2),1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)","C"
1461,1,56,81,2.296000," ","int((x^3-1)^(2/3)*(x^3+1)/x^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{2 x^{6}-5 x^{3}+3}{6 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}}+\frac{\left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{3}\right)}{3 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}}}$&$56$\\ meijerg&$\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}} x \hypergeom \left(\left[-\frac{2}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{3}\right)}{\left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}}}-\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}} \hypergeom \left(\left[-\frac{2}{3}, -\frac{2}{3}\right], \left[\frac{1}{3}\right], x^{3}\right)}{2 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} x^{2}}$&$63$\\ trager&$\frac{\left(x^{3}-1\right)^{\frac{2}{3}} \left(2 x^{3}-3\right)}{6 x^{2}}+\frac{4 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) \ln \left(182271728 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)^{2} x^{3}+775851456 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +775851456 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+730283524 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) x^{3}-1508552373 x \left(x^{3}-1\right)^{\frac{2}{3}}-1508552373 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-1497160390 x^{3}-1458173824 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)^{2}+1858712316 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)+476369215\right)}{9}+\frac{\ln \left(182271728 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)^{2} x^{3}-775851456 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -775851456 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-821419388 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) x^{3}-1314589509 x \left(x^{3}-1\right)^{\frac{2}{3}}-1314589509 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-1303197526 x^{3}-1458173824 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)^{2}-1129625404 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)+849911430\right)}{9}-\frac{4 \ln \left(182271728 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)^{2} x^{3}-775851456 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -775851456 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-821419388 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) x^{3}-1314589509 x \left(x^{3}-1\right)^{\frac{2}{3}}-1314589509 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-1303197526 x^{3}-1458173824 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)^{2}-1129625404 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)+849911430\right) \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)}{9}$&$457$\\ \hline \end{longtable}"," ",0,"1/6*(2*x^6-5*x^3+3)/x^2/(x^3-1)^(1/3)+1/3/signum(x^3-1)^(1/3)*(-signum(x^3-1))^(1/3)*x*hypergeom([1/3,1/3],[4/3],x^3)","C"
1462,0,0,83,0.006000," ","int(x^8*(a*x^4+b)^(3/4),x)","\[\int x^{8} \left(a \,x^{4}+b \right)^{\frac{3}{4}}\, dx\]"," ",0,"int(x^8*(a*x^4+b)^(3/4),x)","F"
1463,0,0,79,0.034000," ","int(1/(a*x^3-b)/(a*x^4+b*x)^(1/4),x)","\[\int \frac{1}{\left(a \,x^{3}-b \right) \left(a \,x^{4}+b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(a*x^3-b)/(a*x^4+b*x)^(1/4),x)","F"
1464,1,6670,24,223.527000," ","int((x^3-2)*(x^3+1)^(2/3)/x^3/(2*x^6+x^3-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$6670$\\ trager&$\text{Expression too large to display}$&$8758$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1465,1,6665,24,193.925000," ","int((x^3-2)*(x^3+1)^(2/3)/x^3/(2*x^6+x^3-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$6665$\\ trager&$\text{Expression too large to display}$&$8758$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1466,1,626,83,53.165000," ","int(x^2*(x^4-2)/(x^5-x)^(1/3)/(x^8+x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\ln \left(-\frac{1027936778409280454041232991842640 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right)^{2} x^{8}+4529039623257700492643576695162024 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) x^{8}+610884417613243258599747967858176 x^{8}-6458608904506033300021952070673408 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) \left(x^{5}-x \right)^{\frac{1}{3}} x^{5}-17543454351518386415637043060781056 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right)^{2} x^{4}-25262880761481365661024699935681 \left(x^{5}-x \right)^{\frac{1}{3}} x^{5}+6458608904506033300021952070673408 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) \left(x^{5}-x \right)^{\frac{2}{3}} x^{2}-6572417063730249524797944388667308 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) x^{4}+25262880761481365661024699935681 \left(x^{5}-x \right)^{\frac{2}{3}} x^{2}-575090408768717286416168985366486 x^{4}+17543454351518386415637043060781056 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right)^{2}+6572417063730249524797944388667308 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right)+575090408768717286416168985366486}{x^{8}+x^{4}-1}\right)}{4}-\ln \left(-\frac{1027936778409280454041232991842640 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right)^{2} x^{8}+4529039623257700492643576695162024 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) x^{8}+610884417613243258599747967858176 x^{8}-6458608904506033300021952070673408 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) \left(x^{5}-x \right)^{\frac{1}{3}} x^{5}-17543454351518386415637043060781056 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right)^{2} x^{4}-25262880761481365661024699935681 \left(x^{5}-x \right)^{\frac{1}{3}} x^{5}+6458608904506033300021952070673408 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) \left(x^{5}-x \right)^{\frac{2}{3}} x^{2}-6572417063730249524797944388667308 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) x^{4}+25262880761481365661024699935681 \left(x^{5}-x \right)^{\frac{2}{3}} x^{2}-575090408768717286416168985366486 x^{4}+17543454351518386415637043060781056 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right)^{2}+6572417063730249524797944388667308 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right)+575090408768717286416168985366486}{x^{8}+x^{4}-1}\right) \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right)+\RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) \ln \left(-\frac{1027936778409280454041232991842640 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right)^{2} x^{8}-4015071234053060265622960199240704 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) x^{8}-457129439550601836183569143942165 x^{8}+6458608904506033300021952070673408 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) \left(x^{5}-x \right)^{\frac{1}{3}} x^{5}-17543454351518386415637043060781056 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right)^{2} x^{4}+1589389345365026959344463317732671 \left(x^{5}-x \right)^{\frac{1}{3}} x^{5}-6458608904506033300021952070673408 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) \left(x^{5}-x \right)^{\frac{2}{3}} x^{2}-2199310112028943683020577141723220 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right) x^{4}-1589389345365026959344463317732671 \left(x^{5}-x \right)^{\frac{2}{3}} x^{2}-28452039806054056193998079498475 x^{4}+17543454351518386415637043060781056 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right)^{2}+2199310112028943683020577141723220 \RootOf \left(16 \textit{\_Z}^{2}+4 \textit{\_Z} +1\right)+28452039806054056193998079498475}{x^{8}+x^{4}-1}\right)$&$626$\\ \hline \end{longtable}"," ",0,"-1/4*ln(-(1027936778409280454041232991842640*RootOf(16*_Z^2+4*_Z+1)^2*x^8+4529039623257700492643576695162024*RootOf(16*_Z^2+4*_Z+1)*x^8+610884417613243258599747967858176*x^8-6458608904506033300021952070673408*RootOf(16*_Z^2+4*_Z+1)*(x^5-x)^(1/3)*x^5-17543454351518386415637043060781056*RootOf(16*_Z^2+4*_Z+1)^2*x^4-25262880761481365661024699935681*(x^5-x)^(1/3)*x^5+6458608904506033300021952070673408*RootOf(16*_Z^2+4*_Z+1)*(x^5-x)^(2/3)*x^2-6572417063730249524797944388667308*RootOf(16*_Z^2+4*_Z+1)*x^4+25262880761481365661024699935681*(x^5-x)^(2/3)*x^2-575090408768717286416168985366486*x^4+17543454351518386415637043060781056*RootOf(16*_Z^2+4*_Z+1)^2+6572417063730249524797944388667308*RootOf(16*_Z^2+4*_Z+1)+575090408768717286416168985366486)/(x^8+x^4-1))-ln(-(1027936778409280454041232991842640*RootOf(16*_Z^2+4*_Z+1)^2*x^8+4529039623257700492643576695162024*RootOf(16*_Z^2+4*_Z+1)*x^8+610884417613243258599747967858176*x^8-6458608904506033300021952070673408*RootOf(16*_Z^2+4*_Z+1)*(x^5-x)^(1/3)*x^5-17543454351518386415637043060781056*RootOf(16*_Z^2+4*_Z+1)^2*x^4-25262880761481365661024699935681*(x^5-x)^(1/3)*x^5+6458608904506033300021952070673408*RootOf(16*_Z^2+4*_Z+1)*(x^5-x)^(2/3)*x^2-6572417063730249524797944388667308*RootOf(16*_Z^2+4*_Z+1)*x^4+25262880761481365661024699935681*(x^5-x)^(2/3)*x^2-575090408768717286416168985366486*x^4+17543454351518386415637043060781056*RootOf(16*_Z^2+4*_Z+1)^2+6572417063730249524797944388667308*RootOf(16*_Z^2+4*_Z+1)+575090408768717286416168985366486)/(x^8+x^4-1))*RootOf(16*_Z^2+4*_Z+1)+RootOf(16*_Z^2+4*_Z+1)*ln(-(1027936778409280454041232991842640*RootOf(16*_Z^2+4*_Z+1)^2*x^8-4015071234053060265622960199240704*RootOf(16*_Z^2+4*_Z+1)*x^8-457129439550601836183569143942165*x^8+6458608904506033300021952070673408*RootOf(16*_Z^2+4*_Z+1)*(x^5-x)^(1/3)*x^5-17543454351518386415637043060781056*RootOf(16*_Z^2+4*_Z+1)^2*x^4+1589389345365026959344463317732671*(x^5-x)^(1/3)*x^5-6458608904506033300021952070673408*RootOf(16*_Z^2+4*_Z+1)*(x^5-x)^(2/3)*x^2-2199310112028943683020577141723220*RootOf(16*_Z^2+4*_Z+1)*x^4-1589389345365026959344463317732671*(x^5-x)^(2/3)*x^2-28452039806054056193998079498475*x^4+17543454351518386415637043060781056*RootOf(16*_Z^2+4*_Z+1)^2+2199310112028943683020577141723220*RootOf(16*_Z^2+4*_Z+1)+28452039806054056193998079498475)/(x^8+x^4-1))","C"
1467,0,0,11,0.024000," ","int((2*a*x^4-b)/(a*x^4-b)^(1/4)/(x^8-a*x^4-b),x)","\[\int \frac{2 a \,x^{4}-b}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(x^{8}-a \,x^{4}-b \right)}\, dx\]"," ",0,"int((2*a*x^4-b)/(a*x^4-b)^(1/4)/(x^8-a*x^4-b),x)","F"
1468,0,0,11,0.022000," ","int((a*x^4-2*b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-2*b),x)","\[\int \frac{a \,x^{4}-2 b}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(x^{8}+a \,x^{4}-2 b \right)}\, dx\]"," ",0,"int((a*x^4-2*b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-2*b),x)","F"
1469,0,0,83,180.000000," ","int(1/x^2/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{1}{x^{2} \sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int(1/x^2/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","F"
1470,1,89,82,2.756000," ","int((x^3-1)^(1/3)/x^10,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \left(-\frac{10 \Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{11}{3}\right], \left[2, 5\right], x^{3}\right)}{81}-\frac{5 \left(\frac{4}{15}+\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{2}{3}\right)}{27}-\frac{\Gamma \left(\frac{2}{3}\right)}{x^{9}}+\frac{\Gamma \left(\frac{2}{3}\right)}{2 x^{6}}+\frac{\Gamma \left(\frac{2}{3}\right)}{3 x^{3}}\right)}{9 \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}}}$&$89$\\ risch&$\frac{5 x^{9}-2 x^{6}-21 x^{3}+18}{162 x^{9} \left(x^{3}-1\right)^{\frac{2}{3}}}+\frac{5 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} \left(\frac{2 \Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 2\right], x^{3}\right)}{3}+\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{2}{3}\right)\right)}{243 \Gamma \left(\frac{2}{3}\right) \mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}}}$&$96$\\ trager&$\frac{\left(x^{3}-1\right)^{\frac{1}{3}} \left(5 x^{6}+3 x^{3}-18\right)}{162 x^{9}}-\frac{5 \ln \left(\frac{-376963072 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)^{2} x^{3}-5045760 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right) x^{3}+2817024 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}+1477 x^{3}-14247 \left(x^{3}-1\right)^{\frac{2}{3}}-2817024 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)+3015704576 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)^{2}+14247 \left(x^{3}-1\right)^{\frac{1}{3}}+8707072 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)-2743}{x^{3}}\right)}{243}-\frac{2560 \ln \left(\frac{-376963072 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)^{2} x^{3}-5045760 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right) x^{3}+2817024 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}+1477 x^{3}-14247 \left(x^{3}-1\right)^{\frac{2}{3}}-2817024 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)+3015704576 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)^{2}+14247 \left(x^{3}-1\right)^{\frac{1}{3}}+8707072 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)-2743}{x^{3}}\right) \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)}{243}+\frac{2560 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right) \ln \left(-\frac{376963072 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)^{2} x^{3}-3573248 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right) x^{3}+2817024 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}-9894 x^{3}+19749 \left(x^{3}-1\right)^{\frac{2}{3}}-2817024 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)-3015704576 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)^{2}-19749 \left(x^{3}-1\right)^{\frac{1}{3}}-3073024 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)+8245}{x^{3}}\right)}{243}$&$451$\\ \hline \end{longtable}"," ",0,"1/9/GAMMA(2/3)*signum(x^3-1)^(1/3)/(-signum(x^3-1))^(1/3)*(-10/81*GAMMA(2/3)*x^3*hypergeom([1,1,11/3],[2,5],x^3)-5/27*(4/15+1/6*Pi*3^(1/2)-3/2*ln(3)+3*ln(x)+I*Pi)*GAMMA(2/3)-GAMMA(2/3)/x^9+1/2*GAMMA(2/3)/x^6+1/3*GAMMA(2/3)/x^3)","C"
1471,1,33,82,1.495000," ","int(x^4*(x^3-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} x^{5} \hypergeom \left(\left[-\frac{1}{3}, \frac{5}{3}\right], \left[\frac{8}{3}\right], x^{3}\right)}{5 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}}}$&$33$\\ risch&$\frac{x^{2} \left(3 x^{3}-1\right) \left(x^{3}-1\right)^{\frac{1}{3}}}{18}-\frac{\left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} x^{2} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], x^{3}\right)}{18 \mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}}}$&$53$\\ trager&$\frac{x^{2} \left(3 x^{3}-1\right) \left(x^{3}-1\right)^{\frac{1}{3}}}{18}+\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}-1\right)^{\frac{2}{3}}+3 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}+2 x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2\right)}{27}-\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}-1\right)^{\frac{2}{3}}+3 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}+4 x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{27}-\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}-1\right)^{\frac{2}{3}}+3 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}+4 x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2\right)}{27}$&$306$\\ \hline \end{longtable}"," ",0,"1/5*signum(x^3-1)^(1/3)/(-signum(x^3-1))^(1/3)*x^5*hypergeom([-1/3,5/3],[8/3],x^3)","C"
1472,1,33,82,3.199000," ","int((x^3-x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}} x^{\frac{4}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], x^{2}\right)}{4 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}}}$&$33$\\ trager&$\frac{x \left(x^{3}-x \right)^{\frac{1}{3}}}{2}-\frac{\ln \left(1395 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}-6768 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}-6768 \left(x^{3}-x \right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -6303 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+5355 \left(x^{3}-x \right)^{\frac{2}{3}}+5355 x \left(x^{3}-x \right)^{\frac{1}{3}}-5580 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+5510 x^{2}+8007 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-1653\right)}{6}-\frac{\ln \left(1395 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}-6768 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}-6768 \left(x^{3}-x \right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -6303 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+5355 \left(x^{3}-x \right)^{\frac{2}{3}}+5355 x \left(x^{3}-x \right)^{\frac{1}{3}}-5580 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+5510 x^{2}+8007 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-1653\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{2}+\frac{\RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(1395 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}+6768 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}+6768 \left(x^{3}-x \right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x +7233 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+7611 \left(x^{3}-x \right)^{\frac{2}{3}}+7611 x \left(x^{3}-x \right)^{\frac{1}{3}}-5580 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+7766 x^{2}-11727 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-4942\right)}{2}$&$456$\\ risch&$\frac{x \left(x \left(x^{2}-1\right)\right)^{\frac{1}{3}}}{2}+\frac{\left(\frac{\RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \ln \left(-\frac{47 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{4}+3207 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{4}+2925 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{2}-235 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{2}+6930 x^{4}+2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}+5238 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}-5601 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{2}+5238 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}-2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}+188 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2}-11340 x^{2}-5238 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}+2394 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)+4410}{\left(-1+x \right) \left(1+x \right)}\right)}{36}-\frac{\ln \left(\frac{-47 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{4}+2643 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{4}+2925 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{2}+235 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{2}+10620 x^{4}+2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}+12312 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}-2781 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{2}+12312 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}-2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}-188 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2}-13806 x^{2}-12312 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}+138 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)+3186}{\left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)}{36}-\frac{\ln \left(\frac{-47 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{4}+2643 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{4}+2925 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{2}+235 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{2}+10620 x^{4}+2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}+12312 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}-2781 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{2}+12312 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}-2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}-188 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2}-13806 x^{2}-12312 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}+138 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)+3186}{\left(-1+x \right) \left(1+x \right)}\right)}{6}\right) \left(x \left(x^{2}-1\right)\right)^{\frac{1}{3}} \left(x^{2} \left(x^{2}-1\right)^{2}\right)^{\frac{1}{3}}}{x \left(x^{2}-1\right)}$&$784$\\ \hline \end{longtable}"," ",0,"3/4*signum(x^2-1)^(1/3)/(-signum(x^2-1))^(1/3)*x^(4/3)*hypergeom([-1/3,2/3],[5/3],x^2)","C"
1473,1,96,82,2.657000," ","int((x^3-1)^(1/3)*(2*x^3-1)/x^10,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{13 x^{9}-70 x^{6}+75 x^{3}-18}{162 x^{9} \left(x^{3}-1\right)^{\frac{2}{3}}}+\frac{13 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} \left(\frac{2 \Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 2\right], x^{3}\right)}{3}+\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{2}{3}\right)\right)}{243 \Gamma \left(\frac{2}{3}\right) \mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}}}$&$96$\\ meijerg&$-\frac{2 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \left(\frac{5 \Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{8}{3}\right], \left[2, 4\right], x^{3}\right)}{27}+\frac{\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{2}{3}\right)}{3}+\frac{3 \Gamma \left(\frac{2}{3}\right)}{2 x^{6}}-\frac{\Gamma \left(\frac{2}{3}\right)}{x^{3}}\right)}{9 \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}}}-\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \left(-\frac{10 \Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{11}{3}\right], \left[2, 5\right], x^{3}\right)}{81}-\frac{5 \left(\frac{4}{15}+\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{2}{3}\right)}{27}-\frac{\Gamma \left(\frac{2}{3}\right)}{x^{9}}+\frac{\Gamma \left(\frac{2}{3}\right)}{2 x^{6}}+\frac{\Gamma \left(\frac{2}{3}\right)}{3 x^{3}}\right)}{9 \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}}}$&$170$\\ trager&$\frac{\left(x^{3}-1\right)^{\frac{1}{3}} \left(13 x^{6}-57 x^{3}+18\right)}{162 x^{9}}+\frac{6656 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right) \ln \left(-\frac{376963072 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)^{2} x^{3}-3573248 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right) x^{3}+2817024 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}-9894 x^{3}+19749 \left(x^{3}-1\right)^{\frac{2}{3}}-2817024 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)-3015704576 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)^{2}-19749 \left(x^{3}-1\right)^{\frac{1}{3}}-3073024 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)+8245}{x^{3}}\right)}{243}-\frac{13 \ln \left(-\frac{163840 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)^{2} x^{3}+1728 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right) x^{3}+2496 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}-7 x^{3}-1310720 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)^{2}-2496 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)+18 \left(x^{3}-1\right)^{\frac{2}{3}}-64 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)-18 \left(x^{3}-1\right)^{\frac{1}{3}}+13}{x^{3}}\right)}{243}-\frac{6656 \ln \left(-\frac{163840 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)^{2} x^{3}+1728 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right) x^{3}+2496 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}-7 x^{3}-1310720 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)^{2}-2496 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)+18 \left(x^{3}-1\right)^{\frac{2}{3}}-64 \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)-18 \left(x^{3}-1\right)^{\frac{1}{3}}+13}{x^{3}}\right) \RootOf \left(262144 \textit{\_Z}^{2}+512 \textit{\_Z} +1\right)}{243}$&$453$\\ \hline \end{longtable}"," ",0,"1/162*(13*x^9-70*x^6+75*x^3-18)/x^9/(x^3-1)^(2/3)+13/243/GAMMA(2/3)/signum(x^3-1)^(2/3)*(-signum(x^3-1))^(2/3)*(2/3*GAMMA(2/3)*x^3*hypergeom([1,1,5/3],[2,2],x^3)+(1/6*Pi*3^(1/2)-3/2*ln(3)+3*ln(x)+I*Pi)*GAMMA(2/3))","C"
1474,1,363,94,0.146000," ","int((k^3*x^3+1)/((1-x)*x*(-k^2*x+1))^(1/2)/(k^3*x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}-\frac{4 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{3 k^{3} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}-\frac{4 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(k^{2} \textit{\_Z}^{2}+k \textit{\_Z} +1\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha  k -2\right) \left(\underline{\hspace{1.25 ex}}\alpha  \,k^{2}+k +1\right) \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{\underline{\hspace{1.25 ex}}\alpha  \,k^{2}+k +1}{k^{2}+k +1}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(2 \underline{\hspace{1.25 ex}}\alpha  k +1\right) \left(k^{2}+k +1\right) \sqrt{x \left(k^{2} x^{2}-k^{2} x -x +1\right)}}\right)}{3 k}$&$363$\\ elliptic&$-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}-\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{3 k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}-1\right)}-\frac{4 k^{2} \sqrt{-k^{2} x +1}\, \sqrt{-\frac{\left(-1+x \right) k^{2}}{k^{2}-1}}\, \sqrt{k^{2} x}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(k^{2} \textit{\_Z}^{2}+k \textit{\_Z} +1\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-k^{2} x +1}, \frac{\underline{\hspace{1.25 ex}}\alpha  \,k^{2}+k +1}{k^{2}+k +1}, \sqrt{-\frac{1}{k^{2}-1}}\right) \underline{\hspace{1.25 ex}}\alpha^{2}}{2 \underline{\hspace{1.25 ex}}\alpha  k +1}\right)}{3 \left(k^{2}+k +1\right) \sqrt{x \left(k^{2} x^{2}-k^{2} x -x +1\right)}}-\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{\left(-1+x \right) k^{2}}{k^{2}-1}}\, \sqrt{k^{2} x}\, k \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(k^{2} \textit{\_Z}^{2}+k \textit{\_Z} +1\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-k^{2} x +1}, \frac{\underline{\hspace{1.25 ex}}\alpha  \,k^{2}+k +1}{k^{2}+k +1}, \sqrt{-\frac{1}{k^{2}-1}}\right) \underline{\hspace{1.25 ex}}\alpha }{2 \underline{\hspace{1.25 ex}}\alpha  k +1}\right)}{\left(k^{2}+k +1\right) \sqrt{x \left(k^{2} x^{2}-k^{2} x -x +1\right)}}-\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{\left(-1+x \right) k^{2}}{k^{2}-1}}\, \sqrt{k^{2} x}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(k^{2} \textit{\_Z}^{2}+k \textit{\_Z} +1\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-k^{2} x +1}, \frac{\underline{\hspace{1.25 ex}}\alpha  \,k^{2}+k +1}{k^{2}+k +1}, \sqrt{-\frac{1}{k^{2}-1}}\right) \underline{\hspace{1.25 ex}}\alpha }{2 \underline{\hspace{1.25 ex}}\alpha  k +1}\right)}{3 \left(k^{2}+k +1\right) \sqrt{x \left(k^{2} x^{2}-k^{2} x -x +1\right)}}-\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{\left(-1+x \right) k^{2}}{k^{2}-1}}\, \sqrt{k^{2} x}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(k^{2} \textit{\_Z}^{2}+k \textit{\_Z} +1\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-k^{2} x +1}, \frac{\underline{\hspace{1.25 ex}}\alpha  \,k^{2}+k +1}{k^{2}+k +1}, \sqrt{-\frac{1}{k^{2}-1}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  k +1}\right)}{3 \left(k^{2}+k +1\right) \sqrt{x \left(k^{2} x^{2}-k^{2} x -x +1\right)}}-\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{\left(-1+x \right) k^{2}}{k^{2}-1}}\, \sqrt{k^{2} x}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(k^{2} \textit{\_Z}^{2}+k \textit{\_Z} +1\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-k^{2} x +1}, \frac{\underline{\hspace{1.25 ex}}\alpha  \,k^{2}+k +1}{k^{2}+k +1}, \sqrt{-\frac{1}{k^{2}-1}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  k +1}\right)}{3 k \left(k^{2}+k +1\right) \sqrt{x \left(k^{2} x^{2}-k^{2} x -x +1\right)}}$&$872$\\ \hline \end{longtable}"," ",0,"-2/k^2*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticF((-(x-1/k^2)*k^2)^(1/2),(1/k^2/(1/k^2-1))^(1/2))-4/3/k^3*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-1/k)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-1/k),(1/k^2/(1/k^2-1))^(1/2))-4/3/k*sum((-_alpha*k-2)/(2*_alpha*k+1)*(_alpha*k^2+k+1)/(k^2+k+1)*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(x*(k^2*x^2-k^2*x-x+1))^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),(_alpha*k^2+k+1)/(k^2+k+1),(1/k^2/(1/k^2-1))^(1/2)),_alpha=RootOf(_Z^2*k^2+_Z*k+1))","C"
1475,1,292,86,6.917000," ","int((x^4-3)*(x^4+1)^(2/3)*(x^4+2*x^3+1)/x^6/(x^4-x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\frac{3}{5} x^{8}+\frac{6}{5} x^{4}+\frac{3}{5}+\frac{9}{2} x^{7}+\frac{9}{2} x^{3}}{x^{5} \left(x^{4}+1\right)^{\frac{1}{3}}}+3 \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x -\left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+x^{4}-2 \left(x^{4}+1\right)^{\frac{2}{3}} x +x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}+x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1}{x^{4}-x^{3}+1}\right)+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x +2 \left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-x^{4}+\left(x^{4}+1\right)^{\frac{2}{3}} x +x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1}{x^{4}-x^{3}+1}\right)$&$292$\\ trager&$\frac{3 \left(x^{4}+1\right)^{\frac{2}{3}} \left(2 x^{4}+15 x^{3}+2\right)}{10 x^{5}}-9 \ln \left(-\frac{72 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}-144 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}-33 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}+51 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x +60 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{1}{3}} x^{2}-102 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}-10 x^{4}-20 \left(x^{4}+1\right)^{\frac{2}{3}} x +37 x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}-15 x^{3}+72 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-33 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-10}{x^{4}-x^{3}+1}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+3 \ln \left(\frac{12357 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}-24714 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+8922 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}+9621 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x -33651 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{1}{3}} x^{2}+10989 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}-3435 x^{4}+11217 \left(x^{4}+1\right)^{\frac{2}{3}} x -8010 x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}-1145 x^{3}+12357 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+8922 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-3435}{x^{4}-x^{3}+1}\right)-3 \ln \left(-\frac{72 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}-144 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}-33 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}+51 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}} x +60 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{1}{3}} x^{2}-102 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}-10 x^{4}-20 \left(x^{4}+1\right)^{\frac{2}{3}} x +37 x^{2} \left(x^{4}+1\right)^{\frac{1}{3}}-15 x^{3}+72 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-33 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-10}{x^{4}-x^{3}+1}\right)$&$609$\\ \hline \end{longtable}"," ",0,"3/10*(2*x^8+15*x^7+4*x^4+15*x^3+2)/x^5/(x^4+1)^(1/3)+3*ln((RootOf(_Z^2+_Z+1)^2*x^3+RootOf(_Z^2+_Z+1)*x^4-RootOf(_Z^2+_Z+1)*(x^4+1)^(2/3)*x-(x^4+1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2+2*RootOf(_Z^2+_Z+1)*x^3+x^4-2*(x^4+1)^(2/3)*x+x^2*(x^4+1)^(1/3)+x^3+RootOf(_Z^2+_Z+1)+1)/(x^4-x^3+1))+3*RootOf(_Z^2+_Z+1)*ln(-(RootOf(_Z^2+_Z+1)^2*x^3-RootOf(_Z^2+_Z+1)*x^4-RootOf(_Z^2+_Z+1)*(x^4+1)^(2/3)*x+2*(x^4+1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2+RootOf(_Z^2+_Z+1)*x^3-x^4+(x^4+1)^(2/3)*x+x^2*(x^4+1)^(1/3)-RootOf(_Z^2+_Z+1)-1)/(x^4-x^3+1))","C"
1476,0,0,78,0.011000," ","int((a*x^4+b)^(3/4)/x^4/(a*x^4+2*b),x)","\[\int \frac{\left(a \,x^{4}+b \right)^{\frac{3}{4}}}{x^{4} \left(a \,x^{4}+2 b \right)}\, dx\]"," ",0,"int((a*x^4+b)^(3/4)/x^4/(a*x^4+2*b),x)","F"
1477,0,0,84,0.008000," ","int((a*x^3-b)/x^3/(a*x^4-b*x)^(1/4),x)","\[\int \frac{a \,x^{3}-b}{x^{3} \left(a \,x^{4}-b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^3-b)/x^3/(a*x^4-b*x)^(1/4),x)","F"
1478,0,0,84,0.008000," ","int((a*x^3+b)/x^3/(a*x^4-b*x)^(1/4),x)","\[\int \frac{a \,x^{3}+b}{x^{3} \left(a \,x^{4}-b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^3+b)/x^3/(a*x^4-b*x)^(1/4),x)","F"
1479,0,0,84,0.006000," ","int((a*x^4-b*x)^(1/4)/x^2,x)","\[\int \frac{\left(a \,x^{4}-b x \right)^{\frac{1}{4}}}{x^{2}}\, dx\]"," ",0,"int((a*x^4-b*x)^(1/4)/x^2,x)","F"
1480,0,0,14,0.023000," ","int(1/(x^4-a*x^2+b)/(a*x^4-b*x^2)^(1/4),x)","\[\int \frac{1}{\left(x^{4}-a \,x^{2}+b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(x^4-a*x^2+b)/(a*x^4-b*x^2)^(1/4),x)","F"
1481,0,0,14,0.001000," ","int(1/(x^4-a*x^2+b)/(a*x^4-b*x^2)^(1/4),x)","\[\int \frac{1}{\left(x^{4}-a \,x^{2}+b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(x^4-a*x^2+b)/(a*x^4-b*x^2)^(1/4),x)","F"
1482,0,0,76,0.010000," ","int((a*x^4-b)/x^4/(2*a*x^4-b)^(1/4),x)","\[\int \frac{a \,x^{4}-b}{x^{4} \left(2 a \,x^{4}-b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^4-b)/x^4/(2*a*x^4-b)^(1/4),x)","F"
1483,0,0,86,0.033000," ","int(x^4*(a*x^5+4*b)/(a*x^5-b)^2/(a*x^5+c*x^4-b)^(1/4),x)","\[\int \frac{x^{4} \left(a \,x^{5}+4 b \right)}{\left(a \,x^{5}-b \right)^{2} \left(a \,x^{5}+c \,x^{4}-b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(x^4*(a*x^5+4*b)/(a*x^5-b)^2/(a*x^5+c*x^4-b)^(1/4),x)","F"
1484,1,113,82,7.854000," ","int(1/x^19/(x^6-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{28 x^{18}-7 x^{12}-3 x^{6}-18}{324 x^{18} \left(x^{6}-1\right)^{\frac{1}{3}}}+\frac{7 \sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} \left(\frac{2 \pi  \sqrt{3}\, x^{6} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], x^{6}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+6 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{486 \pi  \mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}}}$&$113$\\ meijerg&$-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} \left(-\frac{70 \pi  \sqrt{3}\, x^{6} \hypergeom \left(\left[1, 1, \frac{13}{3}\right], \left[2, 5\right], x^{6}\right)}{729 \Gamma \left(\frac{2}{3}\right)}-\frac{28 \left(\frac{197}{84}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+6 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{243 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \pi  \sqrt{3}}{9 \Gamma \left(\frac{2}{3}\right) x^{18}}+\frac{\pi  \sqrt{3}}{9 \Gamma \left(\frac{2}{3}\right) x^{12}}+\frac{4 \pi  \sqrt{3}}{27 \Gamma \left(\frac{2}{3}\right) x^{6}}\right)}{12 \pi  \mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}}}$&$123$\\ trager&$\frac{\left(x^{6}-1\right)^{\frac{2}{3}} \left(28 x^{12}+21 x^{6}+18\right)}{324 x^{18}}+\frac{12845056 \RootOf \left(272747603165184 \textit{\_Z}^{2}-16515072 \textit{\_Z} +1\right) \ln \left(-\frac{410491845751654482455753265946558464 \RootOf \left(272747603165184 \textit{\_Z}^{2}-16515072 \textit{\_Z} +1\right)^{2} x^{6}-1559827880909604667500868141056 \RootOf \left(272747603165184 \textit{\_Z}^{2}-16515072 \textit{\_Z} +1\right) x^{6}-23171389162410581752275 x^{6}+1127439542090463244013057605632 \left(x^{6}-1\right)^{\frac{2}{3}} \RootOf \left(272747603165184 \textit{\_Z}^{2}-16515072 \textit{\_Z} +1\right)-26271478128105886877168209020579741696 \RootOf \left(272747603165184 \textit{\_Z}^{2}-16515072 \textit{\_Z} +1\right)^{2}-1127439542090463244013057605632 \RootOf \left(272747603165184 \textit{\_Z}^{2}-16515072 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}}+142296551347461340528569 \left(x^{6}-1\right)^{\frac{2}{3}}+2718197252871614357200345497600 \RootOf \left(272747603165184 \textit{\_Z}^{2}-16515072 \textit{\_Z} +1\right)-142296551347461340528569 \left(x^{6}-1\right)^{\frac{1}{3}}+45974978496846392365625}{x^{6}}\right)}{27}+\frac{7 \ln \left(\frac{151613680100373352009382957678592 \RootOf \left(272747603165184 \textit{\_Z}^{2}-16515072 \textit{\_Z} +1\right)^{2} x^{6}+549259830886362994300944384 \RootOf \left(272747603165184 \textit{\_Z}^{2}-16515072 \textit{\_Z} +1\right) x^{6}-74783116455558560258 x^{6}+127348568797268153299894272 \left(x^{6}-1\right)^{\frac{2}{3}} \RootOf \left(272747603165184 \textit{\_Z}^{2}-16515072 \textit{\_Z} +1\right)-9703275526423894528600509291429888 \RootOf \left(272747603165184 \textit{\_Z}^{2}-16515072 \textit{\_Z} +1\right)^{2}-127348568797268153299894272 \RootOf \left(272747603165184 \textit{\_Z}^{2}-16515072 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}}+109152962075501576931 \left(x^{6}-1\right)^{\frac{2}{3}}+714889181785446135727128576 \RootOf \left(272747603165184 \textit{\_Z}^{2}-16515072 \textit{\_Z} +1\right)-109152962075501576931 \left(x^{6}-1\right)^{\frac{1}{3}}+73576937157888260899}{x^{6}}\right)}{243}-\frac{12845056 \ln \left(\frac{151613680100373352009382957678592 \RootOf \left(272747603165184 \textit{\_Z}^{2}-16515072 \textit{\_Z} +1\right)^{2} x^{6}+549259830886362994300944384 \RootOf \left(272747603165184 \textit{\_Z}^{2}-16515072 \textit{\_Z} +1\right) x^{6}-74783116455558560258 x^{6}+127348568797268153299894272 \left(x^{6}-1\right)^{\frac{2}{3}} \RootOf \left(272747603165184 \textit{\_Z}^{2}-16515072 \textit{\_Z} +1\right)-9703275526423894528600509291429888 \RootOf \left(272747603165184 \textit{\_Z}^{2}-16515072 \textit{\_Z} +1\right)^{2}-127348568797268153299894272 \RootOf \left(272747603165184 \textit{\_Z}^{2}-16515072 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}}+109152962075501576931 \left(x^{6}-1\right)^{\frac{2}{3}}+714889181785446135727128576 \RootOf \left(272747603165184 \textit{\_Z}^{2}-16515072 \textit{\_Z} +1\right)-109152962075501576931 \left(x^{6}-1\right)^{\frac{1}{3}}+73576937157888260899}{x^{6}}\right) \RootOf \left(272747603165184 \textit{\_Z}^{2}-16515072 \textit{\_Z} +1\right)}{27}$&$451$\\ \hline \end{longtable}"," ",0,"1/324*(28*x^18-7*x^12-3*x^6-18)/x^18/(x^6-1)^(1/3)+7/486/Pi*3^(1/2)*GAMMA(2/3)/signum(x^6-1)^(1/3)*(-signum(x^6-1))^(1/3)*(2/9*Pi*3^(1/2)/GAMMA(2/3)*x^6*hypergeom([1,1,4/3],[2,2],x^6)+2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)+6*ln(x)+I*Pi)*Pi*3^(1/2)/GAMMA(2/3))","C"
1485,1,33,82,3.300000," ","int(x^7/(x^6-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} x^{8} \hypergeom \left(\left[\frac{1}{3}, \frac{4}{3}\right], \left[\frac{7}{3}\right], x^{6}\right)}{8 \mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}}}$&$33$\\ risch&$\frac{x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}}{6}+\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} x^{2} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{6}\right)}{6 \mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}}}$&$46$\\ trager&$\frac{x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}}{6}+\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}-4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}+4 x^{6}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}+3 x^{4} \left(x^{6}-1\right)^{\frac{1}{3}}+3 x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-2\right)}{18}-\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}+x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-1\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)}{18}+\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}+x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-1\right)}{18}$&$326$\\ \hline \end{longtable}"," ",0,"1/8/signum(x^6-1)^(1/3)*(-signum(x^6-1))^(1/3)*x^8*hypergeom([1/3,4/3],[7/3],x^6)","C"
1486,1,33,82,3.099000," ","int(x^3*(x^6-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}} x^{4} \hypergeom \left(\left[-\frac{1}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], x^{6}\right)}{4 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}}}$&$33$\\ risch&$\frac{x^{4} \left(x^{6}-1\right)^{\frac{1}{3}}}{6}-\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{2}{3}} x^{4} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], x^{6}\right)}{12 \mathrm{signum}\left(x^{6}-1\right)^{\frac{2}{3}}}$&$46$\\ trager&$\frac{x^{4} \left(x^{6}-1\right)^{\frac{1}{3}}}{6}+\frac{\ln \left(-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}+x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+x^{6}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}-3 x^{4} \left(x^{6}-1\right)^{\frac{1}{3}}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1\right)}{18}+\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}+x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}-2 x^{6}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}+3 x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1\right)}{18}$&$187$\\ \hline \end{longtable}"," ",0,"1/4*signum(x^6-1)^(1/3)/(-signum(x^6-1))^(1/3)*x^4*hypergeom([-1/3,2/3],[5/3],x^6)","C"
1487,1,33,82,3.421000," ","int(x*(x^6-1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{2}{3}} x^{2} \hypergeom \left(\left[-\frac{2}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{6}\right)}{2 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{2}{3}}}$&$33$\\ risch&$\frac{x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}}{6}-\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} x^{2} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{6}\right)}{3 \mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}}}$&$46$\\ trager&$\frac{x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}}{6}+\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}+4 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}+4 x^{6}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}+3 x^{4} \left(x^{6}-1\right)^{\frac{1}{3}}+3 x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2\right)}{9}-\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}-2 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}+x^{6}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{9}-\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}-2 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}+x^{6}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1\right)}{9}$&$290$\\ \hline \end{longtable}"," ",0,"1/2*signum(x^6-1)^(2/3)/(-signum(x^6-1))^(2/3)*x^2*hypergeom([-2/3,1/3],[4/3],x^6)","C"
1488,1,17,82,3.556000," ","int(x^7/(x^6+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{x^{8} \hypergeom \left(\left[\frac{1}{3}, \frac{4}{3}\right], \left[\frac{7}{3}\right], -x^{6}\right)}{8}$&$17$\\ risch&$\frac{x^{2} \left(x^{6}+1\right)^{\frac{2}{3}}}{6}-\frac{x^{2} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{6}\right)}{6}$&$30$\\ trager&$\frac{x^{2} \left(x^{6}+1\right)^{\frac{2}{3}}}{6}+\frac{\ln \left(-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}-5 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2 x^{6}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x^{2}-3 x^{4} \left(x^{6}+1\right)^{\frac{1}{3}}+3 x^{2} \left(x^{6}+1\right)^{\frac{2}{3}}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1\right)}{18}+\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}+x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}} x^{4}-2 x^{6}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x^{2}+3 x^{4} \left(x^{6}+1\right)^{\frac{1}{3}}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2\right)}{18}$&$202$\\ \hline \end{longtable}"," ",0,"1/8*x^8*hypergeom([1/3,4/3],[7/3],-x^6)","C"
1489,1,17,82,2.910000," ","int(x^3*(x^6+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{x^{4} \hypergeom \left(\left[-\frac{1}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], -x^{6}\right)}{4}$&$17$\\ risch&$\frac{x^{4} \left(x^{6}+1\right)^{\frac{1}{3}}}{6}+\frac{x^{4} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], -x^{6}\right)}{12}$&$30$\\ trager&$\frac{x^{4} \left(x^{6}+1\right)^{\frac{1}{3}}}{6}+\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}} x^{4}+x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+1\right)}{18}-\frac{\ln \left(-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}+2 x^{6}+3 x^{4} \left(x^{6}+1\right)^{\frac{1}{3}}+3 x^{2} \left(x^{6}+1\right)^{\frac{2}{3}}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+1\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)}{18}+\frac{\ln \left(-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}+2 x^{6}+3 x^{4} \left(x^{6}+1\right)^{\frac{1}{3}}+3 x^{2} \left(x^{6}+1\right)^{\frac{2}{3}}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+1\right)}{18}$&$264$\\ \hline \end{longtable}"," ",0,"1/4*x^4*hypergeom([-1/3,2/3],[5/3],-x^6)","C"
1490,1,17,82,3.515000," ","int(x*(x^6+1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{x^{2} \hypergeom \left(\left[-\frac{2}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{6}\right)}{2}$&$17$\\ risch&$\frac{x^{2} \left(x^{6}+1\right)^{\frac{2}{3}}}{6}+\frac{x^{2} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{6}\right)}{3}$&$30$\\ trager&$\frac{x^{2} \left(x^{6}+1\right)^{\frac{2}{3}}}{6}-\frac{\ln \left(-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}+5 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}-2 x^{6}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x^{2}-3 x^{4} \left(x^{6}+1\right)^{\frac{1}{3}}+3 x^{2} \left(x^{6}+1\right)^{\frac{2}{3}}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-1\right)}{9}+\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}} x^{4}-2 x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x^{2}+3 x^{4} \left(x^{6}+1\right)^{\frac{1}{3}}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-2\right)}{9}$&$221$\\ \hline \end{longtable}"," ",0,"1/2*x^2*hypergeom([-2/3,1/3],[4/3],-x^6)","C"
1491,1,213,84,18.154000," ","int((x^5-x^3+1)*(2*x^5-3)/x^3/(x^5+x^3+1)/(x^6+x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{6}+x \right)^{\frac{3}{4}}}{3 x^{3}}-2 \RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{2 \sqrt{x^{6}+x}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x -\RootOf \left(\textit{\_Z}^{4}+1\right) x^{5}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} \left(x^{6}+x \right)^{\frac{1}{4}} x^{2}+\RootOf \left(\textit{\_Z}^{4}+1\right) x^{3}+2 \left(x^{6}+x \right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}+1\right)}{x^{5}+x^{3}+1}\right)+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{5}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{3}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} \left(x^{6}+x \right)^{\frac{1}{4}} x^{2}-2 \sqrt{x^{6}+x}\, \RootOf \left(\textit{\_Z}^{4}+1\right) x +\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+2 \left(x^{6}+x \right)^{\frac{3}{4}}}{x^{5}+x^{3}+1}\right)$&$213$\\ risch&$\frac{\frac{4 x^{5}}{3}+\frac{4}{3}}{x^{2} \left(x \left(x^{5}+1\right)\right)^{\frac{1}{4}}}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{5}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{3}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} \left(x^{6}+x \right)^{\frac{1}{4}} x^{2}-2 \sqrt{x^{6}+x}\, \RootOf \left(\textit{\_Z}^{4}+1\right) x +\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}-2 \left(x^{6}+x \right)^{\frac{3}{4}}}{x^{5}+x^{3}+1}\right)+2 \RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(-\frac{2 \sqrt{x^{6}+x}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x -\RootOf \left(\textit{\_Z}^{4}+1\right) x^{5}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} \left(x^{6}+x \right)^{\frac{1}{4}} x^{2}+\RootOf \left(\textit{\_Z}^{4}+1\right) x^{3}-2 \left(x^{6}+x \right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}+1\right)}{x^{5}+x^{3}+1}\right)$&$221$\\ \hline \end{longtable}"," ",0,"4/3*(x^6+x)^(3/4)/x^3-2*RootOf(_Z^4+1)*ln((2*(x^6+x)^(1/2)*RootOf(_Z^4+1)^3*x-RootOf(_Z^4+1)*x^5-2*RootOf(_Z^4+1)^2*(x^6+x)^(1/4)*x^2+RootOf(_Z^4+1)*x^3+2*(x^6+x)^(3/4)-RootOf(_Z^4+1))/(x^5+x^3+1))+2*RootOf(_Z^4+1)^3*ln(-(RootOf(_Z^4+1)^3*x^5-RootOf(_Z^4+1)^3*x^3+2*RootOf(_Z^4+1)^2*(x^6+x)^(1/4)*x^2-2*(x^6+x)^(1/2)*RootOf(_Z^4+1)*x+RootOf(_Z^4+1)^3+2*(x^6+x)^(3/4))/(x^5+x^3+1))","C"
1492,1,33,86,3.788000," ","int(x/(x^6-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{3}} x^{\frac{4}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{4}\right)}{4 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{3}}}$&$33$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \ln \left(-2192545 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{4}-204782686 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{4}-209167776 \left(x^{6}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-282306232 x^{4}-209167776 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}-x^{2}\right)^{\frac{2}{3}}-273536052 x^{2} \left(x^{6}-x^{2}\right)^{\frac{1}{3}}-273536052 \left(x^{6}-x^{2}\right)^{\frac{2}{3}}+35080720 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2}+114873086 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)+92056380\right)}{8}-\frac{\ln \left(-2192545 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{4}+213552866 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{4}+209167776 \left(x^{6}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-700641784 x^{4}+209167776 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}-x^{2}\right)^{\frac{2}{3}}-691871604 x^{2} \left(x^{6}-x^{2}\right)^{\frac{1}{3}}-691871604 \left(x^{6}-x^{2}\right)^{\frac{2}{3}}+35080720 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2}-255195966 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)+462125432\right) \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)}{8}+\frac{\ln \left(-2192545 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{4}+213552866 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{4}+209167776 \left(x^{6}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-700641784 x^{4}+209167776 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}-x^{2}\right)^{\frac{2}{3}}-691871604 x^{2} \left(x^{6}-x^{2}\right)^{\frac{1}{3}}-691871604 \left(x^{6}-x^{2}\right)^{\frac{2}{3}}+35080720 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2}-255195966 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)+462125432\right)}{4}$&$440$\\ \hline \end{longtable}"," ",0,"3/4/signum(x^4-1)^(1/3)*(-signum(x^4-1))^(1/3)*x^(4/3)*hypergeom([1/3,1/3],[4/3],x^4)","C"
1493,1,7989,24,275.839000," ","int((x^3-1)^(2/3)*(x^3+2)/x^3/(x^6+x^3-4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$7989$\\ trager&$\text{Expression too large to display}$&$10402$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1494,1,5732,24,238.255000," ","int((x^3-1)^(2/3)*(x^3+2)/x^3/(x^6+x^3-4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$5732$\\ trager&$\text{Expression too large to display}$&$10423$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1495,1,3489,86,37.718000," ","int((-3+2*x)*(x^3-x+1)^(2/3)/(2*x^6-2*x^4+2*x^3+x^2-2*x+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$3489$\\ \hline \end{longtable}"," ",0,"-1/2*RootOf(_Z^2+1)*ln(-(3-6*x+28*RootOf(_Z^2+1)^2*x^3-6*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)+28*RootOf(_Z^2+1)^2*x^6-28*RootOf(_Z^2+1)^2*x^4-14*RootOf(_Z^2+1)*x+7*RootOf(_Z^2+1)*x^2+26*RootOf(_Z^2+1)*x^6-26*RootOf(_Z^2+1)*x^4+26*RootOf(_Z^2+1)*x^3-42*x^2*(x^3-x+1)^(2/3)+6*x^6+3*x^2+6*x^3-6*x^4+96*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)^2*RootOf(_Z^2+1)*x^4+24*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)^2*x^4-14*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)+7*RootOf(_Z^2+1)+224*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)^2*x^4-224*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)^2*x^3-44*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)*x^4+44*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)*x^3-6*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)*x^2+12*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)*x-20*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*x^4+20*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*x^3-14*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*x^2+28*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*x-96*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)^2*RootOf(_Z^2+1)*x^3-24*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)^2*x^3+20*x^6*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)+44*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)*x^6-96*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)^2*RootOf(_Z^2+1)*x^6-24*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)^2*x^6-224*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)^2*x^6-6*RootOf(_Z^2+1)^2*(x^3-x+1)^(2/3)*x^4-28*RootOf(_Z^2+1)^2*(x^3-x+1)^(1/3)*x^5+144*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*(x^3-x+1)^(2/3)*x^4-84*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*(x^3-x+1)^(1/3)*x^5+36*RootOf(_Z^2+1)*(x^3-x+1)^(2/3)*x^4-84*RootOf(_Z^2+1)*(x^3-x+1)^(1/3)*x^5+24*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*(x^3-x+1)^(2/3)*x^2+84*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*(x^3-x+1)^(1/3)*x^3+6*RootOf(_Z^2+1)*(x^3-x+1)^(2/3)*x^2+84*RootOf(_Z^2+1)*(x^3-x+1)^(1/3)*x^3-24*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*(x^3-x+1)^(2/3)*x-84*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*(x^3-x+1)^(1/3)*x^2-6*RootOf(_Z^2+1)*(x^3-x+1)^(2/3)*x-84*RootOf(_Z^2+1)*(x^3-x+1)^(1/3)*x^2-96*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)^2*(x^3-x+1)^(2/3)*x^4-112*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)^2*(x^3-x+1)^(1/3)*x^5+42*(x^3-x+1)^(2/3)*x^4+42*(x^3-x+1)^(2/3)*x+48*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)^2*RootOf(_Z^2+1)*(x^3-x+1)^(1/3)*x^5+12*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)^2*(x^3-x+1)^(1/3)*x^5-36*(x^3-x+1)^(1/3)*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)*x^3+36*(x^3-x+1)^(1/3)*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)*x^2-48*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)*(x^3-x+1)^(2/3)*x^4-104*(x^3-x+1)^(1/3)*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)*x^5)/(2*x^6-2*x^4+2*x^3+x^2-2*x+1))-ln((3-6*x-28*RootOf(_Z^2+1)^2*x^3-28*RootOf(_Z^2+1)^2*x^6+28*RootOf(_Z^2+1)^2*x^4+14*RootOf(_Z^2+1)*x-7*RootOf(_Z^2+1)*x^2-2*RootOf(_Z^2+1)*x^6+2*RootOf(_Z^2+1)*x^4-2*RootOf(_Z^2+1)*x^3+42*x^2*(x^3-x+1)^(2/3)+6*x^6+3*x^2+6*x^3-6*x^4-28*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)-7*RootOf(_Z^2+1)+448*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)^2*x^4-448*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)^2*x^3+224*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)*x^4-224*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)*x^3+8*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*x^4-8*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*x^3-28*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*x^2+56*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*x-8*x^6*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)-224*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)*x^6-448*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)^2*x^6+6*RootOf(_Z^2+1)^2*(x^3-x+1)^(2/3)*x^4-14*RootOf(_Z^2+1)^2*(x^3-x+1)^(1/3)*x^5-144*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*(x^3-x+1)^(2/3)*x^4-144*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*(x^3-x+1)^(1/3)*x^5-36*RootOf(_Z^2+1)*(x^3-x+1)^(2/3)*x^4-36*RootOf(_Z^2+1)*(x^3-x+1)^(1/3)*x^5-24*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*(x^3-x+1)^(2/3)*x^2+168*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*(x^3-x+1)^(1/3)*x^3-6*RootOf(_Z^2+1)*(x^3-x+1)^(2/3)*x^2+42*RootOf(_Z^2+1)*(x^3-x+1)^(1/3)*x^3+24*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*(x^3-x+1)^(2/3)*x-168*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*(x^3-x+1)^(1/3)*x^2+6*RootOf(_Z^2+1)*(x^3-x+1)^(2/3)*x-42*RootOf(_Z^2+1)*(x^3-x+1)^(1/3)*x^2+96*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)^2*(x^3-x+1)^(2/3)*x^4-224*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)^2*(x^3-x+1)^(1/3)*x^5-42*(x^3-x+1)^(2/3)*x^4-42*(x^3-x+1)^(2/3)*x+18*(x^3-x+1)^(1/3)*x^5-18*(x^3-x+1)^(1/3)*x^3+18*(x^3-x+1)^(1/3)*x^2+48*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)*(x^3-x+1)^(2/3)*x^4-112*(x^3-x+1)^(1/3)*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)*x^5)/(2*x^6-2*x^4+2*x^3+x^2-2*x+1))*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)-1/2*ln((3-6*x-28*RootOf(_Z^2+1)^2*x^3-28*RootOf(_Z^2+1)^2*x^6+28*RootOf(_Z^2+1)^2*x^4+14*RootOf(_Z^2+1)*x-7*RootOf(_Z^2+1)*x^2-2*RootOf(_Z^2+1)*x^6+2*RootOf(_Z^2+1)*x^4-2*RootOf(_Z^2+1)*x^3+42*x^2*(x^3-x+1)^(2/3)+6*x^6+3*x^2+6*x^3-6*x^4-28*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)-7*RootOf(_Z^2+1)+448*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)^2*x^4-448*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)^2*x^3+224*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)*x^4-224*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)*x^3+8*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*x^4-8*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*x^3-28*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*x^2+56*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*x-8*x^6*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)-224*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)*x^6-448*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)^2*x^6+6*RootOf(_Z^2+1)^2*(x^3-x+1)^(2/3)*x^4-14*RootOf(_Z^2+1)^2*(x^3-x+1)^(1/3)*x^5-144*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*(x^3-x+1)^(2/3)*x^4-144*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*(x^3-x+1)^(1/3)*x^5-36*RootOf(_Z^2+1)*(x^3-x+1)^(2/3)*x^4-36*RootOf(_Z^2+1)*(x^3-x+1)^(1/3)*x^5-24*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*(x^3-x+1)^(2/3)*x^2+168*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*(x^3-x+1)^(1/3)*x^3-6*RootOf(_Z^2+1)*(x^3-x+1)^(2/3)*x^2+42*RootOf(_Z^2+1)*(x^3-x+1)^(1/3)*x^3+24*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*(x^3-x+1)^(2/3)*x-168*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*(x^3-x+1)^(1/3)*x^2+6*RootOf(_Z^2+1)*(x^3-x+1)^(2/3)*x-42*RootOf(_Z^2+1)*(x^3-x+1)^(1/3)*x^2+96*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)^2*(x^3-x+1)^(2/3)*x^4-224*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)^2*(x^3-x+1)^(1/3)*x^5-42*(x^3-x+1)^(2/3)*x^4-42*(x^3-x+1)^(2/3)*x+18*(x^3-x+1)^(1/3)*x^5-18*(x^3-x+1)^(1/3)*x^3+18*(x^3-x+1)^(1/3)*x^2+48*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)*(x^3-x+1)^(2/3)*x^4-112*(x^3-x+1)^(1/3)*RootOf(2*_Z*RootOf(_Z^2+1)+4*_Z^2-1)*RootOf(_Z^2+1)*x^5)/(2*x^6-2*x^4+2*x^3+x^2-2*x+1))*RootOf(_Z^2+1)","C"
1496,1,333,90,61.584000," ","int((x^6-2)*(x^6+4)*(x^6+2*x^4-2)^(1/4)/x^6/(2*x^6-x^4-4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{6}+2 x^{4}-2\right)^{\frac{1}{4}} \left(2 x^{6}+9 x^{4}-4\right)}{10 x^{5}}+\frac{\RootOf \left(\textit{\_Z}^{4}-40\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{4}-40\right)^{3} x^{6}+9 \RootOf \left(\textit{\_Z}^{4}-40\right)^{3} x^{4}-20 \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} \left(x^{6}+2 x^{4}-2\right)^{\frac{1}{4}} x^{3}+40 \RootOf \left(\textit{\_Z}^{4}-40\right) \sqrt{x^{6}+2 x^{4}-2}\, x^{2}-80 \left(x^{6}+2 x^{4}-2\right)^{\frac{3}{4}} x -4 \RootOf \left(\textit{\_Z}^{4}-40\right)^{3}}{2 x^{6}-x^{4}-4}\right)}{16}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-40\right)^{2}\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-40\right)^{2}\right) x^{6}+9 \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-40\right)^{2}\right) x^{4}-20 \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} \left(x^{6}+2 x^{4}-2\right)^{\frac{1}{4}} x^{3}-40 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-40\right)^{2}\right) \sqrt{x^{6}+2 x^{4}-2}\, x^{2}+80 \left(x^{6}+2 x^{4}-2\right)^{\frac{3}{4}} x -4 \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-40\right)^{2}\right)}{2 x^{6}-x^{4}-4}\right)}{16}$&$333$\\ risch&$\frac{2 x^{12}+13 x^{10}+18 x^{8}-8 x^{6}-26 x^{4}+8}{10 x^{5} \left(x^{6}+2 x^{4}-2\right)^{\frac{3}{4}}}+\frac{\left(-\frac{\RootOf \left(\textit{\_Z}^{4}-40\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} x^{18}+17 \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} x^{16}+2 \left(x^{18}+6 x^{16}+12 x^{14}+2 x^{12}-24 x^{10}-24 x^{8}+12 x^{6}+24 x^{4}-8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-40\right)^{3} x^{13}+44 \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} x^{14}+8 \left(x^{18}+6 x^{16}+12 x^{14}+2 x^{12}-24 x^{10}-24 x^{8}+12 x^{6}+24 x^{4}-8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-40\right)^{3} x^{11}+24 \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} x^{12}+8 \left(x^{18}+6 x^{16}+12 x^{14}+2 x^{12}-24 x^{10}-24 x^{8}+12 x^{6}+24 x^{4}-8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-40\right)^{3} x^{9}-68 \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} x^{10}-8 \left(x^{18}+6 x^{16}+12 x^{14}+2 x^{12}-24 x^{10}-24 x^{8}+12 x^{6}+24 x^{4}-8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-40\right)^{3} x^{7}-88 \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} x^{8}+40 \sqrt{x^{18}+6 x^{16}+12 x^{14}+2 x^{12}-24 x^{10}-24 x^{8}+12 x^{6}+24 x^{4}-8}\, x^{8}-16 \left(x^{18}+6 x^{16}+12 x^{14}+2 x^{12}-24 x^{10}-24 x^{8}+12 x^{6}+24 x^{4}-8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-40\right)^{3} x^{5}+24 \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} x^{6}+80 \sqrt{x^{18}+6 x^{16}+12 x^{14}+2 x^{12}-24 x^{10}-24 x^{8}+12 x^{6}+24 x^{4}-8}\, x^{6}+20 \left(x^{18}+6 x^{16}+12 x^{14}+2 x^{12}-24 x^{10}-24 x^{8}+12 x^{6}+24 x^{4}-8\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{4}-40\right) x^{3}+68 \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} x^{4}+8 \left(x^{18}+6 x^{16}+12 x^{14}+2 x^{12}-24 x^{10}-24 x^{8}+12 x^{6}+24 x^{4}-8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-40\right)^{3} x -80 \sqrt{x^{18}+6 x^{16}+12 x^{14}+2 x^{12}-24 x^{10}-24 x^{8}+12 x^{6}+24 x^{4}-8}\, x^{2}-16 \RootOf \left(\textit{\_Z}^{4}-40\right)^{2}}{\left(2 x^{6}-x^{4}-4\right) \left(x^{6}+2 x^{4}-2\right)^{2}}\right)}{16}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-40\right)^{2}\right) \ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} x^{18}-17 \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} x^{16}+2 \left(x^{18}+6 x^{16}+12 x^{14}+2 x^{12}-24 x^{10}-24 x^{8}+12 x^{6}+24 x^{4}-8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-40\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} x^{13}-44 \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} x^{14}+8 \left(x^{18}+6 x^{16}+12 x^{14}+2 x^{12}-24 x^{10}-24 x^{8}+12 x^{6}+24 x^{4}-8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-40\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} x^{11}-24 \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} x^{12}+8 \left(x^{18}+6 x^{16}+12 x^{14}+2 x^{12}-24 x^{10}-24 x^{8}+12 x^{6}+24 x^{4}-8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-40\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} x^{9}+68 \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} x^{10}-8 \left(x^{18}+6 x^{16}+12 x^{14}+2 x^{12}-24 x^{10}-24 x^{8}+12 x^{6}+24 x^{4}-8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-40\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} x^{7}+88 \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} x^{8}+40 \sqrt{x^{18}+6 x^{16}+12 x^{14}+2 x^{12}-24 x^{10}-24 x^{8}+12 x^{6}+24 x^{4}-8}\, x^{8}-16 \left(x^{18}+6 x^{16}+12 x^{14}+2 x^{12}-24 x^{10}-24 x^{8}+12 x^{6}+24 x^{4}-8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-40\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} x^{5}-24 \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} x^{6}+80 \sqrt{x^{18}+6 x^{16}+12 x^{14}+2 x^{12}-24 x^{10}-24 x^{8}+12 x^{6}+24 x^{4}-8}\, x^{6}-20 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-40\right)^{2}\right) \left(x^{18}+6 x^{16}+12 x^{14}+2 x^{12}-24 x^{10}-24 x^{8}+12 x^{6}+24 x^{4}-8\right)^{\frac{3}{4}} x^{3}-68 \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} x^{4}+8 \left(x^{18}+6 x^{16}+12 x^{14}+2 x^{12}-24 x^{10}-24 x^{8}+12 x^{6}+24 x^{4}-8\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-40\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-40\right)^{2} x -80 \sqrt{x^{18}+6 x^{16}+12 x^{14}+2 x^{12}-24 x^{10}-24 x^{8}+12 x^{6}+24 x^{4}-8}\, x^{2}+16 \RootOf \left(\textit{\_Z}^{4}-40\right)^{2}}{\left(2 x^{6}-x^{4}-4\right) \left(x^{6}+2 x^{4}-2\right)^{2}}\right)}{16}\right) \left(\left(x^{6}+2 x^{4}-2\right)^{3}\right)^{\frac{1}{4}}}{\left(x^{6}+2 x^{4}-2\right)^{\frac{3}{4}}}$&$1514$\\ \hline \end{longtable}"," ",0,"1/10*(x^6+2*x^4-2)^(1/4)*(2*x^6+9*x^4-4)/x^5+1/16*RootOf(_Z^4-40)*ln((2*RootOf(_Z^4-40)^3*x^6+9*RootOf(_Z^4-40)^3*x^4-20*RootOf(_Z^4-40)^2*(x^6+2*x^4-2)^(1/4)*x^3+40*RootOf(_Z^4-40)*(x^6+2*x^4-2)^(1/2)*x^2-80*(x^6+2*x^4-2)^(3/4)*x-4*RootOf(_Z^4-40)^3)/(2*x^6-x^4-4))+1/16*RootOf(_Z^2+RootOf(_Z^4-40)^2)*ln(-(2*RootOf(_Z^4-40)^2*RootOf(_Z^2+RootOf(_Z^4-40)^2)*x^6+9*RootOf(_Z^4-40)^2*RootOf(_Z^2+RootOf(_Z^4-40)^2)*x^4-20*RootOf(_Z^4-40)^2*(x^6+2*x^4-2)^(1/4)*x^3-40*RootOf(_Z^2+RootOf(_Z^4-40)^2)*(x^6+2*x^4-2)^(1/2)*x^2+80*(x^6+2*x^4-2)^(3/4)*x-4*RootOf(_Z^4-40)^2*RootOf(_Z^2+RootOf(_Z^4-40)^2))/(2*x^6-x^4-4))","C"
1497,1,425,85,3.956000," ","int((x^3+1)^(2/3)*(3*x^6-1)/x^9/(2*x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x^{9}-13 x^{6}-9 x^{3}+5}{40 x^{8} \left(x^{3}+1\right)^{\frac{1}{3}}}-\frac{\ln \left(-\frac{9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +3 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}-2 x \left(x^{3}+1\right)^{\frac{2}{3}}+2 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}+x^{3}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+1}{2 x^{3}+1}\right)}{3}-\ln \left(-\frac{9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +3 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}-2 x \left(x^{3}+1\right)^{\frac{2}{3}}+2 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}+x^{3}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+1}{2 x^{3}+1}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+\RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(-\frac{9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x -3 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}-x \left(x^{3}+1\right)^{\frac{2}{3}}+x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{2 x^{3}+1}\right)$&$425$\\ trager&$\frac{\left(x^{3}+1\right)^{\frac{2}{3}} \left(x^{6}-14 x^{3}+5\right)}{40 x^{8}}+\RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(\frac{63 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x -18 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}-15 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}-15 x \left(x^{3}+1\right)^{\frac{2}{3}}+15 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}-2 x^{3}-63 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-48 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-4}{2 x^{3}+1}\right)-\frac{\ln \left(\frac{63 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}-18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +18 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+57 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}-21 x \left(x^{3}+1\right)^{\frac{2}{3}}+21 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}+10 x^{3}-63 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+5}{2 x^{3}+1}\right)}{3}-\ln \left(\frac{63 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}-18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +18 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+57 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}-21 x \left(x^{3}+1\right)^{\frac{2}{3}}+21 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}+10 x^{3}-63 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+5}{2 x^{3}+1}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)$&$489$\\ \hline \end{longtable}"," ",0,"1/40*(x^9-13*x^6-9*x^3+5)/x^8/(x^3+1)^(1/3)-1/3*ln(-(9*RootOf(9*_Z^2+3*_Z+1)^2*x^3-3*RootOf(9*_Z^2+3*_Z+1)*(x^3+1)^(2/3)*x+3*(x^3+1)^(1/3)*RootOf(9*_Z^2+3*_Z+1)*x^2+6*RootOf(9*_Z^2+3*_Z+1)*x^3-2*x*(x^3+1)^(2/3)+2*x^2*(x^3+1)^(1/3)+x^3+3*RootOf(9*_Z^2+3*_Z+1)+1)/(2*x^3+1))-ln(-(9*RootOf(9*_Z^2+3*_Z+1)^2*x^3-3*RootOf(9*_Z^2+3*_Z+1)*(x^3+1)^(2/3)*x+3*(x^3+1)^(1/3)*RootOf(9*_Z^2+3*_Z+1)*x^2+6*RootOf(9*_Z^2+3*_Z+1)*x^3-2*x*(x^3+1)^(2/3)+2*x^2*(x^3+1)^(1/3)+x^3+3*RootOf(9*_Z^2+3*_Z+1)+1)/(2*x^3+1))*RootOf(9*_Z^2+3*_Z+1)+RootOf(9*_Z^2+3*_Z+1)*ln(-(9*RootOf(9*_Z^2+3*_Z+1)^2*x^3+3*RootOf(9*_Z^2+3*_Z+1)*(x^3+1)^(2/3)*x-3*(x^3+1)^(1/3)*RootOf(9*_Z^2+3*_Z+1)*x^2-x*(x^3+1)^(2/3)+x^2*(x^3+1)^(1/3)-3*RootOf(9*_Z^2+3*_Z+1))/(2*x^3+1))","C"
1498,1,114,83,1.072000," ","int((-x^4+1)^(1/2)*(x^4+1)/(x^8-x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(\frac{\ln \left(\frac{-x^{4}+1}{x^{2}}+\frac{\sqrt{-x^{4}+1}\, \sqrt{2}}{x}+1\right)}{4}-\frac{\arctan \left(1+\frac{\sqrt{-x^{4}+1}\, \sqrt{2}}{x}\right)}{2}-\frac{\ln \left(\frac{-x^{4}+1}{x^{2}}-\frac{\sqrt{-x^{4}+1}\, \sqrt{2}}{x}+1\right)}{4}-\frac{\arctan \left(-1+\frac{\sqrt{-x^{4}+1}\, \sqrt{2}}{x}\right)}{2}\right) \sqrt{2}}{2}$&$114$\\ elliptic&$\frac{\left(\frac{\ln \left(\frac{-x^{4}+1}{x^{2}}+\frac{\sqrt{-x^{4}+1}\, \sqrt{2}}{x}+1\right)}{4}-\frac{\arctan \left(1+\frac{\sqrt{-x^{4}+1}\, \sqrt{2}}{x}\right)}{2}-\frac{\ln \left(\frac{-x^{4}+1}{x^{2}}-\frac{\sqrt{-x^{4}+1}\, \sqrt{2}}{x}+1\right)}{4}-\frac{\arctan \left(-1+\frac{\sqrt{-x^{4}+1}\, \sqrt{2}}{x}\right)}{2}\right) \sqrt{2}}{2}$&$114$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}+\RootOf \left(\textit{\_Z}^{4}+1\right) x^{4}+2 \sqrt{-x^{4}+1}\, x -\RootOf \left(\textit{\_Z}^{4}+1\right)}{\left(\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}-\RootOf \left(\textit{\_Z}^{4}+1\right) x +1\right) \left(\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{4}+1\right) x +1\right)}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{5} x^{2}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{4}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+2 \sqrt{-x^{4}+1}\, x}{\left(\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x +\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}-1\right) \left(\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x -\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}+1\right)}\right)}{4}$&$217$\\ \hline \end{longtable}"," ",0,"1/2*(1/4*ln((-x^4+1)/x^2+(-x^4+1)^(1/2)*2^(1/2)/x+1)-1/2*arctan(1+(-x^4+1)^(1/2)*2^(1/2)/x)-1/4*ln((-x^4+1)/x^2-(-x^4+1)^(1/2)*2^(1/2)/x+1)-1/2*arctan(-1+(-x^4+1)^(1/2)*2^(1/2)/x))*2^(1/2)","A"
1499,0,0,76,0.045000," ","int(x^2/(a*x^4+b)^(3/4)/(a^2*x^8-b^2),x)","\[\int \frac{x^{2}}{\left(a \,x^{4}+b \right)^{\frac{3}{4}} \left(a^{2} x^{8}-b^{2}\right)}\, dx\]"," ",0,"int(x^2/(a*x^4+b)^(3/4)/(a^2*x^8-b^2),x)","F"
1500,0,0,78,0.011000," ","int((1+(x^2+1)^(1/2))^(1/2)/(x+(x^2+1)^(1/2)),x)","\[\int \frac{\sqrt{1+\sqrt{x^{2}+1}}}{x +\sqrt{x^{2}+1}}\, dx\]"," ",0,"int((1+(x^2+1)^(1/2))^(1/2)/(x+(x^2+1)^(1/2)),x)","F"
1501,1,398,86,1.911000," ","int((2+x)^2/x/(x^2-2*x+4)/(x^2+x+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+x +1\right)^{\frac{1}{3}} x^{2}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x -6 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+x +1\right)^{\frac{1}{3}} x -10 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-3 x \left(x^{2}+x +1\right)^{\frac{2}{3}}+2 x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+3 \left(x^{2}+x +1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+8 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +3 \left(x^{2}+x +1\right)^{\frac{2}{3}}-8 x^{2}-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+4 x -4}{\left(x^{2}-2 x +4\right) x}\right)+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-6 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+x +1\right)^{\frac{1}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+6 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x +6 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+x +1\right)^{\frac{1}{3}} x -\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+3 x \left(x^{2}+x +1\right)^{\frac{2}{3}}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-3 \left(x^{2}+x +1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+5 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x -3 \left(x^{2}+x +1\right)^{\frac{2}{3}}+x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+x +1}{\left(x^{2}-2 x +4\right) x}\right)$&$398$\\ \hline \end{longtable}"," ",0,"ln(-(RootOf(_Z^2+_Z+1)^2*x^3-3*RootOf(_Z^2+_Z+1)^2*x^2+3*RootOf(_Z^2+_Z+1)*(x^2+x+1)^(1/3)*x^2+3*RootOf(_Z^2+_Z+1)*x^3+3*RootOf(_Z^2+_Z+1)^2*x-6*RootOf(_Z^2+_Z+1)*(x^2+x+1)^(1/3)*x-10*RootOf(_Z^2+_Z+1)*x^2-3*x*(x^2+x+1)^(2/3)+2*x^3-RootOf(_Z^2+_Z+1)^2+3*(x^2+x+1)^(1/3)*RootOf(_Z^2+_Z+1)+8*RootOf(_Z^2+_Z+1)*x+3*(x^2+x+1)^(2/3)-8*x^2-4*RootOf(_Z^2+_Z+1)+4*x-4)/(x^2-2*x+4)/x)+RootOf(_Z^2+_Z+1)*ln((2*RootOf(_Z^2+_Z+1)^2*x^3-6*RootOf(_Z^2+_Z+1)^2*x^2-3*RootOf(_Z^2+_Z+1)*(x^2+x+1)^(1/3)*x^2+RootOf(_Z^2+_Z+1)*x^3+6*RootOf(_Z^2+_Z+1)^2*x+6*RootOf(_Z^2+_Z+1)*(x^2+x+1)^(1/3)*x-RootOf(_Z^2+_Z+1)*x^2+3*x*(x^2+x+1)^(2/3)-2*RootOf(_Z^2+_Z+1)^2-3*(x^2+x+1)^(1/3)*RootOf(_Z^2+_Z+1)+5*RootOf(_Z^2+_Z+1)*x-3*(x^2+x+1)^(2/3)+x^2+RootOf(_Z^2+_Z+1)+x+1)/(x^2-2*x+4)/x)","C"
1502,0,0,73,0.045000," ","int(1/(a*x^2-2*b)/(a*x^2-b)^(1/4),x)","\[\int \frac{1}{\left(a \,x^{2}-2 b \right) \left(a \,x^{2}-b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(a*x^2-2*b)/(a*x^2-b)^(1/4),x)","F"
1503,1,101,83,2.760000," ","int((-1+x)/x^7/(x^3+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{27 x^{7}-20 x^{6}+9 x^{4}-5 x^{3}-18 x +15}{90 x^{6} \left(x^{3}+1\right)^{\frac{1}{3}}}-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\frac{2 \pi  \sqrt{3}\, x^{3} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], -x^{3}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{27 \pi}$&$101$\\ meijerg&$-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\frac{28 \pi  \sqrt{3}\, x^{3} \hypergeom \left(\left[1, 1, \frac{10}{3}\right], \left[2, 4\right], -x^{3}\right)}{243 \Gamma \left(\frac{2}{3}\right)}+\frac{4 \left(\frac{9}{4}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)\right) \pi  \sqrt{3}}{27 \Gamma \left(\frac{2}{3}\right)}-\frac{\pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right) x^{6}}+\frac{2 \pi  \sqrt{3}}{9 \Gamma \left(\frac{2}{3}\right) x^{3}}\right)}{6 \pi}-\frac{\left(1-\frac{3 x^{3}}{2}\right) \left(x^{3}+1\right)^{\frac{2}{3}}}{5 x^{5}}$&$110$\\ trager&$\frac{\left(x^{3}+1\right)^{\frac{2}{3}} \left(27 x^{4}-20 x^{3}-18 x +15\right)}{90 x^{6}}+\frac{4 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \ln \left(-\frac{16 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x^{3}+18 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x^{3}+30 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}+2 x^{3}-16 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2}+30 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}+9 \left(x^{3}+1\right)^{\frac{2}{3}}+38 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)+9 \left(x^{3}+1\right)^{\frac{1}{3}}+5}{x^{3}}\right)}{27}+\frac{2 \ln \left(-\frac{16 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x^{3}-34 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x^{3}-30 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}+15 x^{3}-16 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2}-30 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}+24 \left(x^{3}+1\right)^{\frac{2}{3}}-22 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)+24 \left(x^{3}+1\right)^{\frac{1}{3}}+20}{x^{3}}\right)}{27}-\frac{4 \ln \left(-\frac{16 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x^{3}-34 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x^{3}-30 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}+15 x^{3}-16 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2}-30 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}+24 \left(x^{3}+1\right)^{\frac{2}{3}}-22 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)+24 \left(x^{3}+1\right)^{\frac{1}{3}}+20}{x^{3}}\right) \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)}{27}$&$456$\\ \hline \end{longtable}"," ",0,"1/90*(27*x^7-20*x^6+9*x^4-5*x^3-18*x+15)/x^6/(x^3+1)^(1/3)-1/27/Pi*3^(1/2)*GAMMA(2/3)*(-2/9*Pi*3^(1/2)/GAMMA(2/3)*x^3*hypergeom([1,1,4/3],[2,2],-x^3)+2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)+3*ln(x))*Pi*3^(1/2)/GAMMA(2/3))","C"
1504,0,0,89,0.092000," ","int((a*x^2+2*b*x+3*c)/(a*x^2+b*x+c)^(1/3)/(a*x^2+x^3+b*x+c),x)","\[\int \frac{a \,x^{2}+2 b x +3 c}{\left(a \,x^{2}+b x +c \right)^{\frac{1}{3}} \left(a \,x^{2}+x^{3}+b x +c \right)}\, dx\]"," ",0,"int((a*x^2+2*b*x+3*c)/(a*x^2+b*x+c)^(1/3)/(a*x^2+x^3+b*x+c),x)","F"
1505,0,0,11,0.036000," ","int((a*x^2-b)/(a*x^4+b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{a \,x^{2}-b}{\left(a \,x^{4}+b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2-b)/(a*x^4+b)/(a*x^4+b*x^2)^(1/4),x)","F"
1506,0,0,11,0.001000," ","int((a*x^2-b)/(a*x^4+b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{a \,x^{2}-b}{\left(a \,x^{4}+b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2-b)/(a*x^4+b)/(a*x^4+b*x^2)^(1/4),x)","F"
1507,0,0,44,0.014000," ","int((a*x^4+b*x^2)^(1/4)/x^4/(a*x^4+b),x)","\[\int \frac{\left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}{x^{4} \left(a \,x^{4}+b \right)}\, dx\]"," ",0,"int((a*x^4+b*x^2)^(1/4)/x^4/(a*x^4+b),x)","F"
1508,0,0,44,0.001000," ","int((a*x^4+b*x^2)^(1/4)/x^4/(a*x^4+b),x)","\[\int \frac{\left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}{x^{4} \left(a \,x^{4}+b \right)}\, dx\]"," ",0,"int((a*x^4+b*x^2)^(1/4)/x^4/(a*x^4+b),x)","F"
1509,0,0,44,0.003000," ","int((a*x^4+b*x^2)^(1/4)/x^4/(a*x^4+b),x)","\[\int \frac{\left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}{x^{4} \left(a \,x^{4}+b \right)}\, dx\]"," ",0,"int((a*x^4+b*x^2)^(1/4)/x^4/(a*x^4+b),x)","F"
1510,1,272,85,3.561000," ","int(x*(5*x^2+3)/(x^2+1)^(1/3)/(x^5+x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{5}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{5}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+x^{2} \left(x^{2}+1\right)^{\frac{2}{3}}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{1}{3}} x +x \left(x^{2}+1\right)^{\frac{1}{3}}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1}{x^{5}+x^{3}-1}\right)+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{5}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{5}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{2}{3}} x^{2}+x^{5}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-2 x^{2} \left(x^{2}+1\right)^{\frac{2}{3}}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}+1\right)^{\frac{1}{3}} x +x^{3}+x \left(x^{2}+1\right)^{\frac{1}{3}}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1}{x^{5}+x^{3}-1}\right)$&$272$\\ \hline \end{longtable}"," ",0,"ln((RootOf(_Z^2+_Z+1)^2*x^5+RootOf(_Z^2+_Z+1)*x^5+RootOf(_Z^2+_Z+1)^2*x^3-RootOf(_Z^2+_Z+1)*(x^2+1)^(2/3)*x^2+RootOf(_Z^2+_Z+1)*x^3+x^2*(x^2+1)^(2/3)+2*RootOf(_Z^2+_Z+1)*(x^2+1)^(1/3)*x+x*(x^2+1)^(1/3)-RootOf(_Z^2+_Z+1)-1)/(x^5+x^3-1))+RootOf(_Z^2+_Z+1)*ln(-(RootOf(_Z^2+_Z+1)^2*x^5+2*RootOf(_Z^2+_Z+1)*x^5+RootOf(_Z^2+_Z+1)^2*x^3-RootOf(_Z^2+_Z+1)*(x^2+1)^(2/3)*x^2+x^5+2*RootOf(_Z^2+_Z+1)*x^3-2*x^2*(x^2+1)^(2/3)-RootOf(_Z^2+_Z+1)*(x^2+1)^(1/3)*x+x^3+x*(x^2+1)^(1/3)+RootOf(_Z^2+_Z+1)+1)/(x^5+x^3-1))","C"
1511,1,333,87,14.270000," ","int((x^5-1)^(2/3)*(2*x^5+3)*(2*x^5+x^3-2)/x^6/(x^5+x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{-\frac{12}{5} x^{5}+\frac{6}{5}-\frac{3}{2} x^{8}+\frac{3}{2} x^{3}+\frac{6}{5} x^{10}}{x^{5} \left(x^{5}-1\right)^{\frac{1}{3}}}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{5}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-x^{5}+3 \left(x^{5}-1\right)^{\frac{2}{3}} x -3 \left(x^{5}-1\right)^{\frac{1}{3}} x^{2}+x^{3}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+1}{x^{5}+x^{3}-1}\right)-\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{5}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-2 x^{5}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+3 \left(x^{5}-1\right)^{\frac{2}{3}} x -3 \left(x^{5}-1\right)^{\frac{1}{3}} x^{2}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+2}{x^{5}+x^{3}-1}\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{5}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-2 x^{5}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+3 \left(x^{5}-1\right)^{\frac{2}{3}} x -3 \left(x^{5}-1\right)^{\frac{1}{3}} x^{2}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+2}{x^{5}+x^{3}-1}\right)$&$333$\\ trager&$\frac{3 \left(x^{5}-1\right)^{\frac{2}{3}} \left(4 x^{5}-5 x^{3}-4\right)}{10 x^{5}}-96 \ln \left(\frac{309594604009335349248 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x^{5}-1274461068424225440 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{5}-1199679090536174478336 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x^{3}-315835954172064748 x^{5}+29644229945602756800 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{2}{3}} x -29644229945602756800 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{1}{3}} x^{2}+44091369862027592064 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{3}+369746647037727189 \left(x^{5}-1\right)^{\frac{2}{3}} x -369746647037727189 \left(x^{5}-1\right)^{\frac{1}{3}} x^{2}-109855984059848608 x^{3}-309594604009335349248 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2}+1274461068424225440 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)+315835954172064748}{x^{5}+x^{3}-1}\right) \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)+96 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \ln \left(\frac{309594604009335349248 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x^{5}-5175426515103594336 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{5}-1199679090536174478336 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x^{3}-295518425803943035 x^{5}-29644229945602756800 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{2}{3}} x +29644229945602756800 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{1}{3}} x^{2}-19098055475857290432 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{3}+678540708971089239 \left(x^{5}-1\right)^{\frac{2}{3}} x -678540708971089239 \left(x^{5}-1\right)^{\frac{1}{3}} x^{2}+219255606241635155 x^{3}-309594604009335349248 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2}+5175426515103594336 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)+295518425803943035}{x^{5}+x^{3}-1}\right)+\ln \left(\frac{309594604009335349248 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x^{5}-1274461068424225440 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{5}-1199679090536174478336 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x^{3}-315835954172064748 x^{5}+29644229945602756800 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{2}{3}} x -29644229945602756800 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \left(x^{5}-1\right)^{\frac{1}{3}} x^{2}+44091369862027592064 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{3}+369746647037727189 \left(x^{5}-1\right)^{\frac{2}{3}} x -369746647037727189 \left(x^{5}-1\right)^{\frac{1}{3}} x^{2}-109855984059848608 x^{3}-309594604009335349248 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2}+1274461068424225440 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)+315835954172064748}{x^{5}+x^{3}-1}\right)$&$610$\\ \hline \end{longtable}"," ",0,"3/10*(4*x^10-5*x^8-8*x^5+5*x^3+4)/x^5/(x^5-1)^(1/3)+RootOf(_Z^2-_Z+1)*ln(-(-RootOf(_Z^2-_Z+1)*x^5-RootOf(_Z^2-_Z+1)^2*x^3-x^5+3*(x^5-1)^(2/3)*x-3*(x^5-1)^(1/3)*x^2+x^3+RootOf(_Z^2-_Z+1)+1)/(x^5+x^3-1))-ln(-(RootOf(_Z^2-_Z+1)*x^5-RootOf(_Z^2-_Z+1)^2*x^3-2*x^5+2*RootOf(_Z^2-_Z+1)*x^3+3*(x^5-1)^(2/3)*x-3*(x^5-1)^(1/3)*x^2-RootOf(_Z^2-_Z+1)+2)/(x^5+x^3-1))*RootOf(_Z^2-_Z+1)+ln(-(RootOf(_Z^2-_Z+1)*x^5-RootOf(_Z^2-_Z+1)^2*x^3-2*x^5+2*RootOf(_Z^2-_Z+1)*x^3+3*(x^5-1)^(2/3)*x-3*(x^5-1)^(1/3)*x^2-RootOf(_Z^2-_Z+1)+2)/(x^5+x^3-1))","C"
1512,1,44,86,2.388000," ","int((x^3+1)^(2/3)*(x^6+x^3-2)/x^9,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{17 x^{9}+19 x^{6}-3 x^{3}-5}{20 x^{8} \left(x^{3}+1\right)^{\frac{1}{3}}}+x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{3}\right)$&$44$\\ meijerg&$-\frac{\hypergeom \left(\left[-\frac{2}{3}, -\frac{2}{3}\right], \left[\frac{1}{3}\right], -x^{3}\right)}{2 x^{2}}-\frac{\left(x^{3}+1\right)^{\frac{5}{3}}}{5 x^{5}}+\frac{\left(-\frac{3}{5} x^{6}+\frac{2}{5} x^{3}+1\right) \left(x^{3}+1\right)^{\frac{2}{3}}}{4 x^{8}}$&$54$\\ trager&$-\frac{\left(17 x^{6}+2 x^{3}-5\right) \left(x^{3}+1\right)^{\frac{2}{3}}}{20 x^{8}}+\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(218 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-555 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x -555 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-773 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-1803 x \left(x^{3}+1\right)^{\frac{2}{3}}-1803 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}-1585 x^{3}-218 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}-753 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-634\right)}{3}-\frac{\ln \left(218 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+555 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +555 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+337 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-2358 x \left(x^{3}+1\right)^{\frac{2}{3}}-2358 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}-2140 x^{3}-218 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}+1189 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-1605\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)}{3}+\frac{\ln \left(218 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+555 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +555 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+337 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-2358 x \left(x^{3}+1\right)^{\frac{2}{3}}-2358 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}-2140 x^{3}-218 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}+1189 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-1605\right)}{3}$&$422$\\ \hline \end{longtable}"," ",0,"-1/20*(17*x^9+19*x^6-3*x^3-5)/x^8/(x^3+1)^(1/3)+x*hypergeom([1/3,1/3],[4/3],-x^3)","C"
1513,1,298,85,28.882000," ","int((x^6-1)^(2/3)*(x^6+1)*(x^6-x^3-1)/x^6/(x^6+x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x^{12}-5 x^{9}-2 x^{6}+5 x^{3}+1}{5 x^{5} \left(x^{6}-1\right)^{\frac{1}{3}}}-\frac{2 \ln \left(-\frac{3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{6}+x^{6}+9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x +9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{2}-3 x^{2} \left(x^{6}-1\right)^{\frac{1}{3}}-x^{3}-3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-1}{x^{6}+x^{3}-1}\right)}{3}+2 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \ln \left(\frac{3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{6}+x^{6}-9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{3}+9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x -3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{3}-3 x \left(x^{6}-1\right)^{\frac{2}{3}}-3 x^{2} \left(x^{6}-1\right)^{\frac{1}{3}}-3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-1}{x^{6}+x^{3}-1}\right)$&$298$\\ trager&$\frac{\left(x^{6}-1\right)^{\frac{2}{3}} \left(x^{6}-5 x^{3}-1\right)}{5 x^{5}}+\frac{2 \ln \left(\frac{241382040842688197903703905476608 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x^{6}+14360235166545558502709989692576 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{6}-209561394779200926893843501540 x^{6}-1900883571636169558491668255628288 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x^{3}-11116972693065830085107918919360 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x +11116972693065830085107918919360 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{2}+25558529270134496713387197451392 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{3}+411530433155258870911591637547 x \left(x^{6}-1\right)^{\frac{2}{3}}-411530433155258870911591637547 x^{2} \left(x^{6}-1\right)^{\frac{1}{3}}-30481657422429225730013600224 x^{3}-241382040842688197903703905476608 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2}-14360235166545558502709989692576 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)+209561394779200926893843501540}{x^{6}+x^{3}-1}\right)}{3}-64 \ln \left(\frac{241382040842688197903703905476608 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x^{6}+14360235166545558502709989692576 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{6}-209561394779200926893843501540 x^{6}-1900883571636169558491668255628288 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x^{3}-11116972693065830085107918919360 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x +11116972693065830085107918919360 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{2}+25558529270134496713387197451392 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{3}+411530433155258870911591637547 x \left(x^{6}-1\right)^{\frac{2}{3}}-411530433155258870911591637547 x^{2} \left(x^{6}-1\right)^{\frac{1}{3}}-30481657422429225730013600224 x^{3}-241382040842688197903703905476608 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2}-14360235166545558502709989692576 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)+209561394779200926893843501540}{x^{6}+x^{3}-1}\right) \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)+64 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \ln \left(\frac{241382040842688197903703905476608 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x^{6}-19389027684101562625703821056672 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{6}-33783984098747171016688237221 x^{6}-1900883571636169558491668255628288 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x^{3}+11116972693065830085107918919360 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x -11116972693065830085107918919360 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{2}+14043211805619035755189224540864 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{3}+295728634269156474191717482137 x \left(x^{6}-1\right)^{\frac{2}{3}}-295728634269156474191717482137 x^{2} \left(x^{6}-1\right)^{\frac{1}{3}}+29493954371922133427267508685 x^{3}-241382040842688197903703905476608 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2}+19389027684101562625703821056672 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)+33783984098747171016688237221}{x^{6}+x^{3}-1}\right)$&$610$\\ \hline \end{longtable}"," ",0,"1/5*(x^12-5*x^9-2*x^6+5*x^3+1)/x^5/(x^6-1)^(1/3)-2/3*ln(-(3*RootOf(9*_Z^2-3*_Z+1)*x^6+x^6+9*RootOf(9*_Z^2-3*_Z+1)^2*x^3+9*RootOf(9*_Z^2-3*_Z+1)*(x^6-1)^(2/3)*x+9*RootOf(9*_Z^2-3*_Z+1)*(x^6-1)^(1/3)*x^2-3*x^2*(x^6-1)^(1/3)-x^3-3*RootOf(9*_Z^2-3*_Z+1)-1)/(x^6+x^3-1))+2*RootOf(9*_Z^2-3*_Z+1)*ln((3*RootOf(9*_Z^2-3*_Z+1)*x^6+x^6-9*RootOf(9*_Z^2-3*_Z+1)^2*x^3+9*RootOf(9*_Z^2-3*_Z+1)*(x^6-1)^(2/3)*x-3*RootOf(9*_Z^2-3*_Z+1)*x^3-3*x*(x^6-1)^(2/3)-3*x^2*(x^6-1)^(1/3)-3*RootOf(9*_Z^2-3*_Z+1)-1)/(x^6+x^3-1))","C"
1514,1,56,86,2.651000," ","int((x^3-1)^(2/3)*(x^6+2*x^3-2)/x^9,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{x^{9}+x^{6}-3 x^{3}+1}{4 x^{8} \left(x^{3}-1\right)^{\frac{1}{3}}}+\frac{\left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{3}\right)}{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}}}$&$56$\\ meijerg&$-\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}} \hypergeom \left(\left[-\frac{2}{3}, -\frac{2}{3}\right], \left[\frac{1}{3}\right], x^{3}\right)}{2 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} x^{2}}-\frac{2 \mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}} \left(-x^{3}+1\right)^{\frac{5}{3}}}{5 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} x^{5}}+\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}} \left(-\frac{3}{5} x^{6}-\frac{2}{5} x^{3}+1\right) \left(-x^{3}+1\right)^{\frac{2}{3}}}{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} x^{8}}$&$110$\\ trager&$-\frac{\left(x^{6}+2 x^{3}-1\right) \left(x^{3}-1\right)^{\frac{2}{3}}}{4 x^{8}}+\frac{\ln \left(746584997888 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)^{2} x^{3}-49654493184 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -49654493184 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-52570840832 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) x^{3}-1314589509 x \left(x^{3}-1\right)^{\frac{2}{3}}-1314589509 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-1303197526 x^{3}-5972679983104 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)^{2}-72296025856 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)+849911430\right)}{3}-\frac{256 \ln \left(746584997888 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)^{2} x^{3}-49654493184 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -49654493184 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-52570840832 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) x^{3}-1314589509 x \left(x^{3}-1\right)^{\frac{2}{3}}-1314589509 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-1303197526 x^{3}-5972679983104 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)^{2}-72296025856 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)+849911430\right) \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)}{3}+\frac{256 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) \ln \left(746584997888 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)^{2} x^{3}+49654493184 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +49654493184 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+46738145536 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) x^{3}-1508552373 x \left(x^{3}-1\right)^{\frac{2}{3}}-1508552373 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-1497160390 x^{3}-5972679983104 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)^{2}+118957588224 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)+476369215\right)}{3}$&$460$\\ \hline \end{longtable}"," ",0,"-1/4*(x^9+x^6-3*x^3+1)/x^8/(x^3-1)^(1/3)+1/signum(x^3-1)^(1/3)*(-signum(x^3-1))^(1/3)*x*hypergeom([1/3,1/3],[4/3],x^3)","C"
1515,1,457,75,2.931000," ","int((x^4-2)/(x^4+1)^(1/4)/(x^8+x^4-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} \left(x^{4}+1\right)^{\frac{1}{4}} x^{3}+3 \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{4}+4 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{4}+1\right)^{\frac{3}{4}} x +8 x^{2} \sqrt{x^{4}+1}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)}{24}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(\frac{\sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+2 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{4}-4 \left(x^{4}+1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right)}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)}{24}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \ln \left(\frac{3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{4}-4 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}-8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \sqrt{x^{4}+1}\, x^{2}+16 \left(x^{4}+1\right)^{\frac{3}{4}} x +2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2}}{x^{4}+2}\right)}{24}+\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} \ln \left(\frac{3 \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{4}+4 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}+8 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}-8\right) x^{2}+16 \left(x^{4}+1\right)^{\frac{3}{4}} x +2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{3}}{x^{4}+2}\right)}{24}$&$457$\\ \hline \end{longtable}"," ",0,"1/24*RootOf(_Z^4-8)*ln((2*RootOf(_Z^4-8)^3*(x^4+1)^(1/4)*x^3+3*RootOf(_Z^4-8)^2*x^4+4*RootOf(_Z^4-8)*(x^4+1)^(3/4)*x+8*x^2*(x^4+1)^(1/2)+RootOf(_Z^4-8)^2)/(-1+x)/(1+x)/(x^2+1))+1/24*RootOf(_Z^2+RootOf(_Z^4-8)^2)*ln(((x^4+1)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x^2+2*(x^4+1)^(1/4)*RootOf(_Z^4-8)^2*x^3-3*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^4-4*(x^4+1)^(3/4)*x-RootOf(_Z^2+RootOf(_Z^4-8)^2))/(-1+x)/(1+x)/(x^2+1))+1/24*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*ln((3*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x^4-4*(x^4+1)^(1/4)*RootOf(_Z^4-8)^2*x^3-8*RootOf(_Z^2+RootOf(_Z^4-8)^2)*(x^4+1)^(1/2)*x^2+16*(x^4+1)^(3/4)*x+2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2)/(x^4+2))+1/24*RootOf(_Z^4-8)^3*ln((3*RootOf(_Z^4-8)^3*x^4+4*(x^4+1)^(1/4)*RootOf(_Z^4-8)^2*x^3+8*(x^4+1)^(1/2)*RootOf(_Z^4-8)*x^2+16*(x^4+1)^(3/4)*x+2*RootOf(_Z^4-8)^3)/(x^4+2))","C"
1516,1,4180,24,21.287000," ","int((x^4-1)^(1/4)*(x^4+2)/x^2/(x^8+2*x^4+2),x)","\[\text{output too large to display}\]"," ",0,"-(x^4-1)^(1/4)/x+(-1024*ln(-(4096*x^12*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2+16384*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x^9-8192*x^8*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2-4*x^12*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2-32768*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x^5-6*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x^9-8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6-24576*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)*x^3+4096*x^4*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2+9*x^8*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2+16384*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x+12*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x^5+8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2+6*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6+8*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)*x^3-6*x^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2-6*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x-6*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2+RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2)/(4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x^4-2*x^4-1)/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x-1)^2/(-1+x)^2/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x+1)^2/(1+x)^2)*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)+3/8*ln(-(4096*x^12*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2+16384*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x^9-8192*x^8*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2-4*x^12*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2-32768*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x^5-6*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x^9-8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6-24576*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)*x^3+4096*x^4*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2+9*x^8*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2+16384*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x+12*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x^5+8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2+6*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6+8*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)*x^3-6*x^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2-6*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x-6*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2+RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2)/(4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x^4-2*x^4-1)/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x-1)^2/(-1+x)^2/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x+1)^2/(1+x)^2)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)+8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^5*ln(-(-16384*RootOf(33554432*_Z^8-24576*_Z^4+5)^5*x^12-524288*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^6*x^9+32768*RootOf(33554432*_Z^8-24576*_Z^4+5)^5*x^8-4*RootOf(33554432*_Z^8-24576*_Z^4+5)*x^12+1048576*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^6*x^5+192*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^2*x^9+512*RootOf(33554432*_Z^8-24576*_Z^4+5)^3*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6+12288*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3-16384*RootOf(33554432*_Z^8-24576*_Z^4+5)^5*x^4+12*RootOf(33554432*_Z^8-24576*_Z^4+5)*x^8-524288*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^6*x-384*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^2*x^5-512*RootOf(33554432*_Z^8-24576*_Z^4+5)^3*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2-5*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3-12*RootOf(33554432*_Z^8-24576*_Z^4+5)*x^4+192*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^2*x+4*RootOf(33554432*_Z^8-24576*_Z^4+5))/(4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x^4-x^4+1)/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x-1)^2/(-1+x)^2/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x+1)^2/(1+x)^2)-3*RootOf(33554432*_Z^8-24576*_Z^4+5)*ln(-(-16384*RootOf(33554432*_Z^8-24576*_Z^4+5)^5*x^12-524288*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^6*x^9+32768*RootOf(33554432*_Z^8-24576*_Z^4+5)^5*x^8-4*RootOf(33554432*_Z^8-24576*_Z^4+5)*x^12+1048576*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^6*x^5+192*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^2*x^9+512*RootOf(33554432*_Z^8-24576*_Z^4+5)^3*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6+12288*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3-16384*RootOf(33554432*_Z^8-24576*_Z^4+5)^5*x^4+12*RootOf(33554432*_Z^8-24576*_Z^4+5)*x^8-524288*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^6*x-384*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^2*x^5-512*RootOf(33554432*_Z^8-24576*_Z^4+5)^3*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2-5*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3-12*RootOf(33554432*_Z^8-24576*_Z^4+5)*x^4+192*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^2*x+4*RootOf(33554432*_Z^8-24576*_Z^4+5))/(4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x^4-x^4+1)/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x-1)^2/(-1+x)^2/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x+1)^2/(1+x)^2)+1/8*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)*ln(-(-4096*x^12*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2+8192*x^8*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2+4*x^12*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2+2*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x^9-8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6-8192*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)*x^3-4096*x^4*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2-9*x^8*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2-4*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x^5+8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2+6*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6+6*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)*x^3+6*x^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2+2*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x-6*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2-RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2)/(4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x^4-2*x^4-1)/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x-1)^2/(-1+x)^2/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x+1)^2/(1+x)^2)+RootOf(33554432*_Z^8-24576*_Z^4+5)*ln(-(4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x^12-8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x^8+x^12+16*RootOf(33554432*_Z^8-24576*_Z^4+5)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9+128*RootOf(33554432*_Z^8-24576*_Z^4+5)^2*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6+1024*RootOf(33554432*_Z^8-24576*_Z^4+5)^3*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x^4-3*x^8-32*RootOf(33554432*_Z^8-24576*_Z^4+5)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5-128*RootOf(33554432*_Z^8-24576*_Z^4+5)^2*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2+3*x^4+16*RootOf(33554432*_Z^8-24576*_Z^4+5)*(x^12-3*x^8+3*x^4-1)^(1/4)*x-1)/(4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x^4-x^4+1)/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x-1)^2/(-1+x)^2/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x+1)^2/(1+x)^2))/(x^4-1)^(3/4)*((x^4-1)^3)^(1/4)","B"
1517,1,4177,24,21.476000," ","int((x^4-1)^(1/4)*(x^4+2)/x^2/(x^8+2*x^4+2),x)","\[\text{output too large to display}\]"," ",0,"-(x^4-1)^(1/4)/x+(-RootOf(33554432*_Z^8-24576*_Z^4+5)*ln((-4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x^12+8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x^8-x^12+16*RootOf(33554432*_Z^8-24576*_Z^4+5)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9-128*RootOf(33554432*_Z^8-24576*_Z^4+5)^2*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6+1024*RootOf(33554432*_Z^8-24576*_Z^4+5)^3*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3-4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x^4+3*x^8-32*RootOf(33554432*_Z^8-24576*_Z^4+5)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5+128*RootOf(33554432*_Z^8-24576*_Z^4+5)^2*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2-3*x^4+16*RootOf(33554432*_Z^8-24576*_Z^4+5)*(x^12-3*x^8+3*x^4-1)^(1/4)*x+1)/(4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x^4-x^4+1)/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x-1)^2/(-1+x)^2/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x+1)^2/(1+x)^2)-1/8*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)*ln((4096*x^12*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2-8192*x^8*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2-4*x^12*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2+2*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x^9+8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6-8192*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)*x^3+4096*x^4*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2+9*x^8*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2-4*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x^5-8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2-6*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6+6*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)*x^3-6*x^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2+2*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x+6*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2+RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2)/(4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x^4-2*x^4-1)/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x-1)^2/(-1+x)^2/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x+1)^2/(1+x)^2)-8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^5*ln((16384*RootOf(33554432*_Z^8-24576*_Z^4+5)^5*x^12-524288*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^6*x^9-32768*RootOf(33554432*_Z^8-24576*_Z^4+5)^5*x^8+4*RootOf(33554432*_Z^8-24576*_Z^4+5)*x^12+1048576*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^6*x^5+192*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^2*x^9-512*RootOf(33554432*_Z^8-24576*_Z^4+5)^3*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6+12288*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3+16384*RootOf(33554432*_Z^8-24576*_Z^4+5)^5*x^4-12*RootOf(33554432*_Z^8-24576*_Z^4+5)*x^8-524288*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^6*x-384*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^2*x^5+512*RootOf(33554432*_Z^8-24576*_Z^4+5)^3*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2-5*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3+12*RootOf(33554432*_Z^8-24576*_Z^4+5)*x^4+192*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^2*x-4*RootOf(33554432*_Z^8-24576*_Z^4+5))/(4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x^4-x^4+1)/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x-1)^2/(-1+x)^2/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x+1)^2/(1+x)^2)+3*RootOf(33554432*_Z^8-24576*_Z^4+5)*ln((16384*RootOf(33554432*_Z^8-24576*_Z^4+5)^5*x^12-524288*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^6*x^9-32768*RootOf(33554432*_Z^8-24576*_Z^4+5)^5*x^8+4*RootOf(33554432*_Z^8-24576*_Z^4+5)*x^12+1048576*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^6*x^5+192*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^2*x^9-512*RootOf(33554432*_Z^8-24576*_Z^4+5)^3*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6+12288*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3+16384*RootOf(33554432*_Z^8-24576*_Z^4+5)^5*x^4-12*RootOf(33554432*_Z^8-24576*_Z^4+5)*x^8-524288*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^6*x-384*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^2*x^5+512*RootOf(33554432*_Z^8-24576*_Z^4+5)^3*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2-5*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3+12*RootOf(33554432*_Z^8-24576*_Z^4+5)*x^4+192*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^2*x-4*RootOf(33554432*_Z^8-24576*_Z^4+5))/(4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x^4-x^4+1)/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x-1)^2/(-1+x)^2/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x+1)^2/(1+x)^2)-1024*ln(-(4096*x^12*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2+16384*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x^9-8192*x^8*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2-4*x^12*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2-32768*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x^5-6*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x^9-8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6-24576*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)*x^3+4096*x^4*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2+9*x^8*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2+16384*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x+12*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x^5+8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2+6*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6+8*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)*x^3-6*x^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2-6*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x-6*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2+RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2)/(4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x^4-2*x^4-1)/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x-1)^2/(-1+x)^2/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x+1)^2/(1+x)^2)*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)+3/8*ln(-(4096*x^12*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2+16384*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x^9-8192*x^8*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2-4*x^12*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2-32768*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x^5-6*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x^9-8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6-24576*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)*x^3+4096*x^4*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2+9*x^8*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2+16384*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x+12*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x^5+8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2+6*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6+8*(x^12-3*x^8+3*x^4-1)^(3/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)*x^3-6*x^4*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2-6*(x^12-3*x^8+3*x^4-1)^(1/4)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^3*x-6*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2+RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3)^2)/(4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x^4-2*x^4-1)/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x-1)^2/(-1+x)^2/(8192*RootOf(33554432*_Z^8-24576*_Z^4+5)^4*x-3*x+1)^2/(1+x)^2)*RootOf(_Z^4+4096*RootOf(33554432*_Z^8-24576*_Z^4+5)^4-3))/(x^4-1)^(3/4)*((x^4-1)^3)^(1/4)","B"
1518,0,0,85,0.010000," ","int((x^8-2*a*x^4-2*b)/x^4/(a*x^4+b)^(1/4),x)","\[\int \frac{x^{8}-2 a \,x^{4}-2 b}{x^{4} \left(a \,x^{4}+b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((x^8-2*a*x^4-2*b)/x^4/(a*x^4+b)^(1/4),x)","F"
1519,0,0,81,0.012000," ","int((2*x^8-2*x^4+1)/(x^4+1)^(1/4)/(x^8-x^4-2),x)","\[\int \frac{2 x^{8}-2 x^{4}+1}{\left(x^{4}+1\right)^{\frac{1}{4}} \left(x^{8}-x^{4}-2\right)}\, dx\]"," ",0,"int((2*x^8-2*x^4+1)/(x^4+1)^(1/4)/(x^8-x^4-2),x)","F"
1520,1,400,87,27.630000," ","int((x^8+x^3+1)^(2/3)*(5*x^8-3)/x^3/(x^8+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 \left(x^{8}+x^{3}+1\right)^{\frac{2}{3}}}{2 x^{2}}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\frac{x^{8}+\left(x^{8}+x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{8}+x^{3}+1\right)^{\frac{1}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+2 \left(x^{8}+x^{3}+1\right)^{\frac{2}{3}} x +2 \left(x^{8}+x^{3}+1\right)^{\frac{1}{3}} x^{2}+2 x^{3}+1}{x^{8}+1}\right)-\ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{8}+x^{8}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \left(x^{8}+x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{8}+x^{3}+1\right)^{\frac{1}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 \left(x^{8}+x^{3}+1\right)^{\frac{2}{3}} x +3 \left(x^{8}+x^{3}+1\right)^{\frac{1}{3}} x^{2}+x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1}{x^{8}+1}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-\ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{8}+x^{8}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \left(x^{8}+x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{8}+x^{3}+1\right)^{\frac{1}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 \left(x^{8}+x^{3}+1\right)^{\frac{2}{3}} x +3 \left(x^{8}+x^{3}+1\right)^{\frac{1}{3}} x^{2}+x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1}{x^{8}+1}\right)$&$400$\\ trager&$\frac{3 \left(x^{8}+x^{3}+1\right)^{\frac{2}{3}}}{2 x^{2}}-3 \ln \left(\frac{76347793493881633656 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{8}+8735547596920157721 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{8}-85083341090801791377 x^{8}-152695586987763267312 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+544684858639691450535 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{8}+x^{3}+1\right)^{\frac{2}{3}} x -247271853968285145021 \left(x^{8}+x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}-348311533667327394618 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+82423951322761715007 \left(x^{8}+x^{3}+1\right)^{\frac{2}{3}} x +99137668223802101838 \left(x^{8}+x^{3}+1\right)^{\frac{1}{3}} x^{2}-198527795878537513213 x^{3}+76347793493881633656 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+8735547596920157721 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-85083341090801791377}{x^{8}+1}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+\ln \left(-\frac{-178902229778523740475 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{8}-323619647462166778677 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{8}-113444454787735721836 x^{8}+357804459557047480950 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+544684858639691450535 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{8}+x^{3}+1\right)^{\frac{2}{3}} x -297413004671406305514 \left(x^{8}+x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}-128003700782602651371 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+99137668223802101838 \left(x^{8}+x^{3}+1\right)^{\frac{2}{3}} x +82423951322761715007 \left(x^{8}+x^{3}+1\right)^{\frac{1}{3}} x^{2}-141805568484669652295 x^{3}-178902229778523740475 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-323619647462166778677 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-113444454787735721836}{x^{8}+1}\right)-\ln \left(\frac{76347793493881633656 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{8}+8735547596920157721 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{8}-85083341090801791377 x^{8}-152695586987763267312 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+544684858639691450535 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{8}+x^{3}+1\right)^{\frac{2}{3}} x -247271853968285145021 \left(x^{8}+x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}-348311533667327394618 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+82423951322761715007 \left(x^{8}+x^{3}+1\right)^{\frac{2}{3}} x +99137668223802101838 \left(x^{8}+x^{3}+1\right)^{\frac{1}{3}} x^{2}-198527795878537513213 x^{3}+76347793493881633656 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+8735547596920157721 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-85083341090801791377}{x^{8}+1}\right)$&$618$\\ \hline \end{longtable}"," ",0,"3/2*(x^8+x^3+1)^(2/3)/x^2+RootOf(_Z^2+_Z+1)*ln((x^8+(x^8+x^3+1)^(2/3)*RootOf(_Z^2+_Z+1)*x+RootOf(_Z^2+_Z+1)*(x^8+x^3+1)^(1/3)*x^2+RootOf(_Z^2+_Z+1)*x^3+2*(x^8+x^3+1)^(2/3)*x+2*(x^8+x^3+1)^(1/3)*x^2+2*x^3+1)/(x^8+1))-ln((2*RootOf(_Z^2+_Z+1)*x^8+x^8-2*RootOf(_Z^2+_Z+1)^2*x^3+3*(x^8+x^3+1)^(2/3)*RootOf(_Z^2+_Z+1)*x+3*RootOf(_Z^2+_Z+1)*(x^8+x^3+1)^(1/3)*x^2+RootOf(_Z^2+_Z+1)*x^3+3*(x^8+x^3+1)^(2/3)*x+3*(x^8+x^3+1)^(1/3)*x^2+x^3+2*RootOf(_Z^2+_Z+1)+1)/(x^8+1))*RootOf(_Z^2+_Z+1)-ln((2*RootOf(_Z^2+_Z+1)*x^8+x^8-2*RootOf(_Z^2+_Z+1)^2*x^3+3*(x^8+x^3+1)^(2/3)*RootOf(_Z^2+_Z+1)*x+3*RootOf(_Z^2+_Z+1)*(x^8+x^3+1)^(1/3)*x^2+RootOf(_Z^2+_Z+1)*x^3+3*(x^8+x^3+1)^(2/3)*x+3*(x^8+x^3+1)^(1/3)*x^2+x^3+2*RootOf(_Z^2+_Z+1)+1)/(x^8+1))","C"
1521,0,0,50,0.042000," ","int((2*a*x^8-b)/(a*x^4+b)^(1/4)/(a*x^8-b),x)","\[\int \frac{2 a \,x^{8}-b}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(a \,x^{8}-b \right)}\, dx\]"," ",0,"int((2*a*x^8-b)/(a*x^4+b)^(1/4)/(a*x^8-b),x)","F"
1522,1,577,71,4.315000," ","int((x^6-x^2-1)^(1/2)*(2*x^6+1)/(8*x^12-16*x^6-x^4+8),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right) \ln \left(\frac{16384 \RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right)^{3} x^{6}+2097152 \RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right)^{5} x^{2}+112 \RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right) x^{6}-2048 \RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right)^{3} x^{2}-2048 \sqrt{x^{6}-x^{2}-1}\, \RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right)^{2} x -16384 \RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right)^{3}-112 \RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right) x^{2}-7 \sqrt{x^{6}-x^{2}-1}\, x -112 \RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right)}{-x^{6}+128 x^{2} \RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right)^{2}+x^{2}+1}\right)+\frac{\RootOf \left(\textit{\_Z}^{2}+64 \RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right)^{2}+1\right) \ln \left(\frac{-2048 \RootOf \left(\textit{\_Z}^{2}+64 \RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right)^{2}+1\right) \RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right)^{2} x^{6}+262144 \RootOf \left(\textit{\_Z}^{2}+64 \RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right)^{2}+1\right) \RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right)^{4} x^{2}-18 \RootOf \left(\textit{\_Z}^{2}+64 \RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right)^{2}+1\right) x^{6}+8448 \RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right)^{2} \RootOf \left(\textit{\_Z}^{2}+64 \RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right)^{2}+1\right) x^{2}+2048 \sqrt{x^{6}-x^{2}-1}\, \RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right)^{2} x +2048 \RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right)^{2} \RootOf \left(\textit{\_Z}^{2}+64 \RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right)^{2}+1\right)+54 \RootOf \left(\textit{\_Z}^{2}+64 \RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right)^{2}+1\right) x^{2}+25 \sqrt{x^{6}-x^{2}-1}\, x +18 \RootOf \left(\textit{\_Z}^{2}+64 \RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right)^{2}+1\right)}{x^{6}+128 x^{2} \RootOf \left(131072 \textit{\_Z}^{4}+2048 \textit{\_Z}^{2}+7\right)^{2}+x^{2}-1}\right)}{8}$&$577$\\ \hline \end{longtable}"," ",0,"RootOf(131072*_Z^4+2048*_Z^2+7)*ln((16384*RootOf(131072*_Z^4+2048*_Z^2+7)^3*x^6+2097152*RootOf(131072*_Z^4+2048*_Z^2+7)^5*x^2+112*RootOf(131072*_Z^4+2048*_Z^2+7)*x^6-2048*RootOf(131072*_Z^4+2048*_Z^2+7)^3*x^2-2048*(x^6-x^2-1)^(1/2)*RootOf(131072*_Z^4+2048*_Z^2+7)^2*x-16384*RootOf(131072*_Z^4+2048*_Z^2+7)^3-112*RootOf(131072*_Z^4+2048*_Z^2+7)*x^2-7*(x^6-x^2-1)^(1/2)*x-112*RootOf(131072*_Z^4+2048*_Z^2+7))/(-x^6+128*x^2*RootOf(131072*_Z^4+2048*_Z^2+7)^2+x^2+1))+1/8*RootOf(_Z^2+64*RootOf(131072*_Z^4+2048*_Z^2+7)^2+1)*ln((-2048*RootOf(_Z^2+64*RootOf(131072*_Z^4+2048*_Z^2+7)^2+1)*RootOf(131072*_Z^4+2048*_Z^2+7)^2*x^6+262144*RootOf(_Z^2+64*RootOf(131072*_Z^4+2048*_Z^2+7)^2+1)*RootOf(131072*_Z^4+2048*_Z^2+7)^4*x^2-18*RootOf(_Z^2+64*RootOf(131072*_Z^4+2048*_Z^2+7)^2+1)*x^6+8448*RootOf(131072*_Z^4+2048*_Z^2+7)^2*RootOf(_Z^2+64*RootOf(131072*_Z^4+2048*_Z^2+7)^2+1)*x^2+2048*(x^6-x^2-1)^(1/2)*RootOf(131072*_Z^4+2048*_Z^2+7)^2*x+2048*RootOf(131072*_Z^4+2048*_Z^2+7)^2*RootOf(_Z^2+64*RootOf(131072*_Z^4+2048*_Z^2+7)^2+1)+54*RootOf(_Z^2+64*RootOf(131072*_Z^4+2048*_Z^2+7)^2+1)*x^2+25*(x^6-x^2-1)^(1/2)*x+18*RootOf(_Z^2+64*RootOf(131072*_Z^4+2048*_Z^2+7)^2+1))/(x^6+128*x^2*RootOf(131072*_Z^4+2048*_Z^2+7)^2+x^2-1))","C"
1523,0,0,83,0.016000," ","int(1/(x^2+1)/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{1}{\left(x^{2}+1\right) \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int(1/(x^2+1)/(x+(x^2+1)^(1/2))^(1/2),x)","F"
1524,0,0,9,0.020000," ","int((x-(x^2+1)^(1/2))^(1/2)/(x^2+(x^2+1)^(1/2)),x)","\[\int \frac{\sqrt{x -\sqrt{x^{2}+1}}}{x^{2}+\sqrt{x^{2}+1}}\, dx\]"," ",0,"int((x-(x^2+1)^(1/2))^(1/2)/(x^2+(x^2+1)^(1/2)),x)","F"
1525,0,0,85,180.000000," ","int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/x^2,x)","\[\int \frac{\sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}{x^{2}}\, dx\]"," ",0,"int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/x^2,x)","F"
1526,1,86,75,0.188000," ","int((-1+x)/(1+x)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{7}{2}}}{7}-\frac{24 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}+\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}+\frac{8}{\sqrt{1+\sqrt{1+\sqrt{1+x}}}}+4 \sqrt{2}\, \arctanh \left(\frac{\sqrt{1+\sqrt{1+\sqrt{1+x}}}\, \sqrt{2}}{2}\right)$&$86$\\ default&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{7}{2}}}{7}-\frac{24 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}+\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}+\frac{8}{\sqrt{1+\sqrt{1+\sqrt{1+x}}}}+4 \sqrt{2}\, \arctanh \left(\frac{\sqrt{1+\sqrt{1+\sqrt{1+x}}}\, \sqrt{2}}{2}\right)$&$86$\\ \hline \end{longtable}"," ",0,"8/7*(1+(1+(1+x)^(1/2))^(1/2))^(7/2)-24/5*(1+(1+(1+x)^(1/2))^(1/2))^(5/2)+16/3*(1+(1+(1+x)^(1/2))^(1/2))^(3/2)+8/(1+(1+(1+x)^(1/2))^(1/2))^(1/2)+4*2^(1/2)*arctanh(1/2*(1+(1+(1+x)^(1/2))^(1/2))^(1/2)*2^(1/2))","A"
1527,1,942,79,3.135000," ","int(1/(-2+x)/(x^2+2*x+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-3\right)+9 \textit{\_Z}^{2}\right) \ln \left(-\frac{63 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-3\right)+9 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-3\right)^{2} x^{2}+6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-3\right)+9 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-3\right)^{3} x^{2}+63 \left(x^{2}+2 x +1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-3\right)+9 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+63 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-3\right)+9 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-3\right)^{2} x +6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-3\right)+9 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-3\right)^{3} x +72 \left(x^{2}+2 x +1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-3\right)+9 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-3\right) x -21 \left(x^{2}+2 x +1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-3\right)^{2} x +72 \left(x^{2}+2 x +1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-3\right)+9 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-3\right)-21 \left(x^{2}+2 x +1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-3\right)^{2}-21 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-3\right)+9 \textit{\_Z}^{2}\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{3}-3\right) x^{2}+135 \left(x^{2}+2 x +1\right)^{\frac{2}{3}}-294 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-3\right)+9 \textit{\_Z}^{2}\right) x -28 \RootOf \left(\textit{\_Z}^{3}-3\right) x -273 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-3\right)+9 \textit{\_Z}^{2}\right)-26 \RootOf \left(\textit{\_Z}^{3}-3\right)}{\left(-2+x \right) \left(1+x \right)}\right)+\frac{\RootOf \left(\textit{\_Z}^{3}-3\right) \ln \left(\frac{18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-3\right)+9 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-3\right)^{2} x^{2}+21 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-3\right)+9 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-3\right)^{3} x^{2}+63 \left(x^{2}+2 x +1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-3\right)+9 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-3\right)+9 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-3\right)^{2} x +21 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-3\right)+9 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-3\right)^{3} x -135 \left(x^{2}+2 x +1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-3\right)+9 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-3\right) x -21 \left(x^{2}+2 x +1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-3\right)^{2} x -135 \left(x^{2}+2 x +1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-3\right)+9 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-3\right)-21 \left(x^{2}+2 x +1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+24 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-3\right)+9 \textit{\_Z}^{2}\right) x^{2}+28 \RootOf \left(\textit{\_Z}^{3}-3\right) x^{2}-72 \left(x^{2}+2 x +1\right)^{\frac{2}{3}}+102 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-3\right)+9 \textit{\_Z}^{2}\right) x +119 \RootOf \left(\textit{\_Z}^{3}-3\right) x +78 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-3\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-3\right)+9 \textit{\_Z}^{2}\right)+91 \RootOf \left(\textit{\_Z}^{3}-3\right)}{\left(-2+x \right) \left(1+x \right)}\right)}{3}$&$942$\\ \hline \end{longtable}"," ",0,"RootOf(RootOf(_Z^3-3)^2+3*_Z*RootOf(_Z^3-3)+9*_Z^2)*ln(-(63*RootOf(RootOf(_Z^3-3)^2+3*_Z*RootOf(_Z^3-3)+9*_Z^2)^2*RootOf(_Z^3-3)^2*x^2+6*RootOf(RootOf(_Z^3-3)^2+3*_Z*RootOf(_Z^3-3)+9*_Z^2)*RootOf(_Z^3-3)^3*x^2+63*(x^2+2*x+1)^(2/3)*RootOf(RootOf(_Z^3-3)^2+3*_Z*RootOf(_Z^3-3)+9*_Z^2)*RootOf(_Z^3-3)^2+63*RootOf(RootOf(_Z^3-3)^2+3*_Z*RootOf(_Z^3-3)+9*_Z^2)^2*RootOf(_Z^3-3)^2*x+6*RootOf(RootOf(_Z^3-3)^2+3*_Z*RootOf(_Z^3-3)+9*_Z^2)*RootOf(_Z^3-3)^3*x+72*(x^2+2*x+1)^(1/3)*RootOf(RootOf(_Z^3-3)^2+3*_Z*RootOf(_Z^3-3)+9*_Z^2)*RootOf(_Z^3-3)*x-21*(x^2+2*x+1)^(1/3)*RootOf(_Z^3-3)^2*x+72*(x^2+2*x+1)^(1/3)*RootOf(RootOf(_Z^3-3)^2+3*_Z*RootOf(_Z^3-3)+9*_Z^2)*RootOf(_Z^3-3)-21*(x^2+2*x+1)^(1/3)*RootOf(_Z^3-3)^2-21*RootOf(RootOf(_Z^3-3)^2+3*_Z*RootOf(_Z^3-3)+9*_Z^2)*x^2-2*RootOf(_Z^3-3)*x^2+135*(x^2+2*x+1)^(2/3)-294*RootOf(RootOf(_Z^3-3)^2+3*_Z*RootOf(_Z^3-3)+9*_Z^2)*x-28*RootOf(_Z^3-3)*x-273*RootOf(RootOf(_Z^3-3)^2+3*_Z*RootOf(_Z^3-3)+9*_Z^2)-26*RootOf(_Z^3-3))/(-2+x)/(1+x))+1/3*RootOf(_Z^3-3)*ln((18*RootOf(RootOf(_Z^3-3)^2+3*_Z*RootOf(_Z^3-3)+9*_Z^2)^2*RootOf(_Z^3-3)^2*x^2+21*RootOf(RootOf(_Z^3-3)^2+3*_Z*RootOf(_Z^3-3)+9*_Z^2)*RootOf(_Z^3-3)^3*x^2+63*(x^2+2*x+1)^(2/3)*RootOf(RootOf(_Z^3-3)^2+3*_Z*RootOf(_Z^3-3)+9*_Z^2)*RootOf(_Z^3-3)^2+18*RootOf(RootOf(_Z^3-3)^2+3*_Z*RootOf(_Z^3-3)+9*_Z^2)^2*RootOf(_Z^3-3)^2*x+21*RootOf(RootOf(_Z^3-3)^2+3*_Z*RootOf(_Z^3-3)+9*_Z^2)*RootOf(_Z^3-3)^3*x-135*(x^2+2*x+1)^(1/3)*RootOf(RootOf(_Z^3-3)^2+3*_Z*RootOf(_Z^3-3)+9*_Z^2)*RootOf(_Z^3-3)*x-21*(x^2+2*x+1)^(1/3)*RootOf(_Z^3-3)^2*x-135*(x^2+2*x+1)^(1/3)*RootOf(RootOf(_Z^3-3)^2+3*_Z*RootOf(_Z^3-3)+9*_Z^2)*RootOf(_Z^3-3)-21*(x^2+2*x+1)^(1/3)*RootOf(_Z^3-3)^2+24*RootOf(RootOf(_Z^3-3)^2+3*_Z*RootOf(_Z^3-3)+9*_Z^2)*x^2+28*RootOf(_Z^3-3)*x^2-72*(x^2+2*x+1)^(2/3)+102*RootOf(RootOf(_Z^3-3)^2+3*_Z*RootOf(_Z^3-3)+9*_Z^2)*x+119*RootOf(_Z^3-3)*x+78*RootOf(RootOf(_Z^3-3)^2+3*_Z*RootOf(_Z^3-3)+9*_Z^2)+91*RootOf(_Z^3-3))/(-2+x)/(1+x))","C"
1528,1,33,84,3.930000," ","int((x^3-x)^(1/3)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{3 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{1}{3}, -\frac{1}{3}\right], \left[\frac{2}{3}\right], x^{2}\right)}{2 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}} x^{\frac{2}{3}}}$&$33$\\ trager&$-\frac{3 \left(x^{3}-x \right)^{\frac{1}{3}}}{2 x}+6 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) \ln \left(22320 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)^{2} x^{2}-27072 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}-27072 \left(x^{3}-x \right)^{\frac{1}{3}} \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) x -28932 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) x^{2}+7611 \left(x^{3}-x \right)^{\frac{2}{3}}+7611 x \left(x^{3}-x \right)^{\frac{1}{3}}-89280 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)^{2}+7766 x^{2}+46908 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)-4942\right)+\frac{\ln \left(22320 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)^{2} x^{2}+27072 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}+27072 \left(x^{3}-x \right)^{\frac{1}{3}} \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) x +25212 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) x^{2}+5355 \left(x^{3}-x \right)^{\frac{2}{3}}+5355 x \left(x^{3}-x \right)^{\frac{1}{3}}-89280 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)^{2}+5510 x^{2}-32028 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)-1653\right)}{2}-6 \ln \left(22320 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)^{2} x^{2}+27072 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}+27072 \left(x^{3}-x \right)^{\frac{1}{3}} \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) x +25212 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) x^{2}+5355 \left(x^{3}-x \right)^{\frac{2}{3}}+5355 x \left(x^{3}-x \right)^{\frac{1}{3}}-89280 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)^{2}+5510 x^{2}-32028 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)-1653\right) \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)$&$458$\\ risch&$-\frac{3 \left(x \left(x^{2}-1\right)\right)^{\frac{1}{3}}}{2 x}+\frac{\left(-\frac{\ln \left(\frac{35 \RootOf \left(\textit{\_Z}^{2}-6 \textit{\_Z} +36\right)^{2} x^{4}-1956 \RootOf \left(\textit{\_Z}^{2}-6 \textit{\_Z} +36\right) x^{4}-4104 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-6 \textit{\_Z} +36\right) x^{2}-175 \RootOf \left(\textit{\_Z}^{2}-6 \textit{\_Z} +36\right)^{2} x^{2}-23364 x^{4}+5850 \RootOf \left(\textit{\_Z}^{2}-6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}+35100 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}+2010 \RootOf \left(\textit{\_Z}^{2}-6 \textit{\_Z} +36\right) x^{2}-10476 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}+4104 \RootOf \left(\textit{\_Z}^{2}-6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}+140 \RootOf \left(\textit{\_Z}^{2}-6 \textit{\_Z} +36\right)^{2}+38232 x^{2}-35100 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}-54 \RootOf \left(\textit{\_Z}^{2}-6 \textit{\_Z} +36\right)-14868}{\left(-1+x \right) \left(1+x \right)}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}-6 \textit{\_Z} +36\right) \ln \left(-\frac{-59 \RootOf \left(\textit{\_Z}^{2}-6 \textit{\_Z} +36\right)^{2} x^{4}-3750 \RootOf \left(\textit{\_Z}^{2}-6 \textit{\_Z} +36\right) x^{4}-1746 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-6 \textit{\_Z} +36\right) x^{2}+295 \RootOf \left(\textit{\_Z}^{2}-6 \textit{\_Z} +36\right)^{2} x^{2}-12600 x^{4}+5850 \RootOf \left(\textit{\_Z}^{2}-6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}+35100 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}+5652 \RootOf \left(\textit{\_Z}^{2}-6 \textit{\_Z} +36\right) x^{2}-24624 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}+1746 \RootOf \left(\textit{\_Z}^{2}-6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}-236 \RootOf \left(\textit{\_Z}^{2}-6 \textit{\_Z} +36\right)^{2}+16380 x^{2}-35100 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}-1902 \RootOf \left(\textit{\_Z}^{2}-6 \textit{\_Z} +36\right)-3780}{\left(-1+x \right) \left(1+x \right)}\right)}{12}\right) \left(x \left(x^{2}-1\right)\right)^{\frac{1}{3}} \left(x^{2} \left(x^{2}-1\right)^{2}\right)^{\frac{1}{3}}}{x \left(x^{2}-1\right)}$&$538$\\ \hline \end{longtable}"," ",0,"-3/2*signum(x^2-1)^(1/3)/(-signum(x^2-1))^(1/3)/x^(2/3)*hypergeom([-1/3,-1/3],[2/3],x^2)","C"
1529,1,27,89,0.946000," ","int((x^3-x^2)^(1/3)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 \mathrm{signum}\left(-1+x \right)^{\frac{1}{3}} x^{\frac{2}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], x\right)}{2 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{3}}}$&$27$\\ trager&$\left(x^{3}-x^{2}\right)^{\frac{1}{3}}-\frac{\ln \left(-\frac{-180 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{2}+144 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+144 \left(x^{3}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x +360 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x +114 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{2}+9 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+9 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}-18 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x +4 x^{2}-x}{x}\right)}{3}-2 \ln \left(-\frac{-180 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{2}+144 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+144 \left(x^{3}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x +360 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x +114 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{2}+9 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+9 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}-18 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x +4 x^{2}-x}{x}\right) \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)+2 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \ln \left(\frac{180 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{2}+144 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+144 \left(x^{3}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x -360 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x +174 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{2}+15 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+15 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}-138 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x +20 x^{2}-12 x}{x}\right)$&$505$\\ risch&$\left(\left(-1+x \right) x^{2}\right)^{\frac{1}{3}}+\frac{\left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}-12 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x +15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-2 x^{2}+x \right)^{\frac{2}{3}}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-2 x^{2}+x \right)^{\frac{1}{3}} x +19 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+8 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-2 x^{2}+x \right)^{\frac{1}{3}}-29 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x -9 \left(x^{3}-2 x^{2}+x \right)^{\frac{2}{3}}-9 \left(x^{3}-2 x^{2}+x \right)^{\frac{1}{3}} x -5 x^{2}+10 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+9 \left(x^{3}-2 x^{2}+x \right)^{\frac{1}{3}}+8 x -3}{-1+x}\right)}{3}-\frac{\ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}-12 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x -15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-2 x^{2}+x \right)^{\frac{2}{3}}-15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-2 x^{2}+x \right)^{\frac{1}{3}} x -11 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+8 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-2 x^{2}+x \right)^{\frac{1}{3}}+5 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x -24 \left(x^{3}-2 x^{2}+x \right)^{\frac{2}{3}}-24 \left(x^{3}-2 x^{2}+x \right)^{\frac{1}{3}} x -20 x^{2}+6 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+24 \left(x^{3}-2 x^{2}+x \right)^{\frac{1}{3}}+25 x -5}{-1+x}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{3}-\frac{\ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}-12 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x -15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-2 x^{2}+x \right)^{\frac{2}{3}}-15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-2 x^{2}+x \right)^{\frac{1}{3}} x -11 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+8 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-2 x^{2}+x \right)^{\frac{1}{3}}+5 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x -24 \left(x^{3}-2 x^{2}+x \right)^{\frac{2}{3}}-24 \left(x^{3}-2 x^{2}+x \right)^{\frac{1}{3}} x -20 x^{2}+6 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+24 \left(x^{3}-2 x^{2}+x \right)^{\frac{1}{3}}+25 x -5}{-1+x}\right)}{3}\right) \left(\left(-1+x \right) x^{2}\right)^{\frac{1}{3}} \left(\left(-1+x \right)^{2} x \right)^{\frac{1}{3}}}{x \left(-1+x \right)}$&$638$\\ \hline \end{longtable}"," ",0,"3/2*signum(-1+x)^(1/3)/(-signum(-1+x))^(1/3)*x^(2/3)*hypergeom([-1/3,2/3],[5/3],x)","C"
1530,0,0,89,0.027000," ","int((a*x^2-3*b)/(a*x^2+x^3-b)/(a*x^3-b*x)^(1/4),x)","\[\int \frac{a \,x^{2}-3 b}{\left(a \,x^{2}+x^{3}-b \right) \left(a \,x^{3}-b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2-3*b)/(a*x^2+x^3-b)/(a*x^3-b*x)^(1/4),x)","F"
1531,0,0,79,0.039000," ","int(1/(a*x-2*b)/(a*x^3-b*x^2)^(1/4),x)","\[\int \frac{1}{\left(a x -2 b \right) \left(a \,x^{3}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(a*x-2*b)/(a*x^3-b*x^2)^(1/4),x)","F"
1532,0,0,44,0.013000," ","int((a*x^4-b)*(a*x^4-b*x^2)^(1/4)/x^4/(a*x^4+b),x)","\[\int \frac{\left(a \,x^{4}-b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}{x^{4} \left(a \,x^{4}+b \right)}\, dx\]"," ",0,"int((a*x^4-b)*(a*x^4-b*x^2)^(1/4)/x^4/(a*x^4+b),x)","F"
1533,0,0,44,0.002000," ","int((a*x^4-b)*(a*x^4-b*x^2)^(1/4)/x^4/(a*x^4+b),x)","\[\int \frac{\left(a \,x^{4}-b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}{x^{4} \left(a \,x^{4}+b \right)}\, dx\]"," ",0,"int((a*x^4-b)*(a*x^4-b*x^2)^(1/4)/x^4/(a*x^4+b),x)","F"
1534,0,0,11,0.027000," ","int((a*x^2-b)/(x^4-a*x^2+b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{a \,x^{2}-b}{\left(x^{4}-a \,x^{2}+b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2-b)/(x^4-a*x^2+b)/(a*x^4+b*x^2)^(1/4),x)","F"
1535,0,0,11,0.002000," ","int((a*x^2-b)/(x^4-a*x^2+b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{a \,x^{2}-b}{\left(x^{4}-a \,x^{2}+b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2-b)/(x^4-a*x^2+b)/(a*x^4+b*x^2)^(1/4),x)","F"
1536,0,0,44,0.012000," ","int((a*x^4+b*x^2)^(1/4)/x^4/(a*x^4-b),x)","\[\int \frac{\left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}{x^{4} \left(a \,x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^4+b*x^2)^(1/4)/x^4/(a*x^4-b),x)","F"
1537,0,0,44,0.001000," ","int((a*x^4+b*x^2)^(1/4)/x^4/(a*x^4-b),x)","\[\int \frac{\left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}{x^{4} \left(a \,x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^4+b*x^2)^(1/4)/x^4/(a*x^4-b),x)","F"
1538,1,443,94,0.269000," ","int((a^3*x^3+b^3)/(a^3*x^3-b^3)/(a^4*x^4+b^4)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, i\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}+b^{4}}}+\frac{b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{2} \textit{\_Z}^{2}+a b \textit{\_Z} +b^{2}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha  a -2 b \right) \left(\frac{\arctanh \left(\frac{\left(\underline{\hspace{1.25 ex}}\alpha  a +b \right) a b \left(a \,x^{2}+b \underline{\hspace{1.25 ex}}\alpha  \right)}{\sqrt{b^{3} \left(\underline{\hspace{1.25 ex}}\alpha  a +b \right)}\, \sqrt{a^{4} x^{4}+b^{4}}}\right)}{\sqrt{b^{3} \left(\underline{\hspace{1.25 ex}}\alpha  a +b \right)}}+\frac{2 a \left(\underline{\hspace{1.25 ex}}\alpha  a +b \right) \sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, -\frac{i \underline{\hspace{1.25 ex}}\alpha  a}{b}, \frac{\sqrt{-\frac{i a^{2}}{b^{2}}}}{\sqrt{\frac{i a^{2}}{b^{2}}}}\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, b^{2} \sqrt{a^{4} x^{4}+b^{4}}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  a +b}\right)}{3 a}+\frac{2 b \left(-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 a^{2} b^{2} x^{2}+2 b^{4}\right) \sqrt{2}}{4 \sqrt{b^{4}}\, \sqrt{a^{4} x^{4}+b^{4}}}\right)}{4 \sqrt{b^{4}}}-\frac{a \sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, -i, \frac{\sqrt{-\frac{i a^{2}}{b^{2}}}}{\sqrt{\frac{i a^{2}}{b^{2}}}}\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, b \sqrt{a^{4} x^{4}+b^{4}}}\right)}{3 a}$&$443$\\ elliptic&$\frac{a^{3} b^{5} \sqrt{2}\, \ln \left(\frac{\frac{b^{2} \left(a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}+\left(-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right) \left(x^{2}-\frac{-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{b^{2} \left(a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}\, \sqrt{4 \left(x^{2}-\frac{-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)^{2} a^{4}+4 \left(-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right) \left(x^{2}-\frac{-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)+\frac{2 b^{2} \left(a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}}{2}}{x^{2}-\frac{-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}}\right)}{\left(-3 a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right) \sqrt{-3 a^{4} b^{4}}\, \sqrt{\frac{b^{2} \left(a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}}-\frac{a \,b^{3} \sqrt{2}\, \ln \left(\frac{\frac{b^{2} \left(a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}+\left(-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right) \left(x^{2}-\frac{-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{b^{2} \left(a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}\, \sqrt{4 \left(x^{2}-\frac{-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)^{2} a^{4}+4 \left(-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right) \left(x^{2}-\frac{-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)+\frac{2 b^{2} \left(a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}}{2}}{x^{2}-\frac{-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}}\right)}{\left(-3 a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right) \sqrt{\frac{b^{2} \left(a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}}+\frac{2 a^{3} b^{5} \sqrt{2}\, \ln \left(\frac{4 b^{4}+2 a^{2} b^{2} \left(x^{2}-\frac{b^{2}}{a^{2}}\right)+2 \sqrt{2}\, \sqrt{b^{4}}\, \sqrt{\left(x^{2}-\frac{b^{2}}{a^{2}}\right)^{2} a^{4}+2 a^{2} b^{2} \left(x^{2}-\frac{b^{2}}{a^{2}}\right)+2 b^{4}}}{x^{2}-\frac{b^{2}}{a^{2}}}\right)}{\left(-3 a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right) \left(3 a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right) \sqrt{b^{4}}}+\frac{a^{3} b^{5} \sqrt{2}\, \ln \left(\frac{\frac{b^{2} \left(a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}+\left(-a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right) \left(x^{2}+\frac{a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{b^{2} \left(a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}\, \sqrt{4 \left(x^{2}+\frac{a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)^{2} a^{4}+4 \left(-a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right) \left(x^{2}+\frac{a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)+\frac{2 b^{2} \left(a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}}{2}}{x^{2}+\frac{a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}}\right)}{\left(3 a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right) \sqrt{-3 a^{4} b^{4}}\, \sqrt{\frac{b^{2} \left(a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}}+\frac{a \,b^{3} \sqrt{2}\, \ln \left(\frac{\frac{b^{2} \left(a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}+\left(-a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right) \left(x^{2}+\frac{a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{b^{2} \left(a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}\, \sqrt{4 \left(x^{2}+\frac{a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)^{2} a^{4}+4 \left(-a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right) \left(x^{2}+\frac{a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)+\frac{2 b^{2} \left(a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}}{2}}{x^{2}+\frac{a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}}\right)}{\left(3 a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right) \sqrt{\frac{b^{2} \left(a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}}+\frac{\left(-\frac{\ln \left(a b +\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{2 x}\right)}{6 a b}+\frac{2 \sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}+b^{4}}}{a b x}\right)}{3 a b}+\frac{\ln \left(-a b +\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{2 x}\right)}{6 a b}\right) \sqrt{2}}{2}$&$1537$\\ \hline \end{longtable}"," ",0,"1/(I*a^2/b^2)^(1/2)*(1-I*a^2/b^2*x^2)^(1/2)*(1+I*a^2/b^2*x^2)^(1/2)/(a^4*x^4+b^4)^(1/2)*EllipticF(x*(I*a^2/b^2)^(1/2),I)+1/3*b/a*sum((-_alpha*a-2*b)/(2*_alpha*a+b)*(1/(b^3*(_alpha*a+b))^(1/2)*arctanh((_alpha*a+b)*a*b*(a*x^2+_alpha*b)/(b^3*(_alpha*a+b))^(1/2)/(a^4*x^4+b^4)^(1/2))+2/(I*a^2/b^2)^(1/2)*a*(_alpha*a+b)/b^2*(1-I*a^2/b^2*x^2)^(1/2)*(1+I*a^2/b^2*x^2)^(1/2)/(a^4*x^4+b^4)^(1/2)*EllipticPi(x*(I*a^2/b^2)^(1/2),-I*_alpha*a/b,(-I*a^2/b^2)^(1/2)/(I*a^2/b^2)^(1/2))),_alpha=RootOf(_Z^2*a^2+_Z*a*b+b^2))+2/3*b/a*(-1/4*2^(1/2)/(b^4)^(1/2)*arctanh(1/4*(2*a^2*b^2*x^2+2*b^4)*2^(1/2)/(b^4)^(1/2)/(a^4*x^4+b^4)^(1/2))-1/(I*a^2/b^2)^(1/2)/b*a*(1-I*a^2/b^2*x^2)^(1/2)*(1+I*a^2/b^2*x^2)^(1/2)/(a^4*x^4+b^4)^(1/2)*EllipticPi(x*(I*a^2/b^2)^(1/2),-I,(-I*a^2/b^2)^(1/2)/(I*a^2/b^2)^(1/2)))","C"
1539,1,6315,31,144.053000," ","int((x^3+1)^(2/3)*(2*x^6+x^3+1)/x^6/(2*x^6-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$6315$\\ trager&$\text{Expression too large to display}$&$8835$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1540,1,8812,31,147.763000," ","int((x^3+1)^(2/3)*(2*x^6+x^3+1)/x^6/(2*x^6-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$8812$\\ risch&$\text{Expression too large to display}$&$11003$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1541,1,362,90,109.515000," ","int((x^6+1)*(2*x^6-1)*(2*x^6+x^4-1)^(5/4)/x^10/(2*x^6-x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(2 x^{6}+x^{4}-1\right)^{\frac{1}{4}} \left(20 x^{12}+38 x^{10}+104 x^{8}-20 x^{6}-19 x^{4}+5\right)}{45 x^{9}}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(\frac{-2 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{6} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)-3 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{4}-4 \left(2 x^{6}+x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{3}+4 \sqrt{2 x^{6}+x^{4}-1}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{2}+4 \left(2 x^{6}+x^{4}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)}{\left(-1+x \right) \left(1+x \right) \left(2 x^{4}+x^{2}+1\right)}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{6}+3 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{4}+4 \left(2 x^{6}+x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{3}+4 \sqrt{2 x^{6}+x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}-2\right) x^{2}+4 \left(2 x^{6}+x^{4}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}-2\right)^{3}}{\left(-1+x \right) \left(1+x \right) \left(2 x^{4}+x^{2}+1\right)}\right)}{2}$&$362$\\ risch&$\frac{40 x^{18}+96 x^{16}+246 x^{14}+44 x^{12}-96 x^{10}-123 x^{8}+30 x^{6}+24 x^{4}-5}{45 x^{9} \left(2 x^{6}+x^{4}-1\right)^{\frac{3}{4}}}+\frac{\left(\frac{\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(\frac{-8 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{18}-20 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{16}+8 \left(8 x^{18}+12 x^{16}+6 x^{14}-11 x^{12}-12 x^{10}-3 x^{8}+6 x^{6}+3 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{13}-14 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{14}+8 \left(8 x^{18}+12 x^{16}+6 x^{14}-11 x^{12}-12 x^{10}-3 x^{8}+6 x^{6}+3 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{11}+9 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{12}+2 \left(8 x^{18}+12 x^{16}+6 x^{14}-11 x^{12}-12 x^{10}-3 x^{8}+6 x^{6}+3 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{9}+20 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{10}-8 \left(8 x^{18}+12 x^{16}+6 x^{14}-11 x^{12}-12 x^{10}-3 x^{8}+6 x^{6}+3 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{7}+7 x^{8} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-8 \sqrt{8 x^{18}+12 x^{16}+6 x^{14}-11 x^{12}-12 x^{10}-3 x^{8}+6 x^{6}+3 x^{4}-1}\, x^{8}-4 \left(8 x^{18}+12 x^{16}+6 x^{14}-11 x^{12}-12 x^{10}-3 x^{8}+6 x^{6}+3 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{5}-6 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{6}-4 \sqrt{8 x^{18}+12 x^{16}+6 x^{14}-11 x^{12}-12 x^{10}-3 x^{8}+6 x^{6}+3 x^{4}-1}\, x^{6}+4 \left(8 x^{18}+12 x^{16}+6 x^{14}-11 x^{12}-12 x^{10}-3 x^{8}+6 x^{6}+3 x^{4}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right) x^{3}-5 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{4}+2 \left(8 x^{18}+12 x^{16}+6 x^{14}-11 x^{12}-12 x^{10}-3 x^{8}+6 x^{6}+3 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x +4 \sqrt{8 x^{18}+12 x^{16}+6 x^{14}-11 x^{12}-12 x^{10}-3 x^{8}+6 x^{6}+3 x^{4}-1}\, x^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}}{\left(2 x^{6}+x^{4}-1\right)^{2} \left(-1+x \right) \left(1+x \right) \left(2 x^{4}+x^{2}+1\right)}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(-\frac{-8 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{18}-20 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{16}+8 \left(8 x^{18}+12 x^{16}+6 x^{14}-11 x^{12}-12 x^{10}-3 x^{8}+6 x^{6}+3 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{13}-14 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{14}+8 \left(8 x^{18}+12 x^{16}+6 x^{14}-11 x^{12}-12 x^{10}-3 x^{8}+6 x^{6}+3 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{11}+9 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{12}+2 \left(8 x^{18}+12 x^{16}+6 x^{14}-11 x^{12}-12 x^{10}-3 x^{8}+6 x^{6}+3 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{9}+20 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{10}-8 \left(8 x^{18}+12 x^{16}+6 x^{14}-11 x^{12}-12 x^{10}-3 x^{8}+6 x^{6}+3 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{7}+7 x^{8} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+8 \sqrt{8 x^{18}+12 x^{16}+6 x^{14}-11 x^{12}-12 x^{10}-3 x^{8}+6 x^{6}+3 x^{4}-1}\, x^{8}-4 \left(8 x^{18}+12 x^{16}+6 x^{14}-11 x^{12}-12 x^{10}-3 x^{8}+6 x^{6}+3 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{5}-6 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{6}+4 \sqrt{8 x^{18}+12 x^{16}+6 x^{14}-11 x^{12}-12 x^{10}-3 x^{8}+6 x^{6}+3 x^{4}-1}\, x^{6}-4 \left(8 x^{18}+12 x^{16}+6 x^{14}-11 x^{12}-12 x^{10}-3 x^{8}+6 x^{6}+3 x^{4}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{3}-5 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{4}+2 \left(8 x^{18}+12 x^{16}+6 x^{14}-11 x^{12}-12 x^{10}-3 x^{8}+6 x^{6}+3 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x -4 \sqrt{8 x^{18}+12 x^{16}+6 x^{14}-11 x^{12}-12 x^{10}-3 x^{8}+6 x^{6}+3 x^{4}-1}\, x^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}}{\left(2 x^{6}+x^{4}-1\right)^{2} \left(-1+x \right) \left(1+x \right) \left(2 x^{4}+x^{2}+1\right)}\right)}{2}\right) \left(\left(2 x^{6}+x^{4}-1\right)^{3}\right)^{\frac{1}{4}}}{\left(2 x^{6}+x^{4}-1\right)^{\frac{3}{4}}}$&$1580$\\ \hline \end{longtable}"," ",0,"1/45*(2*x^6+x^4-1)^(1/4)*(20*x^12+38*x^10+104*x^8-20*x^6-19*x^4+5)/x^9-1/2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln((-2*RootOf(_Z^4-2)^2*x^6*RootOf(_Z^2+RootOf(_Z^4-2)^2)-3*RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^4-4*(2*x^6+x^4-1)^(1/4)*RootOf(_Z^4-2)^2*x^3+4*(2*x^6+x^4-1)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^2+4*(2*x^6+x^4-1)^(3/4)*x+RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2))/(-1+x)/(1+x)/(2*x^4+x^2+1))-1/2*RootOf(_Z^4-2)*ln((2*RootOf(_Z^4-2)^3*x^6+3*RootOf(_Z^4-2)^3*x^4+4*(2*x^6+x^4-1)^(1/4)*RootOf(_Z^4-2)^2*x^3+4*(2*x^6+x^4-1)^(1/2)*RootOf(_Z^4-2)*x^2+4*(2*x^6+x^4-1)^(3/4)*x-RootOf(_Z^4-2)^3)/(-1+x)/(1+x)/(2*x^4+x^2+1))","C"
1542,0,0,14,0.039000," ","int(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6+b),x)","\[\int \frac{1}{\left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}} \left(a^{6} x^{6}+b \right)}\, dx\]"," ",0,"int(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6+b),x)","F"
1543,0,0,14,0.000000," ","int(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6+b),x)","\[\int \frac{1}{\left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}} \left(a^{6} x^{6}+b \right)}\, dx\]"," ",0,"int(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6+b),x)","F"
1544,0,0,90,0.025000," ","int(((-3*k^2+1)*x+2*k^2*x^3)*(k^4*x^4-2*k^2*x^2+1)/((-x^2+1)*(-k^2*x^2+1))^(3/4)/(1-d+(3*d*k^2-1)*x^2-3*d*k^4*x^4+d*k^6*x^6),x)","\[\int \frac{\left(\left(-3 k^{2}+1\right) x +2 k^{2} x^{3}\right) \left(k^{4} x^{4}-2 k^{2} x^{2}+1\right)}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{3}{4}} \left(1-d +\left(3 d \,k^{2}-1\right) x^{2}-3 d \,k^{4} x^{4}+d \,k^{6} x^{6}\right)}\, dx\]"," ",0,"int(((-3*k^2+1)*x+2*k^2*x^3)*(k^4*x^4-2*k^2*x^2+1)/((-x^2+1)*(-k^2*x^2+1))^(3/4)/(1-d+(3*d*k^2-1)*x^2-3*d*k^4*x^4+d*k^6*x^6),x)","F"
1545,1,448,83,17.940000," ","int((2*x^4-1)^(1/4)*(x^8+x^4-1)/x^6/(x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(2 x^{4}-1\right)^{\frac{5}{4}}}{5 x^{5}}-\frac{\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(-4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{4}+4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(2 x^{4}-1\right)^{\frac{1}{4}} x^{3}-4 \RootOf \left(\textit{\_Z}^{4}-2\right) \sqrt{2 x^{4}-1}\, x^{2}+4 \left(2 x^{4}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}-2\right)^{3}\right)}{4}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{4}-4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(2 x^{4}-1\right)^{\frac{1}{4}} x^{3}-4 \sqrt{2 x^{4}-1}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{2}+4 \left(2 x^{4}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)\right)}{4}-\frac{\ln \left(\frac{2 \left(2 x^{4}-1\right)^{\frac{3}{4}} x +2 \sqrt{2 x^{4}-1}\, x^{2}+2 \left(2 x^{4}-1\right)^{\frac{1}{4}} x^{3}+3 x^{4}-1}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)}{4}-\frac{\RootOf \left(\textit{\_Z}^{4}-2\right)^{3} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} \sqrt{2 x^{4}-1}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{4}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{3} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)+4 \left(2 x^{4}-1\right)^{\frac{3}{4}} x -4 \left(2 x^{4}-1\right)^{\frac{1}{4}} x^{3}}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)}{8}$&$448$\\ \hline \end{longtable}"," ",0,"1/5*(2*x^4-1)^(5/4)/x^5-1/4*RootOf(_Z^4-2)*ln(-4*RootOf(_Z^4-2)^3*x^4+4*RootOf(_Z^4-2)^2*(2*x^4-1)^(1/4)*x^3-4*RootOf(_Z^4-2)*(2*x^4-1)^(1/2)*x^2+4*(2*x^4-1)^(3/4)*x+RootOf(_Z^4-2)^3)-1/4*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln(4*RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^4-4*RootOf(_Z^4-2)^2*(2*x^4-1)^(1/4)*x^3-4*(2*x^4-1)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^2+4*(2*x^4-1)^(3/4)*x-RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2))-1/4*ln((2*(2*x^4-1)^(3/4)*x+2*(2*x^4-1)^(1/2)*x^2+2*(2*x^4-1)^(1/4)*x^3+3*x^4-1)/(-1+x)/(1+x)/(x^2+1))-1/8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln((2*RootOf(_Z^4-2)^3*(2*x^4-1)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^2-3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^3*x^4+RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)+4*(2*x^4-1)^(3/4)*x-4*(2*x^4-1)^(1/4)*x^3)/(-1+x)/(1+x)/(x^2+1))","C"
1546,0,0,14,0.025000," ","int(1/(a*x^4-b)^(1/4)/(x^8-a*x^4-b),x)","\[\int \frac{1}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(x^{8}-a \,x^{4}-b \right)}\, dx\]"," ",0,"int(1/(a*x^4-b)^(1/4)/(x^8-a*x^4-b),x)","F"
1547,0,0,14,0.001000," ","int(1/(a*x^4-b)^(1/4)/(x^8-a*x^4-b),x)","\[\int \frac{1}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(x^{8}-a \,x^{4}-b \right)}\, dx\]"," ",0,"int(1/(a*x^4-b)^(1/4)/(x^8-a*x^4-b),x)","F"
1548,1,33,85,1.798000," ","int(x^6*(x^3-1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}} x^{7} \hypergeom \left(\left[-\frac{2}{3}, \frac{7}{3}\right], \left[\frac{10}{3}\right], x^{3}\right)}{7 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}}}$&$33$\\ risch&$\frac{x \left(9 x^{6}-3 x^{3}-4\right) \left(x^{3}-1\right)^{\frac{2}{3}}}{81}-\frac{4 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{3}\right)}{81 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}}}$&$54$\\ trager&$\frac{x \left(9 x^{6}-3 x^{3}-4\right) \left(x^{3}-1\right)^{\frac{2}{3}}}{81}+\frac{4 \ln \left(-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -5 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}-1\right)^{\frac{2}{3}}-3 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-2 x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1\right)}{243}+\frac{4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-2 x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+2\right)}{243}$&$204$\\ \hline \end{longtable}"," ",0,"1/7*signum(x^3-1)^(2/3)/(-signum(x^3-1))^(2/3)*x^7*hypergeom([-2/3,7/3],[10/3],x^3)","C"
1549,1,17,85,1.837000," ","int(x^6*(x^3+1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{x^{7} \hypergeom \left(\left[-\frac{2}{3}, \frac{7}{3}\right], \left[\frac{10}{3}\right], -x^{3}\right)}{7}$&$17$\\ risch&$\frac{x \left(9 x^{6}+3 x^{3}-4\right) \left(x^{3}+1\right)^{\frac{2}{3}}}{81}+\frac{4 x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{3}\right)}{81}$&$38$\\ trager&$\frac{x \left(9 x^{6}+3 x^{3}-4\right) \left(x^{3}+1\right)^{\frac{2}{3}}}{81}-\frac{4 \ln \left(-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +5 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}+1\right)^{\frac{2}{3}}-3 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}-2 x^{3}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-1\right)}{243}+\frac{4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x -3 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+3 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}-2 x^{3}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-2\right)}{243}$&$225$\\ \hline \end{longtable}"," ",0,"1/7*x^7*hypergeom([-2/3,7/3],[10/3],-x^3)","C"
1550,1,17,85,3.813000," ","int(x^4*(x^3+x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 x^{\frac{16}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{8}{3}\right], \left[\frac{11}{3}\right], -x^{2}\right)}{16}$&$17$\\ trager&$\frac{x \left(18 x^{4}+3 x^{2}-5\right) \left(x^{3}+x \right)^{\frac{1}{3}}}{108}-\frac{5 \ln \left(-36 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}+72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}-27 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x -33 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}+36 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}-9 \left(x^{3}+x \right)^{\frac{2}{3}}-15 x \left(x^{3}+x \right)^{\frac{1}{3}}+20 x^{2}-51 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)+15\right)}{162}+\frac{5 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \ln \left(-9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}-72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}+45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x +30 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}+9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}+15 \left(x^{3}+x \right)^{\frac{2}{3}}+9 x \left(x^{3}+x \right)^{\frac{1}{3}}-25 x^{2}-9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-10\right)}{54}$&$299$\\ risch&$\frac{x \left(18 x^{4}+3 x^{2}-5\right) \left(x \left(x^{2}+1\right)\right)^{\frac{1}{3}}}{108}+\frac{\left(-\frac{5 \ln \left(-\frac{-5 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{4}-38 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{4}+18 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}+16 x^{4}+30 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}+60 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}-70 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-96 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}+18 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}+5 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2}+28 x^{2}+60 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}-32 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)+12}{x^{2}+1}\right)}{162}+\frac{5 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{4}+20 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{4}-48 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-100 x^{4}+30 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}+60 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}+14 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}+36 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}-48 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}+\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2}-140 x^{2}+60 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}-6 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)-40}{x^{2}+1}\right)}{324}\right) \left(x \left(x^{2}+1\right)\right)^{\frac{1}{3}} \left(x^{2} \left(x^{2}+1\right)^{2}\right)^{\frac{1}{3}}}{x \left(x^{2}+1\right)}$&$508$\\ \hline \end{longtable}"," ",0,"3/16*x^(16/3)*hypergeom([-1/3,8/3],[11/3],-x^2)","C"
1551,0,0,95,0.020000," ","int(x^2*(3*a*b^2-2*b*(2*a+b)*x+(a+2*b)*x^2)/(x*(-a+x)*(-b+x)^2)^(3/4)/(a*b^2-b*(2*a+b)*x+(a+2*b)*x^2+(-1+d)*x^3),x)","\[\int \frac{x^{2} \left(3 a \,b^{2}-2 b \left(2 a +b \right) x +\left(a +2 b \right) x^{2}\right)}{\left(x \left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{3}{4}} \left(a \,b^{2}-b \left(2 a +b \right) x +\left(a +2 b \right) x^{2}+\left(-1+d \right) x^{3}\right)}\, dx\]"," ",0,"int(x^2*(3*a*b^2-2*b*(2*a+b)*x+(a+2*b)*x^2)/(x*(-a+x)*(-b+x)^2)^(3/4)/(a*b^2-b*(2*a+b)*x+(a+2*b)*x^2+(-1+d)*x^3),x)","F"
1552,1,81,85,4.458000," ","int((x^4+1)^(1/3)*(x^4+3)/x^17,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{10 x^{16}+4 x^{12}+39 x^{8}+126 x^{4}+81}{432 x^{16} \left(x^{4}+1\right)^{\frac{2}{3}}}-\frac{5 \left(-\frac{2 \Gamma \left(\frac{2}{3}\right) x^{4} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 2\right], -x^{4}\right)}{3}+\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)\right)}{324 \Gamma \left(\frac{2}{3}\right)}$&$81$\\ meijerg&$-\frac{\frac{10 \Gamma \left(\frac{2}{3}\right) x^{4} \hypergeom \left(\left[1, 1, \frac{11}{3}\right], \left[2, 5\right], -x^{4}\right)}{81}-\frac{5 \left(\frac{4}{15}+\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)}{27}+\frac{\Gamma \left(\frac{2}{3}\right)}{x^{12}}+\frac{\Gamma \left(\frac{2}{3}\right)}{2 x^{8}}-\frac{\Gamma \left(\frac{2}{3}\right)}{3 x^{4}}}{12 \Gamma \left(\frac{2}{3}\right)}-\frac{-\frac{22 \Gamma \left(\frac{2}{3}\right) x^{4} \hypergeom \left(\left[1, 1, \frac{14}{3}\right], \left[2, 6\right], -x^{4}\right)}{243}+\frac{10 \left(\frac{47}{120}+\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+4 \ln \left(x \right)\right) \Gamma \left(\frac{2}{3}\right)}{81}+\frac{3 \Gamma \left(\frac{2}{3}\right)}{4 x^{16}}+\frac{\Gamma \left(\frac{2}{3}\right)}{3 x^{12}}-\frac{\Gamma \left(\frac{2}{3}\right)}{6 x^{8}}+\frac{5 \Gamma \left(\frac{2}{3}\right)}{27 x^{4}}}{4 \Gamma \left(\frac{2}{3}\right)}$&$144$\\ trager&$-\frac{\left(10 x^{12}-6 x^{8}+45 x^{4}+81\right) \left(x^{4}+1\right)^{\frac{1}{3}}}{432 x^{16}}-\frac{5 \ln \left(\frac{1801935 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{4}+2398401 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{4}+798074 x^{4}-7791669 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}}-1801935 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}+6586200 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{1}{3}}+401823 \left(x^{4}+1\right)^{\frac{2}{3}}+1806114 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-2597223 \left(x^{4}+1\right)^{\frac{1}{3}}+1995185}{x^{4}}\right)}{324}+\frac{5 \ln \left(\frac{153 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{4}-264 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{4}+111 x^{4}-351 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}}-153 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}+495 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{1}{3}}-48 \left(x^{4}+1\right)^{\frac{2}{3}}-93 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-117 \left(x^{4}+1\right)^{\frac{1}{3}}+148}{x^{4}}\right)}{324}-\frac{5 \ln \left(\frac{153 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{4}-264 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{4}+111 x^{4}-351 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{2}{3}}-153 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}+495 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{4}+1\right)^{\frac{1}{3}}-48 \left(x^{4}+1\right)^{\frac{2}{3}}-93 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-117 \left(x^{4}+1\right)^{\frac{1}{3}}+148}{x^{4}}\right) \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)}{108}$&$444$\\ \hline \end{longtable}"," ",0,"-1/432*(10*x^16+4*x^12+39*x^8+126*x^4+81)/x^16/(x^4+1)^(2/3)-5/324/GAMMA(2/3)*(-2/3*GAMMA(2/3)*x^4*hypergeom([1,1,5/3],[2,2],-x^4)+(1/6*Pi*3^(1/2)-3/2*ln(3)+4*ln(x))*GAMMA(2/3))","C"
1553,1,2048,24,368.431000," ","int((x^2-2)*(x^3+x)^(1/3)/x^2/(x^4-2*x^2+4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2048$\\ risch&$\text{Expression too large to display}$&$8598$\\ \hline \end{longtable}"," ",0,"3/4*(x^3+x)^(1/3)/x+1/24*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)*ln(-(40310784*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^6*x^2-40310784*RootOf(5038848*_Z^6+3888*_Z^3+7)^6*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2+360288*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^3*x^2-917568*(x^3+x)^(1/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^3*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)*x+145152*RootOf(5038848*_Z^6+3888*_Z^3+7)^3*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2+886464*(x^3+x)^(2/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^3-47*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2*x^2+846*(x^3+x)^(1/3)*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)*x-18*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2-5028*(x^3+x)^(2/3))/(2592*x^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^3-2592*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+x^2+4))-162/5*ln(-(3359232*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^6*x^2-3359232*RootOf(5038848*_Z^6+3888*_Z^3+7)^6*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2-21168*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^3*x^2+25920*(x^3+x)^(1/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^3*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)*x+1728*RootOf(5038848*_Z^6+3888*_Z^3+7)^3*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2+233280*(x^3+x)^(2/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+33*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2*x^2-190*(x^3+x)^(1/3)*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)*x+22*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2+740*(x^3+x)^(2/3))/(2592*x^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^3-2592*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+x^2+4))*RootOf(5038848*_Z^6+3888*_Z^3+7)^3*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)-1/30*ln(-(3359232*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^6*x^2-3359232*RootOf(5038848*_Z^6+3888*_Z^3+7)^6*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2-21168*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^3*x^2+25920*(x^3+x)^(1/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^3*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)*x+1728*RootOf(5038848*_Z^6+3888*_Z^3+7)^3*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2+233280*(x^3+x)^(2/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+33*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2*x^2-190*(x^3+x)^(1/3)*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)*x+22*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2+740*(x^3+x)^(2/3))/(2592*x^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^3-2592*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+x^2+4))*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)-5832/5*ln((544195584*x^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^8-544195584*RootOf(5038848*_Z^6+3888*_Z^3+7)^8+2344464*RootOf(5038848*_Z^6+3888*_Z^3+7)^5*x^2+5219640*(x^3+x)^(1/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^4*x-9167904*RootOf(5038848*_Z^6+3888*_Z^3+7)^5+92340*(x^3+x)^(2/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^3-56889*RootOf(5038848*_Z^6+3888*_Z^3+7)^2*x^2+945*(x^3+x)^(1/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)*x-29106*RootOf(5038848*_Z^6+3888*_Z^3+7)^2+595*(x^3+x)^(2/3))/(2592*x^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^3-2592*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+x^2-6))*RootOf(5038848*_Z^6+3888*_Z^3+7)^4-6/5*ln((544195584*x^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^8-544195584*RootOf(5038848*_Z^6+3888*_Z^3+7)^8+2344464*RootOf(5038848*_Z^6+3888*_Z^3+7)^5*x^2+5219640*(x^3+x)^(1/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^4*x-9167904*RootOf(5038848*_Z^6+3888*_Z^3+7)^5+92340*(x^3+x)^(2/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^3-56889*RootOf(5038848*_Z^6+3888*_Z^3+7)^2*x^2+945*(x^3+x)^(1/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)*x-29106*RootOf(5038848*_Z^6+3888*_Z^3+7)^2+595*(x^3+x)^(2/3))/(2592*x^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^3-2592*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+x^2-6))*RootOf(5038848*_Z^6+3888*_Z^3+7)+3/2*RootOf(5038848*_Z^6+3888*_Z^3+7)*ln(-(544195584*x^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^8-544195584*RootOf(5038848*_Z^6+3888*_Z^3+7)^8+1819584*RootOf(5038848*_Z^6+3888*_Z^3+7)^5*x^2+379080*(x^3+x)^(1/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^4*x+1329696*RootOf(5038848*_Z^6+3888*_Z^3+7)^5-14580*(x^3+x)^(2/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^3-2079*RootOf(5038848*_Z^6+3888*_Z^3+7)^2*x^2+315*(x^3+x)^(1/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)*x-756*RootOf(5038848*_Z^6+3888*_Z^3+7)^2+35*(x^3+x)^(2/3))/(2592*x^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^3-2592*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+x^2-6))","B"
1554,1,2048,24,293.635000," ","int((x^2-2)*(x^3+x)^(1/3)/x^2/(x^4-2*x^2+4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2048$\\ risch&$\text{Expression too large to display}$&$7003$\\ \hline \end{longtable}"," ",0,"3/4*(x^3+x)^(1/3)/x+1/24*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)*ln(-(6718464*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^6*x^2-6718464*RootOf(5038848*_Z^6+3888*_Z^3+7)^6*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2-12096*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^3*x^2-168480*(x^3+x)^(1/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^3*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)*x-26784*RootOf(5038848*_Z^6+3888*_Z^3+7)^3*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2+233280*(x^3+x)^(2/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^3-39*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2*x^2+10*(x^3+x)^(1/3)*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)*x-26*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2+740*(x^3+x)^(2/3))/(2592*x^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^3-2592*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+x^2+4))+162/5*ln((10077696*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^6*x^2-10077696*RootOf(5038848*_Z^6+3888*_Z^3+7)^6*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2-27864*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^3*x^2-3479760*(x^3+x)^(1/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^3*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)*x+154224*RootOf(5038848*_Z^6+3888*_Z^3+7)^3*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2-2216160*(x^3+x)^(2/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^3-1081*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2*x^2-2055*(x^3+x)^(1/3)*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)*x-414*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2+12570*(x^3+x)^(2/3))/(2592*x^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^3-2592*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+x^2+4))*RootOf(5038848*_Z^6+3888*_Z^3+7)^3*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)-1/120*ln((10077696*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^6*x^2-10077696*RootOf(5038848*_Z^6+3888*_Z^3+7)^6*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2-27864*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^3*x^2-3479760*(x^3+x)^(1/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^3*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)*x+154224*RootOf(5038848*_Z^6+3888*_Z^3+7)^3*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2-2216160*(x^3+x)^(2/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^3-1081*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2*x^2-2055*(x^3+x)^(1/3)*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)*x-414*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)^2+12570*(x^3+x)^(2/3))/(2592*x^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^3-2592*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+x^2+4))*RootOf(_Z^3+46656*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+36)+5832/5*ln(-(544195584*x^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^8-544195584*RootOf(5038848*_Z^6+3888*_Z^3+7)^8+4269024*RootOf(5038848*_Z^6+3888*_Z^3+7)^5*x^2-116640*(x^3+x)^(1/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^4*x-1119744*RootOf(5038848*_Z^6+3888*_Z^3+7)^5-29160*(x^3+x)^(2/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+8316*RootOf(5038848*_Z^6+3888*_Z^3+7)^2*x^2-945*(x^3+x)^(1/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)*x+3024*RootOf(5038848*_Z^6+3888*_Z^3+7)^2+70*(x^3+x)^(2/3))/(2592*x^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^3-2592*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+x^2-6))*RootOf(5038848*_Z^6+3888*_Z^3+7)^4-3/10*ln(-(544195584*x^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^8-544195584*RootOf(5038848*_Z^6+3888*_Z^3+7)^8+4269024*RootOf(5038848*_Z^6+3888*_Z^3+7)^5*x^2-116640*(x^3+x)^(1/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^4*x-1119744*RootOf(5038848*_Z^6+3888*_Z^3+7)^5-29160*(x^3+x)^(2/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+8316*RootOf(5038848*_Z^6+3888*_Z^3+7)^2*x^2-945*(x^3+x)^(1/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)*x+3024*RootOf(5038848*_Z^6+3888*_Z^3+7)^2+70*(x^3+x)^(2/3))/(2592*x^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^3-2592*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+x^2-6))*RootOf(5038848*_Z^6+3888*_Z^3+7)+3/2*RootOf(5038848*_Z^6+3888*_Z^3+7)*ln(-(2176782336*x^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^8-2176782336*RootOf(5038848*_Z^6+3888*_Z^3+7)^8-16096320*RootOf(5038848*_Z^6+3888*_Z^3+7)^5*x^2+1376352*(x^3+x)^(1/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^4*x-11197440*RootOf(5038848*_Z^6+3888*_Z^3+7)^5-36936*(x^3+x)^(2/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)^3-16254*RootOf(5038848*_Z^6+3888*_Z^3+7)^2*x^2+2331*(x^3+x)^(1/3)*RootOf(5038848*_Z^6+3888*_Z^3+7)*x-8316*RootOf(5038848*_Z^6+3888*_Z^3+7)^2-238*(x^3+x)^(2/3))/(2592*x^2*RootOf(5038848*_Z^6+3888*_Z^3+7)^3-2592*RootOf(5038848*_Z^6+3888*_Z^3+7)^3+x^2-6))","B"
1555,1,273,87,8.349000," ","int(1/(x^4-1)^2/(x^4-x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x \left(67 x^{4}+2 x^{2}-85\right)}{80 \left(x^{2} \left(x^{2}-1\right)\right)^{\frac{1}{4}} \left(x^{2}-1\right) \left(x^{2}+1\right)}-\frac{15 \RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(\frac{-\sqrt{x^{4}-x^{2}}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x +2 \left(x^{4}-x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-3 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{3}+4 \left(x^{4}-x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}-8\right) x}{x \left(x^{2}+1\right)}\right)}{128}-\frac{15 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(\frac{\sqrt{x^{4}-x^{2}}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x -2 \left(x^{4}-x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{3}+4 \left(x^{4}-x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x}{x \left(x^{2}+1\right)}\right)}{128}$&$273$\\ trager&$\frac{\left(x^{4}-x^{2}\right)^{\frac{3}{4}} \left(67 x^{4}+2 x^{2}-85\right)}{80 x \left(x^{2}-1\right)^{2} \left(x^{2}+1\right)}+\frac{15 \RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(\frac{\sqrt{x^{4}-x^{2}}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x +2 \left(x^{4}-x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+3 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{3}+4 \left(x^{4}-x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}-8\right) x}{x \left(x^{2}+1\right)}\right)}{128}-\frac{15 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(\frac{\sqrt{x^{4}-x^{2}}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x -2 \left(x^{4}-x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{3}+4 \left(x^{4}-x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x}{x \left(x^{2}+1\right)}\right)}{128}$&$275$\\ \hline \end{longtable}"," ",0,"1/80*x*(67*x^4+2*x^2-85)/(x^2*(x^2-1))^(1/4)/(x^2-1)/(x^2+1)-15/128*RootOf(_Z^4-8)*ln((-(x^4-x^2)^(1/2)*RootOf(_Z^4-8)^3*x+2*(x^4-x^2)^(1/4)*RootOf(_Z^4-8)^2*x^2-3*RootOf(_Z^4-8)*x^3+4*(x^4-x^2)^(3/4)+RootOf(_Z^4-8)*x)/x/(x^2+1))-15/128*RootOf(_Z^2+RootOf(_Z^4-8)^2)*ln(((x^4-x^2)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x-2*(x^4-x^2)^(1/4)*RootOf(_Z^4-8)^2*x^2-3*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^3+4*(x^4-x^2)^(3/4)+RootOf(_Z^2+RootOf(_Z^4-8)^2)*x)/x/(x^2+1))","C"
1556,1,320,90,1.649000," ","int((x^2-1)*(x^4-x^3+x^2-x+1)/(x^2-x+1)^2/(x^2+x+1)/(x^4+3*x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{4}+3 x^{2}+1}}{4 x^{2}-4 x +4}+\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{-7 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{10}-29 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{9}+10 \sqrt{x^{4}+3 x^{2}+1}\, x^{8}-89 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{8}+40 \sqrt{x^{4}+3 x^{2}+1}\, x^{7}-190 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{7}+116 \sqrt{x^{4}+3 x^{2}+1}\, x^{6}-283 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{6}+192 \sqrt{x^{4}+3 x^{2}+1}\, x^{5}-363 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{5}+270 \sqrt{x^{4}+3 x^{2}+1}\, x^{4}-283 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{4}+192 \sqrt{x^{4}+3 x^{2}+1}\, x^{3}-190 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{3}+116 \sqrt{x^{4}+3 x^{2}+1}\, x^{2}-89 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}+40 \sqrt{x^{4}+3 x^{2}+1}\, x -29 \RootOf \left(\textit{\_Z}^{2}-2\right) x +10 \sqrt{x^{4}+3 x^{2}+1}-7 \RootOf \left(\textit{\_Z}^{2}-2\right)}{\left(x^{2}+x +1\right) \left(x^{2}-x +1\right)^{4}}\right)}{8}$&$320$\\ elliptic&$-\frac{\sqrt{-\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}+5}\, \left(3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}+5}\, \sqrt{2}}{4}\right)+\sqrt{6}\, \arctan \left(\frac{2 \sqrt{6}\, \sqrt{-\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}+5}\, \left(x^{2}-1\right)}{3 \left(\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}-5\right) \left(-x^{2}-1\right)}\right)\right)}{12 \sqrt{-\frac{\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}-5}{\left(\frac{x^{2}-1}{-x^{2}-1}+1\right)^{2}}}\, \left(\frac{x^{2}-1}{-x^{2}-1}+1\right)}-\frac{\sqrt{-\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}+5}\, \left(\frac{3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}+5}\, \sqrt{2}}{4}\right) \left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}-\frac{2 \sqrt{6}\, \arctan \left(\frac{2 \sqrt{6}\, \sqrt{-\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}+5}\, \left(x^{2}-1\right)}{3 \left(\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}-5\right) \left(-x^{2}-1\right)}\right) \left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}+9 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}+5}\, \sqrt{2}}{4}\right)-6 \sqrt{6}\, \arctan \left(\frac{2 \sqrt{6}\, \sqrt{-\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}+5}\, \left(x^{2}-1\right)}{3 \left(\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}-5\right) \left(-x^{2}-1\right)}\right)-12 \sqrt{-\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}+5}\right)}{24 \sqrt{-\frac{\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}-5}{\left(\frac{x^{2}-1}{-x^{2}-1}+1\right)^{2}}}\, \left(\frac{x^{2}-1}{-x^{2}-1}+1\right) \left(\frac{\left(x^{2}-1\right)^{2}}{\left(-x^{2}-1\right)^{2}}+3\right)}+\frac{\left(\frac{1}{-8+\frac{4 \sqrt{x^{4}+3 x^{2}+1}\, \sqrt{2}}{x}}+\frac{5 \ln \left(-1+\frac{\sqrt{x^{4}+3 x^{2}+1}\, \sqrt{2}}{2 x}\right)}{8}+\frac{1}{8+\frac{4 \sqrt{x^{4}+3 x^{2}+1}\, \sqrt{2}}{x}}-\frac{5 \ln \left(1+\frac{\sqrt{x^{4}+3 x^{2}+1}\, \sqrt{2}}{2 x}\right)}{8}\right) \sqrt{2}}{2}$&$661$\\ risch&$\frac{\sqrt{x^{4}+3 x^{2}+1}}{4 x^{2}-4 x +4}+\frac{5 \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{3}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{3}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticF \left(x \left(\frac{i \sqrt{5}}{2}-\frac{i}{2}\right), \frac{3}{2}+\frac{\sqrt{5}}{2}\right)}{4 \left(\frac{i \sqrt{5}}{2}-\frac{i}{2}\right) \sqrt{x^{4}+3 x^{2}+1}}+\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{\arctanh \left(\frac{\left(-2+i \sqrt{3}\right) \left(7 x^{2}+\frac{11}{2}-\frac{5 i \sqrt{3}}{2}\right)}{14 \sqrt{-1-i \sqrt{3}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{2 \sqrt{-1-i \sqrt{3}}}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{3}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{3}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, x , -\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{5}}{2}+\frac{3}{4}-\frac{3 i \sqrt{3}}{4}, \frac{\sqrt{-\frac{3}{2}-\frac{\sqrt{5}}{2}}}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}}\right)}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{4}+\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(\frac{\arctanh \left(\frac{\left(-2-i \sqrt{3}\right) \left(7 x^{2}+\frac{11}{2}+\frac{5 i \sqrt{3}}{2}\right)}{14 \sqrt{-1+i \sqrt{3}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{2 \sqrt{-1+i \sqrt{3}}}-\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{3}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{3}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, x , -\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{5}}{2}+\frac{3}{4}+\frac{3 i \sqrt{3}}{4}, \frac{\sqrt{-\frac{3}{2}-\frac{\sqrt{5}}{2}}}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}}\right)}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{4}+\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{\arctanh \left(\frac{\left(2+i \sqrt{3}\right) \left(7 x^{2}+\frac{11}{2}+\frac{5 i \sqrt{3}}{2}\right)}{14 \sqrt{-1+i \sqrt{3}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{2 \sqrt{-1+i \sqrt{3}}}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{3}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{3}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, x , \frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{5}}{2}+\frac{3}{4}+\frac{3 i \sqrt{3}}{4}, \frac{\sqrt{-\frac{3}{2}-\frac{\sqrt{5}}{2}}}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}}\right)}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)+\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-\frac{\arctanh \left(\frac{\left(2-i \sqrt{3}\right) \left(7 x^{2}+\frac{11}{2}-\frac{5 i \sqrt{3}}{2}\right)}{14 \sqrt{-1-i \sqrt{3}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{2 \sqrt{-1-i \sqrt{3}}}-\frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{3}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{3}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, x , \frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{5}}{2}+\frac{3}{4}-\frac{3 i \sqrt{3}}{4}, \frac{\sqrt{-\frac{3}{2}-\frac{\sqrt{5}}{2}}}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}}\right)}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)$&$836$\\ default&$\frac{5 \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{3}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{3}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticF \left(x \left(\frac{i \sqrt{5}}{2}-\frac{i}{2}\right), \frac{3}{2}+\frac{\sqrt{5}}{2}\right)}{4 \left(\frac{i \sqrt{5}}{2}-\frac{i}{2}\right) \sqrt{x^{4}+3 x^{2}+1}}+\frac{\left(\frac{1}{2}+\frac{5 i \sqrt{3}}{2}\right) \left(-\frac{\arctanh \left(\frac{\left(2+i \sqrt{3}\right) \left(7 x^{2}+\frac{11}{2}+\frac{5 i \sqrt{3}}{2}\right)}{14 \sqrt{-1+i \sqrt{3}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{2 \sqrt{-1+i \sqrt{3}}}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{3}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{3}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, x , \frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{5}}{2}+\frac{3}{4}+\frac{3 i \sqrt{3}}{4}, \frac{\sqrt{-\frac{3}{2}-\frac{\sqrt{5}}{2}}}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}}\right)}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{4}+\frac{\left(\frac{1}{2}-\frac{5 i \sqrt{3}}{2}\right) \left(-\frac{\arctanh \left(\frac{\left(2-i \sqrt{3}\right) \left(7 x^{2}+\frac{11}{2}-\frac{5 i \sqrt{3}}{2}\right)}{14 \sqrt{-1-i \sqrt{3}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{2 \sqrt{-1-i \sqrt{3}}}-\frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{3}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{3}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, x , \frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{5}}{2}+\frac{3}{4}-\frac{3 i \sqrt{3}}{4}, \frac{\sqrt{-\frac{3}{2}-\frac{\sqrt{5}}{2}}}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}}\right)}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{4}+\frac{\sqrt{x^{4}+3 x^{2}+1}}{4 x^{2}-4 x +4}+\frac{\left(\frac{3}{4}-\frac{i \sqrt{3}}{4}\right) \left(-\frac{\arctanh \left(\frac{\left(2+i \sqrt{3}\right) \left(7 x^{2}+\frac{11}{2}+\frac{5 i \sqrt{3}}{2}\right)}{14 \sqrt{-1+i \sqrt{3}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{2 \sqrt{-1+i \sqrt{3}}}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{3}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{3}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, x , \frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{5}}{2}+\frac{3}{4}+\frac{3 i \sqrt{3}}{4}, \frac{\sqrt{-\frac{3}{2}-\frac{\sqrt{5}}{2}}}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}}\right)}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{2}+\frac{\left(\frac{3}{4}+\frac{i \sqrt{3}}{4}\right) \left(-\frac{\arctanh \left(\frac{\left(2-i \sqrt{3}\right) \left(7 x^{2}+\frac{11}{2}-\frac{5 i \sqrt{3}}{2}\right)}{14 \sqrt{-1-i \sqrt{3}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{2 \sqrt{-1-i \sqrt{3}}}-\frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{3}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{3}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, x , \frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{5}}{2}+\frac{3}{4}-\frac{3 i \sqrt{3}}{4}, \frac{\sqrt{-\frac{3}{2}-\frac{\sqrt{5}}{2}}}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}}\right)}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{2}+\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{\arctanh \left(\frac{\left(-2+i \sqrt{3}\right) \left(7 x^{2}+\frac{11}{2}-\frac{5 i \sqrt{3}}{2}\right)}{14 \sqrt{-1-i \sqrt{3}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{2 \sqrt{-1-i \sqrt{3}}}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{3}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{3}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, x , -\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{5}}{2}+\frac{3}{4}-\frac{3 i \sqrt{3}}{4}, \frac{\sqrt{-\frac{3}{2}-\frac{\sqrt{5}}{2}}}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}}\right)}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{4}+\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(\frac{\arctanh \left(\frac{\left(-2-i \sqrt{3}\right) \left(7 x^{2}+\frac{11}{2}+\frac{5 i \sqrt{3}}{2}\right)}{14 \sqrt{-1+i \sqrt{3}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{2 \sqrt{-1+i \sqrt{3}}}-\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{3}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{3}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, x , -\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{5}}{2}+\frac{3}{4}+\frac{3 i \sqrt{3}}{4}, \frac{\sqrt{-\frac{3}{2}-\frac{\sqrt{5}}{2}}}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}}\right)}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{4}$&$1206$\\ \hline \end{longtable}"," ",0,"1/4*(x^4+3*x^2+1)^(1/2)/(x^2-x+1)+1/8*RootOf(_Z^2-2)*ln(-(-7*RootOf(_Z^2-2)*x^10-29*RootOf(_Z^2-2)*x^9+10*(x^4+3*x^2+1)^(1/2)*x^8-89*RootOf(_Z^2-2)*x^8+40*(x^4+3*x^2+1)^(1/2)*x^7-190*RootOf(_Z^2-2)*x^7+116*(x^4+3*x^2+1)^(1/2)*x^6-283*RootOf(_Z^2-2)*x^6+192*(x^4+3*x^2+1)^(1/2)*x^5-363*RootOf(_Z^2-2)*x^5+270*(x^4+3*x^2+1)^(1/2)*x^4-283*RootOf(_Z^2-2)*x^4+192*(x^4+3*x^2+1)^(1/2)*x^3-190*RootOf(_Z^2-2)*x^3+116*(x^4+3*x^2+1)^(1/2)*x^2-89*RootOf(_Z^2-2)*x^2+40*(x^4+3*x^2+1)^(1/2)*x-29*RootOf(_Z^2-2)*x+10*(x^4+3*x^2+1)^(1/2)-7*RootOf(_Z^2-2))/(x^2+x+1)/(x^2-x+1)^4)","C"
1557,0,0,87,0.013000," ","int((a*x^3+b)*(2*a*x^3+b)/x^6/(a*x^4+b*x)^(1/4),x)","\[\int \frac{\left(a \,x^{3}+b \right) \left(2 a \,x^{3}+b \right)}{x^{6} \left(a \,x^{4}+b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^3+b)*(2*a*x^3+b)/x^6/(a*x^4+b*x)^(1/4),x)","F"
1558,1,457,95,0.220000," ","int((a^3*x^3-b^3)/(a^3*x^3+b^3)/(a^4*x^4+b^4)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, i\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}+b^{4}}}-\frac{b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{2} \textit{\_Z}^{2}-a b \textit{\_Z} +b^{2}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha  a +2 b \right) \left(-\frac{\arctanh \left(\frac{\left(\underline{\hspace{1.25 ex}}\alpha  a -b \right) a b \left(a \,x^{2}-b \underline{\hspace{1.25 ex}}\alpha  \right)}{\sqrt{-b^{3} \left(\underline{\hspace{1.25 ex}}\alpha  a -b \right)}\, \sqrt{a^{4} x^{4}+b^{4}}}\right)}{\sqrt{-b^{3} \left(\underline{\hspace{1.25 ex}}\alpha  a -b \right)}}+\frac{2 a \left(\underline{\hspace{1.25 ex}}\alpha  a -b \right) \sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, \frac{i \underline{\hspace{1.25 ex}}\alpha  a}{b}, \frac{\sqrt{-\frac{i a^{2}}{b^{2}}}}{\sqrt{\frac{i a^{2}}{b^{2}}}}\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, b^{2} \sqrt{a^{4} x^{4}+b^{4}}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  a -b}\right)}{3 a}-\frac{2 b \left(-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 a^{2} b^{2} x^{2}+2 b^{4}\right) \sqrt{2}}{4 \sqrt{b^{4}}\, \sqrt{a^{4} x^{4}+b^{4}}}\right)}{4 \sqrt{b^{4}}}+\frac{a \sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, -i, \frac{\sqrt{-\frac{i a^{2}}{b^{2}}}}{\sqrt{\frac{i a^{2}}{b^{2}}}}\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, b \sqrt{a^{4} x^{4}+b^{4}}}\right)}{3 a}$&$457$\\ elliptic&$-\frac{a^{3} b^{5} \sqrt{2}\, \ln \left(\frac{\frac{b^{2} \left(a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}+\left(-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right) \left(x^{2}-\frac{-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{b^{2} \left(a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}\, \sqrt{4 \left(x^{2}-\frac{-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)^{2} a^{4}+4 \left(-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right) \left(x^{2}-\frac{-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)+\frac{2 b^{2} \left(a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}}{2}}{x^{2}-\frac{-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}}\right)}{\left(-3 a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right) \sqrt{-3 a^{4} b^{4}}\, \sqrt{\frac{b^{2} \left(a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}}+\frac{a \,b^{3} \sqrt{2}\, \ln \left(\frac{\frac{b^{2} \left(a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}+\left(-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right) \left(x^{2}-\frac{-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{b^{2} \left(a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}\, \sqrt{4 \left(x^{2}-\frac{-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)^{2} a^{4}+4 \left(-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right) \left(x^{2}-\frac{-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)+\frac{2 b^{2} \left(a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}}{2}}{x^{2}-\frac{-a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}}\right)}{\left(-3 a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right) \sqrt{\frac{b^{2} \left(a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}}-\frac{2 a^{3} b^{5} \sqrt{2}\, \ln \left(\frac{4 b^{4}+2 a^{2} b^{2} \left(x^{2}-\frac{b^{2}}{a^{2}}\right)+2 \sqrt{2}\, \sqrt{b^{4}}\, \sqrt{\left(x^{2}-\frac{b^{2}}{a^{2}}\right)^{2} a^{4}+2 a^{2} b^{2} \left(x^{2}-\frac{b^{2}}{a^{2}}\right)+2 b^{4}}}{x^{2}-\frac{b^{2}}{a^{2}}}\right)}{\left(-3 a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right) \left(3 a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right) \sqrt{b^{4}}}-\frac{a^{3} b^{5} \sqrt{2}\, \ln \left(\frac{\frac{b^{2} \left(a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}+\left(-a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right) \left(x^{2}+\frac{a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{b^{2} \left(a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}\, \sqrt{4 \left(x^{2}+\frac{a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)^{2} a^{4}+4 \left(-a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right) \left(x^{2}+\frac{a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)+\frac{2 b^{2} \left(a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}}{2}}{x^{2}+\frac{a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}}\right)}{\left(3 a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right) \sqrt{-3 a^{4} b^{4}}\, \sqrt{\frac{b^{2} \left(a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}}-\frac{a \,b^{3} \sqrt{2}\, \ln \left(\frac{\frac{b^{2} \left(a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}+\left(-a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right) \left(x^{2}+\frac{a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{b^{2} \left(a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}\, \sqrt{4 \left(x^{2}+\frac{a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)^{2} a^{4}+4 \left(-a^{2} b^{2}-\sqrt{-3 a^{4} b^{4}}\right) \left(x^{2}+\frac{a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}\right)+\frac{2 b^{2} \left(a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}}{2}}{x^{2}+\frac{a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}}{2 a^{4}}}\right)}{\left(3 a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right) \sqrt{\frac{b^{2} \left(a^{2} b^{2}+\sqrt{-3 a^{4} b^{4}}\right)}{a^{2}}}}+\frac{\left(-\frac{\ln \left(a b +\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{2 x}\right)}{6 a b}+\frac{2 \sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}+b^{4}}}{a b x}\right)}{3 a b}+\frac{\ln \left(-a b +\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{2 x}\right)}{6 a b}\right) \sqrt{2}}{2}$&$1539$\\ \hline \end{longtable}"," ",0,"1/(I*a^2/b^2)^(1/2)*(1-I*a^2/b^2*x^2)^(1/2)*(1+I*a^2/b^2*x^2)^(1/2)/(a^4*x^4+b^4)^(1/2)*EllipticF(x*(I*a^2/b^2)^(1/2),I)-1/3*b/a*sum((-_alpha*a+2*b)/(2*_alpha*a-b)*(-1/(-b^3*(_alpha*a-b))^(1/2)*arctanh((_alpha*a-b)*a*b*(a*x^2-_alpha*b)/(-b^3*(_alpha*a-b))^(1/2)/(a^4*x^4+b^4)^(1/2))+2/(I*a^2/b^2)^(1/2)*a*(_alpha*a-b)/b^2*(1-I*a^2/b^2*x^2)^(1/2)*(1+I*a^2/b^2*x^2)^(1/2)/(a^4*x^4+b^4)^(1/2)*EllipticPi(x*(I*a^2/b^2)^(1/2),I*_alpha*a/b,(-I*a^2/b^2)^(1/2)/(I*a^2/b^2)^(1/2))),_alpha=RootOf(_Z^2*a^2-_Z*a*b+b^2))-2/3*b/a*(-1/4*2^(1/2)/(b^4)^(1/2)*arctanh(1/4*(2*a^2*b^2*x^2+2*b^4)*2^(1/2)/(b^4)^(1/2)/(a^4*x^4+b^4)^(1/2))+1/(I*a^2/b^2)^(1/2)/b*a*(1-I*a^2/b^2*x^2)^(1/2)*(1+I*a^2/b^2*x^2)^(1/2)/(a^4*x^4+b^4)^(1/2)*EllipticPi(x*(I*a^2/b^2)^(1/2),-I,(-I*a^2/b^2)^(1/2)/(I*a^2/b^2)^(1/2)))","C"
1559,0,0,87,0.039000," ","int(x^4*(a*x^2-2*b)/(a*x^2-b)^2/(c*x^4+a*x^2-b)^(1/4),x)","\[\int \frac{x^{4} \left(a \,x^{2}-2 b \right)}{\left(a \,x^{2}-b \right)^{2} \left(c \,x^{4}+a \,x^{2}-b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(x^4*(a*x^2-2*b)/(a*x^2-b)^2/(c*x^4+a*x^2-b)^(1/4),x)","F"
1560,1,517,91,7.779000," ","int((x^2-2*x-1)*(x^2+2*x-1)/(x^4+x^3+2*x^2-x+1)/(x^5-x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(-\frac{130149507345815310 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{4}-542289613940897125 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-66362067078692233 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}+260299014691630620 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}-1421624873572223196 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{5}-x \right)^{\frac{1}{3}} x^{2}-1570891338664105235 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-1094963791801900343 x^{4}+542289613940897125 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x -2253715023870923763 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{5}-x \right)^{\frac{2}{3}}-132724134157384466 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-2253715023870923763 \left(x^{5}-x \right)^{\frac{1}{3}} x^{2}-345778039516389582 x^{3}+130149507345815310 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-1421624873572223196 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{5}-x \right)^{\frac{1}{3}}+1570891338664105235 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x -832090150298700567 \left(x^{5}-x \right)^{\frac{2}{3}}-2189927583603800686 x^{2}-66362067078692233 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2253715023870923763 \left(x^{5}-x \right)^{\frac{1}{3}}+345778039516389582 x -1094963791801900343}{x^{4}+x^{3}+2 x^{2}-x +1}\right)+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\frac{345778039516389582 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{4}-1440741831318289925 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+1570891338664105235 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}+691556079032779164 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}-832090150298700567 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{5}-x \right)^{\frac{1}{3}} x^{2}-1637253405742797468 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+542289613940897125 x^{4}+1440741831318289925 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x -2253715023870923763 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{5}-x \right)^{\frac{2}{3}}+3141782677328210470 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-2253715023870923763 \left(x^{5}-x \right)^{\frac{1}{3}} x^{2}-412140106595081815 x^{3}+345778039516389582 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-832090150298700567 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{5}-x \right)^{\frac{1}{3}}+1637253405742797468 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x -1421624873572223196 \left(x^{5}-x \right)^{\frac{2}{3}}+1084579227881794250 x^{2}+1570891338664105235 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2253715023870923763 \left(x^{5}-x \right)^{\frac{1}{3}}+412140106595081815 x +542289613940897125}{x^{4}+x^{3}+2 x^{2}-x +1}\right)$&$517$\\ \hline \end{longtable}"," ",0,"ln(-(130149507345815310*RootOf(_Z^2+_Z+1)^2*x^4-542289613940897125*RootOf(_Z^2+_Z+1)^2*x^3-66362067078692233*RootOf(_Z^2+_Z+1)*x^4+260299014691630620*RootOf(_Z^2+_Z+1)^2*x^2-1421624873572223196*RootOf(_Z^2+_Z+1)*(x^5-x)^(1/3)*x^2-1570891338664105235*RootOf(_Z^2+_Z+1)*x^3-1094963791801900343*x^4+542289613940897125*RootOf(_Z^2+_Z+1)^2*x-2253715023870923763*RootOf(_Z^2+_Z+1)*(x^5-x)^(2/3)-132724134157384466*RootOf(_Z^2+_Z+1)*x^2-2253715023870923763*(x^5-x)^(1/3)*x^2-345778039516389582*x^3+130149507345815310*RootOf(_Z^2+_Z+1)^2-1421624873572223196*RootOf(_Z^2+_Z+1)*(x^5-x)^(1/3)+1570891338664105235*RootOf(_Z^2+_Z+1)*x-832090150298700567*(x^5-x)^(2/3)-2189927583603800686*x^2-66362067078692233*RootOf(_Z^2+_Z+1)-2253715023870923763*(x^5-x)^(1/3)+345778039516389582*x-1094963791801900343)/(x^4+x^3+2*x^2-x+1))+RootOf(_Z^2+_Z+1)*ln((345778039516389582*RootOf(_Z^2+_Z+1)^2*x^4-1440741831318289925*RootOf(_Z^2+_Z+1)^2*x^3+1570891338664105235*RootOf(_Z^2+_Z+1)*x^4+691556079032779164*RootOf(_Z^2+_Z+1)^2*x^2-832090150298700567*RootOf(_Z^2+_Z+1)*(x^5-x)^(1/3)*x^2-1637253405742797468*RootOf(_Z^2+_Z+1)*x^3+542289613940897125*x^4+1440741831318289925*RootOf(_Z^2+_Z+1)^2*x-2253715023870923763*RootOf(_Z^2+_Z+1)*(x^5-x)^(2/3)+3141782677328210470*RootOf(_Z^2+_Z+1)*x^2-2253715023870923763*(x^5-x)^(1/3)*x^2-412140106595081815*x^3+345778039516389582*RootOf(_Z^2+_Z+1)^2-832090150298700567*RootOf(_Z^2+_Z+1)*(x^5-x)^(1/3)+1637253405742797468*RootOf(_Z^2+_Z+1)*x-1421624873572223196*(x^5-x)^(2/3)+1084579227881794250*x^2+1570891338664105235*RootOf(_Z^2+_Z+1)-2253715023870923763*(x^5-x)^(1/3)+412140106595081815*x+542289613940897125)/(x^4+x^3+2*x^2-x+1))","C"
1561,0,0,87,0.010000," ","int((x^6-a*x^3-b)/x^6/(a*x^4+b*x)^(1/4),x)","\[\int \frac{x^{6}-a \,x^{3}-b}{x^{6} \left(a \,x^{4}+b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((x^6-a*x^3-b)/x^6/(a*x^4+b*x)^(1/4),x)","F"
1562,0,0,14,0.043000," ","int(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6-b),x)","\[\int \frac{1}{\left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}} \left(a^{6} x^{6}-b \right)}\, dx\]"," ",0,"int(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6-b),x)","F"
1563,0,0,14,0.001000," ","int(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6-b),x)","\[\int \frac{1}{\left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}} \left(a^{6} x^{6}-b \right)}\, dx\]"," ",0,"int(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6-b),x)","F"
1564,0,0,14,0.046000," ","int(1/(a^3*x^3+b^2*x^2)^(1/3)/(2*a^6*x^6-b),x)","\[\int \frac{1}{\left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}} \left(2 a^{6} x^{6}-b \right)}\, dx\]"," ",0,"int(1/(a^3*x^3+b^2*x^2)^(1/3)/(2*a^6*x^6-b),x)","F"
1565,0,0,14,0.001000," ","int(1/(a^3*x^3+b^2*x^2)^(1/3)/(2*a^6*x^6-b),x)","\[\int \frac{1}{\left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}} \left(2 a^{6} x^{6}-b \right)}\, dx\]"," ",0,"int(1/(a^3*x^3+b^2*x^2)^(1/3)/(2*a^6*x^6-b),x)","F"
1566,0,0,14,0.042000," ","int(1/(a^3*x^3+b^2*x^2)^(1/3)/(2*a^6*x^6+b),x)","\[\int \frac{1}{\left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}} \left(2 a^{6} x^{6}+b \right)}\, dx\]"," ",0,"int(1/(a^3*x^3+b^2*x^2)^(1/3)/(2*a^6*x^6+b),x)","F"
1567,0,0,14,0.001000," ","int(1/(a^3*x^3+b^2*x^2)^(1/3)/(2*a^6*x^6+b),x)","\[\int \frac{1}{\left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}} \left(2 a^{6} x^{6}+b \right)}\, dx\]"," ",0,"int(1/(a^3*x^3+b^2*x^2)^(1/3)/(2*a^6*x^6+b),x)","F"
1568,1,368,89,3.249000," ","int(x^4*(x^3-4)/(x^3-1)^(1/4)/(x^8-x^6+2*x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(\frac{2 \left(x^{3}-1\right)^{\frac{3}{4}} x -2 x^{2} \sqrt{x^{3}-1}+2 \left(x^{3}-1\right)^{\frac{1}{4}} x^{3}-x^{4}-x^{3}+1}{x^{4}-x^{3}+1}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(-\frac{2 \sqrt{x^{3}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}-2 \left(x^{3}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{4}+1\right) x^{4}-\RootOf \left(\textit{\_Z}^{4}+1\right) x^{3}+2 \left(x^{3}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}+1\right)}{x^{4}+x^{3}-1}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{4}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{3}-2 \left(x^{3}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}+2 \sqrt{x^{3}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right) x^{2}-2 \left(x^{3}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{x^{4}+x^{3}-1}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} \sqrt{x^{3}-1}\, x^{2}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{4}-x^{3} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+2 \left(x^{3}-1\right)^{\frac{3}{4}} x -2 \left(x^{3}-1\right)^{\frac{1}{4}} x^{3}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{2}}{x^{4}-x^{3}+1}\right)}{2}$&$368$\\ \hline \end{longtable}"," ",0,"1/2*ln((2*(x^3-1)^(3/4)*x-2*x^2*(x^3-1)^(1/2)+2*(x^3-1)^(1/4)*x^3-x^4-x^3+1)/(x^4-x^3+1))-1/2*RootOf(_Z^4+1)*ln(-(2*(x^3-1)^(1/2)*RootOf(_Z^4+1)^3*x^2-2*(x^3-1)^(1/4)*RootOf(_Z^4+1)^2*x^3+RootOf(_Z^4+1)*x^4-RootOf(_Z^4+1)*x^3+2*(x^3-1)^(3/4)*x+RootOf(_Z^4+1))/(x^4+x^3-1))+1/2*RootOf(_Z^4+1)^3*ln((RootOf(_Z^4+1)^3*x^4-RootOf(_Z^4+1)^3*x^3-2*(x^3-1)^(1/4)*RootOf(_Z^4+1)^2*x^3+2*(x^3-1)^(1/2)*RootOf(_Z^4+1)*x^2-2*(x^3-1)^(3/4)*x+RootOf(_Z^4+1)^3)/(x^4+x^3-1))+1/2*RootOf(_Z^4+1)^2*ln((2*RootOf(_Z^4+1)^2*(x^3-1)^(1/2)*x^2-RootOf(_Z^4+1)^2*x^4-x^3*RootOf(_Z^4+1)^2+2*(x^3-1)^(3/4)*x-2*(x^3-1)^(1/4)*x^3+RootOf(_Z^4+1)^2)/(x^4-x^3+1))","C"
1569,0,0,79,0.046000," ","int(x^6/(a*x^4+b)^(3/4)/(a^2*x^8-b^2),x)","\[\int \frac{x^{6}}{\left(a \,x^{4}+b \right)^{\frac{3}{4}} \left(a^{2} x^{8}-b^{2}\right)}\, dx\]"," ",0,"int(x^6/(a*x^4+b)^(3/4)/(a^2*x^8-b^2),x)","F"
1570,0,0,81,0.032000," ","int((a*x^2-b^2)*(b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2),x)","\[\int \frac{\left(a \,x^{2}-b^{2}\right) \sqrt{b +\sqrt{a \,x^{2}+b^{2}}}}{a \,x^{2}+b^{2}}\, dx\]"," ",0,"int((a*x^2-b^2)*(b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2),x)","F"
1571,1,15,86,1.040000," ","int((x^3+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 x^{\frac{5}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{5}{3}\right], \left[\frac{8}{3}\right], -x \right)}{5}$&$15$\\ risch&$\frac{\left(1+3 x \right) \left(x^{2} \left(1+x \right)\right)^{\frac{1}{3}}}{6}+\frac{\left(\frac{\ln \left(-\frac{x^{2} \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)^{2}+48 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{2}{3}}-30 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}} x -16 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)^{2}-30 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}}-14 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) x +36 \left(x^{3}+2 x^{2}+x \right)^{\frac{2}{3}}-96 \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}} x +64 x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)-96 \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}}+112 x +48}{1+x}\right)}{9}+\frac{\RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \ln \left(-\frac{2 x^{2} \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)^{2}-24 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{2}{3}}+9 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}} x +19 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)^{2}+9 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}}+28 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) x -30 \left(x^{3}+2 x^{2}+x \right)^{\frac{2}{3}}+48 \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}} x -10 x^{2}+9 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)+48 \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}}-14 x -4}{1+x}\right)}{18}\right) \left(x^{2} \left(1+x \right)\right)^{\frac{1}{3}} \left(\left(1+x \right)^{2} x \right)^{\frac{1}{3}}}{x \left(1+x \right)}$&$452$\\ trager&$\left(\frac{1}{6}+\frac{x}{2}\right) \left(x^{3}+x^{2}\right)^{\frac{1}{3}}+\frac{\RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(\frac{-36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}+45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{2}{3}}+45 \left(x^{3}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x +36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x +33 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+24 \left(x^{3}+x^{2}\right)^{\frac{2}{3}}+24 x \left(x^{3}+x^{2}\right)^{\frac{1}{3}}+51 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x +20 x^{2}+15 x}{x}\right)}{3}-\frac{\ln \left(-\frac{36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}+45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{2}{3}}+45 \left(x^{3}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x +57 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}-9 \left(x^{3}+x^{2}\right)^{\frac{2}{3}}-9 x \left(x^{3}+x^{2}\right)^{\frac{1}{3}}+27 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -5 x^{2}-2 x}{x}\right)}{9}-\frac{\ln \left(-\frac{36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}+45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{2}{3}}+45 \left(x^{3}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x +57 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}-9 \left(x^{3}+x^{2}\right)^{\frac{2}{3}}-9 x \left(x^{3}+x^{2}\right)^{\frac{1}{3}}+27 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -5 x^{2}-2 x}{x}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{3}$&$485$\\ \hline \end{longtable}"," ",0,"3/5*x^(5/3)*hypergeom([-1/3,5/3],[8/3],-x)","C"
1572,1,368,98,0.183000," ","int((k^3*x^3-1)/((1-x)*x*(-k^2*x+1))^(1/2)/(k^3*x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{4 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{3 k^{3} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}+\frac{4 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(k^{2} \textit{\_Z}^{2}-k \textit{\_Z} +1\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha  k +2\right) \left(\underline{\hspace{1.25 ex}}\alpha  \,k^{2}-k +1\right) \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{\underline{\hspace{1.25 ex}}\alpha  \,k^{2}-k +1}{k^{2}-k +1}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(2 \underline{\hspace{1.25 ex}}\alpha  k -1\right) \left(k^{2}-k +1\right) \sqrt{x \left(k^{2} x^{2}-k^{2} x -x +1\right)}}\right)}{3 k}$&$368$\\ elliptic&$-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+1\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{3 k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+1\right)}+\frac{4 k^{2} \sqrt{-k^{2} x +1}\, \sqrt{-\frac{\left(-1+x \right) k^{2}}{k^{2}-1}}\, \sqrt{k^{2} x}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(k^{2} \textit{\_Z}^{2}-k \textit{\_Z} +1\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-k^{2} x +1}, \frac{\underline{\hspace{1.25 ex}}\alpha  \,k^{2}-k +1}{k^{2}-k +1}, \sqrt{-\frac{1}{k^{2}-1}}\right) \underline{\hspace{1.25 ex}}\alpha^{2}}{2 \underline{\hspace{1.25 ex}}\alpha  k -1}\right)}{3 \left(k^{2}-k +1\right) \sqrt{x \left(k^{2} x^{2}-k^{2} x -x +1\right)}}-\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{\left(-1+x \right) k^{2}}{k^{2}-1}}\, \sqrt{k^{2} x}\, k \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(k^{2} \textit{\_Z}^{2}-k \textit{\_Z} +1\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-k^{2} x +1}, \frac{\underline{\hspace{1.25 ex}}\alpha  \,k^{2}-k +1}{k^{2}-k +1}, \sqrt{-\frac{1}{k^{2}-1}}\right) \underline{\hspace{1.25 ex}}\alpha }{2 \underline{\hspace{1.25 ex}}\alpha  k -1}\right)}{\left(k^{2}-k +1\right) \sqrt{x \left(k^{2} x^{2}-k^{2} x -x +1\right)}}+\frac{4 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{\left(-1+x \right) k^{2}}{k^{2}-1}}\, \sqrt{k^{2} x}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(k^{2} \textit{\_Z}^{2}-k \textit{\_Z} +1\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-k^{2} x +1}, \frac{\underline{\hspace{1.25 ex}}\alpha  \,k^{2}-k +1}{k^{2}-k +1}, \sqrt{-\frac{1}{k^{2}-1}}\right) \underline{\hspace{1.25 ex}}\alpha }{2 \underline{\hspace{1.25 ex}}\alpha  k -1}\right)}{3 \left(k^{2}-k +1\right) \sqrt{x \left(k^{2} x^{2}-k^{2} x -x +1\right)}}+\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{\left(-1+x \right) k^{2}}{k^{2}-1}}\, \sqrt{k^{2} x}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(k^{2} \textit{\_Z}^{2}-k \textit{\_Z} +1\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-k^{2} x +1}, \frac{\underline{\hspace{1.25 ex}}\alpha  \,k^{2}-k +1}{k^{2}-k +1}, \sqrt{-\frac{1}{k^{2}-1}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  k -1}\right)}{3 \left(k^{2}-k +1\right) \sqrt{x \left(k^{2} x^{2}-k^{2} x -x +1\right)}}-\frac{8 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{\left(-1+x \right) k^{2}}{k^{2}-1}}\, \sqrt{k^{2} x}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(k^{2} \textit{\_Z}^{2}-k \textit{\_Z} +1\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-k^{2} x +1}, \frac{\underline{\hspace{1.25 ex}}\alpha  \,k^{2}-k +1}{k^{2}-k +1}, \sqrt{-\frac{1}{k^{2}-1}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  k -1}\right)}{3 k \left(k^{2}-k +1\right) \sqrt{x \left(k^{2} x^{2}-k^{2} x -x +1\right)}}$&$907$\\ \hline \end{longtable}"," ",0,"-2/k^2*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticF((-(x-1/k^2)*k^2)^(1/2),(1/k^2/(1/k^2-1))^(1/2))+4/3/k^3*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/k)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+1/k),(1/k^2/(1/k^2-1))^(1/2))+4/3/k*sum((-_alpha*k+2)/(2*_alpha*k-1)*(_alpha*k^2-k+1)/(k^2-k+1)*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(x*(k^2*x^2-k^2*x-x+1))^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),(_alpha*k^2-k+1)/(k^2-k+1),(1/k^2/(1/k^2-1))^(1/2)),_alpha=RootOf(_Z^2*k^2-_Z*k+1))","C"
1573,0,0,11,0.028000," ","int((a*x^2+b)/(x^4+a*x^2+b)/(a*x^4-b*x^2)^(1/4),x)","\[\int \frac{a \,x^{2}+b}{\left(x^{4}+a \,x^{2}+b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2+b)/(x^4+a*x^2+b)/(a*x^4-b*x^2)^(1/4),x)","F"
1574,0,0,11,0.001000," ","int((a*x^2+b)/(x^4+a*x^2+b)/(a*x^4-b*x^2)^(1/4),x)","\[\int \frac{a \,x^{2}+b}{\left(x^{4}+a \,x^{2}+b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2+b)/(x^4+a*x^2+b)/(a*x^4-b*x^2)^(1/4),x)","F"
1575,1,174,100,0.137000," ","int((c*k^2*x^4+b*x^2+c)/((-x^2+1)*(-k^2*x^2+1))^(1/2)/(k^2*x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{c \sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticF \left(x , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}+\frac{\left(-2 c k +b \right) \sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticPi \left(x , -k , k\right)}{2 k \sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}-\frac{\left(2 c k +b \right) \sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticPi \left(x , k , k\right)}{2 k \sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}$&$174$\\ elliptic&$\frac{\left(\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)}}{x \left(-1+k \right)}\right) c}{-2+2 k}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)}}{x \left(-1+k \right)}\right) b}{4 k \left(-1+k \right)}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)}}{x \left(1+k \right)}\right) c}{2+2 k}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)}}{x \left(1+k \right)}\right) b}{4 k \left(1+k \right)}\right) \sqrt{2}}{2}$&$177$\\ \hline \end{longtable}"," ",0,"c*(-x^2+1)^(1/2)*(-k^2*x^2+1)^(1/2)/(k^2*x^4-k^2*x^2-x^2+1)^(1/2)*EllipticF(x,k)+1/2*(-2*c*k+b)/k*(-x^2+1)^(1/2)*(-k^2*x^2+1)^(1/2)/(k^2*x^4-k^2*x^2-x^2+1)^(1/2)*EllipticPi(x,-k,k)-1/2*(2*c*k+b)/k*(-x^2+1)^(1/2)*(-k^2*x^2+1)^(1/2)/(k^2*x^4-k^2*x^2-x^2+1)^(1/2)*EllipticPi(x,k,k)","C"
1576,0,0,92,0.028000," ","int((a*x^4+3*b)/(a*x^4+x^3-b)/(a*x^5-b*x)^(1/4),x)","\[\int \frac{a \,x^{4}+3 b}{\left(a \,x^{4}+x^{3}-b \right) \left(a \,x^{5}-b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^4+3*b)/(a*x^4+x^3-b)/(a*x^5-b*x)^(1/4),x)","F"
1577,1,42,86,1.663000," ","int((x^6-1)/x^6/(x^3+x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 \left(\frac{9}{5} x^{4}-\frac{6}{5} x^{2}+1\right) \left(x^{2}+1\right)^{\frac{2}{3}}}{16 x^{\frac{16}{3}}}+\frac{3 x^{\frac{2}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{2}\right)}{2}$&$42$\\ risch&$\frac{-\frac{3}{80} x^{2}+\frac{3}{16}+\frac{9}{80} x^{4}+\frac{27}{80} x^{6}}{x^{5} \left(x \left(x^{2}+1\right)\right)^{\frac{1}{3}}}+\frac{3 x^{\frac{2}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{2}\right)}{2}$&$49$\\ trager&$\frac{3 \left(x^{3}+x \right)^{\frac{2}{3}} \left(9 x^{4}-6 x^{2}+5\right)}{80 x^{6}}+\frac{\ln \left(180 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{2}+144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}+144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x +114 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}-180 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2}-9 \left(x^{3}+x \right)^{\frac{2}{3}}-9 x \left(x^{3}+x \right)^{\frac{1}{3}}-4 x^{2}+96 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)-3\right)}{2}-3 \ln \left(180 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{2}+144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}+144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x +114 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}-180 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2}-9 \left(x^{3}+x \right)^{\frac{2}{3}}-9 x \left(x^{3}+x \right)^{\frac{1}{3}}-4 x^{2}+96 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)-3\right) \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)+3 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \ln \left(180 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{2}-144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}-144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x -174 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}-180 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2}+15 \left(x^{3}+x \right)^{\frac{2}{3}}+15 x \left(x^{3}+x \right)^{\frac{1}{3}}+20 x^{2}-36 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)+8\right)$&$444$\\ \hline \end{longtable}"," ",0,"3/16/x^(16/3)*(9/5*x^4-6/5*x^2+1)*(x^2+1)^(2/3)+3/2*x^(2/3)*hypergeom([1/3,1/3],[4/3],-x^2)","C"
1578,1,59,86,2.994000," ","int((x^3-1)^(2/3)*(x^6+2)/x^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{5 x^{9}+x^{6}-12 x^{3}+6}{15 x^{5} \left(x^{3}-1\right)^{\frac{1}{3}}}-\frac{2 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{3}\right)}{3 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}}}$&$59$\\ meijerg&$\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}} x \hypergeom \left(\left[-\frac{2}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{3}\right)}{\left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}}}-\frac{2 \mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}} \left(-x^{3}+1\right)^{\frac{5}{3}}}{5 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} x^{5}}$&$63$\\ trager&$\frac{\left(x^{3}-1\right)^{\frac{2}{3}} \left(5 x^{6}+6 x^{3}-6\right)}{15 x^{5}}+\frac{64 \RootOf \left(1024 \textit{\_Z}^{2}+32 \textit{\_Z} +1\right) \ln \left(11665390592 \RootOf \left(1024 \textit{\_Z}^{2}+32 \textit{\_Z} +1\right)^{2} x^{3}-6206811648 \RootOf \left(1024 \textit{\_Z}^{2}+32 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -6206811648 \RootOf \left(1024 \textit{\_Z}^{2}+32 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-5842268192 \RootOf \left(1024 \textit{\_Z}^{2}+32 \textit{\_Z} +1\right) x^{3}-1508552373 x \left(x^{3}-1\right)^{\frac{2}{3}}-1508552373 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-1497160390 x^{3}-93323124736 \RootOf \left(1024 \textit{\_Z}^{2}+32 \textit{\_Z} +1\right)^{2}-14869698528 \RootOf \left(1024 \textit{\_Z}^{2}+32 \textit{\_Z} +1\right)+476369215\right)}{9}-\frac{2 \ln \left(11665390592 \RootOf \left(1024 \textit{\_Z}^{2}+32 \textit{\_Z} +1\right)^{2} x^{3}+6206811648 \RootOf \left(1024 \textit{\_Z}^{2}+32 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +6206811648 \RootOf \left(1024 \textit{\_Z}^{2}+32 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+6571355104 \RootOf \left(1024 \textit{\_Z}^{2}+32 \textit{\_Z} +1\right) x^{3}-1314589509 x \left(x^{3}-1\right)^{\frac{2}{3}}-1314589509 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-1303197526 x^{3}-93323124736 \RootOf \left(1024 \textit{\_Z}^{2}+32 \textit{\_Z} +1\right)^{2}+9037003232 \RootOf \left(1024 \textit{\_Z}^{2}+32 \textit{\_Z} +1\right)+849911430\right)}{9}-\frac{64 \ln \left(11665390592 \RootOf \left(1024 \textit{\_Z}^{2}+32 \textit{\_Z} +1\right)^{2} x^{3}+6206811648 \RootOf \left(1024 \textit{\_Z}^{2}+32 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +6206811648 \RootOf \left(1024 \textit{\_Z}^{2}+32 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+6571355104 \RootOf \left(1024 \textit{\_Z}^{2}+32 \textit{\_Z} +1\right) x^{3}-1314589509 x \left(x^{3}-1\right)^{\frac{2}{3}}-1314589509 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-1303197526 x^{3}-93323124736 \RootOf \left(1024 \textit{\_Z}^{2}+32 \textit{\_Z} +1\right)^{2}+9037003232 \RootOf \left(1024 \textit{\_Z}^{2}+32 \textit{\_Z} +1\right)+849911430\right) \RootOf \left(1024 \textit{\_Z}^{2}+32 \textit{\_Z} +1\right)}{9}$&$462$\\ \hline \end{longtable}"," ",0,"1/15*(5*x^9+x^6-12*x^3+6)/x^5/(x^3-1)^(1/3)-2/3/signum(x^3-1)^(1/3)*(-signum(x^3-1))^(1/3)*x*hypergeom([1/3,1/3],[4/3],x^3)","C"
1579,1,61,86,2.994000," ","int((x^3-1)^(2/3)*(x^6+x^3-2)/x^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{10 x^{9}-37 x^{6}+39 x^{3}-12}{30 x^{5} \left(x^{3}-1\right)^{\frac{1}{3}}}+\frac{\left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{3}\right)}{3 \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}}}$&$61$\\ meijerg&$\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}} x \hypergeom \left(\left[-\frac{2}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{3}\right)}{\left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}}}-\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}} \hypergeom \left(\left[-\frac{2}{3}, -\frac{2}{3}\right], \left[\frac{1}{3}\right], x^{3}\right)}{2 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} x^{2}}+\frac{2 \mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}} \left(-x^{3}+1\right)^{\frac{5}{3}}}{5 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} x^{5}}$&$95$\\ trager&$\frac{\left(x^{3}-1\right)^{\frac{2}{3}} \left(10 x^{6}-27 x^{3}+12\right)}{30 x^{5}}+\frac{32 \RootOf \left(1024 \textit{\_Z}^{2}-32 \textit{\_Z} +1\right) \ln \left(11665390592 \RootOf \left(1024 \textit{\_Z}^{2}-32 \textit{\_Z} +1\right)^{2} x^{3}+6206811648 \RootOf \left(1024 \textit{\_Z}^{2}-32 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +6206811648 \RootOf \left(1024 \textit{\_Z}^{2}-32 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+5842268192 \RootOf \left(1024 \textit{\_Z}^{2}-32 \textit{\_Z} +1\right) x^{3}-1508552373 x \left(x^{3}-1\right)^{\frac{2}{3}}-1508552373 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-1497160390 x^{3}-93323124736 \RootOf \left(1024 \textit{\_Z}^{2}-32 \textit{\_Z} +1\right)^{2}+14869698528 \RootOf \left(1024 \textit{\_Z}^{2}-32 \textit{\_Z} +1\right)+476369215\right)}{9}+\frac{\ln \left(11665390592 \RootOf \left(1024 \textit{\_Z}^{2}-32 \textit{\_Z} +1\right)^{2} x^{3}-6206811648 \RootOf \left(1024 \textit{\_Z}^{2}-32 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -6206811648 \RootOf \left(1024 \textit{\_Z}^{2}-32 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-6571355104 \RootOf \left(1024 \textit{\_Z}^{2}-32 \textit{\_Z} +1\right) x^{3}-1314589509 x \left(x^{3}-1\right)^{\frac{2}{3}}-1314589509 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-1303197526 x^{3}-93323124736 \RootOf \left(1024 \textit{\_Z}^{2}-32 \textit{\_Z} +1\right)^{2}-9037003232 \RootOf \left(1024 \textit{\_Z}^{2}-32 \textit{\_Z} +1\right)+849911430\right)}{9}-\frac{32 \ln \left(11665390592 \RootOf \left(1024 \textit{\_Z}^{2}-32 \textit{\_Z} +1\right)^{2} x^{3}-6206811648 \RootOf \left(1024 \textit{\_Z}^{2}-32 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -6206811648 \RootOf \left(1024 \textit{\_Z}^{2}-32 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-6571355104 \RootOf \left(1024 \textit{\_Z}^{2}-32 \textit{\_Z} +1\right) x^{3}-1314589509 x \left(x^{3}-1\right)^{\frac{2}{3}}-1314589509 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-1303197526 x^{3}-93323124736 \RootOf \left(1024 \textit{\_Z}^{2}-32 \textit{\_Z} +1\right)^{2}-9037003232 \RootOf \left(1024 \textit{\_Z}^{2}-32 \textit{\_Z} +1\right)+849911430\right) \RootOf \left(1024 \textit{\_Z}^{2}-32 \textit{\_Z} +1\right)}{9}$&$462$\\ \hline \end{longtable}"," ",0,"1/30*(10*x^9-37*x^6+39*x^3-12)/x^5/(x^3-1)^(1/3)+1/3/signum(x^3-1)^(1/3)*(-signum(x^3-1))^(1/3)*x*hypergeom([1/3,1/3],[4/3],x^3)","C"
1580,1,28,86,2.976000," ","int((x^3+1)^(2/3)*(2*x^6+1)/x^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$2 x \hypergeom \left(\left[-\frac{2}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{3}\right)-\frac{\left(x^{3}+1\right)^{\frac{5}{3}}}{5 x^{5}}$&$28$\\ risch&$\frac{10 x^{9}+7 x^{6}-6 x^{3}-3}{15 x^{5} \left(x^{3}+1\right)^{\frac{1}{3}}}+\frac{4 x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{3}\right)}{3}$&$45$\\ trager&$\frac{\left(x^{3}+1\right)^{\frac{2}{3}} \left(10 x^{6}-3 x^{3}-3\right)}{15 x^{5}}-\frac{4 \ln \left(317 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-555 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +2358 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-2120 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-1803 x \left(x^{3}+1\right)^{\frac{2}{3}}-555 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}+2675 x^{3}-317 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}-99 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+1070\right)}{9}+\frac{4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(-535 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+555 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x +1803 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-1823 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-2358 x \left(x^{3}+1\right)^{\frac{2}{3}}+555 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}+1268 x^{3}+535 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}-1922 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+951\right)}{9}$&$287$\\ \hline \end{longtable}"," ",0,"2*x*hypergeom([-2/3,1/3],[4/3],-x^3)-1/5*(x^3+1)^(5/3)/x^5","C"
1581,0,0,92,0.029000," ","int((2*a*x^5+3*b)/(a*x^5+x^3-b)/(a*x^6-b*x)^(1/4),x)","\[\int \frac{2 a \,x^{5}+3 b}{\left(a \,x^{5}+x^{3}-b \right) \left(a \,x^{6}-b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((2*a*x^5+3*b)/(a*x^5+x^3-b)/(a*x^6-b*x)^(1/4),x)","F"
1582,1,15605,31,32.464000," ","int((x^4-1)^(1/4)*(x^8+x^4+1)/x^6/(2*x^8-1),x)","\[\text{output too large to display}\]"," ",0,"result too large to display","B"
1583,1,15604,31,32.385000," ","int((x^4-1)^(1/4)*(x^8+x^4+1)/x^6/(2*x^8-1),x)","\[\text{output too large to display}\]"," ",0,"result too large to display","B"
1584,0,0,94,0.047000," ","int((a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x)","\[\int \frac{\sqrt{a^{2} x^{2}-b x}}{\left(a \,x^{2}+x \sqrt{a^{2} x^{2}-b x}\right)^{\frac{3}{2}}}\, dx\]"," ",0,"int((a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x)","F"
1585,1,33,87,1.703000," ","int(x^7*(x^3-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} x^{8} \hypergeom \left(\left[-\frac{1}{3}, \frac{8}{3}\right], \left[\frac{11}{3}\right], x^{3}\right)}{8 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}}}$&$33$\\ risch&$\frac{x^{2} \left(18 x^{6}-3 x^{3}-5\right) \left(x^{3}-1\right)^{\frac{1}{3}}}{162}-\frac{5 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} x^{2} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], x^{3}\right)}{162 \mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}}}$&$58$\\ trager&$\frac{x^{2} \left(18 x^{6}-3 x^{3}-5\right) \left(x^{3}-1\right)^{\frac{1}{3}}}{162}+\frac{5 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1\right)}{243}-\frac{5 \ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}-1\right)^{\frac{2}{3}}+3 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}+4 x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{243}-\frac{5 \ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}-1\right)^{\frac{2}{3}}+3 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}+4 x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2\right)}{243}$&$320$\\ \hline \end{longtable}"," ",0,"1/8*signum(x^3-1)^(1/3)/(-signum(x^3-1))^(1/3)*x^8*hypergeom([-1/3,8/3],[11/3],x^3)","C"
1586,1,17,87,1.824000," ","int(x^7*(x^3+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{x^{8} \hypergeom \left(\left[-\frac{1}{3}, \frac{8}{3}\right], \left[\frac{11}{3}\right], -x^{3}\right)}{8}$&$17$\\ risch&$\frac{x^{2} \left(18 x^{6}+3 x^{3}-5\right) \left(x^{3}+1\right)^{\frac{1}{3}}}{162}+\frac{5 x^{2} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], -x^{3}\right)}{162}$&$42$\\ trager&$\frac{x^{2} \left(18 x^{6}+3 x^{3}-5\right) \left(x^{3}+1\right)^{\frac{1}{3}}}{162}-\frac{5 \ln \left(-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}} x -\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-3 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}+x^{3}-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+1\right)}{243}+\frac{5 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+3 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-5 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}+1\right)^{\frac{2}{3}}-3 x^{2} \left(x^{3}+1\right)^{\frac{1}{3}}+2 x^{3}-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+1\right)}{243}$&$209$\\ \hline \end{longtable}"," ",0,"1/8*x^8*hypergeom([-1/3,8/3],[11/3],-x^3)","C"
1587,1,101,87,3.045000," ","int((x^3-1)^(1/3)*(x^3+1)/x^13,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{50 x^{12}-20 x^{9}-129 x^{6}+18 x^{3}+81}{972 x^{12} \left(x^{3}-1\right)^{\frac{2}{3}}}+\frac{25 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} \left(\frac{2 \Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 2\right], x^{3}\right)}{3}+\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{2}{3}\right)\right)}{729 \Gamma \left(\frac{2}{3}\right) \mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}}}$&$101$\\ meijerg&$\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \left(-\frac{10 \Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{11}{3}\right], \left[2, 5\right], x^{3}\right)}{81}-\frac{5 \left(\frac{4}{15}+\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{2}{3}\right)}{27}-\frac{\Gamma \left(\frac{2}{3}\right)}{x^{9}}+\frac{\Gamma \left(\frac{2}{3}\right)}{2 x^{6}}+\frac{\Gamma \left(\frac{2}{3}\right)}{3 x^{3}}\right)}{9 \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}}}-\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} \left(\frac{22 \Gamma \left(\frac{2}{3}\right) x^{3} \hypergeom \left(\left[1, 1, \frac{14}{3}\right], \left[2, 6\right], x^{3}\right)}{243}+\frac{10 \left(\frac{47}{120}+\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)+i \pi \right) \Gamma \left(\frac{2}{3}\right)}{81}+\frac{3 \Gamma \left(\frac{2}{3}\right)}{4 x^{12}}-\frac{\Gamma \left(\frac{2}{3}\right)}{3 x^{9}}-\frac{\Gamma \left(\frac{2}{3}\right)}{6 x^{6}}-\frac{5 \Gamma \left(\frac{2}{3}\right)}{27 x^{3}}\right)}{9 \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}}}$&$185$\\ trager&$\frac{\left(x^{3}-1\right)^{\frac{1}{3}} \left(50 x^{9}+30 x^{6}-99 x^{3}-81\right)}{972 x^{12}}+\frac{102400 \RootOf \left(16777216 \textit{\_Z}^{2}+4096 \textit{\_Z} +1\right) \ln \left(-\frac{24125636608 \RootOf \left(16777216 \textit{\_Z}^{2}+4096 \textit{\_Z} +1\right)^{2} x^{3}-28585984 \RootOf \left(16777216 \textit{\_Z}^{2}+4096 \textit{\_Z} +1\right) x^{3}+22536192 \RootOf \left(16777216 \textit{\_Z}^{2}+4096 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}-9894 x^{3}-193005092864 \RootOf \left(16777216 \textit{\_Z}^{2}+4096 \textit{\_Z} +1\right)^{2}-22536192 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(16777216 \textit{\_Z}^{2}+4096 \textit{\_Z} +1\right)+19749 \left(x^{3}-1\right)^{\frac{2}{3}}-24584192 \RootOf \left(16777216 \textit{\_Z}^{2}+4096 \textit{\_Z} +1\right)-19749 \left(x^{3}-1\right)^{\frac{1}{3}}+8245}{x^{3}}\right)}{729}-\frac{25 \ln \left(-\frac{24125636608 \RootOf \left(16777216 \textit{\_Z}^{2}+4096 \textit{\_Z} +1\right)^{2} x^{3}+40366080 \RootOf \left(16777216 \textit{\_Z}^{2}+4096 \textit{\_Z} +1\right) x^{3}-22536192 \RootOf \left(16777216 \textit{\_Z}^{2}+4096 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}-1477 x^{3}-193005092864 \RootOf \left(16777216 \textit{\_Z}^{2}+4096 \textit{\_Z} +1\right)^{2}+22536192 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(16777216 \textit{\_Z}^{2}+4096 \textit{\_Z} +1\right)+14247 \left(x^{3}-1\right)^{\frac{2}{3}}-69656576 \RootOf \left(16777216 \textit{\_Z}^{2}+4096 \textit{\_Z} +1\right)-14247 \left(x^{3}-1\right)^{\frac{1}{3}}+2743}{x^{3}}\right)}{729}-\frac{102400 \ln \left(-\frac{24125636608 \RootOf \left(16777216 \textit{\_Z}^{2}+4096 \textit{\_Z} +1\right)^{2} x^{3}+40366080 \RootOf \left(16777216 \textit{\_Z}^{2}+4096 \textit{\_Z} +1\right) x^{3}-22536192 \RootOf \left(16777216 \textit{\_Z}^{2}+4096 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}}-1477 x^{3}-193005092864 \RootOf \left(16777216 \textit{\_Z}^{2}+4096 \textit{\_Z} +1\right)^{2}+22536192 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(16777216 \textit{\_Z}^{2}+4096 \textit{\_Z} +1\right)+14247 \left(x^{3}-1\right)^{\frac{2}{3}}-69656576 \RootOf \left(16777216 \textit{\_Z}^{2}+4096 \textit{\_Z} +1\right)-14247 \left(x^{3}-1\right)^{\frac{1}{3}}+2743}{x^{3}}\right) \RootOf \left(16777216 \textit{\_Z}^{2}+4096 \textit{\_Z} +1\right)}{729}$&$458$\\ \hline \end{longtable}"," ",0,"1/972*(50*x^12-20*x^9-129*x^6+18*x^3+81)/x^12/(x^3-1)^(2/3)+25/729/GAMMA(2/3)/signum(x^3-1)^(2/3)*(-signum(x^3-1))^(2/3)*(2/3*GAMMA(2/3)*x^3*hypergeom([1,1,5/3],[2,2],x^3)+(1/6*Pi*3^(1/2)-3/2*ln(3)+3*ln(x)+I*Pi)*GAMMA(2/3))","C"
1588,0,0,95,0.082000," ","int((-b+x)*(a-3*b+2*x)/(-a+x)/((-a+x)*(-b+x))^(3/4)/(b-a^3*d-(-3*a^2*d+1)*x-3*a*d*x^2+d*x^3),x)","\[\int \frac{\left(-b +x \right) \left(a -3 b +2 x \right)}{\left(-a +x \right) \left(\left(-a +x \right) \left(-b +x \right)\right)^{\frac{3}{4}} \left(b -a^{3} d -\left(-3 a^{2} d +1\right) x -3 a d \,x^{2}+d \,x^{3}\right)}\, dx\]"," ",0,"int((-b+x)*(a-3*b+2*x)/(-a+x)/((-a+x)*(-b+x))^(3/4)/(b-a^3*d-(-3*a^2*d+1)*x-3*a*d*x^2+d*x^3),x)","F"
1589,0,0,89,0.007000," ","int(x^8*(a*x^4-b)^(3/4),x)","\[\int x^{8} \left(a \,x^{4}-b \right)^{\frac{3}{4}}\, dx\]"," ",0,"int(x^8*(a*x^4-b)^(3/4),x)","F"
1590,0,0,85,0.038000," ","int(1/(a*x^3+b)/(a*x^4-b*x)^(1/4),x)","\[\int \frac{1}{\left(a \,x^{3}+b \right) \left(a \,x^{4}-b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(a*x^3+b)/(a*x^4-b*x)^(1/4),x)","F"
1591,0,0,46,0.013000," ","int((a*x^4-b*x^2)^(1/4)/x^4/(a*x^4-b),x)","\[\int \frac{\left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}{x^{4} \left(a \,x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^4-b*x^2)^(1/4)/x^4/(a*x^4-b),x)","F"
1592,0,0,46,0.001000," ","int((a*x^4-b*x^2)^(1/4)/x^4/(a*x^4-b),x)","\[\int \frac{\left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}{x^{4} \left(a \,x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^4-b*x^2)^(1/4)/x^4/(a*x^4-b),x)","F"
1593,0,0,11,0.058000," ","int((-2+(1+k)*x)*(1-(1+k)*x+(a+k)*x^2)/((1-x)*x*(-k*x+1))^(1/3)/(1-2*(1+k)*x+(k^2+c+4*k+1)*x^2-(c*k+2*k^2+c+2*k)*x^3+(c*k+k^2-b)*x^4),x)","\[\int \frac{\left(-2+\left(1+k \right) x \right) \left(1-\left(1+k \right) x +\left(a +k \right) x^{2}\right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(1-2 \left(1+k \right) x +\left(k^{2}+c +4 k +1\right) x^{2}-\left(c k +2 k^{2}+c +2 k \right) x^{3}+\left(c k +k^{2}-b \right) x^{4}\right)}\, dx\]"," ",0,"int((-2+(1+k)*x)*(1-(1+k)*x+(a+k)*x^2)/((1-x)*x*(-k*x+1))^(1/3)/(1-2*(1+k)*x+(k^2+c+4*k+1)*x^2-(c*k+2*k^2+c+2*k)*x^3+(c*k+k^2-b)*x^4),x)","F"
1594,1,56,87,6.980000," ","int((x^6-1)^(1/3)*(x^6+1)/x^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x^{12}-4 x^{6}+3}{6 x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}}+\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{2}{3}} x^{4} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], x^{6}\right)}{6 \mathrm{signum}\left(x^{6}-1\right)^{\frac{2}{3}}}$&$56$\\ meijerg&$\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}} x^{4} \hypergeom \left(\left[-\frac{1}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], x^{6}\right)}{4 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}}}-\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{1}{3}, -\frac{1}{3}\right], \left[\frac{2}{3}\right], x^{6}\right)}{2 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} x^{2}}$&$66$\\ trager&$\frac{\left(x^{6}-3\right) \left(x^{6}-1\right)^{\frac{1}{3}}}{6 x^{2}}+\frac{4 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) \ln \left(-25091500048 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)^{2} x^{6}+1210241551876 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) x^{6}+1203968676864 \left(x^{6}-1\right)^{\frac{1}{3}} \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) x^{4}-578845773886 x^{6}+1203968676864 \left(x^{6}-1\right)^{\frac{2}{3}} \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) x^{2}-577277555133 x^{4} \left(x^{6}-1\right)^{\frac{1}{3}}-577277555133 x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}+1605856003072 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)^{2}-1572490299900 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)+384886980542\right)}{9}+\frac{\ln \left(-25091500048 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)^{2} x^{6}-1197695801852 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) x^{6}-1203968676864 \left(x^{6}-1\right)^{\frac{1}{3}} \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) x^{4}-277853604670 x^{6}-1203968676864 \left(x^{6}-1\right)^{\frac{2}{3}} \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) x^{2}-276285385917 x^{4} \left(x^{6}-1\right)^{\frac{1}{3}}-276285385917 x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}+1605856003072 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)^{2}+769562298364 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)+92130405759\right)}{9}-\frac{4 \ln \left(-25091500048 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)^{2} x^{6}-1197695801852 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) x^{6}-1203968676864 \left(x^{6}-1\right)^{\frac{1}{3}} \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) x^{4}-277853604670 x^{6}-1203968676864 \left(x^{6}-1\right)^{\frac{2}{3}} \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right) x^{2}-276285385917 x^{4} \left(x^{6}-1\right)^{\frac{1}{3}}-276285385917 x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}+1605856003072 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)^{2}+769562298364 \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)+92130405759\right) \RootOf \left(16 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)}{9}$&$467$\\ \hline \end{longtable}"," ",0,"1/6*(x^12-4*x^6+3)/x^2/(x^6-1)^(2/3)+1/6/signum(x^6-1)^(2/3)*(-signum(x^6-1))^(2/3)*x^4*hypergeom([2/3,2/3],[5/3],x^6)","C"
1595,1,7804,31,251.294000," ","int((x^3+1)^(2/3)*(x^6-2*x^3+1)/x^6/(x^6-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$7804$\\ trager&$\text{Expression too large to display}$&$10431$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1596,1,6590,31,239.106000," ","int((x^3+1)^(2/3)*(x^6-2*x^3+1)/x^6/(x^6-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$6590$\\ trager&$\text{Expression too large to display}$&$9174$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1597,1,58,89,8.472000," ","int((x^6-1)^(1/3)*(2*x^6-1)/x^9,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{9 x^{12}-10 x^{6}+1}{8 x^{8} \left(x^{6}-1\right)^{\frac{2}{3}}}+\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{2}{3}} x^{4} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], x^{6}\right)}{2 \mathrm{signum}\left(x^{6}-1\right)^{\frac{2}{3}}}$&$58$\\ meijerg&$-\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{1}{3}, -\frac{1}{3}\right], \left[\frac{2}{3}\right], x^{6}\right)}{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} x^{2}}+\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}} \left(-x^{6}+1\right)^{\frac{4}{3}}}{8 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} x^{8}}$&$66$\\ trager&$-\frac{\left(9 x^{6}-1\right) \left(x^{6}-1\right)^{\frac{1}{3}}}{8 x^{8}}-\frac{\ln \left(-95839020187648 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)^{2} x^{6}-70354687622144 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) x^{6}+147783054114048 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}+575815167740 x^{6}-77053995319296 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}-300992169216 x^{4} \left(x^{6}-1\right)^{\frac{1}{3}}-276285385917 x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}+6133697292009472 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)^{2}-26068067221760 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)-190928187198\right)}{3}+\frac{\ln \left(198613804384256 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)^{2} x^{6}-148558889287424 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) x^{6}+70729058794752 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}+279315992063 x^{6}+77053995319296 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}+300992169216 x^{4} \left(x^{6}-1\right)^{\frac{1}{3}}-577277555133 x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}-12711283480592384 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)^{2}+122490822065664 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)-185723198911\right)}{3}-\frac{256 \ln \left(198613804384256 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)^{2} x^{6}-148558889287424 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) x^{6}+70729058794752 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}+279315992063 x^{6}+77053995319296 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}+300992169216 x^{4} \left(x^{6}-1\right)^{\frac{1}{3}}-577277555133 x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}-12711283480592384 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)^{2}+122490822065664 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)-185723198911\right) \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)}{3}$&$458$\\ \hline \end{longtable}"," ",0,"-1/8*(9*x^12-10*x^6+1)/x^8/(x^6-1)^(2/3)+1/2/signum(x^6-1)^(2/3)*(-signum(x^6-1))^(2/3)*x^4*hypergeom([2/3,2/3],[5/3],x^6)","C"
1598,1,7065,31,38.117000," ","int((x^3-1)^(2/3)*(x^6-1)/x^6/(2*x^6+x^3-2),x)","\[\text{output too large to display}\]"," ",0,"result too large to display","B"
1599,1,7065,31,354.813000," ","int((x^3-1)^(2/3)*(x^6-1)/x^6/(2*x^6+x^3-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$7065$\\ trager&$\text{Expression too large to display}$&$8767$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1600,1,182,89,8.946000," ","int((x^4-1)^(1/4)*(2*x^8-x^4+2)/x^10/(2*x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{4}-1\right)^{\frac{1}{4}} \left(65 x^{8}+5 x^{4}+2\right)}{9 x^{9}}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{-2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}-2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}+2 \left(x^{4}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}+1\right)}{2 x^{4}-1}\right)-2 \RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}+2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right) x^{2}+2 \left(x^{4}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{2 x^{4}-1}\right)$&$182$\\ risch&$\frac{65 x^{12}-60 x^{8}-3 x^{4}-2}{9 x^{9} \left(x^{4}-1\right)^{\frac{3}{4}}}+\frac{\left(2 \RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{12}-3 x^{8}+3 x^{4}-1\right)^{\frac{1}{4}} x^{9}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{8}-4 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{12}-3 x^{8}+3 x^{4}-1\right)^{\frac{1}{4}} x^{5}+2 \sqrt{x^{12}-3 x^{8}+3 x^{4}-1}\, x^{6}-2 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{12}-3 x^{8}+3 x^{4}-1\right)^{\frac{3}{4}} x^{3}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{4}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{12}-3 x^{8}+3 x^{4}-1\right)^{\frac{1}{4}} x -2 \sqrt{x^{12}-3 x^{8}+3 x^{4}-1}\, x^{2}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{2}}{\left(-1+x \right)^{2} \left(1+x \right)^{2} \left(x^{2}+1\right)^{2} \left(2 x^{4}-1\right)}\right)-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{12}-3 x^{8}+3 x^{4}-1\right)^{\frac{1}{4}} x^{9}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{8}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{12}-3 x^{8}+3 x^{4}-1\right)^{\frac{3}{4}} x^{3}+2 \sqrt{x^{12}-3 x^{8}+3 x^{4}-1}\, x^{6}+4 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{12}-3 x^{8}+3 x^{4}-1\right)^{\frac{1}{4}} x^{5}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{4}-2 \sqrt{x^{12}-3 x^{8}+3 x^{4}-1}\, x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{12}-3 x^{8}+3 x^{4}-1\right)^{\frac{1}{4}} x -\RootOf \left(\textit{\_Z}^{4}+1\right)^{2}}{\left(-1+x \right)^{2} \left(1+x \right)^{2} \left(x^{2}+1\right)^{2} \left(2 x^{4}-1\right)}\right)\right) \left(\left(x^{4}-1\right)^{3}\right)^{\frac{1}{4}}}{\left(x^{4}-1\right)^{\frac{3}{4}}}$&$512$\\ \hline \end{longtable}"," ",0,"1/9*(x^4-1)^(1/4)*(65*x^8+5*x^4+2)/x^9+2*RootOf(_Z^4+1)^3*ln((-2*(x^4-1)^(1/2)*RootOf(_Z^4+1)^3*x^2-2*(x^4-1)^(1/4)*RootOf(_Z^4+1)^2*x^3+2*(x^4-1)^(3/4)*x-RootOf(_Z^4+1))/(2*x^4-1))-2*RootOf(_Z^4+1)*ln((2*(x^4-1)^(1/4)*RootOf(_Z^4+1)^2*x^3+2*(x^4-1)^(1/2)*RootOf(_Z^4+1)*x^2+2*(x^4-1)^(3/4)*x+RootOf(_Z^4+1)^3)/(2*x^4-1))","C"
1601,1,231,89,75.180000," ","int((x^6+2)*(x^12+x^8-2*x^6+1)/x^8/(x^6-1)^(1/4)/(x^6+x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{6}-1\right)^{\frac{3}{4}} \left(3 x^{6}-7 x^{4}-3\right)}{21 x^{7}}-\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \sqrt{x^{6}-1}\, x^{2}-\RootOf \left(\textit{\_Z}^{4}+1\right) x^{6}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} \left(x^{6}-1\right)^{\frac{1}{4}} x^{3}+\RootOf \left(\textit{\_Z}^{4}+1\right) x^{4}-2 \left(x^{6}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}+1\right)}{x^{6}+x^{4}-1}\right)+\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{6}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{4}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} \left(x^{6}-1\right)^{\frac{1}{4}} x^{3}-2 \RootOf \left(\textit{\_Z}^{4}+1\right) \sqrt{x^{6}-1}\, x^{2}-2 \left(x^{6}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{x^{6}+x^{4}-1}\right)$&$231$\\ risch&$\frac{\frac{2}{7} x^{12}-\frac{4}{7} x^{6}+\frac{2}{7}-\frac{2}{3} x^{10}+\frac{2}{3} x^{4}}{x^{7} \left(x^{6}-1\right)^{\frac{1}{4}}}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{6}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{4}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} \left(x^{6}-1\right)^{\frac{1}{4}} x^{3}-2 \RootOf \left(\textit{\_Z}^{4}+1\right) \sqrt{x^{6}-1}\, x^{2}-2 \left(x^{6}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{x^{6}+x^{4}-1}\right)+\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \sqrt{x^{6}-1}\, x^{2}-\RootOf \left(\textit{\_Z}^{4}+1\right) x^{6}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} \left(x^{6}-1\right)^{\frac{1}{4}} x^{3}+\RootOf \left(\textit{\_Z}^{4}+1\right) x^{4}+2 \left(x^{6}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}+1\right)}{x^{6}+x^{4}-1}\right)$&$239$\\ \hline \end{longtable}"," ",0,"2/21*(x^6-1)^(3/4)*(3*x^6-7*x^4-3)/x^7-RootOf(_Z^4+1)*ln(-(2*RootOf(_Z^4+1)^3*(x^6-1)^(1/2)*x^2-RootOf(_Z^4+1)*x^6+2*RootOf(_Z^4+1)^2*(x^6-1)^(1/4)*x^3+RootOf(_Z^4+1)*x^4-2*(x^6-1)^(3/4)*x+RootOf(_Z^4+1))/(x^6+x^4-1))+RootOf(_Z^4+1)^3*ln(-(RootOf(_Z^4+1)^3*x^6-RootOf(_Z^4+1)^3*x^4-2*RootOf(_Z^4+1)^2*(x^6-1)^(1/4)*x^3-2*RootOf(_Z^4+1)*(x^6-1)^(1/2)*x^2-2*(x^6-1)^(3/4)*x-RootOf(_Z^4+1)^3)/(x^6+x^4-1))","C"
1602,0,0,87,0.028000," ","int((x^2+x)^(1/2)/x/(x^2+x*(x^2+x)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{x^{2}+x}}{x \sqrt{x^{2}+x \sqrt{x^{2}+x}}}\, dx\]"," ",0,"int((x^2+x)^(1/2)/x/(x^2+x*(x^2+x)^(1/2))^(1/2),x)","F"
1603,0,0,81,0.021000," ","int((x^2+x*(x^2+x)^(1/2))^(1/2)/(x^2+x)^(1/2),x)","\[\int \frac{\sqrt{x^{2}+x \sqrt{x^{2}+x}}}{\sqrt{x^{2}+x}}\, dx\]"," ",0,"int((x^2+x*(x^2+x)^(1/2))^(1/2)/(x^2+x)^(1/2),x)","F"
1604,1,29,82,0.040000," ","int(1/(b+(a*x^2+b^2)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\sqrt{2}\, x \hypergeom \left(\left[\frac{1}{4}, \frac{1}{2}, \frac{3}{4}\right], \left[\frac{3}{2}, \frac{3}{2}\right], -\frac{x^{2} a}{b^{2}}\right)}{2 \left(b^{2}\right)^{\frac{1}{4}}}$&$29$\\ \hline \end{longtable}"," ",0,"1/2/(b^2)^(1/4)*2^(1/2)*x*hypergeom([1/4,1/2,3/4],[3/2,3/2],-x^2*a/b^2)","C"
1605,1,189,95,0.122000," ","int((a*x^2+b^2)^2*(b+(a*x^2+b^2)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\left(b^{2}\right)^{\frac{1}{4}} a^{2} \sqrt{2}\, x^{5} \hypergeom \left(\left[-\frac{1}{4}, \frac{1}{4}, \frac{5}{2}\right], \left[\frac{1}{2}, \frac{7}{2}\right], -\frac{x^{2} a}{b^{2}}\right)}{5}+\frac{2 b^{2} \left(b^{2}\right)^{\frac{1}{4}} a \sqrt{2}\, x^{3} \hypergeom \left(\left[-\frac{1}{4}, \frac{1}{4}, \frac{3}{2}\right], \left[\frac{1}{2}, \frac{5}{2}\right], -\frac{x^{2} a}{b^{2}}\right)}{3}-\frac{b^{4} \left(b^{2}\right)^{\frac{1}{4}} \left(-\frac{32 \sqrt{\pi}\, \sqrt{2}\, x^{3} \sqrt{\frac{a}{b^{2}}}\, a \cosh \left(\frac{3 \arcsinh \left(\frac{x \sqrt{a}}{b}\right)}{2}\right)}{3 b^{2}}-\frac{8 \sqrt{\pi}\, \sqrt{2}\, \sqrt{\frac{a}{b^{2}}}\, \left(-\frac{4 x^{4} a^{2}}{3 b^{4}}-\frac{2 x^{2} a}{3 b^{2}}+\frac{2}{3}\right) \sinh \left(\frac{3 \arcsinh \left(\frac{x \sqrt{a}}{b}\right)}{2}\right) b}{\sqrt{a}\, \sqrt{\frac{x^{2} a}{b^{2}}+1}}\right)}{8 \sqrt{\pi}\, \sqrt{\frac{a}{b^{2}}}}$&$189$\\ \hline \end{longtable}"," ",0,"1/5*(b^2)^(1/4)*a^2*2^(1/2)*x^5*hypergeom([-1/4,1/4,5/2],[1/2,7/2],-x^2*a/b^2)+2/3*b^2*(b^2)^(1/4)*a*2^(1/2)*x^3*hypergeom([-1/4,1/4,3/2],[1/2,5/2],-x^2*a/b^2)-1/8*b^4*(b^2)^(1/4)/Pi^(1/2)/(a/b^2)^(1/2)*(-32/3*Pi^(1/2)*2^(1/2)*x^3*(a/b^2)^(1/2)*a/b^2*cosh(3/2*arcsinh(x*a^(1/2)/b))-8*Pi^(1/2)*2^(1/2)*(a/b^2)^(1/2)*(-4/3*x^4*a^2/b^4-2/3*x^2*a/b^2+2/3)*sinh(3/2*arcsinh(x*a^(1/2)/b))/a^(1/2)*b/(x^2*a/b^2+1)^(1/2))","C"
1606,1,442,90,2.328000," ","int(1/(1-3*x)/(x^3-x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(-\frac{35769664 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{2}-66429376 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x +31989600 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}+976188 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{1}{3}} x +56895644 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{2}-10219904 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}+976188 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{1}{3}}-79246712 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x +15018612 \left(x^{3}-x \right)^{\frac{2}{3}}+7997400 x \left(x^{3}-x \right)^{\frac{1}{3}}+19718281 x^{2}-7450356 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+7997400 \left(x^{3}-x \right)^{\frac{1}{3}}-23140462 x -1140727}{\left(-1+3 x \right)^{2}}\right)}{4}+\frac{\RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \ln \left(\frac{18251632 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{2}-33895888 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x +15994800 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}+7509306 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{1}{3}} x -1650049 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{2}-5214752 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}+7509306 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{1}{3}}-10414826 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x +488094 \left(x^{3}-x \right)^{\frac{2}{3}}+3998700 x \left(x^{3}-x \right)^{\frac{1}{3}}-5189795 x^{2}-4021625 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+3998700 \left(x^{3}-x \right)^{\frac{1}{3}}+3034034 x -718587}{\left(-1+3 x \right)^{2}}\right)}{2}$&$442$\\ \hline \end{longtable}"," ",0,"1/4*ln(-(35769664*RootOf(4*_Z^2+2*_Z+1)^2*x^2-66429376*RootOf(4*_Z^2+2*_Z+1)^2*x+31989600*RootOf(4*_Z^2+2*_Z+1)*(x^3-x)^(2/3)+976188*RootOf(4*_Z^2+2*_Z+1)*(x^3-x)^(1/3)*x+56895644*RootOf(4*_Z^2+2*_Z+1)*x^2-10219904*RootOf(4*_Z^2+2*_Z+1)^2+976188*RootOf(4*_Z^2+2*_Z+1)*(x^3-x)^(1/3)-79246712*RootOf(4*_Z^2+2*_Z+1)*x+15018612*(x^3-x)^(2/3)+7997400*x*(x^3-x)^(1/3)+19718281*x^2-7450356*RootOf(4*_Z^2+2*_Z+1)+7997400*(x^3-x)^(1/3)-23140462*x-1140727)/(-1+3*x)^2)+1/2*RootOf(4*_Z^2+2*_Z+1)*ln((18251632*RootOf(4*_Z^2+2*_Z+1)^2*x^2-33895888*RootOf(4*_Z^2+2*_Z+1)^2*x+15994800*RootOf(4*_Z^2+2*_Z+1)*(x^3-x)^(2/3)+7509306*RootOf(4*_Z^2+2*_Z+1)*(x^3-x)^(1/3)*x-1650049*RootOf(4*_Z^2+2*_Z+1)*x^2-5214752*RootOf(4*_Z^2+2*_Z+1)^2+7509306*RootOf(4*_Z^2+2*_Z+1)*(x^3-x)^(1/3)-10414826*RootOf(4*_Z^2+2*_Z+1)*x+488094*(x^3-x)^(2/3)+3998700*x*(x^3-x)^(1/3)-5189795*x^2-4021625*RootOf(4*_Z^2+2*_Z+1)+3998700*(x^3-x)^(1/3)+3034034*x-718587)/(-1+3*x)^2)","C"
1607,1,656,90,2.837000," ","int(1/(1+3*x)/(x^3-x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(-\frac{7297600 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{2}-18973760 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x +7258272 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}-19359420 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{1}{3}} x +32081060 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{2}+8757120 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}+19359420 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{1}{3}}+40119368 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x -19359420 \left(x^{3}-x \right)^{\frac{2}{3}}-11494278 x \left(x^{3}-x \right)^{\frac{1}{3}}-10880597 x^{2}-2679436 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+11494278 \left(x^{3}-x \right)^{\frac{1}{3}}-10794014 x -28861}{\left(1+3 x \right)^{2}}\right)}{4}-\frac{\ln \left(\frac{11915360 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{2}-30979936 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x +7258272 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}+22988556 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{1}{3}} x -47884574 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{2}+14298432 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}-22988556 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{1}{3}}-77197364 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x +22988556 \left(x^{3}-x \right)^{\frac{2}{3}}+9679710 x \left(x^{3}-x \right)^{\frac{1}{3}}-9726157 x^{2}+9770930 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)-9679710 \left(x^{3}-x \right)^{\frac{1}{3}}-13795558 x +1356467}{\left(1+3 x \right)^{2}}\right)}{4}-\frac{\ln \left(\frac{11915360 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{2}-30979936 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x +7258272 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}+22988556 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{1}{3}} x -47884574 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{2}+14298432 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}-22988556 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{1}{3}}-77197364 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x +22988556 \left(x^{3}-x \right)^{\frac{2}{3}}+9679710 x \left(x^{3}-x \right)^{\frac{1}{3}}-9726157 x^{2}+9770930 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)-9679710 \left(x^{3}-x \right)^{\frac{1}{3}}-13795558 x +1356467}{\left(1+3 x \right)^{2}}\right) \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)}{2}$&$656$\\ \hline \end{longtable}"," ",0,"1/4*ln(-(7297600*RootOf(4*_Z^2+2*_Z+1)^2*x^2-18973760*RootOf(4*_Z^2+2*_Z+1)^2*x+7258272*RootOf(4*_Z^2+2*_Z+1)*(x^3-x)^(2/3)-19359420*RootOf(4*_Z^2+2*_Z+1)*(x^3-x)^(1/3)*x+32081060*RootOf(4*_Z^2+2*_Z+1)*x^2+8757120*RootOf(4*_Z^2+2*_Z+1)^2+19359420*RootOf(4*_Z^2+2*_Z+1)*(x^3-x)^(1/3)+40119368*RootOf(4*_Z^2+2*_Z+1)*x-19359420*(x^3-x)^(2/3)-11494278*x*(x^3-x)^(1/3)-10880597*x^2-2679436*RootOf(4*_Z^2+2*_Z+1)+11494278*(x^3-x)^(1/3)-10794014*x-28861)/(1+3*x)^2)-1/4*ln((11915360*RootOf(4*_Z^2+2*_Z+1)^2*x^2-30979936*RootOf(4*_Z^2+2*_Z+1)^2*x+7258272*RootOf(4*_Z^2+2*_Z+1)*(x^3-x)^(2/3)+22988556*RootOf(4*_Z^2+2*_Z+1)*(x^3-x)^(1/3)*x-47884574*RootOf(4*_Z^2+2*_Z+1)*x^2+14298432*RootOf(4*_Z^2+2*_Z+1)^2-22988556*RootOf(4*_Z^2+2*_Z+1)*(x^3-x)^(1/3)-77197364*RootOf(4*_Z^2+2*_Z+1)*x+22988556*(x^3-x)^(2/3)+9679710*x*(x^3-x)^(1/3)-9726157*x^2+9770930*RootOf(4*_Z^2+2*_Z+1)-9679710*(x^3-x)^(1/3)-13795558*x+1356467)/(1+3*x)^2)-1/2*ln((11915360*RootOf(4*_Z^2+2*_Z+1)^2*x^2-30979936*RootOf(4*_Z^2+2*_Z+1)^2*x+7258272*RootOf(4*_Z^2+2*_Z+1)*(x^3-x)^(2/3)+22988556*RootOf(4*_Z^2+2*_Z+1)*(x^3-x)^(1/3)*x-47884574*RootOf(4*_Z^2+2*_Z+1)*x^2+14298432*RootOf(4*_Z^2+2*_Z+1)^2-22988556*RootOf(4*_Z^2+2*_Z+1)*(x^3-x)^(1/3)-77197364*RootOf(4*_Z^2+2*_Z+1)*x+22988556*(x^3-x)^(2/3)+9679710*x*(x^3-x)^(1/3)-9726157*x^2+9770930*RootOf(4*_Z^2+2*_Z+1)-9679710*(x^3-x)^(1/3)-13795558*x+1356467)/(1+3*x)^2)*RootOf(4*_Z^2+2*_Z+1)","C"
1608,1,27,93,0.662000," ","int(x/(x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{3}} x^{\frac{4}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{4}{3}\right], \left[\frac{7}{3}\right], x\right)}{4 \mathrm{signum}\left(-1+x \right)^{\frac{1}{3}}}$&$27$\\ risch&$\frac{x \left(-1+x \right)}{\left(\left(-1+x \right) x^{2}\right)^{\frac{1}{3}}}+\frac{\left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{3}} x^{\frac{1}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x\right)}{\mathrm{signum}\left(-1+x \right)^{\frac{1}{3}}}$&$41$\\ trager&$\frac{\left(x^{3}-x^{2}\right)^{\frac{2}{3}}}{x}+\frac{\ln \left(-\frac{-45 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right)^{2} x^{2}+144 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+144 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) \left(x^{3}-x^{2}\right)^{\frac{1}{3}} x +90 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right)^{2} x +174 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) x^{2}-60 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}-60 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}-138 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) x -80 x^{2}+48 x}{x}\right)}{3}-\frac{\ln \left(-\frac{-45 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right)^{2} x^{2}+144 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+144 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) \left(x^{3}-x^{2}\right)^{\frac{1}{3}} x +90 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right)^{2} x +174 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) x^{2}-60 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}-60 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}-138 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) x -80 x^{2}+48 x}{x}\right) \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right)}{2}+\frac{\RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) \ln \left(\frac{45 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right)^{2} x^{2}+144 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+144 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) \left(x^{3}-x^{2}\right)^{\frac{1}{3}} x -90 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right)^{2} x +114 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) x^{2}-36 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}-36 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}-18 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) x -16 x^{2}+4 x}{x}\right)}{2}$&$509$\\ \hline \end{longtable}"," ",0,"3/4/signum(-1+x)^(1/3)*(-signum(-1+x))^(1/3)*x^(4/3)*hypergeom([1/3,4/3],[7/3],x)","C"
1609,1,278,91,5.281000," ","int((-x^3+1)^(2/3)*(x^3-1)/x^6/(2*x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 x^{6}-x^{3}-2}{10 x^{5} \left(-x^{3}+1\right)^{\frac{1}{3}}}-\frac{\ln \left(-\frac{3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(-x^{3}+1\right)^{\frac{2}{3}} x -6 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2}+3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{3}+\left(-x^{3}+1\right)^{\frac{2}{3}} x +\left(-x^{3}+1\right)^{\frac{1}{3}} x^{2}-1}{2 x^{3}-1}\right)}{3}+\RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \ln \left(-\frac{9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{3}-3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(-x^{3}+1\right)^{\frac{2}{3}} x -3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2}-3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{3}+2 \left(-x^{3}+1\right)^{\frac{2}{3}} x -\left(-x^{3}+1\right)^{\frac{1}{3}} x^{2}+3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)}{2 x^{3}-1}\right)$&$278$\\ trager&$-\frac{\left(3 x^{3}+2\right) \left(-x^{3}+1\right)^{\frac{2}{3}}}{10 x^{5}}+32 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \ln \left(\frac{374952960 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x^{3}+10252800 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \left(-x^{3}+1\right)^{\frac{2}{3}} x +10252800 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{2}-34273056 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{3}+421089 \left(-x^{3}+1\right)^{\frac{2}{3}} x +421089 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2}+252248 x^{3}-2999623680 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2}+51556128 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)-220717}{2 x^{3}-1}\right)+\frac{\ln \left(-\frac{-374952960 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x^{3}+10252800 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \left(-x^{3}+1\right)^{\frac{2}{3}} x +10252800 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{2}-26461536 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{3}-527889 \left(-x^{3}+1\right)^{\frac{2}{3}} x -527889 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2}+64078 x^{3}+2999623680 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2}-10936032 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)+9154}{2 x^{3}-1}\right)}{3}-32 \ln \left(-\frac{-374952960 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x^{3}+10252800 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \left(-x^{3}+1\right)^{\frac{2}{3}} x +10252800 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{2}-26461536 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{3}-527889 \left(-x^{3}+1\right)^{\frac{2}{3}} x -527889 \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2}+64078 x^{3}+2999623680 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2}-10936032 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)+9154}{2 x^{3}-1}\right) \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)$&$515$\\ \hline \end{longtable}"," ",0,"1/10*(3*x^6-x^3-2)/x^5/(-x^3+1)^(1/3)-1/3*ln(-(3*RootOf(9*_Z^2-3*_Z+1)*(-x^3+1)^(2/3)*x-6*RootOf(9*_Z^2-3*_Z+1)*(-x^3+1)^(1/3)*x^2+3*RootOf(9*_Z^2-3*_Z+1)*x^3+(-x^3+1)^(2/3)*x+(-x^3+1)^(1/3)*x^2-1)/(2*x^3-1))+RootOf(9*_Z^2-3*_Z+1)*ln(-(9*RootOf(9*_Z^2-3*_Z+1)^2*x^3-3*RootOf(9*_Z^2-3*_Z+1)*(-x^3+1)^(2/3)*x-3*RootOf(9*_Z^2-3*_Z+1)*(-x^3+1)^(1/3)*x^2-3*RootOf(9*_Z^2-3*_Z+1)*x^3+2*(-x^3+1)^(2/3)*x-(-x^3+1)^(1/3)*x^2+3*RootOf(9*_Z^2-3*_Z+1))/(2*x^3-1))","C"
1610,0,0,93,0.092000," ","int((a*x+2*b)/(a*x+x^2+b)/(a*x^3+b*x^2)^(1/4),x)","\[\int \frac{a x +2 b}{\left(a x +x^{2}+b \right) \left(a \,x^{3}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x+2*b)/(a*x+x^2+b)/(a*x^3+b*x^2)^(1/4),x)","F"
1611,1,665,90,0.392000," ","int(x^3*(x^4+x)^(1/2)/(a*x^3-b),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{x \sqrt{x^{4}+x}}{3 a}-\frac{2 \left(\frac{a +b}{a^{2}}-\frac{1}{2 a}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{2 b \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}-b \right)}{\sum}\frac{\left(1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(-1-i \sqrt{3}\right) \sqrt{\frac{x \left(3+i \sqrt{3}\right)}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \sqrt{3}+2 x -1}{\left(1+x \right) \left(1-i \sqrt{3}\right)}}\, \sqrt{-\frac{-1+2 x -i \sqrt{3}}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\frac{\underline{\hspace{1.25 ex}}\alpha^{2} a \EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}\, a +3 \underline{\hspace{1.25 ex}}\alpha^{2} a +i \sqrt{3}\, b +3 b}{6 b}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{b}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(3+i \sqrt{3}\right) \sqrt{x \left(1+x \right) \left(i \sqrt{3}+2 x -1\right) \left(-1+2 x -i \sqrt{3}\right)}}\right)}{3 a^{2}}$&$665$\\ risch&$\frac{x^{2} \left(x^{3}+1\right)}{3 a \sqrt{x \left(x^{3}+1\right)}}+\frac{-\frac{2 \left(a +2 b \right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{a \left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{4 b \left(a +b \right) \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}-b \right)}{\sum}\frac{\left(1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(-1-i \sqrt{3}\right) \sqrt{\frac{x \left(3+i \sqrt{3}\right)}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \sqrt{3}+2 x -1}{\left(1+x \right) \left(1-i \sqrt{3}\right)}}\, \sqrt{-\frac{-1+2 x -i \sqrt{3}}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\frac{\underline{\hspace{1.25 ex}}\alpha^{2} a \EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}\, a +3 \underline{\hspace{1.25 ex}}\alpha^{2} a +i \sqrt{3}\, b +3 b}{6 b}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{b}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(a +b \right) \left(3+i \sqrt{3}\right) \sqrt{x \left(1+x \right) \left(i \sqrt{3}+2 x -1\right) \left(-1+2 x -i \sqrt{3}\right)}}\right)}{3 a}}{2 a}$&$683$\\ default&$\frac{\frac{x \sqrt{x^{4}+x}}{3}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}}{a}+\frac{b \left(-\frac{2 \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{a \left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}-\frac{2 \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}-b \right)}{\sum}\frac{\left(-a -b \right) \left(1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(-1-i \sqrt{3}\right) \sqrt{\frac{x \left(3+i \sqrt{3}\right)}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \sqrt{3}+2 x -1}{\left(1+x \right) \left(1-i \sqrt{3}\right)}}\, \sqrt{-\frac{-1+2 x -i \sqrt{3}}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\frac{\underline{\hspace{1.25 ex}}\alpha^{2} a \EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}\, a +3 \underline{\hspace{1.25 ex}}\alpha^{2} a +i \sqrt{3}\, b +3 b}{6 b}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{b}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(a +b \right) \left(3+i \sqrt{3}\right) \sqrt{x \left(1+x \right) \left(i \sqrt{3}+2 x -1\right) \left(-1+2 x -i \sqrt{3}\right)}}\right)}{3 a}\right)}{a}$&$963$\\ \hline \end{longtable}"," ",0,"1/3*x*(x^4+x)^(1/2)/a-2*((a+b)/a^2-1/2/a)*(-1/2-1/2*I*3^(1/2))*((3/2+1/2*I*3^(1/2))*x/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2)*(1+x)^2*(-(x-1/2+1/2*I*3^(1/2))/(1/2-1/2*I*3^(1/2))/(1+x))^(1/2)*(-(x-1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2)/(3/2+1/2*I*3^(1/2))/(x*(1+x)*(x-1/2+1/2*I*3^(1/2))*(x-1/2-1/2*I*3^(1/2)))^(1/2)*(-EllipticF(((3/2+1/2*I*3^(1/2))*x/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2),((-3/2+1/2*I*3^(1/2))*(-1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+EllipticPi(((3/2+1/2*I*3^(1/2))*x/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2),(1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)),((-3/2+1/2*I*3^(1/2))*(-1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)))+2/3/a^2*b*4^(1/2)*sum(1/_alpha*(1+x)^2*(_alpha^2-_alpha+1)*(-1-I*3^(1/2))*(x/(1+x)*(3+I*3^(1/2))/(1+I*3^(1/2)))^(1/2)*(-1/(1+x)*(I*3^(1/2)+2*x-1)/(1-I*3^(1/2)))^(1/2)*(-1/(1+x)*(-1+2*x-I*3^(1/2))/(1+I*3^(1/2)))^(1/2)/(3+I*3^(1/2))/(x*(1+x)*(I*3^(1/2)+2*x-1)*(-1+2*x-I*3^(1/2)))^(1/2)*(EllipticF(((3/2+1/2*I*3^(1/2))*x/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2),((-3/2+1/2*I*3^(1/2))*(-1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+_alpha^2*a/b*EllipticPi(((3/2+1/2*I*3^(1/2))*x/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2),1/6*(I*_alpha^2*3^(1/2)*a+3*_alpha^2*a+I*3^(1/2)*b+3*b)/b,((-3/2+1/2*I*3^(1/2))*(-1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))),_alpha=RootOf(_Z^3*a-b))","C"
1612,1,17,88,3.527000," ","int(x^9*(x^6+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{x^{10} \hypergeom \left(\left[-\frac{1}{3}, \frac{5}{3}\right], \left[\frac{8}{3}\right], -x^{6}\right)}{10}$&$17$\\ risch&$\frac{x^{4} \left(3 x^{6}+1\right) \left(x^{6}+1\right)^{\frac{1}{3}}}{36}-\frac{x^{4} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], -x^{6}\right)}{36}$&$37$\\ trager&$\frac{x^{4} \left(3 x^{6}+1\right) \left(x^{6}+1\right)^{\frac{1}{3}}}{36}+\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}-2 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}} x^{4}+x^{6}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x^{2}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1\right)}{54}-\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}+4 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}} x^{4}+4 x^{6}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x^{2}+3 x^{4} \left(x^{6}+1\right)^{\frac{1}{3}}+3 x^{2} \left(x^{6}+1\right)^{\frac{2}{3}}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+2\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{54}-\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}+4 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}} x^{4}+4 x^{6}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x^{2}+3 x^{4} \left(x^{6}+1\right)^{\frac{1}{3}}+3 x^{2} \left(x^{6}+1\right)^{\frac{2}{3}}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+2\right)}{54}$&$323$\\ \hline \end{longtable}"," ",0,"1/10*x^10*hypergeom([-1/3,5/3],[8/3],-x^6)","C"
1613,1,9006,31,283.903000," ","int((x^3-1)^(2/3)*(x^3+2)/x^6/(x^6+4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$9006$\\ trager&$\text{Expression too large to display}$&$12174$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1614,1,6835,31,269.169000," ","int((x^3-1)^(2/3)*(x^3+2)/x^6/(x^6+4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$6835$\\ trager&$\text{Expression too large to display}$&$10408$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1615,0,0,90,0.011000," ","int((x^6-a*x^3+b)/x^6/(a*x^4+b*x)^(1/4),x)","\[\int \frac{x^{6}-a \,x^{3}+b}{x^{6} \left(a \,x^{4}+b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((x^6-a*x^3+b)/x^6/(a*x^4+b*x)^(1/4),x)","F"
1616,0,0,90,0.009000," ","int((a*x^6-b)/x^6/(a*x^4+b*x)^(1/4),x)","\[\int \frac{a \,x^{6}-b}{x^{6} \left(a \,x^{4}+b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^6-b)/x^6/(a*x^4+b*x)^(1/4),x)","F"
1617,0,0,90,0.009000," ","int((a*x^6+b)/x^6/(a*x^4+b*x)^(1/4),x)","\[\int \frac{a \,x^{6}+b}{x^{6} \left(a \,x^{4}+b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^6+b)/x^6/(a*x^4+b*x)^(1/4),x)","F"
1618,0,0,92,0.029000," ","int((2*a*x^5-3*b)/(2*a*x^5+x^3+2*b)/(a*x^6+b*x)^(1/4),x)","\[\int \frac{2 a \,x^{5}-3 b}{\left(2 a \,x^{5}+x^{3}+2 b \right) \left(a \,x^{6}+b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((2*a*x^5-3*b)/(2*a*x^5+x^3+2*b)/(a*x^6+b*x)^(1/4),x)","F"
1619,0,0,14,0.040000," ","int(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6+2*b),x)","\[\int \frac{1}{\left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}} \left(a^{6} x^{6}+2 b \right)}\, dx\]"," ",0,"int(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6+2*b),x)","F"
1620,0,0,14,0.002000," ","int(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6+2*b),x)","\[\int \frac{1}{\left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}} \left(a^{6} x^{6}+2 b \right)}\, dx\]"," ",0,"int(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6+2*b),x)","F"
1621,1,152,82,1.850000," ","int((x^4-1)*(x^8+x^6+3*x^4+x^2+1)/(x^4+x^2+1)^(3/2)/(x^8+3*x^6+5*x^4+3*x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{x}{\sqrt{x^{4}+x^{2}+1}}-\frac{\ln \left(\frac{x^{4}+x^{2}+1}{x^{2}}+\frac{\sqrt{x^{4}+x^{2}+1}}{x}+1\right)}{2}-\frac{\sqrt{2}\, \sqrt{6}\, \arctan \left(\frac{\left(\frac{2 \sqrt{x^{4}+x^{2}+1}\, \sqrt{2}}{x}+\sqrt{2}\right) \sqrt{6}}{6}\right)}{6}+\frac{\ln \left(\frac{x^{4}+x^{2}+1}{x^{2}}-\frac{\sqrt{x^{4}+x^{2}+1}}{x}+1\right)}{2}-\frac{\sqrt{2}\, \sqrt{6}\, \arctan \left(\frac{\left(\frac{2 \sqrt{x^{4}+x^{2}+1}\, \sqrt{2}}{x}-\sqrt{2}\right) \sqrt{6}}{6}\right)}{6}$&$152$\\ elliptic&$\frac{\left(-\frac{\sqrt{2}\, \ln \left(\frac{x^{4}+x^{2}+1}{x^{2}}+\frac{\sqrt{x^{4}+x^{2}+1}}{x}+1\right)}{2}-\frac{\sqrt{6}\, \arctan \left(\frac{\left(\frac{2 \sqrt{x^{4}+x^{2}+1}\, \sqrt{2}}{x}+\sqrt{2}\right) \sqrt{6}}{6}\right)}{3}+\frac{\sqrt{2}\, \ln \left(\frac{x^{4}+x^{2}+1}{x^{2}}-\frac{\sqrt{x^{4}+x^{2}+1}}{x}+1\right)}{2}-\frac{\sqrt{6}\, \arctan \left(\frac{\left(\frac{2 \sqrt{x^{4}+x^{2}+1}\, \sqrt{2}}{x}-\sqrt{2}\right) \sqrt{6}}{6}\right)}{3}-\frac{\sqrt{2}\, x}{\sqrt{x^{4}+x^{2}+1}}\right) \sqrt{2}}{2}$&$160$\\ trager&$-\frac{x}{\sqrt{x^{4}+x^{2}+1}}-2 \ln \left(-\frac{x^{4}+12 \sqrt{x^{4}+x^{2}+1}\, \RootOf \left(12 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x -6 \RootOf \left(12 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}-4 \sqrt{x^{4}+x^{2}+1}\, x +2 x^{2}+1}{x^{4}+6 \RootOf \left(12 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}+1}\right) \RootOf \left(12 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)+2 \RootOf \left(12 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \ln \left(\frac{-x^{4}+12 \sqrt{x^{4}+x^{2}+1}\, \RootOf \left(12 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x -6 \RootOf \left(12 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}-2 \sqrt{x^{4}+x^{2}+1}\, x +x^{2}-1}{-x^{4}+6 \RootOf \left(12 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}-3 x^{2}-1}\right)+\ln \left(-\frac{x^{4}+12 \sqrt{x^{4}+x^{2}+1}\, \RootOf \left(12 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x -6 \RootOf \left(12 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}-4 \sqrt{x^{4}+x^{2}+1}\, x +2 x^{2}+1}{x^{4}+6 \RootOf \left(12 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}+1}\right)$&$314$\\ default&$-\frac{2 \left(\frac{1}{6} x^{3}+\frac{1}{3} x \right)}{\sqrt{x^{4}+x^{2}+1}}+\frac{-\frac{4}{3} x^{3}-\frac{2}{3} x}{\sqrt{x^{4}+x^{2}+1}}-\frac{6 \left(-\frac{1}{6} x +\frac{1}{6} x^{3}\right)}{\sqrt{x^{4}+x^{2}+1}}+\frac{\frac{8}{3} x^{3}-\frac{2}{3} x}{\sqrt{x^{4}+x^{2}+1}}-\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{6}+5 \textit{\_Z}^{4}+3 \textit{\_Z}^{2}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{6}+6 \underline{\hspace{1.25 ex}}\alpha^{4}+8 \underline{\hspace{1.25 ex}}\alpha^{2}+3\right) \left(-\frac{\arctanh \left(\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2}+1\right) \left(-12 \underline{\hspace{1.25 ex}}\alpha^{6}-30 \underline{\hspace{1.25 ex}}\alpha^{4}-45 \underline{\hspace{1.25 ex}}\alpha^{2}+7 x^{2}-10\right)}{14 \sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}+\underline{\hspace{1.25 ex}}\alpha^{2}+1}\, \sqrt{x^{4}+x^{2}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}+\underline{\hspace{1.25 ex}}\alpha^{2}+1}}-\frac{\sqrt{2}\, \left(-\underline{\hspace{1.25 ex}}\alpha^{7}-3 \underline{\hspace{1.25 ex}}\alpha^{5}-5 \underline{\hspace{1.25 ex}}\alpha^{3}-3 \underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{x^{2}+2-i \sqrt{3}\, x^{2}}\, \sqrt{x^{2}+2+i \sqrt{3}\, x^{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , \frac{i \underline{\hspace{1.25 ex}}\alpha^{6} \sqrt{3}}{2}+\frac{\underline{\hspace{1.25 ex}}\alpha^{6}}{2}+\frac{3}{2}+\frac{3 i \underline{\hspace{1.25 ex}}\alpha^{4} \sqrt{3}}{2}+\frac{3 \underline{\hspace{1.25 ex}}\alpha^{4}}{2}+\frac{5 i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{5 \underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{3 i \sqrt{3}}{2}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-1+i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}\right)\right)}{6}$&$356$\\ \hline \end{longtable}"," ",0,"-x/(x^4+x^2+1)^(1/2)-1/2*ln((x^4+x^2+1)/x^2+1/x*(x^4+x^2+1)^(1/2)+1)-1/6*2^(1/2)*6^(1/2)*arctan(1/6*(2*(x^4+x^2+1)^(1/2)*2^(1/2)/x+2^(1/2))*6^(1/2))+1/2*ln((x^4+x^2+1)/x^2-1/x*(x^4+x^2+1)^(1/2)+1)-1/6*2^(1/2)*6^(1/2)*arctan(1/6*(2*(x^4+x^2+1)^(1/2)*2^(1/2)/x-2^(1/2))*6^(1/2))","A"
1622,0,0,52,0.041000," ","int((a*x^8-b)/(a*x^4+b)^(1/4)/(a*x^8+b),x)","\[\int \frac{a \,x^{8}-b}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(a \,x^{8}+b \right)}\, dx\]"," ",0,"int((a*x^8-b)/(a*x^4+b)^(1/4)/(a*x^8+b),x)","F"
1623,0,0,52,0.002000," ","int((a*x^8-b)/(a*x^4+b)^(1/4)/(a*x^8+b),x)","\[\int \frac{a \,x^{8}-b}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(a \,x^{8}+b \right)}\, dx\]"," ",0,"int((a*x^8-b)/(a*x^4+b)^(1/4)/(a*x^8+b),x)","F"
1624,1,943,77,8.789000," ","int((2*x^5+2*x-3)*(x^6-x^2+x)^(1/2)/(x^10-x^8-3*x^6+2*x^5+x^4-x^3+x^2-2*x+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2}-5\right) \ln \left(-\frac{225 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{4} \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2}-5\right) x^{5}-225 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{4} \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2}-5\right) x^{3}+85 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2}-5\right) x^{5}-225 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{4} \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2}-5\right) x -40 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2}-5\right) x^{3}+8 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2}-5\right) x^{5}+225 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{4} \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2}-5\right)+350 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2} \sqrt{x^{6}-x^{2}+x}\, x -85 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2}-5\right) x +85 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2}-5\right)+50 \sqrt{x^{6}-x^{2}+x}\, x -8 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2}-5\right) x +8 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2}-5\right)}{5 x^{5} \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2}-5 x^{3} \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2}-x^{5}-5 x \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2}+2 x^{3}+5 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2}+x -1}\right)}{5}-\RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right) \ln \left(-\frac{225 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{5} x^{5}-225 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{5} x^{3}-175 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{3} x^{5}-225 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{5} x +130 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{3} x^{3}+34 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right) x^{5}+225 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{5}+175 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{3} x -70 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2} \sqrt{x^{6}-x^{2}+x}\, x -17 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right) x^{3}-175 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{3}-34 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right) x +24 \sqrt{x^{6}-x^{2}+x}\, x +34 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)}{5 x^{5} \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2}-5 x^{3} \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2}-5 x \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2}-x^{3}+5 \RootOf \left(25 \textit{\_Z}^{4}-5 \textit{\_Z}^{2}-1\right)^{2}}\right)$&$943$\\ \hline \end{longtable}"," ",0,"-1/5*RootOf(_Z^2+25*RootOf(25*_Z^4-5*_Z^2-1)^2-5)*ln(-(225*RootOf(25*_Z^4-5*_Z^2-1)^4*RootOf(_Z^2+25*RootOf(25*_Z^4-5*_Z^2-1)^2-5)*x^5-225*RootOf(25*_Z^4-5*_Z^2-1)^4*RootOf(_Z^2+25*RootOf(25*_Z^4-5*_Z^2-1)^2-5)*x^3+85*RootOf(25*_Z^4-5*_Z^2-1)^2*RootOf(_Z^2+25*RootOf(25*_Z^4-5*_Z^2-1)^2-5)*x^5-225*RootOf(25*_Z^4-5*_Z^2-1)^4*RootOf(_Z^2+25*RootOf(25*_Z^4-5*_Z^2-1)^2-5)*x-40*RootOf(25*_Z^4-5*_Z^2-1)^2*RootOf(_Z^2+25*RootOf(25*_Z^4-5*_Z^2-1)^2-5)*x^3+8*RootOf(_Z^2+25*RootOf(25*_Z^4-5*_Z^2-1)^2-5)*x^5+225*RootOf(25*_Z^4-5*_Z^2-1)^4*RootOf(_Z^2+25*RootOf(25*_Z^4-5*_Z^2-1)^2-5)+350*RootOf(25*_Z^4-5*_Z^2-1)^2*(x^6-x^2+x)^(1/2)*x-85*RootOf(25*_Z^4-5*_Z^2-1)^2*RootOf(_Z^2+25*RootOf(25*_Z^4-5*_Z^2-1)^2-5)*x+85*RootOf(25*_Z^4-5*_Z^2-1)^2*RootOf(_Z^2+25*RootOf(25*_Z^4-5*_Z^2-1)^2-5)+50*(x^6-x^2+x)^(1/2)*x-8*RootOf(_Z^2+25*RootOf(25*_Z^4-5*_Z^2-1)^2-5)*x+8*RootOf(_Z^2+25*RootOf(25*_Z^4-5*_Z^2-1)^2-5))/(5*x^5*RootOf(25*_Z^4-5*_Z^2-1)^2-5*x^3*RootOf(25*_Z^4-5*_Z^2-1)^2-x^5-5*x*RootOf(25*_Z^4-5*_Z^2-1)^2+2*x^3+5*RootOf(25*_Z^4-5*_Z^2-1)^2+x-1))-RootOf(25*_Z^4-5*_Z^2-1)*ln(-(225*RootOf(25*_Z^4-5*_Z^2-1)^5*x^5-225*RootOf(25*_Z^4-5*_Z^2-1)^5*x^3-175*RootOf(25*_Z^4-5*_Z^2-1)^3*x^5-225*RootOf(25*_Z^4-5*_Z^2-1)^5*x+130*RootOf(25*_Z^4-5*_Z^2-1)^3*x^3+34*RootOf(25*_Z^4-5*_Z^2-1)*x^5+225*RootOf(25*_Z^4-5*_Z^2-1)^5+175*RootOf(25*_Z^4-5*_Z^2-1)^3*x-70*RootOf(25*_Z^4-5*_Z^2-1)^2*(x^6-x^2+x)^(1/2)*x-17*RootOf(25*_Z^4-5*_Z^2-1)*x^3-175*RootOf(25*_Z^4-5*_Z^2-1)^3-34*RootOf(25*_Z^4-5*_Z^2-1)*x+24*(x^6-x^2+x)^(1/2)*x+34*RootOf(25*_Z^4-5*_Z^2-1))/(5*x^5*RootOf(25*_Z^4-5*_Z^2-1)^2-5*x^3*RootOf(25*_Z^4-5*_Z^2-1)^2-5*x*RootOf(25*_Z^4-5*_Z^2-1)^2-x^3+5*RootOf(25*_Z^4-5*_Z^2-1)^2))","C"
1625,1,298,82,0.069000," ","int((x+(1+x)^(1/2))^(1/2)/x^2/(1+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\left(\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2\right)^{\frac{3}{2}}}{2 \left(-1+\sqrt{1+x}\right)}+\frac{\sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}}{4}-\frac{\ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}\right)}{4}-\frac{\arctanh \left(\frac{-1+3 \sqrt{1+x}}{2 \sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}}\right)}{4}+\frac{\left(2 \sqrt{1+x}+1\right) \sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}}{4}+\frac{\left(\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2\right)^{\frac{3}{2}}}{2+2 \sqrt{1+x}}+\frac{3 \sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}}{4}+\frac{\ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}\right)}{4}-\frac{3 \arctan \left(\frac{-3-\sqrt{1+x}}{2 \sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}}\right)}{4}-\frac{\left(2 \sqrt{1+x}+1\right) \sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}}{4}$&$298$\\ default&$-\frac{\left(\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2\right)^{\frac{3}{2}}}{2 \left(-1+\sqrt{1+x}\right)}+\frac{\sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}}{4}-\frac{\ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}\right)}{4}-\frac{\arctanh \left(\frac{-1+3 \sqrt{1+x}}{2 \sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}}\right)}{4}+\frac{\left(2 \sqrt{1+x}+1\right) \sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}}{4}+\frac{\left(\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2\right)^{\frac{3}{2}}}{2+2 \sqrt{1+x}}+\frac{3 \sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}}{4}+\frac{\ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}\right)}{4}-\frac{3 \arctan \left(\frac{-3-\sqrt{1+x}}{2 \sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}}\right)}{4}-\frac{\left(2 \sqrt{1+x}+1\right) \sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}}{4}$&$298$\\ \hline \end{longtable}"," ",0,"-1/2/(-1+(1+x)^(1/2))*((-1+(1+x)^(1/2))^2+3*(1+x)^(1/2)-2)^(3/2)+1/4*((-1+(1+x)^(1/2))^2+3*(1+x)^(1/2)-2)^(1/2)-1/4*ln(1/2+(1+x)^(1/2)+((-1+(1+x)^(1/2))^2+3*(1+x)^(1/2)-2)^(1/2))-1/4*arctanh(1/2*(-1+3*(1+x)^(1/2))/((-1+(1+x)^(1/2))^2+3*(1+x)^(1/2)-2)^(1/2))+1/4*(2*(1+x)^(1/2)+1)*((-1+(1+x)^(1/2))^2+3*(1+x)^(1/2)-2)^(1/2)+1/2/(1+(1+x)^(1/2))*((1+(1+x)^(1/2))^2-(1+x)^(1/2)-2)^(3/2)+3/4*((1+(1+x)^(1/2))^2-(1+x)^(1/2)-2)^(1/2)+1/4*ln(1/2+(1+x)^(1/2)+((1+(1+x)^(1/2))^2-(1+x)^(1/2)-2)^(1/2))-3/4*arctan(1/2*(-3-(1+x)^(1/2))/((1+(1+x)^(1/2))^2-(1+x)^(1/2)-2)^(1/2))-1/4*(2*(1+x)^(1/2)+1)*((1+(1+x)^(1/2))^2-(1+x)^(1/2)-2)^(1/2)","B"
1626,1,170,86,0.066000," ","int((x+(1+x)^(1/2))^(1/2)/x/(1+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}+\frac{\ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}\right)}{2}+\arctan \left(\frac{-3-\sqrt{1+x}}{2 \sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}}\right)+\sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}+\frac{3 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}\right)}{2}-\arctanh \left(\frac{-1+3 \sqrt{1+x}}{2 \sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}}\right)$&$170$\\ default&$-\sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}+\frac{\ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}\right)}{2}+\arctan \left(\frac{-3-\sqrt{1+x}}{2 \sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}}\right)+\sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}+\frac{3 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}\right)}{2}-\arctanh \left(\frac{-1+3 \sqrt{1+x}}{2 \sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}}\right)$&$170$\\ \hline \end{longtable}"," ",0,"-((1+(1+x)^(1/2))^2-(1+x)^(1/2)-2)^(1/2)+1/2*ln(1/2+(1+x)^(1/2)+((1+(1+x)^(1/2))^2-(1+x)^(1/2)-2)^(1/2))+arctan(1/2*(-3-(1+x)^(1/2))/((1+(1+x)^(1/2))^2-(1+x)^(1/2)-2)^(1/2))+((-1+(1+x)^(1/2))^2+3*(1+x)^(1/2)-2)^(1/2)+3/2*ln(1/2+(1+x)^(1/2)+((-1+(1+x)^(1/2))^2+3*(1+x)^(1/2)-2)^(1/2))-arctanh(1/2*(-1+3*(1+x)^(1/2))/((-1+(1+x)^(1/2))^2+3*(1+x)^(1/2)-2)^(1/2))","A"
1627,1,71,90,0.075000," ","int((a*x+(a*x-b)^(1/2))^(1/2)/(a*x-b)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{2}+\frac{\left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{4}}{a}$&$71$\\ default&$\frac{\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{2}+\frac{\left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{4}}{a}$&$71$\\ \hline \end{longtable}"," ",0,"2/a*(1/4*(2*(a*x-b)^(1/2)+1)*(a*x+(a*x-b)^(1/2))^(1/2)+1/8*(4*b-1)*ln(1/2+(a*x-b)^(1/2)+(a*x+(a*x-b)^(1/2))^(1/2)))","A"
1628,1,106,96,0.118000," ","int((1-a*x+b*(b*x+a)^(1/2))/(b*x+a)^(1/2)/(x+a*b*(b*x+a)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{2 \left(a \sqrt{b x +a}-b \left(\frac{\left(a^{2} b +b \right) \ln \left(b x +a \,b^{2} \sqrt{b x +a}\right)}{2}-\frac{2 \left(1-\frac{\left(a^{2} b +b \right) a \,b^{2}}{2}\right) \arctanh \left(\frac{a \,b^{2}+2 \sqrt{b x +a}}{\sqrt{a^{2} b^{4}+4 a}}\right)}{\sqrt{a^{2} b^{4}+4 a}}\right)\right)}{b}$&$106$\\ default&$-\frac{2 \left(a \sqrt{b x +a}-b \left(\frac{\left(a^{2} b +b \right) \ln \left(b x +a \,b^{2} \sqrt{b x +a}\right)}{2}-\frac{2 \left(1-\frac{\left(a^{2} b +b \right) a \,b^{2}}{2}\right) \arctanh \left(\frac{a \,b^{2}+2 \sqrt{b x +a}}{\sqrt{a^{2} b^{4}+4 a}}\right)}{\sqrt{a^{2} b^{4}+4 a}}\right)\right)}{b}$&$106$\\ \hline \end{longtable}"," ",0,"-2/b*(a*(b*x+a)^(1/2)-b*(1/2*(a^2*b+b)*ln(b*x+a*b^2*(b*x+a)^(1/2))-2*(1-1/2*(a^2*b+b)*a*b^2)/(a^2*b^4+4*a)^(1/2)*arctanh((a*b^2+2*(b*x+a)^(1/2))/(a^2*b^4+4*a)^(1/2))))","A"
1629,1,31,83,0.043000," ","int((b+(a*x^2+b^2)^(1/2))^(1/2)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \hypergeom \left(\left[-\frac{1}{2}, -\frac{1}{4}, \frac{1}{4}\right], \left[\frac{1}{2}, \frac{1}{2}\right], -\frac{x^{2} a}{b^{2}}\right)}{x}$&$31$\\ \hline \end{longtable}"," ",0,"-(b^2)^(1/4)*2^(1/2)/x*hypergeom([-1/2,-1/4,1/4],[1/2,1/2],-x^2*a/b^2)","C"
1630,0,0,96,0.044000," ","int(1/(a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x)","\[\int \frac{1}{\sqrt{a^{2} x^{2}-b x}\, \left(a \,x^{2}+x \sqrt{a^{2} x^{2}-b x}\right)^{\frac{3}{2}}}\, dx\]"," ",0,"int(1/(a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x)","F"
1631,0,0,90,0.016000," ","int(1/(1+(x+(x^2+1)^(1/2))^(1/2)),x)","\[\int \frac{1}{1+\sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int(1/(1+(x+(x^2+1)^(1/2))^(1/2)),x)","F"
1632,1,552,91,2.236000," ","int((-2+x)/(x^2+2)/(2*x^2+x-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(-\frac{4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{2}+16 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x -6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(2 x^{2}+x -1\right)^{\frac{1}{3}} x +6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{2}-6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(2 x^{2}+x -1\right)^{\frac{1}{3}}+20 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x +3 \left(2 x^{2}+x -1\right)^{\frac{2}{3}}-3 x \left(2 x^{2}+x -1\right)^{\frac{1}{3}}+2 x^{2}+2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)-3 \left(2 x^{2}+x -1\right)^{\frac{1}{3}}+4 x +2}{x^{2}+2}\right)}{2}-\frac{\ln \left(-\frac{4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{2}+16 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x -6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(2 x^{2}+x -1\right)^{\frac{1}{3}} x +4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{2}-6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(2 x^{2}+x -1\right)^{\frac{1}{3}}+20 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x +3 \left(2 x^{2}+x -1\right)^{\frac{2}{3}}-3 x \left(2 x^{2}+x -1\right)^{\frac{1}{3}}-2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)-3 \left(2 x^{2}+x -1\right)^{\frac{1}{3}}+4 x -2}{x^{2}+2}\right)}{2}-\ln \left(-\frac{4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{2}+16 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x -6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(2 x^{2}+x -1\right)^{\frac{1}{3}} x +4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{2}-6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(2 x^{2}+x -1\right)^{\frac{1}{3}}+20 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x +3 \left(2 x^{2}+x -1\right)^{\frac{2}{3}}-3 x \left(2 x^{2}+x -1\right)^{\frac{1}{3}}-2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)-3 \left(2 x^{2}+x -1\right)^{\frac{1}{3}}+4 x -2}{x^{2}+2}\right) \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)$&$552$\\ \hline \end{longtable}"," ",0,"1/2*ln(-(4*RootOf(4*_Z^2+2*_Z+1)^2*x^2+16*RootOf(4*_Z^2+2*_Z+1)^2*x-6*RootOf(4*_Z^2+2*_Z+1)*(2*x^2+x-1)^(1/3)*x+6*RootOf(4*_Z^2+2*_Z+1)*x^2-6*RootOf(4*_Z^2+2*_Z+1)*(2*x^2+x-1)^(1/3)+20*RootOf(4*_Z^2+2*_Z+1)*x+3*(2*x^2+x-1)^(2/3)-3*x*(2*x^2+x-1)^(1/3)+2*x^2+2*RootOf(4*_Z^2+2*_Z+1)-3*(2*x^2+x-1)^(1/3)+4*x+2)/(x^2+2))-1/2*ln(-(4*RootOf(4*_Z^2+2*_Z+1)^2*x^2+16*RootOf(4*_Z^2+2*_Z+1)^2*x-6*RootOf(4*_Z^2+2*_Z+1)*(2*x^2+x-1)^(1/3)*x+4*RootOf(4*_Z^2+2*_Z+1)*x^2-6*RootOf(4*_Z^2+2*_Z+1)*(2*x^2+x-1)^(1/3)+20*RootOf(4*_Z^2+2*_Z+1)*x+3*(2*x^2+x-1)^(2/3)-3*x*(2*x^2+x-1)^(1/3)-2*RootOf(4*_Z^2+2*_Z+1)-3*(2*x^2+x-1)^(1/3)+4*x-2)/(x^2+2))-ln(-(4*RootOf(4*_Z^2+2*_Z+1)^2*x^2+16*RootOf(4*_Z^2+2*_Z+1)^2*x-6*RootOf(4*_Z^2+2*_Z+1)*(2*x^2+x-1)^(1/3)*x+4*RootOf(4*_Z^2+2*_Z+1)*x^2-6*RootOf(4*_Z^2+2*_Z+1)*(2*x^2+x-1)^(1/3)+20*RootOf(4*_Z^2+2*_Z+1)*x+3*(2*x^2+x-1)^(2/3)-3*x*(2*x^2+x-1)^(1/3)-2*RootOf(4*_Z^2+2*_Z+1)-3*(2*x^2+x-1)^(1/3)+4*x-2)/(x^2+2))*RootOf(4*_Z^2+2*_Z+1)","C"
1633,0,0,97,0.015000," ","int((-a+x)*(-b+x)*(-2*a*b+(a+b)*x)/(x^2*(-a+x)*(-b+x))^(3/4)/(-a*b+(a+b)*x+(-1+d)*x^2),x)","\[\int \frac{\left(-a +x \right) \left(-b +x \right) \left(-2 a b +\left(a +b \right) x \right)}{\left(x^{2} \left(-a +x \right) \left(-b +x \right)\right)^{\frac{3}{4}} \left(-a b +\left(a +b \right) x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((-a+x)*(-b+x)*(-2*a*b+(a+b)*x)/(x^2*(-a+x)*(-b+x))^(3/4)/(-a*b+(a+b)*x+(-1+d)*x^2),x)","F"
1634,1,582,79,2.714000," ","int((x^2-x+1)/(x^2+2*x-2)/(x^3+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right) \ln \left(-\frac{-240 \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)^{5} x^{2}+480 \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)^{5} x -232 \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)^{3} x^{2}+304 \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)^{3} x +32 \sqrt{x^{3}+1}\, \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)^{2}-160 \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)^{3}-55 \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right) x^{2}+22 \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right) x +16 \sqrt{x^{3}+1}-88 \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)}{\left(12 \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)^{2} x +5 x -4\right)^{2}}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{2}+4 \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)^{2}+2\right) \ln \left(\frac{-240 \RootOf \left(\textit{\_Z}^{2}+4 \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)^{2}+2\right) \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)^{4} x^{2}+480 \RootOf \left(\textit{\_Z}^{2}+4 \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)^{2}+2\right) \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)^{4} x -8 \RootOf \left(\textit{\_Z}^{2}+4 \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)^{2}+2\right) \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)^{2} x^{2}+176 \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+4 \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)^{2}+2\right) x +64 \sqrt{x^{3}+1}\, \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)^{2}+160 \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+4 \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)^{2}+2\right)+\RootOf \left(\textit{\_Z}^{2}+4 \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)^{2}+2\right) x^{2}-10 \RootOf \left(\textit{\_Z}^{2}+4 \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)^{2}+2\right) x -8 \RootOf \left(\textit{\_Z}^{2}+4 \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)^{2}+2\right)}{\left(12 \RootOf \left(48 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}-1\right)^{2} x +x +4\right)^{2}}\right)}{4}$&$582$\\ default&$\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{3 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}}-\frac{3 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{3 i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}}+\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}-\frac{3 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{3 i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}}+\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}-\frac{3 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}}$&$1501$\\ elliptic&$\frac{3 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}+\frac{3 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}}-\frac{3 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{3 i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}}+\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}-\frac{3 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{3 i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}+1}}+\frac{i \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{\sqrt{x^{3}+1}}-\frac{3 \sqrt{\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{1+x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right) \sqrt{3}}{2 \sqrt{x^{3}+1}}$&$1706$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(48*_Z^4+24*_Z^2-1)*ln(-(-240*RootOf(48*_Z^4+24*_Z^2-1)^5*x^2+480*RootOf(48*_Z^4+24*_Z^2-1)^5*x-232*RootOf(48*_Z^4+24*_Z^2-1)^3*x^2+304*RootOf(48*_Z^4+24*_Z^2-1)^3*x+32*(x^3+1)^(1/2)*RootOf(48*_Z^4+24*_Z^2-1)^2-160*RootOf(48*_Z^4+24*_Z^2-1)^3-55*RootOf(48*_Z^4+24*_Z^2-1)*x^2+22*RootOf(48*_Z^4+24*_Z^2-1)*x+16*(x^3+1)^(1/2)-88*RootOf(48*_Z^4+24*_Z^2-1))/(12*RootOf(48*_Z^4+24*_Z^2-1)^2*x+5*x-4)^2)-1/4*RootOf(_Z^2+4*RootOf(48*_Z^4+24*_Z^2-1)^2+2)*ln((-240*RootOf(_Z^2+4*RootOf(48*_Z^4+24*_Z^2-1)^2+2)*RootOf(48*_Z^4+24*_Z^2-1)^4*x^2+480*RootOf(_Z^2+4*RootOf(48*_Z^4+24*_Z^2-1)^2+2)*RootOf(48*_Z^4+24*_Z^2-1)^4*x-8*RootOf(_Z^2+4*RootOf(48*_Z^4+24*_Z^2-1)^2+2)*RootOf(48*_Z^4+24*_Z^2-1)^2*x^2+176*RootOf(48*_Z^4+24*_Z^2-1)^2*RootOf(_Z^2+4*RootOf(48*_Z^4+24*_Z^2-1)^2+2)*x+64*(x^3+1)^(1/2)*RootOf(48*_Z^4+24*_Z^2-1)^2+160*RootOf(48*_Z^4+24*_Z^2-1)^2*RootOf(_Z^2+4*RootOf(48*_Z^4+24*_Z^2-1)^2+2)+RootOf(_Z^2+4*RootOf(48*_Z^4+24*_Z^2-1)^2+2)*x^2-10*RootOf(_Z^2+4*RootOf(48*_Z^4+24*_Z^2-1)^2+2)*x-8*RootOf(_Z^2+4*RootOf(48*_Z^4+24*_Z^2-1)^2+2))/(12*RootOf(48*_Z^4+24*_Z^2-1)^2*x+x+4)^2)","C"
1635,1,42,93,0.583000," ","int((-1+x)/x/(x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{3 \left(-1+x \right)}{2 \left(\left(-1+x \right) x^{2}\right)^{\frac{1}{3}}}+\frac{3 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{3}} x^{\frac{1}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x\right)}{\mathrm{signum}\left(-1+x \right)^{\frac{1}{3}}}$&$42$\\ meijerg&$\frac{3 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{3}} \left(1-x \right)^{\frac{2}{3}}}{2 \mathrm{signum}\left(-1+x \right)^{\frac{1}{3}} x^{\frac{2}{3}}}+\frac{3 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{3}} x^{\frac{1}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x\right)}{\mathrm{signum}\left(-1+x \right)^{\frac{1}{3}}}$&$54$\\ trager&$-\frac{3 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}}{2 x^{2}}+6 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \ln \left(\frac{180 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{2}-360 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x +144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{1}{3}} x +114 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}-18 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x -9 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}-9 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}-4 x^{2}+x}{x}\right)-6 \ln \left(\frac{180 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{2}-360 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x -144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}-144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{1}{3}} x -174 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}+138 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x +15 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+15 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}+20 x^{2}-12 x}{x}\right) \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)+\ln \left(\frac{180 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{2}-360 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x -144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}-144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{1}{3}} x -174 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}+138 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x +15 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+15 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}+20 x^{2}-12 x}{x}\right)$&$504$\\ \hline \end{longtable}"," ",0,"-3/2*(-1+x)/((-1+x)*x^2)^(1/3)+3/signum(-1+x)^(1/3)*(-signum(-1+x))^(1/3)*x^(1/3)*hypergeom([1/3,1/3],[4/3],x)","C"
1636,1,42,93,0.559000," ","int((1+x)/x/(x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{-\frac{3}{2}+\frac{3 x}{2}}{\left(\left(-1+x \right) x^{2}\right)^{\frac{1}{3}}}+\frac{3 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{3}} x^{\frac{1}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x\right)}{\mathrm{signum}\left(-1+x \right)^{\frac{1}{3}}}$&$42$\\ meijerg&$-\frac{3 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{3}} \left(1-x \right)^{\frac{2}{3}}}{2 \mathrm{signum}\left(-1+x \right)^{\frac{1}{3}} x^{\frac{2}{3}}}+\frac{3 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{3}} x^{\frac{1}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x\right)}{\mathrm{signum}\left(-1+x \right)^{\frac{1}{3}}}$&$54$\\ trager&$\frac{3 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}}{2 x^{2}}-6 \ln \left(\frac{180 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{2}-360 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x -144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}-144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{1}{3}} x -174 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}+138 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x +15 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+15 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}+20 x^{2}-12 x}{x}\right) \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)+6 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \ln \left(\frac{180 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{2}-360 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x +144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{1}{3}} x +114 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}-18 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x -9 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}-9 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}-4 x^{2}+x}{x}\right)+\ln \left(\frac{180 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{2}-360 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x -144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}-144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{1}{3}} x -174 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}+138 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x +15 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+15 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}+20 x^{2}-12 x}{x}\right)$&$504$\\ \hline \end{longtable}"," ",0,"3/2*(-1+x)/((-1+x)*x^2)^(1/3)+3/signum(-1+x)^(1/3)*(-signum(-1+x))^(1/3)*x^(1/3)*hypergeom([1/3,1/3],[4/3],x)","C"
1637,1,15,89,0.595000," ","int(x^2/(x^3+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 x^{\frac{7}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{7}{3}\right], \left[\frac{10}{3}\right], -x \right)}{7}$&$15$\\ risch&$\frac{\left(-4+3 x \right) x \left(1+x \right)}{6 \left(x^{2} \left(1+x \right)\right)^{\frac{1}{3}}}+\frac{2 x^{\frac{1}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x \right)}{3}$&$36$\\ trager&$\frac{\left(-4+3 x \right) \left(x^{3}+x^{2}\right)^{\frac{2}{3}}}{6 x}-\frac{2 \ln \left(\frac{-36 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{2}+90 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{2}{3}}-144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{1}{3}} x +36 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x +60 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}+9 \left(x^{3}+x^{2}\right)^{\frac{2}{3}}+15 x \left(x^{3}+x^{2}\right)^{\frac{1}{3}}-18 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x -25 x^{2}-10 x}{x}\right)}{9}+\frac{4 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \ln \left(-\frac{-180 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{2}+90 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{2}{3}}+54 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{1}{3}} x +180 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x -114 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}-24 \left(x^{3}+x^{2}\right)^{\frac{2}{3}}+15 x \left(x^{3}+x^{2}\right)^{\frac{1}{3}}-96 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x +4 x^{2}+3 x}{x}\right)}{3}$&$329$\\ \hline \end{longtable}"," ",0,"3/7*x^(7/3)*hypergeom([1/3,7/3],[10/3],-x)","C"
1638,0,0,97,0.094000," ","int((a-3*b+2*x)*(-a^3+3*a^2*x-3*a*x^2+x^3)/(-b+x)/((-a+x)*(-b+x))^(1/4)/(-a^3+b*d-(-3*a^2+d)*x-3*a*x^2+x^3),x)","\[\int \frac{\left(a -3 b +2 x \right) \left(-a^{3}+3 a^{2} x -3 a \,x^{2}+x^{3}\right)}{\left(-b +x \right) \left(\left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{4}} \left(-a^{3}+b d -\left(-3 a^{2}+d \right) x -3 a \,x^{2}+x^{3}\right)}\, dx\]"," ",0,"int((a-3*b+2*x)*(-a^3+3*a^2*x-3*a*x^2+x^3)/(-b+x)/((-a+x)*(-b+x))^(1/4)/(-a^3+b*d-(-3*a^2+d)*x-3*a*x^2+x^3),x)","F"
1639,0,0,97,0.049000," ","int(x^3*(3-2*(1+k)*x+k*x^2)/(-1+x)/((1-x)*x*(-k*x+1))^(1/4)/(k*x-1)/(-d+d*(1+k)*x-d*k*x^2+x^3),x)","\[\int \frac{x^{3} \left(3-2 \left(1+k \right) x +k \,x^{2}\right)}{\left(-1+x \right) \left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{4}} \left(k x -1\right) \left(-d +d \left(1+k \right) x -d k \,x^{2}+x^{3}\right)}\, dx\]"," ",0,"int(x^3*(3-2*(1+k)*x+k*x^2)/(-1+x)/((1-x)*x*(-k*x+1))^(1/4)/(k*x-1)/(-d+d*(1+k)*x-d*k*x^2+x^3),x)","F"
1640,1,364,91,4.508000," ","int((x^3+2)*(2*x^3+1)^(2/3)/x^6/(x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{6 x^{6}+11 x^{3}+4}{10 x^{5} \left(2 x^{3}+1\right)^{\frac{1}{3}}}-\frac{\ln \left(-\frac{9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}-3 \left(2 x^{3}+1\right)^{\frac{2}{3}} x -3 \left(2 x^{3}+1\right)^{\frac{1}{3}} x^{2}-4 x^{3}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-2}{\left(1+x \right) \left(x^{2}-x +1\right)}\right)}{3}-\ln \left(-\frac{9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}-3 \left(2 x^{3}+1\right)^{\frac{2}{3}} x -3 \left(2 x^{3}+1\right)^{\frac{1}{3}} x^{2}-4 x^{3}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-2}{\left(1+x \right) \left(x^{2}-x +1\right)}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+\RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(\frac{18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+15 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(2 x^{3}+1\right)^{\frac{2}{3}} x +15 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(2 x^{3}+1\right)^{\frac{1}{3}} x^{2}+27 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+4 \left(2 x^{3}+1\right)^{\frac{2}{3}} x +4 \left(2 x^{3}+1\right)^{\frac{1}{3}} x^{2}+9 x^{3}+6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+3}{\left(1+x \right) \left(x^{2}-x +1\right)}\right)$&$364$\\ trager&$-\frac{\left(3 x^{3}+4\right) \left(2 x^{3}+1\right)^{\frac{2}{3}}}{10 x^{5}}+\frac{\ln \left(\frac{12321 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}-48096 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(2 x^{3}+1\right)^{\frac{2}{3}} x +99369 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(2 x^{3}+1\right)^{\frac{1}{3}} x^{2}-48225 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}-33123 \left(2 x^{3}+1\right)^{\frac{2}{3}} x +17091 \left(2 x^{3}+1\right)^{\frac{1}{3}} x^{2}+33786 x^{3}-12321 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-5166 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+15016}{\left(1+x \right) \left(x^{2}-x +1\right)}\right)}{3}-\frac{\ln \left(-\frac{46107 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}-48096 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(2 x^{3}+1\right)^{\frac{2}{3}} x -51273 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(2 x^{3}+1\right)^{\frac{1}{3}} x^{2}+164952 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+17091 \left(2 x^{3}+1\right)^{\frac{2}{3}} x -33123 \left(2 x^{3}+1\right)^{\frac{1}{3}} x^{2}+37540 x^{3}-46107 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+34845 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+11262}{\left(1+x \right) \left(x^{2}-x +1\right)}\right)}{3}-\ln \left(-\frac{46107 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}-48096 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(2 x^{3}+1\right)^{\frac{2}{3}} x -51273 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(2 x^{3}+1\right)^{\frac{1}{3}} x^{2}+164952 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+17091 \left(2 x^{3}+1\right)^{\frac{2}{3}} x -33123 \left(2 x^{3}+1\right)^{\frac{1}{3}} x^{2}+37540 x^{3}-46107 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+34845 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+11262}{\left(1+x \right) \left(x^{2}-x +1\right)}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)$&$522$\\ \hline \end{longtable}"," ",0,"-1/10*(6*x^6+11*x^3+4)/x^5/(2*x^3+1)^(1/3)-1/3*ln(-(9*RootOf(9*_Z^2+3*_Z+1)^2*x^3-3*(2*x^3+1)^(2/3)*x-3*(2*x^3+1)^(1/3)*x^2-4*x^3-3*RootOf(9*_Z^2+3*_Z+1)-2)/(1+x)/(x^2-x+1))-ln(-(9*RootOf(9*_Z^2+3*_Z+1)^2*x^3-3*(2*x^3+1)^(2/3)*x-3*(2*x^3+1)^(1/3)*x^2-4*x^3-3*RootOf(9*_Z^2+3*_Z+1)-2)/(1+x)/(x^2-x+1))*RootOf(9*_Z^2+3*_Z+1)+RootOf(9*_Z^2+3*_Z+1)*ln((18*RootOf(9*_Z^2+3*_Z+1)^2*x^3+15*RootOf(9*_Z^2+3*_Z+1)*(2*x^3+1)^(2/3)*x+15*RootOf(9*_Z^2+3*_Z+1)*(2*x^3+1)^(1/3)*x^2+27*RootOf(9*_Z^2+3*_Z+1)*x^3+4*(2*x^3+1)^(2/3)*x+4*(2*x^3+1)^(1/3)*x^2+9*x^3+6*RootOf(9*_Z^2+3*_Z+1)+3)/(1+x)/(x^2-x+1))","C"
1641,0,0,99,0.015000," ","int((3*a*b^2-2*b*(2*a+b)*x+(a+2*b)*x^2)/(x*(-a+x)*(-b+x)^2)^(1/4)/(-a*b^2*d+b*(2*a+b)*d*x-(a+2*b)*d*x^2+(-1+d)*x^3),x)","\[\int \frac{3 a \,b^{2}-2 b \left(2 a +b \right) x +\left(a +2 b \right) x^{2}}{\left(x \left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{4}} \left(-a \,b^{2} d +b \left(2 a +b \right) d x -\left(a +2 b \right) d \,x^{2}+\left(-1+d \right) x^{3}\right)}\, dx\]"," ",0,"int((3*a*b^2-2*b*(2*a+b)*x+(a+2*b)*x^2)/(x*(-a+x)*(-b+x)^2)^(1/4)/(-a*b^2*d+b*(2*a+b)*d*x-(a+2*b)*d*x^2+(-1+d)*x^3),x)","F"
1642,0,0,93,0.009000," ","int((c*x+d)*(a*x^4-b*x^3)^(1/4)/x^2,x)","\[\int \frac{\left(c x +d \right) \left(a \,x^{4}-b \,x^{3}\right)^{\frac{1}{4}}}{x^{2}}\, dx\]"," ",0,"int((c*x+d)*(a*x^4-b*x^3)^(1/4)/x^2,x)","F"
1643,1,423,89,9.851000," ","int((x^5+3)*(x^5+x^3-2)^(1/3)/x^2/(x^5-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(x^{5}+x^{3}-2\right)^{\frac{1}{3}}}{2 x}+\frac{\ln \left(\frac{-3687964213260096 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{5}-1951741557610164 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{5}+13829865799725360 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{3}-88450351904093 x^{5}+2398485078249264 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{5}+x^{3}-2\right)^{\frac{2}{3}} x +136263463016940 \left(x^{5}+x^{3}-2\right)^{\frac{1}{3}} \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{2}-1382259724622424 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{3}-11355288584745 \left(x^{5}+x^{3}-2\right)^{\frac{2}{3}} x +211229045105517 \left(x^{5}+x^{3}-2\right)^{\frac{1}{3}} x^{2}-103833021800457 x^{3}+7375928426520192 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}+3903483115220328 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)+176900703808186}{x^{5}-2}\right)}{2}+6 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \ln \left(-\frac{-1472859748183680 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{5}+767599022412408 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{5}+5523224055688800 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{3}-73067682007729 x^{5}+2398485078249264 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{5}+x^{3}-2\right)^{\frac{2}{3}} x -2534748541266204 \left(x^{5}+x^{3}-2\right)^{\frac{1}{3}} \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{2}+596532134324340 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{3}+211229045105517 \left(x^{5}+x^{3}-2\right)^{\frac{2}{3}} x -11355288584745 \left(x^{5}+x^{3}-2\right)^{\frac{1}{3}} x^{2}-161518033911822 x^{3}+2945719496367360 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}-1535198044824816 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)+146135364015458}{x^{5}-2}\right)$&$423$\\ risch&$\frac{3 \left(x^{5}+x^{3}-2\right)^{\frac{1}{3}}}{2 x}+\frac{\left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\frac{-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{10}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{8}-x^{10}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{8}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{10}+2 x^{8}+x^{6}-4 x^{5}-4 x^{3}+4\right)^{\frac{1}{3}} x^{6}-2 x^{8}-x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-3 \left(x^{10}+2 x^{8}+x^{6}-4 x^{5}-4 x^{3}+4\right)^{\frac{1}{3}} x^{6}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{10}+2 x^{8}+x^{6}-4 x^{5}-4 x^{3}+4\right)^{\frac{1}{3}} x^{4}+8 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{5}-x^{6}-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{10}+2 x^{8}+x^{6}-4 x^{5}-4 x^{3}+4\right)^{\frac{2}{3}} x^{2}-3 \left(x^{10}+2 x^{8}+x^{6}-4 x^{5}-4 x^{3}+4\right)^{\frac{1}{3}} x^{4}+4 x^{5}+6 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-3 \left(x^{10}+2 x^{8}+x^{6}-4 x^{5}-4 x^{3}+4\right)^{\frac{2}{3}} x^{2}+6 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{10}+2 x^{8}+x^{6}-4 x^{5}-4 x^{3}+4\right)^{\frac{1}{3}} x +4 x^{3}+6 \left(x^{10}+2 x^{8}+x^{6}-4 x^{5}-4 x^{3}+4\right)^{\frac{1}{3}} x -8 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-4}{\left(-1+x \right) \left(x^{5}-2\right) \left(x^{4}+x^{3}+2 x^{2}+2 x +2\right)}\right)}{2}-\frac{\ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{10}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{8}+x^{10}+7 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{8}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{10}+2 x^{8}+x^{6}-4 x^{5}-4 x^{3}+4\right)^{\frac{1}{3}} x^{6}+3 x^{8}+5 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{10}+2 x^{8}+x^{6}-4 x^{5}-4 x^{3}+4\right)^{\frac{1}{3}} x^{4}-8 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{5}+2 x^{6}-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{10}+2 x^{8}+x^{6}-4 x^{5}-4 x^{3}+4\right)^{\frac{2}{3}} x^{2}-4 x^{5}-14 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-6 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{10}+2 x^{8}+x^{6}-4 x^{5}-4 x^{3}+4\right)^{\frac{1}{3}} x -6 x^{3}+8 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+4}{\left(-1+x \right) \left(x^{5}-2\right) \left(x^{4}+x^{3}+2 x^{2}+2 x +2\right)}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{2}-\frac{\ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{10}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{8}+x^{10}+7 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{8}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{10}+2 x^{8}+x^{6}-4 x^{5}-4 x^{3}+4\right)^{\frac{1}{3}} x^{6}+3 x^{8}+5 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{10}+2 x^{8}+x^{6}-4 x^{5}-4 x^{3}+4\right)^{\frac{1}{3}} x^{4}-8 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{5}+2 x^{6}-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{10}+2 x^{8}+x^{6}-4 x^{5}-4 x^{3}+4\right)^{\frac{2}{3}} x^{2}-4 x^{5}-14 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-6 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{10}+2 x^{8}+x^{6}-4 x^{5}-4 x^{3}+4\right)^{\frac{1}{3}} x -6 x^{3}+8 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+4}{\left(-1+x \right) \left(x^{5}-2\right) \left(x^{4}+x^{3}+2 x^{2}+2 x +2\right)}\right)}{2}\right) \left(\left(x^{5}+x^{3}-2\right)^{2}\right)^{\frac{1}{3}}}{\left(x^{5}+x^{3}-2\right)^{\frac{2}{3}}}$&$1123$\\ \hline \end{longtable}"," ",0,"3/2*(x^5+x^3-2)^(1/3)/x+1/2*ln((-3687964213260096*RootOf(144*_Z^2+12*_Z+1)^2*x^5-1951741557610164*RootOf(144*_Z^2+12*_Z+1)*x^5+13829865799725360*RootOf(144*_Z^2+12*_Z+1)^2*x^3-88450351904093*x^5+2398485078249264*RootOf(144*_Z^2+12*_Z+1)*(x^5+x^3-2)^(2/3)*x+136263463016940*(x^5+x^3-2)^(1/3)*RootOf(144*_Z^2+12*_Z+1)*x^2-1382259724622424*RootOf(144*_Z^2+12*_Z+1)*x^3-11355288584745*(x^5+x^3-2)^(2/3)*x+211229045105517*(x^5+x^3-2)^(1/3)*x^2-103833021800457*x^3+7375928426520192*RootOf(144*_Z^2+12*_Z+1)^2+3903483115220328*RootOf(144*_Z^2+12*_Z+1)+176900703808186)/(x^5-2))+6*RootOf(144*_Z^2+12*_Z+1)*ln(-(-1472859748183680*RootOf(144*_Z^2+12*_Z+1)^2*x^5+767599022412408*RootOf(144*_Z^2+12*_Z+1)*x^5+5523224055688800*RootOf(144*_Z^2+12*_Z+1)^2*x^3-73067682007729*x^5+2398485078249264*RootOf(144*_Z^2+12*_Z+1)*(x^5+x^3-2)^(2/3)*x-2534748541266204*(x^5+x^3-2)^(1/3)*RootOf(144*_Z^2+12*_Z+1)*x^2+596532134324340*RootOf(144*_Z^2+12*_Z+1)*x^3+211229045105517*(x^5+x^3-2)^(2/3)*x-11355288584745*(x^5+x^3-2)^(1/3)*x^2-161518033911822*x^3+2945719496367360*RootOf(144*_Z^2+12*_Z+1)^2-1535198044824816*RootOf(144*_Z^2+12*_Z+1)+146135364015458)/(x^5-2))","C"
1644,1,381,89,10.088000," ","int((x^5-3)*(x^5+x^3+2)^(2/3)/x^3/(x^5+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 \left(x^{5}+x^{3}+2\right)^{\frac{2}{3}}}{4 x^{2}}-\frac{\ln \left(-\frac{2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{5}-4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{3}+2 x^{5}-2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{3}+3 \left(x^{5}+x^{3}+2\right)^{\frac{2}{3}} x +3 \left(x^{5}+x^{3}+2\right)^{\frac{1}{3}} x^{2}+2 x^{3}+4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+4}{x^{5}+2}\right)}{2}-\ln \left(-\frac{2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{5}-4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{3}+2 x^{5}-2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{3}+3 \left(x^{5}+x^{3}+2\right)^{\frac{2}{3}} x +3 \left(x^{5}+x^{3}+2\right)^{\frac{1}{3}} x^{2}+2 x^{3}+4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+4}{x^{5}+2}\right) \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+\RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \ln \left(-\frac{-2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{5}-4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{3}+x^{5}-2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{3}+3 \left(x^{5}+x^{3}+2\right)^{\frac{2}{3}} x +3 \left(x^{5}+x^{3}+2\right)^{\frac{1}{3}} x^{2}+2 x^{3}-4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+2}{x^{5}+2}\right)$&$381$\\ trager&$\frac{3 \left(x^{5}+x^{3}+2\right)^{\frac{2}{3}}}{4 x^{2}}+\frac{\ln \left(-\frac{-1221827760 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{5}-12434247822 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{5}+3665483280 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{3}-9513381685 x^{5}+69107262012 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{5}+x^{3}+2\right)^{\frac{2}{3}} x -101522694438 \left(x^{5}+x^{3}+2\right)^{\frac{1}{3}} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{2}+33026346306 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{3}+16920449073 \left(x^{5}+x^{3}+2\right)^{\frac{2}{3}} x -5402572071 \left(x^{5}+x^{3}+2\right)^{\frac{1}{3}} x^{2}-11416058022 x^{3}-2443655520 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2}-24868495644 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)-19026763370}{x^{5}+2}\right)}{2}-\frac{\ln \left(\frac{67274520372 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{5}-33433622226 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{5}-201823561116 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{3}-7610705348 x^{5}+69107262012 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{5}+x^{3}+2\right)^{\frac{2}{3}} x +32415432426 \left(x^{5}+x^{3}+2\right)^{\frac{1}{3}} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{2}-135159954624 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{3}-5402572071 \left(x^{5}+x^{3}+2\right)^{\frac{2}{3}} x +16920449073 \left(x^{5}+x^{3}+2\right)^{\frac{1}{3}} x^{2}-17124087033 x^{3}+134549040744 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2}-66867244452 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)-15221410696}{x^{5}+2}\right)}{2}-3 \ln \left(\frac{67274520372 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{5}-33433622226 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{5}-201823561116 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{3}-7610705348 x^{5}+69107262012 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{5}+x^{3}+2\right)^{\frac{2}{3}} x +32415432426 \left(x^{5}+x^{3}+2\right)^{\frac{1}{3}} \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{2}-135159954624 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{3}-5402572071 \left(x^{5}+x^{3}+2\right)^{\frac{2}{3}} x +16920449073 \left(x^{5}+x^{3}+2\right)^{\frac{1}{3}} x^{2}-17124087033 x^{3}+134549040744 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2}-66867244452 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)-15221410696}{x^{5}+2}\right) \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)$&$620$\\ \hline \end{longtable}"," ",0,"3/4*(x^5+x^3+2)^(2/3)/x^2-1/2*ln(-(2*RootOf(4*_Z^2+2*_Z+1)*x^5-4*RootOf(4*_Z^2+2*_Z+1)^2*x^3+2*x^5-2*RootOf(4*_Z^2+2*_Z+1)*x^3+3*(x^5+x^3+2)^(2/3)*x+3*(x^5+x^3+2)^(1/3)*x^2+2*x^3+4*RootOf(4*_Z^2+2*_Z+1)+4)/(x^5+2))-ln(-(2*RootOf(4*_Z^2+2*_Z+1)*x^5-4*RootOf(4*_Z^2+2*_Z+1)^2*x^3+2*x^5-2*RootOf(4*_Z^2+2*_Z+1)*x^3+3*(x^5+x^3+2)^(2/3)*x+3*(x^5+x^3+2)^(1/3)*x^2+2*x^3+4*RootOf(4*_Z^2+2*_Z+1)+4)/(x^5+2))*RootOf(4*_Z^2+2*_Z+1)+RootOf(4*_Z^2+2*_Z+1)*ln(-(-2*RootOf(4*_Z^2+2*_Z+1)*x^5-4*RootOf(4*_Z^2+2*_Z+1)^2*x^3+x^5-2*RootOf(4*_Z^2+2*_Z+1)*x^3+3*(x^5+x^3+2)^(2/3)*x+3*(x^5+x^3+2)^(1/3)*x^2+2*x^3-4*RootOf(4*_Z^2+2*_Z+1)+2)/(x^5+2))","C"
1645,1,58,89,7.691000," ","int((x^6-1)^(1/3)*(x^6+1)/x^9,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{3 x^{12}-2 x^{6}-1}{8 x^{8} \left(x^{6}-1\right)^{\frac{2}{3}}}+\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{2}{3}} x^{4} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], x^{6}\right)}{4 \mathrm{signum}\left(x^{6}-1\right)^{\frac{2}{3}}}$&$58$\\ meijerg&$-\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{1}{3}, -\frac{1}{3}\right], \left[\frac{2}{3}\right], x^{6}\right)}{2 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} x^{2}}-\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}} \left(-x^{6}+1\right)^{\frac{4}{3}}}{8 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} x^{8}}$&$66$\\ trager&$-\frac{\left(3 x^{6}+1\right) \left(x^{6}-1\right)^{\frac{1}{3}}}{8 x^{8}}-\frac{\ln \left(-95839020187648 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)^{2} x^{6}+71103429967360 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) x^{6}-147783054114048 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}+299529781823 x^{6}+77053995319296 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}+276285385917 x^{4} \left(x^{6}-1\right)^{\frac{1}{3}}-577277555133 x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}+6133697292009472 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)^{2}-21851442872064 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)-199163781631\right)}{6}+\frac{128 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) \ln \left(198613804384256 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)^{2} x^{6}+147007218940672 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) x^{6}-70729058794752 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}-297961563070 x^{6}-77053995319296 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}+577277555133 x^{4} \left(x^{6}-1\right)^{\frac{1}{3}}-276285385917 x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}-12711283480592384 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)^{2}-23183919873536 \RootOf \left(65536 \textit{\_Z}^{2}-256 \textit{\_Z} +1\right)+98797781439\right)}{3}$&$316$\\ \hline \end{longtable}"," ",0,"-1/8*(3*x^12-2*x^6-1)/x^8/(x^6-1)^(2/3)+1/4/signum(x^6-1)^(2/3)*(-signum(x^6-1))^(2/3)*x^4*hypergeom([2/3,2/3],[5/3],x^6)","C"
1646,0,0,14,0.048000," ","int(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6-2*b),x)","\[\int \frac{1}{\left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}} \left(a^{6} x^{6}-2 b \right)}\, dx\]"," ",0,"int(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6-2*b),x)","F"
1647,0,0,14,0.001000," ","int(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6-2*b),x)","\[\int \frac{1}{\left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}} \left(a^{6} x^{6}-2 b \right)}\, dx\]"," ",0,"int(1/(a^3*x^3+b^2*x^2)^(1/3)/(a^6*x^6-2*b),x)","F"
1648,1,635,97,2.305000," ","int(1/(x^20+3*x^16+2*x^12-2*x^8-3*x^4-1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(\frac{-3 x^{16} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right)-2 \left(x^{20}+3 x^{16}+2 x^{12}-2 x^{8}-3 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{11}-8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{12}+\sqrt{x^{20}+3 x^{16}+2 x^{12}-2 x^{8}-3 x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{6}-4 \left(x^{20}+3 x^{16}+2 x^{12}-2 x^{8}-3 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{7}-6 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{8}+\sqrt{x^{20}+3 x^{16}+2 x^{12}-2 x^{8}-3 x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{2}-2 \left(x^{20}+3 x^{16}+2 x^{12}-2 x^{8}-3 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}+4 \left(x^{20}+3 x^{16}+2 x^{12}-2 x^{8}-3 x^{4}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right)}{\left(x^{4}+1\right)^{4}}\right)}{8}+\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(\frac{3 x^{16} \RootOf \left(\textit{\_Z}^{4}-8\right)+2 \left(x^{20}+3 x^{16}+2 x^{12}-2 x^{8}-3 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{11}+8 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{12}+\sqrt{x^{20}+3 x^{16}+2 x^{12}-2 x^{8}-3 x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{6}+4 \left(x^{20}+3 x^{16}+2 x^{12}-2 x^{8}-3 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{7}+6 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{8}+\sqrt{x^{20}+3 x^{16}+2 x^{12}-2 x^{8}-3 x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{2}+2 \left(x^{20}+3 x^{16}+2 x^{12}-2 x^{8}-3 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}+4 \left(x^{20}+3 x^{16}+2 x^{12}-2 x^{8}-3 x^{4}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}-8\right)}{\left(x^{4}+1\right)^{4}}\right)}{8}$&$635$\\ \hline \end{longtable}"," ",0,"-1/8*RootOf(_Z^2+RootOf(_Z^4-8)^2)*ln((-3*x^16*RootOf(_Z^2+RootOf(_Z^4-8)^2)-2*(x^20+3*x^16+2*x^12-2*x^8-3*x^4-1)^(1/4)*RootOf(_Z^4-8)^2*x^11-8*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^12+(x^20+3*x^16+2*x^12-2*x^8-3*x^4-1)^(1/2)*RootOf(_Z^4-8)^2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^6-4*(x^20+3*x^16+2*x^12-2*x^8-3*x^4-1)^(1/4)*RootOf(_Z^4-8)^2*x^7-6*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^8+(x^20+3*x^16+2*x^12-2*x^8-3*x^4-1)^(1/2)*RootOf(_Z^4-8)^2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^2-2*(x^20+3*x^16+2*x^12-2*x^8-3*x^4-1)^(1/4)*RootOf(_Z^4-8)^2*x^3+4*(x^20+3*x^16+2*x^12-2*x^8-3*x^4-1)^(3/4)*x+RootOf(_Z^2+RootOf(_Z^4-8)^2))/(x^4+1)^4)+1/8*RootOf(_Z^4-8)*ln((3*x^16*RootOf(_Z^4-8)+2*(x^20+3*x^16+2*x^12-2*x^8-3*x^4-1)^(1/4)*RootOf(_Z^4-8)^2*x^11+8*RootOf(_Z^4-8)*x^12+(x^20+3*x^16+2*x^12-2*x^8-3*x^4-1)^(1/2)*RootOf(_Z^4-8)^3*x^6+4*(x^20+3*x^16+2*x^12-2*x^8-3*x^4-1)^(1/4)*RootOf(_Z^4-8)^2*x^7+6*RootOf(_Z^4-8)*x^8+(x^20+3*x^16+2*x^12-2*x^8-3*x^4-1)^(1/2)*RootOf(_Z^4-8)^3*x^2+2*(x^20+3*x^16+2*x^12-2*x^8-3*x^4-1)^(1/4)*RootOf(_Z^4-8)^2*x^3+4*(x^20+3*x^16+2*x^12-2*x^8-3*x^4-1)^(3/4)*x-RootOf(_Z^4-8))/(x^4+1)^4)","C"
1649,1,160,97,0.076000," ","int((x^2+1)/(a*x+b)^(1/2)/(c+(a*x+b)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\frac{4 \left(c +\sqrt{a x +b}\right)^{\frac{9}{2}}}{9}-\frac{16 c \left(c +\sqrt{a x +b}\right)^{\frac{7}{2}}}{7}+\frac{24 c^{2} \left(c +\sqrt{a x +b}\right)^{\frac{5}{2}}}{5}-\frac{8 b \left(c +\sqrt{a x +b}\right)^{\frac{5}{2}}}{5}-\frac{16 c^{3} \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}+\frac{16 b c \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}+4 c^{4} \sqrt{c +\sqrt{a x +b}}-8 b \,c^{2} \sqrt{c +\sqrt{a x +b}}+4 a^{2} \sqrt{c +\sqrt{a x +b}}+4 b^{2} \sqrt{c +\sqrt{a x +b}}}{a^{3}}$&$160$\\ default&$\frac{\frac{4 \left(c +\sqrt{a x +b}\right)^{\frac{9}{2}}}{9}-\frac{16 c \left(c +\sqrt{a x +b}\right)^{\frac{7}{2}}}{7}+\frac{24 c^{2} \left(c +\sqrt{a x +b}\right)^{\frac{5}{2}}}{5}-\frac{8 b \left(c +\sqrt{a x +b}\right)^{\frac{5}{2}}}{5}-\frac{16 c^{3} \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}+\frac{16 b c \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}+4 c^{4} \sqrt{c +\sqrt{a x +b}}-8 b \,c^{2} \sqrt{c +\sqrt{a x +b}}+4 a^{2} \sqrt{c +\sqrt{a x +b}}+4 b^{2} \sqrt{c +\sqrt{a x +b}}}{a^{3}}$&$160$\\ \hline \end{longtable}"," ",0,"2/a^3*(2/9*(c+(a*x+b)^(1/2))^(9/2)-8/7*c*(c+(a*x+b)^(1/2))^(7/2)+12/5*c^2*(c+(a*x+b)^(1/2))^(5/2)-4/5*b*(c+(a*x+b)^(1/2))^(5/2)-8/3*c^3*(c+(a*x+b)^(1/2))^(3/2)+8/3*b*c*(c+(a*x+b)^(1/2))^(3/2)+2*c^4*(c+(a*x+b)^(1/2))^(1/2)-4*b*c^2*(c+(a*x+b)^(1/2))^(1/2)+2*a^2*(c+(a*x+b)^(1/2))^(1/2)+2*b^2*(c+(a*x+b)^(1/2))^(1/2))","A"
1650,0,0,97,180.000000," ","int(x^2/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/4),x)","\[\int \frac{x^{2}}{\sqrt{a^{2} x^{2}-b}\, \left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(x^2/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/4),x)","F"
1651,1,33,90,3.135000," ","int(x^2*(x^3-x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}} x^{\frac{10}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{5}{3}\right], \left[\frac{8}{3}\right], x^{2}\right)}{10 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}}}$&$33$\\ trager&$\frac{x \left(3 x^{2}-1\right) \left(x^{3}-x \right)^{\frac{1}{3}}}{12}+\frac{\RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(1395 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}+6768 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}+6768 \left(x^{3}-x \right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x +7233 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+7611 \left(x^{3}-x \right)^{\frac{2}{3}}+7611 x \left(x^{3}-x \right)^{\frac{1}{3}}-5580 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+7766 x^{2}-11727 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-4942\right)}{6}-\frac{\ln \left(1395 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}-6768 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}-6768 \left(x^{3}-x \right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -6303 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+5355 \left(x^{3}-x \right)^{\frac{2}{3}}+5355 x \left(x^{3}-x \right)^{\frac{1}{3}}-5580 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+5510 x^{2}+8007 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-1653\right)}{18}-\frac{\ln \left(1395 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}-6768 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}-6768 \left(x^{3}-x \right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -6303 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+5355 \left(x^{3}-x \right)^{\frac{2}{3}}+5355 x \left(x^{3}-x \right)^{\frac{1}{3}}-5580 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+5510 x^{2}+8007 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-1653\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{6}$&$463$\\ risch&$\frac{x \left(3 x^{2}-1\right) \left(x \left(x^{2}-1\right)\right)^{\frac{1}{3}}}{12}+\frac{\left(\frac{\RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \ln \left(-\frac{47 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{4}+3207 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{4}-235 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{2}+2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}+6930 x^{4}+2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}-5601 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{2}+5238 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}+188 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2}-2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}+5238 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}-11340 x^{2}+2394 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)-5238 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}+4410}{\left(-1+x \right) \left(1+x \right)}\right)}{108}-\frac{\ln \left(-\frac{47 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{4}-2643 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{4}-235 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{2}-2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}-10620 x^{4}-2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}+2781 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{2}-12312 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}+188 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2}+2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}-12312 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}+13806 x^{2}-138 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)+12312 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}-3186}{\left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)}{108}-\frac{\ln \left(-\frac{47 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{4}-2643 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{4}-235 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{2}-2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}-10620 x^{4}-2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}+2781 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{2}-12312 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}+188 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2}+2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}-12312 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}+13806 x^{2}-138 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)+12312 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}-3186}{\left(-1+x \right) \left(1+x \right)}\right)}{18}\right) \left(x \left(x^{2}-1\right)\right)^{\frac{1}{3}} \left(x^{2} \left(x^{2}-1\right)^{2}\right)^{\frac{1}{3}}}{x \left(x^{2}-1\right)}$&$793$\\ \hline \end{longtable}"," ",0,"3/10*signum(x^2-1)^(1/3)/(-signum(x^2-1))^(1/3)*x^(10/3)*hypergeom([-1/3,5/3],[8/3],x^2)","C"
1652,1,17,90,3.872000," ","int(x^6*(x^3+x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 x^{\frac{22}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{11}{3}\right], \left[\frac{14}{3}\right], -x^{2}\right)}{22}$&$17$\\ trager&$\frac{x \left(81 x^{6}+9 x^{4}-12 x^{2}+20\right) \left(x^{3}+x \right)^{\frac{1}{3}}}{648}+\frac{5 \ln \left(-36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}-72 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}+27 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x +33 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-9 \left(x^{3}+x \right)^{\frac{2}{3}}-15 x \left(x^{3}+x \right)^{\frac{1}{3}}+20 x^{2}+51 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+15\right)}{243}+\frac{5 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}+72 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}-45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x -30 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+15 \left(x^{3}+x \right)^{\frac{2}{3}}+9 x \left(x^{3}+x \right)^{\frac{1}{3}}-25 x^{2}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-10\right)}{81}$&$304$\\ risch&$\frac{x \left(81 x^{6}+9 x^{4}-12 x^{2}+20\right) \left(x \left(x^{2}+1\right)\right)^{\frac{1}{3}}}{648}+\frac{\left(\frac{5 \ln \left(\frac{5 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)^{2} x^{4}-38 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) x^{4}+18 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}-16 x^{4}+30 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}-70 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) x^{2}-60 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}-5 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)^{2}+18 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}+96 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}-28 x^{2}-32 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)-60 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}-12}{x^{2}+1}\right)}{243}+\frac{5 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)^{2} x^{4}+20 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) x^{4}-48 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}+100 x^{4}+30 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}+14 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) x^{2}-60 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}-\RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)^{2}-48 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}-36 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}+140 x^{2}-6 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)-60 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}+40}{x^{2}+1}\right)}{486}\right) \left(x \left(x^{2}+1\right)\right)^{\frac{1}{3}} \left(x^{2} \left(x^{2}+1\right)^{2}\right)^{\frac{1}{3}}}{x \left(x^{2}+1\right)}$&$514$\\ \hline \end{longtable}"," ",0,"3/22*x^(22/3)*hypergeom([-1/3,11/3],[14/3],-x^2)","C"
1653,1,110,87,16.429000," ","int((-3+2*x)/x/(x^4-1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{3 \sqrt{2}\, \Gamma \left(\frac{3}{4}\right) \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \left(\frac{\pi  \sqrt{2}\, x^{4} \hypergeom \left(\left[1, 1, \frac{5}{4}\right], \left[2, 2\right], x^{4}\right)}{4 \Gamma \left(\frac{3}{4}\right)}+\frac{\left(-3 \ln \left(2\right)-\frac{\pi}{2}+4 \ln \left(x \right)+i \pi \right) \pi  \sqrt{2}}{\Gamma \left(\frac{3}{4}\right)}\right)}{8 \pi  \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}}}+\frac{2 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} x \hypergeom \left(\left[\frac{1}{4}, \frac{1}{4}\right], \left[\frac{5}{4}\right], x^{4}\right)}{\mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}}}$&$110$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \left(x^{4}-1\right)^{\frac{3}{4}} x -2 x^{3} \left(x^{4}-1\right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{2}-\frac{\ln \left(2 \left(x^{4}-1\right)^{\frac{3}{4}} x -2 x^{2} \sqrt{x^{4}-1}+2 x^{3} \left(x^{4}-1\right)^{\frac{1}{4}}-2 x^{4}+1\right)}{2}-\frac{3 \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) x^{4}+2 \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}-1}+2 \left(x^{4}-1\right)^{\frac{3}{4}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{4}-1\right)^{\frac{1}{4}}+2 \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{x^{4}}\right)}{4}+\frac{3 \RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \left(x^{4}-1\right)^{\frac{3}{4}}-2 \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \sqrt{x^{4}-1}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{4}-1\right)^{\frac{1}{4}}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{x^{4}}\right)}{4}$&$336$\\ \hline \end{longtable}"," ",0,"-3/8/Pi*2^(1/2)*GAMMA(3/4)/signum(x^4-1)^(1/4)*(-signum(x^4-1))^(1/4)*(1/4*Pi*2^(1/2)/GAMMA(3/4)*x^4*hypergeom([1,1,5/4],[2,2],x^4)+(-3*ln(2)-1/2*Pi+4*ln(x)+I*Pi)*Pi*2^(1/2)/GAMMA(3/4))+2/signum(x^4-1)^(1/4)*(-signum(x^4-1))^(1/4)*x*hypergeom([1/4,1/4],[5/4],x^4)","C"
1654,1,650,96,6.813000," ","int((-x^4+x^3-1)^(1/3)*(x^4-3)/x^2/(x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(-x^{4}+x^{3}-1\right)^{\frac{1}{3}}}{x}-3 \ln \left(\frac{153 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}-306 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}+141 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(-x^{4}+x^{3}-1\right)^{\frac{2}{3}} x +141 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(-x^{4}+x^{3}-1\right)^{\frac{1}{3}} x^{2}+39 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}-15 x^{4}+49 \left(-x^{4}+x^{3}-1\right)^{\frac{2}{3}} x +49 x^{2} \left(-x^{4}+x^{3}-1\right)^{\frac{1}{3}}+15 x^{3}+153 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-15}{x^{4}+1}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(\frac{153 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}-306 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+96 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}-141 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(-x^{4}+x^{3}-1\right)^{\frac{2}{3}} x -141 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(-x^{4}+x^{3}-1\right)^{\frac{1}{3}} x^{2}-243 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+2 \left(-x^{4}+x^{3}-1\right)^{\frac{2}{3}} x +2 x^{2} \left(-x^{4}+x^{3}-1\right)^{\frac{1}{3}}-32 x^{3}+153 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+96 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{x^{4}+1}\right)-\ln \left(\frac{153 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}-306 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}+141 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(-x^{4}+x^{3}-1\right)^{\frac{2}{3}} x +141 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(-x^{4}+x^{3}-1\right)^{\frac{1}{3}} x^{2}+39 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}-15 x^{4}+49 \left(-x^{4}+x^{3}-1\right)^{\frac{2}{3}} x +49 x^{2} \left(-x^{4}+x^{3}-1\right)^{\frac{1}{3}}+15 x^{3}+153 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-15}{x^{4}+1}\right)$&$650$\\ risch&$-\frac{3 \left(x^{4}-x^{3}+1\right)}{x \left(-x^{4}+x^{3}-1\right)^{\frac{2}{3}}}+\frac{\left(\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{7}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{8}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}-3 x^{7} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-x^{8}+2 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+2 x^{7}-3 \left(x^{8}-2 x^{7}+x^{6}+2 x^{4}-2 x^{3}+1\right)^{\frac{1}{3}} x^{5}-x^{6}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-3 \left(x^{8}-2 x^{7}+x^{6}+2 x^{4}-2 x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}+3 \left(x^{8}-2 x^{7}+x^{6}+2 x^{4}-2 x^{3}+1\right)^{\frac{1}{3}} x^{4}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-3 \left(x^{8}-2 x^{7}+x^{6}+2 x^{4}-2 x^{3}+1\right)^{\frac{2}{3}} x^{2}-2 x^{4}+2 x^{3}-3 \left(x^{8}-2 x^{7}+x^{6}+2 x^{4}-2 x^{3}+1\right)^{\frac{1}{3}} x +\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1}{\left(x^{4}-x^{3}+1\right) \left(x^{4}+1\right)}\right)+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{7}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{8}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}+7 x^{7} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-x^{8}-5 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+3 x^{7}+3 \left(x^{8}-2 x^{7}+x^{6}+2 x^{4}-2 x^{3}+1\right)^{\frac{1}{3}} x^{5}-2 x^{6}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \left(x^{8}-2 x^{7}+x^{6}+2 x^{4}-2 x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}-3 \left(x^{8}-2 x^{7}+x^{6}+2 x^{4}-2 x^{3}+1\right)^{\frac{1}{3}} x^{4}+7 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 \left(x^{8}-2 x^{7}+x^{6}+2 x^{4}-2 x^{3}+1\right)^{\frac{2}{3}} x^{2}-2 x^{4}+3 x^{3}+3 \left(x^{8}-2 x^{7}+x^{6}+2 x^{4}-2 x^{3}+1\right)^{\frac{1}{3}} x -2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1}{\left(x^{4}-x^{3}+1\right) \left(x^{4}+1\right)}\right)\right) \left(\left(x^{4}-x^{3}+1\right)^{2}\right)^{\frac{1}{3}}}{\left(-x^{4}+x^{3}-1\right)^{\frac{2}{3}}}$&$689$\\ \hline \end{longtable}"," ",0,"3*(-x^4+x^3-1)^(1/3)/x-3*ln((153*RootOf(9*_Z^2+3*_Z+1)^2*x^4-306*RootOf(9*_Z^2+3*_Z+1)^2*x^3+6*RootOf(9*_Z^2+3*_Z+1)*x^4+141*RootOf(9*_Z^2+3*_Z+1)*(-x^4+x^3-1)^(2/3)*x+141*RootOf(9*_Z^2+3*_Z+1)*(-x^4+x^3-1)^(1/3)*x^2+39*RootOf(9*_Z^2+3*_Z+1)*x^3-15*x^4+49*(-x^4+x^3-1)^(2/3)*x+49*x^2*(-x^4+x^3-1)^(1/3)+15*x^3+153*RootOf(9*_Z^2+3*_Z+1)^2+6*RootOf(9*_Z^2+3*_Z+1)-15)/(x^4+1))*RootOf(9*_Z^2+3*_Z+1)+3*RootOf(9*_Z^2+3*_Z+1)*ln((153*RootOf(9*_Z^2+3*_Z+1)^2*x^4-306*RootOf(9*_Z^2+3*_Z+1)^2*x^3+96*RootOf(9*_Z^2+3*_Z+1)*x^4-141*RootOf(9*_Z^2+3*_Z+1)*(-x^4+x^3-1)^(2/3)*x-141*RootOf(9*_Z^2+3*_Z+1)*(-x^4+x^3-1)^(1/3)*x^2-243*RootOf(9*_Z^2+3*_Z+1)*x^3+2*(-x^4+x^3-1)^(2/3)*x+2*x^2*(-x^4+x^3-1)^(1/3)-32*x^3+153*RootOf(9*_Z^2+3*_Z+1)^2+96*RootOf(9*_Z^2+3*_Z+1))/(x^4+1))-ln((153*RootOf(9*_Z^2+3*_Z+1)^2*x^4-306*RootOf(9*_Z^2+3*_Z+1)^2*x^3+6*RootOf(9*_Z^2+3*_Z+1)*x^4+141*RootOf(9*_Z^2+3*_Z+1)*(-x^4+x^3-1)^(2/3)*x+141*RootOf(9*_Z^2+3*_Z+1)*(-x^4+x^3-1)^(1/3)*x^2+39*RootOf(9*_Z^2+3*_Z+1)*x^3-15*x^4+49*(-x^4+x^3-1)^(2/3)*x+49*x^2*(-x^4+x^3-1)^(1/3)+15*x^3+153*RootOf(9*_Z^2+3*_Z+1)^2+6*RootOf(9*_Z^2+3*_Z+1)-15)/(x^4+1))","C"
1655,1,665,92,0.351000," ","int(x^3*(x^4-x)^(1/2)/(a*x^3-b),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{x \sqrt{x^{4}-x}}{3 a}+\frac{2 \left(-\frac{a -b}{a^{2}}+\frac{1}{2 a}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}-\frac{2 b \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}-b \right)}{\sum}\frac{\left(-1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(1-i \sqrt{3}\right) \sqrt{\frac{x \left(-3+i \sqrt{3}\right)}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{\left(-1+x \right) \left(-1-i \sqrt{3}\right)}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\frac{\underline{\hspace{1.25 ex}}\alpha^{2} a \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}\, a -3 \underline{\hspace{1.25 ex}}\alpha^{2} a -i \sqrt{3}\, b +3 b}{6 b}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{b}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(-3+i \sqrt{3}\right) \sqrt{x \left(-1+x \right) \left(i \sqrt{3}+2 x +1\right) \left(1+2 x -i \sqrt{3}\right)}}\right)}{3 a^{2}}$&$665$\\ risch&$\frac{x^{2} \left(x^{3}-1\right)}{3 a \sqrt{x \left(x^{3}-1\right)}}-\frac{\frac{2 \left(a -2 b \right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{a \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{4 b \left(a -b \right) \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}-b \right)}{\sum}\frac{\left(-1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(1-i \sqrt{3}\right) \sqrt{\frac{x \left(-3+i \sqrt{3}\right)}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{\left(-1+x \right) \left(-1-i \sqrt{3}\right)}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\frac{\underline{\hspace{1.25 ex}}\alpha^{2} a \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}\, a -3 \underline{\hspace{1.25 ex}}\alpha^{2} a -i \sqrt{3}\, b +3 b}{6 b}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{b}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(a -b \right) \left(-3+i \sqrt{3}\right) \sqrt{x \left(-1+x \right) \left(i \sqrt{3}+2 x +1\right) \left(1+2 x -i \sqrt{3}\right)}}\right)}{3 a}}{2 a}$&$682$\\ default&$\frac{\frac{x \sqrt{x^{4}-x}}{3}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}}{a}+\frac{b \left(\frac{2 \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{a \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}-\frac{2 \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}-b \right)}{\sum}\frac{\left(-1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(1-i \sqrt{3}\right) \sqrt{\frac{x \left(-3+i \sqrt{3}\right)}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{\left(-1+x \right) \left(-1-i \sqrt{3}\right)}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\frac{\underline{\hspace{1.25 ex}}\alpha^{2} a \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}\, a -3 \underline{\hspace{1.25 ex}}\alpha^{2} a -i \sqrt{3}\, b +3 b}{6 b}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{b}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(-3+i \sqrt{3}\right) \sqrt{x \left(-1+x \right) \left(i \sqrt{3}+2 x +1\right) \left(1+2 x -i \sqrt{3}\right)}}\right)}{3 a}\right)}{a}$&$946$\\ \hline \end{longtable}"," ",0,"1/3*x*(x^4-x)^(1/2)/a+2*(-(a-b)/a^2+1/2/a)*(1/2-1/2*I*3^(1/2))*((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2)*(-1+x)^2*((x+1/2+1/2*I*3^(1/2))/(-1/2-1/2*I*3^(1/2))/(-1+x))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2)/(-3/2+1/2*I*3^(1/2))/(x*(-1+x)*(x+1/2+1/2*I*3^(1/2))*(x+1/2-1/2*I*3^(1/2)))^(1/2)*(EllipticF(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-EllipticPi(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),(-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)),((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)))-2/3/a^2*b*4^(1/2)*sum(1/_alpha*(-1+x)^2*(_alpha^2+_alpha+1)*(1-I*3^(1/2))*(x/(-1+x)*(-3+I*3^(1/2))/(-1+I*3^(1/2)))^(1/2)*(1/(-1+x)*(I*3^(1/2)+2*x+1)/(-1-I*3^(1/2)))^(1/2)*(1/(-1+x)*(1+2*x-I*3^(1/2))/(-1+I*3^(1/2)))^(1/2)/(-3+I*3^(1/2))/(x*(-1+x)*(I*3^(1/2)+2*x+1)*(1+2*x-I*3^(1/2)))^(1/2)*(EllipticF(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-_alpha^2*a/b*EllipticPi(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),1/6*(I*_alpha^2*3^(1/2)*a-3*_alpha^2*a-I*3^(1/2)*b+3*b)/b,((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))),_alpha=RootOf(_Z^3*a-b))","C"
1656,0,0,90,0.014000," ","int((2*x^4+1)/(x^4-1)/(x^4+x^2)^(1/4),x)","\[\int \frac{2 x^{4}+1}{\left(x^{4}-1\right) \left(x^{4}+x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((2*x^4+1)/(x^4-1)/(x^4+x^2)^(1/4),x)","F"
1657,0,0,88,0.011000," ","int((a*x^2+b)/x^2/(a*x^2-b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{a \,x^{2}+b}{x^{2} \left(a \,x^{2}-b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2+b)/x^2/(a*x^2-b)/(a*x^4+b*x^2)^(1/4),x)","F"
1658,0,0,92,0.005000," ","int(x*(a*x^4+b*x^3)^(1/4),x)","\[\int x \left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}\, dx\]"," ",0,"int(x*(a*x^4+b*x^3)^(1/4),x)","F"
1659,0,0,96,0.028000," ","int((a*x^3-2*b)/(a*x^3+x^2+b)/(a*x^5+b*x^2)^(1/4),x)","\[\int \frac{a \,x^{3}-2 b}{\left(a \,x^{3}+x^{2}+b \right) \left(a \,x^{5}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^3-2*b)/(a*x^3+x^2+b)/(a*x^5+b*x^2)^(1/4),x)","F"
1660,0,0,96,0.116000," ","int((a*x^2-b)/(a*x^2+b+x)/(a*x^5+b*x^3)^(1/4),x)","\[\int \frac{a \,x^{2}-b}{\left(a \,x^{2}+b +x \right) \left(a \,x^{5}+b \,x^{3}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2-b)/(a*x^2+b+x)/(a*x^5+b*x^3)^(1/4),x)","F"
1661,1,33,90,3.967000," ","int(x^13/(x^6-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} x^{14} \hypergeom \left(\left[\frac{1}{3}, \frac{7}{3}\right], \left[\frac{10}{3}\right], x^{6}\right)}{14 \mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}}}$&$33$\\ risch&$\frac{x^{2} \left(3 x^{6}+4\right) \left(x^{6}-1\right)^{\frac{2}{3}}}{36}+\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} x^{2} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{6}\right)}{9 \mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}}}$&$53$\\ trager&$\frac{x^{2} \left(3 x^{6}+4\right) \left(x^{6}-1\right)^{\frac{2}{3}}}{36}-\frac{\ln \left(-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}+5 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}-2 x^{6}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}-3 x^{4} \left(x^{6}-1\right)^{\frac{1}{3}}+3 x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+1\right)}{27}+\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}-2 x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}+3 x^{4} \left(x^{6}-1\right)^{\frac{1}{3}}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+2\right)}{27}$&$230$\\ \hline \end{longtable}"," ",0,"1/14/signum(x^6-1)^(1/3)*(-signum(x^6-1))^(1/3)*x^14*hypergeom([1/3,7/3],[10/3],x^6)","C"
1662,1,33,90,3.434000," ","int(x^9*(x^6-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}} x^{10} \hypergeom \left(\left[-\frac{1}{3}, \frac{5}{3}\right], \left[\frac{8}{3}\right], x^{6}\right)}{10 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}}}$&$33$\\ risch&$\frac{x^{4} \left(3 x^{6}-1\right) \left(x^{6}-1\right)^{\frac{1}{3}}}{36}-\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{2}{3}} x^{4} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], x^{6}\right)}{36 \mathrm{signum}\left(x^{6}-1\right)^{\frac{2}{3}}}$&$53$\\ trager&$\frac{x^{4} \left(3 x^{6}-1\right) \left(x^{6}-1\right)^{\frac{1}{3}}}{36}+\frac{\ln \left(-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}+x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+x^{6}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}-3 x^{4} \left(x^{6}-1\right)^{\frac{1}{3}}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1\right)}{54}+\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}+x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}-2 x^{6}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}+3 x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1\right)}{54}$&$194$\\ \hline \end{longtable}"," ",0,"1/10*signum(x^6-1)^(1/3)/(-signum(x^6-1))^(1/3)*x^10*hypergeom([-1/3,5/3],[8/3],x^6)","C"
1663,1,33,90,3.670000," ","int(x^7*(x^6-1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{2}{3}} x^{8} \hypergeom \left(\left[-\frac{2}{3}, \frac{4}{3}\right], \left[\frac{7}{3}\right], x^{6}\right)}{8 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{2}{3}}}$&$33$\\ risch&$\frac{x^{2} \left(3 x^{6}-2\right) \left(x^{6}-1\right)^{\frac{2}{3}}}{36}-\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} x^{2} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{6}\right)}{18 \mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}}}$&$53$\\ trager&$\frac{x^{2} \left(3 x^{6}-2\right) \left(x^{6}-1\right)^{\frac{2}{3}}}{36}+\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}+4 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}+4 x^{6}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}+3 x^{4} \left(x^{6}-1\right)^{\frac{1}{3}}+3 x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2\right)}{54}-\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}-2 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}+x^{6}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{54}-\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}-2 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}+x^{6}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1\right)}{54}$&$297$\\ \hline \end{longtable}"," ",0,"1/8*signum(x^6-1)^(2/3)/(-signum(x^6-1))^(2/3)*x^8*hypergeom([-2/3,4/3],[7/3],x^6)","C"
1664,1,17,90,3.849000," ","int(x^13/(x^6+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{x^{14} \hypergeom \left(\left[\frac{1}{3}, \frac{7}{3}\right], \left[\frac{10}{3}\right], -x^{6}\right)}{14}$&$17$\\ risch&$\frac{x^{2} \left(3 x^{6}-4\right) \left(x^{6}+1\right)^{\frac{2}{3}}}{36}+\frac{x^{2} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{6}\right)}{9}$&$37$\\ trager&$\frac{x^{2} \left(3 x^{6}-4\right) \left(x^{6}+1\right)^{\frac{2}{3}}}{36}-\frac{\ln \left(-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}+5 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}-2 x^{6}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x^{2}-3 x^{4} \left(x^{6}+1\right)^{\frac{1}{3}}+3 x^{2} \left(x^{6}+1\right)^{\frac{2}{3}}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-1\right)}{27}+\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}} x^{4}-2 x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x^{2}+3 x^{4} \left(x^{6}+1\right)^{\frac{1}{3}}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-2\right)}{27}$&$228$\\ \hline \end{longtable}"," ",0,"1/14*x^14*hypergeom([1/3,7/3],[10/3],-x^6)","C"
1665,1,17,90,3.641000," ","int(x^7*(x^6+1)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{x^{8} \hypergeom \left(\left[-\frac{2}{3}, \frac{4}{3}\right], \left[\frac{7}{3}\right], -x^{6}\right)}{8}$&$17$\\ risch&$\frac{x^{2} \left(3 x^{6}+2\right) \left(x^{6}+1\right)^{\frac{2}{3}}}{36}-\frac{x^{2} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{6}\right)}{18}$&$37$\\ trager&$\frac{x^{2} \left(3 x^{6}+2\right) \left(x^{6}+1\right)^{\frac{2}{3}}}{36}+\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}+4 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}} x^{4}+4 x^{6}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x^{2}+3 x^{4} \left(x^{6}+1\right)^{\frac{1}{3}}+3 x^{2} \left(x^{6}+1\right)^{\frac{2}{3}}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+2\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{54}-\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}-2 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}} x^{4}+x^{6}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x^{2}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1\right)}{54}-\frac{\ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}-2 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}} x^{4}+x^{6}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x^{2}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1\right)}{54}$&$299$\\ \hline \end{longtable}"," ",0,"1/8*x^8*hypergeom([-2/3,4/3],[7/3],-x^6)","C"
1666,1,9666,31,240.523000," ","int((x^3+1)^(2/3)*(x^3+4)/x^6/(x^6-4*x^3+8),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$9666$\\ trager&$\text{Expression too large to display}$&$12545$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1667,1,8085,31,228.826000," ","int((x^3+1)^(2/3)*(x^3+4)/x^6/(x^6-4*x^3+8),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$8085$\\ trager&$\text{Expression too large to display}$&$12523$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1668,0,0,31,180.000000," ","int((x^3+1)^(2/3)*(x^3+2)*(3*x^3+4)/x^6/(x^6+2*x^3+4),x)","\[\int \frac{\left(x^{3}+1\right)^{\frac{2}{3}} \left(x^{3}+2\right) \left(3 x^{3}+4\right)}{x^{6} \left(x^{6}+2 x^{3}+4\right)}\, dx\]"," ",0,"int((x^3+1)^(2/3)*(x^3+2)*(3*x^3+4)/x^6/(x^6+2*x^3+4),x)","F"
1669,1,1805,31,8.892000," ","int((x^3+1)^(2/3)*(x^3+2)*(3*x^3+4)/x^6/(x^6+2*x^3+4),x)","\[\text{Expression too large to display}\]"," ",0,"-1/20*(23*x^6+31*x^3+8)/x^5/(x^3+1)^(1/3)+162/37*ln(-(11757312*x^3*RootOf(34992*_Z^6-324*_Z^3+343)^7-9926064*(x^3+1)^(1/3)*RootOf(34992*_Z^6-324*_Z^3+343)^5*x^2+1065960*RootOf(34992*_Z^6-324*_Z^3+343)^4*x^3+2349648*(x^3+1)^(2/3)*RootOf(34992*_Z^6-324*_Z^3+343)^3*x-397602*(x^3+1)^(1/3)*RootOf(34992*_Z^6-324*_Z^3+343)^2*x^2-1342656*RootOf(34992*_Z^6-324*_Z^3+343)^4-292677*RootOf(34992*_Z^6-324*_Z^3+343)*x^3+56203*x*(x^3+1)^(2/3)-281274*RootOf(34992*_Z^6-324*_Z^3+343))/(324*RootOf(34992*_Z^6-324*_Z^3+343)^3*x^3+17*x^3+74))*RootOf(34992*_Z^6-324*_Z^3+343)^4-10/37*ln(-(11757312*x^3*RootOf(34992*_Z^6-324*_Z^3+343)^7-9926064*(x^3+1)^(1/3)*RootOf(34992*_Z^6-324*_Z^3+343)^5*x^2+1065960*RootOf(34992*_Z^6-324*_Z^3+343)^4*x^3+2349648*(x^3+1)^(2/3)*RootOf(34992*_Z^6-324*_Z^3+343)^3*x-397602*(x^3+1)^(1/3)*RootOf(34992*_Z^6-324*_Z^3+343)^2*x^2-1342656*RootOf(34992*_Z^6-324*_Z^3+343)^4-292677*RootOf(34992*_Z^6-324*_Z^3+343)*x^3+56203*x*(x^3+1)^(2/3)-281274*RootOf(34992*_Z^6-324*_Z^3+343))/(324*RootOf(34992*_Z^6-324*_Z^3+343)^3*x^3+17*x^3+74))*RootOf(34992*_Z^6-324*_Z^3+343)+1/2*RootOf(34992*_Z^6-324*_Z^3+343)*ln((1469664*x^3*RootOf(34992*_Z^6-324*_Z^3+343)^7-215784*(x^3+1)^(1/3)*RootOf(34992*_Z^6-324*_Z^3+343)^5*x^2+573804*RootOf(34992*_Z^6-324*_Z^3+343)^4*x^3+83916*(x^3+1)^(2/3)*RootOf(34992*_Z^6-324*_Z^3+343)^3*x-109890*(x^3+1)^(1/3)*RootOf(34992*_Z^6-324*_Z^3+343)^2*x^2+335664*RootOf(34992*_Z^6-324*_Z^3+343)^4-2688*RootOf(34992*_Z^6-324*_Z^3+343)*x^3+23569*x*(x^3+1)^(2/3)-1554*RootOf(34992*_Z^6-324*_Z^3+343))/(324*RootOf(34992*_Z^6-324*_Z^3+343)^3*x^3+17*x^3+74))+1/24*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16)*ln((489888*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16)*RootOf(34992*_Z^6-324*_Z^3+343)^6*x^3+5994*(x^3+1)^(1/3)*RootOf(34992*_Z^6-324*_Z^3+343)^3*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16)^2*x^2-200340*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16)*RootOf(34992*_Z^6-324*_Z^3+343)^3*x^3-335664*(x^3+1)^(2/3)*RootOf(34992*_Z^6-324*_Z^3+343)^3*x-3108*(x^3+1)^(1/3)*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16)^2*x^2-111888*RootOf(34992*_Z^6-324*_Z^3+343)^3*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16)+917*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16)*x^3+97384*x*(x^3+1)^(2/3)+518*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16))/(162*RootOf(34992*_Z^6-324*_Z^3+343)^3*x^3-10*x^3-37))-27/74*ln(-(7838208*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16)*RootOf(34992*_Z^6-324*_Z^3+343)^6*x^3+551448*(x^3+1)^(1/3)*RootOf(34992*_Z^6-324*_Z^3+343)^3*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16)^2*x^2-855792*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16)*RootOf(34992*_Z^6-324*_Z^3+343)^3*x^3-18797184*(x^3+1)^(2/3)*RootOf(34992*_Z^6-324*_Z^3+343)^3*x-27195*(x^3+1)^(1/3)*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16)^2*x^2+895104*RootOf(34992*_Z^6-324*_Z^3+343)^3*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16)-187866*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16)*x^3+623672*x*(x^3+1)^(2/3)-195804*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16))/(162*RootOf(34992*_Z^6-324*_Z^3+343)^3*x^3-10*x^3-37))*RootOf(34992*_Z^6-324*_Z^3+343)^3*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16)-17/888*ln(-(7838208*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16)*RootOf(34992*_Z^6-324*_Z^3+343)^6*x^3+551448*(x^3+1)^(1/3)*RootOf(34992*_Z^6-324*_Z^3+343)^3*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16)^2*x^2-855792*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16)*RootOf(34992*_Z^6-324*_Z^3+343)^3*x^3-18797184*(x^3+1)^(2/3)*RootOf(34992*_Z^6-324*_Z^3+343)^3*x-27195*(x^3+1)^(1/3)*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16)^2*x^2+895104*RootOf(34992*_Z^6-324*_Z^3+343)^3*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16)-187866*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16)*x^3+623672*x*(x^3+1)^(2/3)-195804*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16))/(162*RootOf(34992*_Z^6-324*_Z^3+343)^3*x^3-10*x^3-37))*RootOf(_Z^3+1728*RootOf(34992*_Z^6-324*_Z^3+343)^3-16)","B"
1670,0,0,31,180.000000," ","int((x^3-1)^(2/3)*(x^6+4)/x^6/(x^6+2*x^3+4),x)","\[\int \frac{\left(x^{3}-1\right)^{\frac{2}{3}} \left(x^{6}+4\right)}{x^{6} \left(x^{6}+2 x^{3}+4\right)}\, dx\]"," ",0,"int((x^3-1)^(2/3)*(x^6+4)/x^6/(x^6+2*x^3+4),x)","F"
1671,0,0,31,180.000000," ","int((x^3-1)^(2/3)*(x^6+4)/x^6/(x^6+2*x^3+4),x)","\[\int \frac{\left(x^{3}-1\right)^{\frac{2}{3}} \left(x^{6}+4\right)}{x^{6} \left(x^{6}+2 x^{3}+4\right)}\, dx\]"," ",0,"int((x^3-1)^(2/3)*(x^6+4)/x^6/(x^6+2*x^3+4),x)","F"
1672,1,5571,31,67.359000," ","int((x^3-1)^(2/3)*(x^6-x^3+1)/x^6/(2*x^6-x^3-2),x)","\[\text{output too large to display}\]"," ",0,"result too large to display","B"
1673,1,7068,31,346.814000," ","int((x^3-1)^(2/3)*(x^6-x^3+1)/x^6/(2*x^6-x^3-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$7068$\\ trager&$\text{Expression too large to display}$&$10410$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1674,1,6679,31,222.170000," ","int((x^3+1)^(2/3)*(3*x^6+6*x^3+4)/x^6/(3*x^6+6*x^3+8),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$6679$\\ trager&$\text{Expression too large to display}$&$9175$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1675,1,8187,31,200.882000," ","int((x^3+1)^(2/3)*(3*x^6+6*x^3+4)/x^6/(3*x^6+6*x^3+8),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$8187$\\ trager&$\text{Expression too large to display}$&$10431$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1676,1,611,96,57.872000," ","int((x^8+2*x^3-1)^(1/3)*(5*x^8+3)/x^2/(x^8+x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(x^{8}+2 x^{3}-1\right)^{\frac{1}{3}}}{x}-3 \ln \left(\frac{5377901481395524539 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{8}-10267890788505543624 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{8}+4455082089494573732 x^{8}-487912174285505454 \left(x^{8}+2 x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -487912174285505454 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{8}+2 x^{3}-1\right)^{\frac{1}{3}} x^{2}-12548436789922890591 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+11735249832780381501 \left(x^{8}+2 x^{3}-1\right)^{\frac{2}{3}} x +11735249832780381501 \left(x^{8}+2 x^{3}-1\right)^{\frac{1}{3}} x^{2}+15592787313231008062 x^{3}-5377901481395524539 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+10267890788505543624 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-4455082089494573732}{x^{8}+x^{3}-1}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(\frac{5377901481395524539 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{8}+13853158442769226650 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{8}+8475256961373702111 x^{8}+487912174285505454 \left(x^{8}+2 x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x +487912174285505454 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{8}+2 x^{3}-1\right)^{\frac{1}{3}} x^{2}+12548436789922890591 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+11897887224208883319 \left(x^{8}+2 x^{3}-1\right)^{\frac{2}{3}} x +11897887224208883319 \left(x^{8}+2 x^{3}-1\right)^{\frac{1}{3}} x^{2}+19775599576538638259 x^{3}-5377901481395524539 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-13853158442769226650 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-8475256961373702111}{x^{8}+x^{3}-1}\right)-\ln \left(\frac{5377901481395524539 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{8}-10267890788505543624 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{8}+4455082089494573732 x^{8}-487912174285505454 \left(x^{8}+2 x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -487912174285505454 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{8}+2 x^{3}-1\right)^{\frac{1}{3}} x^{2}-12548436789922890591 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+11735249832780381501 \left(x^{8}+2 x^{3}-1\right)^{\frac{2}{3}} x +11735249832780381501 \left(x^{8}+2 x^{3}-1\right)^{\frac{1}{3}} x^{2}+15592787313231008062 x^{3}-5377901481395524539 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+10267890788505543624 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-4455082089494573732}{x^{8}+x^{3}-1}\right)$&$611$\\ risch&$\frac{3 \left(x^{8}+2 x^{3}-1\right)^{\frac{1}{3}}}{x}+\frac{\left(\ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{16}+x^{16}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{11}-5 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{11}+4 x^{11}-3 \left(x^{16}+4 x^{11}-2 x^{8}+4 x^{6}-4 x^{3}+1\right)^{\frac{1}{3}} x^{9}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{8}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}-2 x^{8}-6 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+4 x^{6}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{16}+4 x^{11}-2 x^{8}+4 x^{6}-4 x^{3}+1\right)^{\frac{2}{3}} x^{2}-6 \left(x^{16}+4 x^{11}-2 x^{8}+4 x^{6}-4 x^{3}+1\right)^{\frac{1}{3}} x^{4}+5 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 \left(x^{16}+4 x^{11}-2 x^{8}+4 x^{6}-4 x^{3}+1\right)^{\frac{2}{3}} x^{2}-4 x^{3}+3 \left(x^{16}+4 x^{11}-2 x^{8}+4 x^{6}-4 x^{3}+1\right)^{\frac{1}{3}} x -\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1}{\left(x^{8}+2 x^{3}-1\right) \left(x^{8}+x^{3}-1\right)}\right)+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{16}-x^{16}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{11}+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{11}+3 \left(x^{16}+4 x^{11}-2 x^{8}+4 x^{6}-4 x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{9}-5 x^{11}+3 \left(x^{16}+4 x^{11}-2 x^{8}+4 x^{6}-4 x^{3}+1\right)^{\frac{1}{3}} x^{9}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{8}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}+2 x^{8}+4 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+6 \left(x^{16}+4 x^{11}-2 x^{8}+4 x^{6}-4 x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}-6 x^{6}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{16}+4 x^{11}-2 x^{8}+4 x^{6}-4 x^{3}+1\right)^{\frac{2}{3}} x^{2}+6 \left(x^{16}+4 x^{11}-2 x^{8}+4 x^{6}-4 x^{3}+1\right)^{\frac{1}{3}} x^{4}-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-3 \left(x^{16}+4 x^{11}-2 x^{8}+4 x^{6}-4 x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +5 x^{3}-3 \left(x^{16}+4 x^{11}-2 x^{8}+4 x^{6}-4 x^{3}+1\right)^{\frac{1}{3}} x +\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1}{\left(x^{8}+2 x^{3}-1\right) \left(x^{8}+x^{3}-1\right)}\right)\right) \left(\left(x^{8}+2 x^{3}-1\right)^{2}\right)^{\frac{1}{3}}}{\left(x^{8}+2 x^{3}-1\right)^{\frac{2}{3}}}$&$787$\\ \hline \end{longtable}"," ",0,"3*(x^8+2*x^3-1)^(1/3)/x-3*ln((5377901481395524539*RootOf(9*_Z^2+3*_Z+1)^2*x^8-10267890788505543624*RootOf(9*_Z^2+3*_Z+1)*x^8+4455082089494573732*x^8-487912174285505454*(x^8+2*x^3-1)^(2/3)*RootOf(9*_Z^2+3*_Z+1)*x-487912174285505454*RootOf(9*_Z^2+3*_Z+1)*(x^8+2*x^3-1)^(1/3)*x^2-12548436789922890591*RootOf(9*_Z^2+3*_Z+1)*x^3+11735249832780381501*(x^8+2*x^3-1)^(2/3)*x+11735249832780381501*(x^8+2*x^3-1)^(1/3)*x^2+15592787313231008062*x^3-5377901481395524539*RootOf(9*_Z^2+3*_Z+1)^2+10267890788505543624*RootOf(9*_Z^2+3*_Z+1)-4455082089494573732)/(x^8+x^3-1))*RootOf(9*_Z^2+3*_Z+1)+3*RootOf(9*_Z^2+3*_Z+1)*ln((5377901481395524539*RootOf(9*_Z^2+3*_Z+1)^2*x^8+13853158442769226650*RootOf(9*_Z^2+3*_Z+1)*x^8+8475256961373702111*x^8+487912174285505454*(x^8+2*x^3-1)^(2/3)*RootOf(9*_Z^2+3*_Z+1)*x+487912174285505454*RootOf(9*_Z^2+3*_Z+1)*(x^8+2*x^3-1)^(1/3)*x^2+12548436789922890591*RootOf(9*_Z^2+3*_Z+1)*x^3+11897887224208883319*(x^8+2*x^3-1)^(2/3)*x+11897887224208883319*(x^8+2*x^3-1)^(1/3)*x^2+19775599576538638259*x^3-5377901481395524539*RootOf(9*_Z^2+3*_Z+1)^2-13853158442769226650*RootOf(9*_Z^2+3*_Z+1)-8475256961373702111)/(x^8+x^3-1))-ln((5377901481395524539*RootOf(9*_Z^2+3*_Z+1)^2*x^8-10267890788505543624*RootOf(9*_Z^2+3*_Z+1)*x^8+4455082089494573732*x^8-487912174285505454*(x^8+2*x^3-1)^(2/3)*RootOf(9*_Z^2+3*_Z+1)*x-487912174285505454*RootOf(9*_Z^2+3*_Z+1)*(x^8+2*x^3-1)^(1/3)*x^2-12548436789922890591*RootOf(9*_Z^2+3*_Z+1)*x^3+11735249832780381501*(x^8+2*x^3-1)^(2/3)*x+11735249832780381501*(x^8+2*x^3-1)^(1/3)*x^2+15592787313231008062*x^3-5377901481395524539*RootOf(9*_Z^2+3*_Z+1)^2+10267890788505543624*RootOf(9*_Z^2+3*_Z+1)-4455082089494573732)/(x^8+x^3-1))","C"
1677,0,0,47,0.021000," ","int((x^4-1)*(1+(x^2+1)^(1/2))^(1/2)/(x^4+1),x)","\[\int \frac{\left(x^{4}-1\right) \sqrt{1+\sqrt{x^{2}+1}}}{x^{4}+1}\, dx\]"," ",0,"int((x^4-1)*(1+(x^2+1)^(1/2))^(1/2)/(x^4+1),x)","F"
1678,0,0,47,0.003000," ","int((x^4-1)*(1+(x^2+1)^(1/2))^(1/2)/(x^4+1),x)","\[\int \frac{\left(x^{4}-1\right) \sqrt{1+\sqrt{x^{2}+1}}}{x^{4}+1}\, dx\]"," ",0,"int((x^4-1)*(1+(x^2+1)^(1/2))^(1/2)/(x^4+1),x)","F"
1679,0,0,98,180.000000," ","int((a^2*x^2+b^2)^(1/2)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{a^{2} x^{2}+b^{2}}}{\sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int((a^2*x^2+b^2)^(1/2)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","F"
1680,0,0,101,0.090000," ","int((-2*a+b+x)/((-a+x)*(-b+x)^2)^(1/4)/(b^2+a*d-(2*b+d)*x+x^2),x)","\[\int \frac{-2 a +b +x}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{4}} \left(b^{2}+a d -\left(2 b +d \right) x +x^{2}\right)}\, dx\]"," ",0,"int((-2*a+b+x)/((-a+x)*(-b+x)^2)^(1/4)/(b^2+a*d-(2*b+d)*x+x^2),x)","F"
1681,1,15,91,0.903000," ","int(x*(x^3+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 x^{\frac{8}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{8}{3}\right], \left[\frac{11}{3}\right], -x \right)}{8}$&$15$\\ risch&$\frac{\left(18 x^{2}+3 x -5\right) \left(x^{2} \left(1+x \right)\right)^{\frac{1}{3}}}{54}+\frac{\left(-\frac{5 \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{2}-48 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{2}{3}}+30 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}} x +16 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2}+30 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}}+14 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x +36 \left(x^{3}+2 x^{2}+x \right)^{\frac{2}{3}}-96 \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}} x +64 x^{2}-2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)-96 \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}}+112 x +48}{1+x}\right)}{81}+\frac{5 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{2}+24 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{2}{3}}-9 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}} x -19 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2}-9 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}}-28 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x -30 \left(x^{3}+2 x^{2}+x \right)^{\frac{2}{3}}+48 \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}} x -10 x^{2}-9 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)+48 \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}}-14 x -4}{1+x}\right)}{162}\right) \left(x^{2} \left(1+x \right)\right)^{\frac{1}{3}} \left(\left(1+x \right)^{2} x \right)^{\frac{1}{3}}}{x \left(1+x \right)}$&$457$\\ trager&$\left(\frac{1}{3} x^{2}+\frac{1}{18} x -\frac{5}{54}\right) \left(x^{3}+x^{2}\right)^{\frac{1}{3}}+\frac{5 \ln \left(-\frac{36 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}-36 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x -45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{2}{3}}-45 \left(x^{3}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x -57 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}-27 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x -9 \left(x^{3}+x^{2}\right)^{\frac{2}{3}}-9 x \left(x^{3}+x^{2}\right)^{\frac{1}{3}}-5 x^{2}-2 x}{x}\right)}{81}-\frac{5 \ln \left(-\frac{36 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}-36 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x -45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{2}{3}}-45 \left(x^{3}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x -57 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}-27 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x -9 \left(x^{3}+x^{2}\right)^{\frac{2}{3}}-9 x \left(x^{3}+x^{2}\right)^{\frac{1}{3}}-5 x^{2}-2 x}{x}\right) \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)}{27}+\frac{5 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \ln \left(-\frac{36 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}-36 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x +45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{2}{3}}+45 \left(x^{3}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x +33 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}+51 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x -24 \left(x^{3}+x^{2}\right)^{\frac{2}{3}}-24 x \left(x^{3}+x^{2}\right)^{\frac{1}{3}}-20 x^{2}-15 x}{x}\right)}{27}$&$491$\\ \hline \end{longtable}"," ",0,"3/8*x^(8/3)*hypergeom([-1/3,8/3],[11/3],-x)","C"
1682,0,0,101,0.013000," ","int((-(2*a-3*b)*b+2*(a-2*b)*x+x^2)/((-a+x)*(-b+x)^2)^(1/4)/(-a^3-b^2*d+(3*a^2+2*b*d)*x-(3*a+d)*x^2+x^3),x)","\[\int \frac{-\left(2 a -3 b \right) b +2 \left(a -2 b \right) x +x^{2}}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{4}} \left(-a^{3}-b^{2} d +\left(3 a^{2}+2 b d \right) x -\left(3 a +d \right) x^{2}+x^{3}\right)}\, dx\]"," ",0,"int((-(2*a-3*b)*b+2*(a-2*b)*x+x^2)/((-a+x)*(-b+x)^2)^(1/4)/(-a^3-b^2*d+(3*a^2+2*b*d)*x-(3*a+d)*x^2+x^3),x)","F"
1683,0,0,99,0.015000," ","int((-1+x)^3*(-1+2*(-1+k)*x+k*x^2)/x/((1-x)*x*(-k*x+1))^(1/4)/(k*x-1)/(-1+(3+d)*x-(d*k+3)*x^2+x^3),x)","\[\int \frac{\left(-1+x \right)^{3} \left(-1+2 \left(-1+k \right) x +k \,x^{2}\right)}{x \left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{4}} \left(k x -1\right) \left(-1+\left(3+d \right) x -\left(d k +3\right) x^{2}+x^{3}\right)}\, dx\]"," ",0,"int((-1+x)^3*(-1+2*(-1+k)*x+k*x^2)/x/((1-x)*x*(-k*x+1))^(1/4)/(k*x-1)/(-1+(3+d)*x-(d*k+3)*x^2+x^3),x)","F"
1684,1,395,85,0.140000," ","int((a*x^2+b)/(a*x^2-b)/(a*x^3+b*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}+b x}}+\frac{b \sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{\sqrt{a b}\, a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}-\frac{b \sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{\sqrt{a b}\, a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}$&$395$\\ default&$\frac{\sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}+b x}}+2 b \left(\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{a b}\, a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}-\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{a b}\, a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}\right)$&$417$\\ \hline \end{longtable}"," ",0,"1/a*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)*EllipticF(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))+b/(a*b)^(1/2)/a*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2)),1/2*2^(1/2))-b/(a*b)^(1/2)/a*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)+1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)+1/a*(a*b)^(1/2)),1/2*2^(1/2))","C"
1685,0,0,101,0.022000," ","int((a^2-2*a*x+x^2)*(-(2*a-3*b)*b+2*(a-2*b)*x+x^2)/((-a+x)*(-b+x)^2)^(3/4)/(-b^2-a^3*d+(3*a^2*d+2*b)*x-(3*a*d+1)*x^2+d*x^3),x)","\[\int \frac{\left(a^{2}-2 a x +x^{2}\right) \left(-\left(2 a -3 b \right) b +2 \left(a -2 b \right) x +x^{2}\right)}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{3}{4}} \left(-b^{2}-a^{3} d +\left(3 a^{2} d +2 b \right) x -\left(3 a d +1\right) x^{2}+d \,x^{3}\right)}\, dx\]"," ",0,"int((a^2-2*a*x+x^2)*(-(2*a-3*b)*b+2*(a-2*b)*x+x^2)/((-a+x)*(-b+x)^2)^(3/4)/(-b^2-a^3*d+(3*a^2*d+2*b)*x-(3*a*d+1)*x^2+d*x^3),x)","F"
1686,1,1783,56,23.846000," ","int((x^3-1)*(x^4+x^3)^(1/4)/(x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1783$\\ risch&$\text{Expression too large to display}$&$3761$\\ \hline \end{longtable}"," ",0,"(1/8+1/2*x)*(x^4+x^3)^(1/4)+3/32*ln((2*(x^4+x^3)^(3/4)-2*(x^4+x^3)^(1/2)*x+2*x^2*(x^4+x^3)^(1/4)-2*x^3-x^2)/x^2)-3/32*RootOf(_Z^2+1)*ln((2*(x^4+x^3)^(1/2)*RootOf(_Z^2+1)*x-2*RootOf(_Z^2+1)*x^3+2*(x^4+x^3)^(3/4)-2*x^2*(x^4+x^3)^(1/4)-RootOf(_Z^2+1)*x^2)/x^2)-2/3*RootOf(_Z^8+3)*ln(-(-5*x^3*RootOf(_Z^8+3)^11+5*RootOf(_Z^8+3)^11*x^2+86*RootOf(_Z^8+3)^7*x^3+96*(x^4+x^3)^(1/4)*RootOf(_Z^8+3)^6*x^2+44*RootOf(_Z^8+3)^7*x^2-180*(x^4+x^3)^(1/2)*RootOf(_Z^8+3)^5*x+84*(x^4+x^3)^(3/4)*RootOf(_Z^8+3)^4+171*RootOf(_Z^8+3)^3*x^3-264*(x^4+x^3)^(1/4)*RootOf(_Z^8+3)^2*x^2+63*RootOf(_Z^8+3)^3*x^2-12*(x^4+x^3)^(1/2)*RootOf(_Z^8+3)*x+276*(x^4+x^3)^(3/4))/(x*RootOf(_Z^8+3)^4-RootOf(_Z^8+3)^4+x+1)/x^2)+2/3*RootOf(_Z^2+RootOf(_Z^8+3)^2)*ln(-(-5*RootOf(_Z^2+RootOf(_Z^8+3)^2)*RootOf(_Z^8+3)^10*x^3+5*RootOf(_Z^2+RootOf(_Z^8+3)^2)*RootOf(_Z^8+3)^10*x^2+86*RootOf(_Z^8+3)^6*RootOf(_Z^2+RootOf(_Z^8+3)^2)*x^3+44*RootOf(_Z^8+3)^6*RootOf(_Z^2+RootOf(_Z^8+3)^2)*x^2-96*(x^4+x^3)^(1/4)*RootOf(_Z^8+3)^6*x^2+180*(x^4+x^3)^(1/2)*RootOf(_Z^8+3)^4*RootOf(_Z^2+RootOf(_Z^8+3)^2)*x+84*(x^4+x^3)^(3/4)*RootOf(_Z^8+3)^4+171*RootOf(_Z^2+RootOf(_Z^8+3)^2)*RootOf(_Z^8+3)^2*x^3+63*RootOf(_Z^2+RootOf(_Z^8+3)^2)*RootOf(_Z^8+3)^2*x^2+264*(x^4+x^3)^(1/4)*RootOf(_Z^8+3)^2*x^2+12*RootOf(_Z^2+RootOf(_Z^8+3)^2)*(x^4+x^3)^(1/2)*x+276*(x^4+x^3)^(3/4))/(x*RootOf(_Z^8+3)^4-RootOf(_Z^8+3)^4+x+1)/x^2)-2/3*RootOf(_Z^2+RootOf(_Z^8+3)*RootOf(_Z^2+RootOf(_Z^8+3)^2))*ln(-(5*RootOf(_Z^2+RootOf(_Z^8+3)^2)*RootOf(_Z^2+RootOf(_Z^8+3)*RootOf(_Z^2+RootOf(_Z^8+3)^2))*RootOf(_Z^8+3)^9*x^3-5*RootOf(_Z^2+RootOf(_Z^8+3)^2)*RootOf(_Z^2+RootOf(_Z^8+3)*RootOf(_Z^2+RootOf(_Z^8+3)^2))*RootOf(_Z^8+3)^9*x^2+86*RootOf(_Z^2+RootOf(_Z^8+3)^2)*RootOf(_Z^8+3)^5*RootOf(_Z^2+RootOf(_Z^8+3)*RootOf(_Z^2+RootOf(_Z^8+3)^2))*x^3+44*RootOf(_Z^2+RootOf(_Z^8+3)^2)*RootOf(_Z^8+3)^5*RootOf(_Z^2+RootOf(_Z^8+3)*RootOf(_Z^2+RootOf(_Z^8+3)^2))*x^2+96*RootOf(_Z^2+RootOf(_Z^8+3)^2)*(x^4+x^3)^(1/4)*RootOf(_Z^8+3)^5*x^2+180*(x^4+x^3)^(1/2)*RootOf(_Z^8+3)^4*RootOf(_Z^2+RootOf(_Z^8+3)*RootOf(_Z^2+RootOf(_Z^8+3)^2))*x-84*(x^4+x^3)^(3/4)*RootOf(_Z^8+3)^4-171*RootOf(_Z^2+RootOf(_Z^8+3)^2)*RootOf(_Z^2+RootOf(_Z^8+3)*RootOf(_Z^2+RootOf(_Z^8+3)^2))*RootOf(_Z^8+3)*x^3-63*RootOf(_Z^2+RootOf(_Z^8+3)^2)*RootOf(_Z^2+RootOf(_Z^8+3)*RootOf(_Z^2+RootOf(_Z^8+3)^2))*RootOf(_Z^8+3)*x^2+264*RootOf(_Z^2+RootOf(_Z^8+3)^2)*(x^4+x^3)^(1/4)*RootOf(_Z^8+3)*x^2-12*RootOf(_Z^2+RootOf(_Z^8+3)*RootOf(_Z^2+RootOf(_Z^8+3)^2))*(x^4+x^3)^(1/2)*x+276*(x^4+x^3)^(3/4))/(x*RootOf(_Z^8+3)^4-RootOf(_Z^8+3)^4-x-1)/x^2)+2/9*RootOf(_Z^8+3)^7*RootOf(_Z^2+RootOf(_Z^8+3)^2)*RootOf(_Z^2+RootOf(_Z^8+3)*RootOf(_Z^2+RootOf(_Z^8+3)^2))*ln(-(5*RootOf(_Z^2+RootOf(_Z^8+3)*RootOf(_Z^2+RootOf(_Z^8+3)^2))*RootOf(_Z^8+3)^10*x^3-5*RootOf(_Z^2+RootOf(_Z^8+3)*RootOf(_Z^2+RootOf(_Z^8+3)^2))*RootOf(_Z^8+3)^10*x^2+4*RootOf(_Z^2+RootOf(_Z^8+3)*RootOf(_Z^2+RootOf(_Z^8+3)^2))*RootOf(_Z^2+RootOf(_Z^8+3)^2)*(x^4+x^3)^(1/2)*RootOf(_Z^8+3)^7*x+86*RootOf(_Z^8+3)^6*RootOf(_Z^2+RootOf(_Z^8+3)*RootOf(_Z^2+RootOf(_Z^8+3)^2))*x^3+44*RootOf(_Z^8+3)^6*RootOf(_Z^2+RootOf(_Z^8+3)*RootOf(_Z^2+RootOf(_Z^8+3)^2))*x^2-96*RootOf(_Z^2+RootOf(_Z^8+3)^2)*(x^4+x^3)^(1/4)*RootOf(_Z^8+3)^5*x^2+180*(x^4+x^3)^(1/2)*RootOf(_Z^2+RootOf(_Z^8+3)*RootOf(_Z^2+RootOf(_Z^8+3)^2))*RootOf(_Z^2+RootOf(_Z^8+3)^2)*RootOf(_Z^8+3)^3*x-84*(x^4+x^3)^(3/4)*RootOf(_Z^8+3)^4-171*RootOf(_Z^2+RootOf(_Z^8+3)*RootOf(_Z^2+RootOf(_Z^8+3)^2))*RootOf(_Z^8+3)^2*x^3-63*RootOf(_Z^2+RootOf(_Z^8+3)*RootOf(_Z^2+RootOf(_Z^8+3)^2))*RootOf(_Z^8+3)^2*x^2-264*RootOf(_Z^2+RootOf(_Z^8+3)^2)*(x^4+x^3)^(1/4)*RootOf(_Z^8+3)*x^2+276*(x^4+x^3)^(3/4))/(x*RootOf(_Z^8+3)^4-RootOf(_Z^8+3)^4-x-1)/x^2)","B"
1687,0,0,89,0.012000," ","int((a*x^2-b)/x^2/(a*x^2+b)/(a*x^4-b*x^2)^(1/4),x)","\[\int \frac{a \,x^{2}-b}{x^{2} \left(a \,x^{2}+b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2-b)/x^2/(a*x^2+b)/(a*x^4-b*x^2)^(1/4),x)","F"
1688,0,0,101,0.014000," ","int((-b+x)*(-6*a+b+5*x)/((-a+x)*(-b+x)^2)^(1/4)/(b^6+a*d-(6*b^5+d)*x+15*b^4*x^2-20*b^3*x^3+15*b^2*x^4-6*b*x^5+x^6),x)","\[\int \frac{\left(-b +x \right) \left(-6 a +b +5 x \right)}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{4}} \left(b^{6}+a d -\left(6 b^{5}+d \right) x +15 b^{4} x^{2}-20 b^{3} x^{3}+15 b^{2} x^{4}-6 b \,x^{5}+x^{6}\right)}\, dx\]"," ",0,"int((-b+x)*(-6*a+b+5*x)/((-a+x)*(-b+x)^2)^(1/4)/(b^6+a*d-(6*b^5+d)*x+15*b^4*x^2-20*b^3*x^3+15*b^2*x^4-6*b*x^5+x^6),x)","F"
1689,0,0,101,0.020000," ","int((-6*a+b+5*x)*(-b^5+5*b^4*x-10*b^3*x^2+10*b^2*x^3-5*b*x^4+x^5)/((-a+x)*(-b+x)^2)^(3/4)/(a+b^6*d-(6*b^5*d+1)*x+15*b^4*d*x^2-20*b^3*d*x^3+15*b^2*d*x^4-6*b*d*x^5+d*x^6),x)","\[\int \frac{\left(-6 a +b +5 x \right) \left(-b^{5}+5 b^{4} x -10 b^{3} x^{2}+10 b^{2} x^{3}-5 b \,x^{4}+x^{5}\right)}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{3}{4}} \left(a +b^{6} d -\left(6 b^{5} d +1\right) x +15 b^{4} d \,x^{2}-20 b^{3} d \,x^{3}+15 b^{2} d \,x^{4}-6 b d \,x^{5}+d \,x^{6}\right)}\, dx\]"," ",0,"int((-6*a+b+5*x)*(-b^5+5*b^4*x-10*b^3*x^2+10*b^2*x^3-5*b*x^4+x^5)/((-a+x)*(-b+x)^2)^(3/4)/(a+b^6*d-(6*b^5*d+1)*x+15*b^4*d*x^2-20*b^3*d*x^3+15*b^2*d*x^4-6*b*d*x^5+d*x^6),x)","F"
1690,1,3632,52,66.463000," ","int(x^4*(x^4+x^2)^(1/4)/(x^8-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$3632$\\ \hline \end{longtable}"," ",0,"-128*ln(-(243269632*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^8*x^3-973078528*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^8*x-944128*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^3-13074432*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^2-1984512*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x+52297728*(x^4+x^2)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*x-209190912*(x^4+x^2)^(3/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-2369*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x^3+15992*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*(x^4+x^2)^(1/4)*x^2-515*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x-63968*(x^4+x^2)^(1/2)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*x+255872*(x^4+x^2)^(3/4))/x/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^2-16384*RootOf(8388608*_Z^8-4096*_Z^4+1)^4+3*x^2+5))*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)+1/32*ln(-(243269632*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^8*x^3-973078528*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^8*x-944128*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^3-13074432*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^2-1984512*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x+52297728*(x^4+x^2)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*x-209190912*(x^4+x^2)^(3/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-2369*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x^3+15992*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*(x^4+x^2)^(1/4)*x^2-515*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x-63968*(x^4+x^2)^(1/2)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*x+255872*(x^4+x^2)^(3/4))/x/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^2-16384*RootOf(8388608*_Z^8-4096*_Z^4+1)^4+3*x^2+5))*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)+RootOf(8388608*_Z^8-4096*_Z^4+1)*ln(-(-504658657280*RootOf(8388608*_Z^8-4096*_Z^4+1)^11*x^3+2018634629120*RootOf(8388608*_Z^8-4096*_Z^4+1)^11*x-2479357952*x^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^7-104595456*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^6*x^2+52428800*(x^4+x^2)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)^5*x-2033713152*x*RootOf(8388608*_Z^8-4096*_Z^4+1)^7+1634304*(x^4+x^2)^(3/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4+553728*x^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^3-76864*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^2*x^2-15992*(x^4+x^2)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)*x+342784*RootOf(8388608*_Z^8-4096*_Z^4+1)^3*x+1201*(x^4+x^2)^(3/4))/x/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^2-16384*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-5*x^2+3))-1/32*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*ln(-(492830720*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^8*x^3-1971322880*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^8*x-2902528*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^3+3268608*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^2-60928*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x+52428800*(x^4+x^2)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*x-52297728*(x^4+x^2)^(3/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4+759*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x^3-3998*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*(x^4+x^2)^(1/4)*x^2+165*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x-9608*(x^4+x^2)^(1/2)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*x+63968*(x^4+x^2)^(3/4))/x/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^2-16384*RootOf(8388608*_Z^8-4096*_Z^4+1)^4+3*x^2+5))+4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^5*ln(-(62277025792*RootOf(8388608*_Z^8-4096*_Z^4+1)^11*x^3-249108103168*RootOf(8388608*_Z^8-4096*_Z^4+1)^11*x+180879360*x^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^7+104595456*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^6*x^2-13074432*(x^4+x^2)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)^5*x+751304704*x*RootOf(8388608*_Z^8-4096*_Z^4+1)^7+1634304*(x^4+x^2)^(3/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-709632*x^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^3+76864*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^2*x^2-9608*(x^4+x^2)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)*x-439296*RootOf(8388608*_Z^8-4096*_Z^4+1)^3*x+1201*(x^4+x^2)^(3/4))/x/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^2-16384*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-5*x^2+3))-RootOf(8388608*_Z^8-4096*_Z^4+1)*ln(-(62277025792*RootOf(8388608*_Z^8-4096*_Z^4+1)^11*x^3-249108103168*RootOf(8388608*_Z^8-4096*_Z^4+1)^11*x+180879360*x^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^7+104595456*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^6*x^2-13074432*(x^4+x^2)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)^5*x+751304704*x*RootOf(8388608*_Z^8-4096*_Z^4+1)^7+1634304*(x^4+x^2)^(3/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-709632*x^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^3+76864*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^2*x^2-9608*(x^4+x^2)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)*x-439296*RootOf(8388608*_Z^8-4096*_Z^4+1)^3*x+1201*(x^4+x^2)^(3/4))/x/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^2-16384*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-5*x^2+3))+1/4*RootOf(8388608*_Z^8-4096*_Z^4+1)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*ln(-(6*RootOf(8388608*_Z^8-4096*_Z^4+1)^3*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x^3+2*RootOf(8388608*_Z^8-4096*_Z^4+1)^3*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x-4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^2*x^2+2*RootOf(8388608*_Z^8-4096*_Z^4+1)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*(x^4+x^2)^(1/2)*x-(x^4+x^2)^(3/4))/(1+x)/x/(-1+x))-1024*ln(-(24576*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^7*x^3+8192*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^7*x-6*RootOf(8388608*_Z^8-4096*_Z^4+1)^3*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x^3-8192*(x^4+x^2)^(1/2)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*RootOf(8388608*_Z^8-4096*_Z^4+1)^5*x-2*RootOf(8388608*_Z^8-4096*_Z^4+1)^3*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x+4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^2*x^2+2*RootOf(8388608*_Z^8-4096*_Z^4+1)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*(x^4+x^2)^(1/2)*x-(x^4+x^2)^(3/4))/(1+x)/x/(-1+x))*RootOf(8388608*_Z^8-4096*_Z^4+1)^5*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)+1/4*ln(-(24576*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^7*x^3+8192*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^7*x-6*RootOf(8388608*_Z^8-4096*_Z^4+1)^3*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x^3-8192*(x^4+x^2)^(1/2)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*RootOf(8388608*_Z^8-4096*_Z^4+1)^5*x-2*RootOf(8388608*_Z^8-4096*_Z^4+1)^3*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x+4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^2*x^2+2*RootOf(8388608*_Z^8-4096*_Z^4+1)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*(x^4+x^2)^(1/2)*x-(x^4+x^2)^(3/4))/(1+x)/x/(-1+x))*RootOf(8388608*_Z^8-4096*_Z^4+1)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)","B"
1691,1,3624,52,64.332000," ","int(x^4*(x^4+x^2)^(1/4)/(x^8-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$3624$\\ \hline \end{longtable}"," ",0,"-4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^5*ln((62277025792*RootOf(8388608*_Z^8-4096*_Z^4+1)^11*x^3-249108103168*RootOf(8388608*_Z^8-4096*_Z^4+1)^11*x+180879360*x^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^7-104595456*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^6*x^2+751304704*x*RootOf(8388608*_Z^8-4096*_Z^4+1)^7-13074432*(x^4+x^2)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)^5*x-1634304*(x^4+x^2)^(3/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-709632*x^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^3-76864*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^2*x^2-439296*RootOf(8388608*_Z^8-4096*_Z^4+1)^3*x-9608*(x^4+x^2)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)*x-1201*(x^4+x^2)^(3/4))/x/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^2-16384*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-5*x^2+3))+RootOf(8388608*_Z^8-4096*_Z^4+1)*ln((62277025792*RootOf(8388608*_Z^8-4096*_Z^4+1)^11*x^3-249108103168*RootOf(8388608*_Z^8-4096*_Z^4+1)^11*x+180879360*x^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^7-104595456*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^6*x^2+751304704*x*RootOf(8388608*_Z^8-4096*_Z^4+1)^7-13074432*(x^4+x^2)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)^5*x-1634304*(x^4+x^2)^(3/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-709632*x^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^3-76864*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^2*x^2-439296*RootOf(8388608*_Z^8-4096*_Z^4+1)^3*x-9608*(x^4+x^2)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)*x-1201*(x^4+x^2)^(3/4))/x/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^2-16384*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-5*x^2+3))+1/32*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*ln((492830720*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^8*x^3-1971322880*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^8*x-2902528*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^3-3268608*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^2-60928*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x+52428800*(x^4+x^2)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*x+52297728*(x^4+x^2)^(3/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4+759*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x^3+3998*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*(x^4+x^2)^(1/4)*x^2+165*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x-9608*(x^4+x^2)^(1/2)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*x-63968*(x^4+x^2)^(3/4))/x/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^2-16384*RootOf(8388608*_Z^8-4096*_Z^4+1)^4+3*x^2+5))+128*ln((243269632*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^8*x^3-973078528*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^8*x-944128*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^3+13074432*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^2-1984512*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x+52297728*(x^4+x^2)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*x+209190912*(x^4+x^2)^(3/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-2369*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x^3-15992*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*(x^4+x^2)^(1/4)*x^2-515*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x-63968*(x^4+x^2)^(1/2)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*x-255872*(x^4+x^2)^(3/4))/x/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^2-16384*RootOf(8388608*_Z^8-4096*_Z^4+1)^4+3*x^2+5))*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)-1/32*ln((243269632*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^8*x^3-973078528*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^8*x-944128*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^3+13074432*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^2-1984512*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x+52297728*(x^4+x^2)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*x+209190912*(x^4+x^2)^(3/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-2369*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x^3-15992*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*(x^4+x^2)^(1/4)*x^2-515*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x-63968*(x^4+x^2)^(1/2)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*x-255872*(x^4+x^2)^(3/4))/x/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^2-16384*RootOf(8388608*_Z^8-4096*_Z^4+1)^4+3*x^2+5))*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)-RootOf(8388608*_Z^8-4096*_Z^4+1)*ln(-(504658657280*RootOf(8388608*_Z^8-4096*_Z^4+1)^11*x^3-2018634629120*RootOf(8388608*_Z^8-4096*_Z^4+1)^11*x+2479357952*x^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^7-104595456*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^6*x^2+2033713152*x*RootOf(8388608*_Z^8-4096*_Z^4+1)^7-52428800*(x^4+x^2)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)^5*x+1634304*(x^4+x^2)^(3/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-553728*x^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^3-76864*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^2*x^2-342784*RootOf(8388608*_Z^8-4096*_Z^4+1)^3*x+15992*(x^4+x^2)^(1/2)*RootOf(8388608*_Z^8-4096*_Z^4+1)*x+1201*(x^4+x^2)^(3/4))/x/(4096*RootOf(8388608*_Z^8-4096*_Z^4+1)^4*x^2-16384*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-5*x^2+3))-1024*ln(-(24576*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^7*x^3+8192*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^7*x-6*RootOf(8388608*_Z^8-4096*_Z^4+1)^3*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x^3-8192*(x^4+x^2)^(1/2)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*RootOf(8388608*_Z^8-4096*_Z^4+1)^5*x-2*RootOf(8388608*_Z^8-4096*_Z^4+1)^3*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x+4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^2*x^2+2*RootOf(8388608*_Z^8-4096*_Z^4+1)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*(x^4+x^2)^(1/2)*x-(x^4+x^2)^(3/4))/(1+x)/x/(-1+x))*RootOf(8388608*_Z^8-4096*_Z^4+1)^5*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)+1/4*ln(-(24576*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^7*x^3+8192*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*RootOf(8388608*_Z^8-4096*_Z^4+1)^7*x-6*RootOf(8388608*_Z^8-4096*_Z^4+1)^3*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x^3-8192*(x^4+x^2)^(1/2)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*RootOf(8388608*_Z^8-4096*_Z^4+1)^5*x-2*RootOf(8388608*_Z^8-4096*_Z^4+1)^3*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x+4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^2*x^2+2*RootOf(8388608*_Z^8-4096*_Z^4+1)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*(x^4+x^2)^(1/2)*x-(x^4+x^2)^(3/4))/(1+x)/x/(-1+x))*RootOf(8388608*_Z^8-4096*_Z^4+1)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)-1/4*RootOf(8388608*_Z^8-4096*_Z^4+1)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*ln((6*RootOf(8388608*_Z^8-4096*_Z^4+1)^3*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x^3+2*RootOf(8388608*_Z^8-4096*_Z^4+1)^3*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^3*x+4*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)^2*(x^4+x^2)^(1/4)*RootOf(8388608*_Z^8-4096*_Z^4+1)^2*x^2+2*RootOf(8388608*_Z^8-4096*_Z^4+1)*RootOf(_Z^4+1048576*RootOf(8388608*_Z^8-4096*_Z^4+1)^4-512)*(x^4+x^2)^(1/2)*x+(x^4+x^2)^(3/4))/(1+x)/x/(-1+x))","B"
1692,1,5894,23,149.234000," ","int(x^4/(x^4+x^2)^(1/4)/(x^8+x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$5894$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1693,1,5895,23,148.225000," ","int(x^4/(x^4+x^2)^(1/4)/(x^8+x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$5895$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1694,1,444,92,3.073000," ","int(x^6*(x^3+4)/(x^3+1)^(3/4)/(x^8-x^6-2*x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{3}+1}\, x^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \left(x^{3}+1\right)^{\frac{3}{4}} x -2 \left(x^{3}+1\right)^{\frac{1}{4}} x^{3}+\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{4}-x^{3}-1}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \sqrt{x^{3}+1}\, x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{3}+1\right)^{\frac{1}{4}} x^{3}+\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{3}+1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{x^{4}+x^{3}+1}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \ln \left(\frac{-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \sqrt{x^{3}+1}\, x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{3}+1\right)^{\frac{1}{4}} x^{3}-\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) x^{4}+2 \left(x^{3}+1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) x^{3}+\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{x^{4}+x^{3}+1}\right)}{2}+\frac{\ln \left(-\frac{2 \left(x^{3}+1\right)^{\frac{3}{4}} x -2 x^{2} \sqrt{x^{3}+1}+2 \left(x^{3}+1\right)^{\frac{1}{4}} x^{3}-x^{4}-x^{3}-1}{x^{4}-x^{3}-1}\right)}{2}$&$444$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^2+1)*ln(-(-2*RootOf(_Z^2+1)*(x^3+1)^(1/2)*x^2+RootOf(_Z^2+1)*x^4+2*(x^3+1)^(3/4)*x-2*(x^3+1)^(1/4)*x^3+RootOf(_Z^2+1)*x^3+RootOf(_Z^2+1))/(x^4-x^3-1))+1/2*RootOf(_Z^2-RootOf(_Z^2+1))*ln((-RootOf(_Z^2-RootOf(_Z^2+1))*RootOf(_Z^2+1)*x^4-2*RootOf(_Z^2-RootOf(_Z^2+1))*(x^3+1)^(1/2)*x^2+2*RootOf(_Z^2+1)*(x^3+1)^(1/4)*x^3+RootOf(_Z^2-RootOf(_Z^2+1))*RootOf(_Z^2+1)*x^3+2*(x^3+1)^(3/4)*x+RootOf(_Z^2+1)*RootOf(_Z^2-RootOf(_Z^2+1)))/(x^4+x^3+1))+1/2*RootOf(_Z^2+1)*RootOf(_Z^2-RootOf(_Z^2+1))*ln((-2*RootOf(_Z^2+1)*RootOf(_Z^2-RootOf(_Z^2+1))*(x^3+1)^(1/2)*x^2-2*RootOf(_Z^2+1)*(x^3+1)^(1/4)*x^3-RootOf(_Z^2-RootOf(_Z^2+1))*x^4+2*(x^3+1)^(3/4)*x+RootOf(_Z^2-RootOf(_Z^2+1))*x^3+RootOf(_Z^2-RootOf(_Z^2+1)))/(x^4+x^3+1))+1/2*ln(-(2*(x^3+1)^(3/4)*x-2*x^2*(x^3+1)^(1/2)+2*(x^3+1)^(1/4)*x^3-x^4-x^3-1)/(x^4-x^3-1))","C"
1695,1,33,92,1.592000," ","int(x^10*(x^3-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} x^{11} \hypergeom \left(\left[-\frac{1}{3}, \frac{11}{3}\right], \left[\frac{14}{3}\right], x^{3}\right)}{11 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}}}$&$33$\\ risch&$\frac{x^{2} \left(81 x^{9}-9 x^{6}-12 x^{3}-20\right) \left(x^{3}-1\right)^{\frac{1}{3}}}{972}-\frac{5 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} x^{2} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], x^{3}\right)}{243 \mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}}}$&$63$\\ trager&$\frac{x^{2} \left(81 x^{9}-9 x^{6}-12 x^{3}-20\right) \left(x^{3}-1\right)^{\frac{1}{3}}}{972}+\frac{10 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1\right)}{729}-\frac{10 \ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}-1\right)^{\frac{2}{3}}+3 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}+4 x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{729}-\frac{10 \ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}-1\right)^{\frac{2}{3}}+3 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}+4 x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2\right)}{729}$&$325$\\ \hline \end{longtable}"," ",0,"1/11*signum(x^3-1)^(1/3)/(-signum(x^3-1))^(1/3)*x^11*hypergeom([-1/3,11/3],[14/3],x^3)","C"
1696,1,27,98,0.607000," ","int(x/(-1+x)/(x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{3 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{3}} x^{\frac{4}{3}} \hypergeom \left(\left[\frac{4}{3}, \frac{4}{3}\right], \left[\frac{7}{3}\right], x\right)}{4 \mathrm{signum}\left(-1+x \right)^{\frac{1}{3}}}$&$27$\\ risch&$-\frac{3 x}{\left(\left(-1+x \right) x^{2}\right)^{\frac{1}{3}}}+\frac{3 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{3}} x^{\frac{1}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x\right)}{\mathrm{signum}\left(-1+x \right)^{\frac{1}{3}}}$&$40$\\ trager&$-\frac{3 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}}{\left(-1+x \right) x}-\ln \left(-\frac{9 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right)^{2} x^{2}-18 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right)^{2} x +144 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}-90 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) \left(x^{3}-x^{2}\right)^{\frac{1}{3}} x -60 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) x^{2}+78 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) x -60 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}-36 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}+100 x^{2}-60 x}{x}\right)+\ln \left(-\frac{18 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right)^{2} x^{2}-36 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right)^{2} x -72 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+27 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) \left(x^{3}-x^{2}\right)^{\frac{1}{3}} x +33 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) x^{2}+18 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) x +18 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+30 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}-40 x^{2}+10 x}{x}\right)-\frac{3 \ln \left(-\frac{18 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right)^{2} x^{2}-36 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right)^{2} x -72 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+27 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) \left(x^{3}-x^{2}\right)^{\frac{1}{3}} x +33 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) x^{2}+18 \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right) x +18 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+30 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}-40 x^{2}+10 x}{x}\right) \RootOf \left(9 \textit{\_Z}^{2}-6 \textit{\_Z} +4\right)}{2}$&$503$\\ \hline \end{longtable}"," ",0,"-3/4/signum(-1+x)^(1/3)*(-signum(-1+x))^(1/3)*x^(4/3)*hypergeom([4/3,4/3],[7/3],x)","C"
1697,1,40,98,0.556000," ","int((1+x)/(-1+x)/(x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{6 x}{\left(\left(-1+x \right) x^{2}\right)^{\frac{1}{3}}}+\frac{3 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{3}} x^{\frac{1}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x\right)}{\mathrm{signum}\left(-1+x \right)^{\frac{1}{3}}}$&$40$\\ meijerg&$-\frac{3 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{3}} x^{\frac{1}{3}}}{\mathrm{signum}\left(-1+x \right)^{\frac{1}{3}} \left(1-x \right)^{\frac{1}{3}}}-\frac{3 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{3}} x^{\frac{4}{3}} \hypergeom \left(\left[\frac{4}{3}, \frac{4}{3}\right], \left[\frac{7}{3}\right], x\right)}{4 \mathrm{signum}\left(-1+x \right)^{\frac{1}{3}}}$&$54$\\ trager&$-\frac{6 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}}{\left(-1+x \right) x}+3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \ln \left(\frac{45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}+72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{1}{3}} x -90 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x +57 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}-9 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}-9 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}-9 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x -4 x^{2}+x}{x}\right)-3 \ln \left(-\frac{-45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}+72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{1}{3}} x +90 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x +87 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}-15 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}-15 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}-69 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x -20 x^{2}+12 x}{x}\right) \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)+\ln \left(-\frac{-45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}+72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{1}{3}} x +90 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x +87 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}-15 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}-15 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}-69 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x -20 x^{2}+12 x}{x}\right)$&$511$\\ \hline \end{longtable}"," ",0,"-6*x/((-1+x)*x^2)^(1/3)+3/signum(-1+x)^(1/3)*(-signum(-1+x))^(1/3)*x^(1/3)*hypergeom([1/3,1/3],[4/3],x)","C"
1698,0,0,97,0.093000," ","int((a*x-2*b)/(a*x+x^2-b)/(a*x^3-b*x^2)^(1/4),x)","\[\int \frac{a x -2 b}{\left(a x +x^{2}-b \right) \left(a \,x^{3}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x-2*b)/(a*x+x^2-b)/(a*x^3-b*x^2)^(1/4),x)","F"
1699,1,10723,28,234.184000," ","int((x^2+1)*(2*x^3-x)^(1/3)/x^2/(x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$10723$\\ risch&$\text{Expression too large to display}$&$19101$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1700,1,392,92,5.562000," ","int((-1+x)/(x^2+x+1)/(x^4+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{3}+\left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}+3 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}+\sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}+1\right) x^{2}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x +3 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x +2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}+1\right) x +\left(x^{4}+1\right)^{\frac{3}{4}} x +\left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+\sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)+\left(x^{4}+1\right)^{\frac{3}{4}}}{\left(x^{2}+x +1\right)^{2}}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(-\frac{\sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}+2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x +\left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}+\sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+3 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}+3 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x +2 \RootOf \left(\textit{\_Z}^{4}+1\right) x^{3}-\left(x^{4}+1\right)^{\frac{3}{4}} x +\left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+3 \RootOf \left(\textit{\_Z}^{4}+1\right) x^{2}-\left(x^{4}+1\right)^{\frac{3}{4}}+2 \RootOf \left(\textit{\_Z}^{4}+1\right) x}{\left(x^{2}+x +1\right)^{2}}\right)}{2}$&$392$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^4+1)^3*ln((2*RootOf(_Z^4+1)^3*x^3+(x^4+1)^(1/4)*RootOf(_Z^4+1)^2*x^3+3*RootOf(_Z^4+1)^3*x^2+3*(x^4+1)^(1/4)*RootOf(_Z^4+1)^2*x^2+(x^4+1)^(1/2)*RootOf(_Z^4+1)*x^2+2*RootOf(_Z^4+1)^3*x+3*(x^4+1)^(1/4)*RootOf(_Z^4+1)^2*x+2*(x^4+1)^(1/2)*RootOf(_Z^4+1)*x+(x^4+1)^(3/4)*x+(x^4+1)^(1/4)*RootOf(_Z^4+1)^2+(x^4+1)^(1/2)*RootOf(_Z^4+1)+(x^4+1)^(3/4))/(x^2+x+1)^2)-1/2*RootOf(_Z^4+1)*ln(-((x^4+1)^(1/2)*RootOf(_Z^4+1)^3*x^2+2*(x^4+1)^(1/2)*RootOf(_Z^4+1)^3*x+(x^4+1)^(1/4)*RootOf(_Z^4+1)^2*x^3+(x^4+1)^(1/2)*RootOf(_Z^4+1)^3+3*(x^4+1)^(1/4)*RootOf(_Z^4+1)^2*x^2+3*(x^4+1)^(1/4)*RootOf(_Z^4+1)^2*x+2*RootOf(_Z^4+1)*x^3-(x^4+1)^(3/4)*x+(x^4+1)^(1/4)*RootOf(_Z^4+1)^2+3*RootOf(_Z^4+1)*x^2-(x^4+1)^(3/4)+2*RootOf(_Z^4+1)*x)/(x^2+x+1)^2)","C"
1701,1,385,90,3.052000," ","int(x^2*(x^4+x^3)^(1/4)/(-1+x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\left(\frac{1}{3} x^{2}+\frac{13}{24} x +\frac{101}{96}\right) \left(x^{4}+x^{3}\right)^{\frac{1}{4}}+\frac{155 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \sqrt{x^{4}+x^{3}}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{4}+x^{3}\right)^{\frac{3}{4}}-2 x^{2} \left(x^{4}+x^{3}\right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}}{x^{2}}\right)}{128}-\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(\frac{3 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{3}+4 \left(x^{4}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{2}+4 \sqrt{x^{4}+x^{3}}\, \RootOf \left(\textit{\_Z}^{4}-2\right) x +4 \left(x^{4}+x^{3}\right)^{\frac{3}{4}}}{\left(-1+x \right) x^{2}}\right)+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(-\frac{-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}+4 \left(x^{4}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}+4 \sqrt{x^{4}+x^{3}}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x -4 \left(x^{4}+x^{3}\right)^{\frac{3}{4}}}{\left(-1+x \right) x^{2}}\right)+\frac{155 \ln \left(\frac{2 \left(x^{4}+x^{3}\right)^{\frac{3}{4}}+2 \sqrt{x^{4}+x^{3}}\, x +2 x^{2} \left(x^{4}+x^{3}\right)^{\frac{1}{4}}+2 x^{3}+x^{2}}{x^{2}}\right)}{128}$&$385$\\ risch&$\frac{\left(32 x^{2}+52 x +101\right) \left(x^{3} \left(1+x \right)\right)^{\frac{1}{4}}}{96}+\frac{\left(\frac{155 \ln \left(\frac{2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{3}{4}}+2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, x +2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x^{2}+2 x^{3}+2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}+4 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x +5 x^{2}+2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}}+4 x +1}{\left(1+x \right)^{2}}\right)}{128}+\frac{155 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, \RootOf \left(\textit{\_Z}^{2}+1\right)-5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{3}{4}}+2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x^{2}-4 \RootOf \left(\textit{\_Z}^{2}+1\right) x +4 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x -\RootOf \left(\textit{\_Z}^{2}+1\right)+2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}}}{\left(1+x \right)^{2}}\right)}{128}-\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(\frac{2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x +2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}+2 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x^{2}+4 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x +3 \RootOf \left(\textit{\_Z}^{4}-2\right) x^{3}+2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+7 \RootOf \left(\textit{\_Z}^{4}-2\right) x^{2}+4 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{3}{4}}+5 \RootOf \left(\textit{\_Z}^{4}-2\right) x +\RootOf \left(\textit{\_Z}^{4}-2\right)}{\left(-1+x \right) \left(1+x \right)^{2}}\right)+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(\frac{2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x +2 \sqrt{x^{4}+3 x^{3}+3 x^{2}+x}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-2 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{3}-4 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x -7 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{2}-2 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+4 \left(x^{4}+3 x^{3}+3 x^{2}+x \right)^{\frac{3}{4}}-5 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)}{\left(-1+x \right) \left(1+x \right)^{2}}\right)\right) \left(x^{3} \left(1+x \right)\right)^{\frac{1}{4}} \left(\left(1+x \right)^{3} x \right)^{\frac{1}{4}}}{x \left(1+x \right)}$&$877$\\ \hline \end{longtable}"," ",0,"(1/3*x^2+13/24*x+101/96)*(x^4+x^3)^(1/4)+155/128*RootOf(_Z^2+1)*ln((2*(x^4+x^3)^(1/2)*RootOf(_Z^2+1)*x-2*RootOf(_Z^2+1)*x^3+2*(x^4+x^3)^(3/4)-2*x^2*(x^4+x^3)^(1/4)-RootOf(_Z^2+1)*x^2)/x^2)-RootOf(_Z^4-2)*ln((3*RootOf(_Z^4-2)^3*x^3+4*(x^4+x^3)^(1/4)*RootOf(_Z^4-2)^2*x^2+RootOf(_Z^4-2)^3*x^2+4*(x^4+x^3)^(1/2)*RootOf(_Z^4-2)*x+4*(x^4+x^3)^(3/4))/(-1+x)/x^2)+RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln(-(-3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*x^3-RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*x^2+4*(x^4+x^3)^(1/4)*RootOf(_Z^4-2)^2*x^2+4*(x^4+x^3)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x-4*(x^4+x^3)^(3/4))/(-1+x)/x^2)+155/128*ln((2*(x^4+x^3)^(3/4)+2*(x^4+x^3)^(1/2)*x+2*x^2*(x^4+x^3)^(1/4)+2*x^3+x^2)/x^2)","C"
1702,0,0,94,0.011000," ","int((a*x^3-b)*(2*a*x^3-b)/x^6/(a*x^4-b*x)^(1/4),x)","\[\int \frac{\left(a \,x^{3}-b \right) \left(2 a \,x^{3}-b \right)}{x^{6} \left(a \,x^{4}-b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^3-b)*(2*a*x^3-b)/x^6/(a*x^4-b*x)^(1/4),x)","F"
1703,0,0,86,0.013000," ","int((x^8+a*x^4-b)/x^8/(a*x^4-b)/(a*x^4+b)^(1/4),x)","\[\int \frac{x^{8}+a \,x^{4}-b}{x^{8} \left(a \,x^{4}-b \right) \left(a \,x^{4}+b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((x^8+a*x^4-b)/x^8/(a*x^4-b)/(a*x^4+b)^(1/4),x)","F"
1704,1,84,94,0.066000," ","int((x^4+1)/x^4/(x+(x^2+1)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{2}\, \hypergeom \left(\left[\frac{1}{4}, \frac{3}{4}, \frac{7}{4}\right], \left[\frac{3}{2}, \frac{11}{4}\right], -\frac{1}{x^{2}}\right)}{7 x^{\frac{7}{2}}}-\frac{-\frac{32 \sqrt{\pi}\, \sqrt{2}\, \cosh \left(\frac{3 \arcsinh \left(\frac{1}{x}\right)}{2}\right)}{3 x^{\frac{3}{2}}}-\frac{8 \sqrt{\pi}\, \sqrt{2}\, x^{\frac{3}{2}} \left(-\frac{4}{3 x^{4}}-\frac{2}{3 x^{2}}+\frac{2}{3}\right) \sinh \left(\frac{3 \arcsinh \left(\frac{1}{x}\right)}{2}\right)}{\sqrt{1+\frac{1}{x^{2}}}}}{8 \sqrt{\pi}}$&$84$\\ \hline \end{longtable}"," ",0,"-1/7*2^(1/2)/x^(7/2)*hypergeom([1/4,3/4,7/4],[3/2,11/4],-1/x^2)-1/8/Pi^(1/2)*(-32/3*Pi^(1/2)*2^(1/2)/x^(3/2)*cosh(3/2*arcsinh(1/x))-8*Pi^(1/2)*2^(1/2)*x^(3/2)*(-4/3/x^4-2/3/x^2+2/3)*sinh(3/2*arcsinh(1/x))/(1+1/x^2)^(1/2))","C"
1705,0,0,87,0.023000," ","int((b+(a*x^2+b^2)^(1/2))^(1/2)/x^2/(a*x^2+b^2)^(1/2),x)","\[\int \frac{\sqrt{b +\sqrt{a \,x^{2}+b^{2}}}}{x^{2} \sqrt{a \,x^{2}+b^{2}}}\, dx\]"," ",0,"int((b+(a*x^2+b^2)^(1/2))^(1/2)/x^2/(a*x^2+b^2)^(1/2),x)","F"
1706,1,492,96,1.851000," ","int((x^2+2)/x/(x^2-2*x+2)/(x^2-x+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}-x +1\right)^{\frac{2}{3}} x -\left(x^{2}-x +1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{2}-x +1\right)^{\frac{2}{3}}+2 x \left(x^{2}-x +1\right)^{\frac{2}{3}}+2 \left(x^{2}-x +1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +\left(x^{2}-x +1\right)^{\frac{1}{3}} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x +7 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-x^{3}-2 \left(x^{2}-x +1\right)^{\frac{2}{3}}-\left(x^{2}-x +1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2 x \left(x^{2}-x +1\right)^{\frac{1}{3}}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-7 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +4 x^{2}+\left(x^{2}-x +1\right)^{\frac{1}{3}}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-4 x +2}{x \left(x^{2}-2 x +2\right)}\right)+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-3 \left(x^{2}-x +1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-6 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 x \left(x^{2}-x +1\right)^{\frac{2}{3}}+6 \left(x^{2}-x +1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +6 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x -\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-3 \left(x^{2}-x +1\right)^{\frac{2}{3}}-3 \left(x^{2}-x +1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-x +1}{x \left(x^{2}-2 x +2\right)}\right)$&$492$\\ \hline \end{longtable}"," ",0,"ln((-RootOf(_Z^2+_Z+1)^2*x^3+RootOf(_Z^2+_Z+1)*(x^2-x+1)^(2/3)*x-(x^2-x+1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2+3*RootOf(_Z^2+_Z+1)^2*x^2-2*RootOf(_Z^2+_Z+1)*x^3-RootOf(_Z^2+_Z+1)*(x^2-x+1)^(2/3)+2*x*(x^2-x+1)^(2/3)+2*(x^2-x+1)^(1/3)*RootOf(_Z^2+_Z+1)*x+(x^2-x+1)^(1/3)*x^2-3*RootOf(_Z^2+_Z+1)^2*x+7*RootOf(_Z^2+_Z+1)*x^2-x^3-2*(x^2-x+1)^(2/3)-(x^2-x+1)^(1/3)*RootOf(_Z^2+_Z+1)-2*x*(x^2-x+1)^(1/3)+RootOf(_Z^2+_Z+1)^2-7*RootOf(_Z^2+_Z+1)*x+4*x^2+(x^2-x+1)^(1/3)+3*RootOf(_Z^2+_Z+1)-4*x+2)/x/(x^2-2*x+2))+RootOf(_Z^2+_Z+1)*ln((2*RootOf(_Z^2+_Z+1)^2*x^3-3*(x^2-x+1)^(1/3)*RootOf(_Z^2+_Z+1)*x^2-6*RootOf(_Z^2+_Z+1)^2*x^2+RootOf(_Z^2+_Z+1)*x^3+3*x*(x^2-x+1)^(2/3)+6*(x^2-x+1)^(1/3)*RootOf(_Z^2+_Z+1)*x+6*RootOf(_Z^2+_Z+1)^2*x-RootOf(_Z^2+_Z+1)*x^2-3*(x^2-x+1)^(2/3)-3*(x^2-x+1)^(1/3)*RootOf(_Z^2+_Z+1)-2*RootOf(_Z^2+_Z+1)^2+RootOf(_Z^2+_Z+1)*x+x^2+RootOf(_Z^2+_Z+1)-x+1)/x/(x^2-2*x+2))","C"
1707,1,111,93,2.650000," ","int((-1+x)/x^10/(x^3+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{729 x^{10}-560 x^{9}+243 x^{7}-140 x^{6}-81 x^{4}+60 x^{3}+405 x -360}{3240 x^{9} \left(x^{3}+1\right)^{\frac{1}{3}}}+\frac{7 \sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\frac{2 \pi  \sqrt{3}\, x^{3} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], -x^{3}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{243 \pi}$&$111$\\ meijerg&$-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(\frac{70 \pi  \sqrt{3}\, x^{3} \hypergeom \left(\left[1, 1, \frac{13}{3}\right], \left[2, 5\right], -x^{3}\right)}{729 \Gamma \left(\frac{2}{3}\right)}-\frac{28 \left(\frac{197}{84}-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)\right) \pi  \sqrt{3}}{243 \Gamma \left(\frac{2}{3}\right)}-\frac{2 \pi  \sqrt{3}}{9 \Gamma \left(\frac{2}{3}\right) x^{9}}+\frac{\pi  \sqrt{3}}{9 \Gamma \left(\frac{2}{3}\right) x^{6}}-\frac{4 \pi  \sqrt{3}}{27 \Gamma \left(\frac{2}{3}\right) x^{3}}\right)}{6 \pi}-\frac{\left(\frac{9}{5} x^{6}-\frac{6}{5} x^{3}+1\right) \left(x^{3}+1\right)^{\frac{2}{3}}}{8 x^{8}}$&$128$\\ trager&$-\frac{\left(729 x^{7}-560 x^{6}-486 x^{4}+420 x^{3}+405 x -360\right) \left(x^{3}+1\right)^{\frac{2}{3}}}{3240 x^{9}}+\frac{28 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \ln \left(-\frac{16 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{3}-18 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{3}-30 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}+2 x^{3}-16 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}-30 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}+9 \left(x^{3}+1\right)^{\frac{2}{3}}-38 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+9 \left(x^{3}+1\right)^{\frac{1}{3}}+5}{x^{3}}\right)}{243}-\frac{14 \ln \left(-\frac{16 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{3}+34 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{3}+30 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}+15 x^{3}-16 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}+30 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}+24 \left(x^{3}+1\right)^{\frac{2}{3}}+22 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+24 \left(x^{3}+1\right)^{\frac{1}{3}}+20}{x^{3}}\right)}{243}-\frac{28 \ln \left(-\frac{16 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{3}+34 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{3}+30 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{2}{3}}+15 x^{3}-16 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}+30 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}+1\right)^{\frac{1}{3}}+24 \left(x^{3}+1\right)^{\frac{2}{3}}+22 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+24 \left(x^{3}+1\right)^{\frac{1}{3}}+20}{x^{3}}\right) \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)}{243}$&$466$\\ \hline \end{longtable}"," ",0,"-1/3240*(729*x^10-560*x^9+243*x^7-140*x^6-81*x^4+60*x^3+405*x-360)/x^9/(x^3+1)^(1/3)+7/243/Pi*3^(1/2)*GAMMA(2/3)*(-2/9*Pi*3^(1/2)/GAMMA(2/3)*x^3*hypergeom([1,1,4/3],[2,2],-x^3)+2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)+3*ln(x))*Pi*3^(1/2)/GAMMA(2/3))","C"
1708,0,0,86,0.021000," ","int(1/x/(a*x^3+b)^(1/3),x)","\[\int \frac{1}{x \left(a \,x^{3}+b \right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/x/(a*x^3+b)^(1/3),x)","F"
1709,0,0,101,0.016000," ","int((-1-2*(-1+k)*x+k*x^2)*(k^3*x^3-3*k^2*x^2+3*k*x-1)/(-1+x)/x/((1-x)*x*(-k*x+1))^(1/4)/(-1+(d+3*k)*x-(3*k^2+d)*x^2+k^3*x^3),x)","\[\int \frac{\left(-1-2 \left(-1+k \right) x +k \,x^{2}\right) \left(k^{3} x^{3}-3 k^{2} x^{2}+3 k x -1\right)}{\left(-1+x \right) x \left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{4}} \left(-1+\left(d +3 k \right) x -\left(3 k^{2}+d \right) x^{2}+k^{3} x^{3}\right)}\, dx\]"," ",0,"int((-1-2*(-1+k)*x+k*x^2)*(k^3*x^3-3*k^2*x^2+3*k*x-1)/(-1+x)/x/((1-x)*x*(-k*x+1))^(1/4)/(-1+(d+3*k)*x-(3*k^2+d)*x^2+k^3*x^3),x)","F"
1710,1,431,97,7.618000," ","int((x^4+3)*(x^4-x^3-1)^(2/3)/x^3/(x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 \left(x^{4}-x^{3}-1\right)^{\frac{2}{3}}}{2 x^{2}}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}-x^{3}-1\right)^{\frac{2}{3}} x -3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}-x^{3}-1\right)^{\frac{1}{3}} x^{2}+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-2 x^{4}+3 x \left(x^{4}-x^{3}-1\right)^{\frac{2}{3}}-3 \left(x^{4}-x^{3}-1\right)^{\frac{1}{3}} x^{2}+4 x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+2}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)-\ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}-x^{3}-1\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}-x^{3}-1\right)^{\frac{1}{3}} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-x^{4}+x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-\ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}-x^{3}-1\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}-x^{3}-1\right)^{\frac{1}{3}} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-x^{4}+x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)$&$431$\\ trager&$\frac{3 \left(x^{4}-x^{3}-1\right)^{\frac{2}{3}}}{2 x^{2}}+\ln \left(\frac{-8064 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{4}+15120 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{3}+26868 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{4}+30384 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{4}-x^{3}-1\right)^{\frac{2}{3}} x -21852 \left(x^{4}-x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{2}-50976 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{3}+2002 x^{4}+4353 x \left(x^{4}-x^{3}-1\right)^{\frac{2}{3}}+2532 \left(x^{4}-x^{3}-1\right)^{\frac{1}{3}} x^{2}-1716 x^{3}+8064 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}-26868 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)-2002}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)+12 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \ln \left(-\frac{329472 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{4}-617760 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{3}+2760 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{4}+30384 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{4}-x^{3}-1\right)^{\frac{2}{3}} x +52236 \left(x^{4}-x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{2}-29628 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{3}-7 x^{4}-1821 x \left(x^{4}-x^{3}-1\right)^{\frac{2}{3}}+2532 \left(x^{4}-x^{3}-1\right)^{\frac{1}{3}} x^{2}+63 x^{3}-329472 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}-2760 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)+7}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)$&$459$\\ \hline \end{longtable}"," ",0,"3/2*(x^4-x^3-1)^(2/3)/x^2+RootOf(_Z^2+_Z+1)*ln((RootOf(_Z^2+_Z+1)^2*x^3-RootOf(_Z^2+_Z+1)*x^4+3*RootOf(_Z^2+_Z+1)*(x^4-x^3-1)^(2/3)*x-3*RootOf(_Z^2+_Z+1)*(x^4-x^3-1)^(1/3)*x^2+4*RootOf(_Z^2+_Z+1)*x^3-2*x^4+3*x*(x^4-x^3-1)^(2/3)-3*(x^4-x^3-1)^(1/3)*x^2+4*x^3+RootOf(_Z^2+_Z+1)+2)/(-1+x)/(1+x)/(x^2+1))-ln((RootOf(_Z^2+_Z+1)^2*x^3+RootOf(_Z^2+_Z+1)*x^4-3*RootOf(_Z^2+_Z+1)*(x^4-x^3-1)^(2/3)*x+3*RootOf(_Z^2+_Z+1)*(x^4-x^3-1)^(1/3)*x^2-2*RootOf(_Z^2+_Z+1)*x^3-x^4+x^3-RootOf(_Z^2+_Z+1)+1)/(-1+x)/(1+x)/(x^2+1))*RootOf(_Z^2+_Z+1)-ln((RootOf(_Z^2+_Z+1)^2*x^3+RootOf(_Z^2+_Z+1)*x^4-3*RootOf(_Z^2+_Z+1)*(x^4-x^3-1)^(2/3)*x+3*RootOf(_Z^2+_Z+1)*(x^4-x^3-1)^(1/3)*x^2-2*RootOf(_Z^2+_Z+1)*x^3-x^4+x^3-RootOf(_Z^2+_Z+1)+1)/(-1+x)/(1+x)/(x^2+1))","C"
1711,1,9342,33,229.806000," ","int((2*x^2+1)*(2*x^3+x)^(1/3)/x^4/(2*x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$9342$\\ risch&$\text{Expression too large to display}$&$14917$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1712,1,80,11,0.590000," ","int(1/(x-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-a \,\textit{\_Z}^{3}-2 c \,\textit{\_Z}^{2}+a c \textit{\_Z} +c^{2}-b \right)}{\sum}\frac{\left(-\textit{\_R}^{3}+\textit{\_R} c \right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-3 \textit{\_R}^{2} a -4 \textit{\_R} c +a c}\right)$&$80$\\ default&$\text{Expression too large to display}$&$3177$\\ \hline \end{longtable}"," ",0,"-4*sum((-_R^3+_R*c)/(4*_R^3-3*_R^2*a-4*_R*c+a*c)*ln((c+(a*x+b)^(1/2))^(1/2)-_R),_R=RootOf(_Z^4-_Z^3*a-2*_Z^2*c+_Z*a*c+c^2-b))","B"
1713,1,80,11,0.487000," ","int(1/(x-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-a \,\textit{\_Z}^{3}-2 c \,\textit{\_Z}^{2}+a c \textit{\_Z} +c^{2}-b \right)}{\sum}\frac{\left(-\textit{\_R}^{3}+\textit{\_R} c \right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-3 \textit{\_R}^{2} a -4 \textit{\_R} c +a c}\right)$&$80$\\ default&$\text{Expression too large to display}$&$3177$\\ \hline \end{longtable}"," ",0,"-4*sum((-_R^3+_R*c)/(4*_R^3-3*_R^2*a-4*_R*c+a*c)*ln((c+(a*x+b)^(1/2))^(1/2)-_R),_R=RootOf(_Z^4-_Z^3*a-2*_Z^2*c+_Z*a*c+c^2-b))","B"
1714,1,398,94,3.648000," ","int((x^2-x+2)/(x^2-1)^(1/3)/(x^2+4*x+3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(x^{2}-1\right)^{\frac{2}{3}}}{1+x}-\frac{7 \ln \left(-\frac{4032 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{2}-12096 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x +2592 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{2}{3}}-1548 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{1}{3}} x -1404 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}+1548 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{1}{3}}+9000 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x -948 \left(x^{2}-1\right)^{\frac{2}{3}}-216 x \left(x^{2}-1\right)^{\frac{1}{3}}+119 x^{2}+4788 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)+216 \left(x^{2}-1\right)^{\frac{1}{3}}-1326 x -969}{\left(3+x \right)^{2}}\right)}{4}+\frac{21 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \ln \left(\frac{2448 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{2}-7344 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x +1296 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{2}{3}}+1422 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{1}{3}} x -387 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}-1422 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{1}{3}}-1746 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x +258 \left(x^{2}-1\right)^{\frac{2}{3}}-108 x \left(x^{2}-1\right)^{\frac{1}{3}}+7 x^{2}-2907 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)+108 \left(x^{2}-1\right)^{\frac{1}{3}}+378 x +399}{\left(3+x \right)^{2}}\right)}{2}$&$398$\\ risch&$\frac{-3+3 x}{\left(x^{2}-1\right)^{\frac{1}{3}}}-\frac{7 \ln \left(\frac{-448 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x^{2}+864 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{2}{3}}-516 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{1}{3}} x +1344 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x -20 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x^{2}+516 \left(x^{2}-1\right)^{\frac{2}{3}}+516 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{1}{3}}+474 x \left(x^{2}-1\right)^{\frac{1}{3}}+1656 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x +3 x^{2}-474 \left(x^{2}-1\right)^{\frac{1}{3}}+1596 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)+162 x +171}{\left(3+x \right)^{2}}\right)}{4}+\frac{7 \ln \left(-\frac{-544 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x^{2}+864 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{2}{3}}+948 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{1}{3}} x +1632 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x +286 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x^{2}-948 \left(x^{2}-1\right)^{\frac{2}{3}}-948 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{1}{3}}-258 x \left(x^{2}-1\right)^{\frac{1}{3}}-2796 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x -21 x^{2}+258 \left(x^{2}-1\right)^{\frac{1}{3}}-1938 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)+234 x +171}{\left(3+x \right)^{2}}\right)}{4}-\frac{7 \ln \left(-\frac{-544 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x^{2}+864 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{2}{3}}+948 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{1}{3}} x +1632 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x +286 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x^{2}-948 \left(x^{2}-1\right)^{\frac{2}{3}}-948 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{2}-1\right)^{\frac{1}{3}}-258 x \left(x^{2}-1\right)^{\frac{1}{3}}-2796 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x -21 x^{2}+258 \left(x^{2}-1\right)^{\frac{1}{3}}-1938 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)+234 x +171}{\left(3+x \right)^{2}}\right) \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)}{2}$&$582$\\ \hline \end{longtable}"," ",0,"3*(x^2-1)^(2/3)/(1+x)-7/4*ln(-(4032*RootOf(36*_Z^2-6*_Z+1)^2*x^2-12096*RootOf(36*_Z^2-6*_Z+1)^2*x+2592*RootOf(36*_Z^2-6*_Z+1)*(x^2-1)^(2/3)-1548*RootOf(36*_Z^2-6*_Z+1)*(x^2-1)^(1/3)*x-1404*RootOf(36*_Z^2-6*_Z+1)*x^2+1548*RootOf(36*_Z^2-6*_Z+1)*(x^2-1)^(1/3)+9000*RootOf(36*_Z^2-6*_Z+1)*x-948*(x^2-1)^(2/3)-216*x*(x^2-1)^(1/3)+119*x^2+4788*RootOf(36*_Z^2-6*_Z+1)+216*(x^2-1)^(1/3)-1326*x-969)/(3+x)^2)+21/2*RootOf(36*_Z^2-6*_Z+1)*ln((2448*RootOf(36*_Z^2-6*_Z+1)^2*x^2-7344*RootOf(36*_Z^2-6*_Z+1)^2*x+1296*RootOf(36*_Z^2-6*_Z+1)*(x^2-1)^(2/3)+1422*RootOf(36*_Z^2-6*_Z+1)*(x^2-1)^(1/3)*x-387*RootOf(36*_Z^2-6*_Z+1)*x^2-1422*RootOf(36*_Z^2-6*_Z+1)*(x^2-1)^(1/3)-1746*RootOf(36*_Z^2-6*_Z+1)*x+258*(x^2-1)^(2/3)-108*x*(x^2-1)^(1/3)+7*x^2-2907*RootOf(36*_Z^2-6*_Z+1)+108*(x^2-1)^(1/3)+378*x+399)/(3+x)^2)","C"
1715,0,0,98,0.037000," ","int(x*(k*x-1)*(-1+2*(-1+k)*x+k*x^2)/(-1+x)/((1-x)*x*(-k*x+1))^(3/4)/(-d+(1+3*d)*x-(3*d+k)*x^2+d*x^3),x)","\[\int \frac{x \left(k x -1\right) \left(-1+2 \left(-1+k \right) x +k \,x^{2}\right)}{\left(-1+x \right) \left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{3}{4}} \left(-d +\left(1+3 d \right) x -\left(3 d +k \right) x^{2}+d \,x^{3}\right)}\, dx\]"," ",0,"int(x*(k*x-1)*(-1+2*(-1+k)*x+k*x^2)/(-1+x)/((1-x)*x*(-k*x+1))^(3/4)/(-d+(1+3*d)*x-(3*d+k)*x^2+d*x^3),x)","F"
1716,0,0,102,0.032000," ","int((-1+x)*x*(-1-2*(-1+k)*x+k*x^2)/((1-x)*x*(-k*x+1))^(3/4)/(k*x-1)/(-d+(3*d*k+1)*x-(3*d*k^2+1)*x^2+d*k^3*x^3),x)","\[\int \frac{\left(-1+x \right) x \left(-1-2 \left(-1+k \right) x +k \,x^{2}\right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{3}{4}} \left(k x -1\right) \left(-d +\left(3 d k +1\right) x -\left(3 d \,k^{2}+1\right) x^{2}+d \,k^{3} x^{3}\right)}\, dx\]"," ",0,"int((-1+x)*x*(-1-2*(-1+k)*x+k*x^2)/((1-x)*x*(-k*x+1))^(3/4)/(k*x-1)/(-d+(3*d*k+1)*x-(3*d*k^2+1)*x^2+d*k^3*x^3),x)","F"
1717,1,7672,33,265.772000," ","int((x^2+4)*(x^3-2*x)^(1/3)/x^4/(x^4-4*x^2-4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$7672$\\ risch&$\text{Expression too large to display}$&$16927$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1718,1,9346,33,238.141000," ","int((x^2+4)*(x^3-2*x)^(1/3)/x^4/(x^4-4*x^2-4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$9346$\\ risch&$\text{Expression too large to display}$&$16927$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1719,0,0,100,0.027000," ","int((a*x^3+2*b)/(a*x^3+x^2-b)/(a*x^5-b*x^2)^(1/4),x)","\[\int \frac{a \,x^{3}+2 b}{\left(a \,x^{3}+x^{2}-b \right) \left(a \,x^{5}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^3+2*b)/(a*x^3+x^2-b)/(a*x^5-b*x^2)^(1/4),x)","F"
1720,0,0,100,0.107000," ","int((a*x^2+b)/(a*x^2-b+x)/(a*x^5-b*x^3)^(1/4),x)","\[\int \frac{a \,x^{2}+b}{\left(a \,x^{2}-b +x \right) \left(a \,x^{5}-b \,x^{3}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2+b)/(a*x^2-b+x)/(a*x^5-b*x^3)^(1/4),x)","F"
1721,0,0,100,0.028000," ","int((a*x^4+b)/(a*x^4+x^2-b)/(a*x^6-b*x^2)^(1/4),x)","\[\int \frac{a \,x^{4}+b}{\left(a \,x^{4}+x^{2}-b \right) \left(a \,x^{6}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^4+b)/(a*x^4+x^2-b)/(a*x^6-b*x^2)^(1/4),x)","F"
1722,0,0,100,0.028000," ","int((2*a*x^3+b)/(a*x^3-b+x)/(a*x^6-b*x^3)^(1/4),x)","\[\int \frac{2 a \,x^{3}+b}{\left(a \,x^{3}-b +x \right) \left(a \,x^{6}-b \,x^{3}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((2*a*x^3+b)/(a*x^3-b+x)/(a*x^6-b*x^3)^(1/4),x)","F"
1723,0,0,14,0.026000," ","int(1/(a*x^4-b)^(1/4)/(a*x^8-x^4-b),x)","\[\int \frac{1}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(a \,x^{8}-x^{4}-b \right)}\, dx\]"," ",0,"int(1/(a*x^4-b)^(1/4)/(a*x^8-x^4-b),x)","F"
1724,0,0,14,0.001000," ","int(1/(a*x^4-b)^(1/4)/(a*x^8-x^4-b),x)","\[\int \frac{1}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(a \,x^{8}-x^{4}-b \right)}\, dx\]"," ",0,"int(1/(a*x^4-b)^(1/4)/(a*x^8-x^4-b),x)","F"
1725,0,0,11,0.026000," ","int((a*x^4+b)/(a*x^4-b)^(1/4)/(a*x^8+c*x^4+b),x)","\[\int \frac{a \,x^{4}+b}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(a \,x^{8}+c \,x^{4}+b \right)}\, dx\]"," ",0,"int((a*x^4+b)/(a*x^4-b)^(1/4)/(a*x^8+c*x^4+b),x)","F"
1726,0,0,11,0.002000," ","int((a*x^4+b)/(a*x^4-b)^(1/4)/(a*x^8+c*x^4+b),x)","\[\int \frac{a \,x^{4}+b}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(a \,x^{8}+c \,x^{4}+b \right)}\, dx\]"," ",0,"int((a*x^4+b)/(a*x^4-b)^(1/4)/(a*x^8+c*x^4+b),x)","F"
1727,0,0,27,180.000000," ","int((x^5+1)*(x^5+x^3+1)^(1/3)*(2*x^5-3)/x^2/(2*x^10-2*x^8-x^6+4*x^5-2*x^3+2),x)","\[\int \frac{\left(x^{5}+1\right) \left(x^{5}+x^{3}+1\right)^{\frac{1}{3}} \left(2 x^{5}-3\right)}{x^{2} \left(2 x^{10}-2 x^{8}-x^{6}+4 x^{5}-2 x^{3}+2\right)}\, dx\]"," ",0,"int((x^5+1)*(x^5+x^3+1)^(1/3)*(2*x^5-3)/x^2/(2*x^10-2*x^8-x^6+4*x^5-2*x^3+2),x)","F"
1728,0,0,27,180.000000," ","int((x^5+1)*(x^5+x^3+1)^(1/3)*(2*x^5-3)/x^2/(2*x^10-2*x^8-x^6+4*x^5-2*x^3+2),x)","\[\int \frac{\left(x^{5}+1\right) \left(x^{5}+x^{3}+1\right)^{\frac{1}{3}} \left(2 x^{5}-3\right)}{x^{2} \left(2 x^{10}-2 x^{8}-x^{6}+4 x^{5}-2 x^{3}+2\right)}\, dx\]"," ",0,"int((x^5+1)*(x^5+x^3+1)^(1/3)*(2*x^5-3)/x^2/(2*x^10-2*x^8-x^6+4*x^5-2*x^3+2),x)","F"
1729,1,33,95,3.186000," ","int(x^4*(x^3-x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}} x^{\frac{16}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{8}{3}\right], \left[\frac{11}{3}\right], x^{2}\right)}{16 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}}}$&$33$\\ trager&$\frac{x \left(18 x^{4}-3 x^{2}-5\right) \left(x^{3}-x \right)^{\frac{1}{3}}}{108}-\frac{5 \ln \left(1395 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}-6768 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}-6768 \left(x^{3}-x \right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -6303 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+5355 \left(x^{3}-x \right)^{\frac{2}{3}}+5355 x \left(x^{3}-x \right)^{\frac{1}{3}}-5580 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+5510 x^{2}+8007 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-1653\right)}{162}-\frac{5 \ln \left(1395 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}-6768 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}-6768 \left(x^{3}-x \right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -6303 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+5355 \left(x^{3}-x \right)^{\frac{2}{3}}+5355 x \left(x^{3}-x \right)^{\frac{1}{3}}-5580 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+5510 x^{2}+8007 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-1653\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{54}+\frac{5 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(1395 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}+6768 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}+6768 \left(x^{3}-x \right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x +7233 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+7611 \left(x^{3}-x \right)^{\frac{2}{3}}+7611 x \left(x^{3}-x \right)^{\frac{1}{3}}-5580 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+7766 x^{2}-11727 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-4942\right)}{54}$&$468$\\ risch&$\frac{x \left(18 x^{4}-3 x^{2}-5\right) \left(x \left(x^{2}-1\right)\right)^{\frac{1}{3}}}{108}+\frac{\left(\frac{5 \ln \left(\frac{35 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{4}+1956 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{4}-175 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{2}+4104 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}-23364 x^{4}-5850 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}-2010 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{2}+35100 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}+140 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2}-4104 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}-10476 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}+38232 x^{2}+54 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)-35100 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}-14868}{\left(-1+x \right) \left(1+x \right)}\right)}{162}+\frac{5 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \ln \left(\frac{59 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{4}-3750 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{4}-295 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{2}-1746 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}+12600 x^{4}+5850 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}+5652 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{2}-35100 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}+236 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2}+1746 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}+24624 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}-16380 x^{2}-1902 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)+35100 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}+3780}{\left(-1+x \right) \left(1+x \right)}\right)}{972}\right) \left(x \left(x^{2}-1\right)\right)^{\frac{1}{3}} \left(x^{2} \left(x^{2}-1\right)^{2}\right)^{\frac{1}{3}}}{x \left(x^{2}-1\right)}$&$547$\\ \hline \end{longtable}"," ",0,"3/16*signum(x^2-1)^(1/3)/(-signum(x^2-1))^(1/3)*x^(16/3)*hypergeom([-1/3,8/3],[11/3],x^2)","C"
1730,1,296,85,0.109000," ","int(x/(a*x^2-b)/(a*x^3+b*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}+\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}$&$296$\\ elliptic&$\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}+\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}$&$296$\\ \hline \end{longtable}"," ",0,"1/2/a^2*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2)),1/2*2^(1/2))+1/2/a^2*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)+1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)+1/a*(a*b)^(1/2)),1/2*2^(1/2))","C"
1731,1,296,85,0.115000," ","int((a*x^3+b*x)^(1/2)/(a^2*x^4-b^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}+\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}$&$296$\\ default&$-\frac{\sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a}\right)}{2 b a \sqrt{a \,x^{3}+b x}}+\frac{\frac{2 b \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}+b x}}-\frac{b \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}+b x}}+\frac{b \sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}+\frac{b \sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}}{2 b}$&$631$\\ \hline \end{longtable}"," ",0,"1/2/a^2*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2)),1/2*2^(1/2))+1/2/a^2*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)+1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)+1/a*(a*b)^(1/2)),1/2*2^(1/2))","C"
1732,1,33,95,3.350000," ","int(x^19/(x^6-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} x^{20} \hypergeom \left(\left[\frac{1}{3}, \frac{10}{3}\right], \left[\frac{13}{3}\right], x^{6}\right)}{20 \mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}}}$&$33$\\ risch&$\frac{x^{2} \left(18 x^{12}+21 x^{6}+28\right) \left(x^{6}-1\right)^{\frac{2}{3}}}{324}+\frac{7 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}} x^{2} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{6}\right)}{81 \mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}}}$&$58$\\ trager&$\frac{x^{2} \left(18 x^{12}+21 x^{6}+28\right) \left(x^{6}-1\right)^{\frac{2}{3}}}{324}+\frac{7 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}+2 x^{6}+3 x^{4} \left(x^{6}-1\right)^{\frac{1}{3}}+3 x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-1\right)}{243}-\frac{7 \ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}+x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-1\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)}{243}+\frac{7 \ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}+x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-1\right)}{243}$&$298$\\ \hline \end{longtable}"," ",0,"1/20/signum(x^6-1)^(1/3)*(-signum(x^6-1))^(1/3)*x^20*hypergeom([1/3,10/3],[13/3],x^6)","C"
1733,1,33,95,3.025000," ","int(x^15*(x^6-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\mathrm{signum}\left(x^{6}-1\right)^{\frac{1}{3}} x^{16} \hypergeom \left(\left[-\frac{1}{3}, \frac{8}{3}\right], \left[\frac{11}{3}\right], x^{6}\right)}{16 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{1}{3}}}$&$33$\\ risch&$\frac{x^{4} \left(18 x^{12}-3 x^{6}-5\right) \left(x^{6}-1\right)^{\frac{1}{3}}}{324}-\frac{5 \left(-\mathrm{signum}\left(x^{6}-1\right)\right)^{\frac{2}{3}} x^{4} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], x^{6}\right)}{324 \mathrm{signum}\left(x^{6}-1\right)^{\frac{2}{3}}}$&$58$\\ trager&$\frac{x^{4} \left(18 x^{12}-3 x^{6}-5\right) \left(x^{6}-1\right)^{\frac{1}{3}}}{324}+\frac{5 \ln \left(-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}+2 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}-x^{6}-3 x^{4} \left(x^{6}-1\right)^{\frac{1}{3}}+3 x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1\right)}{486}+\frac{5 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}+x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{1}{3}} x^{4}-2 x^{6}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}-1\right)^{\frac{2}{3}} x^{2}+3 x^{2} \left(x^{6}-1\right)^{\frac{2}{3}}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1\right)}{486}$&$214$\\ \hline \end{longtable}"," ",0,"1/16*signum(x^6-1)^(1/3)/(-signum(x^6-1))^(1/3)*x^16*hypergeom([-1/3,8/3],[11/3],x^6)","C"
1734,1,17,95,3.310000," ","int(x^19/(x^6+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{x^{20} \hypergeom \left(\left[\frac{1}{3}, \frac{10}{3}\right], \left[\frac{13}{3}\right], -x^{6}\right)}{20}$&$17$\\ risch&$\frac{x^{2} \left(18 x^{12}-21 x^{6}+28\right) \left(x^{6}+1\right)^{\frac{2}{3}}}{324}-\frac{7 x^{2} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{6}\right)}{81}$&$42$\\ trager&$\frac{x^{2} \left(18 x^{12}-21 x^{6}+28\right) \left(x^{6}+1\right)^{\frac{2}{3}}}{324}+\frac{7 \ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}+4 x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}} x^{4}+4 x^{6}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x^{2}+3 x^{4} \left(x^{6}+1\right)^{\frac{1}{3}}+3 x^{2} \left(x^{6}+1\right)^{\frac{2}{3}}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+2\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{243}-\frac{7 \ln \left(-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}-x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+2 x^{6}+3 x^{4} \left(x^{6}+1\right)^{\frac{1}{3}}+3 x^{2} \left(x^{6}+1\right)^{\frac{2}{3}}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+2\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{243}-\frac{7 \ln \left(-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{6}-x^{6} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+2 x^{6}+3 x^{4} \left(x^{6}+1\right)^{\frac{1}{3}}+3 x^{2} \left(x^{6}+1\right)^{\frac{2}{3}}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+2\right)}{243}$&$278$\\ \hline \end{longtable}"," ",0,"1/20*x^20*hypergeom([1/3,10/3],[13/3],-x^6)","C"
1735,1,17,95,3.140000," ","int(x^15*(x^6+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{x^{16} \hypergeom \left(\left[-\frac{1}{3}, \frac{8}{3}\right], \left[\frac{11}{3}\right], -x^{6}\right)}{16}$&$17$\\ risch&$\frac{x^{4} \left(18 x^{12}+3 x^{6}-5\right) \left(x^{6}+1\right)^{\frac{1}{3}}}{324}+\frac{5 x^{4} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], -x^{6}\right)}{324}$&$42$\\ trager&$\frac{x^{4} \left(18 x^{12}+3 x^{6}-5\right) \left(x^{6}+1\right)^{\frac{1}{3}}}{324}-\frac{5 \ln \left(-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}+x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x^{2}-3 x^{4} \left(x^{6}+1\right)^{\frac{1}{3}}-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+1\right)}{486}+\frac{5 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{1}{3}} x^{4}-2 x^{6}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}+1\right)^{\frac{2}{3}} x^{2}+3 x^{2} \left(x^{6}+1\right)^{\frac{2}{3}}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-1\right)}{486}$&$221$\\ \hline \end{longtable}"," ",0,"1/16*x^16*hypergeom([-1/3,8/3],[11/3],-x^6)","C"
1736,0,0,97,0.011000," ","int((x^6-a*x^3-b)/x^6/(a*x^4-b*x)^(1/4),x)","\[\int \frac{x^{6}-a \,x^{3}-b}{x^{6} \left(a \,x^{4}-b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((x^6-a*x^3-b)/x^6/(a*x^4-b*x)^(1/4),x)","F"
1737,1,340,103,3.493000," ","int((3*x^6-x^4-3)/(x^6-x^4+1)/(x^6-x^4-x^3+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{4}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-x^{4}-x^{3}+1\right)^{\frac{2}{3}} x +\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-x^{4}-x^{3}+1\right)^{\frac{1}{3}} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-\left(x^{6}-x^{4}-x^{3}+1\right)^{\frac{2}{3}} x -2 \left(x^{6}-x^{4}-x^{3}+1\right)^{\frac{1}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)}{x^{6}-x^{4}+1}\right)+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\frac{x^{6}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-x^{4}-x^{3}+1\right)^{\frac{2}{3}} x +\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{6}-x^{4}-x^{3}+1\right)^{\frac{1}{3}} x^{2}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-x^{4}-\left(x^{6}-x^{4}-x^{3}+1\right)^{\frac{2}{3}} x -2 \left(x^{6}-x^{4}-x^{3}+1\right)^{\frac{1}{3}} x^{2}-x^{3}+1}{x^{6}-x^{4}+1}\right)$&$340$\\ \hline \end{longtable}"," ",0,"-ln(-(RootOf(_Z^2-_Z+1)*x^6+RootOf(_Z^2-_Z+1)^2*x^3-RootOf(_Z^2-_Z+1)*x^4+2*RootOf(_Z^2-_Z+1)*(x^6-x^4-x^3+1)^(2/3)*x+RootOf(_Z^2-_Z+1)*(x^6-x^4-x^3+1)^(1/3)*x^2-2*RootOf(_Z^2-_Z+1)*x^3-(x^6-x^4-x^3+1)^(2/3)*x-2*(x^6-x^4-x^3+1)^(1/3)*x^2+RootOf(_Z^2-_Z+1))/(x^6-x^4+1))+RootOf(_Z^2-_Z+1)*ln((x^6+2*RootOf(_Z^2-_Z+1)*(x^6-x^4-x^3+1)^(2/3)*x+RootOf(_Z^2-_Z+1)*(x^6-x^4-x^3+1)^(1/3)*x^2-RootOf(_Z^2-_Z+1)*x^3-x^4-(x^6-x^4-x^3+1)^(2/3)*x-2*(x^6-x^4-x^3+1)^(1/3)*x^2-x^3+1)/(x^6-x^4+1))","C"
1738,0,0,97,0.009000," ","int((a*x^6-b)/x^6/(a*x^4-b*x)^(1/4),x)","\[\int \frac{a \,x^{6}-b}{x^{6} \left(a \,x^{4}-b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^6-b)/x^6/(a*x^4-b*x)^(1/4),x)","F"
1739,0,0,97,0.010000," ","int((a*x^6+b)/x^6/(a*x^4-b*x)^(1/4),x)","\[\int \frac{a \,x^{6}+b}{x^{6} \left(a \,x^{4}-b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^6+b)/x^6/(a*x^4-b*x)^(1/4),x)","F"
1740,0,0,94,0.016000," ","int((x^4+x^2)^(1/4)*(x^8-x^4-1)/(x^4-1),x)","\[\int \frac{\left(x^{4}+x^{2}\right)^{\frac{1}{4}} \left(x^{8}-x^{4}-1\right)}{x^{4}-1}\, dx\]"," ",0,"int((x^4+x^2)^(1/4)*(x^8-x^4-1)/(x^4-1),x)","F"
1741,0,0,50,0.032000," ","int((2*x^8-a*x^4-b)/(a*x^4+b)^(1/4)/(x^8-a*x^4-b),x)","\[\int \frac{2 x^{8}-a \,x^{4}-b}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(x^{8}-a \,x^{4}-b \right)}\, dx\]"," ",0,"int((2*x^8-a*x^4-b)/(a*x^4+b)^(1/4)/(x^8-a*x^4-b),x)","F"
1742,0,0,50,0.001000," ","int((2*x^8-a*x^4-b)/(a*x^4+b)^(1/4)/(x^8-a*x^4-b),x)","\[\int \frac{2 x^{8}-a \,x^{4}-b}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(x^{8}-a \,x^{4}-b \right)}\, dx\]"," ",0,"int((2*x^8-a*x^4-b)/(a*x^4+b)^(1/4)/(x^8-a*x^4-b),x)","F"
1743,0,0,103,0.028000," ","int((c*x^2-x*(a*x^2-b*x)^(1/2))^(1/2)/x^3/(a*x^2-b*x)^(1/2),x)","\[\int \frac{\sqrt{c \,x^{2}-x \sqrt{a \,x^{2}-b x}}}{x^{3} \sqrt{a \,x^{2}-b x}}\, dx\]"," ",0,"int((c*x^2-x*(a*x^2-b*x)^(1/2))^(1/2)/x^3/(a*x^2-b*x)^(1/2),x)","F"
1744,0,0,94,0.004000," ","int((x^3+b)/(x^3+a)^(1/3),x)","\[\int \frac{x^{3}+b}{\left(x^{3}+a \right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((x^3+b)/(x^3+a)^(1/3),x)","F"
1745,1,36,94,1.487000," ","int((a*x^2+b)/(x^3+x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 a \,x^{\frac{8}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{4}{3}\right], \left[\frac{7}{3}\right], -x^{2}\right)}{8}+\frac{3 b \,x^{\frac{2}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{2}\right)}{2}$&$36$\\ risch&$\frac{a x \left(x^{2}+1\right)}{2 \left(x \left(x^{2}+1\right)\right)^{\frac{1}{3}}}+\frac{3 b \,x^{\frac{2}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{2}\right)}{2}-\frac{a \,x^{\frac{2}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{2}\right)}{2}$&$54$\\ trager&$\frac{a \left(x^{3}+x \right)^{\frac{2}{3}}}{2}+\frac{\left(a -3 b \right) \left(6 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \ln \left(180 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{2}+144 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}+144 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x +174 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{2}-180 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2}+15 \left(x^{3}+x \right)^{\frac{2}{3}}+15 x \left(x^{3}+x \right)^{\frac{1}{3}}+20 x^{2}+36 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)+8\right)-6 \ln \left(180 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{2}-144 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}-144 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x -114 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{2}-180 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2}-9 \left(x^{3}+x \right)^{\frac{2}{3}}-9 x \left(x^{3}+x \right)^{\frac{1}{3}}-4 x^{2}-96 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)-3\right) \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)-\ln \left(180 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2} x^{2}-144 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}-144 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x -114 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right) x^{2}-180 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)^{2}-9 \left(x^{3}+x \right)^{\frac{2}{3}}-9 x \left(x^{3}+x \right)^{\frac{1}{3}}-4 x^{2}-96 \RootOf \left(36 \textit{\_Z}^{2}+6 \textit{\_Z} +1\right)-3\right)\right)}{6}$&$438$\\ \hline \end{longtable}"," ",0,"3/8*a*x^(8/3)*hypergeom([1/3,4/3],[7/3],-x^2)+3/2*b*x^(2/3)*hypergeom([1/3,1/3],[4/3],-x^2)","C"
1746,1,27,96,0.920000," ","int((x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 \mathrm{signum}\left(-1+x \right)^{\frac{1}{3}} x^{\frac{5}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{5}{3}\right], \left[\frac{8}{3}\right], x\right)}{5 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{1}{3}}}$&$27$\\ risch&$\frac{\left(-1+3 x \right) \left(\left(-1+x \right) x^{2}\right)^{\frac{1}{3}}}{6}+\frac{\left(\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x +15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-2 x^{2}+x \right)^{\frac{2}{3}}-24 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-2 x^{2}+x \right)^{\frac{1}{3}} x +10 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+24 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-2 x^{2}+x \right)^{\frac{1}{3}}-23 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x -9 \left(x^{3}-2 x^{2}+x \right)^{\frac{2}{3}}-15 \left(x^{3}-2 x^{2}+x \right)^{\frac{1}{3}} x +25 x^{2}+13 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+15 \left(x^{3}-2 x^{2}+x \right)^{\frac{1}{3}}-40 x +15}{-1+x}\right)}{9}+\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\frac{5 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}-15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x +15 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-2 x^{2}+x \right)^{\frac{2}{3}}+9 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-2 x^{2}+x \right)^{\frac{1}{3}} x -19 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+10 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-9 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-2 x^{2}+x \right)^{\frac{1}{3}}+22 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +24 \left(x^{3}-2 x^{2}+x \right)^{\frac{2}{3}}-15 \left(x^{3}-2 x^{2}+x \right)^{\frac{1}{3}} x -4 x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+15 \left(x^{3}-2 x^{2}+x \right)^{\frac{1}{3}}+5 x -1}{-1+x}\right)}{9}\right) \left(\left(-1+x \right) x^{2}\right)^{\frac{1}{3}} \left(\left(-1+x \right)^{2} x \right)^{\frac{1}{3}}}{x \left(-1+x \right)}$&$441$\\ trager&$\left(-\frac{1}{6}+\frac{x}{2}\right) \left(x^{3}-x^{2}\right)^{\frac{1}{3}}+\frac{\RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(\frac{45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}-90 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x +72 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+72 \left(x^{3}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x +87 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}-69 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x +15 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+15 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}+20 x^{2}-12 x}{x}\right)}{3}-\frac{\ln \left(\frac{45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}-90 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x -72 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}-72 \left(x^{3}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -57 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -9 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}-9 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}-4 x^{2}+x}{x}\right)}{9}-\frac{\ln \left(\frac{45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}-90 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x -72 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}-72 \left(x^{3}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -57 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -9 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}-9 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}-4 x^{2}+x}{x}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{3}$&$505$\\ \hline \end{longtable}"," ",0,"3/5*signum(-1+x)^(1/3)/(-signum(-1+x))^(1/3)*x^(5/3)*hypergeom([-1/3,5/3],[8/3],x)","C"
1747,1,15,96,0.844000," ","int(x^2*(x^3+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 x^{\frac{11}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{11}{3}\right], \left[\frac{14}{3}\right], -x \right)}{11}$&$15$\\ trager&$\left(\frac{1}{4} x^{3}+\frac{1}{36} x^{2}-\frac{1}{27} x +\frac{5}{81}\right) \left(x^{3}+x^{2}\right)^{\frac{1}{3}}-\frac{10 \ln \left(-\frac{36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}-36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x +45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{2}{3}}+45 \left(x^{3}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x +57 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+27 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -9 \left(x^{3}+x^{2}\right)^{\frac{2}{3}}-9 x \left(x^{3}+x^{2}\right)^{\frac{1}{3}}-5 x^{2}-2 x}{x}\right)}{243}-\frac{10 \ln \left(-\frac{36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}-36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x +45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{2}{3}}+45 \left(x^{3}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x +57 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+27 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -9 \left(x^{3}+x^{2}\right)^{\frac{2}{3}}-9 x \left(x^{3}+x^{2}\right)^{\frac{1}{3}}-5 x^{2}-2 x}{x}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{81}+\frac{10 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(-\frac{36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}-36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x -45 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+x^{2}\right)^{\frac{2}{3}}-45 \left(x^{3}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -33 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}-51 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -24 \left(x^{3}+x^{2}\right)^{\frac{2}{3}}-24 x \left(x^{3}+x^{2}\right)^{\frac{1}{3}}-20 x^{2}-15 x}{x}\right)}{81}$&$496$\\ risch&$\frac{\left(81 x^{3}+9 x^{2}-12 x +20\right) \left(x^{2} \left(1+x \right)\right)^{\frac{1}{3}}}{324}+\frac{\left(\frac{5 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \ln \left(-\frac{-5 x^{2} \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)^{2}+48 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{2}{3}}+48 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}} x +38 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) x^{2}+36 \left(x^{3}+2 x^{2}+x \right)^{\frac{2}{3}}+48 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}}+36 \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}} x +5 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)^{2}+70 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) x +16 x^{2}+36 \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}}+32 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)+28 x +12}{1+x}\right)}{243}-\frac{5 \ln \left(\frac{5 x^{2} \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)^{2}+48 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{2}{3}}+48 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}} x +58 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) x^{2}+60 \left(x^{3}+2 x^{2}+x \right)^{\frac{2}{3}}+48 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}}+60 \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}} x -5 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)^{2}+70 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) x +80 x^{2}+60 \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}}+12 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)+112 x +32}{1+x}\right) \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)}{243}-\frac{10 \ln \left(\frac{5 x^{2} \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)^{2}+48 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{2}{3}}+48 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}} x +58 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) x^{2}+60 \left(x^{3}+2 x^{2}+x \right)^{\frac{2}{3}}+48 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}}+60 \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}} x -5 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)^{2}+70 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right) x +80 x^{2}+60 \left(x^{3}+2 x^{2}+x \right)^{\frac{1}{3}}+12 \RootOf \left(\textit{\_Z}^{2}+2 \textit{\_Z} +4\right)+112 x +32}{1+x}\right)}{243}\right) \left(x^{2} \left(1+x \right)\right)^{\frac{1}{3}} \left(\left(1+x \right)^{2} x \right)^{\frac{1}{3}}}{x \left(1+x \right)}$&$669$\\ \hline \end{longtable}"," ",0,"3/11*x^(11/3)*hypergeom([-1/3,11/3],[14/3],-x)","C"
1748,1,2552,38,107.844000," ","int(x^4/(x^4+1)^2/(x^4+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2552$\\ risch&$\text{Expression too large to display}$&$2561$\\ \hline \end{longtable}"," ",0,"1/8*(-1+x)*(1+x)/x/(x^4+1)*(x^4+x^2)^(3/4)-1/128*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*ln((-1099511627776*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^8*x^3+2097152*(x^4+x^2)^(1/2)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^3*x+1099511627776*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^8*x-7340032*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^2*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*(x^4+x^2)^(1/4)*x^2+9437184*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*x^3-25165824*(x^4+x^2)^(3/4)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+(x^4+x^2)^(1/2)*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^3*x+11534336*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*x-16*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^2*(x^4+x^2)^(1/4)*x^2+36*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*x^3-112*(x^4+x^2)^(3/4)+24*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*x)/(262144*x^2*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4-262144*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+x^2)/x)-4096*ln((-549755813888*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^8*x^3+1572864*(x^4+x^2)^(1/2)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^3*x+549755813888*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^8*x+7340032*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^2*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*(x^4+x^2)^(1/4)*x^2+7340032*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*x^3-25165824*(x^4+x^2)^(3/4)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+7*(x^4+x^2)^(1/2)*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^3*x+3145728*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*x+16*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^2*(x^4+x^2)^(1/4)*x^2-12*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*x^3-112*(x^4+x^2)^(3/4)-8*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*x)/(262144*x^2*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4-262144*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+x^2)/x)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)-1/128*ln((-549755813888*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^8*x^3+1572864*(x^4+x^2)^(1/2)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^3*x+549755813888*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^8*x+7340032*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^2*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*(x^4+x^2)^(1/4)*x^2+7340032*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*x^3-25165824*(x^4+x^2)^(3/4)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+7*(x^4+x^2)^(1/2)*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^3*x+3145728*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*x+16*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^2*(x^4+x^2)^(1/4)*x^2-12*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*x^3-112*(x^4+x^2)^(3/4)-8*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*x)/(262144*x^2*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4-262144*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+x^2)/x)*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)-262144*RootOf(137438953472*_Z^8+524288*_Z^4+1)^5*ln((2199023255552*x^3*RootOf(137438953472*_Z^8+524288*_Z^4+1)^9-2199023255552*x*RootOf(137438953472*_Z^8+524288*_Z^4+1)^9+25769803776*(x^4+x^2)^(1/2)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^7*x-1879048192*RootOf(137438953472*_Z^8+524288*_Z^4+1)^6*(x^4+x^2)^(1/4)*x^2+46137344*RootOf(137438953472*_Z^8+524288*_Z^4+1)^5*x^3+1572864*(x^4+x^2)^(3/4)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4-4194304*RootOf(137438953472*_Z^8+524288*_Z^4+1)^5*x-16384*(x^4+x^2)^(1/2)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^3*x-3072*RootOf(137438953472*_Z^8+524288*_Z^4+1)^2*(x^4+x^2)^(1/4)*x^2+192*RootOf(137438953472*_Z^8+524288*_Z^4+1)*x^3-(x^4+x^2)^(3/4)+48*RootOf(137438953472*_Z^8+524288*_Z^4+1)*x)/(262144*x^2*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4-262144*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4-1)/x)-1/2*RootOf(137438953472*_Z^8+524288*_Z^4+1)*ln((2199023255552*x^3*RootOf(137438953472*_Z^8+524288*_Z^4+1)^9-2199023255552*x*RootOf(137438953472*_Z^8+524288*_Z^4+1)^9+25769803776*(x^4+x^2)^(1/2)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^7*x-1879048192*RootOf(137438953472*_Z^8+524288*_Z^4+1)^6*(x^4+x^2)^(1/4)*x^2+46137344*RootOf(137438953472*_Z^8+524288*_Z^4+1)^5*x^3+1572864*(x^4+x^2)^(3/4)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4-4194304*RootOf(137438953472*_Z^8+524288*_Z^4+1)^5*x-16384*(x^4+x^2)^(1/2)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^3*x-3072*RootOf(137438953472*_Z^8+524288*_Z^4+1)^2*(x^4+x^2)^(1/4)*x^2+192*RootOf(137438953472*_Z^8+524288*_Z^4+1)*x^3-(x^4+x^2)^(3/4)+48*RootOf(137438953472*_Z^8+524288*_Z^4+1)*x)/(262144*x^2*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4-262144*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4-1)/x)-1/2*RootOf(137438953472*_Z^8+524288*_Z^4+1)*ln(-(4398046511104*x^3*RootOf(137438953472*_Z^8+524288*_Z^4+1)^9-4398046511104*x*RootOf(137438953472*_Z^8+524288*_Z^4+1)^9+34359738368*(x^4+x^2)^(1/2)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^7*x-1879048192*RootOf(137438953472*_Z^8+524288*_Z^4+1)^6*(x^4+x^2)^(1/4)*x^2+71303168*RootOf(137438953472*_Z^8+524288*_Z^4+1)^5*x^3-1572864*(x^4+x^2)^(3/4)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+12582912*RootOf(137438953472*_Z^8+524288*_Z^4+1)^5*x+114688*(x^4+x^2)^(1/2)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^3*x-3072*RootOf(137438953472*_Z^8+524288*_Z^4+1)^2*(x^4+x^2)^(1/4)*x^2+64*RootOf(137438953472*_Z^8+524288*_Z^4+1)*x^3+(x^4+x^2)^(3/4)+16*RootOf(137438953472*_Z^8+524288*_Z^4+1)*x)/(262144*x^2*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4-262144*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4-1)/x)","B"
1749,1,2552,38,103.167000," ","int(x^4/(x^4+1)^2/(x^4+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2552$\\ risch&$\text{Expression too large to display}$&$2560$\\ \hline \end{longtable}"," ",0,"1/8*(-1+x)*(1+x)/x/(x^4+1)*(x^4+x^2)^(3/4)+1/2*RootOf(137438953472*_Z^8+524288*_Z^4+1)*ln((4398046511104*x^3*RootOf(137438953472*_Z^8+524288*_Z^4+1)^9-4398046511104*x*RootOf(137438953472*_Z^8+524288*_Z^4+1)^9+34359738368*(x^4+x^2)^(1/2)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^7*x+1879048192*RootOf(137438953472*_Z^8+524288*_Z^4+1)^6*(x^4+x^2)^(1/4)*x^2+71303168*RootOf(137438953472*_Z^8+524288*_Z^4+1)^5*x^3+1572864*(x^4+x^2)^(3/4)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+12582912*RootOf(137438953472*_Z^8+524288*_Z^4+1)^5*x+114688*(x^4+x^2)^(1/2)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^3*x+3072*RootOf(137438953472*_Z^8+524288*_Z^4+1)^2*(x^4+x^2)^(1/4)*x^2+64*RootOf(137438953472*_Z^8+524288*_Z^4+1)*x^3-(x^4+x^2)^(3/4)+16*RootOf(137438953472*_Z^8+524288*_Z^4+1)*x)/(262144*x^2*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4-262144*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4-1)/x)+1/128*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*ln(-(-1099511627776*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^8*x^3+2097152*(x^4+x^2)^(1/2)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^3*x+1099511627776*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^8*x+7340032*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^2*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*(x^4+x^2)^(1/4)*x^2+9437184*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*x^3+25165824*(x^4+x^2)^(3/4)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+(x^4+x^2)^(1/2)*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^3*x+11534336*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*x+16*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^2*(x^4+x^2)^(1/4)*x^2+36*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*x^3+112*(x^4+x^2)^(3/4)+24*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*x)/(262144*x^2*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4-262144*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+x^2)/x)-4096*ln((-549755813888*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^8*x^3+1572864*(x^4+x^2)^(1/2)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^3*x+549755813888*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^8*x+7340032*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^2*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*(x^4+x^2)^(1/4)*x^2+7340032*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*x^3-25165824*(x^4+x^2)^(3/4)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+7*(x^4+x^2)^(1/2)*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^3*x+3145728*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*x+16*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^2*(x^4+x^2)^(1/4)*x^2-12*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*x^3-112*(x^4+x^2)^(3/4)-8*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*x)/(262144*x^2*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4-262144*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+x^2)/x)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)-1/128*ln((-549755813888*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^8*x^3+1572864*(x^4+x^2)^(1/2)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^3*x+549755813888*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^8*x+7340032*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^2*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*(x^4+x^2)^(1/4)*x^2+7340032*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*x^3-25165824*(x^4+x^2)^(3/4)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+7*(x^4+x^2)^(1/2)*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^3*x+3145728*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4*x+16*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)^2*(x^4+x^2)^(1/4)*x^2-12*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*x^3-112*(x^4+x^2)^(3/4)-8*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)*x)/(262144*x^2*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4-262144*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+x^2)/x)*RootOf(_Z^4+16777216*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4+64)+262144*RootOf(137438953472*_Z^8+524288*_Z^4+1)^5*ln(-(2199023255552*x^3*RootOf(137438953472*_Z^8+524288*_Z^4+1)^9-2199023255552*x*RootOf(137438953472*_Z^8+524288*_Z^4+1)^9+25769803776*(x^4+x^2)^(1/2)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^7*x+1879048192*RootOf(137438953472*_Z^8+524288*_Z^4+1)^6*(x^4+x^2)^(1/4)*x^2+46137344*RootOf(137438953472*_Z^8+524288*_Z^4+1)^5*x^3-1572864*(x^4+x^2)^(3/4)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4-4194304*RootOf(137438953472*_Z^8+524288*_Z^4+1)^5*x-16384*(x^4+x^2)^(1/2)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^3*x+3072*RootOf(137438953472*_Z^8+524288*_Z^4+1)^2*(x^4+x^2)^(1/4)*x^2+192*RootOf(137438953472*_Z^8+524288*_Z^4+1)*x^3+(x^4+x^2)^(3/4)+48*RootOf(137438953472*_Z^8+524288*_Z^4+1)*x)/(262144*x^2*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4-262144*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4-1)/x)+1/2*RootOf(137438953472*_Z^8+524288*_Z^4+1)*ln(-(2199023255552*x^3*RootOf(137438953472*_Z^8+524288*_Z^4+1)^9-2199023255552*x*RootOf(137438953472*_Z^8+524288*_Z^4+1)^9+25769803776*(x^4+x^2)^(1/2)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^7*x+1879048192*RootOf(137438953472*_Z^8+524288*_Z^4+1)^6*(x^4+x^2)^(1/4)*x^2+46137344*RootOf(137438953472*_Z^8+524288*_Z^4+1)^5*x^3-1572864*(x^4+x^2)^(3/4)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4-4194304*RootOf(137438953472*_Z^8+524288*_Z^4+1)^5*x-16384*(x^4+x^2)^(1/2)*RootOf(137438953472*_Z^8+524288*_Z^4+1)^3*x+3072*RootOf(137438953472*_Z^8+524288*_Z^4+1)^2*(x^4+x^2)^(1/4)*x^2+192*RootOf(137438953472*_Z^8+524288*_Z^4+1)*x^3+(x^4+x^2)^(3/4)+48*RootOf(137438953472*_Z^8+524288*_Z^4+1)*x)/(262144*x^2*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4-262144*RootOf(137438953472*_Z^8+524288*_Z^4+1)^4-1)/x)","B"
1750,1,435,100,6.025000," ","int((x^4-3)*(x^4-x^3+1)*(x^4+x^3+1)^(2/3)/x^6/(x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(x^{4}+x^{3}+1\right)^{\frac{2}{3}} \left(2 x^{4}-3 x^{3}+2\right)}{10 x^{5}}-\ln \left(\frac{31401 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{4}-62802 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{3}+9177 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{4}+37851 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{4}+x^{3}+1\right)^{\frac{2}{3}} x -134634 \left(x^{4}+x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}+117717 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{3}-22224 x^{4}+32261 x \left(x^{4}+x^{3}+1\right)^{\frac{2}{3}}+12617 \left(x^{4}+x^{3}+1\right)^{\frac{1}{3}} x^{2}-51856 x^{3}+31401 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}+9177 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-22224}{x^{4}+1}\right)+3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \ln \left(-\frac{66672 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{4}-133344 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{3}-99363 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{4}+37851 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{4}+x^{3}+1\right)^{\frac{2}{3}} x +96783 \left(x^{4}+x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}-90186 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{3}+13956 x^{4}-44878 x \left(x^{4}+x^{3}+1\right)^{\frac{2}{3}}+12617 \left(x^{4}+x^{3}+1\right)^{\frac{1}{3}} x^{2}+17445 x^{3}+66672 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}-99363 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)+13956}{x^{4}+1}\right)$&$435$\\ risch&$\frac{\frac{3}{5} x^{8}-\frac{3}{10} x^{7}-\frac{9}{10} x^{6}+\frac{6}{5} x^{4}-\frac{3}{10} x^{3}+\frac{3}{5}}{x^{5} \left(x^{4}+x^{3}+1\right)^{\frac{1}{3}}}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{4}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{4}+x^{3}+1\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{4}+x^{3}+1\right)^{\frac{1}{3}} x^{2}+4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-2 x^{4}-3 x \left(x^{4}+x^{3}+1\right)^{\frac{2}{3}}-3 \left(x^{4}+x^{3}+1\right)^{\frac{1}{3}} x^{2}-4 x^{3}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-2}{x^{4}+1}\right)-\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{4}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{4}+x^{3}+1\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{4}+x^{3}+1\right)^{\frac{1}{3}} x^{2}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+x^{4}+x^{3}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+1}{x^{4}+1}\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{4}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{4}+x^{3}+1\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{4}+x^{3}+1\right)^{\frac{1}{3}} x^{2}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+x^{4}+x^{3}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+1}{x^{4}+1}\right)$&$442$\\ \hline \end{longtable}"," ",0,"3/10*(x^4+x^3+1)^(2/3)*(2*x^4-3*x^3+2)/x^5-ln((31401*RootOf(9*_Z^2-3*_Z+1)^2*x^4-62802*RootOf(9*_Z^2-3*_Z+1)^2*x^3+9177*RootOf(9*_Z^2-3*_Z+1)*x^4+37851*RootOf(9*_Z^2-3*_Z+1)*(x^4+x^3+1)^(2/3)*x-134634*(x^4+x^3+1)^(1/3)*RootOf(9*_Z^2-3*_Z+1)*x^2+117717*RootOf(9*_Z^2-3*_Z+1)*x^3-22224*x^4+32261*x*(x^4+x^3+1)^(2/3)+12617*(x^4+x^3+1)^(1/3)*x^2-51856*x^3+31401*RootOf(9*_Z^2-3*_Z+1)^2+9177*RootOf(9*_Z^2-3*_Z+1)-22224)/(x^4+1))+3*RootOf(9*_Z^2-3*_Z+1)*ln(-(66672*RootOf(9*_Z^2-3*_Z+1)^2*x^4-133344*RootOf(9*_Z^2-3*_Z+1)^2*x^3-99363*RootOf(9*_Z^2-3*_Z+1)*x^4+37851*RootOf(9*_Z^2-3*_Z+1)*(x^4+x^3+1)^(2/3)*x+96783*(x^4+x^3+1)^(1/3)*RootOf(9*_Z^2-3*_Z+1)*x^2-90186*RootOf(9*_Z^2-3*_Z+1)*x^3+13956*x^4-44878*x*(x^4+x^3+1)^(2/3)+12617*(x^4+x^3+1)^(1/3)*x^2+17445*x^3+66672*RootOf(9*_Z^2-3*_Z+1)^2-99363*RootOf(9*_Z^2-3*_Z+1)+13956)/(x^4+1))","C"
1751,0,0,60,0.043000," ","int((2*a*x^4-b)/(a*x^4+b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{2 a \,x^{4}-b}{\left(a \,x^{4}+b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((2*a*x^4-b)/(a*x^4+b)/(a*x^4+b*x^2)^(1/4),x)","F"
1752,0,0,60,0.000000," ","int((2*a*x^4-b)/(a*x^4+b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{2 a \,x^{4}-b}{\left(a \,x^{4}+b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((2*a*x^4-b)/(a*x^4+b)/(a*x^4+b*x^2)^(1/4),x)","F"
1753,1,1436,86,21.246000," ","int((x^2+1)/(x^2-1)/(x^5+x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1436$\\ \hline \end{longtable}"," ",0,"-1/4*ln(-(17033446708883816*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x^4+13884449784656120*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x^4-72392148512756218*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x^2-59008911584788510*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x^2+58185583206163764*(x^5+x)^(2/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^2+106459041930523850*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^4+86777811154100750*RootOf(_Z^3-4)*x^4+17033446708883816*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2+116371166412327528*(x^5+x)^(1/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)*x+13884449784656120*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3+133709338270907283*RootOf(_Z^3-4)^2*(x^5+x)^(1/3)*x+68133786835535264*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^2+55537799138624480*RootOf(_Z^3-4)*x^2+267418676541814566*(x^5+x)^(2/3)+106459041930523850*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)+86777811154100750*RootOf(_Z^3-4))/(-1+x)^2/(1+x)^2)*RootOf(_Z^3-4)-1/2*ln(-(17033446708883816*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x^4+13884449784656120*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x^4-72392148512756218*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x^2-59008911584788510*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x^2+58185583206163764*(x^5+x)^(2/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^2+106459041930523850*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^4+86777811154100750*RootOf(_Z^3-4)*x^4+17033446708883816*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2+116371166412327528*(x^5+x)^(1/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)*x+13884449784656120*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3+133709338270907283*RootOf(_Z^3-4)^2*(x^5+x)^(1/3)*x+68133786835535264*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^2+55537799138624480*RootOf(_Z^3-4)*x^2+267418676541814566*(x^5+x)^(2/3)+106459041930523850*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)+86777811154100750*RootOf(_Z^3-4))/(-1+x)^2/(1+x)^2)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)+1/2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*ln(-(17033446708883816*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x^4-5367726430214212*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x^4-72392148512756218*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x^2+22812837328410401*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x^2-58185583206163764*(x^5+x)^(2/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^2-72392148512756218*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^4+22812837328410401*RootOf(_Z^3-4)*x^4+17033446708883816*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2-116371166412327528*(x^5+x)^(1/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)*x-5367726430214212*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3+75523755064743519*RootOf(_Z^3-4)^2*(x^5+x)^(1/3)*x-212918083861047700*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^2+67096580377677650*RootOf(_Z^3-4)*x^2+151047510129487038*(x^5+x)^(2/3)-72392148512756218*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)+22812837328410401*RootOf(_Z^3-4))/(-1+x)^2/(1+x)^2)","C"
1754,0,0,98,0.010000," ","int((x^2-1)*(x^6+x^2)^(1/4)/x^2/(x^2+1),x)","\[\int \frac{\left(x^{2}-1\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}}}{x^{2} \left(x^{2}+1\right)}\, dx\]"," ",0,"int((x^2-1)*(x^6+x^2)^(1/4)/x^2/(x^2+1),x)","F"
1755,0,0,98,0.002000," ","int((x^2-1)*(x^6+x^2)^(1/4)/x^2/(x^2+1),x)","\[\int \frac{\left(x^{2}-1\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}}}{x^{2} \left(x^{2}+1\right)}\, dx\]"," ",0,"int((x^2-1)*(x^6+x^2)^(1/4)/x^2/(x^2+1),x)","F"
1756,1,274,96,4.253000," ","int((x^3-1)^(2/3)*(4*x^6-5*x^3+1)/x^6/(2*x^3-1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{62 x^{9}-95 x^{6}+39 x^{3}-6}{30 \left(2 x^{3}-1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{5}}+\frac{7 \ln \left(\frac{3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}-x \left(x^{3}-1\right)^{\frac{2}{3}}+x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}+1}{2 x^{3}-1}\right)}{9}+\frac{7 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(-\frac{9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+2 x \left(x^{3}-1\right)^{\frac{2}{3}}+x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{2 x^{3}-1}\right)}{3}$&$274$\\ trager&$\frac{\left(x^{3}-1\right)^{\frac{2}{3}} \left(62 x^{6}-33 x^{3}+6\right)}{30 x^{5} \left(2 x^{3}-1\right)}+\frac{7 \ln \left(-\frac{65382681600 \RootOf \left(2073600 \textit{\_Z}^{2}+1440 \textit{\_Z} +1\right)^{2} x^{3}+153792000 \RootOf \left(2073600 \textit{\_Z}^{2}+1440 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +760160160 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(2073600 \textit{\_Z}^{2}+1440 \textit{\_Z} +1\right) x^{2}+350055360 \RootOf \left(2073600 \textit{\_Z}^{2}+1440 \textit{\_Z} +1\right) x^{3}-421089 x \left(x^{3}-1\right)^{\frac{2}{3}}+106800 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-73232 x^{3}-523061452800 \RootOf \left(2073600 \textit{\_Z}^{2}+1440 \textit{\_Z} +1\right)^{2}-212378400 \RootOf \left(2073600 \textit{\_Z}^{2}+1440 \textit{\_Z} +1\right)+64078}{2 x^{3}-1}\right)}{9}+1120 \RootOf \left(2073600 \textit{\_Z}^{2}+1440 \textit{\_Z} +1\right) \ln \left(\frac{-18981734400 \RootOf \left(2073600 \textit{\_Z}^{2}+1440 \textit{\_Z} +1\right)^{2} x^{3}+153792000 \RootOf \left(2073600 \textit{\_Z}^{2}+1440 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -606368160 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(2073600 \textit{\_Z}^{2}+1440 \textit{\_Z} +1\right) x^{2}+137676960 \RootOf \left(2073600 \textit{\_Z}^{2}+1440 \textit{\_Z} +1\right) x^{3}+527889 x \left(x^{3}-1\right)^{\frac{2}{3}}+106800 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-220717 x^{3}+151853875200 \RootOf \left(2073600 \textit{\_Z}^{2}+1440 \textit{\_Z} +1\right)^{2}-350055360 \RootOf \left(2073600 \textit{\_Z}^{2}+1440 \textit{\_Z} +1\right)-31531}{2 x^{3}-1}\right)$&$343$\\ \hline \end{longtable}"," ",0,"1/30*(62*x^9-95*x^6+39*x^3-6)/(2*x^3-1)/(x^3-1)^(1/3)/x^5+7/9*ln((3*RootOf(9*_Z^2+3*_Z+1)*(x^3-1)^(2/3)*x+6*RootOf(9*_Z^2+3*_Z+1)*(x^3-1)^(1/3)*x^2+3*RootOf(9*_Z^2+3*_Z+1)*x^3-x*(x^3-1)^(2/3)+x^2*(x^3-1)^(1/3)+1)/(2*x^3-1))+7/3*RootOf(9*_Z^2+3*_Z+1)*ln(-(9*RootOf(9*_Z^2+3*_Z+1)^2*x^3+3*RootOf(9*_Z^2+3*_Z+1)*(x^3-1)^(2/3)*x-3*RootOf(9*_Z^2+3*_Z+1)*(x^3-1)^(1/3)*x^2+3*RootOf(9*_Z^2+3*_Z+1)*x^3+2*x*(x^3-1)^(2/3)+x^2*(x^3-1)^(1/3)-3*RootOf(9*_Z^2+3*_Z+1))/(2*x^3-1))","C"
1757,1,110,84,0.070000," ","int((1+x)^(1/2)*(1+(1+x)^(1/2))^(1/2)/(x-(1+x)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}+4 \sqrt{1+\sqrt{1+x}}+2 \ln \left(\sqrt{1+x}-\sqrt{1+\sqrt{1+x}}\right)-\frac{8 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}-1\right) \sqrt{5}}{5}\right)}{5}-2 \ln \left(\sqrt{1+x}+\sqrt{1+\sqrt{1+x}}\right)-\frac{8 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}+1\right) \sqrt{5}}{5}\right)}{5}$&$110$\\ default&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}+4 \sqrt{1+\sqrt{1+x}}+2 \ln \left(\sqrt{1+x}-\sqrt{1+\sqrt{1+x}}\right)-\frac{8 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}-1\right) \sqrt{5}}{5}\right)}{5}-2 \ln \left(\sqrt{1+x}+\sqrt{1+\sqrt{1+x}}\right)-\frac{8 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}+1\right) \sqrt{5}}{5}\right)}{5}$&$110$\\ \hline \end{longtable}"," ",0,"4/3*(1+(1+x)^(1/2))^(3/2)+4*(1+(1+x)^(1/2))^(1/2)+2*ln((1+x)^(1/2)-(1+(1+x)^(1/2))^(1/2))-8/5*5^(1/2)*arctanh(1/5*(2*(1+(1+x)^(1/2))^(1/2)-1)*5^(1/2))-2*ln((1+x)^(1/2)+(1+(1+x)^(1/2))^(1/2))-8/5*5^(1/2)*arctanh(1/5*(2*(1+(1+x)^(1/2))^(1/2)+1)*5^(1/2))","A"
1758,1,161,98,0.082000," ","int((a*x+b)^(1/2)/(a*b*x+(a*x+b)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\frac{\sqrt{a x +b}\, \sqrt{-b^{2}+\sqrt{a x +b}+b \left(a x +b \right)}}{b}-\frac{3 \left(\frac{\sqrt{-b^{2}+\sqrt{a x +b}+b \left(a x +b \right)}}{b}-\frac{\ln \left(\frac{\frac{1}{2}+b \sqrt{a x +b}}{\sqrt{b}}+\sqrt{-b^{2}+\sqrt{a x +b}+b \left(a x +b \right)}\right)}{2 b^{\frac{3}{2}}}\right)}{2 b}+\sqrt{b}\, \ln \left(\frac{\frac{1}{2}+b \sqrt{a x +b}}{\sqrt{b}}+\sqrt{-b^{2}+\sqrt{a x +b}+b \left(a x +b \right)}\right)}{a}$&$161$\\ default&$\frac{\frac{\sqrt{a x +b}\, \sqrt{-b^{2}+\sqrt{a x +b}+b \left(a x +b \right)}}{b}-\frac{3 \left(\frac{\sqrt{-b^{2}+\sqrt{a x +b}+b \left(a x +b \right)}}{b}-\frac{\ln \left(\frac{\frac{1}{2}+b \sqrt{a x +b}}{\sqrt{b}}+\sqrt{-b^{2}+\sqrt{a x +b}+b \left(a x +b \right)}\right)}{2 b^{\frac{3}{2}}}\right)}{2 b}+\sqrt{b}\, \ln \left(\frac{\frac{1}{2}+b \sqrt{a x +b}}{\sqrt{b}}+\sqrt{-b^{2}+\sqrt{a x +b}+b \left(a x +b \right)}\right)}{a}$&$161$\\ \hline \end{longtable}"," ",0,"2/a*(1/2*(a*x+b)^(1/2)/b*(-b^2+(a*x+b)^(1/2)+b*(a*x+b))^(1/2)-3/4/b*(1/b*(-b^2+(a*x+b)^(1/2)+b*(a*x+b))^(1/2)-1/2/b^(3/2)*ln((1/2+b*(a*x+b)^(1/2))/b^(1/2)+(-b^2+(a*x+b)^(1/2)+b*(a*x+b))^(1/2)))+1/2*b^(1/2)*ln((1/2+b*(a*x+b)^(1/2))/b^(1/2)+(-b^2+(a*x+b)^(1/2)+b*(a*x+b))^(1/2)))","A"
1759,0,0,88,180.000000," ","int((a^2*x^4+b)^(1/2)/(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{a^{2} x^{4}+b}}{\sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}\, dx\]"," ",0,"int((a^2*x^4+b)^(1/2)/(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x)","F"
1760,1,165,13,0.596000," ","int(1/(e*x+f)/(d+(c+(a*x+b)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\munderset{\textit{\_R} =\RootOf \left(e \,\textit{\_Z}^{8}-4 e d \,\textit{\_Z}^{6}+\left(6 d^{2} e -2 c e \right) \textit{\_Z}^{4}+\left(-4 d^{3} e +4 c d e \right) \textit{\_Z}^{2}+d^{4} e -2 c \,d^{2} e +c^{2} e +a f -b e \right)}{\sum}\frac{\left(\textit{\_R}^{6}-3 d \,\textit{\_R}^{4}+\left(3 d^{2}-c \right) \textit{\_R}^{2}-d^{3}+c d \right) \ln \left(\sqrt{d +\sqrt{c +\sqrt{a x +b}}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5} d +3 \textit{\_R}^{3} d^{2}-\textit{\_R}^{3} c -\textit{\_R} \,d^{3}+\textit{\_R} c d}}{e}$&$165$\\ default&$\frac{\munderset{\textit{\_R} =\RootOf \left(e \,\textit{\_Z}^{8}-4 e d \,\textit{\_Z}^{6}+\left(6 d^{2} e -2 c e \right) \textit{\_Z}^{4}+\left(-4 d^{3} e +4 c d e \right) \textit{\_Z}^{2}+d^{4} e -2 c \,d^{2} e +c^{2} e +a f -b e \right)}{\sum}\frac{\left(\textit{\_R}^{6}-3 d \,\textit{\_R}^{4}+\left(3 d^{2}-c \right) \textit{\_R}^{2}-d^{3}+c d \right) \ln \left(\sqrt{d +\sqrt{c +\sqrt{a x +b}}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5} d +3 \textit{\_R}^{3} d^{2}-\textit{\_R}^{3} c -\textit{\_R} \,d^{3}+\textit{\_R} c d}}{e}$&$165$\\ \hline \end{longtable}"," ",0,"1/e*sum((_R^6-3*d*_R^4+(3*d^2-c)*_R^2-d^3+c*d)/(_R^7-3*_R^5*d+3*_R^3*d^2-_R^3*c-_R*d^3+_R*c*d)*ln((d+(c+(a*x+b)^(1/2))^(1/2))^(1/2)-_R),_R=RootOf(e*_Z^8-4*e*d*_Z^6+(6*d^2*e-2*c*e)*_Z^4+(-4*d^3*e+4*c*d*e)*_Z^2+d^4*e-2*c*d^2*e+c^2*e+a*f-b*e))","B"
1761,0,0,107,0.109000," ","int((-a*b+(-a+2*b)*x)/(x*(-a+x)*(-b+x)^2)^(1/4)/(-b^2+(-a*d+2*b)*x+(-1+d)*x^2),x)","\[\int \frac{-a b +\left(-a +2 b \right) x}{\left(x \left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{4}} \left(-b^{2}+\left(-a d +2 b \right) x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((-a*b+(-a+2*b)*x)/(x*(-a+x)*(-b+x)^2)^(1/4)/(-b^2+(-a*d+2*b)*x+(-1+d)*x^2),x)","F"
1762,1,33,97,1.488000," ","int(x^13*(x^3-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}} x^{14} \hypergeom \left(\left[-\frac{1}{3}, \frac{14}{3}\right], \left[\frac{17}{3}\right], x^{3}\right)}{14 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}}}$&$33$\\ risch&$\frac{x^{2} \left(972 x^{12}-81 x^{9}-99 x^{6}-132 x^{3}-220\right) \left(x^{3}-1\right)^{\frac{1}{3}}}{14580}-\frac{11 \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{2}{3}} x^{2} \hypergeom \left(\left[\frac{2}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], x^{3}\right)}{729 \mathrm{signum}\left(x^{3}-1\right)^{\frac{2}{3}}}$&$68$\\ trager&$\frac{x^{2} \left(972 x^{12}-81 x^{9}-99 x^{6}-132 x^{3}-220\right) \left(x^{3}-1\right)^{\frac{1}{3}}}{14580}+\frac{22 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+x^{3}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-1\right)}{2187}-\frac{22 \ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}-1\right)^{\frac{2}{3}}+3 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}+4 x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{2187}-\frac{22 \ln \left(\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}-1\right)^{\frac{2}{3}}+3 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}+4 x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2\right)}{2187}$&$330$\\ \hline \end{longtable}"," ",0,"1/14*signum(x^3-1)^(1/3)/(-signum(x^3-1))^(1/3)*x^14*hypergeom([-1/3,14/3],[17/3],x^3)","C"
1763,0,0,107,0.016000," ","int((a*b^2-2*(2*a-b)*b*x+(3*a-2*b)*x^2)/(x*(-a+x)*(-b+x)^2)^(1/4)/(a^3+(b^2*d-3*a^2)*x+(-2*b*d+3*a)*x^2+(-1+d)*x^3),x)","\[\int \frac{a \,b^{2}-2 \left(2 a -b \right) b x +\left(3 a -2 b \right) x^{2}}{\left(x \left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{4}} \left(a^{3}+\left(b^{2} d -3 a^{2}\right) x +\left(-2 b d +3 a \right) x^{2}+\left(-1+d \right) x^{3}\right)}\, dx\]"," ",0,"int((a*b^2-2*(2*a-b)*b*x+(3*a-2*b)*x^2)/(x*(-a+x)*(-b+x)^2)^(1/4)/(a^3+(b^2*d-3*a^2)*x+(-2*b*d+3*a)*x^2+(-1+d)*x^3),x)","F"
1764,1,12390,33,257.409000," ","int((2*x^3+x)^(1/3)*(x^4-1)/x^4/(x^4-x^2+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$12390$\\ risch&$\text{Expression too large to display}$&$13837$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1765,0,0,60,0.045000," ","int((2*a*x^4+b)/(a*x^4-b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{2 a \,x^{4}+b}{\left(a \,x^{4}-b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((2*a*x^4+b)/(a*x^4-b)/(a*x^4+b*x^2)^(1/4),x)","F"
1766,0,0,60,0.001000," ","int((2*a*x^4+b)/(a*x^4-b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{2 a \,x^{4}+b}{\left(a \,x^{4}-b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((2*a*x^4+b)/(a*x^4-b)/(a*x^4+b*x^2)^(1/4),x)","F"
1767,1,554,100,19.674000," ","int((x^6+1)*(x^6-x^3-1)^(2/3)/x^3/(x^6-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(x^{6}-x^{3}-1\right)^{\frac{2}{3}}}{2 x^{2}}-\frac{\ln \left(-\frac{-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}-x^{6}-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+3 \left(x^{6}-x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}-x^{3}-1\right)^{\frac{1}{3}} x^{2}+2 \left(x^{6}-x^{3}-1\right)^{\frac{2}{3}} x -2 \left(x^{6}-x^{3}-1\right)^{\frac{1}{3}} x^{2}+x^{3}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+1}{\left(-1+x \right) \left(x^{2}+x +1\right) \left(1+x \right) \left(x^{2}-x +1\right)}\right)}{3}-\ln \left(-\frac{-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}-x^{6}-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+3 \left(x^{6}-x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}-x^{3}-1\right)^{\frac{1}{3}} x^{2}+2 \left(x^{6}-x^{3}-1\right)^{\frac{2}{3}} x -2 \left(x^{6}-x^{3}-1\right)^{\frac{1}{3}} x^{2}+x^{3}+3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+1}{\left(-1+x \right) \left(x^{2}+x +1\right) \left(1+x \right) \left(x^{2}-x +1\right)}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+\RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(-\frac{-6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}-x^{6}+18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{3}+9 \left(x^{6}-x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{6}-x^{3}-1\right)^{\frac{1}{3}} x^{2}+15 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{3}+2 x^{3}+6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+1}{\left(-1+x \right) \left(x^{2}+x +1\right) \left(1+x \right) \left(x^{2}-x +1\right)}\right)$&$554$\\ trager&$\frac{\left(x^{6}-x^{3}-1\right)^{\frac{2}{3}}}{2 x^{2}}+\frac{\ln \left(\frac{-52381306816671365032443820416 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{6}+6321152051824005595778093916 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{6}+9460641135004029091636028597 x^{6}+412502791181286999630495085776 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{3}+128579063474650915534151073816 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{6}-x^{3}-1\right)^{\frac{2}{3}} x +225099344089661973022856910780 \left(x^{6}-x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{2}+130895513213451640791247094112 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{3}+18758278674138497751904742565 \left(x^{6}-x^{3}-1\right)^{\frac{2}{3}} x +8043356717917588124058819747 \left(x^{6}-x^{3}-1\right)^{\frac{1}{3}} x^{2}-7850319239684194352634151389 x^{3}+52381306816671365032443820416 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}-6321152051824005595778093916 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)-9460641135004029091636028597}{\left(-1+x \right) \left(x^{2}+x +1\right) \left(1+x \right) \left(x^{2}-x +1\right)}\right)}{3}-\frac{\ln \left(-\frac{179505046109384837383826497536 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{6}+122165295410673079952506457376 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{6}+11070963030323863830637905805 x^{6}-1413602238111405594397633668096 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{3}+128579063474650915534151073816 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{6}-x^{3}-1\right)^{\frac{2}{3}} x -96520280615011057488705836964 \left(x^{6}-x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{2}-342899530598945772555993049788 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{3}-8043356717917588124058819747 \left(x^{6}-x^{3}-1\right)^{\frac{2}{3}} x -18758278674138497751904742565 \left(x^{6}-x^{3}-1\right)^{\frac{1}{3}} x^{2}-20531604165327892922273934402 x^{3}-179505046109384837383826497536 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}-122165295410673079952506457376 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)-11070963030323863830637905805}{\left(-1+x \right) \left(x^{2}+x +1\right) \left(1+x \right) \left(x^{2}-x +1\right)}\right)}{3}-4 \ln \left(-\frac{179505046109384837383826497536 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{6}+122165295410673079952506457376 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{6}+11070963030323863830637905805 x^{6}-1413602238111405594397633668096 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{3}+128579063474650915534151073816 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{6}-x^{3}-1\right)^{\frac{2}{3}} x -96520280615011057488705836964 \left(x^{6}-x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{2}-342899530598945772555993049788 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{3}-8043356717917588124058819747 \left(x^{6}-x^{3}-1\right)^{\frac{2}{3}} x -18758278674138497751904742565 \left(x^{6}-x^{3}-1\right)^{\frac{1}{3}} x^{2}-20531604165327892922273934402 x^{3}-179505046109384837383826497536 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}-122165295410673079952506457376 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)-11070963030323863830637905805}{\left(-1+x \right) \left(x^{2}+x +1\right) \left(1+x \right) \left(x^{2}-x +1\right)}\right) \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)$&$710$\\ \hline \end{longtable}"," ",0,"1/2*(x^6-x^3-1)^(2/3)/x^2-1/3*ln(-(-3*RootOf(9*_Z^2+3*_Z+1)*x^6-x^6-9*RootOf(9*_Z^2+3*_Z+1)^2*x^3+3*(x^6-x^3-1)^(2/3)*RootOf(9*_Z^2+3*_Z+1)*x-3*RootOf(9*_Z^2+3*_Z+1)*(x^6-x^3-1)^(1/3)*x^2+2*(x^6-x^3-1)^(2/3)*x-2*(x^6-x^3-1)^(1/3)*x^2+x^3+3*RootOf(9*_Z^2+3*_Z+1)+1)/(-1+x)/(x^2+x+1)/(1+x)/(x^2-x+1))-ln(-(-3*RootOf(9*_Z^2+3*_Z+1)*x^6-x^6-9*RootOf(9*_Z^2+3*_Z+1)^2*x^3+3*(x^6-x^3-1)^(2/3)*RootOf(9*_Z^2+3*_Z+1)*x-3*RootOf(9*_Z^2+3*_Z+1)*(x^6-x^3-1)^(1/3)*x^2+2*(x^6-x^3-1)^(2/3)*x-2*(x^6-x^3-1)^(1/3)*x^2+x^3+3*RootOf(9*_Z^2+3*_Z+1)+1)/(-1+x)/(x^2+x+1)/(1+x)/(x^2-x+1))*RootOf(9*_Z^2+3*_Z+1)+RootOf(9*_Z^2+3*_Z+1)*ln(-(-6*RootOf(9*_Z^2+3*_Z+1)*x^6-x^6+18*RootOf(9*_Z^2+3*_Z+1)^2*x^3+9*(x^6-x^3-1)^(2/3)*RootOf(9*_Z^2+3*_Z+1)*x-9*RootOf(9*_Z^2+3*_Z+1)*(x^6-x^3-1)^(1/3)*x^2+15*RootOf(9*_Z^2+3*_Z+1)*x^3+2*x^3+6*RootOf(9*_Z^2+3*_Z+1)+1)/(-1+x)/(x^2+x+1)/(1+x)/(x^2-x+1))","C"
1768,1,251,102,14.947000," ","int((x^6+4)*(x^6-x^4-2)^(1/4)/x^2/(x^6-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{6}-x^{4}-2\right)^{\frac{1}{4}}}{x}-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{2 \sqrt{x^{6}-x^{4}-2}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}-\RootOf \left(\textit{\_Z}^{4}+1\right) x^{6}-2 \left(x^{6}-x^{4}-2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}+2 \RootOf \left(\textit{\_Z}^{4}+1\right) x^{4}+2 \left(x^{6}-x^{4}-2\right)^{\frac{3}{4}} x +2 \RootOf \left(\textit{\_Z}^{4}+1\right)}{x^{6}-2}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{6}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{4}+2 \left(x^{6}-x^{4}-2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}+2 \sqrt{x^{6}-x^{4}-2}\, \RootOf \left(\textit{\_Z}^{4}+1\right) x^{2}+2 \left(x^{6}-x^{4}-2\right)^{\frac{3}{4}} x +2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{x^{6}-2}\right)}{2}$&$251$\\ risch&$\frac{2 \left(x^{6}-x^{4}-2\right)^{\frac{1}{4}}}{x}+\frac{\left(\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{18}+4 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{16}-5 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{14}-2 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{18}-3 x^{16}+3 x^{14}-7 x^{12}+12 x^{10}-6 x^{8}+12 x^{6}-12 x^{4}-8\right)^{\frac{1}{4}} x^{13}+8 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{12}+4 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{18}-3 x^{16}+3 x^{14}-7 x^{12}+12 x^{10}-6 x^{8}+12 x^{6}-12 x^{4}-8\right)^{\frac{1}{4}} x^{11}-16 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{10}-2 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{18}-3 x^{16}+3 x^{14}-7 x^{12}+12 x^{10}-6 x^{8}+12 x^{6}-12 x^{4}-8\right)^{\frac{1}{4}} x^{9}+10 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{8}-2 \sqrt{x^{18}-3 x^{16}+3 x^{14}-7 x^{12}+12 x^{10}-6 x^{8}+12 x^{6}-12 x^{4}-8}\, x^{8}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{18}-3 x^{16}+3 x^{14}-7 x^{12}+12 x^{10}-6 x^{8}+12 x^{6}-12 x^{4}-8\right)^{\frac{3}{4}} x^{3}+8 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{18}-3 x^{16}+3 x^{14}-7 x^{12}+12 x^{10}-6 x^{8}+12 x^{6}-12 x^{4}-8\right)^{\frac{1}{4}} x^{7}-12 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{6}+2 \sqrt{x^{18}-3 x^{16}+3 x^{14}-7 x^{12}+12 x^{10}-6 x^{8}+12 x^{6}-12 x^{4}-8}\, x^{6}-8 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{18}-3 x^{16}+3 x^{14}-7 x^{12}+12 x^{10}-6 x^{8}+12 x^{6}-12 x^{4}-8\right)^{\frac{1}{4}} x^{5}+16 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{4}+4 \sqrt{x^{18}-3 x^{16}+3 x^{14}-7 x^{12}+12 x^{10}-6 x^{8}+12 x^{6}-12 x^{4}-8}\, x^{2}-8 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{18}-3 x^{16}+3 x^{14}-7 x^{12}+12 x^{10}-6 x^{8}+12 x^{6}-12 x^{4}-8\right)^{\frac{1}{4}} x +8 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}}{\left(x^{6}-2\right) \left(x^{6}-x^{4}-2\right)^{2}}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{18}-4 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{16}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{18}-3 x^{16}+3 x^{14}-7 x^{12}+12 x^{10}-6 x^{8}+12 x^{6}-12 x^{4}-8\right)^{\frac{1}{4}} x^{13}+5 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{14}-4 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{18}-3 x^{16}+3 x^{14}-7 x^{12}+12 x^{10}-6 x^{8}+12 x^{6}-12 x^{4}-8\right)^{\frac{1}{4}} x^{11}-8 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{12}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{18}-3 x^{16}+3 x^{14}-7 x^{12}+12 x^{10}-6 x^{8}+12 x^{6}-12 x^{4}-8\right)^{\frac{1}{4}} x^{9}+16 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{10}-8 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{18}-3 x^{16}+3 x^{14}-7 x^{12}+12 x^{10}-6 x^{8}+12 x^{6}-12 x^{4}-8\right)^{\frac{1}{4}} x^{7}-10 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{8}-2 \sqrt{x^{18}-3 x^{16}+3 x^{14}-7 x^{12}+12 x^{10}-6 x^{8}+12 x^{6}-12 x^{4}-8}\, x^{8}+8 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{18}-3 x^{16}+3 x^{14}-7 x^{12}+12 x^{10}-6 x^{8}+12 x^{6}-12 x^{4}-8\right)^{\frac{1}{4}} x^{5}+12 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{6}+2 \sqrt{x^{18}-3 x^{16}+3 x^{14}-7 x^{12}+12 x^{10}-6 x^{8}+12 x^{6}-12 x^{4}-8}\, x^{6}-2 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{18}-3 x^{16}+3 x^{14}-7 x^{12}+12 x^{10}-6 x^{8}+12 x^{6}-12 x^{4}-8\right)^{\frac{3}{4}} x^{3}-16 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{4}+8 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{18}-3 x^{16}+3 x^{14}-7 x^{12}+12 x^{10}-6 x^{8}+12 x^{6}-12 x^{4}-8\right)^{\frac{1}{4}} x +4 \sqrt{x^{18}-3 x^{16}+3 x^{14}-7 x^{12}+12 x^{10}-6 x^{8}+12 x^{6}-12 x^{4}-8}\, x^{2}-8 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}}{\left(x^{6}-2\right) \left(x^{6}-x^{4}-2\right)^{2}}\right)}{2}\right) \left(\left(x^{6}-x^{4}-2\right)^{3}\right)^{\frac{1}{4}}}{\left(x^{6}-x^{4}-2\right)^{\frac{3}{4}}}$&$1370$\\ \hline \end{longtable}"," ",0,"2*(x^6-x^4-2)^(1/4)/x-1/2*RootOf(_Z^4+1)^3*ln((2*(x^6-x^4-2)^(1/2)*RootOf(_Z^4+1)^3*x^2-RootOf(_Z^4+1)*x^6-2*(x^6-x^4-2)^(1/4)*RootOf(_Z^4+1)^2*x^3+2*RootOf(_Z^4+1)*x^4+2*(x^6-x^4-2)^(3/4)*x+2*RootOf(_Z^4+1))/(x^6-2))-1/2*RootOf(_Z^4+1)*ln((-RootOf(_Z^4+1)^3*x^6+2*RootOf(_Z^4+1)^3*x^4+2*(x^6-x^4-2)^(1/4)*RootOf(_Z^4+1)^2*x^3+2*(x^6-x^4-2)^(1/2)*RootOf(_Z^4+1)*x^2+2*(x^6-x^4-2)^(3/4)*x+2*RootOf(_Z^4+1)^3)/(x^6-2))","C"
1769,0,0,99,0.020000," ","int((a*x^8+b*x^7)^(1/4),x)","\[\int \left(a \,x^{8}+b \,x^{7}\right)^{\frac{1}{4}}\, dx\]"," ",0,"int((a*x^8+b*x^7)^(1/4),x)","F"
1770,1,87,81,2.539000," ","int((x^10-1)/(x^4+1)^(1/2)/(x^10+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\arctan \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{5}+\frac{4 \arctan \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{x \sqrt{\sqrt{5}-1}}\right)}{5 \sqrt{\sqrt{5}-1}}-\frac{4 \arctanh \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{x \sqrt{\sqrt{5}+1}}\right)}{5 \sqrt{\sqrt{5}+1}}\right) \sqrt{2}}{2}$&$87$\\ default&$\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{2 \left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{5 \sqrt{x^{4}+1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{6}+\textit{\_Z}^{4}-\textit{\_Z}^{2}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{6}+\underline{\hspace{1.25 ex}}\alpha^{4}-\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}+1\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}+1}\, \sqrt{x^{4}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}+1}}+\frac{2 \left(-1\right)^{\frac{3}{4}} \left(-\underline{\hspace{1.25 ex}}\alpha^{7}+\underline{\hspace{1.25 ex}}\alpha^{5}-\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \underline{\hspace{1.25 ex}}\alpha^{6}-i \underline{\hspace{1.25 ex}}\alpha^{4}+i \underline{\hspace{1.25 ex}}\alpha^{2}-i, i\right)}{\sqrt{x^{4}+1}}\right)\right)}{10}$&$260$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x +\sqrt{x^{4}+1}}{x^{2}+1}\right)}{10}-\frac{\RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}+25 \textit{\_Z}^{2}-1\right)^{2}+1\right) \ln \left(-\frac{25 \RootOf \left(625 \textit{\_Z}^{4}+25 \textit{\_Z}^{2}-1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}+25 \textit{\_Z}^{2}-1\right)^{2}+1\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}+25 \textit{\_Z}^{2}-1\right)^{2}+1\right) x^{4}-2 \sqrt{x^{4}+1}\, x -\RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}+25 \textit{\_Z}^{2}-1\right)^{2}+1\right)}{25 \RootOf \left(625 \textit{\_Z}^{4}+25 \textit{\_Z}^{2}-1\right)^{2} x^{2}+x^{4}+1}\right)}{5}-\RootOf \left(625 \textit{\_Z}^{4}+25 \textit{\_Z}^{2}-1\right) \ln \left(-\frac{125 \RootOf \left(625 \textit{\_Z}^{4}+25 \textit{\_Z}^{2}-1\right)^{3} x^{2}+5 \RootOf \left(625 \textit{\_Z}^{4}+25 \textit{\_Z}^{2}-1\right) x^{4}+5 \RootOf \left(625 \textit{\_Z}^{4}+25 \textit{\_Z}^{2}-1\right) x^{2}+2 \sqrt{x^{4}+1}\, x +5 \RootOf \left(625 \textit{\_Z}^{4}+25 \textit{\_Z}^{2}-1\right)}{25 \RootOf \left(625 \textit{\_Z}^{4}+25 \textit{\_Z}^{2}-1\right)^{2} x^{2}-x^{4}+x^{2}-1}\right)$&$329$\\ \hline \end{longtable}"," ",0,"1/2*(1/5*arctan(1/2*2^(1/2)/x*(x^4+1)^(1/2))+4/5/(5^(1/2)-1)^(1/2)*arctan(2^(1/2)/x*(x^4+1)^(1/2)/(5^(1/2)-1)^(1/2))-4/5/(5^(1/2)+1)^(1/2)*arctanh(2^(1/2)/x*(x^4+1)^(1/2)/(5^(1/2)+1)^(1/2)))*2^(1/2)","A"
1771,1,109,81,2.724000," ","int((x^10+1)/(x^4+1)^(1/2)/(x^10-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\ln \left(-1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{10}-\frac{\ln \left(1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{10}-\frac{4 \arctanh \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{x \sqrt{\sqrt{5}-1}}\right)}{5 \sqrt{\sqrt{5}-1}}+\frac{4 \arctan \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{x \sqrt{\sqrt{5}+1}}\right)}{5 \sqrt{\sqrt{5}+1}}\right) \sqrt{2}}{2}$&$109$\\ default&$\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{2 \left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{5 \sqrt{x^{4}+1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-\textit{\_Z} +1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{3}+x^{2}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha }\, \sqrt{x^{4}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha }}+\frac{2 \left(-1\right)^{\frac{3}{4}} \left(-\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +1\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \underline{\hspace{1.25 ex}}\alpha^{3}, i\right)}{\sqrt{x^{4}+1}}\right)\right)}{10}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+\textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{3}+x^{2}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha }\, \sqrt{x^{4}+1}}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha }}+\frac{2 \left(-1\right)^{\frac{3}{4}} \left(-\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  -1\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i \underline{\hspace{1.25 ex}}\alpha^{3}, i\right)}{\sqrt{x^{4}+1}}\right)\right)}{10}$&$377$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}-2\right) x +\sqrt{x^{4}+1}}{\left(-1+x \right) \left(1+x \right)}\right)}{10}+\frac{\RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-25 \textit{\_Z}^{2}-1\right)^{2}-1\right) \ln \left(\frac{25 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-25 \textit{\_Z}^{2}-1\right)^{2}-1\right) \RootOf \left(625 \textit{\_Z}^{4}-25 \textit{\_Z}^{2}-1\right)^{2} x^{2}-\RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-25 \textit{\_Z}^{2}-1\right)^{2}-1\right) x^{4}+2 \sqrt{x^{4}+1}\, x -\RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-25 \textit{\_Z}^{2}-1\right)^{2}-1\right)}{\left(25 \RootOf \left(625 \textit{\_Z}^{4}-25 \textit{\_Z}^{2}-1\right)^{2} x -x^{2}-x -1\right) \left(25 \RootOf \left(625 \textit{\_Z}^{4}-25 \textit{\_Z}^{2}-1\right)^{2} x +x^{2}-x +1\right)}\right)}{5}-\RootOf \left(625 \textit{\_Z}^{4}-25 \textit{\_Z}^{2}-1\right) \ln \left(\frac{125 \RootOf \left(625 \textit{\_Z}^{4}-25 \textit{\_Z}^{2}-1\right)^{3} x^{2}+5 \RootOf \left(625 \textit{\_Z}^{4}-25 \textit{\_Z}^{2}-1\right) x^{4}-5 \RootOf \left(625 \textit{\_Z}^{4}-25 \textit{\_Z}^{2}-1\right) x^{2}+2 \sqrt{x^{4}+1}\, x +5 \RootOf \left(625 \textit{\_Z}^{4}-25 \textit{\_Z}^{2}-1\right)}{\left(25 \RootOf \left(625 \textit{\_Z}^{4}-25 \textit{\_Z}^{2}-1\right)^{2} x +x^{2}+1\right) \left(25 \RootOf \left(625 \textit{\_Z}^{4}-25 \textit{\_Z}^{2}-1\right)^{2} x -x^{2}-1\right)}\right)$&$383$\\ \hline \end{longtable}"," ",0,"1/2*(1/10*ln(-1+1/2*2^(1/2)/x*(x^4+1)^(1/2))-1/10*ln(1+1/2*2^(1/2)/x*(x^4+1)^(1/2))-4/5/(5^(1/2)-1)^(1/2)*arctanh(2^(1/2)/x*(x^4+1)^(1/2)/(5^(1/2)-1)^(1/2))+4/5/(5^(1/2)+1)^(1/2)*arctan(2^(1/2)/x*(x^4+1)^(1/2)/(5^(1/2)+1)^(1/2)))*2^(1/2)","A"
1772,1,150,83,2.406000," ","int((x^16+1)/(x^4+1)^(1/2)/(x^16-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\ln \left(-1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{16}-\frac{2^{\frac{1}{4}} \ln \left(\frac{\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}+\frac{2^{\frac{3}{4}}}{2}}{\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}-\frac{2^{\frac{3}{4}}}{2}}\right)}{8}+\frac{2^{\frac{1}{4}} \arctan \left(\frac{2^{\frac{3}{4}} \sqrt{x^{4}+1}}{2 x}\right)}{4}+\frac{\arctan \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{8}-\frac{\ln \left(1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{16}-\frac{\sqrt{2}\, x}{4 \sqrt{x^{4}+1}}\right) \sqrt{2}}{2}$&$150$\\ default&$\frac{3 \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{4 \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{8}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{6}+x^{2}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}+1}\, \sqrt{x^{4}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}+1}}-\frac{2 \left(-1\right)^{\frac{3}{4}} \underline{\hspace{1.25 ex}}\alpha^{7} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \underline{\hspace{1.25 ex}}\alpha^{6}, i\right)}{\sqrt{x^{4}+1}}\right)\right)}{16}+\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{4 \sqrt{x^{4}+1}}+\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{4 \sqrt{x^{4}+1}}-\frac{x}{4 \sqrt{x^{4}+1}}$&$272$\\ risch&$\frac{3 \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{4 \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{8}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{6}+x^{2}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}+1}\, \sqrt{x^{4}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}+1}}-\frac{2 \left(-1\right)^{\frac{3}{4}} \underline{\hspace{1.25 ex}}\alpha^{7} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \underline{\hspace{1.25 ex}}\alpha^{6}, i\right)}{\sqrt{x^{4}+1}}\right)\right)}{16}+\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{4 \sqrt{x^{4}+1}}+\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{4 \sqrt{x^{4}+1}}-\frac{x}{4 \sqrt{x^{4}+1}}$&$272$\\ trager&$-\frac{x}{4 \sqrt{x^{4}+1}}-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x +\sqrt{x^{4}+1}}{\left(-1+x \right) \left(1+x \right)}\right)}{16}+\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x +\sqrt{x^{4}+1}}{x^{2}+1}\right)}{16}-\frac{\RootOf \left(\textit{\_Z}^{2}-2 \RootOf \left(\textit{\_Z}^{2}-2\right)\right) \ln \left(-\frac{x^{4} \RootOf \left(\textit{\_Z}^{2}-2 \RootOf \left(\textit{\_Z}^{2}-2\right)\right)+x^{2} \RootOf \left(\textit{\_Z}^{2}-2 \RootOf \left(\textit{\_Z}^{2}-2\right)\right) \RootOf \left(\textit{\_Z}^{2}-2\right)+4 \sqrt{x^{4}+1}\, x +\RootOf \left(\textit{\_Z}^{2}-2 \RootOf \left(\textit{\_Z}^{2}-2\right)\right)}{-x^{4}+\RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}-1}\right)}{16}+\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \RootOf \left(\textit{\_Z}^{2}+2\right) \RootOf \left(\textit{\_Z}^{2}-2 \RootOf \left(\textit{\_Z}^{2}-2\right)\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}-2\right) \RootOf \left(\textit{\_Z}^{2}-2 \RootOf \left(\textit{\_Z}^{2}-2\right)\right) \RootOf \left(\textit{\_Z}^{2}+2\right) x^{4}+\RootOf \left(\textit{\_Z}^{2}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}-2 \RootOf \left(\textit{\_Z}^{2}-2\right)\right) \RootOf \left(\textit{\_Z}^{2}+2\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}-2\right) \RootOf \left(\textit{\_Z}^{2}+2\right) \RootOf \left(\textit{\_Z}^{2}-2 \RootOf \left(\textit{\_Z}^{2}-2\right)\right)+8 \sqrt{x^{4}+1}\, x}{x^{4}+\RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}+1}\right)}{32}$&$329$\\ \hline \end{longtable}"," ",0,"1/2*(1/16*ln(-1+1/2*2^(1/2)/x*(x^4+1)^(1/2))-1/8*2^(1/4)*ln((1/2*2^(1/2)/x*(x^4+1)^(1/2)+1/2*2^(3/4))/(1/2*2^(1/2)/x*(x^4+1)^(1/2)-1/2*2^(3/4)))+1/4*2^(1/4)*arctan(1/2*2^(3/4)/x*(x^4+1)^(1/2))+1/8*arctan(1/2*2^(1/2)/x*(x^4+1)^(1/2))-1/16*ln(1+1/2*2^(1/2)/x*(x^4+1)^(1/2))-1/4*2^(1/2)*x/(x^4+1)^(1/2))*2^(1/2)","A"
1773,1,85,97,0.084000," ","int((a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)/(1-(a*x+b)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{2 \left(\frac{2 \left(c +\sqrt{a x +b}\right)^{\frac{5}{2}}}{5}-\frac{2 c \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}+\frac{2 \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}+2 \sqrt{c +\sqrt{a x +b}}-2 \sqrt{1+c}\, \arctanh \left(\frac{\sqrt{c +\sqrt{a x +b}}}{\sqrt{1+c}}\right)\right)}{a}$&$85$\\ default&$-\frac{2 \left(\frac{2 \left(c +\sqrt{a x +b}\right)^{\frac{5}{2}}}{5}-\frac{2 c \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}+\frac{2 \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}+2 \sqrt{c +\sqrt{a x +b}}-2 \sqrt{1+c}\, \arctanh \left(\frac{\sqrt{c +\sqrt{a x +b}}}{\sqrt{1+c}}\right)\right)}{a}$&$85$\\ \hline \end{longtable}"," ",0,"-2/a*(2/5*(c+(a*x+b)^(1/2))^(5/2)-2/3*c*(c+(a*x+b)^(1/2))^(3/2)+2/3*(c+(a*x+b)^(1/2))^(3/2)+2*(c+(a*x+b)^(1/2))^(1/2)-2*(1+c)^(1/2)*arctanh((c+(a*x+b)^(1/2))^(1/2)/(1+c)^(1/2)))","A"
1774,0,0,93,0.036000," ","int(x*(x^2-1)^(1/2)*(x^2+x*(x^2-1)^(1/2))^(1/2),x)","\[\int x \sqrt{x^{2}-1}\, \sqrt{x^{2}+x \sqrt{x^{2}-1}}\, dx\]"," ",0,"int(x*(x^2-1)^(1/2)*(x^2+x*(x^2-1)^(1/2))^(1/2),x)","F"
1775,1,172,113,0.254000," ","int((p*x^2-q)*(p^2*x^4+q^2)^(1/2)*(b*x^3+a*(p*x^2+q)^3)/x^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{p b \sqrt{p^{2} x^{4}+q^{2}}}{2}-\frac{b \,p^{2} q \ln \left(\frac{p^{2} x^{2}}{\sqrt{p^{2}}}+\sqrt{p^{2} x^{4}+q^{2}}\right)}{2 \sqrt{p^{2}}}+\frac{b q \sqrt{p^{2} x^{4}+q^{2}}}{2 x^{2}}-\frac{p b \,q^{2} \ln \left(\frac{2 q^{2}+2 \sqrt{q^{2}}\, \sqrt{p^{2} x^{4}+q^{2}}}{x^{2}}\right)}{2 \sqrt{q^{2}}}+4 a \left(\frac{p q \left(p^{2} x^{4}+q^{2}\right)^{\frac{3}{2}} \sqrt{2}}{12 x^{3}}+\frac{\left(p^{2} x^{4}+q^{2}\right)^{\frac{5}{2}} \sqrt{2}}{40 x^{5}}\right) \sqrt{2}$&$172$\\ risch&$\frac{\sqrt{p^{2} x^{4}+q^{2}}\, q \left(12 a \,p^{2} q \,x^{4}+20 a p \,q^{2} x^{2}+6 a \,q^{3}+15 b \,x^{3}\right)}{30 x^{5}}+\frac{a \,p^{4} x^{3} \sqrt{p^{2} x^{4}+q^{2}}}{5}+\frac{2 a \,p^{3} q x \sqrt{p^{2} x^{4}+q^{2}}}{3}+\frac{p b \sqrt{p^{2} x^{4}+q^{2}}}{2}-\frac{b \,p^{2} q \ln \left(\frac{p^{2} x^{2}}{\sqrt{p^{2}}}+\sqrt{p^{2} x^{4}+q^{2}}\right)}{2 \sqrt{p^{2}}}-\frac{p b \,q^{2} \ln \left(\frac{2 q^{2}+2 \sqrt{q^{2}}\, \sqrt{p^{2} x^{4}+q^{2}}}{x^{2}}\right)}{2 \sqrt{q^{2}}}$&$196$\\ default&$a \,p^{4} \left(\frac{x^{3} \sqrt{p^{2} x^{4}+q^{2}}}{5}+\frac{2 i q^{3} \sqrt{1-\frac{i p \,x^{2}}{q}}\, \sqrt{1+\frac{i p \,x^{2}}{q}}\, \left(\EllipticF \left(x \sqrt{\frac{i p}{q}}, i\right)-\EllipticE \left(x \sqrt{\frac{i p}{q}}, i\right)\right)}{5 \sqrt{\frac{i p}{q}}\, \sqrt{p^{2} x^{4}+q^{2}}\, p}\right)+2 q a \,p^{3} \left(\frac{x \sqrt{p^{2} x^{4}+q^{2}}}{3}+\frac{2 q^{2} \sqrt{1-\frac{i p \,x^{2}}{q}}\, \sqrt{1+\frac{i p \,x^{2}}{q}}\, \EllipticF \left(x \sqrt{\frac{i p}{q}}, i\right)}{3 \sqrt{\frac{i p}{q}}\, \sqrt{p^{2} x^{4}+q^{2}}}\right)-2 q^{3} a p \left(-\frac{\sqrt{p^{2} x^{4}+q^{2}}}{3 x^{3}}+\frac{2 p^{2} \sqrt{1-\frac{i p \,x^{2}}{q}}\, \sqrt{1+\frac{i p \,x^{2}}{q}}\, \EllipticF \left(x \sqrt{\frac{i p}{q}}, i\right)}{3 \sqrt{\frac{i p}{q}}\, \sqrt{p^{2} x^{4}+q^{2}}}\right)+p b \left(\frac{\sqrt{p^{2} x^{4}+q^{2}}}{2}-\frac{q^{2} \ln \left(\frac{2 q^{2}+2 \sqrt{q^{2}}\, \sqrt{p^{2} x^{4}+q^{2}}}{x^{2}}\right)}{2 \sqrt{q^{2}}}\right)-q b \left(-\frac{\left(p^{2} x^{4}+q^{2}\right)^{\frac{3}{2}}}{2 q^{2} x^{2}}+\frac{p^{2} x^{2} \sqrt{p^{2} x^{4}+q^{2}}}{2 q^{2}}+\frac{p^{2} \ln \left(\frac{p^{2} x^{2}}{\sqrt{p^{2}}}+\sqrt{p^{2} x^{4}+q^{2}}\right)}{2 \sqrt{p^{2}}}\right)-a \,q^{4} \left(-\frac{\sqrt{p^{2} x^{4}+q^{2}}}{5 x^{5}}-\frac{2 p^{2} \sqrt{p^{2} x^{4}+q^{2}}}{5 q^{2} x}+\frac{2 i p^{3} \sqrt{1-\frac{i p \,x^{2}}{q}}\, \sqrt{1+\frac{i p \,x^{2}}{q}}\, \left(\EllipticF \left(x \sqrt{\frac{i p}{q}}, i\right)-\EllipticE \left(x \sqrt{\frac{i p}{q}}, i\right)\right)}{5 q \sqrt{\frac{i p}{q}}\, \sqrt{p^{2} x^{4}+q^{2}}}\right)$&$590$\\ \hline \end{longtable}"," ",0,"1/2*p*b*(p^2*x^4+q^2)^(1/2)-1/2*b*p^2*q*ln(p^2*x^2/(p^2)^(1/2)+(p^2*x^4+q^2)^(1/2))/(p^2)^(1/2)+1/2*b*q/x^2*(p^2*x^4+q^2)^(1/2)-1/2*p*b*q^2/(q^2)^(1/2)*ln((2*q^2+2*(q^2)^(1/2)*(p^2*x^4+q^2)^(1/2))/x^2)+4*a*(1/12*p*q*(p^2*x^4+q^2)^(3/2)*2^(1/2)/x^3+1/40*(p^2*x^4+q^2)^(5/2)*2^(1/2)/x^5)*2^(1/2)","A"
1776,0,0,93,0.020000," ","int((x^2-1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2),x)","\[\int \frac{\left(x^{2}-1\right) \sqrt{x^{2}+\sqrt{x^{4}+1}}}{\sqrt{x^{4}+1}}\, dx\]"," ",0,"int((x^2-1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2),x)","F"
1777,1,85,82,0.076000," ","int(x*(1+x)^(1/2)/(x+(1+(1+x)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{2 \left(1+\sqrt{1+x}\right)^{3}}{3}-2 \left(1+\sqrt{1+x}\right)^{2}-\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}+2 \sqrt{1+x}+2+2 \ln \left(\sqrt{1+x}+\sqrt{1+\sqrt{1+x}}\right)+\frac{4 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}+1\right) \sqrt{5}}{5}\right)}{5}$&$85$\\ default&$\frac{2 \left(1+\sqrt{1+x}\right)^{3}}{3}-2 \left(1+\sqrt{1+x}\right)^{2}-\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}+2 \sqrt{1+x}+2+2 \ln \left(\sqrt{1+x}+\sqrt{1+\sqrt{1+x}}\right)+\frac{4 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}+1\right) \sqrt{5}}{5}\right)}{5}$&$85$\\ \hline \end{longtable}"," ",0,"2/3*(1+(1+x)^(1/2))^3-2*(1+(1+x)^(1/2))^2-4/3*(1+(1+x)^(1/2))^(3/2)+2*(1+x)^(1/2)+2+2*ln((1+x)^(1/2)+(1+(1+x)^(1/2))^(1/2))+4/5*5^(1/2)*arctanh(1/5*(2*(1+(1+x)^(1/2))^(1/2)+1)*5^(1/2))","A"
1778,1,3326,33,43.110000," ","int((x^3-x)^(1/3)*(x^4-10*x^2+8)/x^4/(x^4-2*x^2+4),x)","\[\text{output too large to display}\]"," ",0,"3/4*(4*x^4-5*x^2+1)/x^3*(x*(x^2-1))^(1/3)/(x^2-1)+(-53/408*ln((-1976*RootOf(4*_Z^6+1602*_Z^3+177957)^6*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*x^4+9880*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^6*x^2+99042*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2*x^2-1779258*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^4-7904*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^6-99042*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2+5721846*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^2+13652496*(x^6-2*x^4+x^2)^(2/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3+23426442*(x^6-2*x^4+x^2)^(1/3)*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2*x^2-314185365*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*x^4-3942588*RootOf(4*_Z^6+1602*_Z^3+177957)^3*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)-23426442*(x^6-2*x^4+x^2)^(1/3)*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2+805301055*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*x^2+3184910118*(x^6-2*x^4+x^2)^(2/3)-491115690*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204))/(-1+x)/(1+x)/(2*RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^2-8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+171*x^2-1602))*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)-1/1836*ln((-1976*RootOf(4*_Z^6+1602*_Z^3+177957)^6*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*x^4+9880*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^6*x^2+99042*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2*x^2-1779258*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^4-7904*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^6-99042*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2+5721846*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^2+13652496*(x^6-2*x^4+x^2)^(2/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3+23426442*(x^6-2*x^4+x^2)^(1/3)*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2*x^2-314185365*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*x^4-3942588*RootOf(4*_Z^6+1602*_Z^3+177957)^3*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)-23426442*(x^6-2*x^4+x^2)^(1/3)*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2+805301055*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*x^2+3184910118*(x^6-2*x^4+x^2)^(2/3)-491115690*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204))/(-1+x)/(1+x)/(2*RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^2-8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+171*x^2-1602))*RootOf(4*_Z^6+1602*_Z^3+177957)^3*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)+1/12*RootOf(4*_Z^6+1602*_Z^3+177957)*ln((-2054*RootOf(4*_Z^6+1602*_Z^3+177957)^7*x^4+10270*RootOf(4*_Z^6+1602*_Z^3+177957)^7*x^2+518976*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^5*x^2-4195971*RootOf(4*_Z^6+1602*_Z^3+177957)^4*x^4-8216*RootOf(4*_Z^6+1602*_Z^3+177957)^7-518976*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^5+8723637*RootOf(4*_Z^6+1602*_Z^3+177957)^4*x^2+18384327*(x^6-2*x^4+x^2)^(2/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3+59611707*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^2*x^2-478857015*RootOf(4*_Z^6+1602*_Z^3+177957)*x^4-4527666*RootOf(4*_Z^6+1602*_Z^3+177957)^4-59611707*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^2+907249005*RootOf(4*_Z^6+1602*_Z^3+177957)*x^2+2230554105*(x^6-2*x^4+x^2)^(2/3)-428391990*RootOf(4*_Z^6+1602*_Z^3+177957))/(-1+x)/(1+x)/(RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^2-4*RootOf(4*_Z^6+1602*_Z^3+177957)^3+315*x^2-801))+1/918*ln(-(1976*RootOf(4*_Z^6+1602*_Z^3+177957)^7*x^4-9880*RootOf(4*_Z^6+1602*_Z^3+177957)^7*x^2+198084*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^5*x^2-196482*RootOf(4*_Z^6+1602*_Z^3+177957)^4*x^4+7904*RootOf(4*_Z^6+1602*_Z^3+177957)^7-198084*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^5-2192034*RootOf(4*_Z^6+1602*_Z^3+177957)^4*x^2+6826248*(x^6-2*x^4+x^2)^(2/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3+32479758*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^2*x^2-81456570*RootOf(4*_Z^6+1602*_Z^3+177957)*x^4+2388516*RootOf(4*_Z^6+1602*_Z^3+177957)^4-32479758*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^2-98456202*RootOf(4*_Z^6+1602*_Z^3+177957)*x^2+1141457265*(x^6-2*x^4+x^2)^(2/3)+179912772*RootOf(4*_Z^6+1602*_Z^3+177957))/(-1+x)/(1+x)/(RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^2-4*RootOf(4*_Z^6+1602*_Z^3+177957)^3+315*x^2-801))*RootOf(4*_Z^6+1602*_Z^3+177957)^4+3/17*ln(-(1976*RootOf(4*_Z^6+1602*_Z^3+177957)^7*x^4-9880*RootOf(4*_Z^6+1602*_Z^3+177957)^7*x^2+198084*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^5*x^2-196482*RootOf(4*_Z^6+1602*_Z^3+177957)^4*x^4+7904*RootOf(4*_Z^6+1602*_Z^3+177957)^7-198084*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^5-2192034*RootOf(4*_Z^6+1602*_Z^3+177957)^4*x^2+6826248*(x^6-2*x^4+x^2)^(2/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3+32479758*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^2*x^2-81456570*RootOf(4*_Z^6+1602*_Z^3+177957)*x^4+2388516*RootOf(4*_Z^6+1602*_Z^3+177957)^4-32479758*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^2-98456202*RootOf(4*_Z^6+1602*_Z^3+177957)*x^2+1141457265*(x^6-2*x^4+x^2)^(2/3)+179912772*RootOf(4*_Z^6+1602*_Z^3+177957))/(-1+x)/(1+x)/(RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^2-4*RootOf(4*_Z^6+1602*_Z^3+177957)^3+315*x^2-801))*RootOf(4*_Z^6+1602*_Z^3+177957)+1/24*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*ln(-(4108*RootOf(4*_Z^6+1602*_Z^3+177957)^6*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*x^4-20540*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^6*x^2+518976*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2*x^2-5101434*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^4+16432*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^6-518976*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2+994734*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^2+73537308*(x^6-2*x^4+x^2)^(2/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3+148238181*(x^6-2*x^4+x^2)^(1/3)*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2*x^2-1744334514*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*x^4+4106700*RootOf(4*_Z^6+1602*_Z^3+177957)^3*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)-148238181*(x^6-2*x^4+x^2)^(1/3)*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2+1878514092*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*x^2+20529475434*(x^6-2*x^4+x^2)^(2/3)-134179578*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204))/(-1+x)/(1+x)/(2*RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^2-8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+171*x^2-1602)))*(x*(x^2-1))^(1/3)/x*(x^2*(x^2-1)^2)^(1/3)/(x^2-1)","B"
1779,1,3327,33,41.613000," ","int((x^3-x)^(1/3)*(x^4-10*x^2+8)/x^4/(x^4-2*x^2+4),x)","\[\text{output too large to display}\]"," ",0,"3/4*(4*x^4-5*x^2+1)/x^3*(x*(x^2-1))^(1/3)/(x^2-1)+(1/24*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*ln(-(4108*RootOf(4*_Z^6+1602*_Z^3+177957)^6*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*x^4-20540*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^6*x^2+518976*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2*x^2-5101434*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^4+16432*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^6-518976*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2+994734*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^2+73537308*(x^6-2*x^4+x^2)^(2/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3+148238181*(x^6-2*x^4+x^2)^(1/3)*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2*x^2-1744334514*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*x^4+4106700*RootOf(4*_Z^6+1602*_Z^3+177957)^3*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)-148238181*(x^6-2*x^4+x^2)^(1/3)*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2+1878514092*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*x^2+20529475434*(x^6-2*x^4+x^2)^(2/3)-134179578*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204))/(-1+x)/(1+x)/(2*RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^2-8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+171*x^2-1602))+1/918*ln(-(1976*RootOf(4*_Z^6+1602*_Z^3+177957)^7*x^4-9880*RootOf(4*_Z^6+1602*_Z^3+177957)^7*x^2+198084*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^5*x^2-196482*RootOf(4*_Z^6+1602*_Z^3+177957)^4*x^4+7904*RootOf(4*_Z^6+1602*_Z^3+177957)^7-198084*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^5-2192034*RootOf(4*_Z^6+1602*_Z^3+177957)^4*x^2+6826248*(x^6-2*x^4+x^2)^(2/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3+32479758*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^2*x^2-81456570*RootOf(4*_Z^6+1602*_Z^3+177957)*x^4+2388516*RootOf(4*_Z^6+1602*_Z^3+177957)^4-32479758*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^2-98456202*RootOf(4*_Z^6+1602*_Z^3+177957)*x^2+1141457265*(x^6-2*x^4+x^2)^(2/3)+179912772*RootOf(4*_Z^6+1602*_Z^3+177957))/(-1+x)/(1+x)/(RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^2-4*RootOf(4*_Z^6+1602*_Z^3+177957)^3+315*x^2-801))*RootOf(4*_Z^6+1602*_Z^3+177957)^4+3/17*ln(-(1976*RootOf(4*_Z^6+1602*_Z^3+177957)^7*x^4-9880*RootOf(4*_Z^6+1602*_Z^3+177957)^7*x^2+198084*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^5*x^2-196482*RootOf(4*_Z^6+1602*_Z^3+177957)^4*x^4+7904*RootOf(4*_Z^6+1602*_Z^3+177957)^7-198084*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^5-2192034*RootOf(4*_Z^6+1602*_Z^3+177957)^4*x^2+6826248*(x^6-2*x^4+x^2)^(2/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3+32479758*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^2*x^2-81456570*RootOf(4*_Z^6+1602*_Z^3+177957)*x^4+2388516*RootOf(4*_Z^6+1602*_Z^3+177957)^4-32479758*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^2-98456202*RootOf(4*_Z^6+1602*_Z^3+177957)*x^2+1141457265*(x^6-2*x^4+x^2)^(2/3)+179912772*RootOf(4*_Z^6+1602*_Z^3+177957))/(-1+x)/(1+x)/(RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^2-4*RootOf(4*_Z^6+1602*_Z^3+177957)^3+315*x^2-801))*RootOf(4*_Z^6+1602*_Z^3+177957)+1/12*RootOf(4*_Z^6+1602*_Z^3+177957)*ln(-(2054*RootOf(4*_Z^6+1602*_Z^3+177957)^7*x^4-10270*RootOf(4*_Z^6+1602*_Z^3+177957)^7*x^2-518976*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^5*x^2+4195971*RootOf(4*_Z^6+1602*_Z^3+177957)^4*x^4+8216*RootOf(4*_Z^6+1602*_Z^3+177957)^7+518976*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^5-8723637*RootOf(4*_Z^6+1602*_Z^3+177957)^4*x^2-18384327*(x^6-2*x^4+x^2)^(2/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3-59611707*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^2*x^2+478857015*RootOf(4*_Z^6+1602*_Z^3+177957)*x^4+4527666*RootOf(4*_Z^6+1602*_Z^3+177957)^4+59611707*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^2-907249005*RootOf(4*_Z^6+1602*_Z^3+177957)*x^2-2230554105*(x^6-2*x^4+x^2)^(2/3)+428391990*RootOf(4*_Z^6+1602*_Z^3+177957))/(-1+x)/(1+x)/(RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^2-4*RootOf(4*_Z^6+1602*_Z^3+177957)^3+315*x^2-801))-53/408*ln((-1976*RootOf(4*_Z^6+1602*_Z^3+177957)^6*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*x^4+9880*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^6*x^2+99042*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2*x^2-1779258*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^4-7904*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^6-99042*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2+5721846*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^2+13652496*(x^6-2*x^4+x^2)^(2/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3+23426442*(x^6-2*x^4+x^2)^(1/3)*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2*x^2-314185365*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*x^4-3942588*RootOf(4*_Z^6+1602*_Z^3+177957)^3*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)-23426442*(x^6-2*x^4+x^2)^(1/3)*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2+805301055*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*x^2+3184910118*(x^6-2*x^4+x^2)^(2/3)-491115690*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204))/(-1+x)/(1+x)/(2*RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^2-8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+171*x^2-1602))*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)-1/1836*ln((-1976*RootOf(4*_Z^6+1602*_Z^3+177957)^6*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*x^4+9880*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^6*x^2+99042*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2*x^2-1779258*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^4-7904*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^6-99042*(x^6-2*x^4+x^2)^(1/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2+5721846*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^2+13652496*(x^6-2*x^4+x^2)^(2/3)*RootOf(4*_Z^6+1602*_Z^3+177957)^3+23426442*(x^6-2*x^4+x^2)^(1/3)*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2*x^2-314185365*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*x^4-3942588*RootOf(4*_Z^6+1602*_Z^3+177957)^3*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)-23426442*(x^6-2*x^4+x^2)^(1/3)*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)^2+805301055*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204)*x^2+3184910118*(x^6-2*x^4+x^2)^(2/3)-491115690*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204))/(-1+x)/(1+x)/(2*RootOf(4*_Z^6+1602*_Z^3+177957)^3*x^2-8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+171*x^2-1602))*RootOf(4*_Z^6+1602*_Z^3+177957)^3*RootOf(_Z^3+8*RootOf(4*_Z^6+1602*_Z^3+177957)^3+3204))*(x*(x^2-1))^(1/3)/x*(x^2*(x^2-1)^2)^(1/3)/(x^2-1)","B"
1780,1,576,11,3.530000," ","int((x^2-1)/(x^2+1)/(x^4+x^3-x^2-x+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right) \ln \left(-\frac{8112 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{5} x +3536 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{3} x^{2}+4147 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{3} x -3536 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{3}+1820 \sqrt{x^{4}+x^{3}-x^{2}-x +1}\, \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}+85 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right) x^{2}+95 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right) x -85 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)+762 \sqrt{x^{4}+x^{3}-x^{2}-x +1}}{\left(13 x \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}+3 x -2\right)^{2}}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}+169 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}+78\right) \ln \left(-\frac{624 \RootOf \left(\textit{\_Z}^{2}+169 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}+78\right) \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{4} x -272 \RootOf \left(\textit{\_Z}^{2}+169 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}+78\right) \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2} x^{2}+257 \RootOf \left(\textit{\_Z}^{2}+169 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}+78\right) \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2} x +272 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+169 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}+78\right)-119 \RootOf \left(\textit{\_Z}^{2}+169 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}+78\right) x^{2}-1820 \sqrt{x^{4}+x^{3}-x^{2}-x +1}\, \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}-7 \RootOf \left(\textit{\_Z}^{2}+169 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}+78\right) x +119 \RootOf \left(\textit{\_Z}^{2}+169 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}+78\right)-78 \sqrt{x^{4}+x^{3}-x^{2}-x +1}}{\left(13 x \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}+3 x +2\right)^{2}}\right)}{26}$&$576$\\ default&$\text{Expression too large to display}$&$92318$\\ elliptic&$\text{Expression too large to display}$&$105692$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(13*_Z^4+6*_Z^2+1)*ln(-(8112*RootOf(13*_Z^4+6*_Z^2+1)^5*x+3536*RootOf(13*_Z^4+6*_Z^2+1)^3*x^2+4147*RootOf(13*_Z^4+6*_Z^2+1)^3*x-3536*RootOf(13*_Z^4+6*_Z^2+1)^3+1820*(x^4+x^3-x^2-x+1)^(1/2)*RootOf(13*_Z^4+6*_Z^2+1)^2+85*RootOf(13*_Z^4+6*_Z^2+1)*x^2+95*RootOf(13*_Z^4+6*_Z^2+1)*x-85*RootOf(13*_Z^4+6*_Z^2+1)+762*(x^4+x^3-x^2-x+1)^(1/2))/(13*x*RootOf(13*_Z^4+6*_Z^2+1)^2+3*x-2)^2)+1/26*RootOf(_Z^2+169*RootOf(13*_Z^4+6*_Z^2+1)^2+78)*ln(-(624*RootOf(_Z^2+169*RootOf(13*_Z^4+6*_Z^2+1)^2+78)*RootOf(13*_Z^4+6*_Z^2+1)^4*x-272*RootOf(_Z^2+169*RootOf(13*_Z^4+6*_Z^2+1)^2+78)*RootOf(13*_Z^4+6*_Z^2+1)^2*x^2+257*RootOf(_Z^2+169*RootOf(13*_Z^4+6*_Z^2+1)^2+78)*RootOf(13*_Z^4+6*_Z^2+1)^2*x+272*RootOf(13*_Z^4+6*_Z^2+1)^2*RootOf(_Z^2+169*RootOf(13*_Z^4+6*_Z^2+1)^2+78)-119*RootOf(_Z^2+169*RootOf(13*_Z^4+6*_Z^2+1)^2+78)*x^2-1820*(x^4+x^3-x^2-x+1)^(1/2)*RootOf(13*_Z^4+6*_Z^2+1)^2-7*RootOf(_Z^2+169*RootOf(13*_Z^4+6*_Z^2+1)^2+78)*x+119*RootOf(_Z^2+169*RootOf(13*_Z^4+6*_Z^2+1)^2+78)-78*(x^4+x^3-x^2-x+1)^(1/2))/(13*x*RootOf(13*_Z^4+6*_Z^2+1)^2+3*x+2)^2)","B"
1781,1,574,11,2.092000," ","int((x^2-1)/(x^2+1)/(x^4+x^3-x^2-x+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right) \ln \left(\frac{8112 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{5} x +3536 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{3} x^{2}+4147 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{3} x -3536 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{3}-1820 \sqrt{x^{4}+x^{3}-x^{2}-x +1}\, \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}+85 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right) x^{2}+95 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right) x -85 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)-762 \sqrt{x^{4}+x^{3}-x^{2}-x +1}}{\left(13 x \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}+3 x -2\right)^{2}}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{2}+169 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}+78\right) \ln \left(\frac{624 \RootOf \left(\textit{\_Z}^{2}+169 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}+78\right) \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{4} x -272 \RootOf \left(\textit{\_Z}^{2}+169 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}+78\right) \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2} x^{2}+257 \RootOf \left(\textit{\_Z}^{2}+169 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}+78\right) \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2} x +272 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+169 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}+78\right)+1820 \sqrt{x^{4}+x^{3}-x^{2}-x +1}\, \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}-119 \RootOf \left(\textit{\_Z}^{2}+169 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}+78\right) x^{2}-7 \RootOf \left(\textit{\_Z}^{2}+169 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}+78\right) x +119 \RootOf \left(\textit{\_Z}^{2}+169 \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}+78\right)+78 \sqrt{x^{4}+x^{3}-x^{2}-x +1}}{\left(13 x \RootOf \left(13 \textit{\_Z}^{4}+6 \textit{\_Z}^{2}+1\right)^{2}+3 x +2\right)^{2}}\right)}{26}$&$574$\\ default&$\text{Expression too large to display}$&$92318$\\ elliptic&$\text{Expression too large to display}$&$105692$\\ \hline \end{longtable}"," ",0,"-1/2*RootOf(13*_Z^4+6*_Z^2+1)*ln((8112*RootOf(13*_Z^4+6*_Z^2+1)^5*x+3536*RootOf(13*_Z^4+6*_Z^2+1)^3*x^2+4147*RootOf(13*_Z^4+6*_Z^2+1)^3*x-3536*RootOf(13*_Z^4+6*_Z^2+1)^3-1820*(x^4+x^3-x^2-x+1)^(1/2)*RootOf(13*_Z^4+6*_Z^2+1)^2+85*RootOf(13*_Z^4+6*_Z^2+1)*x^2+95*RootOf(13*_Z^4+6*_Z^2+1)*x-85*RootOf(13*_Z^4+6*_Z^2+1)-762*(x^4+x^3-x^2-x+1)^(1/2))/(13*x*RootOf(13*_Z^4+6*_Z^2+1)^2+3*x-2)^2)-1/26*RootOf(_Z^2+169*RootOf(13*_Z^4+6*_Z^2+1)^2+78)*ln((624*RootOf(_Z^2+169*RootOf(13*_Z^4+6*_Z^2+1)^2+78)*RootOf(13*_Z^4+6*_Z^2+1)^4*x-272*RootOf(_Z^2+169*RootOf(13*_Z^4+6*_Z^2+1)^2+78)*RootOf(13*_Z^4+6*_Z^2+1)^2*x^2+257*RootOf(_Z^2+169*RootOf(13*_Z^4+6*_Z^2+1)^2+78)*RootOf(13*_Z^4+6*_Z^2+1)^2*x+272*RootOf(13*_Z^4+6*_Z^2+1)^2*RootOf(_Z^2+169*RootOf(13*_Z^4+6*_Z^2+1)^2+78)+1820*(x^4+x^3-x^2-x+1)^(1/2)*RootOf(13*_Z^4+6*_Z^2+1)^2-119*RootOf(_Z^2+169*RootOf(13*_Z^4+6*_Z^2+1)^2+78)*x^2-7*RootOf(_Z^2+169*RootOf(13*_Z^4+6*_Z^2+1)^2+78)*x+119*RootOf(_Z^2+169*RootOf(13*_Z^4+6*_Z^2+1)^2+78)+78*(x^4+x^3-x^2-x+1)^(1/2))/(13*x*RootOf(13*_Z^4+6*_Z^2+1)^2+3*x+2)^2)","B"
1782,1,399,11,2.360000," ","int((x^4-1)/(x^4+1)/(x^4+x^3-x^2-x+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right) \ln \left(-\frac{12 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{3} x +8 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2} \sqrt{x^{4}+x^{3}-x^{2}-x +1}+3 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right) x^{2}+3 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right) x -3 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)+\sqrt{x^{4}+x^{3}-x^{2}-x +1}}{12 x \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+x^{2}+x -1}\right)+\frac{\RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+6\right) \ln \left(-\frac{12 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+6\right) x -48 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2} \sqrt{x^{4}+x^{3}-x^{2}-x +1}-3 \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+6\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+6\right) x +3 \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+6\right)-2 \sqrt{x^{4}+x^{3}-x^{2}-x +1}}{12 x \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}-x^{2}+x +1}\right)}{6}$&$399$\\ default&$\text{Expression too large to display}$&$3623$\\ elliptic&$\text{Expression too large to display}$&$3623$\\ \hline \end{longtable}"," ",0,"-RootOf(48*_Z^4+8*_Z^2+1)*ln(-(12*RootOf(48*_Z^4+8*_Z^2+1)^3*x+8*RootOf(48*_Z^4+8*_Z^2+1)^2*(x^4+x^3-x^2-x+1)^(1/2)+3*RootOf(48*_Z^4+8*_Z^2+1)*x^2+3*RootOf(48*_Z^4+8*_Z^2+1)*x-3*RootOf(48*_Z^4+8*_Z^2+1)+(x^4+x^3-x^2-x+1)^(1/2))/(12*x*RootOf(48*_Z^4+8*_Z^2+1)^2+x^2+x-1))+1/6*RootOf(_Z^2+36*RootOf(48*_Z^4+8*_Z^2+1)^2+6)*ln(-(12*RootOf(48*_Z^4+8*_Z^2+1)^2*RootOf(_Z^2+36*RootOf(48*_Z^4+8*_Z^2+1)^2+6)*x-48*RootOf(48*_Z^4+8*_Z^2+1)^2*(x^4+x^3-x^2-x+1)^(1/2)-3*RootOf(_Z^2+36*RootOf(48*_Z^4+8*_Z^2+1)^2+6)*x^2-RootOf(_Z^2+36*RootOf(48*_Z^4+8*_Z^2+1)^2+6)*x+3*RootOf(_Z^2+36*RootOf(48*_Z^4+8*_Z^2+1)^2+6)-2*(x^4+x^3-x^2-x+1)^(1/2))/(12*x*RootOf(48*_Z^4+8*_Z^2+1)^2-x^2+x+1))","B"
1783,1,397,11,1.951000," ","int((x^4-1)/(x^4+1)/(x^4+x^3-x^2-x+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right) \ln \left(-\frac{-12 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{3} x +8 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2} \sqrt{x^{4}+x^{3}-x^{2}-x +1}-3 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right) x^{2}-3 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right) x +\sqrt{x^{4}+x^{3}-x^{2}-x +1}+3 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)}{12 x \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+x^{2}+x -1}\right)-\frac{\RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+6\right) \ln \left(\frac{12 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+6\right) x +48 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2} \sqrt{x^{4}+x^{3}-x^{2}-x +1}-3 \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+6\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+6\right) x +2 \sqrt{x^{4}+x^{3}-x^{2}-x +1}+3 \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+6\right)}{12 x \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}-x^{2}+x +1}\right)}{6}$&$397$\\ default&$\text{Expression too large to display}$&$3623$\\ elliptic&$\text{Expression too large to display}$&$3623$\\ \hline \end{longtable}"," ",0,"RootOf(48*_Z^4+8*_Z^2+1)*ln(-(-12*RootOf(48*_Z^4+8*_Z^2+1)^3*x+8*RootOf(48*_Z^4+8*_Z^2+1)^2*(x^4+x^3-x^2-x+1)^(1/2)-3*RootOf(48*_Z^4+8*_Z^2+1)*x^2-3*RootOf(48*_Z^4+8*_Z^2+1)*x+(x^4+x^3-x^2-x+1)^(1/2)+3*RootOf(48*_Z^4+8*_Z^2+1))/(12*x*RootOf(48*_Z^4+8*_Z^2+1)^2+x^2+x-1))-1/6*RootOf(_Z^2+36*RootOf(48*_Z^4+8*_Z^2+1)^2+6)*ln((12*RootOf(48*_Z^4+8*_Z^2+1)^2*RootOf(_Z^2+36*RootOf(48*_Z^4+8*_Z^2+1)^2+6)*x+48*RootOf(48*_Z^4+8*_Z^2+1)^2*(x^4+x^3-x^2-x+1)^(1/2)-3*RootOf(_Z^2+36*RootOf(48*_Z^4+8*_Z^2+1)^2+6)*x^2-RootOf(_Z^2+36*RootOf(48*_Z^4+8*_Z^2+1)^2+6)*x+2*(x^4+x^3-x^2-x+1)^(1/2)+3*RootOf(_Z^2+36*RootOf(48*_Z^4+8*_Z^2+1)^2+6))/(12*x*RootOf(48*_Z^4+8*_Z^2+1)^2-x^2+x+1))","B"
1784,0,0,88,0.014000," ","int((a*x^8+b)/x^6/(a*x^4-b)/(a*x^4+b)^(3/4),x)","\[\int \frac{a \,x^{8}+b}{x^{6} \left(a \,x^{4}-b \right) \left(a \,x^{4}+b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int((a*x^8+b)/x^6/(a*x^4-b)/(a*x^4+b)^(3/4),x)","F"
1785,0,0,11,0.026000," ","int((2*a*x^4-b)/(a*x^4-b)^(1/4)/(2*a*x^8-c*x^4-2*b),x)","\[\int \frac{2 a \,x^{4}-b}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(2 a \,x^{8}-c \,x^{4}-2 b \right)}\, dx\]"," ",0,"int((2*a*x^4-b)/(a*x^4-b)^(1/4)/(2*a*x^8-c*x^4-2*b),x)","F"
1786,0,0,11,0.001000," ","int((2*a*x^4-b)/(a*x^4-b)^(1/4)/(2*a*x^8-c*x^4-2*b),x)","\[\int \frac{2 a \,x^{4}-b}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(2 a \,x^{8}-c \,x^{4}-2 b \right)}\, dx\]"," ",0,"int((2*a*x^4-b)/(a*x^4-b)^(1/4)/(2*a*x^8-c*x^4-2*b),x)","F"
1787,0,0,109,0.020000," ","int((-a*b-a*c+3*b*c+2*(a-b-c)*x+x^2)/((-a+x)*(-b+x)*(-c+x))^(1/4)/(-a^3-b*c*d+(3*a^2+b*d+c*d)*x-(3*a+d)*x^2+x^3),x)","\[\int \frac{-a b -a c +3 b c +2 \left(a -b -c \right) x +x^{2}}{\left(\left(-a +x \right) \left(-b +x \right) \left(-c +x \right)\right)^{\frac{1}{4}} \left(-a^{3}-b c d +\left(3 a^{2}+b d +c d \right) x -\left(3 a +d \right) x^{2}+x^{3}\right)}\, dx\]"," ",0,"int((-a*b-a*c+3*b*c+2*(a-b-c)*x+x^2)/((-a+x)*(-b+x)*(-c+x))^(1/4)/(-a^3-b*c*d+(3*a^2+b*d+c*d)*x-(3*a+d)*x^2+x^3),x)","F"
1788,0,0,89,0.040000," ","int(1/(a*x-b)/(a^2*x^3+b^2*x)^(1/4),x)","\[\int \frac{1}{\left(a x -b \right) \left(a^{2} x^{3}+b^{2} x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(a*x-b)/(a^2*x^3+b^2*x)^(1/4),x)","F"
1789,1,360,101,2.133000," ","int((x^2+2)*(x^2-2*x-2)*(x^4-3*x^2+4)^(1/2)/x^2/(x^2-2)/(2*x^2+x-4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\frac{5 \arcsinh \left(\frac{2 \sqrt{7}\, \left(x^{2}-\frac{3}{2}\right)}{7}\right)}{8}-\frac{160 \arctanh \left(\frac{-3 x^{2}+8}{4 \sqrt{x^{4}-3 x^{2}+4}}\right)}{\left(17+\sqrt{33}\right) \left(-17+\sqrt{33}\right)}-\frac{25 \left(-297+25 \sqrt{33}\right) \sqrt{33}\, \arctanh \left(\frac{\frac{85}{4}-\frac{5 \sqrt{33}}{4}+4 \left(\frac{5}{4}-\frac{\sqrt{33}}{4}\right) \left(x^{2}-\frac{17}{8}+\frac{\sqrt{33}}{8}\right)}{\left(\frac{\sqrt{165}}{8}-\frac{\sqrt{5}}{8}\right) \sqrt{64 \left(x^{2}-\frac{17}{8}+\frac{\sqrt{33}}{8}\right)^{2}+64 \left(\frac{5}{4}-\frac{\sqrt{33}}{4}\right) \left(x^{2}-\frac{17}{8}+\frac{\sqrt{33}}{8}\right)+170-10 \sqrt{33}}}\right)}{1056 \left(-17+\sqrt{33}\right) \left(\frac{\sqrt{165}}{8}-\frac{\sqrt{5}}{8}\right)}+\frac{25 \left(297+25 \sqrt{33}\right) \sqrt{33}\, \arctanh \left(\frac{\frac{85}{4}+\frac{5 \sqrt{33}}{4}+4 \left(\frac{5}{4}+\frac{\sqrt{33}}{4}\right) \left(x^{2}-\frac{17}{8}-\frac{\sqrt{33}}{8}\right)}{\left(\frac{\sqrt{165}}{8}+\frac{\sqrt{5}}{8}\right) \sqrt{64 \left(x^{2}-\frac{17}{8}-\frac{\sqrt{33}}{8}\right)^{2}+64 \left(\frac{5}{4}+\frac{\sqrt{33}}{4}\right) \left(x^{2}-\frac{17}{8}-\frac{\sqrt{33}}{8}\right)+170+10 \sqrt{33}}}\right)}{1056 \left(17+\sqrt{33}\right) \left(\frac{\sqrt{165}}{8}+\frac{\sqrt{5}}{8}\right)}+\frac{\left(\frac{\sqrt{x^{4}-3 x^{2}+4}\, \sqrt{2}}{2 x}-\frac{5 \sqrt{10}\, \arctanh \left(\frac{\sqrt{10}\, \sqrt{x^{4}-3 x^{2}+4}\, \sqrt{2}}{5 x}\right)}{4}+2 \sqrt{2}\, \arctanh \left(\frac{\sqrt{x^{4}-3 x^{2}+4}}{x}\right)\right) \sqrt{2}}{2}$&$360$\\ trager&$\frac{\sqrt{x^{4}-3 x^{2}+4}}{2 x}+\frac{5 \RootOf \left(\textit{\_Z}^{2}-5\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-5\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{2}-5\right) x +5 \sqrt{x^{4}-3 x^{2}+4}-2 \RootOf \left(\textit{\_Z}^{2}-5\right)}{2 x^{2}+x -4}\right)}{4}-\frac{\ln \left(\frac{-131072-524288 x +65536 \sqrt{x^{4}-3 x^{2}+4}+30198 x^{20}-1296128 x^{9}-4373760 x^{10}+2095616 x^{7}-2336768 x^{5}-3865344 x^{6}-237568 x^{2}+1605632 x^{3}+4931072 x^{8}+1795584 x^{4}+624256 x^{11}+2875968 x^{12}+546720 x^{16}-128 x^{25}-3507 x^{22}+32744 x^{19}+16 x^{26}+1568 x^{23}+116 x^{24}-9128 x^{21}-154096 x^{18}-81008 x^{17}+156064 x^{15}-1437984 x^{14}-292096 x^{13}+16 \sqrt{x^{4}-3 x^{2}+4}\, x^{24}-128 \sqrt{x^{4}-3 x^{2}+4}\, x^{23}+140 \sqrt{x^{4}-3 x^{2}+4}\, x^{22}+1376 \sqrt{x^{4}-3 x^{2}+4}\, x^{21}-3311 \sqrt{x^{4}-3 x^{2}+4}\, x^{20}-6952 \sqrt{x^{4}-3 x^{2}+4}\, x^{19}+25088 \sqrt{x^{4}-3 x^{2}+4}\, x^{18}+21280 \sqrt{x^{4}-3 x^{2}+4}\, x^{17}-113776 \sqrt{x^{4}-3 x^{2}+4}\, x^{16}-44608 \sqrt{x^{4}-3 x^{2}+4}\, x^{15}+358208 \sqrt{x^{4}-3 x^{2}+4}\, x^{14}+77632 \sqrt{x^{4}-3 x^{2}+4}\, x^{13}-828960 \sqrt{x^{4}-3 x^{2}+4}\, x^{12}-155264 \sqrt{x^{4}-3 x^{2}+4}\, x^{11}+1432832 \sqrt{x^{4}-3 x^{2}+4}\, x^{10}+356864 \sqrt{x^{4}-3 x^{2}+4}\, x^{9}-1820416 \sqrt{x^{4}-3 x^{2}+4}\, x^{8}-680960 \sqrt{x^{4}-3 x^{2}+4}\, x^{7}+1605632 \sqrt{x^{4}-3 x^{2}+4}\, x^{6}+889856 \sqrt{x^{4}-3 x^{2}+4}\, x^{5}-847616 \sqrt{x^{4}-3 x^{2}+4}\, x^{4}-704512 \sqrt{x^{4}-3 x^{2}+4}\, x^{3}+143360 \sqrt{x^{4}-3 x^{2}+4}\, x^{2}+262144 \sqrt{x^{4}-3 x^{2}+4}\, x}{\left(x^{2}-2\right)^{8} x^{5}}\right)}{4}$&$646$\\ risch&$\frac{\sqrt{x^{4}-3 x^{2}+4}}{2 x}-\frac{5 \arcsinh \left(\frac{2 \sqrt{7}\, \left(x^{2}-\frac{3}{2}\right)}{7}\right)}{8}+\frac{9 \sqrt{1-\left(\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}}\, \sqrt{1-\left(\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{6+2 i \sqrt{7}}}{4}, \frac{\sqrt{2-6 i \sqrt{7}}}{4}\right)}{2 \sqrt{6+2 i \sqrt{7}}\, \sqrt{x^{4}-3 x^{2}+4}}+\frac{25 \sqrt{33}\, \arctanh \left(-\frac{5 x^{2}}{8 \sqrt{\frac{85}{32}-\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}+\frac{x^{2} \sqrt{33}}{8 \sqrt{\frac{85}{32}-\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}-\frac{13}{16 \sqrt{\frac{85}{32}-\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}-\frac{3 \sqrt{33}}{16 \sqrt{\frac{85}{32}-\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}\right)}{64 \sqrt{\frac{85}{32}-\frac{5 \sqrt{33}}{32}}}-\frac{25 \sqrt{33}\, \sqrt{1-\frac{3 x^{2}}{8}-\frac{i x^{2} \sqrt{7}}{8}}\, \sqrt{1-\frac{3 x^{2}}{8}+\frac{i x^{2} \sqrt{7}}{8}}\, \EllipticPi \left(\sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, x , \frac{1}{\left(\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) \left(-\frac{1}{4}+\frac{\sqrt{33}}{4}\right)^{2}}, \frac{\sqrt{\frac{3}{8}-\frac{i \sqrt{7}}{8}}}{\sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}}\right)}{32 \sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, \left(-\frac{1}{4}+\frac{\sqrt{33}}{4}\right) \sqrt{x^{4}-3 x^{2}+4}}-\frac{25 \arctanh \left(-\frac{5 x^{2}}{8 \sqrt{\frac{85}{32}-\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}+\frac{x^{2} \sqrt{33}}{8 \sqrt{\frac{85}{32}-\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}-\frac{13}{16 \sqrt{\frac{85}{32}-\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}-\frac{3 \sqrt{33}}{16 \sqrt{\frac{85}{32}-\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}\right)}{64 \sqrt{\frac{85}{32}-\frac{5 \sqrt{33}}{32}}}+\frac{25 \sqrt{1-\frac{3 x^{2}}{8}-\frac{i x^{2} \sqrt{7}}{8}}\, \sqrt{1-\frac{3 x^{2}}{8}+\frac{i x^{2} \sqrt{7}}{8}}\, \EllipticPi \left(\sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, x , \frac{1}{\left(\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) \left(-\frac{1}{4}+\frac{\sqrt{33}}{4}\right)^{2}}, \frac{\sqrt{\frac{3}{8}-\frac{i \sqrt{7}}{8}}}{\sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}}\right)}{32 \sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, \left(-\frac{1}{4}+\frac{\sqrt{33}}{4}\right) \sqrt{x^{4}-3 x^{2}+4}}+\frac{25 \sqrt{33}\, \arctanh \left(\frac{5 x^{2}}{8 \sqrt{\frac{85}{32}+\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}+\frac{x^{2} \sqrt{33}}{8 \sqrt{\frac{85}{32}+\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}+\frac{13}{16 \sqrt{\frac{85}{32}+\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}-\frac{3 \sqrt{33}}{16 \sqrt{\frac{85}{32}+\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}\right)}{64 \sqrt{\frac{85}{32}+\frac{5 \sqrt{33}}{32}}}+\frac{25 \sqrt{33}\, \sqrt{1-\frac{3 x^{2}}{8}-\frac{i x^{2} \sqrt{7}}{8}}\, \sqrt{1-\frac{3 x^{2}}{8}+\frac{i x^{2} \sqrt{7}}{8}}\, \EllipticPi \left(\sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, x , \frac{1}{\left(\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) \left(-\frac{1}{4}-\frac{\sqrt{33}}{4}\right)^{2}}, \frac{\sqrt{\frac{3}{8}-\frac{i \sqrt{7}}{8}}}{\sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}}\right)}{32 \sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, \left(-\frac{1}{4}-\frac{\sqrt{33}}{4}\right) \sqrt{x^{4}-3 x^{2}+4}}+\frac{25 \arctanh \left(\frac{5 x^{2}}{8 \sqrt{\frac{85}{32}+\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}+\frac{x^{2} \sqrt{33}}{8 \sqrt{\frac{85}{32}+\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}+\frac{13}{16 \sqrt{\frac{85}{32}+\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}-\frac{3 \sqrt{33}}{16 \sqrt{\frac{85}{32}+\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}\right)}{64 \sqrt{\frac{85}{32}+\frac{5 \sqrt{33}}{32}}}+\frac{25 \sqrt{1-\frac{3 x^{2}}{8}-\frac{i x^{2} \sqrt{7}}{8}}\, \sqrt{1-\frac{3 x^{2}}{8}+\frac{i x^{2} \sqrt{7}}{8}}\, \EllipticPi \left(\sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, x , \frac{1}{\left(\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) \left(-\frac{1}{4}-\frac{\sqrt{33}}{4}\right)^{2}}, \frac{\sqrt{\frac{3}{8}-\frac{i \sqrt{7}}{8}}}{\sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}}\right)}{32 \sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, \left(-\frac{1}{4}-\frac{\sqrt{33}}{4}\right) \sqrt{x^{4}-3 x^{2}+4}}+\frac{5 \arctanh \left(\frac{-3 x^{2}+8}{4 \sqrt{x^{4}-3 x^{2}+4}}\right)}{8}+\frac{4 \sqrt{1-\frac{3 x^{2}}{8}-\frac{i x^{2} \sqrt{7}}{8}}\, \sqrt{1-\frac{3 x^{2}}{8}+\frac{i x^{2} \sqrt{7}}{8}}\, \EllipticPi \left(\sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, x , \frac{1}{\frac{3}{4}+\frac{i \sqrt{7}}{4}}, \frac{\sqrt{\frac{3}{8}-\frac{i \sqrt{7}}{8}}}{\sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}}\right)}{\sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, \sqrt{x^{4}-3 x^{2}+4}}$&$1218$\\ default&$-\frac{3 \sqrt{1-\frac{3 x^{2}}{8}-\frac{i x^{2} \sqrt{7}}{8}}\, \sqrt{1-\frac{3 x^{2}}{8}+\frac{i x^{2} \sqrt{7}}{8}}\, \EllipticF \left(\frac{x \sqrt{6+2 i \sqrt{7}}}{4}, \frac{\sqrt{2-6 i \sqrt{7}}}{4}\right)}{2 \sqrt{6+2 i \sqrt{7}}\, \sqrt{x^{4}-3 x^{2}+4}}-\frac{35 \ln \left(2 x^{2}-3+2 \sqrt{x^{4}-3 x^{2}+4}\right)}{32}-\frac{32 \sqrt{1-\frac{3 x^{2}}{8}-\frac{i x^{2} \sqrt{7}}{8}}\, \sqrt{1-\frac{3 x^{2}}{8}+\frac{i x^{2} \sqrt{7}}{8}}\, \EllipticF \left(\frac{x \sqrt{6+2 i \sqrt{7}}}{4}, \frac{\sqrt{2-6 i \sqrt{7}}}{4}\right)}{\sqrt{6+2 i \sqrt{7}}\, \sqrt{x^{4}-3 x^{2}+4}\, \left(i \sqrt{7}-3\right)}+\frac{32 \sqrt{1-\frac{3 x^{2}}{8}-\frac{i x^{2} \sqrt{7}}{8}}\, \sqrt{1-\frac{3 x^{2}}{8}+\frac{i x^{2} \sqrt{7}}{8}}\, \EllipticE \left(\frac{x \sqrt{6+2 i \sqrt{7}}}{4}, \frac{\sqrt{2-6 i \sqrt{7}}}{4}\right)}{\sqrt{6+2 i \sqrt{7}}\, \sqrt{x^{4}-3 x^{2}+4}\, \left(i \sqrt{7}-3\right)}+\frac{25 \sqrt{33}\, \arctanh \left(-\frac{5 x^{2}}{8 \sqrt{\frac{85}{32}-\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}+\frac{x^{2} \sqrt{33}}{8 \sqrt{\frac{85}{32}-\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}-\frac{13}{16 \sqrt{\frac{85}{32}-\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}-\frac{3 \sqrt{33}}{16 \sqrt{\frac{85}{32}-\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}\right)}{64 \sqrt{\frac{85}{32}-\frac{5 \sqrt{33}}{32}}}-\frac{25 \sqrt{33}\, \sqrt{1-\frac{3 x^{2}}{8}-\frac{i x^{2} \sqrt{7}}{8}}\, \sqrt{1-\frac{3 x^{2}}{8}+\frac{i x^{2} \sqrt{7}}{8}}\, \EllipticPi \left(\sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, x , \frac{1}{\left(\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) \left(-\frac{1}{4}+\frac{\sqrt{33}}{4}\right)^{2}}, \frac{\sqrt{\frac{3}{8}-\frac{i \sqrt{7}}{8}}}{\sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}}\right)}{32 \sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, \left(-\frac{1}{4}+\frac{\sqrt{33}}{4}\right) \sqrt{x^{4}-3 x^{2}+4}}-\frac{25 \arctanh \left(-\frac{5 x^{2}}{8 \sqrt{\frac{85}{32}-\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}+\frac{x^{2} \sqrt{33}}{8 \sqrt{\frac{85}{32}-\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}-\frac{13}{16 \sqrt{\frac{85}{32}-\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}-\frac{3 \sqrt{33}}{16 \sqrt{\frac{85}{32}-\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}\right)}{64 \sqrt{\frac{85}{32}-\frac{5 \sqrt{33}}{32}}}+\frac{25 \sqrt{1-\frac{3 x^{2}}{8}-\frac{i x^{2} \sqrt{7}}{8}}\, \sqrt{1-\frac{3 x^{2}}{8}+\frac{i x^{2} \sqrt{7}}{8}}\, \EllipticPi \left(\sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, x , \frac{1}{\left(\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) \left(-\frac{1}{4}+\frac{\sqrt{33}}{4}\right)^{2}}, \frac{\sqrt{\frac{3}{8}-\frac{i \sqrt{7}}{8}}}{\sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}}\right)}{32 \sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, \left(-\frac{1}{4}+\frac{\sqrt{33}}{4}\right) \sqrt{x^{4}-3 x^{2}+4}}+\frac{25 \sqrt{33}\, \arctanh \left(\frac{5 x^{2}}{8 \sqrt{\frac{85}{32}+\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}+\frac{x^{2} \sqrt{33}}{8 \sqrt{\frac{85}{32}+\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}+\frac{13}{16 \sqrt{\frac{85}{32}+\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}-\frac{3 \sqrt{33}}{16 \sqrt{\frac{85}{32}+\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}\right)}{64 \sqrt{\frac{85}{32}+\frac{5 \sqrt{33}}{32}}}+\frac{25 \sqrt{33}\, \sqrt{1-\frac{3 x^{2}}{8}-\frac{i x^{2} \sqrt{7}}{8}}\, \sqrt{1-\frac{3 x^{2}}{8}+\frac{i x^{2} \sqrt{7}}{8}}\, \EllipticPi \left(\sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, x , \frac{1}{\left(\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) \left(-\frac{1}{4}-\frac{\sqrt{33}}{4}\right)^{2}}, \frac{\sqrt{\frac{3}{8}-\frac{i \sqrt{7}}{8}}}{\sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}}\right)}{32 \sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, \left(-\frac{1}{4}-\frac{\sqrt{33}}{4}\right) \sqrt{x^{4}-3 x^{2}+4}}+\frac{25 \arctanh \left(\frac{5 x^{2}}{8 \sqrt{\frac{85}{32}+\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}+\frac{x^{2} \sqrt{33}}{8 \sqrt{\frac{85}{32}+\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}+\frac{13}{16 \sqrt{\frac{85}{32}+\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}-\frac{3 \sqrt{33}}{16 \sqrt{\frac{85}{32}+\frac{5 \sqrt{33}}{32}}\, \sqrt{x^{4}-3 x^{2}+4}}\right)}{64 \sqrt{\frac{85}{32}+\frac{5 \sqrt{33}}{32}}}+\frac{25 \sqrt{1-\frac{3 x^{2}}{8}-\frac{i x^{2} \sqrt{7}}{8}}\, \sqrt{1-\frac{3 x^{2}}{8}+\frac{i x^{2} \sqrt{7}}{8}}\, \EllipticPi \left(\sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, x , \frac{1}{\left(\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) \left(-\frac{1}{4}-\frac{\sqrt{33}}{4}\right)^{2}}, \frac{\sqrt{\frac{3}{8}-\frac{i \sqrt{7}}{8}}}{\sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}}\right)}{32 \sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, \left(-\frac{1}{4}-\frac{\sqrt{33}}{4}\right) \sqrt{x^{4}-3 x^{2}+4}}+\frac{4 \sqrt{1-\frac{3 x^{2}}{8}-\frac{i x^{2} \sqrt{7}}{8}}\, \sqrt{1-\frac{3 x^{2}}{8}+\frac{i x^{2} \sqrt{7}}{8}}\, \EllipticPi \left(\sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, x , \frac{1}{\frac{3}{4}+\frac{i \sqrt{7}}{4}}, \frac{\sqrt{\frac{3}{8}-\frac{i \sqrt{7}}{8}}}{\sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}}\right)}{\sqrt{\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, \sqrt{x^{4}-3 x^{2}+4}}+\frac{\sqrt{x^{4}-3 x^{2}+4}}{2 x}+\frac{6 \sqrt{1-\left(\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}}\, \sqrt{1-\left(\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{6+2 i \sqrt{7}}}{4}, \frac{\sqrt{2-6 i \sqrt{7}}}{4}\right)}{\sqrt{6+2 i \sqrt{7}}\, \sqrt{x^{4}-3 x^{2}+4}}+\frac{32 \sqrt{1-\left(\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}}\, \sqrt{1-\left(\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}}\, \left(\EllipticF \left(\frac{x \sqrt{6+2 i \sqrt{7}}}{4}, \frac{\sqrt{2-6 i \sqrt{7}}}{4}\right)-\EllipticE \left(\frac{x \sqrt{6+2 i \sqrt{7}}}{4}, \frac{\sqrt{2-6 i \sqrt{7}}}{4}\right)\right)}{\sqrt{6+2 i \sqrt{7}}\, \sqrt{x^{4}-3 x^{2}+4}\, \left(i \sqrt{7}-3\right)}+\frac{15 \arcsinh \left(\frac{2 \sqrt{7}\, \left(x^{2}-\frac{3}{2}\right)}{7}\right)}{32}+\frac{5 \arctanh \left(\frac{-3 x^{2}+8}{4 \sqrt{x^{4}-3 x^{2}+4}}\right)}{8}$&$1643$\\ \hline \end{longtable}"," ",0,"-5/8*arcsinh(2/7*7^(1/2)*(x^2-3/2))-160/(17+33^(1/2))/(-17+33^(1/2))*arctanh(1/4*(-3*x^2+8)/(x^4-3*x^2+4)^(1/2))-25/1056*(-297+25*33^(1/2))*33^(1/2)/(-17+33^(1/2))/(1/8*165^(1/2)-1/8*5^(1/2))*arctanh(4*(85/16-5/16*33^(1/2)+(5/4-1/4*33^(1/2))*(x^2-17/8+1/8*33^(1/2)))/(1/8*165^(1/2)-1/8*5^(1/2))/(64*(x^2-17/8+1/8*33^(1/2))^2+64*(5/4-1/4*33^(1/2))*(x^2-17/8+1/8*33^(1/2))+170-10*33^(1/2))^(1/2))+25/1056*(297+25*33^(1/2))*33^(1/2)/(17+33^(1/2))/(1/8*165^(1/2)+1/8*5^(1/2))*arctanh(4*(85/16+5/16*33^(1/2)+(5/4+1/4*33^(1/2))*(x^2-17/8-1/8*33^(1/2)))/(1/8*165^(1/2)+1/8*5^(1/2))/(64*(x^2-17/8-1/8*33^(1/2))^2+64*(5/4+1/4*33^(1/2))*(x^2-17/8-1/8*33^(1/2))+170+10*33^(1/2))^(1/2))+1/2*(1/2*(x^4-3*x^2+4)^(1/2)*2^(1/2)/x-5/4*10^(1/2)*arctanh(1/5*10^(1/2)*(x^4-3*x^2+4)^(1/2)*2^(1/2)/x)+2*2^(1/2)*arctanh((x^4-3*x^2+4)^(1/2)/x))*2^(1/2)","B"
1790,1,1448,94,10.004000," ","int((1+x)/(-1+x)/(x^4+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1448$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^3-4)*ln(-(8332*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^3-1334*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^3-20830*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^2+3335*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^2+8332*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x-52824*(x^4+x^2)^(2/3)*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2-1334*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x+91368*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^2*x+151332*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*x+149976*RootOf(_Z^3-4)*x^3-24012*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*x^3+133312*RootOf(_Z^3-4)*x^2-21344*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*x^2+149976*RootOf(_Z^3-4)*x-605328*(x^4+x^2)^(2/3)-24012*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*x)/(-1+x)^2/x)-1/2*ln(-(4166*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^3+2750*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^3-10415*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^2-6875*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^2+4166*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x+26412*(x^4+x^2)^(2/3)*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2+2750*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x+151332*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^2*x+22842*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*x-41660*RootOf(_Z^3-4)*x^3-27500*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*x^3-149976*RootOf(_Z^3-4)*x^2-99000*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*x^2-41660*RootOf(_Z^3-4)*x-91368*(x^4+x^2)^(2/3)-27500*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*x)/(-1+x)^2/x)*RootOf(_Z^3-4)-1/4*ln(-(4166*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^3+2750*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^3-10415*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^2-6875*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^2+4166*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x+26412*(x^4+x^2)^(2/3)*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2+2750*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x+151332*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^2*x+22842*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*x-41660*RootOf(_Z^3-4)*x^3-27500*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*x^3-149976*RootOf(_Z^3-4)*x^2-99000*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*x^2-41660*RootOf(_Z^3-4)*x-91368*(x^4+x^2)^(2/3)-27500*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*x)/(-1+x)^2/x)*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)","C"
1791,1,303,93,0.175000," ","int((a^4*x^4-b^2)/(a^2*x^3+b*x)^(1/2)/(a^4*x^4+b^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{-b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}\, \sqrt{-\frac{x a}{\sqrt{-b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}+b x}}-\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{4} \textit{\_Z}^{4}+b^{2}\right)}{\sum}\frac{\sqrt{-b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}\, \sqrt{-\frac{\left(x -\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}\, \sqrt{-\frac{x a}{\sqrt{-b}}}\, \left(a \left(a^{2} \underline{\hspace{1.25 ex}}\alpha^{3}-b \underline{\hspace{1.25 ex}}\alpha  \right)-a^{2} \sqrt{-b}\, \underline{\hspace{1.25 ex}}\alpha^{2}+b \sqrt{-b}\right) \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}, -\frac{\underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{-b}\, a^{3}+\underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b -\underline{\hspace{1.25 ex}}\alpha  \sqrt{-b}\, a b -b^{2}}{2 b^{2}}, \frac{\sqrt{2}}{2}\right)}{\underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{x \left(a^{2} x^{2}+b \right)}}\right)}{4 a^{4}}$&$303$\\ elliptic&$\frac{\sqrt{-b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}\, \sqrt{-\frac{x a}{\sqrt{-b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}+b x}}-\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{4} \textit{\_Z}^{4}+b^{2}\right)}{\sum}\frac{\sqrt{-b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}\, \sqrt{-\frac{\left(x -\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}\, \sqrt{-\frac{x a}{\sqrt{-b}}}\, \left(a \left(a^{2} \underline{\hspace{1.25 ex}}\alpha^{3}-b \underline{\hspace{1.25 ex}}\alpha  \right)-a^{2} \sqrt{-b}\, \underline{\hspace{1.25 ex}}\alpha^{2}+b \sqrt{-b}\right) \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-b}}{a}\right) a}{\sqrt{-b}}}, -\frac{\underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{-b}\, a^{3}+\underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b -\underline{\hspace{1.25 ex}}\alpha  \sqrt{-b}\, a b -b^{2}}{2 b^{2}}, \frac{\sqrt{2}}{2}\right)}{\underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{x \left(a^{2} x^{2}+b \right)}}\right)}{4 a^{4}}$&$303$\\ \hline \end{longtable}"," ",0,"(-b)^(1/2)/a*((x+(-b)^(1/2)/a)/(-b)^(1/2)*a)^(1/2)*(-2*(x-(-b)^(1/2)/a)/(-b)^(1/2)*a)^(1/2)*(-x/(-b)^(1/2)*a)^(1/2)/(a^2*x^3+b*x)^(1/2)*EllipticF(((x+(-b)^(1/2)/a)/(-b)^(1/2)*a)^(1/2),1/2*2^(1/2))-1/4/a^4*2^(1/2)*sum(1/_alpha^3*(-b)^(1/2)*((x+(-b)^(1/2)/a)/(-b)^(1/2)*a)^(1/2)*(-(x-(-b)^(1/2)/a)/(-b)^(1/2)*a)^(1/2)*(-x/(-b)^(1/2)*a)^(1/2)/(x*(a^2*x^2+b))^(1/2)*(a*(_alpha^3*a^2-_alpha*b)-a^2*(-b)^(1/2)*_alpha^2+b*(-b)^(1/2))*EllipticPi(((x+(-b)^(1/2)/a)/(-b)^(1/2)*a)^(1/2),-1/2*(_alpha^3*(-b)^(1/2)*a^3+_alpha^2*a^2*b-_alpha*(-b)^(1/2)*a*b-b^2)/b^2,1/2*2^(1/2)),_alpha=RootOf(_Z^4*a^4+b^2))","C"
1792,1,1133,89,18.253000," ","int((x^2-1)/(x^2+1)/(x^5+x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1133$\\ \hline \end{longtable}"," ",0,"1/4*RootOf(_Z^3+4)*ln(-(RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^3*x^4+4*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*RootOf(_Z^3+4)^2*x^4-2*RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^2-8*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*x^2+6*(x^5+x)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)+RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^3+4*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*RootOf(_Z^3+4)^2-12*(x^5+x)^(1/3)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)*x+4*RootOf(_Z^3+4)*x^2+16*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^2-12*(x^5+x)^(2/3))/(x^2+1)^2)-1/4*ln(-(RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^3*x^4-2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*RootOf(_Z^3+4)^2*x^4-2*RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^2+4*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*x^2-6*(x^5+x)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)-2*RootOf(_Z^3+4)*x^4+4*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^4+RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^3-2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*RootOf(_Z^3+4)^2-6*(x^5+x)^(1/3)*RootOf(_Z^3+4)^2*x-2*RootOf(_Z^3+4)+4*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2))/(x^2+1)^2)*RootOf(_Z^3+4)-1/2*ln(-(RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^3*x^4-2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*RootOf(_Z^3+4)^2*x^4-2*RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^2+4*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*x^2-6*(x^5+x)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)-2*RootOf(_Z^3+4)*x^4+4*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^4+RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^3-2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*RootOf(_Z^3+4)^2-6*(x^5+x)^(1/3)*RootOf(_Z^3+4)^2*x-2*RootOf(_Z^3+4)+4*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2))/(x^2+1)^2)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)","C"
1793,1,11446,23,157.275000," ","int((x^4+1)*(x^4-x^2)^(1/4)/(x^8+x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$11446$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1794,1,11453,23,147.928000," ","int((x^4+1)*(x^4-x^2)^(1/4)/(x^8+x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$11453$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1795,0,0,36,0.036000," ","int((2*x^8-2*x^4+1)/(x^4-1)^(1/4)/(2*x^8-x^4-2),x)","\[\int \frac{2 x^{8}-2 x^{4}+1}{\left(x^{4}-1\right)^{\frac{1}{4}} \left(2 x^{8}-x^{4}-2\right)}\, dx\]"," ",0,"int((2*x^8-2*x^4+1)/(x^4-1)^(1/4)/(2*x^8-x^4-2),x)","F"
1796,0,0,95,0.036000," ","int((x^2-x)^(1/2)*(x^2-x*(x^2-x)^(1/2))^(1/2)/x^3,x)","\[\int \frac{\sqrt{x^{2}-x}\, \sqrt{x^{2}-x \sqrt{x^{2}-x}}}{x^{3}}\, dx\]"," ",0,"int((x^2-x)^(1/2)*(x^2-x*(x^2-x)^(1/2))^(1/2)/x^3,x)","F"
1797,0,0,92,0.194000," ","int((2*a*x+b)/(a*x^2+b*x+c)^(1/4)/(4*a*x^2+4*b*x+5*c),x)","\[\int \frac{2 a x +b}{\left(a \,x^{2}+b x +c \right)^{\frac{1}{4}} \left(4 a \,x^{2}+4 b x +5 c \right)}\, dx\]"," ",0,"int((2*a*x+b)/(a*x^2+b*x+c)^(1/4)/(4*a*x^2+4*b*x+5*c),x)","F"
1798,1,33,100,3.099000," ","int(x^6*(x^3-x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}} x^{\frac{22}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{11}{3}\right], \left[\frac{14}{3}\right], x^{2}\right)}{22 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}}}$&$33$\\ trager&$\frac{x \left(81 x^{6}-9 x^{4}-12 x^{2}-20\right) \left(x^{3}-x \right)^{\frac{1}{3}}}{648}+\frac{5 \ln \left(4959 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}+6768 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}-22833 \left(x^{3}-x \right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x +17718 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}-19836 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+7611 \left(x^{3}-x \right)^{\frac{2}{3}}-5355 x \left(x^{3}-x \right)^{\frac{1}{3}}-1705 x^{2}-9711 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+1085\right)}{243}+\frac{5 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(-6354 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}-6768 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}-16065 \left(x^{3}-x \right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x +20715 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+25416 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}+5355 \left(x^{3}-x \right)^{\frac{2}{3}}-7611 x \left(x^{3}-x \right)^{\frac{1}{3}}+1550 x^{2}-4494 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-465\right)}{81}$&$322$\\ risch&$\frac{x \left(81 x^{6}-9 x^{4}-12 x^{2}-20\right) \left(x \left(x^{2}-1\right)\right)^{\frac{1}{3}}}{648}+\frac{\left(\frac{5 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \ln \left(-\frac{47 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{4}+3207 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{4}-235 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{2}+2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}+6930 x^{4}+2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}-5601 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{2}+5238 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}+188 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2}-2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}+5238 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}-11340 x^{2}+2394 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)-5238 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}+4410}{\left(-1+x \right) \left(1+x \right)}\right)}{1458}-\frac{5 \ln \left(-\frac{47 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{4}-2643 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{4}-235 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{2}-2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}-10620 x^{4}-2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}+2781 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{2}-12312 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}+188 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2}+2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}-12312 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}+13806 x^{2}-138 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)+12312 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}-3186}{\left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)}{1458}-\frac{5 \ln \left(-\frac{47 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{4}-2643 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{4}-235 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{2}-2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}-10620 x^{4}-2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}+2781 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{2}-12312 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}+188 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2}+2925 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}-12312 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}+13806 x^{2}-138 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)+12312 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}-3186}{\left(-1+x \right) \left(1+x \right)}\right)}{243}\right) \left(x \left(x^{2}-1\right)\right)^{\frac{1}{3}} \left(x^{2} \left(x^{2}-1\right)^{2}\right)^{\frac{1}{3}}}{x \left(x^{2}-1\right)}$&$803$\\ \hline \end{longtable}"," ",0,"3/22*signum(x^2-1)^(1/3)/(-signum(x^2-1))^(1/3)*x^(22/3)*hypergeom([-1/3,11/3],[14/3],x^2)","C"
1799,1,352,106,0.441000," ","int(1/(x^3+x^2-x-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}+4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x +3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x -4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x +3 x \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}+x^{2}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+3 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-1}{1+x}\right)+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x +3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}-5 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-6 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x -3 \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}+3 x \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}+2 x^{2}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+3 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}+4 x +2}{1+x}\right)$&$352$\\ \hline \end{longtable}"," ",0,"-ln(-(4*RootOf(_Z^2-_Z+1)^2*x^2+4*RootOf(_Z^2-_Z+1)^2*x+3*RootOf(_Z^2-_Z+1)*(x^3+x^2-x-1)^(2/3)-3*RootOf(_Z^2-_Z+1)*(x^3+x^2-x-1)^(1/3)*x-4*RootOf(_Z^2-_Z+1)*x^2-3*RootOf(_Z^2-_Z+1)*(x^3+x^2-x-1)^(1/3)-2*RootOf(_Z^2-_Z+1)*x+3*x*(x^3+x^2-x-1)^(1/3)+x^2+2*RootOf(_Z^2-_Z+1)+3*(x^3+x^2-x-1)^(1/3)-1)/(1+x))+RootOf(_Z^2-_Z+1)*ln((2*RootOf(_Z^2-_Z+1)^2*x^2+2*RootOf(_Z^2-_Z+1)^2*x+3*RootOf(_Z^2-_Z+1)*(x^3+x^2-x-1)^(2/3)-5*RootOf(_Z^2-_Z+1)*x^2-6*RootOf(_Z^2-_Z+1)*x-3*(x^3+x^2-x-1)^(2/3)+3*x*(x^3+x^2-x-1)^(1/3)+2*x^2-RootOf(_Z^2-_Z+1)+3*(x^3+x^2-x-1)^(1/3)+4*x+2)/(1+x))","C"
1800,0,0,100,0.015000," ","int((2*x^4+1)/(x^4-1)/(x^4-x^2)^(1/4),x)","\[\int \frac{2 x^{4}+1}{\left(x^{4}-1\right) \left(x^{4}-x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((2*x^4+1)/(x^4-1)/(x^4-x^2)^(1/4),x)","F"
1801,0,0,102,0.010000," ","int((a*x^4-b)*(a*x^4+b*x^2)^(1/4)/x^2,x)","\[\int \frac{\left(a \,x^{4}-b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}{x^{2}}\, dx\]"," ",0,"int((a*x^4-b)*(a*x^4+b*x^2)^(1/4)/x^2,x)","F"
1802,0,0,102,0.009000," ","int((a*x^4+b)*(a*x^4+b*x^2)^(1/4)/x^2,x)","\[\int \frac{\left(a \,x^{4}+b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}{x^{2}}\, dx\]"," ",0,"int((a*x^4+b)*(a*x^4+b*x^2)^(1/4)/x^2,x)","F"
1803,0,0,62,0.044000," ","int((2*a*x^4+b)/(a*x^4-b)/(a*x^4-b*x^2)^(1/4),x)","\[\int \frac{2 a \,x^{4}+b}{\left(a \,x^{4}-b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((2*a*x^4+b)/(a*x^4-b)/(a*x^4-b*x^2)^(1/4),x)","F"
1804,0,0,62,0.002000," ","int((2*a*x^4+b)/(a*x^4-b)/(a*x^4-b*x^2)^(1/4),x)","\[\int \frac{2 a \,x^{4}+b}{\left(a \,x^{4}-b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((2*a*x^4+b)/(a*x^4-b)/(a*x^4-b*x^2)^(1/4),x)","F"
1805,0,0,102,0.008000," ","int((2*x^8-2*a*x^4-b)/(a*x^4-b)^(1/4),x)","\[\int \frac{2 x^{8}-2 a \,x^{4}-b}{\left(a \,x^{4}-b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((2*x^8-2*a*x^4-b)/(a*x^4-b)^(1/4),x)","F"
1806,1,1042,92,9.087000," ","int((-1+x)/(x^2-2*x-4)/(x^2-2*x-2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) \ln \left(\frac{2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{2}+\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{2}+3 \left(x^{2}-2 x -2\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x -2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x +6 \left(x^{2}-2 x -2\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)+2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) x^{2}+\RootOf \left(\textit{\_Z}^{3}-4\right) x^{2}-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) x -2 \RootOf \left(\textit{\_Z}^{3}-4\right) x -4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right)-2 \RootOf \left(\textit{\_Z}^{3}-4\right)}{x^{2}-2 x -4}\right)-\frac{\ln \left(-\frac{-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{2}+\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{2}+6 \left(x^{2}-2 x -2\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x -2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x +12 \left(x^{2}-2 x -2\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)+3 \left(x^{2}-2 x -2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \left(x^{2}-2 x -2\right)^{\frac{2}{3}}-8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right)+2 \RootOf \left(\textit{\_Z}^{3}-4\right)}{x^{2}-2 x -4}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)}{4}-\ln \left(-\frac{-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{2}+\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{2}+6 \left(x^{2}-2 x -2\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x -2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x +12 \left(x^{2}-2 x -2\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)+3 \left(x^{2}-2 x -2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \left(x^{2}-2 x -2\right)^{\frac{2}{3}}-8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right)+2 \RootOf \left(\textit{\_Z}^{3}-4\right)}{x^{2}-2 x -4}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right)$&$1042$\\ \hline \end{longtable}"," ",0,"RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*ln((2*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)^2*RootOf(_Z^3-4)^2*x^2+RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*RootOf(_Z^3-4)^3*x^2+3*(x^2-2*x-2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*RootOf(_Z^3-4)^2-4*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)^2*RootOf(_Z^3-4)^2*x-2*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*RootOf(_Z^3-4)^3*x+6*(x^2-2*x-2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*RootOf(_Z^3-4)+2*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*x^2+RootOf(_Z^3-4)*x^2-4*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*x-2*RootOf(_Z^3-4)*x-4*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)-2*RootOf(_Z^3-4))/(x^2-2*x-4))-1/4*ln(-(-4*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)^2*RootOf(_Z^3-4)^2*x^2+RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*RootOf(_Z^3-4)^3*x^2+6*(x^2-2*x-2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*RootOf(_Z^3-4)^2+8*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)^2*RootOf(_Z^3-4)^2*x-2*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*RootOf(_Z^3-4)^3*x+12*(x^2-2*x-2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*RootOf(_Z^3-4)+3*(x^2-2*x-2)^(1/3)*RootOf(_Z^3-4)^2+6*(x^2-2*x-2)^(2/3)-8*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)+2*RootOf(_Z^3-4))/(x^2-2*x-4))*RootOf(_Z^3-4)-ln(-(-4*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)^2*RootOf(_Z^3-4)^2*x^2+RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*RootOf(_Z^3-4)^3*x^2+6*(x^2-2*x-2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*RootOf(_Z^3-4)^2+8*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)^2*RootOf(_Z^3-4)^2*x-2*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*RootOf(_Z^3-4)^3*x+12*(x^2-2*x-2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*RootOf(_Z^3-4)+3*(x^2-2*x-2)^(1/3)*RootOf(_Z^3-4)^2+6*(x^2-2*x-2)^(2/3)-8*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)+2*RootOf(_Z^3-4))/(x^2-2*x-4))*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)","C"
1807,1,1196,92,8.277000," ","int(1/(1+x)/(x^2+2*x+3)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1196$\\ \hline \end{longtable}"," ",0,"1/4*RootOf(_Z^3-4)*ln((7*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x^2-2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x^2+14*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x-4*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x-48*(x^2+2*x+3)^(2/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^2+15*(x^2+2*x+3)^(1/3)*RootOf(_Z^3-4)^2+126*(x^2+2*x+3)^(1/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)+35*RootOf(_Z^3-4)*x^2-10*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^2+70*RootOf(_Z^3-4)*x-20*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x-126*(x^2+2*x+3)^(2/3)+133*RootOf(_Z^3-4)-38*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2))/(1+x)^2)-1/4*ln((7*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x^2+16*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x^2+14*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x+32*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x+48*(x^2+2*x+3)^(2/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^2+63*(x^2+2*x+3)^(1/3)*RootOf(_Z^3-4)^2+30*(x^2+2*x+3)^(1/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)-21*RootOf(_Z^3-4)*x^2-48*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^2-42*RootOf(_Z^3-4)*x-96*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x-30*(x^2+2*x+3)^(2/3)-133*RootOf(_Z^3-4)-304*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2))/(1+x)^2)*RootOf(_Z^3-4)-1/2*ln((7*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x^2+16*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x^2+14*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x+32*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x+48*(x^2+2*x+3)^(2/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^2+63*(x^2+2*x+3)^(1/3)*RootOf(_Z^3-4)^2+30*(x^2+2*x+3)^(1/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)-21*RootOf(_Z^3-4)*x^2-48*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^2-42*RootOf(_Z^3-4)*x-96*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x-30*(x^2+2*x+3)^(2/3)-133*RootOf(_Z^3-4)-304*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2))/(1+x)^2)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)","C"
1808,0,0,96,0.023000," ","int(1/x/(a*x^2-b)^(3/4),x)","\[\int \frac{1}{x \left(a \,x^{2}-b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x/(a*x^2-b)^(3/4),x)","F"
1809,0,0,93,0.022000," ","int(1/x/(a*x^3-b)^(1/3),x)","\[\int \frac{1}{x \left(a \,x^{3}-b \right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/x/(a*x^3-b)^(1/3),x)","F"
1810,1,391,95,0.207000," ","int((a^3*x^3-b^3)/(a^2*x^3+b^2*x)^(1/2)/(a^3*x^3+b^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{i b \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticF \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}+b^{2} x}}+\frac{2 i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}-\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha  a +2 b \right) \left(i \underline{\hspace{1.25 ex}}\alpha  a -i b +b \right) \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, -\frac{\underline{\hspace{1.25 ex}}\alpha  a -i b -b}{b}, \frac{\sqrt{2}}{2}\right)}{\left(2 \underline{\hspace{1.25 ex}}\alpha  a -b \right) \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}\right)}{3 a}-\frac{2 i b^{2} \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, -\frac{i b}{a \left(-\frac{i b}{a}+\frac{b}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{3 a^{2} \sqrt{a^{2} x^{3}+b^{2} x}\, \left(-\frac{i b}{a}+\frac{b}{a}\right)}$&$391$\\ elliptic&$\frac{i b \sqrt{-\frac{i x a}{b}+1}\, \sqrt{2}\, \sqrt{\frac{i x a}{b}+1}\, \sqrt{\frac{i x a}{b}}\, \EllipticF \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}+b^{2} x}}-\frac{2 a \sqrt{2}\, \sqrt{-\frac{i \left(a x +i b \right)}{b}}\, \sqrt{-\frac{i \left(-a x +i b \right)}{b}}\, \sqrt{\frac{i x a}{b}}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}-\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-\frac{i \left(a x +i b \right)}{b}}, \frac{-\underline{\hspace{1.25 ex}}\alpha  a +i b +b}{b}, \frac{\sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha^{2}}{2 \underline{\hspace{1.25 ex}}\alpha  a -b}\right)}{3 \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}+\frac{2 \sqrt{2}\, \sqrt{-\frac{i \left(a x +i b \right)}{b}}\, \sqrt{-\frac{i \left(-a x +i b \right)}{b}}\, \sqrt{\frac{i x a}{b}}\, b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}-\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-\frac{i \left(a x +i b \right)}{b}}, \frac{-\underline{\hspace{1.25 ex}}\alpha  a +i b +b}{b}, \frac{\sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha }{2 \underline{\hspace{1.25 ex}}\alpha  a -b}\right)}{\sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}-\frac{4 \sqrt{2}\, \sqrt{-\frac{i \left(a x +i b \right)}{b}}\, \sqrt{-\frac{i \left(-a x +i b \right)}{b}}\, \sqrt{\frac{i x a}{b}}\, b^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}-\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-\frac{i \left(a x +i b \right)}{b}}, \frac{-\underline{\hspace{1.25 ex}}\alpha  a +i b +b}{b}, \frac{\sqrt{2}}{2}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  a -b}\right)}{3 a \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}+\frac{2 i \sqrt{2}\, \sqrt{-\frac{i \left(a x +i b \right)}{b}}\, \sqrt{-\frac{i \left(-a x +i b \right)}{b}}\, \sqrt{\frac{i x a}{b}}\, b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}-\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-\frac{i \left(a x +i b \right)}{b}}, \frac{-\underline{\hspace{1.25 ex}}\alpha  a +i b +b}{b}, \frac{\sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha }{2 \underline{\hspace{1.25 ex}}\alpha  a -b}\right)}{3 \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}-\frac{4 i \sqrt{2}\, \sqrt{-\frac{i \left(a x +i b \right)}{b}}\, \sqrt{-\frac{i \left(-a x +i b \right)}{b}}\, \sqrt{\frac{i x a}{b}}\, b^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}-\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-\frac{i \left(a x +i b \right)}{b}}, \frac{-\underline{\hspace{1.25 ex}}\alpha  a +i b +b}{b}, \frac{\sqrt{2}}{2}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  a -b}\right)}{3 a \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}-\frac{2 i b^{2} \sqrt{-\frac{i x a}{b}+1}\, \sqrt{2}\, \sqrt{\frac{i x a}{b}+1}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, -\frac{i b}{a \left(-\frac{i b}{a}+b \right)}, \frac{\sqrt{2}}{2}\right)}{3 a \sqrt{a^{2} x^{3}+b^{2} x}\, \left(-\frac{i b}{a}+b \right)}$&$871$\\ \hline \end{longtable}"," ",0,"I*b/a*(-I*(x+I*b/a)/b*a)^(1/2)*2^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(a^2*x^3+b^2*x)^(1/2)*EllipticF((-I*(x+I*b/a)/b*a)^(1/2),1/2*2^(1/2))+2/3*I/a*2^(1/2)*sum((-_alpha*a+2*b)/(2*_alpha*a-b)*(I*_alpha*a-I*b+b)*(-I*(x+I*b/a)/b*a)^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(x*(a^2*x^2+b^2))^(1/2)*EllipticPi((-I*(x+I*b/a)/b*a)^(1/2),-(_alpha*a-b-I*b)/b,1/2*2^(1/2)),_alpha=RootOf(_Z^2*a^2-_Z*a*b+b^2))-2/3*I*b^2/a^2*(-I*(x+I*b/a)/b*a)^(1/2)*2^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(a^2*x^3+b^2*x)^(1/2)/(-I*b/a+b/a)*EllipticPi((-I*(x+I*b/a)/b*a)^(1/2),-I*b/a/(-I*b/a+b/a),1/2*2^(1/2))","C"
1811,1,387,95,0.194000," ","int((a^3*x^3+b^3)/(a^2*x^3+b^2*x)^(1/2)/(a^3*x^3-b^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{i b \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticF \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}+b^{2} x}}+\frac{2 i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}+\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha  a -2 b \right) \left(i \underline{\hspace{1.25 ex}}\alpha  a +i b +b \right) \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, \frac{\underline{\hspace{1.25 ex}}\alpha  a -i b +b}{b}, \frac{\sqrt{2}}{2}\right)}{\left(2 \underline{\hspace{1.25 ex}}\alpha  a +b \right) \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}\right)}{3 a}+\frac{2 i b^{2} \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, -\frac{i b}{a \left(-\frac{i b}{a}-\frac{b}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{3 a^{2} \sqrt{a^{2} x^{3}+b^{2} x}\, \left(-\frac{i b}{a}-\frac{b}{a}\right)}$&$387$\\ elliptic&$\frac{i b \sqrt{-\frac{i x a}{b}+1}\, \sqrt{2}\, \sqrt{\frac{i x a}{b}+1}\, \sqrt{\frac{i x a}{b}}\, \EllipticF \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}+b^{2} x}}-\frac{2 a \sqrt{2}\, \sqrt{-\frac{i \left(a x +i b \right)}{b}}\, \sqrt{-\frac{i \left(-a x +i b \right)}{b}}\, \sqrt{\frac{i x a}{b}}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}+\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-\frac{i \left(a x +i b \right)}{b}}, -\frac{-\underline{\hspace{1.25 ex}}\alpha  a +i b -b}{b}, \frac{\sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha^{2}}{2 \underline{\hspace{1.25 ex}}\alpha  a +b}\right)}{3 \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}-\frac{2 \sqrt{2}\, \sqrt{-\frac{i \left(a x +i b \right)}{b}}\, \sqrt{-\frac{i \left(-a x +i b \right)}{b}}\, \sqrt{\frac{i x a}{b}}\, b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}+\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-\frac{i \left(a x +i b \right)}{b}}, -\frac{-\underline{\hspace{1.25 ex}}\alpha  a +i b -b}{b}, \frac{\sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha }{2 \underline{\hspace{1.25 ex}}\alpha  a +b}\right)}{\sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}-\frac{4 \sqrt{2}\, \sqrt{-\frac{i \left(a x +i b \right)}{b}}\, \sqrt{-\frac{i \left(-a x +i b \right)}{b}}\, \sqrt{\frac{i x a}{b}}\, b^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}+\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-\frac{i \left(a x +i b \right)}{b}}, -\frac{-\underline{\hspace{1.25 ex}}\alpha  a +i b -b}{b}, \frac{\sqrt{2}}{2}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  a +b}\right)}{3 a \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}+\frac{2 i \sqrt{2}\, \sqrt{-\frac{i \left(a x +i b \right)}{b}}\, \sqrt{-\frac{i \left(-a x +i b \right)}{b}}\, \sqrt{\frac{i x a}{b}}\, b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}+\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-\frac{i \left(a x +i b \right)}{b}}, -\frac{-\underline{\hspace{1.25 ex}}\alpha  a +i b -b}{b}, \frac{\sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha }{2 \underline{\hspace{1.25 ex}}\alpha  a +b}\right)}{3 \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}+\frac{4 i \sqrt{2}\, \sqrt{-\frac{i \left(a x +i b \right)}{b}}\, \sqrt{-\frac{i \left(-a x +i b \right)}{b}}\, \sqrt{\frac{i x a}{b}}\, b^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}+\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-\frac{i \left(a x +i b \right)}{b}}, -\frac{-\underline{\hspace{1.25 ex}}\alpha  a +i b -b}{b}, \frac{\sqrt{2}}{2}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  a +b}\right)}{3 a \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}+\frac{2 i b^{2} \sqrt{-\frac{i x a}{b}+1}\, \sqrt{2}\, \sqrt{\frac{i x a}{b}+1}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, -\frac{i b}{a \left(-\frac{i b}{a}-b \right)}, \frac{\sqrt{2}}{2}\right)}{3 a \sqrt{a^{2} x^{3}+b^{2} x}\, \left(-\frac{i b}{a}-b \right)}$&$875$\\ \hline \end{longtable}"," ",0,"I*b/a*(-I*(x+I*b/a)/b*a)^(1/2)*2^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(a^2*x^3+b^2*x)^(1/2)*EllipticF((-I*(x+I*b/a)/b*a)^(1/2),1/2*2^(1/2))+2/3*I/a*2^(1/2)*sum((-_alpha*a-2*b)/(2*_alpha*a+b)*(I*_alpha*a+I*b+b)*(-I*(x+I*b/a)/b*a)^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(x*(a^2*x^2+b^2))^(1/2)*EllipticPi((-I*(x+I*b/a)/b*a)^(1/2),(_alpha*a+b-I*b)/b,1/2*2^(1/2)),_alpha=RootOf(_Z^2*a^2+_Z*a*b+b^2))+2/3*I*b^2/a^2*(-I*(x+I*b/a)/b*a)^(1/2)*2^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(a^2*x^3+b^2*x)^(1/2)/(-I*b/a-b/a)*EllipticPi((-I*(x+I*b/a)/b*a)^(1/2),-I*b/a/(-I*b/a-b/a),1/2*2^(1/2))","C"
1812,1,3014,38,14.540000," ","int((x^4+x^3)^(1/4)/(2*x^2+x-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$3014$\\ \hline \end{longtable}"," ",0,"1/2*ln((2*(x^4+x^3)^(3/4)+2*(x^4+x^3)^(1/2)*x+2*x^2*(x^4+x^3)^(1/4)+2*x^3+x^2)/x^2)+1/2*RootOf(_Z^2+1)*ln((2*(x^4+x^3)^(1/2)*RootOf(_Z^2+1)*x-2*RootOf(_Z^2+1)*x^3+2*(x^4+x^3)^(3/4)-2*x^2*(x^4+x^3)^(1/4)-RootOf(_Z^2+1)*x^2)/x^2)-RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)*ln((-195917548288*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)*RootOf(1336336*_Z^8-6647*_Z^4+8)^10*x^3+195917548288*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)*RootOf(1336336*_Z^8-6647*_Z^4+8)^10*x^2+357351968*x^3*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)*RootOf(1336336*_Z^8-6647*_Z^4+8)^6-162561344*(x^4+x^3)^(1/4)*RootOf(1336336*_Z^8-6647*_Z^4+8)^6*x^2-1162376496*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)*RootOf(1336336*_Z^8-6647*_Z^4+8)^6*x^2+30777344*(x^4+x^3)^(1/2)*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)*RootOf(1336336*_Z^8-6647*_Z^4+8)^4*x+5826240*(x^4+x^3)^(3/4)*RootOf(1336336*_Z^8-6647*_Z^4+8)^4+86445*x^3*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)*RootOf(1336336*_Z^8-6647*_Z^4+8)^2+331772*(x^4+x^3)^(1/4)*RootOf(1336336*_Z^8-6647*_Z^4+8)^2*x^2+1556010*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)*RootOf(1336336*_Z^8-6647*_Z^4+8)^2*x^2-62808*(x^4+x^3)^(1/2)*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)*x-11888*(x^4+x^3)^(3/4))/(4624*x*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-4624*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-9*x+10)/x^2)+RootOf(1336336*_Z^8-6647*_Z^4+8)*ln((-195917548288*RootOf(1336336*_Z^8-6647*_Z^4+8)^11*x^3+195917548288*RootOf(1336336*_Z^8-6647*_Z^4+8)^11*x^2+357351968*RootOf(1336336*_Z^8-6647*_Z^4+8)^7*x^3+162561344*(x^4+x^3)^(1/4)*RootOf(1336336*_Z^8-6647*_Z^4+8)^6*x^2-1162376496*RootOf(1336336*_Z^8-6647*_Z^4+8)^7*x^2-30777344*(x^4+x^3)^(1/2)*RootOf(1336336*_Z^8-6647*_Z^4+8)^5*x+5826240*(x^4+x^3)^(3/4)*RootOf(1336336*_Z^8-6647*_Z^4+8)^4+86445*RootOf(1336336*_Z^8-6647*_Z^4+8)^3*x^3-331772*(x^4+x^3)^(1/4)*RootOf(1336336*_Z^8-6647*_Z^4+8)^2*x^2+1556010*RootOf(1336336*_Z^8-6647*_Z^4+8)^3*x^2+62808*(x^4+x^3)^(1/2)*RootOf(1336336*_Z^8-6647*_Z^4+8)*x-11888*(x^4+x^3)^(3/4))/(4624*x*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-4624*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-9*x+10)/x^2)+289*ln(-(9771288832*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^3*RootOf(1336336*_Z^8-6647*_Z^4+8)^11*x^3-9771288832*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^3*RootOf(1336336*_Z^8-6647*_Z^4+8)^11*x^2-79380208*x^3*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^3*RootOf(1336336*_Z^8-6647*_Z^4+8)^7+39230016*x^2*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^3*RootOf(1336336*_Z^8-6647*_Z^4+8)^7+512738759840*(x^4+x^3)^(1/2)*RootOf(1336336*_Z^8-6647*_Z^4+8)^7*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)*x+148776*x^3*RootOf(1336336*_Z^8-6647*_Z^4+8)^3*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^3*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)-9562432*(x^4+x^3)^(1/4)*RootOf(1336336*_Z^8-6647*_Z^4+8)^4*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^2*x^2-30995*x^2*RootOf(1336336*_Z^8-6647*_Z^4+8)^3*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^3*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)-1503957734*(x^4+x^3)^(1/2)*RootOf(1336336*_Z^8-6647*_Z^4+8)^3*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)*x+114497268480*(x^4+x^3)^(3/4)*RootOf(1336336*_Z^8-6647*_Z^4+8)^4+28048*(x^4+x^3)^(1/4)*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^2*x^2-335891984*(x^4+x^3)^(3/4))/(4624*x*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-4624*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-14*x+13)/x^2)*RootOf(1336336*_Z^8-6647*_Z^4+8)^7*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)-23/16*ln(-(9771288832*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^3*RootOf(1336336*_Z^8-6647*_Z^4+8)^11*x^3-9771288832*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^3*RootOf(1336336*_Z^8-6647*_Z^4+8)^11*x^2-79380208*x^3*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^3*RootOf(1336336*_Z^8-6647*_Z^4+8)^7+39230016*x^2*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^3*RootOf(1336336*_Z^8-6647*_Z^4+8)^7+512738759840*(x^4+x^3)^(1/2)*RootOf(1336336*_Z^8-6647*_Z^4+8)^7*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)*x+148776*x^3*RootOf(1336336*_Z^8-6647*_Z^4+8)^3*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^3*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)-9562432*(x^4+x^3)^(1/4)*RootOf(1336336*_Z^8-6647*_Z^4+8)^4*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^2*x^2-30995*x^2*RootOf(1336336*_Z^8-6647*_Z^4+8)^3*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^3*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)-1503957734*(x^4+x^3)^(1/2)*RootOf(1336336*_Z^8-6647*_Z^4+8)^3*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)*x+114497268480*(x^4+x^3)^(3/4)*RootOf(1336336*_Z^8-6647*_Z^4+8)^4+28048*(x^4+x^3)^(1/4)*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^2*x^2-335891984*(x^4+x^3)^(3/4))/(4624*x*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-4624*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-14*x+13)/x^2)*RootOf(1336336*_Z^8-6647*_Z^4+8)^3*RootOf(RootOf(1336336*_Z^8-6647*_Z^4+8)^2+_Z^2)*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)-1/578*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)*ln(-(-720285104*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^3*RootOf(1336336*_Z^8-6647*_Z^4+8)^8*x^3+720285104*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^3*RootOf(1336336*_Z^8-6647*_Z^4+8)^8*x^2+5851672*x^3*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^3*RootOf(1336336*_Z^8-6647*_Z^4+8)^4+345442856*(x^4+x^3)^(1/4)*RootOf(1336336*_Z^8-6647*_Z^4+8)^4*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^2*x^2-2892023*x^2*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^3*RootOf(1336336*_Z^8-6647*_Z^4+8)^4+37802272768*(x^4+x^3)^(1/2)*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)*RootOf(1336336*_Z^8-6647*_Z^4+8)^4*x+4136213823840*(x^4+x^3)^(3/4)*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-10968*x^3*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^3-1013234*(x^4+x^3)^(1/4)*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^2*x^2+2285*x^2*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)^3-110886410*(x^4+x^3)^(1/2)*RootOf(_Z^4+111612119056*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-555164087)*x-12134097922*(x^4+x^3)^(3/4))/(4624*x*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-4624*RootOf(1336336*_Z^8-6647*_Z^4+8)^4-14*x+13)/x^2)","B"
1813,0,0,102,0.014000," ","int((a*x^3-4*b)*(-a*x^3+x^4+b)/x^4/(a*x^3-b)^(1/4)/(a*x^3+x^4-b),x)","\[\int \frac{\left(a \,x^{3}-4 b \right) \left(-a \,x^{3}+x^{4}+b \right)}{x^{4} \left(a \,x^{3}-b \right)^{\frac{1}{4}} \left(a \,x^{3}+x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^3-4*b)*(-a*x^3+x^4+b)/x^4/(a*x^3-b)^(1/4)/(a*x^3+x^4-b),x)","F"
1814,1,239,103,8.982000," ","int((x^2-2)*(x^2-1)*(x^4+x^2-1)^(1/4)/x^6/(2*x^4+x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{4}+x^{2}-1\right)^{\frac{1}{4}} \left(9 x^{4}-x^{2}+1\right)}{5 x^{5}}-\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{2 \left(x^{4}+x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}+2 \sqrt{x^{4}+x^{2}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right) x^{2}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}+2 \left(x^{4}+x^{2}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{\left(x^{2}+1\right) \left(2 x^{2}-1\right)}\right)-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{2 \sqrt{x^{4}+x^{2}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}-2 \left(x^{4}+x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}+2 \left(x^{4}+x^{2}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}+1\right) x^{2}+\RootOf \left(\textit{\_Z}^{4}+1\right)}{\left(x^{2}+1\right) \left(2 x^{2}-1\right)}\right)$&$239$\\ risch&$\frac{\frac{18}{5} x^{8}+\frac{16}{5} x^{6}-\frac{18}{5} x^{4}+\frac{4}{5} x^{2}-\frac{2}{5}}{x^{5} \left(x^{4}+x^{2}-1\right)^{\frac{3}{4}}}+\frac{\left(-\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{12}+3 x^{10}-5 x^{6}+3 x^{2}-1\right)^{\frac{1}{4}} x^{9}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{10}+4 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{12}+3 x^{10}-5 x^{6}+3 x^{2}-1\right)^{\frac{1}{4}} x^{7}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{8}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{12}+3 x^{10}-5 x^{6}+3 x^{2}-1\right)^{\frac{1}{4}} x^{5}-3 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{6}-2 \sqrt{x^{12}+3 x^{10}-5 x^{6}+3 x^{2}-1}\, x^{6}-4 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{12}+3 x^{10}-5 x^{6}+3 x^{2}-1\right)^{\frac{1}{4}} x^{3}-2 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{12}+3 x^{10}-5 x^{6}+3 x^{2}-1\right)^{\frac{3}{4}} x^{3}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{4}-2 \sqrt{x^{12}+3 x^{10}-5 x^{6}+3 x^{2}-1}\, x^{4}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{12}+3 x^{10}-5 x^{6}+3 x^{2}-1\right)^{\frac{1}{4}} x +3 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}+2 \sqrt{x^{12}+3 x^{10}-5 x^{6}+3 x^{2}-1}\, x^{2}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{2}}{\left(x^{4}+x^{2}-1\right)^{2} \left(2 x^{2}-1\right) \left(x^{2}+1\right)}\right)+\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{10}-2 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{12}+3 x^{10}-5 x^{6}+3 x^{2}-1\right)^{\frac{1}{4}} x^{9}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{8}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{12}+3 x^{10}-5 x^{6}+3 x^{2}-1\right)^{\frac{3}{4}} x^{3}-4 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{12}+3 x^{10}-5 x^{6}+3 x^{2}-1\right)^{\frac{1}{4}} x^{7}+3 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{6}-2 \sqrt{x^{12}+3 x^{10}-5 x^{6}+3 x^{2}-1}\, x^{6}+2 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{12}+3 x^{10}-5 x^{6}+3 x^{2}-1\right)^{\frac{1}{4}} x^{5}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{4}-2 \sqrt{x^{12}+3 x^{10}-5 x^{6}+3 x^{2}-1}\, x^{4}+4 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{12}+3 x^{10}-5 x^{6}+3 x^{2}-1\right)^{\frac{1}{4}} x^{3}-3 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}+2 \sqrt{x^{12}+3 x^{10}-5 x^{6}+3 x^{2}-1}\, x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{12}+3 x^{10}-5 x^{6}+3 x^{2}-1\right)^{\frac{1}{4}} x +\RootOf \left(\textit{\_Z}^{4}+1\right)^{2}}{\left(x^{4}+x^{2}-1\right)^{2} \left(2 x^{2}-1\right) \left(x^{2}+1\right)}\right)\right) \left(\left(x^{4}+x^{2}-1\right)^{3}\right)^{\frac{1}{4}}}{\left(x^{4}+x^{2}-1\right)^{\frac{3}{4}}}$&$849$\\ \hline \end{longtable}"," ",0,"2/5*(x^4+x^2-1)^(1/4)*(9*x^4-x^2+1)/x^5-RootOf(_Z^4+1)*ln((2*(x^4+x^2-1)^(1/4)*RootOf(_Z^4+1)^2*x^3+2*(x^4+x^2-1)^(1/2)*RootOf(_Z^4+1)*x^2-RootOf(_Z^4+1)^3*x^2+2*(x^4+x^2-1)^(3/4)*x+RootOf(_Z^4+1)^3)/(x^2+1)/(2*x^2-1))-RootOf(_Z^4+1)^3*ln((2*(x^4+x^2-1)^(1/2)*RootOf(_Z^4+1)^3*x^2-2*(x^4+x^2-1)^(1/4)*RootOf(_Z^4+1)^2*x^3+2*(x^4+x^2-1)^(3/4)*x-RootOf(_Z^4+1)*x^2+RootOf(_Z^4+1))/(x^2+1)/(2*x^2-1))","C"
1815,0,0,103,0.005000," ","int(x^2*(a*x^4+b*x^3)^(1/4),x)","\[\int x^{2} \left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}\, dx\]"," ",0,"int(x^2*(a*x^4+b*x^3)^(1/4),x)","F"
1816,1,181,103,1.255000," ","int((x^6+1)/(x^3+x^2+x)^(1/2)/(-x^6+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \sqrt{x^{3}+x^{2}+x}}{3 \left(x^{2}+x +1\right)}+\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) x^{2}+4 \RootOf \left(\textit{\_Z}^{2}-3\right) x +\RootOf \left(\textit{\_Z}^{2}-3\right)+6 \sqrt{x^{3}+x^{2}+x}}{\left(-1+x \right)^{2}}\right)}{18}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)-2 \sqrt{x^{3}+x^{2}+x}}{\left(1+x \right)^{2}}\right)}{6}-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}-3 \RootOf \left(\textit{\_Z}^{2}-2\right) x +4 \sqrt{x^{3}+x^{2}+x}-\RootOf \left(\textit{\_Z}^{2}-2\right)}{x^{2}-x +1}\right)}{6}$&$181$\\ default&$-\frac{4 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{9 \sqrt{x^{3}+x^{2}+x}}+\frac{2 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{9 \sqrt{x^{3}+x^{2}+x}\, \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{2 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \left(-\frac{5}{8}+\frac{3 i \sqrt{3}}{8}-\frac{i \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{4}\right) \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{9 \sqrt{x^{3}+x^{2}+x}}-\frac{2 \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \left(-\frac{5}{8}+\frac{i \sqrt{3}}{8}-\frac{i \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{4}\right) \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}+\frac{i \sqrt{3}}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{9 \sqrt{x^{3}+x^{2}+x}}-\frac{2 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{9 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}+\frac{2 x}{3 \sqrt{x \left(x^{2}+x +1\right)}}$&$736$\\ risch&$-\frac{4 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{9 \sqrt{x^{3}+x^{2}+x}}+\frac{2 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{9 \sqrt{x^{3}+x^{2}+x}\, \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{2 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \left(-\frac{5}{8}+\frac{3 i \sqrt{3}}{8}-\frac{i \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{4}\right) \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{9 \sqrt{x^{3}+x^{2}+x}}-\frac{2 \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \left(-\frac{5}{8}+\frac{i \sqrt{3}}{8}-\frac{i \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{4}\right) \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}+\frac{i \sqrt{3}}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{9 \sqrt{x^{3}+x^{2}+x}}-\frac{2 \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{9 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}+\frac{2 x}{3 \sqrt{x \left(x^{2}+x +1\right)}}$&$736$\\ elliptic&$\frac{2 x}{3 \sqrt{x \left(x^{2}+x +1\right)}}-\frac{2 \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{9 \sqrt{x^{3}+x^{2}+x}}-\frac{2 i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}}+\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{9 \sqrt{x^{3}+x^{2}+x}\, \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{1}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}\, \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{18 \sqrt{x^{3}+x^{2}+x}}-\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{6 \sqrt{x^{3}+x^{2}+x}}-\frac{2 \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{1}{2}+\frac{i \sqrt{3}}{2}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{9 \sqrt{x^{3}+x^{2}+x}}-\frac{\sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{9 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{\frac{x}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{1+i \sqrt{3}}+\frac{i \sqrt{3}}{1+i \sqrt{3}}}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}}}, \frac{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}, \frac{\sqrt{3}\, \sqrt{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}\right)}{3 \sqrt{x^{3}+x^{2}+x}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}$&$1330$\\ \hline \end{longtable}"," ",0,"2/3*(x^3+x^2+x)^(1/2)/(x^2+x+1)+1/18*RootOf(_Z^2-3)*ln((RootOf(_Z^2-3)*x^2+4*RootOf(_Z^2-3)*x+RootOf(_Z^2-3)+6*(x^3+x^2+x)^(1/2))/(-1+x)^2)-1/6*RootOf(_Z^2+1)*ln(-(RootOf(_Z^2+1)*x^2+RootOf(_Z^2+1)-2*(x^3+x^2+x)^(1/2))/(1+x)^2)-1/6*RootOf(_Z^2-2)*ln((-RootOf(_Z^2-2)*x^2-3*RootOf(_Z^2-2)*x+4*(x^3+x^2+x)^(1/2)-RootOf(_Z^2-2))/(x^2-x+1))","C"
1817,1,181,99,7.328000," ","int((3*x^6-3*x^3+1)/x^6/(2*x^3-1)/(x^4-x)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{3}-1\right) \left(x^{4}-x \right)^{\frac{3}{4}}}{21 x^{6}}+\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{2 \sqrt{x^{4}-x}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x -2 \left(x^{4}-x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}+2 \left(x^{4}-x \right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}+1\right)}{2 x^{3}-1}\right)}{3}+\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{2 \left(x^{4}-x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}+2 \sqrt{x^{4}-x}\, \RootOf \left(\textit{\_Z}^{4}+1\right) x +2 \left(x^{4}-x \right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{2 x^{3}-1}\right)}{3}$&$181$\\ risch&$\frac{\frac{4}{21} x^{6}-\frac{8}{21} x^{3}+\frac{4}{21}}{x^{5} \left(x \left(x^{3}-1\right)\right)^{\frac{1}{4}}}+\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{2 \sqrt{x^{4}-x}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x -2 \left(x^{4}-x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}+2 \left(x^{4}-x \right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}+1\right)}{2 x^{3}-1}\right)}{3}+\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{2 \left(x^{4}-x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}+2 \sqrt{x^{4}-x}\, \RootOf \left(\textit{\_Z}^{4}+1\right) x +2 \left(x^{4}-x \right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{2 x^{3}-1}\right)}{3}$&$186$\\ \hline \end{longtable}"," ",0,"4/21*(x^3-1)*(x^4-x)^(3/4)/x^6+1/3*RootOf(_Z^4+1)*ln((2*(x^4-x)^(1/2)*RootOf(_Z^4+1)^3*x-2*(x^4-x)^(1/4)*RootOf(_Z^4+1)^2*x^2+2*(x^4-x)^(3/4)+RootOf(_Z^4+1))/(2*x^3-1))+1/3*RootOf(_Z^4+1)^3*ln((2*(x^4-x)^(1/4)*RootOf(_Z^4+1)^2*x^2+2*(x^4-x)^(1/2)*RootOf(_Z^4+1)*x+2*(x^4-x)^(3/4)+RootOf(_Z^4+1)^3)/(2*x^3-1))","C"
1818,0,0,103,0.013000," ","int((a*x^6+b)/x^3/(a*x^3+b)/(a*x^4+b*x)^(1/4),x)","\[\int \frac{a \,x^{6}+b}{x^{3} \left(a \,x^{3}+b \right) \left(a \,x^{4}+b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^6+b)/x^3/(a*x^3+b)/(a*x^4+b*x)^(1/4),x)","F"
1819,1,709,80,11.955000," ","int((x^4-x^2-x-1)*(2*x^4+x+2)/(x^4-x-1)^(1/2)/(4*x^8+x^6-8*x^5-7*x^4-x^3+3*x^2+8*x+4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-5 \ln \left(\frac{-400 \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)^{5} x^{2}+80 \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)^{3} x^{4}-120 \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)^{3} x^{2}+36 \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right) x^{4}+160 \sqrt{x^{4}-x -1}\, \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)^{2} x -80 \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)^{3} x -80 \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)^{3}+27 \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right) x^{2}-56 \sqrt{x^{4}-x -1}\, x -36 \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right) x -36 \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)}{20 x^{2} \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)^{2}+4 x^{4}-3 x^{2}-4 x -4}\right) \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)^{3}+\frac{7 \ln \left(\frac{-400 \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)^{5} x^{2}+80 \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)^{3} x^{4}-120 \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)^{3} x^{2}+36 \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right) x^{4}+160 \sqrt{x^{4}-x -1}\, \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)^{2} x -80 \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)^{3} x -80 \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)^{3}+27 \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right) x^{2}-56 \sqrt{x^{4}-x -1}\, x -36 \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right) x -36 \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)}{20 x^{2} \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)^{2}+4 x^{4}-3 x^{2}-4 x -4}\right) \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)}{4}-\RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right) \ln \left(-\frac{-50 \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)^{4} x^{2}-10 \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)^{2} x^{4}+25 x^{2} \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)^{2}+3 x^{4}+5 \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right) \sqrt{x^{4}-x -1}\, x +10 \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)^{2} x +10 \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)^{2}-3 x^{2}-3 x -3}{5 x^{2} \RootOf \left(100 \textit{\_Z}^{4}-35 \textit{\_Z}^{2}+4\right)^{2}-x^{4}-x^{2}+x +1}\right)$&$709$\\ default&$\text{Expression too large to display}$&$8123$\\ elliptic&$\text{Expression too large to display}$&$8123$\\ \hline \end{longtable}"," ",0,"-5*ln((-400*RootOf(100*_Z^4-35*_Z^2+4)^5*x^2+80*RootOf(100*_Z^4-35*_Z^2+4)^3*x^4-120*RootOf(100*_Z^4-35*_Z^2+4)^3*x^2+36*RootOf(100*_Z^4-35*_Z^2+4)*x^4+160*(x^4-x-1)^(1/2)*RootOf(100*_Z^4-35*_Z^2+4)^2*x-80*RootOf(100*_Z^4-35*_Z^2+4)^3*x-80*RootOf(100*_Z^4-35*_Z^2+4)^3+27*RootOf(100*_Z^4-35*_Z^2+4)*x^2-56*(x^4-x-1)^(1/2)*x-36*RootOf(100*_Z^4-35*_Z^2+4)*x-36*RootOf(100*_Z^4-35*_Z^2+4))/(20*x^2*RootOf(100*_Z^4-35*_Z^2+4)^2+4*x^4-3*x^2-4*x-4))*RootOf(100*_Z^4-35*_Z^2+4)^3+7/4*ln((-400*RootOf(100*_Z^4-35*_Z^2+4)^5*x^2+80*RootOf(100*_Z^4-35*_Z^2+4)^3*x^4-120*RootOf(100*_Z^4-35*_Z^2+4)^3*x^2+36*RootOf(100*_Z^4-35*_Z^2+4)*x^4+160*(x^4-x-1)^(1/2)*RootOf(100*_Z^4-35*_Z^2+4)^2*x-80*RootOf(100*_Z^4-35*_Z^2+4)^3*x-80*RootOf(100*_Z^4-35*_Z^2+4)^3+27*RootOf(100*_Z^4-35*_Z^2+4)*x^2-56*(x^4-x-1)^(1/2)*x-36*RootOf(100*_Z^4-35*_Z^2+4)*x-36*RootOf(100*_Z^4-35*_Z^2+4))/(20*x^2*RootOf(100*_Z^4-35*_Z^2+4)^2+4*x^4-3*x^2-4*x-4))*RootOf(100*_Z^4-35*_Z^2+4)-RootOf(100*_Z^4-35*_Z^2+4)*ln(-(-50*RootOf(100*_Z^4-35*_Z^2+4)^4*x^2-10*RootOf(100*_Z^4-35*_Z^2+4)^2*x^4+25*x^2*RootOf(100*_Z^4-35*_Z^2+4)^2+3*x^4+5*RootOf(100*_Z^4-35*_Z^2+4)*(x^4-x-1)^(1/2)*x+10*RootOf(100*_Z^4-35*_Z^2+4)^2*x+10*RootOf(100*_Z^4-35*_Z^2+4)^2-3*x^2-3*x-3)/(5*x^2*RootOf(100*_Z^4-35*_Z^2+4)^2-x^4-x^2+x+1))","C"
1820,1,599,90,7.804000," ","int((x^6+1)^2*(2*x^6-1)/(x^6-x^2+1)^(3/2)/(x^12-x^8+2*x^6-x^4-x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{x}{\sqrt{x^{6}-x^{2}+1}}-\RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right) \ln \left(\frac{1430 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{3} x^{6}+2200 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{5} x^{2}-2093 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right) x^{6}-6960 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{3} x^{2}+130 \sqrt{x^{6}-x^{2}+1}\, \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2} x +1430 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{3}+5474 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right) x^{2}-221 \sqrt{x^{6}-x^{2}+1}\, x -2093 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)}{-13 x^{6}+20 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2} x^{2}-8 x^{2}-13}\right)+\frac{\RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2}-145\right) \ln \left(-\frac{-2860 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2}-145\right) \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2} x^{6}+4400 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2}-145\right) \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{4} x^{2}-39 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2}-145\right) x^{6}+1160 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2}-145\right) \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2} x^{2}+2600 \sqrt{x^{6}-x^{2}+1}\, \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2} x -2860 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2}-145\right)+15 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2}-145\right) x^{2}+650 \sqrt{x^{6}-x^{2}+1}\, x -39 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2}-145\right)}{13 x^{6}+20 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2} x^{2}-21 x^{2}+13}\right)}{10}$&$599$\\ risch&$\frac{x}{\sqrt{x^{6}-x^{2}+1}}-\RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right) \ln \left(\frac{1430 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{3} x^{6}+2200 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{5} x^{2}-2093 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right) x^{6}-6960 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{3} x^{2}+130 \sqrt{x^{6}-x^{2}+1}\, \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2} x +1430 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{3}+5474 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right) x^{2}-221 \sqrt{x^{6}-x^{2}+1}\, x -2093 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)}{-13 x^{6}+20 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2} x^{2}-8 x^{2}-13}\right)-\frac{\RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2}-145\right) \ln \left(-\frac{2860 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2}-145\right) \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2} x^{6}-4400 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2}-145\right) \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{4} x^{2}+39 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2}-145\right) x^{6}-1160 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2}-145\right) \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2} x^{2}+2600 \sqrt{x^{6}-x^{2}+1}\, \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2} x +2860 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2}-145\right)-15 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2}-145\right) x^{2}+650 \sqrt{x^{6}-x^{2}+1}\, x +39 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2}-145\right)}{13 x^{6}+20 \RootOf \left(400 \textit{\_Z}^{4}-580 \textit{\_Z}^{2}-1\right)^{2} x^{2}-21 x^{2}+13}\right)}{10}$&$599$\\ \hline \end{longtable}"," ",0,"x/(x^6-x^2+1)^(1/2)-RootOf(400*_Z^4-580*_Z^2-1)*ln((1430*RootOf(400*_Z^4-580*_Z^2-1)^3*x^6+2200*RootOf(400*_Z^4-580*_Z^2-1)^5*x^2-2093*RootOf(400*_Z^4-580*_Z^2-1)*x^6-6960*RootOf(400*_Z^4-580*_Z^2-1)^3*x^2+130*(x^6-x^2+1)^(1/2)*RootOf(400*_Z^4-580*_Z^2-1)^2*x+1430*RootOf(400*_Z^4-580*_Z^2-1)^3+5474*RootOf(400*_Z^4-580*_Z^2-1)*x^2-221*(x^6-x^2+1)^(1/2)*x-2093*RootOf(400*_Z^4-580*_Z^2-1))/(-13*x^6+20*RootOf(400*_Z^4-580*_Z^2-1)^2*x^2-8*x^2-13))+1/10*RootOf(_Z^2+100*RootOf(400*_Z^4-580*_Z^2-1)^2-145)*ln(-(-2860*RootOf(_Z^2+100*RootOf(400*_Z^4-580*_Z^2-1)^2-145)*RootOf(400*_Z^4-580*_Z^2-1)^2*x^6+4400*RootOf(_Z^2+100*RootOf(400*_Z^4-580*_Z^2-1)^2-145)*RootOf(400*_Z^4-580*_Z^2-1)^4*x^2-39*RootOf(_Z^2+100*RootOf(400*_Z^4-580*_Z^2-1)^2-145)*x^6+1160*RootOf(_Z^2+100*RootOf(400*_Z^4-580*_Z^2-1)^2-145)*RootOf(400*_Z^4-580*_Z^2-1)^2*x^2+2600*(x^6-x^2+1)^(1/2)*RootOf(400*_Z^4-580*_Z^2-1)^2*x-2860*RootOf(400*_Z^4-580*_Z^2-1)^2*RootOf(_Z^2+100*RootOf(400*_Z^4-580*_Z^2-1)^2-145)+15*RootOf(_Z^2+100*RootOf(400*_Z^4-580*_Z^2-1)^2-145)*x^2+650*(x^6-x^2+1)^(1/2)*x-39*RootOf(_Z^2+100*RootOf(400*_Z^4-580*_Z^2-1)^2-145))/(13*x^6+20*RootOf(400*_Z^4-580*_Z^2-1)^2*x^2-21*x^2+13))","C"
1821,1,115,95,0.028000," ","int(1/(2*x^(1/2)+(1+x)^(1/2))^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{8}{9 \left(-1+3 x \right)}+\frac{5 \ln \left(-1+3 x \right)}{9}-\frac{\sqrt{x}\, \sqrt{1+x}\, \left(12 \ln \left(\frac{1}{2}+x +\sqrt{x \left(1+x \right)}\right) x -15 \arctanh \left(\frac{5 x +1}{4 \sqrt{x \left(1+x \right)}}\right) x -4 \ln \left(\frac{1}{2}+x +\sqrt{x \left(1+x \right)}\right)+5 \arctanh \left(\frac{5 x +1}{4 \sqrt{x \left(1+x \right)}}\right)-12 \sqrt{x \left(1+x \right)}\right)}{9 \sqrt{x \left(1+x \right)}\, \left(-1+3 x \right)}$&$115$\\ \hline \end{longtable}"," ",0,"-8/9/(-1+3*x)+5/9*ln(-1+3*x)-1/9*x^(1/2)*(1+x)^(1/2)*(12*ln(1/2+x+(x*(1+x))^(1/2))*x-15*arctanh(1/4*(5*x+1)/(x*(1+x))^(1/2))*x-4*ln(1/2+x+(x*(1+x))^(1/2))+5*arctanh(1/4*(5*x+1)/(x*(1+x))^(1/2))-12*(x*(1+x))^(1/2))/(x*(1+x))^(1/2)/(-1+3*x)","A"
1822,0,0,109,0.022000," ","int(1/x^3/(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2),x)","\[\int \frac{1}{x^{3} \sqrt{a \,x^{2}+b x \sqrt{-\frac{a}{b^{2}}+\frac{a^{2} x^{2}}{b^{2}}}}}\, dx\]"," ",0,"int(1/x^3/(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2),x)","F"
1823,0,0,96,0.023000," ","int(1/x/(a*x^2-b)^(1/4),x)","\[\int \frac{1}{x \left(a \,x^{2}-b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/x/(a*x^2-b)^(1/4),x)","F"
1824,1,1538,110,0.461000," ","int((1+k^(3/2)*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/2)/(-1+k^(3/2)*x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)}}{x \left(-1+k \right)}\right)}{-3+3 k}+\frac{4 \arctan \left(\frac{\sqrt{\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)}\, \sqrt{2}}{x \sqrt{2 k^{2}+2 k +2}}\right)}{3 \sqrt{2 k^{2}+2 k +2}}\right) \sqrt{2}}{2}+\frac{k \sqrt{2}\, \ln \left(\frac{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k}-k \left(k^{2}+\sqrt{-3 k^{2}}+k +1\right) \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k}}\, \sqrt{4 k^{3} \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)^{2}-4 k \left(k^{2}+\sqrt{-3 k^{2}}+k +1\right) \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)+\frac{2 \sqrt{-3 k^{2}}\, k^{2}+2 k^{3}+2 k^{2}+2 \sqrt{-3 k^{2}}\, k +2 \sqrt{-3 k^{2}}+2 k}{k}}}{2}}{x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}}\right)}{\left(\sqrt{-3 k^{2}}+3 k \right) \sqrt{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k}}}+\frac{k^{2} \sqrt{2}\, \ln \left(\frac{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k}-k \left(k^{2}+\sqrt{-3 k^{2}}+k +1\right) \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k}}\, \sqrt{4 k^{3} \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)^{2}-4 k \left(k^{2}+\sqrt{-3 k^{2}}+k +1\right) \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)+\frac{2 \sqrt{-3 k^{2}}\, k^{2}+2 k^{3}+2 k^{2}+2 \sqrt{-3 k^{2}}\, k +2 \sqrt{-3 k^{2}}+2 k}{k}}}{2}}{x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}}\right)}{\left(\sqrt{-3 k^{2}}+3 k \right) \sqrt{-3 k^{2}}\, \sqrt{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k}}}-\frac{k \sqrt{2}\, \ln \left(\frac{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k}-k \left(k^{2}+1+k -\sqrt{-3 k^{2}}\right) \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k}}\, \sqrt{4 k^{3} \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)^{2}-4 k \left(k^{2}+1+k -\sqrt{-3 k^{2}}\right) \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)+\frac{-2 \sqrt{-3 k^{2}}\, k^{2}+2 k^{3}+2 k^{2}-2 \sqrt{-3 k^{2}}\, k -2 \sqrt{-3 k^{2}}+2 k}{k}}}{2}}{x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}}\right)}{\left(\sqrt{-3 k^{2}}-3 k \right) \sqrt{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k}}}+\frac{k^{2} \sqrt{2}\, \ln \left(\frac{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k}-k \left(k^{2}+1+k -\sqrt{-3 k^{2}}\right) \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k}}\, \sqrt{4 k^{3} \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)^{2}-4 k \left(k^{2}+1+k -\sqrt{-3 k^{2}}\right) \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)+\frac{-2 \sqrt{-3 k^{2}}\, k^{2}+2 k^{3}+2 k^{2}-2 \sqrt{-3 k^{2}}\, k -2 \sqrt{-3 k^{2}}+2 k}{k}}}{2}}{x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}}\right)}{\left(\sqrt{-3 k^{2}}-3 k \right) \sqrt{-3 k^{2}}\, \sqrt{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k}}}+\frac{4 k^{2} \ln \left(\frac{-2 k^{2}+4 k -2+\left(-k^{3}+2 k^{2}-k \right) \left(x^{2}-\frac{1}{k}\right)+2 \sqrt{-\left(-1+k \right)^{2}}\, \sqrt{k^{3} \left(x^{2}-\frac{1}{k}\right)^{2}+\left(-k^{3}+2 k^{2}-k \right) \left(x^{2}-\frac{1}{k}\right)-k^{2}+2 k -1}}{x^{2}-\frac{1}{k}}\right)}{\left(\sqrt{-3 k^{2}}-3 k \right) \left(\sqrt{-3 k^{2}}+3 k \right) \sqrt{-\left(-1+k \right)^{2}}}$&$1538$\\ default&$\frac{\sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticF \left(x , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}-\frac{2 \sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticPi \left(x , k , k\right)}{3 \sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}-\frac{\ln \left(\frac{-2 k^{2}+4 k -2+\left(-k^{3}+2 k^{2}-k \right) \left(x^{2}-\frac{1}{k}\right)+2 \sqrt{-\left(-1+k \right)^{2}}\, \sqrt{k^{3} \left(x^{2}-\frac{1}{k}\right)^{2}+\left(-k^{3}+2 k^{2}-k \right) \left(x^{2}-\frac{1}{k}\right)-k^{2}+2 k -1}}{x^{2}-\frac{1}{k}}\right)}{3 \sqrt{-\left(-1+k \right)^{2}}}+\frac{\frac{\sqrt{2}\, \ln \left(\frac{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k^{2}}+\left(-k^{2}-1-\sqrt{-3 k^{2}}-k \right) \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k^{2}}}\, \sqrt{4 k^{2} \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)^{2}+4 \left(-k^{2}-1-\sqrt{-3 k^{2}}-k \right) \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)+\frac{2 \sqrt{-3 k^{2}}\, k^{2}+2 k^{3}+2 k^{2}+2 \sqrt{-3 k^{2}}\, k +2 \sqrt{-3 k^{2}}+2 k}{k^{2}}}}{2}}{x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}}\right)}{6 \sqrt{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k^{2}}}}+\frac{k \sqrt{2}\, \ln \left(\frac{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k^{2}}+\left(-k^{2}-1-\sqrt{-3 k^{2}}-k \right) \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k^{2}}}\, \sqrt{4 k^{2} \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)^{2}+4 \left(-k^{2}-1-\sqrt{-3 k^{2}}-k \right) \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)+\frac{2 \sqrt{-3 k^{2}}\, k^{2}+2 k^{3}+2 k^{2}+2 \sqrt{-3 k^{2}}\, k +2 \sqrt{-3 k^{2}}+2 k}{k^{2}}}}{2}}{x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}}\right)}{2 \sqrt{-3 k^{2}}\, \sqrt{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k^{2}}}}+\frac{\sqrt{2}\, \ln \left(\frac{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k^{2}}+\left(-k^{2}-1-k +\sqrt{-3 k^{2}}\right) \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k^{2}}}\, \sqrt{4 k^{2} \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)^{2}+4 \left(-k^{2}-1-k +\sqrt{-3 k^{2}}\right) \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)+\frac{-2 \sqrt{-3 k^{2}}\, k^{2}+2 k^{3}+2 k^{2}-2 \sqrt{-3 k^{2}}\, k -2 \sqrt{-3 k^{2}}+2 k}{k^{2}}}}{2}}{x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}}\right)}{6 \sqrt{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k^{2}}}}-\frac{k \sqrt{2}\, \ln \left(\frac{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k^{2}}+\left(-k^{2}-1-k +\sqrt{-3 k^{2}}\right) \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k^{2}}}\, \sqrt{4 k^{2} \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)^{2}+4 \left(-k^{2}-1-k +\sqrt{-3 k^{2}}\right) \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)+\frac{-2 \sqrt{-3 k^{2}}\, k^{2}+2 k^{3}+2 k^{2}-2 \sqrt{-3 k^{2}}\, k -2 \sqrt{-3 k^{2}}+2 k}{k^{2}}}}{2}}{x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}}\right)}{2 \sqrt{-3 k^{2}}\, \sqrt{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k^{2}}}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(k^{2} \textit{\_Z}^{4}+k \,\textit{\_Z}^{2}+1\right)}{\sum}\frac{\left(-k \,\underline{\hspace{1.25 ex}}\alpha^{2}-2\right) \left(-\frac{\arctanh \left(\frac{k \left(2 k^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-k^{2}-1\right) \left(\underline{\hspace{1.25 ex}}\alpha^{2} k^{4}+k^{4} x^{2}+2 k^{3} x^{2}-2 k^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+6 k^{2} x^{2}+2 k \,x^{2}+\underline{\hspace{1.25 ex}}\alpha^{2}-4 k^{2}+x^{2}-4 k -4\right)}{2 \left(k^{4}+2 k^{3}+6 k^{2}+2 k +1\right) \sqrt{-k \,\underline{\hspace{1.25 ex}}\alpha^{2} \left(k^{2}+k +1\right)}\, \sqrt{k^{3} x^{4}-k^{3} x^{2}-k \,x^{2}+k}}\right)}{\sqrt{-k \,\underline{\hspace{1.25 ex}}\alpha^{2} \left(k^{2}+k +1\right)}}+\frac{2 k \underline{\hspace{1.25 ex}}\alpha  \left(k \,\underline{\hspace{1.25 ex}}\alpha^{2}+1\right) \sqrt{-k^{2} x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticPi \left(x \sqrt{k^{2}}, -\frac{k \,\underline{\hspace{1.25 ex}}\alpha^{2}+1}{k}, \frac{1}{\sqrt{k^{2}}}\right)}{\sqrt{k^{2}}\, \sqrt{\left(k^{2} x^{4}-k^{2} x^{2}-x^{2}+1\right) k}}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(2 k \,\underline{\hspace{1.25 ex}}\alpha^{2}+1\right)}\right)}{6}}{\sqrt{k}}$&$1765$\\ \hline \end{longtable}"," ",0,"1/2*(1/3*2^(1/2)/(-1+k)*arctan(((-x^2+1)*(-k^2*x^2+1))^(1/2)/x/(-1+k))+4/3/(2*k^2+2*k+2)^(1/2)*arctan(((-x^2+1)*(-k^2*x^2+1))^(1/2)*2^(1/2)/x/(2*k^2+2*k+2)^(1/2)))*2^(1/2)+k/((-3*k^2)^(1/2)+3*k)*2^(1/2)/(((-3*k^2)^(1/2)*k^2+k^3+(-3*k^2)^(1/2)*k+k^2+(-3*k^2)^(1/2)+k)/k)^(1/2)*ln((((-3*k^2)^(1/2)*k^2+k^3+(-3*k^2)^(1/2)*k+k^2+(-3*k^2)^(1/2)+k)/k-k*(k^2+(-3*k^2)^(1/2)+k+1)*(x^2+1/2*((-3*k^2)^(1/2)+k)/k^2)+1/2*2^(1/2)*(((-3*k^2)^(1/2)*k^2+k^3+(-3*k^2)^(1/2)*k+k^2+(-3*k^2)^(1/2)+k)/k)^(1/2)*(4*k^3*(x^2+1/2*((-3*k^2)^(1/2)+k)/k^2)^2-4*k*(k^2+(-3*k^2)^(1/2)+k+1)*(x^2+1/2*((-3*k^2)^(1/2)+k)/k^2)+2*((-3*k^2)^(1/2)*k^2+k^3+(-3*k^2)^(1/2)*k+k^2+(-3*k^2)^(1/2)+k)/k)^(1/2))/(x^2+1/2*((-3*k^2)^(1/2)+k)/k^2))+k^2/((-3*k^2)^(1/2)+3*k)/(-3*k^2)^(1/2)*2^(1/2)/(((-3*k^2)^(1/2)*k^2+k^3+(-3*k^2)^(1/2)*k+k^2+(-3*k^2)^(1/2)+k)/k)^(1/2)*ln((((-3*k^2)^(1/2)*k^2+k^3+(-3*k^2)^(1/2)*k+k^2+(-3*k^2)^(1/2)+k)/k-k*(k^2+(-3*k^2)^(1/2)+k+1)*(x^2+1/2*((-3*k^2)^(1/2)+k)/k^2)+1/2*2^(1/2)*(((-3*k^2)^(1/2)*k^2+k^3+(-3*k^2)^(1/2)*k+k^2+(-3*k^2)^(1/2)+k)/k)^(1/2)*(4*k^3*(x^2+1/2*((-3*k^2)^(1/2)+k)/k^2)^2-4*k*(k^2+(-3*k^2)^(1/2)+k+1)*(x^2+1/2*((-3*k^2)^(1/2)+k)/k^2)+2*((-3*k^2)^(1/2)*k^2+k^3+(-3*k^2)^(1/2)*k+k^2+(-3*k^2)^(1/2)+k)/k)^(1/2))/(x^2+1/2*((-3*k^2)^(1/2)+k)/k^2))-k/((-3*k^2)^(1/2)-3*k)*2^(1/2)/((-(-3*k^2)^(1/2)*k^2+k^3-(-3*k^2)^(1/2)*k+k^2-(-3*k^2)^(1/2)+k)/k)^(1/2)*ln(((-(-3*k^2)^(1/2)*k^2+k^3-(-3*k^2)^(1/2)*k+k^2-(-3*k^2)^(1/2)+k)/k-k*(k^2+1+k-(-3*k^2)^(1/2))*(x^2-1/2*(-k+(-3*k^2)^(1/2))/k^2)+1/2*2^(1/2)*((-(-3*k^2)^(1/2)*k^2+k^3-(-3*k^2)^(1/2)*k+k^2-(-3*k^2)^(1/2)+k)/k)^(1/2)*(4*k^3*(x^2-1/2*(-k+(-3*k^2)^(1/2))/k^2)^2-4*k*(k^2+1+k-(-3*k^2)^(1/2))*(x^2-1/2*(-k+(-3*k^2)^(1/2))/k^2)+2*(-(-3*k^2)^(1/2)*k^2+k^3-(-3*k^2)^(1/2)*k+k^2-(-3*k^2)^(1/2)+k)/k)^(1/2))/(x^2-1/2*(-k+(-3*k^2)^(1/2))/k^2))+k^2/((-3*k^2)^(1/2)-3*k)/(-3*k^2)^(1/2)*2^(1/2)/((-(-3*k^2)^(1/2)*k^2+k^3-(-3*k^2)^(1/2)*k+k^2-(-3*k^2)^(1/2)+k)/k)^(1/2)*ln(((-(-3*k^2)^(1/2)*k^2+k^3-(-3*k^2)^(1/2)*k+k^2-(-3*k^2)^(1/2)+k)/k-k*(k^2+1+k-(-3*k^2)^(1/2))*(x^2-1/2*(-k+(-3*k^2)^(1/2))/k^2)+1/2*2^(1/2)*((-(-3*k^2)^(1/2)*k^2+k^3-(-3*k^2)^(1/2)*k+k^2-(-3*k^2)^(1/2)+k)/k)^(1/2)*(4*k^3*(x^2-1/2*(-k+(-3*k^2)^(1/2))/k^2)^2-4*k*(k^2+1+k-(-3*k^2)^(1/2))*(x^2-1/2*(-k+(-3*k^2)^(1/2))/k^2)+2*(-(-3*k^2)^(1/2)*k^2+k^3-(-3*k^2)^(1/2)*k+k^2-(-3*k^2)^(1/2)+k)/k)^(1/2))/(x^2-1/2*(-k+(-3*k^2)^(1/2))/k^2))+4*k^2/((-3*k^2)^(1/2)-3*k)/((-3*k^2)^(1/2)+3*k)/(-(-1+k)^2)^(1/2)*ln((-2*k^2+4*k-2+(-k^3+2*k^2-k)*(x^2-1/k)+2*(-(-1+k)^2)^(1/2)*(k^3*(x^2-1/k)^2+(-k^3+2*k^2-k)*(x^2-1/k)-k^2+2*k-1)^(1/2))/(x^2-1/k))","B"
1825,0,0,104,0.008000," ","int((2*c*x-d)*(a*x^4+b*x^3)^(1/4)/x,x)","\[\int \frac{\left(2 c x -d \right) \left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}}{x}\, dx\]"," ",0,"int((2*c*x-d)*(a*x^4+b*x^3)^(1/4)/x,x)","F"
1826,0,0,108,0.026000," ","int((x^6-1)/(x^6+1)/(a^3*x^3+x^6+1)^(1/3),x)","\[\int \frac{x^{6}-1}{\left(x^{6}+1\right) \left(a^{3} x^{3}+x^{6}+1\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((x^6-1)/(x^6+1)/(a^3*x^3+x^6+1)^(1/3),x)","F"
1827,1,809,110,27.916000," ","int((4*x^6+x^3+2)*(-x^7-x^4+2*x^3+x)^(1/3)/(x^6+x^3-2*x^2-1)/(x^6+x^3-x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(-\frac{3400786525179064264005064770847424 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}+49922389860154105232202548398473124 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}-3528367946997116762614315330014105 x^{6}+3400786525179064264005064770847424 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-60363960821928390686089899682541776 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}+49922389860154105232202548398473124 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}-99717198298490157965795846237779567 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(-x^{7}-x^{4}+2 x^{3}+x \right)^{\frac{2}{3}}-99717198298490157965795846237779567 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(-x^{7}-x^{4}+2 x^{3}+x \right)^{\frac{1}{3}} x -92676413861894936775913559724558339 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-3528367946997116762614315330014105 x^{3}-3400786525179064264005064770847424 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}+60252330857509350522826993270182077 \left(-x^{7}-x^{4}+2 x^{3}+x \right)^{\frac{2}{3}}+60252330857509350522826993270182077 x \left(-x^{7}-x^{4}+2 x^{3}+x \right)^{\frac{1}{3}}+6817524507757140863356473688501830 x^{2}-49922389860154105232202548398473124 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+3528367946997116762614315330014105}{\left(-1+x \right) \left(x^{5}+x^{4}+x^{3}+2 x^{2}+x +1\right)}\right)-\ln \left(-\frac{3400786525179064264005064770847424 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}-56723962910512233760212677940167972 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}+49794808438336052733593297839306443 x^{6}+3400786525179064264005064770847424 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-60363960821928390686089899682541776 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}-56723962910512233760212677940167972 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+99717198298490157965795846237779567 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(-x^{7}-x^{4}+2 x^{3}+x \right)^{\frac{2}{3}}+99717198298490157965795846237779567 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(-x^{7}-x^{4}+2 x^{3}+x \right)^{\frac{1}{3}} x +213404335505751718148093359089641891 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+49794808438336052733593297839306443 x^{3}-3400786525179064264005064770847424 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}-39464867440980807442968852967597490 \left(-x^{7}-x^{4}+2 x^{3}+x \right)^{\frac{2}{3}}-39464867440980807442968852967597490 x \left(-x^{7}-x^{4}+2 x^{3}+x \right)^{\frac{1}{3}}-146222850176066186598646985718598285 x^{2}+56723962910512233760212677940167972 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-49794808438336052733593297839306443}{\left(-1+x \right) \left(x^{5}+x^{4}+x^{3}+2 x^{2}+x +1\right)}\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+\ln \left(-\frac{3400786525179064264005064770847424 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{6}-56723962910512233760212677940167972 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{6}+49794808438336052733593297839306443 x^{6}+3400786525179064264005064770847424 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-60363960821928390686089899682541776 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}-56723962910512233760212677940167972 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+99717198298490157965795846237779567 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(-x^{7}-x^{4}+2 x^{3}+x \right)^{\frac{2}{3}}+99717198298490157965795846237779567 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(-x^{7}-x^{4}+2 x^{3}+x \right)^{\frac{1}{3}} x +213404335505751718148093359089641891 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+49794808438336052733593297839306443 x^{3}-3400786525179064264005064770847424 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}-39464867440980807442968852967597490 \left(-x^{7}-x^{4}+2 x^{3}+x \right)^{\frac{2}{3}}-39464867440980807442968852967597490 x \left(-x^{7}-x^{4}+2 x^{3}+x \right)^{\frac{1}{3}}-146222850176066186598646985718598285 x^{2}+56723962910512233760212677940167972 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-49794808438336052733593297839306443}{\left(-1+x \right) \left(x^{5}+x^{4}+x^{3}+2 x^{2}+x +1\right)}\right)$&$809$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2-_Z+1)*ln(-(3400786525179064264005064770847424*RootOf(_Z^2-_Z+1)^2*x^6+49922389860154105232202548398473124*RootOf(_Z^2-_Z+1)*x^6-3528367946997116762614315330014105*x^6+3400786525179064264005064770847424*RootOf(_Z^2-_Z+1)^2*x^3-60363960821928390686089899682541776*RootOf(_Z^2-_Z+1)^2*x^2+49922389860154105232202548398473124*RootOf(_Z^2-_Z+1)*x^3-99717198298490157965795846237779567*RootOf(_Z^2-_Z+1)*(-x^7-x^4+2*x^3+x)^(2/3)-99717198298490157965795846237779567*RootOf(_Z^2-_Z+1)*(-x^7-x^4+2*x^3+x)^(1/3)*x-92676413861894936775913559724558339*RootOf(_Z^2-_Z+1)*x^2-3528367946997116762614315330014105*x^3-3400786525179064264005064770847424*RootOf(_Z^2-_Z+1)^2+60252330857509350522826993270182077*(-x^7-x^4+2*x^3+x)^(2/3)+60252330857509350522826993270182077*x*(-x^7-x^4+2*x^3+x)^(1/3)+6817524507757140863356473688501830*x^2-49922389860154105232202548398473124*RootOf(_Z^2-_Z+1)+3528367946997116762614315330014105)/(-1+x)/(x^5+x^4+x^3+2*x^2+x+1))-ln(-(3400786525179064264005064770847424*RootOf(_Z^2-_Z+1)^2*x^6-56723962910512233760212677940167972*RootOf(_Z^2-_Z+1)*x^6+49794808438336052733593297839306443*x^6+3400786525179064264005064770847424*RootOf(_Z^2-_Z+1)^2*x^3-60363960821928390686089899682541776*RootOf(_Z^2-_Z+1)^2*x^2-56723962910512233760212677940167972*RootOf(_Z^2-_Z+1)*x^3+99717198298490157965795846237779567*RootOf(_Z^2-_Z+1)*(-x^7-x^4+2*x^3+x)^(2/3)+99717198298490157965795846237779567*RootOf(_Z^2-_Z+1)*(-x^7-x^4+2*x^3+x)^(1/3)*x+213404335505751718148093359089641891*RootOf(_Z^2-_Z+1)*x^2+49794808438336052733593297839306443*x^3-3400786525179064264005064770847424*RootOf(_Z^2-_Z+1)^2-39464867440980807442968852967597490*(-x^7-x^4+2*x^3+x)^(2/3)-39464867440980807442968852967597490*x*(-x^7-x^4+2*x^3+x)^(1/3)-146222850176066186598646985718598285*x^2+56723962910512233760212677940167972*RootOf(_Z^2-_Z+1)-49794808438336052733593297839306443)/(-1+x)/(x^5+x^4+x^3+2*x^2+x+1))*RootOf(_Z^2-_Z+1)+ln(-(3400786525179064264005064770847424*RootOf(_Z^2-_Z+1)^2*x^6-56723962910512233760212677940167972*RootOf(_Z^2-_Z+1)*x^6+49794808438336052733593297839306443*x^6+3400786525179064264005064770847424*RootOf(_Z^2-_Z+1)^2*x^3-60363960821928390686089899682541776*RootOf(_Z^2-_Z+1)^2*x^2-56723962910512233760212677940167972*RootOf(_Z^2-_Z+1)*x^3+99717198298490157965795846237779567*RootOf(_Z^2-_Z+1)*(-x^7-x^4+2*x^3+x)^(2/3)+99717198298490157965795846237779567*RootOf(_Z^2-_Z+1)*(-x^7-x^4+2*x^3+x)^(1/3)*x+213404335505751718148093359089641891*RootOf(_Z^2-_Z+1)*x^2+49794808438336052733593297839306443*x^3-3400786525179064264005064770847424*RootOf(_Z^2-_Z+1)^2-39464867440980807442968852967597490*(-x^7-x^4+2*x^3+x)^(2/3)-39464867440980807442968852967597490*x*(-x^7-x^4+2*x^3+x)^(1/3)-146222850176066186598646985718598285*x^2+56723962910512233760212677940167972*RootOf(_Z^2-_Z+1)-49794808438336052733593297839306443)/(-1+x)/(x^5+x^4+x^3+2*x^2+x+1))","C"
1828,0,0,94,180.000000," ","int(x^2/(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x)","\[\int \frac{x^{2}}{\sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}\, dx\]"," ",0,"int(x^2/(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x)","F"
1829,0,0,45,0.021000," ","int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(3/2),x)","\[\int \frac{\sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(x^{2}+1\right)^{\frac{3}{2}}}\, dx\]"," ",0,"int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(3/2),x)","F"
1830,0,0,45,0.000000," ","int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(3/2),x)","\[\int \frac{\sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(x^{2}+1\right)^{\frac{3}{2}}}\, dx\]"," ",0,"int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(3/2),x)","F"
1831,0,0,45,0.002000," ","int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(3/2),x)","\[\int \frac{\sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(x^{2}+1\right)^{\frac{3}{2}}}\, dx\]"," ",0,"int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(3/2),x)","F"
1832,1,806,93,8.345000," ","int(1/(-1+x)/(x^2-2*x-3)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{3}+2\right) \ln \left(-\frac{4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+2\right)^{2} x^{2}-20 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right)^{3} x^{2}-8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+2\right)^{2} x +40 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right)^{3} x +120 \left(x^{2}-2 x -3\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right)^{2}-198 \left(x^{2}-2 x -3\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right)+3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right) x^{2}-120 \left(x^{2}-2 x -3\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+2\right)^{2}-15 \RootOf \left(\textit{\_Z}^{3}+2\right) x^{2}-6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right) x +30 \RootOf \left(\textit{\_Z}^{3}+2\right) x -21 \left(x^{2}-2 x -3\right)^{\frac{2}{3}}-37 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right)+185 \RootOf \left(\textit{\_Z}^{3}+2\right)}{\left(-1+x \right)^{2}}\right)}{4}+\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right) \ln \left(-\frac{80 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+2\right)^{2} x^{2}-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right)^{3} x^{2}-160 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+2\right)^{2} x +8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right)^{3} x -240 \left(x^{2}-2 x -3\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+84 \left(x^{2}-2 x -3\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right)-140 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right) x^{2}+240 \left(x^{2}-2 x -3\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+7 \RootOf \left(\textit{\_Z}^{3}+2\right) x^{2}+280 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right) x -14 \RootOf \left(\textit{\_Z}^{3}+2\right) x +198 \left(x^{2}-2 x -3\right)^{\frac{2}{3}}+740 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right)-37 \RootOf \left(\textit{\_Z}^{3}+2\right)}{\left(-1+x \right)^{2}}\right)}{2}$&$806$\\ \hline \end{longtable}"," ",0,"1/4*RootOf(_Z^3+2)*ln(-(4*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^2-20*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^2-8*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x+40*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x+120*(x^2-2*x-3)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2-198*(x^2-2*x-3)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)+3*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^2-120*(x^2-2*x-3)^(1/3)*RootOf(_Z^3+2)^2-15*RootOf(_Z^3+2)*x^2-6*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x+30*RootOf(_Z^3+2)*x-21*(x^2-2*x-3)^(2/3)-37*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)+185*RootOf(_Z^3+2))/(-1+x)^2)+1/2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*ln(-(80*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^2-4*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^2-160*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x+8*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x-240*(x^2-2*x-3)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2+84*(x^2-2*x-3)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)-140*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^2+240*(x^2-2*x-3)^(1/3)*RootOf(_Z^3+2)^2+7*RootOf(_Z^3+2)*x^2+280*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x-14*RootOf(_Z^3+2)*x+198*(x^2-2*x-3)^(2/3)+740*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)-37*RootOf(_Z^3+2))/(-1+x)^2)","C"
1833,1,802,93,8.370000," ","int(1/(-1+x)/(x^2-2*x-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{3}+4\right) \ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) x^{2}+\RootOf \left(\textit{\_Z}^{3}+4\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right)^{2} x^{2}+12 \left(x^{2}-2 x -1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+4 \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) x -2 \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right)^{2} x -12 \left(x^{2}-2 x -1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}-15 \left(x^{2}-2 x -1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)-2 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}+\RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) x^{2}-9 \left(x^{2}-2 x -1\right)^{\frac{2}{3}}+4 \RootOf \left(\textit{\_Z}^{3}+4\right) x -2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) x +14 \RootOf \left(\textit{\_Z}^{3}+4\right)-7 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right)}{\left(-1+x \right)^{2}}\right)}{4}+\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{3}+4\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) x^{2}-8 \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right)^{2} x^{2}+24 \left(x^{2}-2 x -1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}-2 \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) x +16 \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right)^{2} x -24 \left(x^{2}-2 x -1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}-18 \left(x^{2}-2 x -1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)-3 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}+24 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) x^{2}-30 \left(x^{2}-2 x -1\right)^{\frac{2}{3}}+6 \RootOf \left(\textit{\_Z}^{3}+4\right) x -48 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) x +7 \RootOf \left(\textit{\_Z}^{3}+4\right)-56 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right)}{\left(-1+x \right)^{2}}\right)}{2}$&$802$\\ \hline \end{longtable}"," ",0,"1/4*RootOf(_Z^3+4)*ln(-(-2*RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^2+RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*x^2+12*(x^2-2*x-1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^2+4*RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x-2*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*x-12*(x^2-2*x-1)^(1/3)*RootOf(_Z^3+4)^2-15*(x^2-2*x-1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)-2*RootOf(_Z^3+4)*x^2+RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^2-9*(x^2-2*x-1)^(2/3)+4*RootOf(_Z^3+4)*x-2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x+14*RootOf(_Z^3+4)-7*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2))/(-1+x)^2)+1/2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*ln((RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^2-8*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*x^2+24*(x^2-2*x-1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^2-2*RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x+16*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*x-24*(x^2-2*x-1)^(1/3)*RootOf(_Z^3+4)^2-18*(x^2-2*x-1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)-3*RootOf(_Z^3+4)*x^2+24*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^2-30*(x^2-2*x-1)^(2/3)+6*RootOf(_Z^3+4)*x-48*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x+7*RootOf(_Z^3+4)-56*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2))/(-1+x)^2)","C"
1834,1,1212,93,8.212000," ","int(1/(1+x)/(x^2+2*x-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1212$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*ln((RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^2+10*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*x^2+2*RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x+20*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*x-24*(x^2+2*x-1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^2-9*(x^2+2*x-1)^(1/3)*RootOf(_Z^3+4)^2-48*(x^2+2*x-1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)+RootOf(_Z^3+4)*x^2+10*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^2+2*RootOf(_Z^3+4)*x+20*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x+18*(x^2+2*x-1)^(2/3)-7*RootOf(_Z^3+4)-70*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2))/(1+x)^2)-1/4*ln((4*RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^2+10*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*x^2+8*RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x+20*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*x+24*(x^2+2*x-1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^2+15*(x^2+2*x-1)^(1/3)*RootOf(_Z^3+4)^2+48*(x^2+2*x-1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)-12*RootOf(_Z^3+4)*x^2-30*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^2-24*RootOf(_Z^3+4)*x-60*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x-30*(x^2+2*x-1)^(2/3)+28*RootOf(_Z^3+4)+70*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2))/(1+x)^2)*RootOf(_Z^3+4)-1/2*ln((4*RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^2+10*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*x^2+8*RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x+20*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*x+24*(x^2+2*x-1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^2+15*(x^2+2*x-1)^(1/3)*RootOf(_Z^3+4)^2+48*(x^2+2*x-1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)-12*RootOf(_Z^3+4)*x^2-30*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^2-24*RootOf(_Z^3+4)*x-60*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x-30*(x^2+2*x-1)^(2/3)+28*RootOf(_Z^3+4)+70*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2))/(1+x)^2)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)","C"
1835,0,0,111,0.155000," ","int((-2*a*b*x^2+(a+b)*x^3)/(-a+x)/(-b+x)/(x^2*(-a+x)*(-b+x))^(1/4)/(-a*b*d+(a+b)*d*x+(1-d)*x^2),x)","\[\int \frac{-2 a b \,x^{2}+\left(a +b \right) x^{3}}{\left(-a +x \right) \left(-b +x \right) \left(x^{2} \left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{4}} \left(-a b d +\left(a +b \right) d x +\left(1-d \right) x^{2}\right)}\, dx\]"," ",0,"int((-2*a*b*x^2+(a+b)*x^3)/(-a+x)/(-b+x)/(x^2*(-a+x)*(-b+x))^(1/4)/(-a*b*d+(a+b)*d*x+(1-d)*x^2),x)","F"
1836,0,0,113,0.022000," ","int((a^2-2*a*x+x^2)*(a*b^2-2*(2*a-b)*b*x+(3*a-2*b)*x^2)/(x*(-a+x)*(-b+x)^2)^(3/4)/(a^3*d+(-3*a^2*d+b^2)*x+(3*a*d-2*b)*x^2+(1-d)*x^3),x)","\[\int \frac{\left(a^{2}-2 a x +x^{2}\right) \left(a \,b^{2}-2 \left(2 a -b \right) b x +\left(3 a -2 b \right) x^{2}\right)}{\left(x \left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{3}{4}} \left(a^{3} d +\left(-3 a^{2} d +b^{2}\right) x +\left(3 a d -2 b \right) x^{2}+\left(1-d \right) x^{3}\right)}\, dx\]"," ",0,"int((a^2-2*a*x+x^2)*(a*b^2-2*(2*a-b)*b*x+(3*a-2*b)*x^2)/(x*(-a+x)*(-b+x)^2)^(3/4)/(a^3*d+(-3*a^2*d+b^2)*x+(3*a*d-2*b)*x^2+(1-d)*x^3),x)","F"
1837,1,1540,111,0.410000," ","int((-1+k^(3/2)*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/2)/(1+k^(3/2)*x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)}}{x \left(-1+k \right)}\right)}{-3+3 k}+\frac{4 \arctan \left(\frac{\sqrt{\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)}\, \sqrt{2}}{x \sqrt{2 k^{2}+2 k +2}}\right)}{3 \sqrt{2 k^{2}+2 k +2}}\right) \sqrt{2}}{2}-\frac{k \sqrt{2}\, \ln \left(\frac{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k}-k \left(k^{2}+\sqrt{-3 k^{2}}+k +1\right) \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k}}\, \sqrt{4 k^{3} \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)^{2}-4 k \left(k^{2}+\sqrt{-3 k^{2}}+k +1\right) \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)+\frac{2 \sqrt{-3 k^{2}}\, k^{2}+2 k^{3}+2 k^{2}+2 \sqrt{-3 k^{2}}\, k +2 \sqrt{-3 k^{2}}+2 k}{k}}}{2}}{x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}}\right)}{\left(\sqrt{-3 k^{2}}+3 k \right) \sqrt{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k}}}-\frac{k^{2} \sqrt{2}\, \ln \left(\frac{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k}-k \left(k^{2}+\sqrt{-3 k^{2}}+k +1\right) \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k}}\, \sqrt{4 k^{3} \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)^{2}-4 k \left(k^{2}+\sqrt{-3 k^{2}}+k +1\right) \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)+\frac{2 \sqrt{-3 k^{2}}\, k^{2}+2 k^{3}+2 k^{2}+2 \sqrt{-3 k^{2}}\, k +2 \sqrt{-3 k^{2}}+2 k}{k}}}{2}}{x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}}\right)}{\left(\sqrt{-3 k^{2}}+3 k \right) \sqrt{-3 k^{2}}\, \sqrt{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k}}}+\frac{k \sqrt{2}\, \ln \left(\frac{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k}-k \left(k^{2}+1+k -\sqrt{-3 k^{2}}\right) \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k}}\, \sqrt{4 k^{3} \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)^{2}-4 k \left(k^{2}+1+k -\sqrt{-3 k^{2}}\right) \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)+\frac{-2 \sqrt{-3 k^{2}}\, k^{2}+2 k^{3}+2 k^{2}-2 \sqrt{-3 k^{2}}\, k -2 \sqrt{-3 k^{2}}+2 k}{k}}}{2}}{x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}}\right)}{\left(\sqrt{-3 k^{2}}-3 k \right) \sqrt{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k}}}-\frac{k^{2} \sqrt{2}\, \ln \left(\frac{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k}-k \left(k^{2}+1+k -\sqrt{-3 k^{2}}\right) \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k}}\, \sqrt{4 k^{3} \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)^{2}-4 k \left(k^{2}+1+k -\sqrt{-3 k^{2}}\right) \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)+\frac{-2 \sqrt{-3 k^{2}}\, k^{2}+2 k^{3}+2 k^{2}-2 \sqrt{-3 k^{2}}\, k -2 \sqrt{-3 k^{2}}+2 k}{k}}}{2}}{x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}}\right)}{\left(\sqrt{-3 k^{2}}-3 k \right) \sqrt{-3 k^{2}}\, \sqrt{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k}}}-\frac{4 k^{2} \ln \left(\frac{-2 k^{2}+4 k -2+\left(-k^{3}+2 k^{2}-k \right) \left(x^{2}-\frac{1}{k}\right)+2 \sqrt{-\left(-1+k \right)^{2}}\, \sqrt{k^{3} \left(x^{2}-\frac{1}{k}\right)^{2}+\left(-k^{3}+2 k^{2}-k \right) \left(x^{2}-\frac{1}{k}\right)-k^{2}+2 k -1}}{x^{2}-\frac{1}{k}}\right)}{\left(\sqrt{-3 k^{2}}-3 k \right) \left(\sqrt{-3 k^{2}}+3 k \right) \sqrt{-\left(-1+k \right)^{2}}}$&$1540$\\ default&$\frac{\sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticF \left(x , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}+\frac{-\frac{\sqrt{2}\, \ln \left(\frac{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k^{2}}+\left(-k^{2}-1-\sqrt{-3 k^{2}}-k \right) \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k^{2}}}\, \sqrt{4 k^{2} \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)^{2}+4 \left(-k^{2}-1-\sqrt{-3 k^{2}}-k \right) \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)+\frac{2 \sqrt{-3 k^{2}}\, k^{2}+2 k^{3}+2 k^{2}+2 \sqrt{-3 k^{2}}\, k +2 \sqrt{-3 k^{2}}+2 k}{k^{2}}}}{2}}{x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}}\right)}{6 \sqrt{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k^{2}}}}-\frac{k \sqrt{2}\, \ln \left(\frac{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k^{2}}+\left(-k^{2}-1-\sqrt{-3 k^{2}}-k \right) \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k^{2}}}\, \sqrt{4 k^{2} \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)^{2}+4 \left(-k^{2}-1-\sqrt{-3 k^{2}}-k \right) \left(x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}\right)+\frac{2 \sqrt{-3 k^{2}}\, k^{2}+2 k^{3}+2 k^{2}+2 \sqrt{-3 k^{2}}\, k +2 \sqrt{-3 k^{2}}+2 k}{k^{2}}}}{2}}{x^{2}+\frac{\sqrt{-3 k^{2}}+k}{2 k^{2}}}\right)}{2 \sqrt{-3 k^{2}}\, \sqrt{\frac{\sqrt{-3 k^{2}}\, k^{2}+k^{3}+\sqrt{-3 k^{2}}\, k +k^{2}+\sqrt{-3 k^{2}}+k}{k^{2}}}}-\frac{\sqrt{2}\, \ln \left(\frac{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k^{2}}+\left(-k^{2}-1-k +\sqrt{-3 k^{2}}\right) \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k^{2}}}\, \sqrt{4 k^{2} \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)^{2}+4 \left(-k^{2}-1-k +\sqrt{-3 k^{2}}\right) \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)+\frac{-2 \sqrt{-3 k^{2}}\, k^{2}+2 k^{3}+2 k^{2}-2 \sqrt{-3 k^{2}}\, k -2 \sqrt{-3 k^{2}}+2 k}{k^{2}}}}{2}}{x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}}\right)}{6 \sqrt{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k^{2}}}}+\frac{k \sqrt{2}\, \ln \left(\frac{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k^{2}}+\left(-k^{2}-1-k +\sqrt{-3 k^{2}}\right) \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)+\frac{\sqrt{2}\, \sqrt{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k^{2}}}\, \sqrt{4 k^{2} \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)^{2}+4 \left(-k^{2}-1-k +\sqrt{-3 k^{2}}\right) \left(x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}\right)+\frac{-2 \sqrt{-3 k^{2}}\, k^{2}+2 k^{3}+2 k^{2}-2 \sqrt{-3 k^{2}}\, k -2 \sqrt{-3 k^{2}}+2 k}{k^{2}}}}{2}}{x^{2}-\frac{-k +\sqrt{-3 k^{2}}}{2 k^{2}}}\right)}{2 \sqrt{-3 k^{2}}\, \sqrt{\frac{-\sqrt{-3 k^{2}}\, k^{2}+k^{3}-\sqrt{-3 k^{2}}\, k +k^{2}-\sqrt{-3 k^{2}}+k}{k^{2}}}}-\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(k^{2} \textit{\_Z}^{4}+k \,\textit{\_Z}^{2}+1\right)}{\sum}\frac{\left(k \,\underline{\hspace{1.25 ex}}\alpha^{2}+2\right) \left(-\frac{\arctanh \left(\frac{k \left(2 k^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-k^{2}-1\right) \left(\underline{\hspace{1.25 ex}}\alpha^{2} k^{4}+k^{4} x^{2}+2 k^{3} x^{2}-2 k^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+6 k^{2} x^{2}+2 k \,x^{2}+\underline{\hspace{1.25 ex}}\alpha^{2}-4 k^{2}+x^{2}-4 k -4\right)}{2 \left(k^{4}+2 k^{3}+6 k^{2}+2 k +1\right) \sqrt{-k \,\underline{\hspace{1.25 ex}}\alpha^{2} \left(k^{2}+k +1\right)}\, \sqrt{k^{3} x^{4}-k^{3} x^{2}-k \,x^{2}+k}}\right)}{\sqrt{-k \,\underline{\hspace{1.25 ex}}\alpha^{2} \left(k^{2}+k +1\right)}}+\frac{2 k \underline{\hspace{1.25 ex}}\alpha  \left(k \,\underline{\hspace{1.25 ex}}\alpha^{2}+1\right) \sqrt{-k^{2} x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticPi \left(x \sqrt{k^{2}}, -\frac{k \,\underline{\hspace{1.25 ex}}\alpha^{2}+1}{k}, \frac{1}{\sqrt{k^{2}}}\right)}{\sqrt{k^{2}}\, \sqrt{\left(k^{2} x^{4}-k^{2} x^{2}-x^{2}+1\right) k}}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(2 k \,\underline{\hspace{1.25 ex}}\alpha^{2}+1\right)}\right)}{6}}{\sqrt{k}}-\frac{2 \sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticPi \left(x , k , k\right)}{3 \sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}+\frac{\ln \left(\frac{-2 k^{2}+4 k -2+\left(-k^{3}+2 k^{2}-k \right) \left(x^{2}-\frac{1}{k}\right)+2 \sqrt{-\left(-1+k \right)^{2}}\, \sqrt{k^{3} \left(x^{2}-\frac{1}{k}\right)^{2}+\left(-k^{3}+2 k^{2}-k \right) \left(x^{2}-\frac{1}{k}\right)-k^{2}+2 k -1}}{x^{2}-\frac{1}{k}}\right)}{3 \sqrt{-\left(-1+k \right)^{2}}}$&$1764$\\ \hline \end{longtable}"," ",0,"1/2*(1/3*2^(1/2)/(-1+k)*arctan(((-x^2+1)*(-k^2*x^2+1))^(1/2)/x/(-1+k))+4/3/(2*k^2+2*k+2)^(1/2)*arctan(((-x^2+1)*(-k^2*x^2+1))^(1/2)*2^(1/2)/x/(2*k^2+2*k+2)^(1/2)))*2^(1/2)-k/((-3*k^2)^(1/2)+3*k)*2^(1/2)/(((-3*k^2)^(1/2)*k^2+k^3+(-3*k^2)^(1/2)*k+k^2+(-3*k^2)^(1/2)+k)/k)^(1/2)*ln((((-3*k^2)^(1/2)*k^2+k^3+(-3*k^2)^(1/2)*k+k^2+(-3*k^2)^(1/2)+k)/k-k*(k^2+(-3*k^2)^(1/2)+k+1)*(x^2+1/2*((-3*k^2)^(1/2)+k)/k^2)+1/2*2^(1/2)*(((-3*k^2)^(1/2)*k^2+k^3+(-3*k^2)^(1/2)*k+k^2+(-3*k^2)^(1/2)+k)/k)^(1/2)*(4*k^3*(x^2+1/2*((-3*k^2)^(1/2)+k)/k^2)^2-4*k*(k^2+(-3*k^2)^(1/2)+k+1)*(x^2+1/2*((-3*k^2)^(1/2)+k)/k^2)+2*((-3*k^2)^(1/2)*k^2+k^3+(-3*k^2)^(1/2)*k+k^2+(-3*k^2)^(1/2)+k)/k)^(1/2))/(x^2+1/2*((-3*k^2)^(1/2)+k)/k^2))-k^2/((-3*k^2)^(1/2)+3*k)/(-3*k^2)^(1/2)*2^(1/2)/(((-3*k^2)^(1/2)*k^2+k^3+(-3*k^2)^(1/2)*k+k^2+(-3*k^2)^(1/2)+k)/k)^(1/2)*ln((((-3*k^2)^(1/2)*k^2+k^3+(-3*k^2)^(1/2)*k+k^2+(-3*k^2)^(1/2)+k)/k-k*(k^2+(-3*k^2)^(1/2)+k+1)*(x^2+1/2*((-3*k^2)^(1/2)+k)/k^2)+1/2*2^(1/2)*(((-3*k^2)^(1/2)*k^2+k^3+(-3*k^2)^(1/2)*k+k^2+(-3*k^2)^(1/2)+k)/k)^(1/2)*(4*k^3*(x^2+1/2*((-3*k^2)^(1/2)+k)/k^2)^2-4*k*(k^2+(-3*k^2)^(1/2)+k+1)*(x^2+1/2*((-3*k^2)^(1/2)+k)/k^2)+2*((-3*k^2)^(1/2)*k^2+k^3+(-3*k^2)^(1/2)*k+k^2+(-3*k^2)^(1/2)+k)/k)^(1/2))/(x^2+1/2*((-3*k^2)^(1/2)+k)/k^2))+k/((-3*k^2)^(1/2)-3*k)*2^(1/2)/((-(-3*k^2)^(1/2)*k^2+k^3-(-3*k^2)^(1/2)*k+k^2-(-3*k^2)^(1/2)+k)/k)^(1/2)*ln(((-(-3*k^2)^(1/2)*k^2+k^3-(-3*k^2)^(1/2)*k+k^2-(-3*k^2)^(1/2)+k)/k-k*(k^2+1+k-(-3*k^2)^(1/2))*(x^2-1/2*(-k+(-3*k^2)^(1/2))/k^2)+1/2*2^(1/2)*((-(-3*k^2)^(1/2)*k^2+k^3-(-3*k^2)^(1/2)*k+k^2-(-3*k^2)^(1/2)+k)/k)^(1/2)*(4*k^3*(x^2-1/2*(-k+(-3*k^2)^(1/2))/k^2)^2-4*k*(k^2+1+k-(-3*k^2)^(1/2))*(x^2-1/2*(-k+(-3*k^2)^(1/2))/k^2)+2*(-(-3*k^2)^(1/2)*k^2+k^3-(-3*k^2)^(1/2)*k+k^2-(-3*k^2)^(1/2)+k)/k)^(1/2))/(x^2-1/2*(-k+(-3*k^2)^(1/2))/k^2))-k^2/((-3*k^2)^(1/2)-3*k)/(-3*k^2)^(1/2)*2^(1/2)/((-(-3*k^2)^(1/2)*k^2+k^3-(-3*k^2)^(1/2)*k+k^2-(-3*k^2)^(1/2)+k)/k)^(1/2)*ln(((-(-3*k^2)^(1/2)*k^2+k^3-(-3*k^2)^(1/2)*k+k^2-(-3*k^2)^(1/2)+k)/k-k*(k^2+1+k-(-3*k^2)^(1/2))*(x^2-1/2*(-k+(-3*k^2)^(1/2))/k^2)+1/2*2^(1/2)*((-(-3*k^2)^(1/2)*k^2+k^3-(-3*k^2)^(1/2)*k+k^2-(-3*k^2)^(1/2)+k)/k)^(1/2)*(4*k^3*(x^2-1/2*(-k+(-3*k^2)^(1/2))/k^2)^2-4*k*(k^2+1+k-(-3*k^2)^(1/2))*(x^2-1/2*(-k+(-3*k^2)^(1/2))/k^2)+2*(-(-3*k^2)^(1/2)*k^2+k^3-(-3*k^2)^(1/2)*k+k^2-(-3*k^2)^(1/2)+k)/k)^(1/2))/(x^2-1/2*(-k+(-3*k^2)^(1/2))/k^2))-4*k^2/((-3*k^2)^(1/2)-3*k)/((-3*k^2)^(1/2)+3*k)/(-(-1+k)^2)^(1/2)*ln((-2*k^2+4*k-2+(-k^3+2*k^2-k)*(x^2-1/k)+2*(-(-1+k)^2)^(1/2)*(k^3*(x^2-1/k)^2+(-k^3+2*k^2-k)*(x^2-1/k)-k^2+2*k-1)^(1/2))/(x^2-1/k))","B"
1838,1,917,105,3.320000," ","int((x^3-x^2-x)^(1/2)/(x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right) \ln \left(\frac{3935232 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{5} x^{2}-5902848 x \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{5}-3935232 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{5}-1338592 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{3} x^{2}+962592 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{3} x +65024 \sqrt{x^{3}-x^{2}-x}\, \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2}+1338592 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{3}-160080 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right) x^{2}+693680 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right) x -286015 \sqrt{x^{3}-x^{2}-x}+160080 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)}{\left(16 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2} x -32 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2}+5 x \right)^{2}}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{2}+16 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2}+2\right) \ln \left(-\frac{-983808 \RootOf \left(\textit{\_Z}^{2}+16 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2}+2\right) \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{4} x^{2}+1475712 \RootOf \left(\textit{\_Z}^{2}+16 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2}+2\right) \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{4} x +983808 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{4} \RootOf \left(\textit{\_Z}^{2}+16 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2}+2\right)-580600 \RootOf \left(\textit{\_Z}^{2}+16 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2}+2\right) \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2} x^{2}+609576 \RootOf \left(\textit{\_Z}^{2}+16 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2}+2\right) \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2} x +65024 \sqrt{x^{3}-x^{2}-x}\, \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2}+580600 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2} \RootOf \left(\textit{\_Z}^{2}+16 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2}+2\right)-17183 \RootOf \left(\textit{\_Z}^{2}+16 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2}+2\right) x^{2}-120281 \RootOf \left(\textit{\_Z}^{2}+16 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2}+2\right) x +294143 \sqrt{x^{3}-x^{2}-x}+17183 \RootOf \left(\textit{\_Z}^{2}+16 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2}+2\right)}{\left(16 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2} x -32 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2}-3 x -4\right)^{2}}\right)}{8}-2 \ln \left(\frac{-16 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2} x^{2}+32 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2} x +16 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2}-x^{2}+4 \sqrt{x^{3}-x^{2}-x}+2 x +1}{\left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2}-\frac{\ln \left(\frac{-16 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2} x^{2}+32 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2} x +16 \RootOf \left(256 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+5\right)^{2}-x^{2}+4 \sqrt{x^{3}-x^{2}-x}+2 x +1}{\left(-1+x \right) \left(1+x \right)}\right)}{8}$&$917$\\ elliptic&$\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, -\frac{i \sqrt{5}}{5}+\frac{1}{2}-\frac{\sqrt{5}}{10}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{10 \sqrt{x^{3}-x^{2}-x}}+\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, -\frac{i \sqrt{5}}{5}+\frac{1}{2}-\frac{\sqrt{5}}{10}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{20 \sqrt{x^{3}-x^{2}-x}}-\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, -\frac{i \sqrt{5}}{5}+\frac{1}{2}-\frac{\sqrt{5}}{10}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{20 \sqrt{x^{3}-x^{2}-x}}+\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{i \sqrt{5}}{5}+\frac{1}{2}-\frac{\sqrt{5}}{10}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{10 \sqrt{x^{3}-x^{2}-x}}-\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{i \sqrt{5}}{5}+\frac{1}{2}-\frac{\sqrt{5}}{10}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{20 \sqrt{x^{3}-x^{2}-x}}+\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{i \sqrt{5}}{5}+\frac{1}{2}-\frac{\sqrt{5}}{10}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{20 \sqrt{x^{3}-x^{2}-x}}+\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{20 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{20 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{-\frac{1}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{20 \sqrt{x^{3}-x^{2}-x}\, \left(-\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}+\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{-\frac{1}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{20 \sqrt{x^{3}-x^{2}-x}\, \left(-\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}$&$1430$\\ default&$\text{Expression too large to display}$&$2289$\\ \hline \end{longtable}"," ",0,"-1/2*RootOf(256*_Z^4+32*_Z^2+5)*ln((3935232*RootOf(256*_Z^4+32*_Z^2+5)^5*x^2-5902848*x*RootOf(256*_Z^4+32*_Z^2+5)^5-3935232*RootOf(256*_Z^4+32*_Z^2+5)^5-1338592*RootOf(256*_Z^4+32*_Z^2+5)^3*x^2+962592*RootOf(256*_Z^4+32*_Z^2+5)^3*x+65024*(x^3-x^2-x)^(1/2)*RootOf(256*_Z^4+32*_Z^2+5)^2+1338592*RootOf(256*_Z^4+32*_Z^2+5)^3-160080*RootOf(256*_Z^4+32*_Z^2+5)*x^2+693680*RootOf(256*_Z^4+32*_Z^2+5)*x-286015*(x^3-x^2-x)^(1/2)+160080*RootOf(256*_Z^4+32*_Z^2+5))/(16*RootOf(256*_Z^4+32*_Z^2+5)^2*x-32*RootOf(256*_Z^4+32*_Z^2+5)^2+5*x)^2)-1/8*RootOf(_Z^2+16*RootOf(256*_Z^4+32*_Z^2+5)^2+2)*ln(-(-983808*RootOf(_Z^2+16*RootOf(256*_Z^4+32*_Z^2+5)^2+2)*RootOf(256*_Z^4+32*_Z^2+5)^4*x^2+1475712*RootOf(_Z^2+16*RootOf(256*_Z^4+32*_Z^2+5)^2+2)*RootOf(256*_Z^4+32*_Z^2+5)^4*x+983808*RootOf(256*_Z^4+32*_Z^2+5)^4*RootOf(_Z^2+16*RootOf(256*_Z^4+32*_Z^2+5)^2+2)-580600*RootOf(_Z^2+16*RootOf(256*_Z^4+32*_Z^2+5)^2+2)*RootOf(256*_Z^4+32*_Z^2+5)^2*x^2+609576*RootOf(_Z^2+16*RootOf(256*_Z^4+32*_Z^2+5)^2+2)*RootOf(256*_Z^4+32*_Z^2+5)^2*x+65024*(x^3-x^2-x)^(1/2)*RootOf(256*_Z^4+32*_Z^2+5)^2+580600*RootOf(256*_Z^4+32*_Z^2+5)^2*RootOf(_Z^2+16*RootOf(256*_Z^4+32*_Z^2+5)^2+2)-17183*RootOf(_Z^2+16*RootOf(256*_Z^4+32*_Z^2+5)^2+2)*x^2-120281*RootOf(_Z^2+16*RootOf(256*_Z^4+32*_Z^2+5)^2+2)*x+294143*(x^3-x^2-x)^(1/2)+17183*RootOf(_Z^2+16*RootOf(256*_Z^4+32*_Z^2+5)^2+2))/(16*RootOf(256*_Z^4+32*_Z^2+5)^2*x-32*RootOf(256*_Z^4+32*_Z^2+5)^2-3*x-4)^2)-2*ln((-16*RootOf(256*_Z^4+32*_Z^2+5)^2*x^2+32*RootOf(256*_Z^4+32*_Z^2+5)^2*x+16*RootOf(256*_Z^4+32*_Z^2+5)^2-x^2+4*(x^3-x^2-x)^(1/2)+2*x+1)/(-1+x)/(1+x))*RootOf(256*_Z^4+32*_Z^2+5)^2-1/8*ln((-16*RootOf(256*_Z^4+32*_Z^2+5)^2*x^2+32*RootOf(256*_Z^4+32*_Z^2+5)^2*x+16*RootOf(256*_Z^4+32*_Z^2+5)^2-x^2+4*(x^3-x^2-x)^(1/2)+2*x+1)/(-1+x)/(1+x))","C"
1839,1,701,105,0.395000," ","int((a*x^3+b)*(x^4+x)^(1/2)/(c*x^3-d),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{a x \sqrt{x^{4}+x}}{3 c}-\frac{2 \left(\frac{a c +a d +b c}{c^{2}}-\frac{a}{2 c}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}-\frac{2 \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(c \,\textit{\_Z}^{3}-d \right)}{\sum}\frac{\left(-a c d -a \,d^{2}-b \,c^{2}-b c d \right) \left(1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(-1-i \sqrt{3}\right) \sqrt{\frac{x \left(3+i \sqrt{3}\right)}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \sqrt{3}+2 x -1}{\left(1+x \right) \left(1-i \sqrt{3}\right)}}\, \sqrt{-\frac{-1+2 x -i \sqrt{3}}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\frac{\underline{\hspace{1.25 ex}}\alpha^{2} c \EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}\, c +i \sqrt{3}\, d +3 \underline{\hspace{1.25 ex}}\alpha^{2} c +3 d}{6 d}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{d}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(c +d \right) \left(3+i \sqrt{3}\right) \sqrt{x \left(1+x \right) \left(i \sqrt{3}+2 x -1\right) \left(-1+2 x -i \sqrt{3}\right)}}\right)}{3 c^{2}}$&$701$\\ risch&$\frac{a \,x^{2} \left(x^{3}+1\right)}{3 c \sqrt{x \left(x^{3}+1\right)}}+\frac{-\frac{2 \left(a c +2 a d +2 b c \right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{c \left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{4 \left(a c d +a \,d^{2}+b \,c^{2}+b c d \right) \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(c \,\textit{\_Z}^{3}-d \right)}{\sum}\frac{\left(1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(-1-i \sqrt{3}\right) \sqrt{\frac{x \left(3+i \sqrt{3}\right)}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \sqrt{3}+2 x -1}{\left(1+x \right) \left(1-i \sqrt{3}\right)}}\, \sqrt{-\frac{-1+2 x -i \sqrt{3}}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\frac{\underline{\hspace{1.25 ex}}\alpha^{2} c \EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}\, c +i \sqrt{3}\, d +3 \underline{\hspace{1.25 ex}}\alpha^{2} c +3 d}{6 d}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{d}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(c +d \right) \left(3+i \sqrt{3}\right) \sqrt{x \left(1+x \right) \left(i \sqrt{3}+2 x -1\right) \left(-1+2 x -i \sqrt{3}\right)}}\right)}{3 c}}{2 c}$&$706$\\ default&$\frac{a \left(\frac{x \sqrt{x^{4}+x}}{3}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{c}+\frac{\left(a d +b c \right) \left(-\frac{2 \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{c \left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}-\frac{2 \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(c \,\textit{\_Z}^{3}-d \right)}{\sum}\frac{\left(-c -d \right) \left(1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(-1-i \sqrt{3}\right) \sqrt{\frac{x \left(3+i \sqrt{3}\right)}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \sqrt{3}+2 x -1}{\left(1+x \right) \left(1-i \sqrt{3}\right)}}\, \sqrt{-\frac{-1+2 x -i \sqrt{3}}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\frac{\underline{\hspace{1.25 ex}}\alpha^{2} c \EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}\, c +i \sqrt{3}\, d +3 \underline{\hspace{1.25 ex}}\alpha^{2} c +3 d}{6 d}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{d}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(c +d \right) \left(3+i \sqrt{3}\right) \sqrt{x \left(1+x \right) \left(i \sqrt{3}+2 x -1\right) \left(-1+2 x -i \sqrt{3}\right)}}\right)}{3 c}\right)}{c}$&$970$\\ \hline \end{longtable}"," ",0,"1/3*a*x*(x^4+x)^(1/2)/c-2*((a*c+a*d+b*c)/c^2-1/2/c*a)*(-1/2-1/2*I*3^(1/2))*((3/2+1/2*I*3^(1/2))*x/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2)*(1+x)^2*(-(x-1/2+1/2*I*3^(1/2))/(1/2-1/2*I*3^(1/2))/(1+x))^(1/2)*(-(x-1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2)/(3/2+1/2*I*3^(1/2))/(x*(1+x)*(x-1/2+1/2*I*3^(1/2))*(x-1/2-1/2*I*3^(1/2)))^(1/2)*(-EllipticF(((3/2+1/2*I*3^(1/2))*x/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2),((-3/2+1/2*I*3^(1/2))*(-1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+EllipticPi(((3/2+1/2*I*3^(1/2))*x/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2),(1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)),((-3/2+1/2*I*3^(1/2))*(-1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)))-2/3/c^2*4^(1/2)*sum((-a*c*d-a*d^2-b*c^2-b*c*d)/_alpha*(1+x)^2*(_alpha^2-_alpha+1)/(c+d)*(-1-I*3^(1/2))*(x/(1+x)*(3+I*3^(1/2))/(1+I*3^(1/2)))^(1/2)*(-1/(1+x)*(I*3^(1/2)+2*x-1)/(1-I*3^(1/2)))^(1/2)*(-1/(1+x)*(-1+2*x-I*3^(1/2))/(1+I*3^(1/2)))^(1/2)/(3+I*3^(1/2))/(x*(1+x)*(I*3^(1/2)+2*x-1)*(-1+2*x-I*3^(1/2)))^(1/2)*(EllipticF(((3/2+1/2*I*3^(1/2))*x/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2),((-3/2+1/2*I*3^(1/2))*(-1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+_alpha^2*c/d*EllipticPi(((3/2+1/2*I*3^(1/2))*x/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2),1/6*(I*_alpha^2*3^(1/2)*c+I*3^(1/2)*d+3*_alpha^2*c+3*d)/d,((-3/2+1/2*I*3^(1/2))*(-1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))),_alpha=RootOf(_Z^3*c-d))","C"
1840,1,142,96,11.650000," ","int((2*x^4-2*x+1)/x/(x^4-1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\sqrt{2}\, \Gamma \left(\frac{3}{4}\right) \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} \left(\frac{\pi  \sqrt{2}\, x^{4} \hypergeom \left(\left[1, 1, \frac{5}{4}\right], \left[2, 2\right], x^{4}\right)}{4 \Gamma \left(\frac{3}{4}\right)}+\frac{\left(-3 \ln \left(2\right)-\frac{\pi}{2}+4 \ln \left(x \right)+i \pi \right) \pi  \sqrt{2}}{\Gamma \left(\frac{3}{4}\right)}\right)}{8 \pi  \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}}}+\frac{\left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} x^{4} \hypergeom \left(\left[\frac{1}{4}, 1\right], \left[2\right], x^{4}\right)}{2 \mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}}}-\frac{2 \left(-\mathrm{signum}\left(x^{4}-1\right)\right)^{\frac{1}{4}} x \hypergeom \left(\left[\frac{1}{4}, \frac{1}{4}\right], \left[\frac{5}{4}\right], x^{4}\right)}{\mathrm{signum}\left(x^{4}-1\right)^{\frac{1}{4}}}$&$142$\\ trager&$\frac{2 \left(x^{4}-1\right)^{\frac{3}{4}}}{3}+\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{4}+2 \left(x^{4}-1\right)^{\frac{3}{4}}+2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)+2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{x^{4}}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(-\frac{2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}-\RootOf \left(\textit{\_Z}^{4}+1\right) x^{4}+2 \left(x^{4}-1\right)^{\frac{3}{4}}-2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)}{x^{4}}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} \ln \left(2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{4}+2 \left(x^{4}-1\right)^{\frac{3}{4}} x -2 x^{3} \left(x^{4}-1\right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{2}\right)}{2}+\frac{\ln \left(2 \left(x^{4}-1\right)^{\frac{3}{4}} x -2 x^{2} \sqrt{x^{4}-1}+2 x^{3} \left(x^{4}-1\right)^{\frac{1}{4}}-2 x^{4}+1\right)}{2}$&$287$\\ \hline \end{longtable}"," ",0,"1/8/Pi*2^(1/2)*GAMMA(3/4)/signum(x^4-1)^(1/4)*(-signum(x^4-1))^(1/4)*(1/4*Pi*2^(1/2)/GAMMA(3/4)*x^4*hypergeom([1,1,5/4],[2,2],x^4)+(-3*ln(2)-1/2*Pi+4*ln(x)+I*Pi)*Pi*2^(1/2)/GAMMA(3/4))+1/2/signum(x^4-1)^(1/4)*(-signum(x^4-1))^(1/4)*x^4*hypergeom([1/4,1],[2],x^4)-2/signum(x^4-1)^(1/4)*(-signum(x^4-1))^(1/4)*x*hypergeom([1/4,1/4],[5/4],x^4)","C"
1841,0,0,97,0.034000," ","int(x^2*(a*x^5-4*b)/(a*x^5+b)^(3/4)/(a*x^5+c*x^4+b),x)","\[\int \frac{x^{2} \left(a \,x^{5}-4 b \right)}{\left(a \,x^{5}+b \right)^{\frac{3}{4}} \left(a \,x^{5}+c \,x^{4}+b \right)}\, dx\]"," ",0,"int(x^2*(a*x^5-4*b)/(a*x^5+b)^(3/4)/(a*x^5+c*x^4+b),x)","F"
1842,0,0,95,0.007000," ","int(1/(x^6+2*x^5-x^4-4*x^3-x^2+2*x+1)^(1/6),x)","\[\int \frac{1}{\left(x^{6}+2 x^{5}-x^{4}-4 x^{3}-x^{2}+2 x +1\right)^{\frac{1}{6}}}\, dx\]"," ",0,"int(1/(x^6+2*x^5-x^4-4*x^3-x^2+2*x+1)^(1/6),x)","F"
1843,0,0,98,0.034000," ","int(x^2*(a*x^6-2*b)/(a*x^6+b)^(3/4)/(a*x^6+c*x^4+b),x)","\[\int \frac{x^{2} \left(a \,x^{6}-2 b \right)}{\left(a \,x^{6}+b \right)^{\frac{3}{4}} \left(a \,x^{6}+c \,x^{4}+b \right)}\, dx\]"," ",0,"int(x^2*(a*x^6-2*b)/(a*x^6+b)^(3/4)/(a*x^6+c*x^4+b),x)","F"
1844,1,435,101,18.009000," ","int((x^3+4)*(x^8+x^6+2*x^3+1)/x^4/(x^3+1)^(1/4)/(x^8-x^6-2*x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{4 \left(x^{3}+1\right)^{\frac{3}{4}}}{3 x^{3}}-\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{3}+1}\, x^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-2 \left(x^{3}+1\right)^{\frac{3}{4}} x +2 \left(x^{3}+1\right)^{\frac{1}{4}} x^{3}-\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{4}-x^{3}-1}\right)-\ln \left(-\frac{2 \left(x^{3}+1\right)^{\frac{3}{4}} x +2 x^{2} \sqrt{x^{3}+1}+2 \left(x^{3}+1\right)^{\frac{1}{4}} x^{3}+x^{4}+x^{3}+1}{x^{4}-x^{3}-1}\right)+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \sqrt{x^{3}+1}\, x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{3}+1\right)^{\frac{1}{4}} x^{3}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right) x^{4}+2 \left(x^{3}+1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right) x^{3}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{x^{4}+x^{3}+1}\right)-\RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{3}+1\right)^{\frac{1}{4}} x^{3}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \sqrt{x^{3}+1}\, x^{2}-2 \left(x^{3}+1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{x^{4}+x^{3}+1}\right)$&$435$\\ trager&$\frac{4 \left(x^{3}+1\right)^{\frac{3}{4}}}{3 x^{3}}+\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{3}+1\right)^{\frac{3}{4}} x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{3}+1\right)^{\frac{1}{4}} x^{3}-2 x^{2} \sqrt{x^{3}+1}+x^{4}+x^{3}+1}{x^{4}-x^{3}-1}\right)-\ln \left(-\frac{2 \left(x^{3}+1\right)^{\frac{3}{4}} x +2 x^{2} \sqrt{x^{3}+1}+2 \left(x^{3}+1\right)^{\frac{1}{4}} x^{3}+x^{4}+x^{3}+1}{x^{4}-x^{3}-1}\right)+\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{3}+1}\, \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{3}+1\right)^{\frac{1}{4}} x^{3}+\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) x^{4}-2 \left(x^{3}+1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) x^{3}-\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{x^{4}+x^{3}+1}\right)+\RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{3}+1\right)^{\frac{1}{4}} x^{3}+\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-2 \sqrt{x^{3}+1}\, \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) x^{2}+2 \left(x^{3}+1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{x^{4}+x^{3}+1}\right)$&$439$\\ \hline \end{longtable}"," ",0,"4/3*(x^3+1)^(3/4)/x^3-RootOf(_Z^2+1)*ln((2*RootOf(_Z^2+1)*(x^3+1)^(1/2)*x^2-RootOf(_Z^2+1)*x^4-RootOf(_Z^2+1)*x^3-2*(x^3+1)^(3/4)*x+2*(x^3+1)^(1/4)*x^3-RootOf(_Z^2+1))/(x^4-x^3-1))-ln(-(2*(x^3+1)^(3/4)*x+2*x^2*(x^3+1)^(1/2)+2*(x^3+1)^(1/4)*x^3+x^4+x^3+1)/(x^4-x^3-1))+RootOf(_Z^2+RootOf(_Z^2+1))*ln((2*RootOf(_Z^2+1)*RootOf(_Z^2+RootOf(_Z^2+1))*(x^3+1)^(1/2)*x^2+2*RootOf(_Z^2+1)*(x^3+1)^(1/4)*x^3-RootOf(_Z^2+RootOf(_Z^2+1))*x^4+2*(x^3+1)^(3/4)*x+RootOf(_Z^2+RootOf(_Z^2+1))*x^3+RootOf(_Z^2+RootOf(_Z^2+1)))/(x^4+x^3+1))-RootOf(_Z^2+1)*RootOf(_Z^2+RootOf(_Z^2+1))*ln(-(-RootOf(_Z^2+RootOf(_Z^2+1))*RootOf(_Z^2+1)*x^4+2*RootOf(_Z^2+1)*(x^3+1)^(1/4)*x^3+RootOf(_Z^2+RootOf(_Z^2+1))*RootOf(_Z^2+1)*x^3+2*RootOf(_Z^2+RootOf(_Z^2+1))*(x^3+1)^(1/2)*x^2-2*(x^3+1)^(3/4)*x+RootOf(_Z^2+1)*RootOf(_Z^2+RootOf(_Z^2+1)))/(x^4+x^3+1))","C"
1845,0,0,95,0.033000," ","int((2*x^8-x^4+2)/(x^4+1)^(1/4)/(x^8+x^4-2),x)","\[\int \frac{2 x^{8}-x^{4}+2}{\left(x^{4}+1\right)^{\frac{1}{4}} \left(x^{8}+x^{4}-2\right)}\, dx\]"," ",0,"int((2*x^8-x^4+2)/(x^4+1)^(1/4)/(x^8+x^4-2),x)","F"
1846,0,0,97,0.026000," ","int((b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2)^2,x)","\[\int \frac{\sqrt{b +\sqrt{a \,x^{2}+b^{2}}}}{\left(a \,x^{2}+b^{2}\right)^{2}}\, dx\]"," ",0,"int((b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2)^2,x)","F"
1847,1,701,106,0.404000," ","int((a*x^3+b)*(x^4-x)^(1/2)/(c*x^3-d),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{a x \sqrt{x^{4}-x}}{3 c}+\frac{2 \left(-\frac{a c -a d -b c}{c^{2}}+\frac{a}{2 c}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}-\frac{2 \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(c \,\textit{\_Z}^{3}-d \right)}{\sum}\frac{\left(a c d -a \,d^{2}+b \,c^{2}-b c d \right) \left(-1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(1-i \sqrt{3}\right) \sqrt{\frac{x \left(-3+i \sqrt{3}\right)}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{\left(-1+x \right) \left(-1-i \sqrt{3}\right)}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\frac{\underline{\hspace{1.25 ex}}\alpha^{2} c \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}\, c -3 \underline{\hspace{1.25 ex}}\alpha^{2} c -i \sqrt{3}\, d +3 d}{6 d}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{d}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(c -d \right) \left(-3+i \sqrt{3}\right) \sqrt{x \left(-1+x \right) \left(i \sqrt{3}+2 x +1\right) \left(1+2 x -i \sqrt{3}\right)}}\right)}{3 c^{2}}$&$701$\\ risch&$\frac{a \,x^{2} \left(x^{3}-1\right)}{3 c \sqrt{x \left(x^{3}-1\right)}}-\frac{\frac{2 \left(a c -2 a d -2 b c \right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{c \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{4 \left(a c d -a \,d^{2}+b \,c^{2}-b c d \right) \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(c \,\textit{\_Z}^{3}-d \right)}{\sum}\frac{\left(-1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(1-i \sqrt{3}\right) \sqrt{\frac{x \left(-3+i \sqrt{3}\right)}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{\left(-1+x \right) \left(-1-i \sqrt{3}\right)}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\frac{\underline{\hspace{1.25 ex}}\alpha^{2} c \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}\, c -3 \underline{\hspace{1.25 ex}}\alpha^{2} c -i \sqrt{3}\, d +3 d}{6 d}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{d}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(c -d \right) \left(-3+i \sqrt{3}\right) \sqrt{x \left(-1+x \right) \left(i \sqrt{3}+2 x +1\right) \left(1+2 x -i \sqrt{3}\right)}}\right)}{3 c}}{2 c}$&$705$\\ default&$\frac{a \left(\frac{x \sqrt{x^{4}-x}}{3}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{c}+\frac{\left(a d +b c \right) \left(\frac{2 \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{c \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}-\frac{2 \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(c \,\textit{\_Z}^{3}-d \right)}{\sum}\frac{\left(-1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(1-i \sqrt{3}\right) \sqrt{\frac{x \left(-3+i \sqrt{3}\right)}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{\left(-1+x \right) \left(-1-i \sqrt{3}\right)}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\frac{\underline{\hspace{1.25 ex}}\alpha^{2} c \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{3}\, c -3 \underline{\hspace{1.25 ex}}\alpha^{2} c -i \sqrt{3}\, d +3 d}{6 d}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{d}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(-3+i \sqrt{3}\right) \sqrt{x \left(-1+x \right) \left(i \sqrt{3}+2 x +1\right) \left(1+2 x -i \sqrt{3}\right)}}\right)}{3 c}\right)}{c}$&$953$\\ \hline \end{longtable}"," ",0,"1/3*a*x*(x^4-x)^(1/2)/c+2*(-(a*c-a*d-b*c)/c^2+1/2/c*a)*(1/2-1/2*I*3^(1/2))*((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2)*(-1+x)^2*((x+1/2+1/2*I*3^(1/2))/(-1/2-1/2*I*3^(1/2))/(-1+x))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2)/(-3/2+1/2*I*3^(1/2))/(x*(-1+x)*(x+1/2+1/2*I*3^(1/2))*(x+1/2-1/2*I*3^(1/2)))^(1/2)*(EllipticF(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-EllipticPi(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),(-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)),((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)))-2/3/c^2*4^(1/2)*sum((a*c*d-a*d^2+b*c^2-b*c*d)/_alpha*(-1+x)^2*(_alpha^2+_alpha+1)/(c-d)*(1-I*3^(1/2))*(x/(-1+x)*(-3+I*3^(1/2))/(-1+I*3^(1/2)))^(1/2)*(1/(-1+x)*(I*3^(1/2)+2*x+1)/(-1-I*3^(1/2)))^(1/2)*(1/(-1+x)*(1+2*x-I*3^(1/2))/(-1+I*3^(1/2)))^(1/2)/(-3+I*3^(1/2))/(x*(-1+x)*(I*3^(1/2)+2*x+1)*(1+2*x-I*3^(1/2)))^(1/2)*(EllipticF(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-_alpha^2*c/d*EllipticPi(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),1/6*(I*_alpha^2*3^(1/2)*c-3*_alpha^2*c-I*3^(1/2)*d+3*d)/d,((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))),_alpha=RootOf(_Z^3*c-d))","C"
1848,0,0,98,0.011000," ","int((a*x^3+b)/x^3/(a*x^3-b)/(a*x^4+b*x)^(1/4),x)","\[\int \frac{a \,x^{3}+b}{x^{3} \left(a \,x^{3}-b \right) \left(a \,x^{4}+b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^3+b)/x^3/(a*x^3-b)/(a*x^4+b*x)^(1/4),x)","F"
1849,1,476,106,48.870000," ","int((2*x^6+1)*(-x^7+x^3+x)^(1/3)/(x^6-1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{x \left(-x^{7}+x^{3}+x \right)^{\frac{1}{3}}}{2 \left(x^{6}-1\right)}-\frac{\ln \left(\frac{23084281021492945478344725970280579664 \RootOf \left(142884 \textit{\_Z}^{2}-378 \textit{\_Z} +1\right)^{2} x^{6}+779765626827203872050827736565976550 \RootOf \left(142884 \textit{\_Z}^{2}-378 \textit{\_Z} +1\right) x^{6}-2180370336718022168439941441690525 x^{6}-363577426088513891283929434031919129708 \RootOf \left(142884 \textit{\_Z}^{2}-378 \textit{\_Z} +1\right)^{2} x^{2}+1726084667130388450019245844753992776 \RootOf \left(142884 \textit{\_Z}^{2}-378 \textit{\_Z} +1\right) \left(-x^{7}+x^{3}+x \right)^{\frac{2}{3}}-929663874243506986438828114966559238 \RootOf \left(142884 \textit{\_Z}^{2}-378 \textit{\_Z} +1\right) \left(-x^{7}+x^{3}+x \right)^{\frac{1}{3}} x +165424249675324598017279185640923948 \RootOf \left(142884 \textit{\_Z}^{2}-378 \textit{\_Z} +1\right) x^{2}-2459428238739436472060391838535871 \left(-x^{7}+x^{3}+x \right)^{\frac{2}{3}}-2106933314515559427461422565575221 x \left(-x^{7}+x^{3}+x \right)^{\frac{1}{3}}-23084281021492945478344725970280579664 \RootOf \left(142884 \textit{\_Z}^{2}-378 \textit{\_Z} +1\right)^{2}+2021797948593075101644309336840305 x^{2}-779765626827203872050827736565976550 \RootOf \left(142884 \textit{\_Z}^{2}-378 \textit{\_Z} +1\right)+2180370336718022168439941441690525}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right)}\right)}{6}+63 \RootOf \left(142884 \textit{\_Z}^{2}-378 \textit{\_Z} +1\right) \ln \left(-\frac{426823916648008786317628300861745184 \RootOf \left(142884 \textit{\_Z}^{2}-378 \textit{\_Z} +1\right)^{2} x^{6}+43285196651552399719158942411926172 \RootOf \left(142884 \textit{\_Z}^{2}-378 \textit{\_Z} +1\right) x^{6}-2338942724842969235235573546540745 x^{6}-6722476687206138384502645738572486648 \RootOf \left(142884 \textit{\_Z}^{2}-378 \textit{\_Z} +1\right)^{2} x^{2}+1726084667130388450019245844753992776 \RootOf \left(142884 \textit{\_Z}^{2}-378 \textit{\_Z} +1\right) \left(-x^{7}+x^{3}+x \right)^{\frac{2}{3}}-796420792886881463580417729787433538 \RootOf \left(142884 \textit{\_Z}^{2}-378 \textit{\_Z} +1\right) \left(-x^{7}+x^{3}+x \right)^{\frac{1}{3}} x -911879544383173287008926935763986522 \RootOf \left(142884 \textit{\_Z}^{2}-378 \textit{\_Z} +1\right) x^{2}-2106933314515559427461422565575221 \left(-x^{7}+x^{3}+x \right)^{\frac{2}{3}}-2459428238739436472060391838535871 x \left(-x^{7}+x^{3}+x \right)^{\frac{1}{3}}-426823916648008786317628300861745184 \RootOf \left(142884 \textit{\_Z}^{2}-378 \textit{\_Z} +1\right)^{2}+4519313061560991403675514988231270 x^{2}-43285196651552399719158942411926172 \RootOf \left(142884 \textit{\_Z}^{2}-378 \textit{\_Z} +1\right)+2338942724842969235235573546540745}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right)}\right)$&$476$\\ risch&$\text{Expression too large to display}$&$1670$\\ \hline \end{longtable}"," ",0,"-1/2*x/(x^6-1)*(-x^7+x^3+x)^(1/3)-1/6*ln((23084281021492945478344725970280579664*RootOf(142884*_Z^2-378*_Z+1)^2*x^6+779765626827203872050827736565976550*RootOf(142884*_Z^2-378*_Z+1)*x^6-2180370336718022168439941441690525*x^6-363577426088513891283929434031919129708*RootOf(142884*_Z^2-378*_Z+1)^2*x^2+1726084667130388450019245844753992776*RootOf(142884*_Z^2-378*_Z+1)*(-x^7+x^3+x)^(2/3)-929663874243506986438828114966559238*RootOf(142884*_Z^2-378*_Z+1)*(-x^7+x^3+x)^(1/3)*x+165424249675324598017279185640923948*RootOf(142884*_Z^2-378*_Z+1)*x^2-2459428238739436472060391838535871*(-x^7+x^3+x)^(2/3)-2106933314515559427461422565575221*x*(-x^7+x^3+x)^(1/3)-23084281021492945478344725970280579664*RootOf(142884*_Z^2-378*_Z+1)^2+2021797948593075101644309336840305*x^2-779765626827203872050827736565976550*RootOf(142884*_Z^2-378*_Z+1)+2180370336718022168439941441690525)/(-1+x)/(1+x)/(x^2+x+1)/(x^2-x+1))+63*RootOf(142884*_Z^2-378*_Z+1)*ln(-(426823916648008786317628300861745184*RootOf(142884*_Z^2-378*_Z+1)^2*x^6+43285196651552399719158942411926172*RootOf(142884*_Z^2-378*_Z+1)*x^6-2338942724842969235235573546540745*x^6-6722476687206138384502645738572486648*RootOf(142884*_Z^2-378*_Z+1)^2*x^2+1726084667130388450019245844753992776*RootOf(142884*_Z^2-378*_Z+1)*(-x^7+x^3+x)^(2/3)-796420792886881463580417729787433538*RootOf(142884*_Z^2-378*_Z+1)*(-x^7+x^3+x)^(1/3)*x-911879544383173287008926935763986522*RootOf(142884*_Z^2-378*_Z+1)*x^2-2106933314515559427461422565575221*(-x^7+x^3+x)^(2/3)-2459428238739436472060391838535871*x*(-x^7+x^3+x)^(1/3)-426823916648008786317628300861745184*RootOf(142884*_Z^2-378*_Z+1)^2+4519313061560991403675514988231270*x^2-43285196651552399719158942411926172*RootOf(142884*_Z^2-378*_Z+1)+2338942724842969235235573546540745)/(-1+x)/(1+x)/(x^2+x+1)/(x^2-x+1))","C"
1850,0,0,115,0.109000," ","int((-(2*a-b)*b^2+(4*a-b)*b*x-(2*a+b)*x^2+x^3)/((-a+x)*(-b+x)^2)^(3/4)/(a+b^2*d-(2*b*d+1)*x+d*x^2),x)","\[\int \frac{-\left(2 a -b \right) b^{2}+\left(4 a -b \right) b x -\left(2 a +b \right) x^{2}+x^{3}}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{3}{4}} \left(a +b^{2} d -\left(2 b d +1\right) x +d \,x^{2}\right)}\, dx\]"," ",0,"int((-(2*a-b)*b^2+(4*a-b)*b*x-(2*a+b)*x^2+x^3)/((-a+x)*(-b+x)^2)^(3/4)/(a+b^2*d-(2*b*d+1)*x+d*x^2),x)","F"
1851,0,0,73,180.000000," ","int((x^4+2)/(x^4+x^2)^(1/4)/(2*x^8-x^4-1),x)","\[\int \frac{x^{4}+2}{\left(x^{4}+x^{2}\right)^{\frac{1}{4}} \left(2 x^{8}-x^{4}-1\right)}\, dx\]"," ",0,"int((x^4+2)/(x^4+x^2)^(1/4)/(2*x^8-x^4-1),x)","F"
1852,0,0,73,180.000000," ","int((x^4+2)/(x^4+x^2)^(1/4)/(2*x^8-x^4-1),x)","\[\int \frac{x^{4}+2}{\left(x^{4}+x^{2}\right)^{\frac{1}{4}} \left(2 x^{8}-x^{4}-1\right)}\, dx\]"," ",0,"int((x^4+2)/(x^4+x^2)^(1/4)/(2*x^8-x^4-1),x)","F"
1853,1,298,97,0.046000," ","int((x+(1+x)^(1/2))^(1/2)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\left(\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2\right)^{\frac{3}{2}}}{2 \left(-1+\sqrt{1+x}\right)}+\frac{3 \sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}}{4}+\frac{\ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}\right)}{2}-\frac{3 \arctanh \left(\frac{-1+3 \sqrt{1+x}}{2 \sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}}\right)}{4}+\frac{\left(2 \sqrt{1+x}+1\right) \sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}}{4}-\frac{\left(\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2\right)^{\frac{3}{2}}}{2 \left(1+\sqrt{1+x}\right)}-\frac{\sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}}{4}-\frac{\ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}\right)}{2}+\frac{\arctan \left(\frac{-3-\sqrt{1+x}}{2 \sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}}\right)}{4}+\frac{\left(2 \sqrt{1+x}+1\right) \sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}}{4}$&$298$\\ default&$-\frac{\left(\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2\right)^{\frac{3}{2}}}{2 \left(-1+\sqrt{1+x}\right)}+\frac{3 \sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}}{4}+\frac{\ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}\right)}{2}-\frac{3 \arctanh \left(\frac{-1+3 \sqrt{1+x}}{2 \sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}}\right)}{4}+\frac{\left(2 \sqrt{1+x}+1\right) \sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}}{4}-\frac{\left(\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2\right)^{\frac{3}{2}}}{2 \left(1+\sqrt{1+x}\right)}-\frac{\sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}}{4}-\frac{\ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}\right)}{2}+\frac{\arctan \left(\frac{-3-\sqrt{1+x}}{2 \sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}}\right)}{4}+\frac{\left(2 \sqrt{1+x}+1\right) \sqrt{\left(1+\sqrt{1+x}\right)^{2}-\sqrt{1+x}-2}}{4}$&$298$\\ \hline \end{longtable}"," ",0,"-1/2/(-1+(1+x)^(1/2))*((-1+(1+x)^(1/2))^2+3*(1+x)^(1/2)-2)^(3/2)+3/4*((-1+(1+x)^(1/2))^2+3*(1+x)^(1/2)-2)^(1/2)+1/2*ln(1/2+(1+x)^(1/2)+((-1+(1+x)^(1/2))^2+3*(1+x)^(1/2)-2)^(1/2))-3/4*arctanh(1/2*(-1+3*(1+x)^(1/2))/((-1+(1+x)^(1/2))^2+3*(1+x)^(1/2)-2)^(1/2))+1/4*(2*(1+x)^(1/2)+1)*((-1+(1+x)^(1/2))^2+3*(1+x)^(1/2)-2)^(1/2)-1/2/(1+(1+x)^(1/2))*((1+(1+x)^(1/2))^2-(1+x)^(1/2)-2)^(3/2)-1/4*((1+(1+x)^(1/2))^2-(1+x)^(1/2)-2)^(1/2)-1/2*ln(1/2+(1+x)^(1/2)+((1+(1+x)^(1/2))^2-(1+x)^(1/2)-2)^(1/2))+1/4*arctan(1/2*(-3-(1+x)^(1/2))/((1+(1+x)^(1/2))^2-(1+x)^(1/2)-2)^(1/2))+1/4*(2*(1+x)^(1/2)+1)*((1+(1+x)^(1/2))^2-(1+x)^(1/2)-2)^(1/2)","B"
1854,0,0,94,0.020000," ","int((-1+x)*(x+(x^2+1)^(1/2))^(1/2)/(1+x),x)","\[\int \frac{\left(-1+x \right) \sqrt{x +\sqrt{x^{2}+1}}}{1+x}\, dx\]"," ",0,"int((-1+x)*(x+(x^2+1)^(1/2))^(1/2)/(1+x),x)","F"
1855,0,0,94,0.029000," ","int((1+x)*(x+(x^2+1)^(1/2))^(1/2)/(-1+x),x)","\[\int \frac{\left(1+x \right) \sqrt{x +\sqrt{x^{2}+1}}}{-1+x}\, dx\]"," ",0,"int((1+x)*(x+(x^2+1)^(1/2))^(1/2)/(-1+x),x)","F"
1856,1,943,98,5.827000," ","int((x^2+2*x+6)/(1+x)/(x^2+x+2)^(1/3)/(2*x^2-x+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\ln \left(\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{3}+4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{3}+3 \left(x^{2}+x +2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{2}+6 \left(x^{2}+x +2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{2}+2 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{3}+8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{3}+6 \left(x^{2}+x +2\right)^{\frac{2}{3}} x -\RootOf \left(\textit{\_Z}^{3}-4\right) x^{2}-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{2}-\RootOf \left(\textit{\_Z}^{3}-4\right) x -4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x -2 \RootOf \left(\textit{\_Z}^{3}-4\right)-8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)}{\left(2 x^{2}-x +2\right) \left(1+x \right)}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)}{2}-\ln \left(\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{3}+4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{3}+3 \left(x^{2}+x +2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{2}+6 \left(x^{2}+x +2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{2}+2 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{3}+8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{3}+6 \left(x^{2}+x +2\right)^{\frac{2}{3}} x -\RootOf \left(\textit{\_Z}^{3}-4\right) x^{2}-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{2}-\RootOf \left(\textit{\_Z}^{3}-4\right) x -4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x -2 \RootOf \left(\textit{\_Z}^{3}-4\right)-8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)}{\left(2 x^{2}-x +2\right) \left(1+x \right)}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)+\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(-\frac{2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{3}+\left(x^{2}+x +2\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x -2 \left(x^{2}+x +2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{2}-2 \left(x^{2}+x +2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{2}-2 \left(x^{2}+x +2\right)^{\frac{2}{3}} x +2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{2}+2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x +4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)}{\left(2 x^{2}-x +2\right) \left(1+x \right)}\right)}{2}$&$943$\\ \hline \end{longtable}"," ",0,"-1/2*ln((RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x^3+4*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+3*(x^2+x+2)^(1/3)*RootOf(_Z^3-4)^2*x^2+6*(x^2+x+2)^(1/3)*RootOf(_Z^3-4)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^2+2*RootOf(_Z^3-4)*x^3+8*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^3+6*(x^2+x+2)^(2/3)*x-RootOf(_Z^3-4)*x^2-4*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^2-RootOf(_Z^3-4)*x-4*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x-2*RootOf(_Z^3-4)-8*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2))/(2*x^2-x+2)/(1+x))*RootOf(_Z^3-4)-ln((RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x^3+4*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+3*(x^2+x+2)^(1/3)*RootOf(_Z^3-4)^2*x^2+6*(x^2+x+2)^(1/3)*RootOf(_Z^3-4)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^2+2*RootOf(_Z^3-4)*x^3+8*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^3+6*(x^2+x+2)^(2/3)*x-RootOf(_Z^3-4)*x^2-4*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^2-RootOf(_Z^3-4)*x-4*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x-2*RootOf(_Z^3-4)-8*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2))/(2*x^2-x+2)/(1+x))*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)+1/2*RootOf(_Z^3-4)*ln(-(2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+(x^2+x+2)^(2/3)*RootOf(_Z^3-4)^2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x-2*(x^2+x+2)^(1/3)*RootOf(_Z^3-4)^2*x^2-2*(x^2+x+2)^(1/3)*RootOf(_Z^3-4)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^2-2*(x^2+x+2)^(2/3)*x+2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^2+2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x+4*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2))/(2*x^2-x+2)/(1+x))","C"
1857,0,0,96,0.022000," ","int(1/x/(a*x^3-b)^(3/4),x)","\[\int \frac{1}{x \left(a \,x^{3}-b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x/(a*x^3-b)^(3/4),x)","F"
1858,0,0,96,0.024000," ","int(1/x/(a*x^3-b)^(1/4),x)","\[\int \frac{1}{x \left(a \,x^{3}-b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/x/(a*x^3-b)^(1/4),x)","F"
1859,0,0,107,0.017000," ","int((a*x^2-3*b)*(-a*x^2+x^3+b)/x^3/(a*x^2+x^3-b)/(a*x^3-b*x)^(1/4),x)","\[\int \frac{\left(a \,x^{2}-3 b \right) \left(-a \,x^{2}+x^{3}+b \right)}{x^{3} \left(a \,x^{2}+x^{3}-b \right) \left(a \,x^{3}-b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2-3*b)*(-a*x^2+x^3+b)/x^3/(a*x^2+x^3-b)/(a*x^3-b*x)^(1/4),x)","F"
1860,0,0,96,0.025000," ","int(1/x/(a*x^4-b)^(3/4),x)","\[\int \frac{1}{x \left(a \,x^{4}-b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x/(a*x^4-b)^(3/4),x)","F"
1861,0,0,96,0.022000," ","int(1/x/(a*x^4-b)^(1/4),x)","\[\int \frac{1}{x \left(a \,x^{4}-b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/x/(a*x^4-b)^(1/4),x)","F"
1862,1,265,27,0.194000," ","int((-x^5+1)/(b*x+a)^(1/2)/(x^5+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{2 \sqrt{b x +a}}{b}+\frac{4 \arctan \left(\frac{\sqrt{b x +a}}{\sqrt{-a +b}}\right)}{5 \sqrt{-a +b}}+\frac{2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}+\left(-4 a -b \right) \textit{\_Z}^{6}+\left(6 a^{2}+3 a b +b^{2}\right) \textit{\_Z}^{4}+\left(-4 a^{3}-3 a^{2} b -2 a \,b^{2}-b^{3}\right) \textit{\_Z}^{2}+a^{4}+a^{3} b +a^{2} b^{2}+a \,b^{3}+b^{4}\right)}{\sum}\frac{\left(-\textit{\_R}^{6}+\left(3 a +2 b \right) \textit{\_R}^{4}+\left(-3 a^{2}-4 a b -3 b^{2}\right) \textit{\_R}^{2}+a^{3}+2 a^{2} b +3 a \,b^{2}+4 b^{3}\right) \ln \left(\sqrt{b x +a}-\textit{\_R} \right)}{4 \textit{\_R}^{7}-12 \textit{\_R}^{5} a -3 \textit{\_R}^{5} b +12 \textit{\_R}^{3} a^{2}+6 \textit{\_R}^{3} a b +2 \textit{\_R}^{3} b^{2}-4 \textit{\_R} \,a^{3}-3 \textit{\_R} \,a^{2} b -2 \textit{\_R} a \,b^{2}-\textit{\_R} \,b^{3}}\right)}{5}$&$265$\\ derivativedivides&$-\frac{2 \left(\sqrt{b x +a}-\frac{b \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}+\left(-4 a -b \right) \textit{\_Z}^{6}+\left(6 a^{2}+3 a b +b^{2}\right) \textit{\_Z}^{4}+\left(-4 a^{3}-3 a^{2} b -2 a \,b^{2}-b^{3}\right) \textit{\_Z}^{2}+a^{4}+a^{3} b +a^{2} b^{2}+a \,b^{3}+b^{4}\right)}{\sum}\frac{\left(-\textit{\_R}^{6}+\left(3 a +2 b \right) \textit{\_R}^{4}+\left(-3 a^{2}-4 a b -3 b^{2}\right) \textit{\_R}^{2}+a^{3}+2 a^{2} b +3 a \,b^{2}+4 b^{3}\right) \ln \left(\sqrt{b x +a}-\textit{\_R} \right)}{4 \textit{\_R}^{7}-12 \textit{\_R}^{5} a -3 \textit{\_R}^{5} b +12 \textit{\_R}^{3} a^{2}+6 \textit{\_R}^{3} a b +2 \textit{\_R}^{3} b^{2}-4 \textit{\_R} \,a^{3}-3 \textit{\_R} \,a^{2} b -2 \textit{\_R} a \,b^{2}-\textit{\_R} \,b^{3}}\right)}{5}-\frac{2 b \arctan \left(\frac{\sqrt{b x +a}}{\sqrt{-a +b}}\right)}{5 \sqrt{-a +b}}\right)}{b}$&$267$\\ default&$-\frac{2 \left(\sqrt{b x +a}-\frac{b \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}+\left(-4 a -b \right) \textit{\_Z}^{6}+\left(6 a^{2}+3 a b +b^{2}\right) \textit{\_Z}^{4}+\left(-4 a^{3}-3 a^{2} b -2 a \,b^{2}-b^{3}\right) \textit{\_Z}^{2}+a^{4}+a^{3} b +a^{2} b^{2}+a \,b^{3}+b^{4}\right)}{\sum}\frac{\left(-\textit{\_R}^{6}+\left(3 a +2 b \right) \textit{\_R}^{4}+\left(-3 a^{2}-4 a b -3 b^{2}\right) \textit{\_R}^{2}+a^{3}+2 a^{2} b +3 a \,b^{2}+4 b^{3}\right) \ln \left(\sqrt{b x +a}-\textit{\_R} \right)}{4 \textit{\_R}^{7}-12 \textit{\_R}^{5} a -3 \textit{\_R}^{5} b +12 \textit{\_R}^{3} a^{2}+6 \textit{\_R}^{3} a b +2 \textit{\_R}^{3} b^{2}-4 \textit{\_R} \,a^{3}-3 \textit{\_R} \,a^{2} b -2 \textit{\_R} a \,b^{2}-\textit{\_R} \,b^{3}}\right)}{5}-\frac{2 b \arctan \left(\frac{\sqrt{b x +a}}{\sqrt{-a +b}}\right)}{5 \sqrt{-a +b}}\right)}{b}$&$267$\\ \hline \end{longtable}"," ",0,"-2*(b*x+a)^(1/2)/b+4/5/(-a+b)^(1/2)*arctan((b*x+a)^(1/2)/(-a+b)^(1/2))+2/5*sum((-_R^6+(3*a+2*b)*_R^4+(-3*a^2-4*a*b-3*b^2)*_R^2+a^3+2*a^2*b+3*a*b^2+4*b^3)/(4*_R^7-12*_R^5*a-3*_R^5*b+12*_R^3*a^2+6*_R^3*a*b+2*_R^3*b^2-4*_R*a^3-3*_R*a^2*b-2*_R*a*b^2-_R*b^3)*ln((b*x+a)^(1/2)-_R),_R=RootOf(_Z^8+(-4*a-b)*_Z^6+(6*a^2+3*a*b+b^2)*_Z^4+(-4*a^3-3*a^2*b-2*a*b^2-b^3)*_Z^2+a^4+a^3*b+a^2*b^2+a*b^3+b^4))","B"
1863,0,0,96,0.025000," ","int(1/x/(a*x^5-b)^(3/4),x)","\[\int \frac{1}{x \left(a \,x^{5}-b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x/(a*x^5-b)^(3/4),x)","F"
1864,0,0,96,0.021000," ","int(1/x/(a*x^6-b)^(3/4),x)","\[\int \frac{1}{x \left(a \,x^{6}-b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x/(a*x^6-b)^(3/4),x)","F"
1865,1,566,88,2.834000," ","int((x^4+1)*(x^4+x^2-1)^(3/2)/(x^4-1)/(x^8-x^6-x^4+x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\ln \left(-\frac{x^{4}+2 x \sqrt{x^{4}+x^{2}-1}+2 x^{2}-1}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)}{2}+\RootOf \left(16 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+3\right) \ln \left(-\frac{8 x^{2} \RootOf \left(16 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+3\right)^{5}+2 \RootOf \left(16 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+3\right)^{3} x^{4}+8 \RootOf \left(16 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+3\right)^{3} x^{2}-6 \RootOf \left(16 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+3\right)^{2} \sqrt{x^{4}+x^{2}-1}\, x -2 \RootOf \left(16 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+3\right)^{3}-3 x \sqrt{x^{4}+x^{2}-1}}{4 x^{2} \RootOf \left(16 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+3\right)^{2}-x^{4}+2 x^{2}+1}\right)-\frac{\RootOf \left(\textit{\_Z}^{2}+4 \RootOf \left(16 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+3\right)^{2}+3\right) \ln \left(\frac{16 \RootOf \left(\textit{\_Z}^{2}+4 \RootOf \left(16 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+3\right)^{2}+3\right) \RootOf \left(16 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+3\right)^{4} x^{2}-4 \RootOf \left(\textit{\_Z}^{2}+4 \RootOf \left(16 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+3\right)^{2}+3\right) \RootOf \left(16 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+3\right)^{2} x^{4}+8 \RootOf \left(\textit{\_Z}^{2}+4 \RootOf \left(16 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+3\right)^{2}+3\right) \RootOf \left(16 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+3\right)^{2} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+4 \RootOf \left(16 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+3\right)^{2}+3\right) x^{4}-24 \RootOf \left(16 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+3\right)^{2} \sqrt{x^{4}+x^{2}-1}\, x +4 \RootOf \left(16 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+3\right)^{2} \RootOf \left(\textit{\_Z}^{2}+4 \RootOf \left(16 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+3\right)^{2}+3\right)-3 \RootOf \left(\textit{\_Z}^{2}+4 \RootOf \left(16 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+3\right)^{2}+3\right) x^{2}-6 x \sqrt{x^{4}+x^{2}-1}+3 \RootOf \left(\textit{\_Z}^{2}+4 \RootOf \left(16 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+3\right)^{2}+3\right)}{4 x^{2} \RootOf \left(16 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+3\right)^{2}+x^{4}+x^{2}-1}\right)}{2}$&$566$\\ elliptic&$\frac{\left(-\frac{\ln \left(\frac{x^{4}+x^{2}-1}{x^{2}}+\frac{\sqrt{x^{4}+x^{2}-1}\, \sqrt{2}\, \sqrt{6+4 \sqrt{3}}}{2 x}+\sqrt{3}\right) \sqrt{6+4 \sqrt{3}}\, \sqrt{3}}{4}+\frac{\ln \left(\frac{x^{4}+x^{2}-1}{x^{2}}+\frac{\sqrt{x^{4}+x^{2}-1}\, \sqrt{2}\, \sqrt{6+4 \sqrt{3}}}{2 x}+\sqrt{3}\right) \sqrt{6+4 \sqrt{3}}}{2}+\frac{\arctan \left(\frac{\frac{2 \sqrt{x^{4}+x^{2}-1}\, \sqrt{2}}{x}+\sqrt{6+4 \sqrt{3}}}{\sqrt{4 \sqrt{3}-6}}\right) \left(6+4 \sqrt{3}\right) \sqrt{3}}{2 \sqrt{4 \sqrt{3}-6}}-\frac{\arctan \left(\frac{\frac{2 \sqrt{x^{4}+x^{2}-1}\, \sqrt{2}}{x}+\sqrt{6+4 \sqrt{3}}}{\sqrt{4 \sqrt{3}-6}}\right) \left(6+4 \sqrt{3}\right)}{\sqrt{4 \sqrt{3}-6}}+\frac{2 \arctan \left(\frac{\frac{2 \sqrt{x^{4}+x^{2}-1}\, \sqrt{2}}{x}+\sqrt{6+4 \sqrt{3}}}{\sqrt{4 \sqrt{3}-6}}\right) \sqrt{3}}{\sqrt{4 \sqrt{3}-6}}+\frac{\ln \left(\frac{x^{4}+x^{2}-1}{x^{2}}-\frac{\sqrt{x^{4}+x^{2}-1}\, \sqrt{2}\, \sqrt{6+4 \sqrt{3}}}{2 x}+\sqrt{3}\right) \sqrt{6+4 \sqrt{3}}\, \sqrt{3}}{4}-\frac{\ln \left(\frac{x^{4}+x^{2}-1}{x^{2}}-\frac{\sqrt{x^{4}+x^{2}-1}\, \sqrt{2}\, \sqrt{6+4 \sqrt{3}}}{2 x}+\sqrt{3}\right) \sqrt{6+4 \sqrt{3}}}{2}+\frac{\arctan \left(\frac{\frac{2 \sqrt{x^{4}+x^{2}-1}\, \sqrt{2}}{x}-\sqrt{6+4 \sqrt{3}}}{\sqrt{4 \sqrt{3}-6}}\right) \left(6+4 \sqrt{3}\right) \sqrt{3}}{2 \sqrt{4 \sqrt{3}-6}}-\frac{\arctan \left(\frac{\frac{2 \sqrt{x^{4}+x^{2}-1}\, \sqrt{2}}{x}-\sqrt{6+4 \sqrt{3}}}{\sqrt{4 \sqrt{3}-6}}\right) \left(6+4 \sqrt{3}\right)}{\sqrt{4 \sqrt{3}-6}}+\frac{2 \arctan \left(\frac{\frac{2 \sqrt{x^{4}+x^{2}-1}\, \sqrt{2}}{x}-\sqrt{6+4 \sqrt{3}}}{\sqrt{4 \sqrt{3}-6}}\right) \sqrt{3}}{\sqrt{4 \sqrt{3}-6}}-\sqrt{2}\, \arctanh \left(\frac{\sqrt{x^{4}+x^{2}-1}}{x}\right)\right) \sqrt{2}}{2}$&$599$\\ default&$-\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{6}-\textit{\_Z}^{4}+\textit{\_Z}^{2}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{6}-2 \underline{\hspace{1.25 ex}}\alpha^{4}+1\right) \left(-\frac{\arctanh \left(\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2}+1\right) \left(20 \underline{\hspace{1.25 ex}}\alpha^{6}-30 \underline{\hspace{1.25 ex}}\alpha^{4}-5 \underline{\hspace{1.25 ex}}\alpha^{2}+7 x^{2}+26\right)}{14 \sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}+\underline{\hspace{1.25 ex}}\alpha^{2}-1}\, \sqrt{x^{4}+x^{2}-1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}+\underline{\hspace{1.25 ex}}\alpha^{2}-1}}-\frac{\sqrt{2}\, \left(-\underline{\hspace{1.25 ex}}\alpha^{7}+\underline{\hspace{1.25 ex}}\alpha^{5}+\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{-x^{2}+2+\sqrt{5}\, x^{2}}\, \sqrt{-x^{2}+2-\sqrt{5}\, x^{2}}\, \EllipticPi \left(\sqrt{\frac{1}{2}-\frac{\sqrt{5}}{2}}\, x , \frac{\underline{\hspace{1.25 ex}}\alpha^{6} \sqrt{5}}{2}+\frac{\underline{\hspace{1.25 ex}}\alpha^{6}}{2}-\frac{\underline{\hspace{1.25 ex}}\alpha^{4} \sqrt{5}}{2}-\frac{\underline{\hspace{1.25 ex}}\alpha^{4}}{2}-\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{5}}{2}-\frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{\sqrt{5}}{2}+\frac{1}{2}, \frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}}}{\sqrt{\frac{1}{2}-\frac{\sqrt{5}}{2}}}\right)}{\sqrt{-\sqrt{5}+1}\, \sqrt{x^{4}+x^{2}-1}}\right)\right)}{4}+\frac{92 \sqrt{1-\frac{x^{2}}{2}+\frac{\sqrt{5}\, x^{2}}{2}}\, \sqrt{1-\frac{x^{2}}{2}-\frac{\sqrt{5}\, x^{2}}{2}}\, \EllipticF \left(\frac{x \sqrt{2-2 \sqrt{5}}}{2}, \frac{i}{2}+\frac{i \sqrt{5}}{2}\right)}{15 \sqrt{2-2 \sqrt{5}}\, \sqrt{x^{4}+x^{2}-1}\, \left(\sqrt{5}+1\right)}-\frac{92 \sqrt{1-\frac{x^{2}}{2}+\frac{\sqrt{5}\, x^{2}}{2}}\, \sqrt{1-\frac{x^{2}}{2}-\frac{\sqrt{5}\, x^{2}}{2}}\, \EllipticE \left(\frac{x \sqrt{2-2 \sqrt{5}}}{2}, \frac{i}{2}+\frac{i \sqrt{5}}{2}\right)}{15 \sqrt{2-2 \sqrt{5}}\, \sqrt{x^{4}+x^{2}-1}\, \left(\sqrt{5}+1\right)}-\frac{92 \sqrt{1-\left(\frac{1}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \sqrt{1-\left(\frac{1}{2}+\frac{\sqrt{5}}{2}\right) x^{2}}\, \left(\EllipticF \left(\frac{x \sqrt{2-2 \sqrt{5}}}{2}, \frac{i}{2}+\frac{i \sqrt{5}}{2}\right)-\EllipticE \left(\frac{x \sqrt{2-2 \sqrt{5}}}{2}, \frac{i}{2}+\frac{i \sqrt{5}}{2}\right)\right)}{15 \sqrt{2-2 \sqrt{5}}\, \sqrt{x^{4}+x^{2}-1}\, \left(\sqrt{5}+1\right)}-\frac{\sqrt{1-\left(\frac{1}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \sqrt{1-\left(\frac{1}{2}+\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{\frac{1}{2}-\frac{\sqrt{5}}{2}}\, x , \frac{1}{\frac{1}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}}}{\sqrt{\frac{1}{2}-\frac{\sqrt{5}}{2}}}\right)}{\sqrt{\frac{1}{2}-\frac{\sqrt{5}}{2}}\, \sqrt{x^{4}+x^{2}-1}}-\frac{2 \sqrt{1-\frac{x^{2}}{2}+\frac{\sqrt{5}\, x^{2}}{2}}\, \sqrt{1-\frac{x^{2}}{2}-\frac{\sqrt{5}\, x^{2}}{2}}\, \EllipticF \left(\frac{x \sqrt{2-2 \sqrt{5}}}{2}, \frac{i}{2}+\frac{i \sqrt{5}}{2}\right)}{15 \sqrt{2-2 \sqrt{5}}\, \sqrt{x^{4}+x^{2}-1}}-\frac{\sqrt{1-\frac{x^{2}}{2}+\frac{\sqrt{5}\, x^{2}}{2}}\, \sqrt{1-\frac{x^{2}}{2}-\frac{\sqrt{5}\, x^{2}}{2}}\, \EllipticPi \left(\sqrt{\frac{1}{2}-\frac{\sqrt{5}}{2}}\, x , -\frac{1}{\frac{1}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{\frac{1}{2}+\frac{\sqrt{5}}{2}}}{\sqrt{\frac{1}{2}-\frac{\sqrt{5}}{2}}}\right)}{\sqrt{\frac{1}{2}-\frac{\sqrt{5}}{2}}\, \sqrt{x^{4}+x^{2}-1}}+\frac{32 \sqrt{1-\left(\frac{1}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \sqrt{1-\left(\frac{1}{2}+\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{2-2 \sqrt{5}}}{2}, \frac{i}{2}+\frac{i \sqrt{5}}{2}\right)}{15 \sqrt{2-2 \sqrt{5}}\, \sqrt{x^{4}+x^{2}-1}}$&$871$\\ \hline \end{longtable}"," ",0,"-1/2*ln(-(x^4+2*x*(x^4+x^2-1)^(1/2)+2*x^2-1)/(-1+x)/(1+x)/(x^2+1))+RootOf(16*_Z^4+12*_Z^2+3)*ln(-(8*x^2*RootOf(16*_Z^4+12*_Z^2+3)^5+2*RootOf(16*_Z^4+12*_Z^2+3)^3*x^4+8*RootOf(16*_Z^4+12*_Z^2+3)^3*x^2-6*RootOf(16*_Z^4+12*_Z^2+3)^2*(x^4+x^2-1)^(1/2)*x-2*RootOf(16*_Z^4+12*_Z^2+3)^3-3*x*(x^4+x^2-1)^(1/2))/(4*x^2*RootOf(16*_Z^4+12*_Z^2+3)^2-x^4+2*x^2+1))-1/2*RootOf(_Z^2+4*RootOf(16*_Z^4+12*_Z^2+3)^2+3)*ln((16*RootOf(_Z^2+4*RootOf(16*_Z^4+12*_Z^2+3)^2+3)*RootOf(16*_Z^4+12*_Z^2+3)^4*x^2-4*RootOf(_Z^2+4*RootOf(16*_Z^4+12*_Z^2+3)^2+3)*RootOf(16*_Z^4+12*_Z^2+3)^2*x^4+8*RootOf(_Z^2+4*RootOf(16*_Z^4+12*_Z^2+3)^2+3)*RootOf(16*_Z^4+12*_Z^2+3)^2*x^2-3*RootOf(_Z^2+4*RootOf(16*_Z^4+12*_Z^2+3)^2+3)*x^4-24*RootOf(16*_Z^4+12*_Z^2+3)^2*(x^4+x^2-1)^(1/2)*x+4*RootOf(16*_Z^4+12*_Z^2+3)^2*RootOf(_Z^2+4*RootOf(16*_Z^4+12*_Z^2+3)^2+3)-3*RootOf(_Z^2+4*RootOf(16*_Z^4+12*_Z^2+3)^2+3)*x^2-6*x*(x^4+x^2-1)^(1/2)+3*RootOf(_Z^2+4*RootOf(16*_Z^4+12*_Z^2+3)^2+3))/(4*x^2*RootOf(16*_Z^4+12*_Z^2+3)^2+x^4+x^2-1))","C"
1866,1,1054,98,8.087000," ","int((x^6-1)*(x^6+x^3+1)^(2/3)/(x^12+x^6+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) \ln \left(-\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{3}+90 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{3}-4\right) x^{6}+30 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) x^{6}+18 \left(x^{6}+x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) x -3 \left(x^{6}+x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{2}+36 \left(x^{6}+x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x^{2}+3 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{3}+90 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) x^{3}-6 \left(x^{6}+x^{3}+1\right)^{\frac{2}{3}} x +\RootOf \left(\textit{\_Z}^{3}-4\right)+30 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right)}{x^{6}-x^{3}+1}\right)-\frac{\ln \left(-\frac{12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{3}+90 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{3}-4 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{6}-30 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) x^{6}-18 \left(x^{6}+x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) x -9 \left(x^{6}+x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{2}-36 \left(x^{6}+x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x^{2}-4 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{3}-30 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) x^{3}-18 \left(x^{6}+x^{3}+1\right)^{\frac{2}{3}} x -4 \RootOf \left(\textit{\_Z}^{3}-4\right)-30 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right)}{x^{6}-x^{3}+1}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)}{6}-\ln \left(-\frac{12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{3}+90 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{3}-4 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{6}-30 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) x^{6}-18 \left(x^{6}+x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) x -9 \left(x^{6}+x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{2}-36 \left(x^{6}+x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x^{2}-4 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{3}-30 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) x^{3}-18 \left(x^{6}+x^{3}+1\right)^{\frac{2}{3}} x -4 \RootOf \left(\textit{\_Z}^{3}-4\right)-30 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right)}{x^{6}-x^{3}+1}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right)$&$1054$\\ \hline \end{longtable}"," ",0,"RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*ln(-(3*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+90*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+RootOf(_Z^3-4)*x^6+30*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^6+18*(x^6+x^3+1)^(2/3)*RootOf(_Z^3-4)^2*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x-3*(x^6+x^3+1)^(1/3)*RootOf(_Z^3-4)^2*x^2+36*(x^6+x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^2+3*RootOf(_Z^3-4)*x^3+90*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-6*(x^6+x^3+1)^(2/3)*x+RootOf(_Z^3-4)+30*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x^6-x^3+1))-1/6*ln(-(12*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+90*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3-4*RootOf(_Z^3-4)*x^6-30*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^6-18*(x^6+x^3+1)^(2/3)*RootOf(_Z^3-4)^2*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x-9*(x^6+x^3+1)^(1/3)*RootOf(_Z^3-4)^2*x^2-36*(x^6+x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^2-4*RootOf(_Z^3-4)*x^3-30*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-18*(x^6+x^3+1)^(2/3)*x-4*RootOf(_Z^3-4)-30*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x^6-x^3+1))*RootOf(_Z^3-4)-ln(-(12*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^3+90*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^3-4*RootOf(_Z^3-4)*x^6-30*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^6-18*(x^6+x^3+1)^(2/3)*RootOf(_Z^3-4)^2*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x-9*(x^6+x^3+1)^(1/3)*RootOf(_Z^3-4)^2*x^2-36*(x^6+x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^2-4*RootOf(_Z^3-4)*x^3-30*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^3-18*(x^6+x^3+1)^(2/3)*x-4*RootOf(_Z^3-4)-30*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(x^6-x^3+1))*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)","C"
1867,1,129,102,2.306000," ","int((x^3-1)^3*(x^3+1)*(2*x^12+3*x^6+2)^(1/2)/x^7/(x^6+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{6}-4 x^{3}+1\right) \sqrt{2 x^{12}+3 x^{6}+2}}{6 x^{6}}-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x^{6}+\RootOf \left(\textit{\_Z}^{2}-2\right)+\sqrt{2 x^{12}+3 x^{6}+2}}{x^{3}}\right)}{12}+\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+\sqrt{2 x^{12}+3 x^{6}+2}}{\left(x^{2}+1\right) \left(x^{4}-x^{2}+1\right)}\right)}{3}$&$129$\\ risch&$-\frac{8 x^{15}-2 x^{12}+12 x^{9}-3 x^{6}+8 x^{3}-2}{6 x^{6} \sqrt{2 x^{12}+3 x^{6}+2}}+\frac{\sqrt{2 x^{12}+3 x^{6}+2}}{6}-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x^{6}+\RootOf \left(\textit{\_Z}^{2}-2\right)+\sqrt{2 x^{12}+3 x^{6}+2}}{x^{3}}\right)}{12}+\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+\sqrt{2 x^{12}+3 x^{6}+2}}{\left(x^{2}+1\right) \left(x^{4}-x^{2}+1\right)}\right)}{3}$&$162$\\ \hline \end{longtable}"," ",0,"1/6*(x^6-4*x^3+1)*(2*x^12+3*x^6+2)^(1/2)/x^6-1/12*RootOf(_Z^2-2)*ln((RootOf(_Z^2-2)*x^6+RootOf(_Z^2-2)+(2*x^12+3*x^6+2)^(1/2))/x^3)+2/3*RootOf(_Z^2+1)*ln((RootOf(_Z^2+1)*x^3+(2*x^12+3*x^6+2)^(1/2))/(x^2+1)/(x^4-x^2+1))","C"
1868,0,0,14,180.000000," ","int((a*x-(a^2*x^2+b)^(1/2))^(1/2)/(a^2*x^2+(a^2*x^2+b)^(1/2)),x)","\[\int \frac{\sqrt{a x -\sqrt{a^{2} x^{2}+b}}}{a^{2} x^{2}+\sqrt{a^{2} x^{2}+b}}\, dx\]"," ",0,"int((a*x-(a^2*x^2+b)^(1/2))^(1/2)/(a^2*x^2+(a^2*x^2+b)^(1/2)),x)","F"
1869,0,0,106,180.000000," ","int((c*x+d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{c x +d}{\sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int((c*x+d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","F"
1870,1,47,86,0.110000," ","int(1/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{7}{2}}}{7}-\frac{24 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}+\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}$&$47$\\ default&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{7}{2}}}{7}-\frac{24 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}+\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}$&$47$\\ \hline \end{longtable}"," ",0,"8/7*(1+(1+(1+x)^(1/2))^(1/2))^(7/2)-24/5*(1+(1+(1+x)^(1/2))^(1/2))^(5/2)+16/3*(1+(1+(1+x)^(1/2))^(1/2))^(3/2)","A"
1871,1,36,105,3.317000," ","int((a*x^2-b)*(x^3+x)^(1/3)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 a \,x^{\frac{4}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], -x^{2}\right)}{4}+\frac{3 b \hypergeom \left(\left[-\frac{1}{3}, -\frac{1}{3}\right], \left[\frac{2}{3}\right], -x^{2}\right)}{2 x^{\frac{2}{3}}}$&$36$\\ trager&$\frac{\left(a \,x^{2}+3 b \right) \left(x^{3}+x \right)^{\frac{1}{3}}}{2 x}-\frac{\left(a -3 b \right) \left(3 \ln \left(45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}-72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}-72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x -87 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}-45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}+15 \left(x^{3}+x \right)^{\frac{2}{3}}+15 x \left(x^{3}+x \right)^{\frac{1}{3}}+20 x^{2}-18 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)+8\right) \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \ln \left(45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}+72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}+72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x +57 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}-45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}-9 \left(x^{3}+x \right)^{\frac{2}{3}}-9 x \left(x^{3}+x \right)^{\frac{1}{3}}-4 x^{2}+48 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-3\right)-\ln \left(45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}-72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}-72 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x -87 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}-45 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}+15 \left(x^{3}+x \right)^{\frac{2}{3}}+15 x \left(x^{3}+x \right)^{\frac{1}{3}}+20 x^{2}-18 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)+8\right)\right)}{6}$&$449$\\ risch&$\frac{\left(a \,x^{2}+3 b \right) \left(x \left(x^{2}+1\right)\right)^{\frac{1}{3}}}{2 x}-\frac{\left(a -3 b \right) \left(-\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{4}-20 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{4}+48 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}+100 x^{4}-30 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}-14 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-60 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}-\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2}+48 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}-36 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}+140 x^{2}+6 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)-60 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}+40}{x^{2}+1}\right)+2 \ln \left(\frac{5 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{4}+38 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{4}-18 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-16 x^{4}-30 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}+70 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-60 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}-5 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2}-18 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}+96 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{2}{3}}-28 x^{2}+32 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)-60 \left(x^{6}+2 x^{4}+x^{2}\right)^{\frac{1}{3}}-12}{x^{2}+1}\right)\right) \left(x \left(x^{2}+1\right)\right)^{\frac{1}{3}} \left(x^{2} \left(x^{2}+1\right)^{2}\right)^{\frac{1}{3}}}{12 x \left(x^{2}+1\right)}$&$514$\\ \hline \end{longtable}"," ",0,"3/4*a*x^(4/3)*hypergeom([-1/3,2/3],[5/3],-x^2)+3/2*b/x^(2/3)*hypergeom([-1/3,-1/3],[2/3],-x^2)","C"
1872,0,0,60,0.012000," ","int(1/x^3/(a*x^3-b*x^2)^(1/3)/(c*x^3+d),x)","\[\int \frac{1}{x^{3} \left(a \,x^{3}-b \,x^{2}\right)^{\frac{1}{3}} \left(x^{3} c +d \right)}\, dx\]"," ",0,"int(1/x^3/(a*x^3-b*x^2)^(1/3)/(c*x^3+d),x)","F"
1873,1,288,97,2.898000," ","int((x^4-1)/(x^3-x^2-x)^(1/2)/(x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \sqrt{-5 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{5}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}}+\frac{5^{\frac{3}{4}} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+1\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(\sqrt{5}-1\right) \sqrt{\frac{2 x -1+\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-2 x +1+\sqrt{5}}\, \sqrt{-\frac{x}{\sqrt{5}-1}}\, \left(3 \underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}+2 \underline{\hspace{1.25 ex}}\alpha  +1+\sqrt{5}\, \left(\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)\right) \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, -\frac{\underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{5}}{6}-\frac{\underline{\hspace{1.25 ex}}\alpha^{3}}{6}+\frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{3}+\frac{\underline{\hspace{1.25 ex}}\alpha}{6}-\frac{\sqrt{5}}{6}+\frac{1}{2}-\frac{\underline{\hspace{1.25 ex}}\alpha  \sqrt{5}}{6}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{\sqrt{x \left(x^{2}-x -1\right)}}\right)}{60}$&$288$\\ elliptic&$\frac{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \sqrt{-5 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{5}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}}+\frac{5^{\frac{3}{4}} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+1\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(\sqrt{5}-1\right) \sqrt{\frac{2 x -1+\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-2 x +1+\sqrt{5}}\, \sqrt{-\frac{x}{\sqrt{5}-1}}\, \left(3 \underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}+2 \underline{\hspace{1.25 ex}}\alpha  +1+\sqrt{5}\, \left(\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)\right) \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, -\frac{\underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{5}}{6}-\frac{\underline{\hspace{1.25 ex}}\alpha^{3}}{6}+\frac{\underline{\hspace{1.25 ex}}\alpha^{2}}{3}+\frac{\underline{\hspace{1.25 ex}}\alpha}{6}-\frac{\sqrt{5}}{6}+\frac{1}{2}-\frac{\underline{\hspace{1.25 ex}}\alpha  \sqrt{5}}{6}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{\sqrt{x \left(x^{2}-x -1\right)}}\right)}{60}$&$288$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+6\right) \ln \left(\frac{496 \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+6\right) \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{4} x^{2}-496 \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+6\right) \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{4}+120 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+6\right) x^{2}-248 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+6\right) x -120 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+6\right)-\RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+6\right) x^{2}+224 \sqrt{x^{3}-x^{2}-x}\, \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+2 \RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+6\right) x +\RootOf \left(\textit{\_Z}^{2}+36 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+6\right)-68 \sqrt{x^{3}-x^{2}-x}}{12 x^{2} \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}-12 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+x^{2}+2 x -1}\right)}{6}+\RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right) \ln \left(-\frac{4464 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{5} x^{2}-4464 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{5}+408 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{3} x^{2}+2232 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{3} x -408 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{3}+336 \sqrt{x^{3}-x^{2}-x}\, \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}-65 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right) x^{2}+390 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right) x +65 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)+158 \sqrt{x^{3}-x^{2}-x}}{12 x^{2} \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}-12 \RootOf \left(48 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+x^{2}-2 x -1}\right)$&$661$\\ \hline \end{longtable}"," ",0,"2/5*(1/2*5^(1/2)-1/2)*((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2)*(-5*(x-1/2-1/2*5^(1/2))*5^(1/2))^(1/2)*(-x/(1/2*5^(1/2)-1/2))^(1/2)/(x^3-x^2-x)^(1/2)*EllipticF(((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2),1/5*5^(1/2)*((1/2*5^(1/2)-1/2)*5^(1/2))^(1/2))+1/60*5^(3/4)*sum(_alpha*(5^(1/2)-1)*((2*x-1+5^(1/2))/(5^(1/2)-1))^(1/2)*(-2*x+1+5^(1/2))^(1/2)*(-x/(5^(1/2)-1))^(1/2)/(x*(x^2-x-1))^(1/2)*(3*_alpha^3-_alpha^2+2*_alpha+1+5^(1/2)*(_alpha^3-_alpha^2-1))*EllipticPi(((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2),-1/6*_alpha^3*5^(1/2)-1/6*_alpha^3+1/3*_alpha^2+1/6*_alpha-1/6*5^(1/2)+1/2-1/6*_alpha*5^(1/2),1/5*5^(1/2)*((1/2*5^(1/2)-1/2)*5^(1/2))^(1/2)),_alpha=RootOf(_Z^4+1))","C"
1874,1,107,120,0.127000," ","int((x^6+9*x^5+16*x^4-27*x^3-36*x^2-11*x-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(16 x^{3}+104 x^{2}-6 x -185\right) \sqrt{\left(x^{2}-x -1\right) \left(x^{2}+5 x +1\right)^{2}}}{64 x^{2}+320 x +64}-\frac{325 \ln \left(x -\frac{1}{2}+\sqrt{x^{2}-x -1}\right) \sqrt{\left(x^{2}-x -1\right) \left(x^{2}+5 x +1\right)^{2}}}{128 \left(x^{2}+5 x +1\right) \sqrt{x^{2}-x -1}}$&$107$\\ default&$\frac{\sqrt{x^{6}+9 x^{5}+16 x^{4}-27 x^{3}-36 x^{2}-11 x -1}\, \left(32 x \left(x^{2}-x -1\right)^{\frac{3}{2}}+240 \left(x^{2}-x -1\right)^{\frac{3}{2}}+260 x \sqrt{x^{2}-x -1}-130 \sqrt{x^{2}-x -1}-325 \ln \left(x -\frac{1}{2}+\sqrt{x^{2}-x -1}\right)\right)}{128 \left(x^{2}+5 x +1\right) \sqrt{x^{2}-x -1}}$&$120$\\ trager&$\frac{\left(16 x^{3}+104 x^{2}-6 x -185\right) \sqrt{x^{6}+9 x^{5}+16 x^{4}-27 x^{3}-36 x^{2}-11 x -1}}{64 x^{2}+320 x +64}-\frac{325 \ln \left(\frac{2 x^{3}+9 x^{2}+2 \sqrt{x^{6}+9 x^{5}+16 x^{4}-27 x^{3}-36 x^{2}-11 x -1}-3 x -1}{x^{2}+5 x +1}\right)}{128}$&$120$\\ \hline \end{longtable}"," ",0,"1/64*(16*x^3+104*x^2-6*x-185)*((x^2-x-1)*(x^2+5*x+1)^2)^(1/2)/(x^2+5*x+1)-325/128*ln(x-1/2+(x^2-x-1)^(1/2))*((x^2-x-1)*(x^2+5*x+1)^2)^(1/2)/(x^2+5*x+1)/(x^2-x-1)^(1/2)","A"
1875,0,0,123,0.020000," ","int((2*p*x^3-q)*(a*p*x^3+a*q+b*x)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)/x^4,x)","\[\int \frac{\left(2 p \,x^{3}-q \right) \left(a p \,x^{3}+a q +b x \right) \sqrt{p^{2} x^{6}+2 p q \,x^{3}-2 p q \,x^{2}+q^{2}}}{x^{4}}\, dx\]"," ",0,"int((2*p*x^3-q)*(a*p*x^3+a*q+b*x)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)/x^4,x)","F"
1876,0,0,95,0.042000," ","int((2*x^8-x^4-2)/(x^4-1)^(1/4)/(x^8-x^4-2),x)","\[\int \frac{2 x^{8}-x^{4}-2}{\left(x^{4}-1\right)^{\frac{1}{4}} \left(x^{8}-x^{4}-2\right)}\, dx\]"," ",0,"int((2*x^8-x^4-2)/(x^4-1)^(1/4)/(x^8-x^4-2),x)","F"
1877,1,105,44,0.091000," ","int((x^4-1)*(1+(1+x)^(1/2))^(1/2)/(x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{5}{2}}}{5}-\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}-\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+16 \textit{\_Z}^{8}+1\right)}{\sum}\frac{\left(\textit{\_R}^{4}-\textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+8 \textit{\_R}^{7}}\right)}{2}$&$105$\\ default&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{5}{2}}}{5}-\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}-\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+16 \textit{\_Z}^{8}+1\right)}{\sum}\frac{\left(\textit{\_R}^{4}-\textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+8 \textit{\_R}^{7}}\right)}{2}$&$105$\\ \hline \end{longtable}"," ",0,"4/5*(1+(1+x)^(1/2))^(5/2)-4/3*(1+(1+x)^(1/2))^(3/2)-1/2*sum((_R^4-_R^2)/(_R^15-7*_R^13+18*_R^11-20*_R^9+8*_R^7)*ln((1+(1+x)^(1/2))^(1/2)-_R),_R=RootOf(_Z^16-8*_Z^14+24*_Z^12-32*_Z^10+16*_Z^8+1))","B"
1878,1,105,44,0.086000," ","int((x^4-1)*(1+(1+x)^(1/2))^(1/2)/(x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{5}{2}}}{5}-\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}-\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+16 \textit{\_Z}^{8}+1\right)}{\sum}\frac{\left(\textit{\_R}^{4}-\textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+8 \textit{\_R}^{7}}\right)}{2}$&$105$\\ default&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{5}{2}}}{5}-\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}-\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+16 \textit{\_Z}^{8}+1\right)}{\sum}\frac{\left(\textit{\_R}^{4}-\textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+8 \textit{\_R}^{7}}\right)}{2}$&$105$\\ \hline \end{longtable}"," ",0,"4/5*(1+(1+x)^(1/2))^(5/2)-4/3*(1+(1+x)^(1/2))^(3/2)-1/2*sum((_R^4-_R^2)/(_R^15-7*_R^13+18*_R^11-20*_R^9+8*_R^7)*ln((1+(1+x)^(1/2))^(1/2)-_R),_R=RootOf(_Z^16-8*_Z^14+24*_Z^12-32*_Z^10+16*_Z^8+1))","B"
1879,1,318,100,0.190000," ","int((a*x^2+b)*(a*x^3+b*x)^(1/2)/x^2/(a*x^2-b),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{2 a \,x^{2}+2 b}{\sqrt{x \left(a \,x^{2}+b \right)}}+\frac{2 b \sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}+\frac{2 b \sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}$&$318$\\ risch&$\frac{2 a \,x^{2}+2 b}{\sqrt{x \left(a \,x^{2}+b \right)}}+4 b a \left(\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}+\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}\right)$&$321$\\ default&$2 a \left(\frac{2 b \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}+b x}}-\frac{b \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}+b x}}+\frac{b \sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}+\frac{b \sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}\right)+\frac{2 a \,x^{2}+2 b}{\sqrt{x \left(a \,x^{2}+b \right)}}-\frac{2 \sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \left(-\frac{2 \sqrt{-a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a}+\frac{\sqrt{-a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a}\right)}{\sqrt{a \,x^{3}+b x}}$&$643$\\ \hline \end{longtable}"," ",0,"2*(a*x^2+b)/(x*(a*x^2+b))^(1/2)+2*b/a*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2)),1/2*2^(1/2))+2*b/a*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)+1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)+1/a*(a*b)^(1/2)),1/2*2^(1/2))","C"
1880,0,0,116,0.017000," ","int((-2*a*b+(3*a-b)*x)*(-a^3+3*a^2*x-3*a*x^2+x^3)/x/(-b+x)/(x^2*(-a+x)*(-b+x))^(1/4)/(a^3-3*a^2*x+(-b*d+3*a)*x^2+(-1+d)*x^3),x)","\[\int \frac{\left(-2 a b +\left(3 a -b \right) x \right) \left(-a^{3}+3 a^{2} x -3 a \,x^{2}+x^{3}\right)}{x \left(-b +x \right) \left(x^{2} \left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{4}} \left(a^{3}-3 a^{2} x +\left(-b d +3 a \right) x^{2}+\left(-1+d \right) x^{3}\right)}\, dx\]"," ",0,"int((-2*a*b+(3*a-b)*x)*(-a^3+3*a^2*x-3*a*x^2+x^3)/x/(-b+x)/(x^2*(-a+x)*(-b+x))^(1/4)/(a^3-3*a^2*x+(-b*d+3*a)*x^2+(-1+d)*x^3),x)","F"
1881,0,0,103,0.023000," ","int((a*x^2+2*b)/(a*x^2+b)^(1/4)/(2*x^4+1881*a*x^2+1881*b),x)","\[\int \frac{a \,x^{2}+2 b}{\left(a \,x^{2}+b \right)^{\frac{1}{4}} \left(2 x^{4}+1881 a \,x^{2}+1881 b \right)}\, dx\]"," ",0,"int((a*x^2+2*b)/(a*x^2+b)^(1/4)/(2*x^4+1881*a*x^2+1881*b),x)","F"
1882,1,97,44,0.092000," ","int((1+x)^(1/2)*(x^2-1)/(x^2+1)/(1+(1+x)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{5}{2}}}{5}-\frac{8 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}+4 \sqrt{1+\sqrt{1+x}}+\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+4 \textit{\_Z}^{4}+1\right)}{\sum}\frac{\left(-\textit{\_R}^{4}+2 \textit{\_R}^{2}-1\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+2 \textit{\_R}^{3}}\right)$&$97$\\ default&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{5}{2}}}{5}-\frac{8 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}+4 \sqrt{1+\sqrt{1+x}}+\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+4 \textit{\_Z}^{4}+1\right)}{\sum}\frac{\left(-\textit{\_R}^{4}+2 \textit{\_R}^{2}-1\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+2 \textit{\_R}^{3}}\right)$&$97$\\ \hline \end{longtable}"," ",0,"4/5*(1+(1+x)^(1/2))^(5/2)-8/3*(1+(1+x)^(1/2))^(3/2)+4*(1+(1+x)^(1/2))^(1/2)+sum((-_R^4+2*_R^2-1)/(_R^7-3*_R^5+2*_R^3)*ln((1+(1+x)^(1/2))^(1/2)-_R),_R=RootOf(_Z^8-4*_Z^6+4*_Z^4+1))","B"
1883,1,97,44,0.102000," ","int((1+x)^(1/2)*(x^2-1)/(x^2+1)/(1+(1+x)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{5}{2}}}{5}-\frac{8 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}+4 \sqrt{1+\sqrt{1+x}}+\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+4 \textit{\_Z}^{4}+1\right)}{\sum}\frac{\left(-\textit{\_R}^{4}+2 \textit{\_R}^{2}-1\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+2 \textit{\_R}^{3}}\right)$&$97$\\ default&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{5}{2}}}{5}-\frac{8 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}+4 \sqrt{1+\sqrt{1+x}}+\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+4 \textit{\_Z}^{4}+1\right)}{\sum}\frac{\left(-\textit{\_R}^{4}+2 \textit{\_R}^{2}-1\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+2 \textit{\_R}^{3}}\right)$&$97$\\ \hline \end{longtable}"," ",0,"4/5*(1+(1+x)^(1/2))^(5/2)-8/3*(1+(1+x)^(1/2))^(3/2)+4*(1+(1+x)^(1/2))^(1/2)+sum((-_R^4+2*_R^2-1)/(_R^7-3*_R^5+2*_R^3)*ln((1+(1+x)^(1/2))^(1/2)-_R),_R=RootOf(_Z^8-4*_Z^6+4*_Z^4+1))","B"
1884,1,88,39,0.101000," ","int((x^4-1)*(1+(1+x)^(1/2))^(1/2)/(1+x)^(1/2)/(x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}-\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+16 \textit{\_Z}^{8}+1\right)}{\sum}\frac{\textit{\_R}^{2} \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+8 \textit{\_R}^{7}}\right)}{2}$&$88$\\ default&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}-\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+16 \textit{\_Z}^{8}+1\right)}{\sum}\frac{\textit{\_R}^{2} \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+8 \textit{\_R}^{7}}\right)}{2}$&$88$\\ \hline \end{longtable}"," ",0,"4/3*(1+(1+x)^(1/2))^(3/2)-1/2*sum(_R^2/(_R^15-7*_R^13+18*_R^11-20*_R^9+8*_R^7)*ln((1+(1+x)^(1/2))^(1/2)-_R),_R=RootOf(_Z^16-8*_Z^14+24*_Z^12-32*_Z^10+16*_Z^8+1))","B"
1885,1,88,39,0.101000," ","int((x^4-1)*(1+(1+x)^(1/2))^(1/2)/(1+x)^(1/2)/(x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}-\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+16 \textit{\_Z}^{8}+1\right)}{\sum}\frac{\textit{\_R}^{2} \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+8 \textit{\_R}^{7}}\right)}{2}$&$88$\\ default&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}-\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+16 \textit{\_Z}^{8}+1\right)}{\sum}\frac{\textit{\_R}^{2} \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+8 \textit{\_R}^{7}}\right)}{2}$&$88$\\ \hline \end{longtable}"," ",0,"4/3*(1+(1+x)^(1/2))^(3/2)-1/2*sum(_R^2/(_R^15-7*_R^13+18*_R^11-20*_R^9+8*_R^7)*ln((1+(1+x)^(1/2))^(1/2)-_R),_R=RootOf(_Z^16-8*_Z^14+24*_Z^12-32*_Z^10+16*_Z^8+1))","B"
1886,0,0,34,0.029000," ","int((a*x^2+1)/(a*x^2-1)/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{a \,x^{2}+1}{\left(a \,x^{2}-1\right) \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((a*x^2+1)/(a*x^2-1)/(x+(x^2+1)^(1/2))^(1/2),x)","F"
1887,0,0,99,0.029000," ","int(x*(x^2+x)^(1/2)/(x^2+x*(x^2+x)^(1/2))^(1/2),x)","\[\int \frac{x \sqrt{x^{2}+x}}{\sqrt{x^{2}+x \sqrt{x^{2}+x}}}\, dx\]"," ",0,"int(x*(x^2+x)^(1/2)/(x^2+x*(x^2+x)^(1/2))^(1/2),x)","F"
1888,1,238,94,0.081000," ","int((1+x)^(1/2)/(1+(x+(1+x)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\left(2 \sqrt{1+x}+1\right) \sqrt{x +\sqrt{1+x}}}{2}-\frac{5 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{4}+\frac{2 \sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}}{3}+\ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}\right)-\frac{2 \arctanh \left(\frac{-1+3 \sqrt{1+x}}{2 \sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}}\right)}{3}-\frac{8 \sqrt{\left(\sqrt{1+x}+2\right)^{2}-3 \sqrt{1+x}-5}}{3}+4 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(\sqrt{1+x}+2\right)^{2}-3 \sqrt{1+x}-5}\right)+\frac{8 \arctanh \left(\frac{-4-3 \sqrt{1+x}}{2 \sqrt{\left(\sqrt{1+x}+2\right)^{2}-3 \sqrt{1+x}-5}}\right)}{3}-2 \sqrt{1+x}-\frac{2 \ln \left(-1+\sqrt{1+x}\right)}{3}+\frac{8 \ln \left(\sqrt{1+x}+2\right)}{3}$&$238$\\ default&$\frac{\left(2 \sqrt{1+x}+1\right) \sqrt{x +\sqrt{1+x}}}{2}-\frac{5 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{4}+\frac{2 \sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}}{3}+\ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}\right)-\frac{2 \arctanh \left(\frac{-1+3 \sqrt{1+x}}{2 \sqrt{\left(-1+\sqrt{1+x}\right)^{2}+3 \sqrt{1+x}-2}}\right)}{3}-\frac{8 \sqrt{\left(\sqrt{1+x}+2\right)^{2}-3 \sqrt{1+x}-5}}{3}+4 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(\sqrt{1+x}+2\right)^{2}-3 \sqrt{1+x}-5}\right)+\frac{8 \arctanh \left(\frac{-4-3 \sqrt{1+x}}{2 \sqrt{\left(\sqrt{1+x}+2\right)^{2}-3 \sqrt{1+x}-5}}\right)}{3}-2 \sqrt{1+x}-\frac{2 \ln \left(-1+\sqrt{1+x}\right)}{3}+\frac{8 \ln \left(\sqrt{1+x}+2\right)}{3}$&$238$\\ \hline \end{longtable}"," ",0,"1/2*(2*(1+x)^(1/2)+1)*(x+(1+x)^(1/2))^(1/2)-5/4*ln(1/2+(1+x)^(1/2)+(x+(1+x)^(1/2))^(1/2))+2/3*((-1+(1+x)^(1/2))^2+3*(1+x)^(1/2)-2)^(1/2)+ln(1/2+(1+x)^(1/2)+((-1+(1+x)^(1/2))^2+3*(1+x)^(1/2)-2)^(1/2))-2/3*arctanh(1/2*(-1+3*(1+x)^(1/2))/((-1+(1+x)^(1/2))^2+3*(1+x)^(1/2)-2)^(1/2))-8/3*(((1+x)^(1/2)+2)^2-3*(1+x)^(1/2)-5)^(1/2)+4*ln(1/2+(1+x)^(1/2)+(((1+x)^(1/2)+2)^2-3*(1+x)^(1/2)-5)^(1/2))+8/3*arctanh(1/2*(-4-3*(1+x)^(1/2))/(((1+x)^(1/2)+2)^2-3*(1+x)^(1/2)-5)^(1/2))-2*(1+x)^(1/2)-2/3*ln(-1+(1+x)^(1/2))+8/3*ln((1+x)^(1/2)+2)","B"
1889,1,651,100,29.396000," ","int((1+x)/(-1+x)/(1+2*x)/(3*x^2-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+9 \textit{\_Z}^{2}\right) \ln \left(\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+9 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{3}+9 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+9 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{3}-3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+9 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} \left(3 x^{2}-1\right)^{\frac{2}{3}} x +2 \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} \left(3 x^{2}-1\right)^{\frac{1}{3}} x^{2}+12 \RootOf \left(\textit{\_Z}^{3}-4\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+9 \textit{\_Z}^{2}\right) \left(3 x^{2}-1\right)^{\frac{1}{3}} x^{2}-6 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{2}-18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+9 \textit{\_Z}^{2}\right) x^{2}+4 \left(3 x^{2}-1\right)^{\frac{2}{3}} x +2 \RootOf \left(\textit{\_Z}^{3}-4\right)+6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+9 \textit{\_Z}^{2}\right)}{\left(-1+x \right)^{2} \left(1+2 x \right)}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(-\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+9 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{3}+9 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+9 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{3}-3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+9 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} \left(3 x^{2}-1\right)^{\frac{2}{3}} x +2 \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} \left(3 x^{2}-1\right)^{\frac{1}{3}} x^{2}-6 \RootOf \left(\textit{\_Z}^{3}-4\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+9 \textit{\_Z}^{2}\right) \left(3 x^{2}-1\right)^{\frac{1}{3}} x^{2}+4 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{3}+12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+9 \textit{\_Z}^{2}\right) x^{3}+6 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{2}+18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+9 \textit{\_Z}^{2}\right) x^{2}-8 \left(3 x^{2}-1\right)^{\frac{2}{3}} x -2 \RootOf \left(\textit{\_Z}^{3}-4\right)-6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+9 \textit{\_Z}^{2}\right)}{\left(-1+x \right)^{2} \left(1+2 x \right)}\right)}{6}$&$651$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*ln((3*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x^3+9*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x^3-3*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*(3*x^2-1)^(2/3)*x+2*RootOf(_Z^3-4)^2*(3*x^2-1)^(1/3)*x^2+12*RootOf(_Z^3-4)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*(3*x^2-1)^(1/3)*x^2-6*RootOf(_Z^3-4)*x^2-18*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x^2+4*(3*x^2-1)^(2/3)*x+2*RootOf(_Z^3-4)+6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2))/(-1+x)^2/(1+2*x))+1/6*RootOf(_Z^3-4)*ln(-(3*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x^3+9*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x^3-3*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*(3*x^2-1)^(2/3)*x+2*RootOf(_Z^3-4)^2*(3*x^2-1)^(1/3)*x^2-6*RootOf(_Z^3-4)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*(3*x^2-1)^(1/3)*x^2+4*RootOf(_Z^3-4)*x^3+12*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x^3+6*RootOf(_Z^3-4)*x^2+18*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x^2-8*(3*x^2-1)^(2/3)*x-2*RootOf(_Z^3-4)-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2))/(-1+x)^2/(1+2*x))","C"
1890,1,55,101,1.579000," ","int((a*x^2-b)/x^2/(x^3-x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{3 b \left(x^{2}-1\right)}{4 x \left(x \left(x^{2}-1\right)\right)^{\frac{1}{3}}}+\frac{3 a \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}} x^{\frac{2}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{2}\right)}{2 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}}}$&$55$\\ meijerg&$\frac{3 a \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}} x^{\frac{2}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{2}\right)}{2 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}}}+\frac{3 b \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}} \left(-x^{2}+1\right)^{\frac{2}{3}}}{4 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}} x^{\frac{4}{3}}}$&$68$\\ trager&$-\frac{3 b \left(x^{3}-x \right)^{\frac{2}{3}}}{4 x^{2}}-\frac{a \left(72 \ln \left(-3659904 \RootOf \left(5184 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)^{2} x^{2}+162432 \RootOf \left(5184 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}+385560 \RootOf \left(5184 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{1}{3}} x -497160 \RootOf \left(5184 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right) x^{2}+14639616 \RootOf \left(5184 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)^{2}+5355 \left(x^{3}-x \right)^{\frac{2}{3}}-7611 x \left(x^{3}-x \right)^{\frac{1}{3}}+1550 x^{2}+107856 \RootOf \left(5184 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)-465\right) \RootOf \left(5184 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)+\ln \left(2856384 \RootOf \left(5184 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)^{2} x^{2}-162432 \RootOf \left(5184 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}+547992 \RootOf \left(5184 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{1}{3}} x -425232 \RootOf \left(5184 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right) x^{2}-11425536 \RootOf \left(5184 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)^{2}+7611 \left(x^{3}-x \right)^{\frac{2}{3}}-5355 x \left(x^{3}-x \right)^{\frac{1}{3}}-1705 x^{2}+233064 \RootOf \left(5184 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)+1085\right)-\ln \left(-3659904 \RootOf \left(5184 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)^{2} x^{2}+162432 \RootOf \left(5184 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}+385560 \RootOf \left(5184 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{1}{3}} x -497160 \RootOf \left(5184 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right) x^{2}+14639616 \RootOf \left(5184 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)^{2}+5355 \left(x^{3}-x \right)^{\frac{2}{3}}-7611 x \left(x^{3}-x \right)^{\frac{1}{3}}+1550 x^{2}+107856 \RootOf \left(5184 \textit{\_Z}^{2}-72 \textit{\_Z} +1\right)-465\right)\right)}{2}$&$450$\\ \hline \end{longtable}"," ",0,"-3/4*b*(x^2-1)/x/(x*(x^2-1))^(1/3)+3/2*a/signum(x^2-1)^(1/3)*(-signum(x^2-1))^(1/3)*x^(2/3)*hypergeom([1/3,1/3],[4/3],x^2)","C"
1891,1,913,105,3.087000," ","int((x^4+1)/(x^3-x^2-x)^(1/2)/(x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+10\right) \ln \left(\frac{5498560 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+10\right) \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{4} x^{2}-8247840 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+10\right) \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{4} x -5498560 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+10\right) \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{4}+566112 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+10\right) x^{2}-2017612 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+10\right) x -566112 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+10\right)+162560 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2} \sqrt{x^{3}-x^{2}-x}+11529 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+10\right) x^{2}-49959 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+10\right) x -11529 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+10\right)-572030 \sqrt{x^{3}-x^{2}-x}}{\left(4 x \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}-8 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+x \right)^{2}}\right)}{20}+\frac{\RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right) \ln \left(-\frac{27492800 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{5} x^{2}-41239200 x \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{5}-27492800 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{5}+2668000 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{3} x^{2}+1840220 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{3} x -2668000 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{3}+81280 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2} \sqrt{x^{3}-x^{2}-x}+49517 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right) x^{2}+346619 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right) x -49517 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)+294143 \sqrt{x^{3}-x^{2}-x}}{\left(20 x \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}-40 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}-3 x -4\right)^{2}}\right)}{2}+5 \ln \left(-\frac{20 x^{2} \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}-40 x \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}-20 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+x^{2}-4 \sqrt{x^{3}-x^{2}-x}-2 x -1}{\left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+\frac{\ln \left(-\frac{20 x^{2} \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}-40 x \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}-20 \RootOf \left(80 \textit{\_Z}^{4}+8 \textit{\_Z}^{2}+1\right)^{2}+x^{2}-4 \sqrt{x^{3}-x^{2}-x}-2 x -1}{\left(-1+x \right) \left(1+x \right)}\right)}{4}$&$913$\\ default&$\frac{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \sqrt{-5 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{5}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}}+\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}-i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{10 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}-i-\frac{\sqrt{5}}{2}\right)}-\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}-i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{10 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}-i-\frac{\sqrt{5}}{2}\right)}-\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}+i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{10 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}+i-\frac{\sqrt{5}}{2}\right)}+\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}+i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{10 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}+i-\frac{\sqrt{5}}{2}\right)}-\frac{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \sqrt{-5 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{5}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)}+\frac{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \sqrt{-5 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{5}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{-\frac{1}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}\, \left(-\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}$&$1009$\\ elliptic&$\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{5 \sqrt{x^{3}-x^{2}-x}}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{5 \sqrt{x^{3}-x^{2}-x}}+\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, -\frac{i \sqrt{5}}{5}+\frac{1}{2}-\frac{\sqrt{5}}{10}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{10 \sqrt{x^{3}-x^{2}-x}}+\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, -\frac{i \sqrt{5}}{5}+\frac{1}{2}-\frac{\sqrt{5}}{10}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{25 \sqrt{x^{3}-x^{2}-x}}-\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, -\frac{i \sqrt{5}}{5}+\frac{1}{2}-\frac{\sqrt{5}}{10}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{50 \sqrt{x^{3}-x^{2}-x}}-\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{i \sqrt{5}}{5}+\frac{1}{2}-\frac{\sqrt{5}}{10}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{10 \sqrt{x^{3}-x^{2}-x}}+\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{i \sqrt{5}}{5}+\frac{1}{2}-\frac{\sqrt{5}}{10}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{25 \sqrt{x^{3}-x^{2}-x}}+\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{i \sqrt{5}}{5}+\frac{1}{2}-\frac{\sqrt{5}}{10}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{50 \sqrt{x^{3}-x^{2}-x}}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{10 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)}+\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{10 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)}+\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{-\frac{1}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{10 \sqrt{x^{3}-x^{2}-x}\, \left(-\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{-\frac{1}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{10 \sqrt{x^{3}-x^{2}-x}\, \left(-\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}$&$1685$\\ \hline \end{longtable}"," ",0,"-1/20*RootOf(_Z^2+100*RootOf(80*_Z^4+8*_Z^2+1)^2+10)*ln((5498560*RootOf(_Z^2+100*RootOf(80*_Z^4+8*_Z^2+1)^2+10)*RootOf(80*_Z^4+8*_Z^2+1)^4*x^2-8247840*RootOf(_Z^2+100*RootOf(80*_Z^4+8*_Z^2+1)^2+10)*RootOf(80*_Z^4+8*_Z^2+1)^4*x-5498560*RootOf(_Z^2+100*RootOf(80*_Z^4+8*_Z^2+1)^2+10)*RootOf(80*_Z^4+8*_Z^2+1)^4+566112*RootOf(80*_Z^4+8*_Z^2+1)^2*RootOf(_Z^2+100*RootOf(80*_Z^4+8*_Z^2+1)^2+10)*x^2-2017612*RootOf(80*_Z^4+8*_Z^2+1)^2*RootOf(_Z^2+100*RootOf(80*_Z^4+8*_Z^2+1)^2+10)*x-566112*RootOf(80*_Z^4+8*_Z^2+1)^2*RootOf(_Z^2+100*RootOf(80*_Z^4+8*_Z^2+1)^2+10)+162560*RootOf(80*_Z^4+8*_Z^2+1)^2*(x^3-x^2-x)^(1/2)+11529*RootOf(_Z^2+100*RootOf(80*_Z^4+8*_Z^2+1)^2+10)*x^2-49959*RootOf(_Z^2+100*RootOf(80*_Z^4+8*_Z^2+1)^2+10)*x-11529*RootOf(_Z^2+100*RootOf(80*_Z^4+8*_Z^2+1)^2+10)-572030*(x^3-x^2-x)^(1/2))/(4*x*RootOf(80*_Z^4+8*_Z^2+1)^2-8*RootOf(80*_Z^4+8*_Z^2+1)^2+x)^2)+1/2*RootOf(80*_Z^4+8*_Z^2+1)*ln(-(27492800*RootOf(80*_Z^4+8*_Z^2+1)^5*x^2-41239200*x*RootOf(80*_Z^4+8*_Z^2+1)^5-27492800*RootOf(80*_Z^4+8*_Z^2+1)^5+2668000*RootOf(80*_Z^4+8*_Z^2+1)^3*x^2+1840220*RootOf(80*_Z^4+8*_Z^2+1)^3*x-2668000*RootOf(80*_Z^4+8*_Z^2+1)^3+81280*RootOf(80*_Z^4+8*_Z^2+1)^2*(x^3-x^2-x)^(1/2)+49517*RootOf(80*_Z^4+8*_Z^2+1)*x^2+346619*RootOf(80*_Z^4+8*_Z^2+1)*x-49517*RootOf(80*_Z^4+8*_Z^2+1)+294143*(x^3-x^2-x)^(1/2))/(20*x*RootOf(80*_Z^4+8*_Z^2+1)^2-40*RootOf(80*_Z^4+8*_Z^2+1)^2-3*x-4)^2)+5*ln(-(20*x^2*RootOf(80*_Z^4+8*_Z^2+1)^2-40*x*RootOf(80*_Z^4+8*_Z^2+1)^2-20*RootOf(80*_Z^4+8*_Z^2+1)^2+x^2-4*(x^3-x^2-x)^(1/2)-2*x-1)/(-1+x)/(1+x))*RootOf(80*_Z^4+8*_Z^2+1)^2+1/4*ln(-(20*x^2*RootOf(80*_Z^4+8*_Z^2+1)^2-40*x*RootOf(80*_Z^4+8*_Z^2+1)^2-20*RootOf(80*_Z^4+8*_Z^2+1)^2+x^2-4*(x^3-x^2-x)^(1/2)-2*x-1)/(-1+x)/(1+x))","C"
1892,0,0,100,0.015000," ","int((x^3-1)*(x^6+1)^(1/3)/x^2/(x^3+1),x)","\[\int \frac{\left(x^{3}-1\right) \left(x^{6}+1\right)^{\frac{1}{3}}}{x^{2} \left(x^{3}+1\right)}\, dx\]"," ",0,"int((x^3-1)*(x^6+1)^(1/3)/x^2/(x^3+1),x)","F"
1893,1,1516,100,145.590000," ","int((x^6-2)*(x^6+2)^(1/3)/x^2/(x^6+2*x^3+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1516$\\ risch&$\text{Expression too large to display}$&$1600$\\ \hline \end{longtable}"," ",0,"(x^6+2)^(1/3)/x+2*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*ln((4164520586334*RootOf(_Z^3+2)^4*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^6+37852911926640*RootOf(_Z^3+2)^3*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*x^6-12493561759002*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^4*x^3-113558735779920*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^3*x^3+694086764389*RootOf(_Z^3+2)^2*x^6+6308818654440*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)*x^6+4412671686090*RootOf(_Z^3+2)^2*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*(x^6+2)^(2/3)*x+8329041172668*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^4+75705823853280*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^3+2776347057556*x^3*RootOf(_Z^3+2)^2+25235274617760*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)*x^3-9126524228622*RootOf(_Z^3+2)*(x^6+2)^(1/3)*x^2-8825343372180*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*(x^6+2)^(1/3)*x^2-9126524228622*(x^6+2)^(2/3)*x+1388173528778*RootOf(_Z^3+2)^2+12617637308880*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2))/(x^6+2*x^3+2))-1/3*ln((2144298068106*RootOf(_Z^3+2)^4*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^6+37852911926640*RootOf(_Z^3+2)^3*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*x^6-6432894204318*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^4*x^3-113558735779920*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^3*x^3-1072149034053*RootOf(_Z^3+2)^2*x^6-18926455963320*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)*x^6-4412671686090*RootOf(_Z^3+2)^2*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*(x^6+2)^(2/3)*x+4288596136212*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^4+75705823853280*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^3+714766022702*x^3*RootOf(_Z^3+2)^2+12617637308880*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)*x^3-7655633666592*RootOf(_Z^3+2)*(x^6+2)^(1/3)*x^2+8825343372180*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*(x^6+2)^(1/3)*x^2-7655633666592*(x^6+2)^(2/3)*x-2144298068106*RootOf(_Z^3+2)^2-37852911926640*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2))/(x^6+2*x^3+2))*RootOf(_Z^3+2)-2*ln((2144298068106*RootOf(_Z^3+2)^4*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*x^6+37852911926640*RootOf(_Z^3+2)^3*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*x^6-6432894204318*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^4*x^3-113558735779920*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^3*x^3-1072149034053*RootOf(_Z^3+2)^2*x^6-18926455963320*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)*x^6-4412671686090*RootOf(_Z^3+2)^2*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*(x^6+2)^(2/3)*x+4288596136212*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)^4+75705823853280*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)^2*RootOf(_Z^3+2)^3+714766022702*x^3*RootOf(_Z^3+2)^2+12617637308880*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2)*x^3-7655633666592*RootOf(_Z^3+2)*(x^6+2)^(1/3)*x^2+8825343372180*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*(x^6+2)^(1/3)*x^2-7655633666592*(x^6+2)^(2/3)*x-2144298068106*RootOf(_Z^3+2)^2-37852911926640*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)*RootOf(_Z^3+2))/(x^6+2*x^3+2))*RootOf(RootOf(_Z^3+2)^2+6*_Z*RootOf(_Z^3+2)+36*_Z^2)","C"
1894,1,893,104,17.013000," ","int((x^3+1)^(2/3)*(2*x^6-2*x^3-1)/x^6/(2*x^6+x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{17 x^{6}+19 x^{3}+2}{10 x^{5} \left(x^{3}+1\right)^{\frac{1}{3}}}-\frac{2 \ln \left(\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+9\right)^{3} x^{3}-81 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+9\right)^{2} x^{3}+15 \left(x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}+9\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) x +2 \RootOf \left(\textit{\_Z}^{3}+9\right)^{2} \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}+63 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+9\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) x^{2}-4 \RootOf \left(\textit{\_Z}^{3}+9\right) x^{3}+108 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) x^{3}-21 x \left(x^{3}+1\right)^{\frac{2}{3}}-\RootOf \left(\textit{\_Z}^{3}+9\right)+27 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right)}{2 x^{3}-1}\right) \RootOf \left(\textit{\_Z}^{3}+9\right)}{3}-6 \ln \left(\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+9\right)^{3} x^{3}-81 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+9\right)^{2} x^{3}+15 \left(x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}+9\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) x +2 \RootOf \left(\textit{\_Z}^{3}+9\right)^{2} \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}+63 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+9\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) x^{2}-4 \RootOf \left(\textit{\_Z}^{3}+9\right) x^{3}+108 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) x^{3}-21 x \left(x^{3}+1\right)^{\frac{2}{3}}-\RootOf \left(\textit{\_Z}^{3}+9\right)+27 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right)}{2 x^{3}-1}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right)+\frac{2 \RootOf \left(\textit{\_Z}^{3}+9\right) \ln \left(\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+9\right)^{3} x^{3}+108 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+9\right)^{2} x^{3}-15 \left(x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}+9\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) x +7 \RootOf \left(\textit{\_Z}^{3}+9\right)^{2} \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}+18 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+9\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) x^{2}+\RootOf \left(\textit{\_Z}^{3}+9\right) x^{3}+36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) x^{3}-6 x \left(x^{3}+1\right)^{\frac{2}{3}}+\RootOf \left(\textit{\_Z}^{3}+9\right)+36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right)}{2 x^{3}-1}\right)}{3}$&$893$\\ trager&$\text{Expression too large to display}$&$1104$\\ \hline \end{longtable}"," ",0,"-1/10*(17*x^6+19*x^3+2)/x^5/(x^3+1)^(1/3)-2/3*ln((3*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*RootOf(_Z^3+9)^3*x^3-81*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)^2*RootOf(_Z^3+9)^2*x^3+15*(x^3+1)^(2/3)*RootOf(_Z^3+9)^2*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*x+2*RootOf(_Z^3+9)^2*(x^3+1)^(1/3)*x^2+63*(x^3+1)^(1/3)*RootOf(_Z^3+9)*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*x^2-4*RootOf(_Z^3+9)*x^3+108*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*x^3-21*x*(x^3+1)^(2/3)-RootOf(_Z^3+9)+27*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2))/(2*x^3-1))*RootOf(_Z^3+9)-6*ln((3*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*RootOf(_Z^3+9)^3*x^3-81*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)^2*RootOf(_Z^3+9)^2*x^3+15*(x^3+1)^(2/3)*RootOf(_Z^3+9)^2*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*x+2*RootOf(_Z^3+9)^2*(x^3+1)^(1/3)*x^2+63*(x^3+1)^(1/3)*RootOf(_Z^3+9)*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*x^2-4*RootOf(_Z^3+9)*x^3+108*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*x^3-21*x*(x^3+1)^(2/3)-RootOf(_Z^3+9)+27*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2))/(2*x^3-1))*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)+2/3*RootOf(_Z^3+9)*ln((3*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*RootOf(_Z^3+9)^3*x^3+108*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)^2*RootOf(_Z^3+9)^2*x^3-15*(x^3+1)^(2/3)*RootOf(_Z^3+9)^2*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*x+7*RootOf(_Z^3+9)^2*(x^3+1)^(1/3)*x^2+18*(x^3+1)^(1/3)*RootOf(_Z^3+9)*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*x^2+RootOf(_Z^3+9)*x^3+36*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*x^3-6*x*(x^3+1)^(2/3)+RootOf(_Z^3+9)+36*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2))/(2*x^3-1))","C"
1895,1,667,101,1.707000," ","int((x^3+1)*(-x^4+x)^(1/2)/(3*x^6+4*x^3+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{3 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{-x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{\sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(3 \textit{\_Z}^{6}+4 \textit{\_Z}^{3}+2\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{3}-1\right) \left(-1+x \right)^{2} \left(3 \underline{\hspace{1.25 ex}}\alpha^{5}+3 \underline{\hspace{1.25 ex}}\alpha^{4}+3 \underline{\hspace{1.25 ex}}\alpha^{3}+7 \underline{\hspace{1.25 ex}}\alpha^{2}+7 \underline{\hspace{1.25 ex}}\alpha  +7\right) \left(1-i \sqrt{3}\right) \sqrt{\frac{x \left(-3+i \sqrt{3}\right)}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{\left(-1+x \right) \left(-1-i \sqrt{3}\right)}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \left(2 \EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\left(-3 \underline{\hspace{1.25 ex}}\alpha^{5}-4 \underline{\hspace{1.25 ex}}\alpha^{2}\right) \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, -\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5}}{4}+\frac{3 \underline{\hspace{1.25 ex}}\alpha^{5}}{4}-\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{3}+\underline{\hspace{1.25 ex}}\alpha^{2}-\frac{i \sqrt{3}}{6}+\frac{1}{2}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-3+i \sqrt{3}\right) \sqrt{-x \left(-1+x \right) \left(i \sqrt{3}+2 x +1\right) \left(1+2 x -i \sqrt{3}\right)}}\right)}{108}$&$667$\\ elliptic&$-\frac{2 \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{3 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{-x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{\sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(3 \textit{\_Z}^{6}+4 \textit{\_Z}^{3}+2\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{3}-1\right) \left(-1+x \right)^{2} \left(3 \underline{\hspace{1.25 ex}}\alpha^{5}+3 \underline{\hspace{1.25 ex}}\alpha^{4}+3 \underline{\hspace{1.25 ex}}\alpha^{3}+7 \underline{\hspace{1.25 ex}}\alpha^{2}+7 \underline{\hspace{1.25 ex}}\alpha  +7\right) \left(1-i \sqrt{3}\right) \sqrt{\frac{x \left(-3+i \sqrt{3}\right)}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{\left(-1+x \right) \left(-1-i \sqrt{3}\right)}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \left(2 \EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\left(-3 \underline{\hspace{1.25 ex}}\alpha^{5}-4 \underline{\hspace{1.25 ex}}\alpha^{2}\right) \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, -\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5}}{4}+\frac{3 \underline{\hspace{1.25 ex}}\alpha^{5}}{4}-\frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{3}+\underline{\hspace{1.25 ex}}\alpha^{2}-\frac{i \sqrt{3}}{6}+\frac{1}{2}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-3+i \sqrt{3}\right) \sqrt{-x \left(-1+x \right) \left(i \sqrt{3}+2 x +1\right) \left(1+2 x -i \sqrt{3}\right)}}\right)}{108}$&$667$\\ \hline \end{longtable}"," ",0,"-2/3*(1/2-1/2*I*3^(1/2))*((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2)*(-1+x)^2*((x+1/2+1/2*I*3^(1/2))/(-1/2-1/2*I*3^(1/2))/(-1+x))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2)/(-3/2+1/2*I*3^(1/2))/(-x*(-1+x)*(x+1/2+1/2*I*3^(1/2))*(x+1/2-1/2*I*3^(1/2)))^(1/2)*(EllipticF(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-EllipticPi(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),(-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)),((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)))+1/108*4^(1/2)*sum(_alpha^2*(_alpha^3-1)*(-1+x)^2*(3*_alpha^5+3*_alpha^4+3*_alpha^3+7*_alpha^2+7*_alpha+7)*(1-I*3^(1/2))*(x/(-1+x)*(-3+I*3^(1/2))/(-1+I*3^(1/2)))^(1/2)*(1/(-1+x)*(I*3^(1/2)+2*x+1)/(-1-I*3^(1/2)))^(1/2)*(1/(-1+x)*(1+2*x-I*3^(1/2))/(-1+I*3^(1/2)))^(1/2)/(-3+I*3^(1/2))/(-x*(-1+x)*(I*3^(1/2)+2*x+1)*(1+2*x-I*3^(1/2)))^(1/2)*(2*EllipticF(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-(-3*_alpha^5-4*_alpha^2)*EllipticPi(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),-1/4*I*3^(1/2)*_alpha^5+3/4*_alpha^5-1/3*I*3^(1/2)*_alpha^2+_alpha^2-1/6*I*3^(1/2)+1/2,((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))),_alpha=RootOf(3*_Z^6+4*_Z^3+2))","C"
1896,0,0,14,0.026000," ","int((a*x^4-2)/(a*x^4+b)^(1/4)/(2*x^8+a*x^4-b),x)","\[\int \frac{a \,x^{4}-2}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(2 x^{8}+a \,x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^4-2)/(a*x^4+b)^(1/4)/(2*x^8+a*x^4-b),x)","F"
1897,0,0,96,0.026000," ","int((-1+x)/(1+x)/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{-1+x}{\left(1+x \right) \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((-1+x)/(1+x)/(x+(x^2+1)^(1/2))^(1/2),x)","F"
1898,0,0,96,0.033000," ","int((1+x)/(-1+x)/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{1+x}{\left(-1+x \right) \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((1+x)/(-1+x)/(x+(x^2+1)^(1/2))^(1/2),x)","F"
1899,0,0,100,0.044000," ","int((x^2-x)^(1/2)/(x^2-x*(x^2-x)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{x^{2}-x}}{\sqrt{x^{2}-x \sqrt{x^{2}-x}}}\, dx\]"," ",0,"int((x^2-x)^(1/2)/(x^2-x*(x^2-x)^(1/2))^(1/2),x)","F"
1900,1,883,102,5.524000," ","int((x^2+2*x+6)/(2+x)/(x^2+2)/(x^2+x+2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\ln \left(\frac{2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}+2 \left(x^{2}+x +2\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x +\left(x^{2}+x +2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{2}+4 \left(x^{2}+x +2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{2}+2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{3}-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{2}+4 \left(x^{2}+x +2\right)^{\frac{2}{3}} x -4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x -8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)}{\left(2+x \right) \left(x^{2}+2\right)}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)}{2}-\ln \left(\frac{2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}+2 \left(x^{2}+x +2\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x +\left(x^{2}+x +2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{2}+4 \left(x^{2}+x +2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{2}+2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{3}-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{2}+4 \left(x^{2}+x +2\right)^{\frac{2}{3}} x -4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x -8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)}{\left(2+x \right) \left(x^{2}+2\right)}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)+\frac{\RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{3}-2\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{3}-2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}+3 \left(x^{2}+x +2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{2}+6 \left(x^{2}+x +2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{2}+2 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{2}-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{2}+6 \left(x^{2}+x +2\right)^{\frac{2}{3}} x +2 \RootOf \left(\textit{\_Z}^{3}-2\right) x -4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x +4 \RootOf \left(\textit{\_Z}^{3}-2\right)-8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)}{\left(2+x \right) \left(x^{2}+2\right)}\right)}{2}$&$883$\\ \hline \end{longtable}"," ",0,"-1/2*ln((2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3+2*(x^2+x+2)^(2/3)*RootOf(_Z^3-2)^2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x+(x^2+x+2)^(1/3)*RootOf(_Z^3-2)^2*x^2+4*(x^2+x+2)^(1/3)*RootOf(_Z^3-2)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^2+2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3-4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^2+4*(x^2+x+2)^(2/3)*x-4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x-8*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2))/(2+x)/(x^2+2))*RootOf(_Z^3-2)-ln((2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3+2*(x^2+x+2)^(2/3)*RootOf(_Z^3-2)^2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x+(x^2+x+2)^(1/3)*RootOf(_Z^3-2)^2*x^2+4*(x^2+x+2)^(1/3)*RootOf(_Z^3-2)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^2+2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3-4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^2+4*(x^2+x+2)^(2/3)*x-4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x-8*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2))/(2+x)/(x^2+2))*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)+1/2*RootOf(_Z^3-2)*ln((RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3-2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3+3*(x^2+x+2)^(1/3)*RootOf(_Z^3-2)^2*x^2+6*(x^2+x+2)^(1/3)*RootOf(_Z^3-2)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^2+2*RootOf(_Z^3-2)*x^2-4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^2+6*(x^2+x+2)^(2/3)*x+2*RootOf(_Z^3-2)*x-4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x+4*RootOf(_Z^3-2)-8*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2))/(2+x)/(x^2+2))","C"
1901,1,345,116,1.626000," ","int((-1+x)/x/(x^3+2*x^2+2*x+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(\frac{11 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}-22 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x -111 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+2 x^{2}+2 x +1\right)^{\frac{1}{3}} x +100 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+11 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}-111 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+2 x^{2}+2 x +1\right)^{\frac{1}{3}}+207 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x +111 \left(x^{3}+2 x^{2}+2 x +1\right)^{\frac{2}{3}}-100 x^{2}+100 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-170 x -100}{x}\right)+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(-\frac{10 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}-20 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x +111 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+2 x^{2}+2 x +1\right)^{\frac{1}{3}} x -121 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+10 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}+111 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+2 x^{2}+2 x +1\right)^{\frac{1}{3}}-128 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x -111 \left(x^{3}+2 x^{2}+2 x +1\right)^{\frac{2}{3}}+121 x^{2}-121 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+165 x +121}{x}\right)$&$345$\\ \hline \end{longtable}"," ",0,"-ln((11*RootOf(_Z^2-_Z+1)^2*x^2-22*RootOf(_Z^2-_Z+1)^2*x-111*RootOf(_Z^2-_Z+1)*(x^3+2*x^2+2*x+1)^(1/3)*x+100*RootOf(_Z^2-_Z+1)*x^2+11*RootOf(_Z^2-_Z+1)^2-111*RootOf(_Z^2-_Z+1)*(x^3+2*x^2+2*x+1)^(1/3)+207*RootOf(_Z^2-_Z+1)*x+111*(x^3+2*x^2+2*x+1)^(2/3)-100*x^2+100*RootOf(_Z^2-_Z+1)-170*x-100)/x)+RootOf(_Z^2-_Z+1)*ln(-(10*RootOf(_Z^2-_Z+1)^2*x^2-20*RootOf(_Z^2-_Z+1)^2*x+111*RootOf(_Z^2-_Z+1)*(x^3+2*x^2+2*x+1)^(1/3)*x-121*RootOf(_Z^2-_Z+1)*x^2+10*RootOf(_Z^2-_Z+1)^2+111*RootOf(_Z^2-_Z+1)*(x^3+2*x^2+2*x+1)^(1/3)-128*RootOf(_Z^2-_Z+1)*x-111*(x^3+2*x^2+2*x+1)^(2/3)+121*x^2-121*RootOf(_Z^2-_Z+1)+165*x+121)/x)","C"
1902,0,0,126,0.020000," ","int((p*x^3-2*q)*(a*p*x^3+b*x^2+a*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)/x^7,x)","\[\int \frac{\left(p \,x^{3}-2 q \right) \left(a p \,x^{3}+b \,x^{2}+a q \right) \sqrt{p^{2} x^{6}-2 p q \,x^{4}+2 p q \,x^{3}+q^{2}}}{x^{7}}\, dx\]"," ",0,"int((p*x^3-2*q)*(a*p*x^3+b*x^2+a*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)/x^7,x)","F"
1903,0,0,61,0.022000," ","int(x^2/(x^2+1)/(1024*x^10-16640*x^9+112000*x^8-401440*x^7+820340*x^6-954733*x^5+615255*x^4-225810*x^3+47250*x^2-5265*x+243)^(1/10),x)","\[\int \frac{x^{2}}{\left(x^{2}+1\right) \left(1024 x^{10}-16640 x^{9}+112000 x^{8}-401440 x^{7}+820340 x^{6}-954733 x^{5}+615255 x^{4}-225810 x^{3}+47250 x^{2}-5265 x +243\right)^{\frac{1}{10}}}\, dx\]"," ",0,"int(x^2/(x^2+1)/(1024*x^10-16640*x^9+112000*x^8-401440*x^7+820340*x^6-954733*x^5+615255*x^4-225810*x^3+47250*x^2-5265*x+243)^(1/10),x)","F"
1904,0,0,118,0.046000," ","int(1/x/(a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x)","\[\int \frac{1}{x \sqrt{a^{2} x^{2}-b x}\, \left(a \,x^{2}+x \sqrt{a^{2} x^{2}-b x}\right)^{\frac{3}{2}}}\, dx\]"," ",0,"int(1/x/(a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x)","F"
1905,0,0,101,0.039000," ","int((x^2+(x^4+1)^(1/2))^(1/2)/(x^2-1)/(x^4+1)^(1/2),x)","\[\int \frac{\sqrt{x^{2}+\sqrt{x^{4}+1}}}{\left(x^{2}-1\right) \sqrt{x^{4}+1}}\, dx\]"," ",0,"int((x^2+(x^4+1)^(1/2))^(1/2)/(x^2-1)/(x^4+1)^(1/2),x)","F"
1906,1,1244,101,8.970000," ","int(1/(1+2*x)/(4*x^2+4*x-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1244$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)*ln((160*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)^2*RootOf(_Z^3+4)^2*x^2+8*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)*RootOf(_Z^3+4)^3*x^2+160*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)^2*RootOf(_Z^3+4)^2*x-48*(4*x^2+4*x-1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)*RootOf(_Z^3+4)^2+8*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)*RootOf(_Z^3+4)^3*x-96*(4*x^2+4*x-1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)*RootOf(_Z^3+4)+80*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)*x^2-9*(4*x^2+4*x-1)^(1/3)*RootOf(_Z^3+4)^2+4*RootOf(_Z^3+4)*x^2+80*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)*x+18*(4*x^2+4*x-1)^(2/3)+4*RootOf(_Z^3+4)*x-140*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)-7*RootOf(_Z^3+4))/(1+2*x)^2)-1/8*ln((160*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)^2*RootOf(_Z^3+4)^2*x^2+32*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)*RootOf(_Z^3+4)^3*x^2+160*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)^2*RootOf(_Z^3+4)^2*x+48*(4*x^2+4*x-1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)*RootOf(_Z^3+4)^2+32*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)*RootOf(_Z^3+4)^3*x+96*(4*x^2+4*x-1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)*RootOf(_Z^3+4)-240*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)*x^2+15*(4*x^2+4*x-1)^(1/3)*RootOf(_Z^3+4)^2-48*RootOf(_Z^3+4)*x^2-240*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)*x-30*(4*x^2+4*x-1)^(2/3)-48*RootOf(_Z^3+4)*x+140*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)+28*RootOf(_Z^3+4))/(1+2*x)^2)*RootOf(_Z^3+4)-1/2*ln((160*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)^2*RootOf(_Z^3+4)^2*x^2+32*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)*RootOf(_Z^3+4)^3*x^2+160*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)^2*RootOf(_Z^3+4)^2*x+48*(4*x^2+4*x-1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)*RootOf(_Z^3+4)^2+32*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)*RootOf(_Z^3+4)^3*x+96*(4*x^2+4*x-1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)*RootOf(_Z^3+4)-240*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)*x^2+15*(4*x^2+4*x-1)^(1/3)*RootOf(_Z^3+4)^2-48*RootOf(_Z^3+4)*x^2-240*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)*x-30*(4*x^2+4*x-1)^(2/3)-48*RootOf(_Z^3+4)*x+140*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)+28*RootOf(_Z^3+4))/(1+2*x)^2)*RootOf(RootOf(_Z^3+4)^2+4*_Z*RootOf(_Z^3+4)+16*_Z^2)","C"
1907,0,0,64,0.012000," ","int(1/x^3/(a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{1}{x^{3} \left(a \,x^{3}-b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/x^3/(a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
1908,0,0,64,0.001000," ","int(1/x^3/(a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{1}{x^{3} \left(a \,x^{3}-b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/x^3/(a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
1909,0,0,119,0.043000," ","int(x^3*(-b+x)*(-2*a*b+(3*a-b)*x)/(-a+x)/(x^2*(-a+x)*(-b+x))^(3/4)/(-a^3*d+3*a^2*d*x+(-3*a*d+b)*x^2+(-1+d)*x^3),x)","\[\int \frac{x^{3} \left(-b +x \right) \left(-2 a b +\left(3 a -b \right) x \right)}{\left(-a +x \right) \left(x^{2} \left(-a +x \right) \left(-b +x \right)\right)^{\frac{3}{4}} \left(-a^{3} d +3 a^{2} d x +\left(-3 a d +b \right) x^{2}+\left(-1+d \right) x^{3}\right)}\, dx\]"," ",0,"int(x^3*(-b+x)*(-2*a*b+(3*a-b)*x)/(-a+x)/(x^2*(-a+x)*(-b+x))^(3/4)/(-a^3*d+3*a^2*d*x+(-3*a*d+b)*x^2+(-1+d)*x^3),x)","F"
1910,1,898,105,3.435000," ","int(x^2/(x^3-x^2-x)^(1/2)/(x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}-i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{20 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}-i-\frac{\sqrt{5}}{2}\right)}+\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}-i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{20 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}-i-\frac{\sqrt{5}}{2}\right)}+\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}+i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{20 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}+i-\frac{\sqrt{5}}{2}\right)}-\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{1}{2}+i-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{20 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{1}{2}+i-\frac{\sqrt{5}}{2}\right)}-\frac{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \sqrt{-5 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{5}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{10 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)}+\frac{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \sqrt{-5 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{5}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{-\frac{1}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{10 \sqrt{x^{3}-x^{2}-x}\, \left(-\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}$&$898$\\ trager&$-\frac{\RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right) \ln \left(-\frac{879769600 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{5} x^{2}-1319654400 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{5} x -879769600 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{5}+21344000 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{3} x^{2}+14721760 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{3} x -21344000 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{3}+325120 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2} \sqrt{x^{3}-x^{2}-x}+99034 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right) x^{2}+693238 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right) x -99034 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)+294143 \sqrt{x^{3}-x^{2}-x}}{\left(80 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2} x -160 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2}-3 x -4\right)^{2}}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{2}+400 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2}+10\right) \ln \left(-\frac{87976960 \RootOf \left(\textit{\_Z}^{2}+400 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2}+10\right) \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{4} x^{2}-131965440 \RootOf \left(\textit{\_Z}^{2}+400 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2}+10\right) \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{4} x -87976960 \RootOf \left(\textit{\_Z}^{2}+400 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2}+10\right) \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{4}+2264448 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+400 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2}+10\right) x^{2}-8070448 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+400 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2}+10\right) x -2264448 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+400 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2}+10\right)-650240 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2} \sqrt{x^{3}-x^{2}-x}+11529 \RootOf \left(\textit{\_Z}^{2}+400 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2}+10\right) x^{2}-49959 \RootOf \left(\textit{\_Z}^{2}+400 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2}+10\right) x -11529 \RootOf \left(\textit{\_Z}^{2}+400 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2}+10\right)+572030 \sqrt{x^{3}-x^{2}-x}}{\left(16 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2} x -32 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2}+x \right)^{2}}\right)}{40}-10 \ln \left(\frac{80 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2} x^{2}-160 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2} x -80 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2}+x^{2}+4 \sqrt{x^{3}-x^{2}-x}-2 x -1}{\left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2}-\frac{\ln \left(\frac{80 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2} x^{2}-160 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2} x -80 \RootOf \left(1280 \textit{\_Z}^{4}+32 \textit{\_Z}^{2}+1\right)^{2}+x^{2}+4 \sqrt{x^{3}-x^{2}-x}-2 x -1}{\left(-1+x \right) \left(1+x \right)}\right)}{8}$&$912$\\ elliptic&$-\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, -\frac{i \sqrt{5}}{5}+\frac{1}{2}-\frac{\sqrt{5}}{10}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{20 \sqrt{x^{3}-x^{2}-x}}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, -\frac{i \sqrt{5}}{5}+\frac{1}{2}-\frac{\sqrt{5}}{10}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{50 \sqrt{x^{3}-x^{2}-x}}+\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, -\frac{i \sqrt{5}}{5}+\frac{1}{2}-\frac{\sqrt{5}}{10}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{100 \sqrt{x^{3}-x^{2}-x}}+\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{i \sqrt{5}}{5}+\frac{1}{2}-\frac{\sqrt{5}}{10}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{20 \sqrt{x^{3}-x^{2}-x}}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{i \sqrt{5}}{5}+\frac{1}{2}-\frac{\sqrt{5}}{10}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{50 \sqrt{x^{3}-x^{2}-x}}-\frac{i \sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{i \sqrt{5}}{5}+\frac{1}{2}-\frac{\sqrt{5}}{10}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{100 \sqrt{x^{3}-x^{2}-x}}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{20 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)}+\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{\frac{3}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{20 \sqrt{x^{3}-x^{2}-x}\, \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)}+\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{-\frac{1}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right) \sqrt{5}}{20 \sqrt{x^{3}-x^{2}-x}\, \left(-\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}-\frac{\sqrt{\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}-\frac{1}{2 \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}+\frac{\sqrt{5}}{\sqrt{5}-1}}\, \sqrt{-5 x \sqrt{5}+\frac{5 \sqrt{5}}{2}+\frac{25}{2}}\, \sqrt{-\frac{x}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{1}{2}+\frac{\sqrt{5}}{2}}{\frac{\sqrt{5}}{2}-\frac{1}{2}}}, \frac{\frac{1}{2}-\frac{\sqrt{5}}{2}}{-\frac{1}{2}-\frac{\sqrt{5}}{2}}, \frac{\sqrt{5}\, \sqrt{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \sqrt{5}}}{5}\right)}{20 \sqrt{x^{3}-x^{2}-x}\, \left(-\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}$&$1436$\\ \hline \end{longtable}"," ",0,"-1/20*I*(x/(1/2*5^(1/2)-1/2)-1/2/(1/2*5^(1/2)-1/2)+1/2/(1/2*5^(1/2)-1/2)*5^(1/2))^(1/2)*(-5*x*5^(1/2)+5/2*5^(1/2)+25/2)^(1/2)*(-x/(1/2*5^(1/2)-1/2))^(1/2)/(x^3-x^2-x)^(1/2)/(1/2-I-1/2*5^(1/2))*EllipticPi(((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2),(1/2-1/2*5^(1/2))/(1/2-I-1/2*5^(1/2)),1/5*5^(1/2)*((1/2*5^(1/2)-1/2)*5^(1/2))^(1/2))*5^(1/2)+1/20*I*(x/(1/2*5^(1/2)-1/2)-1/2/(1/2*5^(1/2)-1/2)+1/2/(1/2*5^(1/2)-1/2)*5^(1/2))^(1/2)*(-5*x*5^(1/2)+5/2*5^(1/2)+25/2)^(1/2)*(-x/(1/2*5^(1/2)-1/2))^(1/2)/(x^3-x^2-x)^(1/2)/(1/2-I-1/2*5^(1/2))*EllipticPi(((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2),(1/2-1/2*5^(1/2))/(1/2-I-1/2*5^(1/2)),1/5*5^(1/2)*((1/2*5^(1/2)-1/2)*5^(1/2))^(1/2))+1/20*I*(x/(1/2*5^(1/2)-1/2)-1/2/(1/2*5^(1/2)-1/2)+1/2/(1/2*5^(1/2)-1/2)*5^(1/2))^(1/2)*(-5*x*5^(1/2)+5/2*5^(1/2)+25/2)^(1/2)*(-x/(1/2*5^(1/2)-1/2))^(1/2)/(x^3-x^2-x)^(1/2)/(1/2+I-1/2*5^(1/2))*EllipticPi(((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2),(1/2-1/2*5^(1/2))/(1/2+I-1/2*5^(1/2)),1/5*5^(1/2)*((1/2*5^(1/2)-1/2)*5^(1/2))^(1/2))*5^(1/2)-1/20*I*(x/(1/2*5^(1/2)-1/2)-1/2/(1/2*5^(1/2)-1/2)+1/2/(1/2*5^(1/2)-1/2)*5^(1/2))^(1/2)*(-5*x*5^(1/2)+5/2*5^(1/2)+25/2)^(1/2)*(-x/(1/2*5^(1/2)-1/2))^(1/2)/(x^3-x^2-x)^(1/2)/(1/2+I-1/2*5^(1/2))*EllipticPi(((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2),(1/2-1/2*5^(1/2))/(1/2+I-1/2*5^(1/2)),1/5*5^(1/2)*((1/2*5^(1/2)-1/2)*5^(1/2))^(1/2))-1/10*(1/2*5^(1/2)-1/2)*((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2)*(-5*(x-1/2-1/2*5^(1/2))*5^(1/2))^(1/2)*(-x/(1/2*5^(1/2)-1/2))^(1/2)/(x^3-x^2-x)^(1/2)/(3/2-1/2*5^(1/2))*EllipticPi(((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2),(1/2-1/2*5^(1/2))/(3/2-1/2*5^(1/2)),1/5*5^(1/2)*((1/2*5^(1/2)-1/2)*5^(1/2))^(1/2))+1/10*(1/2*5^(1/2)-1/2)*((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2)*(-5*(x-1/2-1/2*5^(1/2))*5^(1/2))^(1/2)*(-x/(1/2*5^(1/2)-1/2))^(1/2)/(x^3-x^2-x)^(1/2)/(-1/2-1/2*5^(1/2))*EllipticPi(((x-1/2+1/2*5^(1/2))/(1/2*5^(1/2)-1/2))^(1/2),(1/2-1/2*5^(1/2))/(-1/2-1/2*5^(1/2)),1/5*5^(1/2)*((1/2*5^(1/2)-1/2)*5^(1/2))^(1/2))","C"
1911,1,186,105,3.564000," ","int((x^2-1)*(x^4+x^2+1)^(1/2)/(x^2+1)/(x^4+x^3+x^2+x+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\frac{\left(\munderset{\textit{\_R} =\RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right)}{\sum}\textit{\_R} \ln \left(\left(\sqrt{x^{4}+x^{2}+1}-x^{2}\right)^{2}+\left(-15 \textit{\_R}^{3}+5 \textit{\_R}^{2}-4 \textit{\_R} \right) \left(\sqrt{x^{4}+x^{2}+1}-x^{2}\right)-15 \textit{\_R}^{3}+5 \textit{\_R}^{2}-4 \textit{\_R} +2\right)\right)}{2}+\frac{\left(-\frac{2 \sqrt{5}\, \arctan \left(\frac{\sqrt{x^{4}+x^{2}+1}\, \sqrt{2}}{x \sqrt{\sqrt{5}-1}}\right)}{5 \sqrt{\sqrt{5}-1}}-\frac{2 \sqrt{5}\, \arctanh \left(\frac{\sqrt{x^{4}+x^{2}+1}\, \sqrt{2}}{x \sqrt{\sqrt{5}+1}}\right)}{5 \sqrt{\sqrt{5}+1}}+\sqrt{2}\, \arctan \left(\frac{\sqrt{x^{4}+x^{2}+1}}{x}\right)\right) \sqrt{2}}{2}$&$186$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right)^{2}+5\right) \ln \left(\frac{25 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right)^{2}+5\right) \RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right)^{4} x -5 \RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right)^{2}+5\right) x^{2}-5 \RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right)^{2}+5\right) x -5 \RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right)^{2}+5\right)+2 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right)^{2}+5\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right)^{2}+5\right) x +2 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right)^{2}+5\right)-5 \sqrt{x^{4}+x^{2}+1}}{5 x \RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right)^{2}-x^{2}-1}\right)}{5}-\RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right) \ln \left(-\frac{-25 \RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right)^{5} x -5 \RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right)^{3} x^{2}-15 \RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right)^{3} x -5 \RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right)^{3}-3 \RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right) x^{2}+\sqrt{x^{4}+x^{2}+1}-3 \RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right)}{5 x \RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right)^{2}+x^{2}+x +1}\right)-\RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right) \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right)^{2}+5\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right)^{2}+5\right) \RootOf \left(25 \textit{\_Z}^{4}+5 \textit{\_Z}^{2}-1\right) x -\sqrt{x^{4}+x^{2}+1}}{x^{2}+1}\right)$&$573$\\ default&$\frac{8 \sqrt{1+\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}}\, \sqrt{1+\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}}\, \EllipticF \left(\frac{x \sqrt{-2+2 i \sqrt{3}}}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}-\frac{8 \sqrt{1+\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}}\, \sqrt{1+\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}}\, \EllipticE \left(\frac{x \sqrt{-2+2 i \sqrt{3}}}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}-\frac{2 \sqrt{1+\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}}\, \sqrt{1+\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , -\frac{1}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+x^{2}+1}}+\frac{2 \sqrt{1-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{-2+2 i \sqrt{3}}}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}-\frac{8 \sqrt{1-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}}\, \left(\EllipticF \left(\frac{x \sqrt{-2+2 i \sqrt{3}}}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)-\EllipticE \left(\frac{x \sqrt{-2+2 i \sqrt{3}}}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+\textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{\sum}\left(-2 \underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  -2\right) \left(-\frac{\arctanh \left(\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2}+1\right) \left(6 \underline{\hspace{1.25 ex}}\alpha^{3}-3 \underline{\hspace{1.25 ex}}\alpha^{2}+11 x^{2}-6 \underline{\hspace{1.25 ex}}\alpha  +4\right)}{22 \sqrt{-\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha }\, \sqrt{x^{4}+x^{2}+1}}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha }}-\frac{\sqrt{2}\, \left(-\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  -1\right) \sqrt{x^{2}+2-i \sqrt{3}\, x^{2}}\, \sqrt{x^{2}+2+i \sqrt{3}\, x^{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , -\frac{i \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{3}}{2}-\frac{\underline{\hspace{1.25 ex}}\alpha^{3}}{2}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-1+i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}\right)\right)}{10}$&$712$\\ \hline \end{longtable}"," ",0,"-1/2*sum(_R*ln(((x^4+x^2+1)^(1/2)-x^2)^2+(-15*_R^3+5*_R^2-4*_R)*((x^4+x^2+1)^(1/2)-x^2)-15*_R^3+5*_R^2-4*_R+2),_R=RootOf(25*_Z^4+5*_Z^2-1))+1/2*(-2/5*5^(1/2)/(5^(1/2)-1)^(1/2)*arctan((x^4+x^2+1)^(1/2)*2^(1/2)/x/(5^(1/2)-1)^(1/2))-2/5*5^(1/2)/(5^(1/2)+1)^(1/2)*arctanh((x^4+x^2+1)^(1/2)*2^(1/2)/x/(5^(1/2)+1)^(1/2))+2^(1/2)*arctan(1/x*(x^4+x^2+1)^(1/2)))*2^(1/2)","C"
1912,0,0,93,0.050000," ","int(x^6/(a*x^4-b)/(a*x^4+b)^(3/4),x)","\[\int \frac{x^{6}}{\left(a \,x^{4}-b \right) \left(a \,x^{4}+b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(x^6/(a*x^4-b)/(a*x^4+b)^(3/4),x)","F"
1913,0,0,105,0.011000," ","int((a*x^3-b)/x^3/(a*x^3+b)/(a*x^4-b*x)^(1/4),x)","\[\int \frac{a \,x^{3}-b}{x^{3} \left(a \,x^{3}+b \right) \left(a \,x^{4}-b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^3-b)/x^3/(a*x^3+b)/(a*x^4-b*x)^(1/4),x)","F"
1914,0,0,93,0.042000," ","int((a*x^4-b)/(a*x^4+b)^(1/4)/(3*a*x^4-b),x)","\[\int \frac{a \,x^{4}-b}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(3 a \,x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^4-b)/(a*x^4+b)^(1/4)/(3*a*x^4-b),x)","F"
1915,0,0,105,0.026000," ","int((a*x^2-2*b)/(a*x^2-b)^(1/4)/(c*x^4+a*x^2-b),x)","\[\int \frac{a \,x^{2}-2 b}{\left(a \,x^{2}-b \right)^{\frac{1}{4}} \left(c \,x^{4}+a \,x^{2}-b \right)}\, dx\]"," ",0,"int((a*x^2-2*b)/(a*x^2-b)^(1/4)/(c*x^4+a*x^2-b),x)","F"
1916,1,6680,123,0.668000," ","int((p*x^2-q)*(p^2*x^4+q^2)^(1/2)/x^2/(a*p*x^2+a*q+b*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$6680$\\ default&$\text{Expression too large to display}$&$6985$\\ elliptic&$\text{Expression too large to display}$&$9277$\\ \hline \end{longtable}"," ",0,"result too large to display","C"
1917,1,1015,97,83.507000," ","int((x^5+1)^(1/3)*(2*x^5-3)/x^2/(2*x^5-x^3+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(x^{5}+1\right)^{\frac{1}{3}}}{2 x}+\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) \ln \left(\frac{76247796 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{4} x^{5}+876387663 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{5}-152495592 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{4} x^{3}-1752775326 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{3}-203327456 \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{5}-2337033768 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x^{5}+496072665 \left(x^{5}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x +76247796 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{4}+876387663 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}-127079660 \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{3}-1460646105 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x^{3}+736754034 \left(x^{5}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right) x^{2}+3428378874 \left(x^{5}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) x^{2}-1142792958 \left(x^{5}+1\right)^{\frac{2}{3}} x -203327456 \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-2337033768 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)}{2 x^{5}-x^{3}+2}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(-\frac{-76247796 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{4} x^{5}+418900887 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{5}+152495592 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{4} x^{3}-837801774 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{3}-254159320 \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{5}+1396336290 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x^{5}+496072665 \left(x^{5}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x -76247796 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{4}+418900887 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}-25415932 \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{3}+139633629 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x^{3}-571396479 \left(x^{5}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right) x^{2}-4420524204 \left(x^{5}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) x^{2}+1473508068 \left(x^{5}+1\right)^{\frac{2}{3}} x -254159320 \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+1396336290 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)}{2 x^{5}-x^{3}+2}\right)}{4}$&$1015$\\ risch&$\frac{3 \left(x^{5}+1\right)^{\frac{1}{3}}}{2 x}+\frac{\left(\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \ln \left(-\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{8}-2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{8}+4 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{10}-8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{10}-6 \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} \left(x^{10}+2 x^{5}+1\right)^{\frac{1}{3}} x^{6}-12 \left(x^{10}+2 x^{5}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x^{6}+2 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{8}-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{8}+6 \left(x^{10}+2 x^{5}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{2}+\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{3}-2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{3}+8 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{5}-16 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{5}-6 \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} \left(x^{10}+2 x^{5}+1\right)^{\frac{1}{3}} x -12 \left(x^{10}+2 x^{5}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x +2 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{3}-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{3}+4 \RootOf \left(\textit{\_Z}^{3}-4\right)-8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)}{\left(2 x^{5}-x^{3}+2\right) \left(x^{4}-x^{3}+x^{2}-x +1\right) \left(1+x \right)}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(\frac{-\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{8}+2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{8}+4 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{10}-8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{10}-6 \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} \left(x^{10}+2 x^{5}+1\right)^{\frac{1}{3}} x^{6}+6 \left(x^{10}+2 x^{5}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{2}-\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{3}+2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{3}+8 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{5}-16 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{5}+12 \left(x^{10}+2 x^{5}+1\right)^{\frac{2}{3}} x^{2}-6 \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} \left(x^{10}+2 x^{5}+1\right)^{\frac{1}{3}} x +4 \RootOf \left(\textit{\_Z}^{3}-4\right)-8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)}{\left(2 x^{5}-x^{3}+2\right) \left(x^{4}-x^{3}+x^{2}-x +1\right) \left(1+x \right)}\right)}{4}\right) \left(\left(x^{5}+1\right)^{2}\right)^{\frac{1}{3}}}{\left(x^{5}+1\right)^{\frac{2}{3}}}$&$1060$\\ \hline \end{longtable}"," ",0,"3/2*(x^5+1)^(1/3)/x+3/2*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*ln((76247796*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^4*x^5+876387663*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^3*x^5-152495592*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^4*x^3-1752775326*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^3*x^3-203327456*RootOf(_Z^3-4)^2*x^5-2337033768*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^5+496072665*(x^5+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*x+76247796*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^4+876387663*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^3-127079660*RootOf(_Z^3-4)^2*x^3-1460646105*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^3+736754034*(x^5+1)^(1/3)*RootOf(_Z^3-4)*x^2+3428378874*(x^5+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^2-1142792958*(x^5+1)^(2/3)*x-203327456*RootOf(_Z^3-4)^2-2337033768*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4))/(2*x^5-x^3+2))+1/4*RootOf(_Z^3-4)*ln(-(-76247796*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^4*x^5+418900887*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^3*x^5+152495592*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^4*x^3-837801774*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^3*x^3-254159320*RootOf(_Z^3-4)^2*x^5+1396336290*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^5+496072665*(x^5+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*x-76247796*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^4+418900887*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^3-25415932*RootOf(_Z^3-4)^2*x^3+139633629*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)*x^3-571396479*(x^5+1)^(1/3)*RootOf(_Z^3-4)*x^2-4420524204*(x^5+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^2+1473508068*(x^5+1)^(2/3)*x-254159320*RootOf(_Z^3-4)^2+1396336290*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4))/(2*x^5-x^3+2))","C"
1918,0,0,105,0.035000," ","int(x^2*(a*x^5+4*b)/(a*x^5-b)^(3/4)/(a*x^5+c*x^4-b),x)","\[\int \frac{x^{2} \left(a \,x^{5}+4 b \right)}{\left(a \,x^{5}-b \right)^{\frac{3}{4}} \left(a \,x^{5}+c \,x^{4}-b \right)}\, dx\]"," ",0,"int(x^2*(a*x^5+4*b)/(a*x^5-b)^(3/4)/(a*x^5+c*x^4-b),x)","F"
1919,0,0,97,5.094000," ","int((x^6-1)*(x^6+1)^(2/3)/x^3/(2*x^6-x^3+2),x)","\[\int \frac{\left(x^{6}-1\right) \left(x^{6}+1\right)^{\frac{2}{3}}}{x^{3} \left(2 x^{6}-x^{3}+2\right)}\, dx\]"," ",0,"int((x^6-1)*(x^6+1)^(2/3)/x^3/(2*x^6-x^3+2),x)","F"
1920,0,0,106,0.034000," ","int(x^2*(a*x^6+2*b)/(a*x^6-b)^(3/4)/(a*x^6+c*x^4-b),x)","\[\int \frac{x^{2} \left(a \,x^{6}+2 b \right)}{\left(a \,x^{6}-b \right)^{\frac{3}{4}} \left(a \,x^{6}+c \,x^{4}-b \right)}\, dx\]"," ",0,"int(x^2*(a*x^6+2*b)/(a*x^6-b)^(3/4)/(a*x^6+c*x^4-b),x)","F"
1921,0,0,108,0.019000," ","int(x^2*(x^4+1)^(1/2)*(x^2+(x^4+1)^(1/2))^(1/2),x)","\[\int x^{2} \sqrt{x^{4}+1}\, \sqrt{x^{2}+\sqrt{x^{4}+1}}\, dx\]"," ",0,"int(x^2*(x^4+1)^(1/2)*(x^2+(x^4+1)^(1/2))^(1/2),x)","F"
1922,1,47,91,0.119000," ","int((1+(1+(1+x)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{9}{2}}}{9}-\frac{24 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{7}{2}}}{7}+\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}$&$47$\\ default&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{9}{2}}}{9}-\frac{24 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{7}{2}}}{7}+\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}$&$47$\\ \hline \end{longtable}"," ",0,"8/9*(1+(1+(1+x)^(1/2))^(1/2))^(9/2)-24/7*(1+(1+(1+x)^(1/2))^(1/2))^(7/2)+16/5*(1+(1+(1+x)^(1/2))^(1/2))^(5/2)","A"
1923,0,0,23,0.032000," ","int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right) \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)/(x+(x^2+1)^(1/2))^(1/2),x)","F"
1924,0,0,23,0.001000," ","int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right) \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)/(x+(x^2+1)^(1/2))^(1/2),x)","F"
1925,1,896,104,1.951000," ","int((x^3-2)*(x^3+1)^(2/3)/x^6/(2*x^3-1),x)","\[-\frac{19 x^{6}+23 x^{3}+4}{10 x^{5} \left(x^{3}+1\right)^{\frac{1}{3}}}+\RootOf \left(\textit{\_Z}^{3}+9\right) \ln \left(-\frac{-3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+9\right)^{3} x^{3}-108 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+9\right)^{2} x^{3}+15 \left(x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}+9\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) x -7 \RootOf \left(\textit{\_Z}^{3}+9\right)^{2} \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}-18 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+9\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) x^{2}-\RootOf \left(\textit{\_Z}^{3}+9\right) x^{3}-36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) x^{3}+6 x \left(x^{3}+1\right)^{\frac{2}{3}}-\RootOf \left(\textit{\_Z}^{3}+9\right)-36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right)}{2 x^{3}-1}\right)-\ln \left(\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+9\right)^{3} x^{3}-81 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+9\right)^{2} x^{3}+15 \left(x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}+9\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) x +2 \RootOf \left(\textit{\_Z}^{3}+9\right)^{2} \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}+63 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+9\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) x^{2}-4 \RootOf \left(\textit{\_Z}^{3}+9\right) x^{3}+108 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) x^{3}-21 x \left(x^{3}+1\right)^{\frac{2}{3}}-\RootOf \left(\textit{\_Z}^{3}+9\right)+27 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right)}{2 x^{3}-1}\right) \RootOf \left(\textit{\_Z}^{3}+9\right)-9 \ln \left(\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+9\right)^{3} x^{3}-81 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+9\right)^{2} x^{3}+15 \left(x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}+9\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) x +2 \RootOf \left(\textit{\_Z}^{3}+9\right)^{2} \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}+63 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+9\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) x^{2}-4 \RootOf \left(\textit{\_Z}^{3}+9\right) x^{3}+108 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right) x^{3}-21 x \left(x^{3}+1\right)^{\frac{2}{3}}-\RootOf \left(\textit{\_Z}^{3}+9\right)+27 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right)}{2 x^{3}-1}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+9\right)+81 \textit{\_Z}^{2}\right)\]"," ",0,"-1/10*(19*x^6+23*x^3+4)/x^5/(x^3+1)^(1/3)+RootOf(_Z^3+9)*ln(-(-3*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*RootOf(_Z^3+9)^3*x^3-108*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)^2*RootOf(_Z^3+9)^2*x^3+15*(x^3+1)^(2/3)*RootOf(_Z^3+9)^2*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*x-7*RootOf(_Z^3+9)^2*(x^3+1)^(1/3)*x^2-18*(x^3+1)^(1/3)*RootOf(_Z^3+9)*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*x^2-RootOf(_Z^3+9)*x^3-36*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*x^3+6*x*(x^3+1)^(2/3)-RootOf(_Z^3+9)-36*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2))/(2*x^3-1))-ln((3*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*RootOf(_Z^3+9)^3*x^3-81*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)^2*RootOf(_Z^3+9)^2*x^3+15*(x^3+1)^(2/3)*RootOf(_Z^3+9)^2*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*x+2*RootOf(_Z^3+9)^2*(x^3+1)^(1/3)*x^2+63*(x^3+1)^(1/3)*RootOf(_Z^3+9)*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*x^2-4*RootOf(_Z^3+9)*x^3+108*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*x^3-21*x*(x^3+1)^(2/3)-RootOf(_Z^3+9)+27*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2))/(2*x^3-1))*RootOf(_Z^3+9)-9*ln((3*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*RootOf(_Z^3+9)^3*x^3-81*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)^2*RootOf(_Z^3+9)^2*x^3+15*(x^3+1)^(2/3)*RootOf(_Z^3+9)^2*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*x+2*RootOf(_Z^3+9)^2*(x^3+1)^(1/3)*x^2+63*(x^3+1)^(1/3)*RootOf(_Z^3+9)*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*x^2-4*RootOf(_Z^3+9)*x^3+108*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)*x^3-21*x*(x^3+1)^(2/3)-RootOf(_Z^3+9)+27*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2))/(2*x^3-1))*RootOf(RootOf(_Z^3+9)^2+9*_Z*RootOf(_Z^3+9)+81*_Z^2)","C"
1926,0,0,64,0.012000," ","int(1/x^3/(a*x^3+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{1}{x^{3} \left(a \,x^{3}+b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/x^3/(a*x^3+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
1927,0,0,64,0.002000," ","int(1/x^3/(a*x^3+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{1}{x^{3} \left(a \,x^{3}+b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/x^3/(a*x^3+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
1928,1,480,110,3.581000," ","int((x^4+x-1)*(x^4-x^3)^(1/4)/(1+x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\left(\frac{1}{5} x^{4}-\frac{21}{80} x^{3}+\frac{65}{192} x^{2}-\frac{53}{1536} x -\frac{6515}{6144}\right) \left(x^{4}-x^{3}\right)^{\frac{1}{4}}-\frac{9869 \ln \left(\frac{2 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}-2 \sqrt{x^{4}-x^{3}}\, x +2 x^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}-2 x^{3}+x^{2}}{x^{2}}\right)}{8192}-\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(\frac{3 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{3}-\RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{2}+4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}} x^{2}+4 \sqrt{x^{4}-x^{3}}\, \RootOf \left(\textit{\_Z}^{4}-2\right) x +4 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(1+x \right)}\right)+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(\frac{3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}-4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}} x^{2}-4 \sqrt{x^{4}-x^{3}}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x +4 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(1+x \right)}\right)+\frac{9869 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(\frac{2 \sqrt{x^{4}-x^{3}}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x -2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{3}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{2}+4 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}-4 x^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}}{x^{2}}\right)}{16384}$&$480$\\ risch&$\frac{\left(6144 x^{4}-8064 x^{3}+10400 x^{2}-1060 x -32575\right) \left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}}}{30720}+\frac{\left(-\frac{9869 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{3}{4}}-2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x^{2}+5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x -4 \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(-1+x \right)^{2}}\right)}{8192}+\frac{9869 \ln \left(\frac{2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{3}{4}}+2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, x +2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x^{2}+2 x^{3}-2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}-4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x -5 x^{2}+2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}}+4 x -1}{\left(-1+x \right)^{2}}\right)}{8192}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(-\frac{2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x -2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)+2 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x^{2}-4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x -3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{3}+2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+7 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{2}-4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{3}{4}}-5 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)}{\left(-1+x \right)^{2} \left(1+x \right)}\right)-\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(\frac{2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x -2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}+2 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x^{2}-4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x +3 \RootOf \left(\textit{\_Z}^{4}-2\right) x^{3}+2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}-7 \RootOf \left(\textit{\_Z}^{4}-2\right) x^{2}+4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{3}{4}}+5 \RootOf \left(\textit{\_Z}^{4}-2\right) x -\RootOf \left(\textit{\_Z}^{4}-2\right)}{\left(-1+x \right)^{2} \left(1+x \right)}\right)\right) \left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}} \left(x \left(-1+x \right)^{3}\right)^{\frac{1}{4}}}{x \left(-1+x \right)}$&$934$\\ \hline \end{longtable}"," ",0,"(1/5*x^4-21/80*x^3+65/192*x^2-53/1536*x-6515/6144)*(x^4-x^3)^(1/4)-9869/8192*ln((2*(x^4-x^3)^(3/4)-2*(x^4-x^3)^(1/2)*x+2*x^2*(x^4-x^3)^(1/4)-2*x^3+x^2)/x^2)-RootOf(_Z^4-2)*ln((3*RootOf(_Z^4-2)^3*x^3-RootOf(_Z^4-2)^3*x^2+4*RootOf(_Z^4-2)^2*(x^4-x^3)^(1/4)*x^2+4*(x^4-x^3)^(1/2)*RootOf(_Z^4-2)*x+4*(x^4-x^3)^(3/4))/x^2/(1+x))+RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln((3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*x^3-RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*x^2-4*RootOf(_Z^4-2)^2*(x^4-x^3)^(1/4)*x^2-4*(x^4-x^3)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x+4*(x^4-x^3)^(3/4))/x^2/(1+x))+9869/16384*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln((2*(x^4-x^3)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^3*x-2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^3*x^3+RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^3*x^2+4*(x^4-x^3)^(3/4)-4*x^2*(x^4-x^3)^(1/4))/x^2)","C"
1929,1,644,98,89.103000," ","int((x^4-3)*(x^4+1)^(2/3)/x^3/(2*x^4+x^3+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 \left(x^{4}+1\right)^{\frac{2}{3}}}{4 x^{2}}+\frac{\RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{3}-2\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{3}+2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}-2 \left(x^{4}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x -\RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \left(x^{4}+1\right)^{\frac{1}{3}} x^{2}+2 \left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{4}-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{4}+\RootOf \left(\textit{\_Z}^{3}-2\right) x^{3}+2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{3}-4 \left(x^{4}+1\right)^{\frac{2}{3}} x -2 \RootOf \left(\textit{\_Z}^{3}-2\right)-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)}{2 x^{4}+x^{3}+2}\right)}{4}+\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{3}-2\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{3}+2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}-2 \left(x^{4}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x -\RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \left(x^{4}+1\right)^{\frac{1}{3}} x^{2}-4 \left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right) x^{2}+2 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{4}+4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{4}+2 \left(x^{4}+1\right)^{\frac{2}{3}} x +2 \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)}{2 x^{4}+x^{3}+2}\right)}{2}$&$644$\\ trager&$\text{Expression too large to display}$&$1469$\\ \hline \end{longtable}"," ",0,"3/4*(x^4+1)^(2/3)/x^2+1/4*RootOf(_Z^3-2)*ln((RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3+2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-2*(x^4+1)^(2/3)*RootOf(_Z^3-2)^2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x-RootOf(_Z^3-2)^2*(x^4+1)^(1/3)*x^2+2*(x^4+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^2-2*RootOf(_Z^3-2)*x^4-4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^4+RootOf(_Z^3-2)*x^3+2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3-4*(x^4+1)^(2/3)*x-2*RootOf(_Z^3-2)-4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2))/(2*x^4+x^3+2))+1/2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*ln(-(RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3+2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-2*(x^4+1)^(2/3)*RootOf(_Z^3-2)^2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x-RootOf(_Z^3-2)^2*(x^4+1)^(1/3)*x^2-4*(x^4+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^2+2*RootOf(_Z^3-2)*x^4+4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^4+2*(x^4+1)^(2/3)*x+2*RootOf(_Z^3-2)+4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2))/(2*x^4+x^3+2))","C"
1930,0,0,100,0.013000," ","int((a*x^4-4*b)*(a*x^4+b)^(3/4)/x^8/(a*x^4+4*b),x)","\[\int \frac{\left(a \,x^{4}-4 b \right) \left(a \,x^{4}+b \right)^{\frac{3}{4}}}{x^{8} \left(a \,x^{4}+4 b \right)}\, dx\]"," ",0,"int((a*x^4-4*b)*(a*x^4+b)^(3/4)/x^8/(a*x^4+4*b),x)","F"
1931,0,0,100,0.012000," ","int((a*x^4+b)^(3/4)*(a*x^4+2*b)/x^8/(a*x^4+4*b),x)","\[\int \frac{\left(a \,x^{4}+b \right)^{\frac{3}{4}} \left(a \,x^{4}+2 b \right)}{x^{8} \left(a \,x^{4}+4 b \right)}\, dx\]"," ",0,"int((a*x^4+b)^(3/4)*(a*x^4+2*b)/x^8/(a*x^4+4*b),x)","F"
1932,0,0,114,0.011000," ","int(x^4*(a*x^4+b*x^3)^(1/4)/(a*x+b),x)","\[\int \frac{x^{4} \left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}}{a x +b}\, dx\]"," ",0,"int(x^4*(a*x^4+b*x^3)^(1/4)/(a*x+b),x)","F"
1933,1,38,97,0.132000," ","int((a*x^2+b)/(a*x^2-b)/(a^2*x^4+b^2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\frac{\arctanh \left(\frac{\sqrt{a^{2} x^{4}+b^{2}}\, \sqrt{2}}{2 x \sqrt{a b}}\right) \sqrt{2}}{2 \sqrt{a b}}$&$38$\\ default&$\frac{\sqrt{1-\frac{i a \,x^{2}}{b}}\, \sqrt{1+\frac{i a \,x^{2}}{b}}\, \EllipticF \left(x \sqrt{\frac{i a}{b}}, i\right)}{\sqrt{\frac{i a}{b}}\, \sqrt{a^{2} x^{4}+b^{2}}}-\frac{2 \sqrt{1-\frac{i a \,x^{2}}{b}}\, \sqrt{1+\frac{i a \,x^{2}}{b}}\, \EllipticPi \left(x \sqrt{\frac{i a}{b}}, -i, \frac{\sqrt{-\frac{i a}{b}}}{\sqrt{\frac{i a}{b}}}\right)}{\sqrt{\frac{i a}{b}}\, \sqrt{a^{2} x^{4}+b^{2}}}$&$152$\\ \hline \end{longtable}"," ",0,"-1/2/(a*b)^(1/2)*arctanh(1/2*(a^2*x^4+b^2)^(1/2)*2^(1/2)/x/(a*b)^(1/2))*2^(1/2)","A"
1934,0,0,96,0.034000," ","int((x^2+1)*(1+(x^2+1)^(1/2))^(1/2)/(x^2-1),x)","\[\int \frac{\left(x^{2}+1\right) \sqrt{1+\sqrt{x^{2}+1}}}{x^{2}-1}\, dx\]"," ",0,"int((x^2+1)*(1+(x^2+1)^(1/2))^(1/2)/(x^2-1),x)","F"
1935,0,0,104,0.038000," ","int(1/(a*x^3-b)^(1/3),x)","\[\int \frac{1}{\left(a \,x^{3}-b \right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(a*x^3-b)^(1/3),x)","F"
1936,0,0,123,0.025000," ","int((a^2-2*a*x+x^2)*(-a*b-a*c+3*b*c+2*(a-b-c)*x+x^2)/((-a+x)*(-b+x)*(-c+x))^(3/4)/(-b*c-a^3*d+(3*a^2*d+b+c)*x-(3*a*d+1)*x^2+d*x^3),x)","\[\int \frac{\left(a^{2}-2 a x +x^{2}\right) \left(-a b -a c +3 b c +2 \left(a -b -c \right) x +x^{2}\right)}{\left(\left(-a +x \right) \left(-b +x \right) \left(-c +x \right)\right)^{\frac{3}{4}} \left(-b c -a^{3} d +\left(3 a^{2} d +b +c \right) x -\left(3 a d +1\right) x^{2}+d \,x^{3}\right)}\, dx\]"," ",0,"int((a^2-2*a*x+x^2)*(-a*b-a*c+3*b*c+2*(a-b-c)*x+x^2)/((-a+x)*(-b+x)*(-c+x))^(3/4)/(-b*c-a^3*d+(3*a^2*d+b+c)*x-(3*a*d+1)*x^2+d*x^3),x)","F"
1937,1,332,113,66.005000," ","int((x^5-4)*(x^5-2*x^4+1)^(1/4)/x^2/(x^5+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{5}-2 x^{4}+1\right)^{\frac{1}{4}}}{x}+\RootOf \left(\textit{\_Z}^{4}+2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+2\right)^{3} x^{5}-4 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} x^{4}+4 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \left(x^{5}-2 x^{4}+1\right)^{\frac{1}{4}} x^{3}-4 \RootOf \left(\textit{\_Z}^{4}+2\right) \sqrt{x^{5}-2 x^{4}+1}\, x^{2}+4 \left(x^{5}-2 x^{4}+1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}+2\right)^{3}}{\left(1+x \right) \left(x^{4}-x^{3}+x^{2}-x +1\right)}\right)-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{5}-4 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{4}-4 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \left(x^{5}-2 x^{4}+1\right)^{\frac{1}{4}} x^{3}+4 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \sqrt{x^{5}-2 x^{4}+1}\, x^{2}+4 \left(x^{5}-2 x^{4}+1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right)}{\left(1+x \right) \left(x^{4}-x^{3}+x^{2}-x +1\right)}\right)$&$332$\\ risch&$\frac{4 \left(x^{5}-2 x^{4}+1\right)^{\frac{1}{4}}}{x}+\frac{\left(-\RootOf \left(\textit{\_Z}^{4}+2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{15}-8 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{14}+2 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} \left(x^{15}-6 x^{14}+12 x^{13}-8 x^{12}+3 x^{10}-12 x^{9}+12 x^{8}+3 x^{5}-6 x^{4}+1\right)^{\frac{1}{4}} x^{11}+20 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{13}-8 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} \left(x^{15}-6 x^{14}+12 x^{13}-8 x^{12}+3 x^{10}-12 x^{9}+12 x^{8}+3 x^{5}-6 x^{4}+1\right)^{\frac{1}{4}} x^{10}-16 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{12}+8 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} \left(x^{15}-6 x^{14}+12 x^{13}-8 x^{12}+3 x^{10}-12 x^{9}+12 x^{8}+3 x^{5}-6 x^{4}+1\right)^{\frac{1}{4}} x^{9}+3 x^{10} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}-16 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{9}+4 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} \left(x^{15}-6 x^{14}+12 x^{13}-8 x^{12}+3 x^{10}-12 x^{9}+12 x^{8}+3 x^{5}-6 x^{4}+1\right)^{\frac{1}{4}} x^{6}+20 x^{8} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}-8 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} \left(x^{15}-6 x^{14}+12 x^{13}-8 x^{12}+3 x^{10}-12 x^{9}+12 x^{8}+3 x^{5}-6 x^{4}+1\right)^{\frac{1}{4}} x^{5}-4 \sqrt{x^{15}-6 x^{14}+12 x^{13}-8 x^{12}+3 x^{10}-12 x^{9}+12 x^{8}+3 x^{5}-6 x^{4}+1}\, x^{7}+8 \sqrt{x^{15}-6 x^{14}+12 x^{13}-8 x^{12}+3 x^{10}-12 x^{9}+12 x^{8}+3 x^{5}-6 x^{4}+1}\, x^{6}+3 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{5}-4 \RootOf \left(\textit{\_Z}^{4}+2\right) \left(x^{15}-6 x^{14}+12 x^{13}-8 x^{12}+3 x^{10}-12 x^{9}+12 x^{8}+3 x^{5}-6 x^{4}+1\right)^{\frac{3}{4}} x^{3}-8 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{4}+2 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} \left(x^{15}-6 x^{14}+12 x^{13}-8 x^{12}+3 x^{10}-12 x^{9}+12 x^{8}+3 x^{5}-6 x^{4}+1\right)^{\frac{1}{4}} x -4 \sqrt{x^{15}-6 x^{14}+12 x^{13}-8 x^{12}+3 x^{10}-12 x^{9}+12 x^{8}+3 x^{5}-6 x^{4}+1}\, x^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}}{\left(-1+x \right)^{2} \left(x^{4}-x^{3}-x^{2}-x -1\right)^{2} \left(1+x \right) \left(x^{4}-x^{3}+x^{2}-x +1\right)}\right)-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{15}-8 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{14}+2 \left(x^{15}-6 x^{14}+12 x^{13}-8 x^{12}+3 x^{10}-12 x^{9}+12 x^{8}+3 x^{5}-6 x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{11}+20 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{13}-8 \left(x^{15}-6 x^{14}+12 x^{13}-8 x^{12}+3 x^{10}-12 x^{9}+12 x^{8}+3 x^{5}-6 x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{10}-16 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{12}+8 \left(x^{15}-6 x^{14}+12 x^{13}-8 x^{12}+3 x^{10}-12 x^{9}+12 x^{8}+3 x^{5}-6 x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{9}+3 x^{10} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}-16 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{9}+4 \left(x^{15}-6 x^{14}+12 x^{13}-8 x^{12}+3 x^{10}-12 x^{9}+12 x^{8}+3 x^{5}-6 x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{6}+20 x^{8} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}-8 \left(x^{15}-6 x^{14}+12 x^{13}-8 x^{12}+3 x^{10}-12 x^{9}+12 x^{8}+3 x^{5}-6 x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{5}+4 \sqrt{x^{15}-6 x^{14}+12 x^{13}-8 x^{12}+3 x^{10}-12 x^{9}+12 x^{8}+3 x^{5}-6 x^{4}+1}\, x^{7}-8 \sqrt{x^{15}-6 x^{14}+12 x^{13}-8 x^{12}+3 x^{10}-12 x^{9}+12 x^{8}+3 x^{5}-6 x^{4}+1}\, x^{6}+4 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \left(x^{15}-6 x^{14}+12 x^{13}-8 x^{12}+3 x^{10}-12 x^{9}+12 x^{8}+3 x^{5}-6 x^{4}+1\right)^{\frac{3}{4}} x^{3}+3 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{5}-8 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{4}+2 \left(x^{15}-6 x^{14}+12 x^{13}-8 x^{12}+3 x^{10}-12 x^{9}+12 x^{8}+3 x^{5}-6 x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x +4 \sqrt{x^{15}-6 x^{14}+12 x^{13}-8 x^{12}+3 x^{10}-12 x^{9}+12 x^{8}+3 x^{5}-6 x^{4}+1}\, x^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}}{\left(-1+x \right)^{2} \left(x^{4}-x^{3}-x^{2}-x -1\right)^{2} \left(1+x \right) \left(x^{4}-x^{3}+x^{2}-x +1\right)}\right)\right) \left(\left(x^{5}-2 x^{4}+1\right)^{3}\right)^{\frac{1}{4}}}{\left(x^{5}-2 x^{4}+1\right)^{\frac{3}{4}}}$&$1650$\\ \hline \end{longtable}"," ",0,"4*(x^5-2*x^4+1)^(1/4)/x+RootOf(_Z^4+2)*ln((RootOf(_Z^4+2)^3*x^5-4*RootOf(_Z^4+2)^3*x^4+4*RootOf(_Z^4+2)^2*(x^5-2*x^4+1)^(1/4)*x^3-4*RootOf(_Z^4+2)*(x^5-2*x^4+1)^(1/2)*x^2+4*(x^5-2*x^4+1)^(3/4)*x+RootOf(_Z^4+2)^3)/(1+x)/(x^4-x^3+x^2-x+1))-RootOf(_Z^2+RootOf(_Z^4+2)^2)*ln((RootOf(_Z^2+RootOf(_Z^4+2)^2)*RootOf(_Z^4+2)^2*x^5-4*RootOf(_Z^4+2)^2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*x^4-4*RootOf(_Z^4+2)^2*(x^5-2*x^4+1)^(1/4)*x^3+4*RootOf(_Z^2+RootOf(_Z^4+2)^2)*(x^5-2*x^4+1)^(1/2)*x^2+4*(x^5-2*x^4+1)^(3/4)*x+RootOf(_Z^4+2)^2*RootOf(_Z^2+RootOf(_Z^4+2)^2))/(1+x)/(x^4-x^3+x^2-x+1))","C"
1938,1,44,105,1.547000," ","int((a*x^6+b)/x^6/(x^3+x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 a \,x^{\frac{2}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{2}\right)}{2}-\frac{3 b \left(\frac{9}{5} x^{4}-\frac{6}{5} x^{2}+1\right) \left(x^{2}+1\right)^{\frac{2}{3}}}{16 x^{\frac{16}{3}}}$&$44$\\ risch&$-\frac{3 b \left(x^{2}+1\right) \left(9 x^{4}-6 x^{2}+5\right)}{80 x^{5} \left(x \left(x^{2}+1\right)\right)^{\frac{1}{3}}}+\frac{3 a \,x^{\frac{2}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], -x^{2}\right)}{2}$&$51$\\ trager&$-\frac{3 b \left(x^{3}+x \right)^{\frac{2}{3}} \left(9 x^{4}-6 x^{2}+5\right)}{80 x^{6}}-\frac{a \left(6 \ln \left(-36 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{2}-144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}+90 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x +60 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}+36 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2}+15 \left(x^{3}+x \right)^{\frac{2}{3}}+9 x \left(x^{3}+x \right)^{\frac{1}{3}}-25 x^{2}-18 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)-10\right) \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)+\ln \left(-144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{2}+144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}-54 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x -66 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}+144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2}-9 \left(x^{3}+x \right)^{\frac{2}{3}}-15 x \left(x^{3}+x \right)^{\frac{1}{3}}+20 x^{2}-102 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)+15\right)-\ln \left(-36 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{2}-144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{2}{3}}+90 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{3}+x \right)^{\frac{1}{3}} x +60 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}+36 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2}+15 \left(x^{3}+x \right)^{\frac{2}{3}}+9 x \left(x^{3}+x \right)^{\frac{1}{3}}-25 x^{2}-18 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)-10\right)\right)}{2}$&$436$\\ \hline \end{longtable}"," ",0,"3/2*a*x^(2/3)*hypergeom([1/3,1/3],[4/3],-x^2)-3/16*b/x^(16/3)*(9/5*x^4-6/5*x^2+1)*(x^2+1)^(2/3)","C"
1939,0,0,121,180.000000," ","int((a^2*x^2+b^2)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{a^{2} x^{2}+b^{2}}{\sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int((a^2*x^2+b^2)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","F"
1940,0,0,100,0.050000," ","int(x^2/(a*x^2+b)^(3/4)/(a*x^2+2*b),x)","\[\int \frac{x^{2}}{\left(a \,x^{2}+b \right)^{\frac{3}{4}} \left(a \,x^{2}+2 b \right)}\, dx\]"," ",0,"int(x^2/(a*x^2+b)^(3/4)/(a*x^2+2*b),x)","F"
1941,0,0,104,0.022000," ","int(x/(a*x^3-b)^(2/3),x)","\[\int \frac{x}{\left(a \,x^{3}-b \right)^{\frac{2}{3}}}\, dx\]"," ",0,"int(x/(a*x^3-b)^(2/3),x)","F"
1942,1,1334,100,22.480000," ","int(x*(x^4+x^2)^(1/3)/(2*x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$1334$\\ \hline \end{longtable}"," ",0,"3/8*(x^2*(x^2+1))^(1/3)+(1/16*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)*ln(-(1698*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)*RootOf(_Z^3+2)^3*x^6-524*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)^2*RootOf(_Z^3+2)^2*x^6+3396*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)*RootOf(_Z^3+2)^3*x^4-1048*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)^2*RootOf(_Z^3+2)^2*x^4-27168*RootOf(_Z^3+2)*x^6+8384*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)*x^6-1698*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)*RootOf(_Z^3+2)^3*x^2+524*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)^2*RootOf(_Z^3+2)^2*x^2+18048*RootOf(_Z^3+2)^2*(x^5+2*x^3+x)^(1/3)*x^3+30186*RootOf(_Z^3+2)*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)*(x^5+2*x^3+x)^(1/3)*x^3-9024*(x^5+2*x^3+x)^(2/3)*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)*RootOf(_Z^3+2)^2-54336*RootOf(_Z^3+2)*x^4+16768*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)*x^4-3396*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)*RootOf(_Z^3+2)^3+1048*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)^2*RootOf(_Z^3+2)^2+18048*RootOf(_Z^3+2)^2*(x^5+2*x^3+x)^(1/3)*x+30186*(x^5+2*x^3+x)^(1/3)*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)*RootOf(_Z^3+2)*x-21225*RootOf(_Z^3+2)*x^2+6550*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)*x^2-12138*(x^5+2*x^3+x)^(2/3)+5943*RootOf(_Z^3+2)-1834*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2))/(2*x^2+1)^2/(x^2+1))+1/16*RootOf(_Z^3+2)*ln(-(524*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)*RootOf(_Z^3+2)^3*x^6-1698*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)^2*RootOf(_Z^3+2)^2*x^6+1048*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)*RootOf(_Z^3+2)^3*x^4-3396*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)^2*RootOf(_Z^3+2)^2*x^4+7336*RootOf(_Z^3+2)*x^6-23772*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)*x^6-524*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)*RootOf(_Z^3+2)^3*x^2+1698*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)^2*RootOf(_Z^3+2)^2*x^2-18048*RootOf(_Z^3+2)^2*(x^5+2*x^3+x)^(1/3)*x^3+12138*RootOf(_Z^3+2)*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)*(x^5+2*x^3+x)^(1/3)*x^3+9024*(x^5+2*x^3+x)^(2/3)*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)*RootOf(_Z^3+2)^2+14672*RootOf(_Z^3+2)*x^4-47544*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)*x^4-1048*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)*RootOf(_Z^3+2)^3+3396*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)^2*RootOf(_Z^3+2)^2-18048*RootOf(_Z^3+2)^2*(x^5+2*x^3+x)^(1/3)*x+12138*(x^5+2*x^3+x)^(1/3)*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)*RootOf(_Z^3+2)*x+7598*RootOf(_Z^3+2)*x^2-24621*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2)*x^2-30186*(x^5+2*x^3+x)^(2/3)+262*RootOf(_Z^3+2)-849*RootOf(RootOf(_Z^3+2)^2+_Z*RootOf(_Z^3+2)+_Z^2))/(2*x^2+1)^2/(x^2+1)))/x*(x^2*(x^2+1))^(1/3)*(x*(x^2+1)^2)^(1/3)/(x^2+1)","C"
1943,0,0,108,0.012000," ","int((a*x^3+b)/x^6/(a*x^3-b)/(a*x^4+b*x)^(1/4),x)","\[\int \frac{a \,x^{3}+b}{x^{6} \left(a \,x^{3}-b \right) \left(a \,x^{4}+b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^3+b)/x^6/(a*x^3-b)/(a*x^4+b*x)^(1/4),x)","F"
1944,1,492,108,10.908000," ","int((x^4-1)*(x^6+x^2)^(1/4)/(x^8+x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\ln \left(-\frac{x^{5}+2 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}+2 \sqrt{x^{6}+x^{2}}\, x +2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x^{2}+x^{3}+x}{\left(x^{4}-x^{2}+1\right) x}\right)}{4}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{5}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right) x}{\left(x^{4}-x^{2}+1\right) x}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) x^{5}+\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \sqrt{x^{6}+x^{2}}\, x +2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) x}{\left(x^{2}+x +1\right) x \left(x^{2}-x +1\right)}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) x^{5}+2 \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{6}+x^{2}}\, x -2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) x^{3}+2 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) x}{\left(x^{2}+x +1\right) x \left(x^{2}-x +1\right)}\right)}{4}$&$492$\\ \hline \end{longtable}"," ",0,"-1/4*ln(-(x^5+2*(x^6+x^2)^(3/4)+2*(x^6+x^2)^(1/2)*x+2*(x^6+x^2)^(1/4)*x^2+x^3+x)/(x^4-x^2+1)/x)-1/4*RootOf(_Z^2+1)*ln(-(-RootOf(_Z^2+1)*x^5+2*RootOf(_Z^2+1)*(x^6+x^2)^(1/2)*x-RootOf(_Z^2+1)*x^3+2*(x^6+x^2)^(3/4)-2*(x^6+x^2)^(1/4)*x^2-RootOf(_Z^2+1)*x)/(x^4-x^2+1)/x)+1/4*RootOf(_Z^2-RootOf(_Z^2+1))*ln(-(-RootOf(_Z^2-RootOf(_Z^2+1))*RootOf(_Z^2+1)*x^5+RootOf(_Z^2-RootOf(_Z^2+1))*RootOf(_Z^2+1)*x^3+2*RootOf(_Z^2-RootOf(_Z^2+1))*(x^6+x^2)^(1/2)*x+2*(x^6+x^2)^(1/4)*RootOf(_Z^2+1)*x^2+2*(x^6+x^2)^(3/4)-RootOf(_Z^2-RootOf(_Z^2+1))*RootOf(_Z^2+1)*x)/(x^2+x+1)/x/(x^2-x+1))+1/4*RootOf(_Z^2+1)*RootOf(_Z^2-RootOf(_Z^2+1))*ln(-(-RootOf(_Z^2-RootOf(_Z^2+1))*x^5+2*RootOf(_Z^2-RootOf(_Z^2+1))*RootOf(_Z^2+1)*(x^6+x^2)^(1/2)*x-2*(x^6+x^2)^(1/4)*RootOf(_Z^2+1)*x^2+RootOf(_Z^2-RootOf(_Z^2+1))*x^3+2*(x^6+x^2)^(3/4)-RootOf(_Z^2-RootOf(_Z^2+1))*x)/(x^2+x+1)/x/(x^2-x+1))","C"
1945,1,490,108,10.253000," ","int((x^4-1)*(x^6+x^2)^(1/4)/(x^8+x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\ln \left(-\frac{x^{5}+2 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}+2 \sqrt{x^{6}+x^{2}}\, x +2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x^{2}+x^{3}+x}{\left(x^{4}-x^{2}+1\right) x}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{5}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-2 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}+2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right) x}{\left(x^{4}-x^{2}+1\right) x}\right)}{4}-\frac{\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) x^{5}-\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-2 \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \sqrt{x^{6}+x^{2}}\, x +2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) x +2 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{\left(x^{2}+x +1\right) x \left(x^{2}-x +1\right)}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) x^{5}+2 \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{6}+x^{2}}\, x -2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) x^{3}+2 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) x}{\left(x^{2}+x +1\right) x \left(x^{2}-x +1\right)}\right)}{4}$&$490$\\ \hline \end{longtable}"," ",0,"-1/4*ln(-(x^5+2*(x^6+x^2)^(3/4)+2*(x^6+x^2)^(1/2)*x+2*(x^6+x^2)^(1/4)*x^2+x^3+x)/(x^4-x^2+1)/x)+1/4*RootOf(_Z^2+1)*ln((-RootOf(_Z^2+1)*x^5+2*RootOf(_Z^2+1)*(x^6+x^2)^(1/2)*x-RootOf(_Z^2+1)*x^3-2*(x^6+x^2)^(3/4)+2*(x^6+x^2)^(1/4)*x^2-RootOf(_Z^2+1)*x)/(x^4-x^2+1)/x)-1/4*RootOf(_Z^2-RootOf(_Z^2+1))*ln(-(RootOf(_Z^2-RootOf(_Z^2+1))*RootOf(_Z^2+1)*x^5-RootOf(_Z^2-RootOf(_Z^2+1))*RootOf(_Z^2+1)*x^3-2*RootOf(_Z^2-RootOf(_Z^2+1))*(x^6+x^2)^(1/2)*x+2*(x^6+x^2)^(1/4)*RootOf(_Z^2+1)*x^2+RootOf(_Z^2-RootOf(_Z^2+1))*RootOf(_Z^2+1)*x+2*(x^6+x^2)^(3/4))/(x^2+x+1)/x/(x^2-x+1))+1/4*RootOf(_Z^2+1)*RootOf(_Z^2-RootOf(_Z^2+1))*ln(-(-RootOf(_Z^2-RootOf(_Z^2+1))*x^5+2*RootOf(_Z^2-RootOf(_Z^2+1))*RootOf(_Z^2+1)*(x^6+x^2)^(1/2)*x-2*(x^6+x^2)^(1/4)*RootOf(_Z^2+1)*x^2+RootOf(_Z^2-RootOf(_Z^2+1))*x^3+2*(x^6+x^2)^(3/4)-RootOf(_Z^2-RootOf(_Z^2+1))*x)/(x^2+x+1)/x/(x^2-x+1))","C"
1946,1,182,114,0.085000," ","int(x*(a*x+(a*x-b)^(1/2))^(1/2)/(a*x-b)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\frac{\sqrt{a x -b}\, \left(a x +\sqrt{a x -b}\right)^{\frac{3}{2}}}{2}-\frac{5 \left(a x +\sqrt{a x -b}\right)^{\frac{3}{2}}}{12}+\frac{5 \left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{32}+\frac{5 \left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{64}+\frac{3 b \left(\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{4}+\frac{\left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{8}\right)}{2}}{a^{2}}$&$182$\\ default&$\frac{\frac{\sqrt{a x -b}\, \left(a x +\sqrt{a x -b}\right)^{\frac{3}{2}}}{2}-\frac{5 \left(a x +\sqrt{a x -b}\right)^{\frac{3}{2}}}{12}+\frac{5 \left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{32}+\frac{5 \left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{64}+\frac{3 b \left(\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{4}+\frac{\left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{8}\right)}{2}}{a^{2}}$&$182$\\ \hline \end{longtable}"," ",0,"2/a^2*(1/4*(a*x-b)^(1/2)*(a*x+(a*x-b)^(1/2))^(3/2)-5/24*(a*x+(a*x-b)^(1/2))^(3/2)+5/64*(2*(a*x-b)^(1/2)+1)*(a*x+(a*x-b)^(1/2))^(1/2)+5/128*(4*b-1)*ln(1/2+(a*x-b)^(1/2)+(a*x+(a*x-b)^(1/2))^(1/2))+3/4*b*(1/4*(2*(a*x-b)^(1/2)+1)*(a*x+(a*x-b)^(1/2))^(1/2)+1/8*(4*b-1)*ln(1/2+(a*x-b)^(1/2)+(a*x+(a*x-b)^(1/2))^(1/2))))","A"
1947,1,182,114,0.096000," ","int((a*x-1)*(a*x+(a*x-b)^(1/2))^(1/2)/(a*x-b)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\frac{\sqrt{a x -b}\, \left(a x +\sqrt{a x -b}\right)^{\frac{3}{2}}}{2}-\frac{5 \left(a x +\sqrt{a x -b}\right)^{\frac{3}{2}}}{12}-\frac{11 \left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{32}-\frac{11 \left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{64}+\frac{3 b \left(\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{4}+\frac{\left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{8}\right)}{2}}{a}$&$182$\\ default&$\frac{\frac{\sqrt{a x -b}\, \left(a x +\sqrt{a x -b}\right)^{\frac{3}{2}}}{2}-\frac{5 \left(a x +\sqrt{a x -b}\right)^{\frac{3}{2}}}{12}-\frac{11 \left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{32}-\frac{11 \left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{64}+\frac{3 b \left(\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{4}+\frac{\left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{8}\right)}{2}}{a}$&$182$\\ \hline \end{longtable}"," ",0,"2/a*(1/4*(a*x-b)^(1/2)*(a*x+(a*x-b)^(1/2))^(3/2)-5/24*(a*x+(a*x-b)^(1/2))^(3/2)-11/64*(2*(a*x-b)^(1/2)+1)*(a*x+(a*x-b)^(1/2))^(1/2)-11/128*(4*b-1)*ln(1/2+(a*x-b)^(1/2)+(a*x+(a*x-b)^(1/2))^(1/2))+3/4*b*(1/4*(2*(a*x-b)^(1/2)+1)*(a*x+(a*x-b)^(1/2))^(1/2)+1/8*(4*b-1)*ln(1/2+(a*x-b)^(1/2)+(a*x+(a*x-b)^(1/2))^(1/2))))","A"
1948,0,0,36,0.028000," ","int((x^4-1)/(x^4+1)/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{x^{4}-1}{\left(x^{4}+1\right) \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^4-1)/(x^4+1)/(x+(x^2+1)^(1/2))^(1/2),x)","F"
1949,0,0,36,0.001000," ","int((x^4-1)/(x^4+1)/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{x^{4}-1}{\left(x^{4}+1\right) \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^4-1)/(x^4+1)/(x+(x^2+1)^(1/2))^(1/2),x)","F"
1950,1,3571,79,131.009000," ","int(1/(x^4-x^2)^(1/4)/(x^8-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$3571$\\ trager&$\text{Expression too large to display}$&$3683$\\ \hline \end{longtable}"," ",0,"-1/2*x/(x^2*(x^2-1))^(1/4)+1/8*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*ln(-(548*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*RootOf(2*_Z^8-2*_Z^4+1)^8*x^3-6076*(x^4-x^2)^(1/2)*RootOf(2*_Z^8-2*_Z^4+1)^4*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)^3*x-2192*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*RootOf(2*_Z^8-2*_Z^4+1)^8*x+6076*(x^4-x^2)^(1/4)*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)^2*RootOf(2*_Z^8-2*_Z^4+1)^4*x^2-5472*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*RootOf(2*_Z^8-2*_Z^4+1)^4*x^3+3772*(x^4-x^2)^(3/4)*RootOf(2*_Z^8-2*_Z^4+1)^4+3772*(x^4-x^2)^(1/2)*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)^3*x+4078*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*RootOf(2*_Z^8-2*_Z^4+1)^4*x-3772*(x^4-x^2)^(1/4)*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)^2*x^2+2527*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*x^3-734*(x^4-x^2)^(3/4)-1463*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*x)/x/(2*x^2*RootOf(2*_Z^8-2*_Z^4+1)^4-8*RootOf(2*_Z^8-2*_Z^4+1)^4+3*x^2+5))-1/4*ln((-16*RootOf(2*_Z^8-2*_Z^4+1)^9*x^3-1468*(x^4-x^2)^(1/2)*RootOf(2*_Z^8-2*_Z^4+1)^7*x+64*RootOf(2*_Z^8-2*_Z^4+1)^9*x-6076*(x^4-x^2)^(1/4)*RootOf(2*_Z^8-2*_Z^4+1)^6*x^2-402*RootOf(2*_Z^8-2*_Z^4+1)^5*x^3+3772*(x^4-x^2)^(3/4)*RootOf(2*_Z^8-2*_Z^4+1)^4+3772*(x^4-x^2)^(1/2)*RootOf(2*_Z^8-2*_Z^4+1)^3*x+1088*RootOf(2*_Z^8-2*_Z^4+1)^5*x+2304*(x^4-x^2)^(1/4)*RootOf(2*_Z^8-2*_Z^4+1)^2*x^2-2261*RootOf(2*_Z^8-2*_Z^4+1)*x^3-3038*(x^4-x^2)^(3/4)+399*RootOf(2*_Z^8-2*_Z^4+1)*x)/x/(2*x^2*RootOf(2*_Z^8-2*_Z^4+1)^4-8*RootOf(2*_Z^8-2*_Z^4+1)^4-5*x^2+3))*RootOf(2*_Z^8-2*_Z^4+1)^5+1/8*ln((-16*RootOf(2*_Z^8-2*_Z^4+1)^9*x^3-1468*(x^4-x^2)^(1/2)*RootOf(2*_Z^8-2*_Z^4+1)^7*x+64*RootOf(2*_Z^8-2*_Z^4+1)^9*x-6076*(x^4-x^2)^(1/4)*RootOf(2*_Z^8-2*_Z^4+1)^6*x^2-402*RootOf(2*_Z^8-2*_Z^4+1)^5*x^3+3772*(x^4-x^2)^(3/4)*RootOf(2*_Z^8-2*_Z^4+1)^4+3772*(x^4-x^2)^(1/2)*RootOf(2*_Z^8-2*_Z^4+1)^3*x+1088*RootOf(2*_Z^8-2*_Z^4+1)^5*x+2304*(x^4-x^2)^(1/4)*RootOf(2*_Z^8-2*_Z^4+1)^2*x^2-2261*RootOf(2*_Z^8-2*_Z^4+1)*x^3-3038*(x^4-x^2)^(3/4)+399*RootOf(2*_Z^8-2*_Z^4+1)*x)/x/(2*x^2*RootOf(2*_Z^8-2*_Z^4+1)^4-8*RootOf(2*_Z^8-2*_Z^4+1)^4-5*x^2+3))*RootOf(2*_Z^8-2*_Z^4+1)-1/4*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*ln(-(-16*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*RootOf(2*_Z^8-2*_Z^4+1)^8*x^3+1468*(x^4-x^2)^(1/2)*RootOf(2*_Z^8-2*_Z^4+1)^4*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)^3*x+64*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*RootOf(2*_Z^8-2*_Z^4+1)^8*x-6076*(x^4-x^2)^(1/4)*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)^2*RootOf(2*_Z^8-2*_Z^4+1)^4*x^2+434*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*RootOf(2*_Z^8-2*_Z^4+1)^4*x^3+3772*(x^4-x^2)^(3/4)*RootOf(2*_Z^8-2*_Z^4+1)^4+2304*(x^4-x^2)^(1/2)*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)^3*x-1216*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*RootOf(2*_Z^8-2*_Z^4+1)^4*x+3772*(x^4-x^2)^(1/4)*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)^2*x^2-2679*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*x^3-734*(x^4-x^2)^(3/4)+1551*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*x)/x/(2*x^2*RootOf(2*_Z^8-2*_Z^4+1)^4-8*RootOf(2*_Z^8-2*_Z^4+1)^4+3*x^2+5))*RootOf(2*_Z^8-2*_Z^4+1)^4+1/8*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*ln(-(-16*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*RootOf(2*_Z^8-2*_Z^4+1)^8*x^3+1468*(x^4-x^2)^(1/2)*RootOf(2*_Z^8-2*_Z^4+1)^4*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)^3*x+64*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*RootOf(2*_Z^8-2*_Z^4+1)^8*x-6076*(x^4-x^2)^(1/4)*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)^2*RootOf(2*_Z^8-2*_Z^4+1)^4*x^2+434*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*RootOf(2*_Z^8-2*_Z^4+1)^4*x^3+3772*(x^4-x^2)^(3/4)*RootOf(2*_Z^8-2*_Z^4+1)^4+2304*(x^4-x^2)^(1/2)*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)^3*x-1216*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*RootOf(2*_Z^8-2*_Z^4+1)^4*x+3772*(x^4-x^2)^(1/4)*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)^2*x^2-2679*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*x^3-734*(x^4-x^2)^(3/4)+1551*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*x)/x/(2*x^2*RootOf(2*_Z^8-2*_Z^4+1)^4-8*RootOf(2*_Z^8-2*_Z^4+1)^4+3*x^2+5))-1/8*RootOf(2*_Z^8-2*_Z^4+1)*ln((548*RootOf(2*_Z^8-2*_Z^4+1)^9*x^3+6076*(x^4-x^2)^(1/2)*RootOf(2*_Z^8-2*_Z^4+1)^7*x-2192*RootOf(2*_Z^8-2*_Z^4+1)^9*x+6076*(x^4-x^2)^(1/4)*RootOf(2*_Z^8-2*_Z^4+1)^6*x^2+4376*RootOf(2*_Z^8-2*_Z^4+1)^5*x^3+3772*(x^4-x^2)^(3/4)*RootOf(2*_Z^8-2*_Z^4+1)^4-2304*(x^4-x^2)^(1/2)*RootOf(2*_Z^8-2*_Z^4+1)^3*x+306*RootOf(2*_Z^8-2*_Z^4+1)^5*x-2304*(x^4-x^2)^(1/4)*RootOf(2*_Z^8-2*_Z^4+1)^2*x^2-2397*RootOf(2*_Z^8-2*_Z^4+1)*x^3-3038*(x^4-x^2)^(3/4)+423*RootOf(2*_Z^8-2*_Z^4+1)*x)/x/(2*x^2*RootOf(2*_Z^8-2*_Z^4+1)^4-8*RootOf(2*_Z^8-2*_Z^4+1)^4-5*x^2+3))+1/8*RootOf(2*_Z^8-2*_Z^4+1)*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*ln((-4*(x^4-x^2)^(1/2)*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)^3*RootOf(2*_Z^8-2*_Z^4+1)^3*x+4*(x^4-x^2)^(1/4)*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)^2*RootOf(2*_Z^8-2*_Z^4+1)^2*x^2-3*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*RootOf(2*_Z^8-2*_Z^4+1)*x^3+2*(x^4-x^2)^(3/4)+RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*RootOf(2*_Z^8-2*_Z^4+1)*x)/x/(x^2+1))+1/4*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*ln((8*(x^4-x^2)^(1/2)*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)^3*RootOf(2*_Z^8-2*_Z^4+1)^7*x-4*(x^4-x^2)^(1/2)*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)^3*RootOf(2*_Z^8-2*_Z^4+1)^3*x-6*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*RootOf(2*_Z^8-2*_Z^4+1)^5*x^3-4*(x^4-x^2)^(1/4)*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)^2*RootOf(2*_Z^8-2*_Z^4+1)^2*x^2+2*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*RootOf(2*_Z^8-2*_Z^4+1)^5*x+3*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*RootOf(2*_Z^8-2*_Z^4+1)*x^3+2*(x^4-x^2)^(3/4)-RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*RootOf(2*_Z^8-2*_Z^4+1)*x)/x/(x^2+1))*RootOf(2*_Z^8-2*_Z^4+1)^5-1/8*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*ln((8*(x^4-x^2)^(1/2)*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)^3*RootOf(2*_Z^8-2*_Z^4+1)^7*x-4*(x^4-x^2)^(1/2)*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)^3*RootOf(2*_Z^8-2*_Z^4+1)^3*x-6*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*RootOf(2*_Z^8-2*_Z^4+1)^5*x^3-4*(x^4-x^2)^(1/4)*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)^2*RootOf(2*_Z^8-2*_Z^4+1)^2*x^2+2*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*RootOf(2*_Z^8-2*_Z^4+1)^5*x+3*RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*RootOf(2*_Z^8-2*_Z^4+1)*x^3+2*(x^4-x^2)^(3/4)-RootOf(RootOf(2*_Z^8-2*_Z^4+1)^4+_Z^4-1)*RootOf(2*_Z^8-2*_Z^4+1)*x)/x/(x^2+1))*RootOf(2*_Z^8-2*_Z^4+1)","B"
1951,0,0,79,180.000000," ","int(1/(x^4-x^2)^(1/4)/(x^8-1),x)","\[\int \frac{1}{\left(x^{4}-x^{2}\right)^{\frac{1}{4}} \left(x^{8}-1\right)}\, dx\]"," ",0,"int(1/(x^4-x^2)^(1/4)/(x^8-1),x)","F"
1952,1,646,101,5.316000," ","int((x^4-2)/(x^4+1)^(1/4)/(2*x^8-x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{5 \RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(-\frac{2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}+2 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}-2 \left(x^{4}+1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}+1\right)}{2 x^{4}+1}\right)}{12}-\frac{5 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(-\frac{-2 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}-2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}+1\right) x^{2}-2 \left(x^{4}+1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{2 x^{4}+1}\right)}{12}-\frac{\RootOf \left(\textit{\_Z}^{2}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)\right) \ln \left(-\frac{2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)\right) \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}-4 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{4}+1\right)^{\frac{1}{4}} x^{3}-2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)\right) \RootOf \left(\textit{\_Z}^{4}+1\right) x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)\right) x^{4}+4 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{4}+1\right)^{\frac{1}{4}} x^{3}+4 \left(x^{4}+1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{2}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)\right)}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)}{24}-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)\right) \ln \left(-\frac{2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)\right) \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)\right) \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{4}+4 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(x^{4}+1\right)^{\frac{1}{4}} x^{3}+2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)\right) \RootOf \left(\textit{\_Z}^{4}+1\right) x^{2}-4 \RootOf \left(\textit{\_Z}^{4}+1\right) \left(x^{4}+1\right)^{\frac{1}{4}} x^{3}+4 \left(x^{4}+1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)\right)}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)}{24}$&$646$\\ \hline \end{longtable}"," ",0,"5/12*RootOf(_Z^4+1)*ln(-(2*(x^4+1)^(1/2)*RootOf(_Z^4+1)^3*x^2+2*(x^4+1)^(1/4)*RootOf(_Z^4+1)^2*x^3-2*(x^4+1)^(3/4)*x-RootOf(_Z^4+1))/(2*x^4+1))-5/12*RootOf(_Z^4+1)^3*ln(-(-2*(x^4+1)^(1/4)*RootOf(_Z^4+1)^2*x^3-2*(x^4+1)^(1/2)*RootOf(_Z^4+1)*x^2-2*(x^4+1)^(3/4)*x+RootOf(_Z^4+1)^3)/(2*x^4+1))-1/24*RootOf(_Z^2+2*RootOf(_Z^4+1)^3-2*RootOf(_Z^4+1))*ln(-(2*(x^4+1)^(1/2)*RootOf(_Z^2+2*RootOf(_Z^4+1)^3-2*RootOf(_Z^4+1))*RootOf(_Z^4+1)^3*x^2-4*RootOf(_Z^4+1)^3*(x^4+1)^(1/4)*x^3-2*(x^4+1)^(1/2)*RootOf(_Z^2+2*RootOf(_Z^4+1)^3-2*RootOf(_Z^4+1))*RootOf(_Z^4+1)*x^2-3*RootOf(_Z^2+2*RootOf(_Z^4+1)^3-2*RootOf(_Z^4+1))*x^4+4*RootOf(_Z^4+1)*(x^4+1)^(1/4)*x^3+4*(x^4+1)^(3/4)*x-RootOf(_Z^2+2*RootOf(_Z^4+1)^3-2*RootOf(_Z^4+1)))/(-1+x)/(1+x)/(x^2+1))-1/24*RootOf(_Z^4+1)^2*RootOf(_Z^2+2*RootOf(_Z^4+1)^3-2*RootOf(_Z^4+1))*ln(-(2*(x^4+1)^(1/2)*RootOf(_Z^2+2*RootOf(_Z^4+1)^3-2*RootOf(_Z^4+1))*RootOf(_Z^4+1)^3*x^2-3*RootOf(_Z^2+2*RootOf(_Z^4+1)^3-2*RootOf(_Z^4+1))*RootOf(_Z^4+1)^2*x^4+4*RootOf(_Z^4+1)^3*(x^4+1)^(1/4)*x^3+2*(x^4+1)^(1/2)*RootOf(_Z^2+2*RootOf(_Z^4+1)^3-2*RootOf(_Z^4+1))*RootOf(_Z^4+1)*x^2-4*RootOf(_Z^4+1)*(x^4+1)^(1/4)*x^3+4*(x^4+1)^(3/4)*x-RootOf(_Z^4+1)^2*RootOf(_Z^2+2*RootOf(_Z^4+1)^3-2*RootOf(_Z^4+1)))/(-1+x)/(1+x)/(x^2+1))","C"
1953,0,0,109,0.027000," ","int((b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2)^(5/2),x)","\[\int \frac{\sqrt{b +\sqrt{a \,x^{2}+b^{2}}}}{\left(a \,x^{2}+b^{2}\right)^{\frac{5}{2}}}\, dx\]"," ",0,"int((b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2)^(5/2),x)","F"
1954,0,0,109,0.023000," ","int((a*x^2-b)^(1/4)/x,x)","\[\int \frac{\left(a \,x^{2}-b \right)^{\frac{1}{4}}}{x}\, dx\]"," ",0,"int((a*x^2-b)^(1/4)/x,x)","F"
1955,1,68,114,2.974000," ","int((a*x^2+b)*(x^3-x)^(1/3)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 a \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}} x^{\frac{4}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], x^{2}\right)}{4 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}}}-\frac{3 b \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}} \hypergeom \left(\left[-\frac{1}{3}, -\frac{1}{3}\right], \left[\frac{2}{3}\right], x^{2}\right)}{2 \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}} x^{\frac{2}{3}}}$&$68$\\ trager&$\frac{\left(a \,x^{2}-3 b \right) \left(x^{3}-x \right)^{\frac{1}{3}}}{2 x}+\frac{\left(a -3 b \right) \left(12 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \ln \left(22320 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{2}+27072 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}+27072 \left(x^{3}-x \right)^{\frac{1}{3}} \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x +28932 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{2}-89280 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}+7611 \left(x^{3}-x \right)^{\frac{2}{3}}+7611 x \left(x^{3}-x \right)^{\frac{1}{3}}+7766 x^{2}-46908 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)-4942\right)-12 \ln \left(22320 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{2}-27072 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}-27072 \left(x^{3}-x \right)^{\frac{1}{3}} \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x -25212 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{2}-89280 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}+5355 \left(x^{3}-x \right)^{\frac{2}{3}}+5355 x \left(x^{3}-x \right)^{\frac{1}{3}}+5510 x^{2}+32028 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)-1653\right) \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)-\ln \left(22320 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{2}-27072 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}-27072 \left(x^{3}-x \right)^{\frac{1}{3}} \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x -25212 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{2}-89280 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}+5355 \left(x^{3}-x \right)^{\frac{2}{3}}+5355 x \left(x^{3}-x \right)^{\frac{1}{3}}+5510 x^{2}+32028 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)-1653\right)\right)}{6}$&$475$\\ risch&$\frac{\left(a \,x^{2}-3 b \right) \left(x \left(x^{2}-1\right)\right)^{\frac{1}{3}}}{2 x}+\frac{\left(a -3 b \right) \left(\RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \ln \left(\frac{59 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{4}-3750 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{4}-1746 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{2}-295 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{2}+12600 x^{4}+5850 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}-35100 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}+5652 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{2}+24624 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}+1746 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}+236 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2}-16380 x^{2}+35100 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}-1902 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)+3780}{\left(-1+x \right) \left(1+x \right)}\right)+6 \ln \left(-\frac{-35 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{4}-1956 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{4}-4104 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{2}+175 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2} x^{2}+23364 x^{4}+5850 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}-35100 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}} x^{2}+2010 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) x^{2}+10476 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{2}{3}}+4104 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right) \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}-140 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)^{2}-38232 x^{2}+35100 \left(x^{6}-2 x^{4}+x^{2}\right)^{\frac{1}{3}}-54 \RootOf \left(\textit{\_Z}^{2}+6 \textit{\_Z} +36\right)+14868}{\left(-1+x \right) \left(1+x \right)}\right)\right) \left(x \left(x^{2}-1\right)\right)^{\frac{1}{3}} \left(x^{2} \left(x^{2}-1\right)^{2}\right)^{\frac{1}{3}}}{36 x \left(x^{2}-1\right)}$&$552$\\ \hline \end{longtable}"," ",0,"3/4*a*signum(x^2-1)^(1/3)/(-signum(x^2-1))^(1/3)*x^(4/3)*hypergeom([-1/3,2/3],[5/3],x^2)-3/2*b*signum(x^2-1)^(1/3)/(-signum(x^2-1))^(1/3)/x^(2/3)*hypergeom([-1/3,-1/3],[2/3],x^2)","C"
1956,0,0,122,0.025000," ","int((a*x-b)/x/(a^3*x^3+b^3)^(1/3),x)","\[\int \frac{a x -b}{x \left(a^{3} x^{3}+b^{3}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a*x-b)/x/(a^3*x^3+b^3)^(1/3),x)","F"
1957,1,474,114,3.723000," ","int(x^2*(x^4-x^3)^(1/4)/(2+x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\left(\frac{1}{3} x^{2}-\frac{25}{24} x +\frac{401}{96}\right) \left(x^{4}-x^{3}\right)^{\frac{1}{4}}-\frac{1135 \ln \left(\frac{2 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}+2 \sqrt{x^{4}-x^{3}}\, x +2 x^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}+2 x^{3}-x^{2}}{x^{2}}\right)}{128}-4 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-24\right)^{2}\right) \ln \left(-\frac{-5 \RootOf \left(\textit{\_Z}^{4}-24\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-24\right)^{2}\right) x^{3}+12 \RootOf \left(\textit{\_Z}^{4}-24\right)^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}-24\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-24\right)^{2}\right) x^{2}+24 \sqrt{x^{4}-x^{3}}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-24\right)^{2}\right) x -48 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(2+x \right)}\right)+4 \RootOf \left(\textit{\_Z}^{4}-24\right) \ln \left(\frac{5 \RootOf \left(\textit{\_Z}^{4}-24\right)^{3} x^{3}-2 \RootOf \left(\textit{\_Z}^{4}-24\right)^{3} x^{2}+12 \RootOf \left(\textit{\_Z}^{4}-24\right)^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}} x^{2}+24 \sqrt{x^{4}-x^{3}}\, \RootOf \left(\textit{\_Z}^{4}-24\right) x +48 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(2+x \right)}\right)-\frac{1135 \RootOf \left(\textit{\_Z}^{4}-24\right)^{3} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-24\right)^{2}\right) \ln \left(\frac{2 \sqrt{x^{4}-x^{3}}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-24\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-24\right)^{3} x -2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-24\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-24\right)^{3} x^{3}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-24\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-24\right)^{3} x^{2}+48 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}-48 x^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}}{x^{2}}\right)}{3072}$&$474$\\ risch&$\frac{\left(32 x^{2}-100 x +401\right) \left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}}}{96}+\frac{\left(\frac{1135 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{3}{4}}-2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{2}+1\right)-2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x^{2}+5 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x -4 \RootOf \left(\textit{\_Z}^{2}+1\right) x -2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(-1+x \right)^{2}}\right)}{128}+\frac{1135 \ln \left(\frac{2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{3}{4}}-2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, x +2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x^{2}-2 x^{3}+2 \sqrt{x^{4}-3 x^{3}+3 x^{2}-x}-4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} x +5 x^{2}+2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}}-4 x +1}{\left(-1+x \right)^{2}}\right)}{128}+4 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-24\right)^{2}\right) \ln \left(\frac{-\sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{4}-24\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-24\right)^{2}\right) x +\sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{4}-24\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-24\right)^{2}\right)-2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-24\right)^{2} x^{2}+4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-24\right)^{2} x +5 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-24\right)^{2}\right) x^{3}+12 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{3}{4}}-2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-24\right)^{2}-12 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-24\right)^{2}\right) x^{2}+9 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-24\right)^{2}\right) x -2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-24\right)^{2}\right)}{\left(-1+x \right)^{2} \left(2+x \right)}\right)-4 \RootOf \left(\textit{\_Z}^{4}-24\right) \ln \left(\frac{-\sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{4}-24\right)^{3} x +\sqrt{x^{4}-3 x^{3}+3 x^{2}-x}\, \RootOf \left(\textit{\_Z}^{4}-24\right)^{3}+2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-24\right)^{2} x^{2}-4 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-24\right)^{2} x -5 \RootOf \left(\textit{\_Z}^{4}-24\right) x^{3}+12 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{3}{4}}+2 \left(x^{4}-3 x^{3}+3 x^{2}-x \right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-24\right)^{2}+12 \RootOf \left(\textit{\_Z}^{4}-24\right) x^{2}-9 \RootOf \left(\textit{\_Z}^{4}-24\right) x +2 \RootOf \left(\textit{\_Z}^{4}-24\right)}{\left(-1+x \right)^{2} \left(2+x \right)}\right)\right) \left(x^{3} \left(-1+x \right)\right)^{\frac{1}{4}} \left(x \left(-1+x \right)^{3}\right)^{\frac{1}{4}}}{x \left(-1+x \right)}$&$923$\\ \hline \end{longtable}"," ",0,"(1/3*x^2-25/24*x+401/96)*(x^4-x^3)^(1/4)-1135/128*ln((2*(x^4-x^3)^(3/4)+2*(x^4-x^3)^(1/2)*x+2*x^2*(x^4-x^3)^(1/4)+2*x^3-x^2)/x^2)-4*RootOf(_Z^2+RootOf(_Z^4-24)^2)*ln(-(-5*RootOf(_Z^4-24)^2*RootOf(_Z^2+RootOf(_Z^4-24)^2)*x^3+12*RootOf(_Z^4-24)^2*(x^4-x^3)^(1/4)*x^2+2*RootOf(_Z^4-24)^2*RootOf(_Z^2+RootOf(_Z^4-24)^2)*x^2+24*(x^4-x^3)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-24)^2)*x-48*(x^4-x^3)^(3/4))/x^2/(2+x))+4*RootOf(_Z^4-24)*ln((5*RootOf(_Z^4-24)^3*x^3-2*RootOf(_Z^4-24)^3*x^2+12*RootOf(_Z^4-24)^2*(x^4-x^3)^(1/4)*x^2+24*(x^4-x^3)^(1/2)*RootOf(_Z^4-24)*x+48*(x^4-x^3)^(3/4))/x^2/(2+x))-1135/3072*RootOf(_Z^4-24)^3*RootOf(_Z^2+RootOf(_Z^4-24)^2)*ln((2*(x^4-x^3)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-24)^2)*RootOf(_Z^4-24)^3*x-2*RootOf(_Z^2+RootOf(_Z^4-24)^2)*RootOf(_Z^4-24)^3*x^3+RootOf(_Z^2+RootOf(_Z^4-24)^2)*RootOf(_Z^4-24)^3*x^2+48*(x^4-x^3)^(3/4)-48*x^2*(x^4-x^3)^(1/4))/x^2)","C"
1958,1,1426,122,5.301000," ","int((-1+x)*(12*x^4-8*x^2+8*x-3)/x/((-2*x^2+1)/(2*x^2+1))^(2/3)/(2*x^2+1)/(2*x^4-6*x^3+7*x^2-7*x+3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(\frac{14-21 x -15 x \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{2}{3}}+15 \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{2}{3}}-18 \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{1}{3}}+36 x \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{1}{3}}-14 x^{5}+21 x^{2}-49 x^{3}+42 x^{4}+58 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+44 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}+12 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{2}{3}} x^{3}-12 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{2}{3}} x^{2}-60 x^{4} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{1}{3}}+120 x^{3} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{1}{3}}-90 x^{2} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{1}{3}}+60 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{1}{3}}+6 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{2}{3}}-88 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{2}-44 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{5}+132 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{4}-154 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{3}+38 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{2}-66 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x -30 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{1}{3}}-6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{2}{3}}-54 \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{1}{3}} x^{2}+30 \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{2}{3}} x^{2}-36 \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{1}{3}} x^{4}+72 \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{1}{3}} x^{3}-30 \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{2}{3}} x^{3}}{x \left(2 x^{4}-6 x^{3}+7 x^{2}-7 x +3\right)}\right)+2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \ln \left(-\frac{7-21 x +18 x \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{2}{3}}-18 \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{2}{3}}+15 \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{1}{3}}-30 x \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{1}{3}}-14 x^{5}+35 x^{2}-49 x^{3}+42 x^{4}-22 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+16 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}+12 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{2}{3}} x^{3}-12 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{2}{3}} x^{2}+72 x^{4} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{1}{3}}-144 x^{3} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{1}{3}}+108 x^{2} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{1}{3}}-72 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{1}{3}}+6 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{2}{3}}-32 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{2}+16 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{5}-48 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{4}+56 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{3}-12 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{2}+24 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x +36 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{1}{3}}-6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{2}{3}}+45 \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{1}{3}} x^{2}-36 \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{2}{3}} x^{2}+30 \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{1}{3}} x^{4}-60 \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{1}{3}} x^{3}+36 \left(-\frac{2 x^{2}-1}{2 x^{2}+1}\right)^{\frac{2}{3}} x^{3}}{x \left(2 x^{4}-6 x^{3}+7 x^{2}-7 x +3\right)}\right)$&$1426$\\ \hline \end{longtable}"," ",0,"ln((14-21*x-88*RootOf(4*_Z^2+2*_Z+1)^2*x^2-44*RootOf(4*_Z^2+2*_Z+1)*x^5-15*x*(-(2*x^2-1)/(2*x^2+1))^(2/3)+132*RootOf(4*_Z^2+2*_Z+1)*x^4-154*RootOf(4*_Z^2+2*_Z+1)*x^3+38*RootOf(4*_Z^2+2*_Z+1)*x^2-66*RootOf(4*_Z^2+2*_Z+1)*x+15*(-(2*x^2-1)/(2*x^2+1))^(2/3)-18*(-(2*x^2-1)/(2*x^2+1))^(1/3)+36*x*(-(2*x^2-1)/(2*x^2+1))^(1/3)-14*x^5+21*x^2-49*x^3+42*x^4+44*RootOf(4*_Z^2+2*_Z+1)^2+58*RootOf(4*_Z^2+2*_Z+1)+12*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(2/3)*x^3-12*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(2/3)*x^2-60*x^4*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3)+120*x^3*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3)-90*x^2*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3)+60*x*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3)+6*x*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(2/3)-54*(-(2*x^2-1)/(2*x^2+1))^(1/3)*x^2+30*(-(2*x^2-1)/(2*x^2+1))^(2/3)*x^2-36*(-(2*x^2-1)/(2*x^2+1))^(1/3)*x^4+72*(-(2*x^2-1)/(2*x^2+1))^(1/3)*x^3-30*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3)-30*(-(2*x^2-1)/(2*x^2+1))^(2/3)*x^3-6*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(2/3))/x/(2*x^4-6*x^3+7*x^2-7*x+3))+2*RootOf(4*_Z^2+2*_Z+1)*ln(-(7-21*x-32*RootOf(4*_Z^2+2*_Z+1)^2*x^2+16*RootOf(4*_Z^2+2*_Z+1)*x^5+18*x*(-(2*x^2-1)/(2*x^2+1))^(2/3)-48*RootOf(4*_Z^2+2*_Z+1)*x^4+56*RootOf(4*_Z^2+2*_Z+1)*x^3-12*RootOf(4*_Z^2+2*_Z+1)*x^2+24*RootOf(4*_Z^2+2*_Z+1)*x-18*(-(2*x^2-1)/(2*x^2+1))^(2/3)+15*(-(2*x^2-1)/(2*x^2+1))^(1/3)-30*x*(-(2*x^2-1)/(2*x^2+1))^(1/3)-14*x^5+35*x^2-49*x^3+42*x^4+16*RootOf(4*_Z^2+2*_Z+1)^2-22*RootOf(4*_Z^2+2*_Z+1)+12*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(2/3)*x^3-12*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(2/3)*x^2+72*x^4*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3)-144*x^3*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3)+108*x^2*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3)-72*x*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3)+6*x*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(2/3)+45*(-(2*x^2-1)/(2*x^2+1))^(1/3)*x^2-36*(-(2*x^2-1)/(2*x^2+1))^(2/3)*x^2+30*(-(2*x^2-1)/(2*x^2+1))^(1/3)*x^4-60*(-(2*x^2-1)/(2*x^2+1))^(1/3)*x^3+36*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3)+36*(-(2*x^2-1)/(2*x^2+1))^(2/3)*x^3-6*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(2/3))/x/(2*x^4-6*x^3+7*x^2-7*x+3))","C"
1959,1,123,36,0.949000," ","int((-a*x^5+b)/(b*x+a)^(1/2)/(x^5+a*b),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{2 \left(a \sqrt{b x +a}+\frac{b^{6} \left(a^{2}+1\right) \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{10}-5 a \,\textit{\_Z}^{8}+10 a^{2} \textit{\_Z}^{6}-10 a^{3} \textit{\_Z}^{4}+a \,b^{6}+5 a^{4} \textit{\_Z}^{2}-a^{5}\right)}{\sum}\frac{\ln \left(\sqrt{b x +a}-\textit{\_R} \right)}{-\textit{\_R}^{9}+4 \textit{\_R}^{7} a -6 \textit{\_R}^{5} a^{2}+4 \textit{\_R}^{3} a^{3}-\textit{\_R} \,a^{4}}\right)}{10}\right)}{b}$&$123$\\ default&$-\frac{2 \left(a \sqrt{b x +a}+\frac{b^{6} \left(a^{2}+1\right) \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{10}-5 a \,\textit{\_Z}^{8}+10 a^{2} \textit{\_Z}^{6}-10 a^{3} \textit{\_Z}^{4}+a \,b^{6}+5 a^{4} \textit{\_Z}^{2}-a^{5}\right)}{\sum}\frac{\ln \left(\sqrt{b x +a}-\textit{\_R} \right)}{-\textit{\_R}^{9}+4 \textit{\_R}^{7} a -6 \textit{\_R}^{5} a^{2}+4 \textit{\_R}^{3} a^{3}-\textit{\_R} \,a^{4}}\right)}{10}\right)}{b}$&$123$\\ risch&$-\frac{2 a \sqrt{b x +a}}{b}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{10}-5 a \,\textit{\_Z}^{8}+10 a^{2} \textit{\_Z}^{6}-10 a^{3} \textit{\_Z}^{4}+a \,b^{6}+5 a^{4} \textit{\_Z}^{2}-a^{5}\right)}{\sum}\frac{\ln \left(\sqrt{b x +a}-\textit{\_R} \right)}{\textit{\_R}^{9}-4 \textit{\_R}^{7} a +6 \textit{\_R}^{5} a^{2}-4 \textit{\_R}^{3} a^{3}+\textit{\_R} \,a^{4}}\right) a^{2} b^{5}}{5}+\frac{b^{5} \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{10}-5 a \,\textit{\_Z}^{8}+10 a^{2} \textit{\_Z}^{6}-10 a^{3} \textit{\_Z}^{4}+a \,b^{6}+5 a^{4} \textit{\_Z}^{2}-a^{5}\right)}{\sum}\frac{\ln \left(\sqrt{b x +a}-\textit{\_R} \right)}{\textit{\_R}^{9}-4 \textit{\_R}^{7} a +6 \textit{\_R}^{5} a^{2}-4 \textit{\_R}^{3} a^{3}+\textit{\_R} \,a^{4}}\right)}{5}$&$216$\\ \hline \end{longtable}"," ",0,"-2/b*(a*(b*x+a)^(1/2)+1/10*b^6*(a^2+1)*sum(1/(-_R^9+4*_R^7*a-6*_R^5*a^2+4*_R^3*a^3-_R*a^4)*ln((b*x+a)^(1/2)-_R),_R=RootOf(_Z^10-5*_Z^8*a+10*_Z^6*a^2-10*_Z^4*a^3+a*b^6+5*_Z^2*a^4-a^5)))","B"
1960,1,760,105,18.059000," ","int((x^3-1)^(2/3)*(x^6+x^3+1)/x^6/(x^6-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{3}-1\right)^{\frac{2}{3}} \left(3 x^{3}+2\right)}{10 x^{5}}+224 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right) \ln \left(-\frac{180768 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}+529256448 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}+9934848 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +14784 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{2}-7011648 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right) x^{2}-1446144 \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right)-4234051584 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}-14795 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}-43317120 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right) x^{3}-40002 x \left(x^{3}-1\right)^{\frac{2}{3}}+6187 \RootOf \left(\textit{\_Z}^{3}+4\right)+18114432 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right)}{\left(1+x \right) \left(x^{2}-x +1\right)}\right)+\frac{\RootOf \left(\textit{\_Z}^{3}+4\right) \ln \left(\frac{-2957791200 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}-12894050405376 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}+172459768320 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +256636560 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{2}-350155647072 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right) x^{2}+23662329600 \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right)+103152403243008 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}-233278175 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}-1016941475424 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right) x^{3}-1034338071 x \left(x^{3}-1\right)^{\frac{2}{3}}+30810325 \RootOf \left(\textit{\_Z}^{3}+4\right)+134313025056 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right)}{\left(1+x \right) \left(x^{2}-x +1\right)}\right)}{6}$&$760$\\ risch&$\frac{3 x^{6}-x^{3}-2}{10 x^{5} \left(x^{3}-1\right)^{\frac{1}{3}}}+\RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \ln \left(-\frac{-9 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}-18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}+12 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x -5 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{2}-24 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}+9 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}+18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) x^{3}-10 x \left(x^{3}-1\right)^{\frac{2}{3}}-3 \RootOf \left(\textit{\_Z}^{3}+4\right)-6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)}{\left(1+x \right) \left(x^{2}-x +1\right)}\right)-\frac{\ln \left(\frac{-6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}+18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}+12 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +\left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{2}-24 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}+6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) x^{3}+2 x \left(x^{3}-1\right)^{\frac{2}{3}}+2 \RootOf \left(\textit{\_Z}^{3}+4\right)-6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)}{\left(1+x \right) \left(x^{2}-x +1\right)}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)}{6}-\ln \left(\frac{-6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}+18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}+12 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +\left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{2}-24 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}+6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) x^{3}+2 x \left(x^{3}-1\right)^{\frac{2}{3}}+2 \RootOf \left(\textit{\_Z}^{3}+4\right)-6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)}{\left(1+x \right) \left(x^{2}-x +1\right)}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)$&$930$\\ \hline \end{longtable}"," ",0,"1/10*(x^3-1)^(2/3)*(3*x^3+2)/x^5+224*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)*ln(-(180768*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)*RootOf(_Z^3+4)^3*x^3+529256448*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+9934848*(x^3-1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)*RootOf(_Z^3+4)^2*x+14784*(x^3-1)^(1/3)*RootOf(_Z^3+4)^2*x^2-7011648*(x^3-1)^(1/3)*RootOf(_Z^3+4)*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)*x^2-1446144*RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)-4234051584*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)^2*RootOf(_Z^3+4)^2-14795*RootOf(_Z^3+4)*x^3-43317120*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)*x^3-40002*x*(x^3-1)^(2/3)+6187*RootOf(_Z^3+4)+18114432*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2))/(1+x)/(x^2-x+1))+1/6*RootOf(_Z^3+4)*ln((-2957791200*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)*RootOf(_Z^3+4)^3*x^3-12894050405376*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+172459768320*(x^3-1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)*RootOf(_Z^3+4)^2*x+256636560*(x^3-1)^(1/3)*RootOf(_Z^3+4)^2*x^2-350155647072*(x^3-1)^(1/3)*RootOf(_Z^3+4)*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)*x^2+23662329600*RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)+103152403243008*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)^2*RootOf(_Z^3+4)^2-233278175*RootOf(_Z^3+4)*x^3-1016941475424*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)*x^3-1034338071*x*(x^3-1)^(2/3)+30810325*RootOf(_Z^3+4)+134313025056*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2))/(1+x)/(x^2-x+1))","C"
1961,1,113,27,0.196000," ","int((x^2-1)/(1+x)^(1/2)/(x^2+1)/(1+(1+x)^(1/2))^(1/2)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$8 \sqrt{1+\sqrt{1+\sqrt{1+x}}}-\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+14 \textit{\_Z}^{8}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{4}+2\right)}{\sum}\frac{\ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+7 \textit{\_R}^{7}+3 \textit{\_R}^{5}-2 \textit{\_R}^{3}}\right)$&$113$\\ default&$8 \sqrt{1+\sqrt{1+\sqrt{1+x}}}-\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+14 \textit{\_Z}^{8}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{4}+2\right)}{\sum}\frac{\ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+7 \textit{\_R}^{7}+3 \textit{\_R}^{5}-2 \textit{\_R}^{3}}\right)$&$113$\\ \hline \end{longtable}"," ",0,"8*(1+(1+(1+x)^(1/2))^(1/2))^(1/2)-sum(1/(_R^15-7*_R^13+18*_R^11-20*_R^9+7*_R^7+3*_R^5-2*_R^3)*ln((1+(1+(1+x)^(1/2))^(1/2))^(1/2)-_R),_R=RootOf(_Z^16-8*_Z^14+24*_Z^12-32*_Z^10+14*_Z^8+8*_Z^6-8*_Z^4+2))","B"
1962,1,113,27,0.185000," ","int((x^2-1)/(1+x)^(1/2)/(x^2+1)/(1+(1+x)^(1/2))^(1/2)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$8 \sqrt{1+\sqrt{1+\sqrt{1+x}}}-\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+14 \textit{\_Z}^{8}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{4}+2\right)}{\sum}\frac{\ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+7 \textit{\_R}^{7}+3 \textit{\_R}^{5}-2 \textit{\_R}^{3}}\right)$&$113$\\ default&$8 \sqrt{1+\sqrt{1+\sqrt{1+x}}}-\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+14 \textit{\_Z}^{8}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{4}+2\right)}{\sum}\frac{\ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+7 \textit{\_R}^{7}+3 \textit{\_R}^{5}-2 \textit{\_R}^{3}}\right)$&$113$\\ \hline \end{longtable}"," ",0,"8*(1+(1+(1+x)^(1/2))^(1/2))^(1/2)-sum(1/(_R^15-7*_R^13+18*_R^11-20*_R^9+7*_R^7+3*_R^5-2*_R^3)*ln((1+(1+(1+x)^(1/2))^(1/2))^(1/2)-_R),_R=RootOf(_Z^16-8*_Z^14+24*_Z^12-32*_Z^10+14*_Z^8+8*_Z^6-8*_Z^4+2))","B"
1963,0,0,111,0.045000," ","int(x/(x^2*(-a+x))^(2/3)/(-a*d+(-1+d)*x),x)","\[\int \frac{x}{\left(x^{2} \left(-a +x \right)\right)^{\frac{2}{3}} \left(-a d +\left(-1+d \right) x \right)}\, dx\]"," ",0,"int(x/(x^2*(-a+x))^(2/3)/(-a*d+(-1+d)*x),x)","F"
1964,0,0,109,0.025000," ","int((a*x^2-b)^(3/4)/x,x)","\[\int \frac{\left(a \,x^{2}-b \right)^{\frac{3}{4}}}{x}\, dx\]"," ",0,"int((a*x^2-b)^(3/4)/x,x)","F"
1965,1,621,111,9.940000," ","int((x^2-2*x)/(x^2-x+1)/(x^4+1)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}+1}\, x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \left(x^{4}+1\right)^{\frac{3}{4}} x -2 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{4}-\frac{\ln \left(2 \left(x^{4}+1\right)^{\frac{3}{4}} x -2 x^{2} \sqrt{x^{4}+1}+2 x^{3} \left(x^{4}+1\right)^{\frac{1}{4}}-2 x^{4}-1\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \ln \left(\frac{\sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) x -\RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{4}+1\right)^{\frac{1}{4}} x^{3}+\left(x^{4}+1\right)^{\frac{3}{4}} x +\sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right)+3 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{4}+1\right)^{\frac{1}{4}} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) x^{3}-\left(x^{4}+1\right)^{\frac{3}{4}}-3 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{4}+1\right)^{\frac{1}{4}} x +3 \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{4}+1\right)^{\frac{1}{4}}-2 \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) x}{\left(x^{2}-x +1\right)^{2}}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \ln \left(\frac{-\sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{4}+1\right)^{\frac{1}{4}} x^{3}+2 \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+\left(x^{4}+1\right)^{\frac{3}{4}} x +2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) x -3 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{4}+1\right)^{\frac{1}{4}} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-\left(x^{4}+1\right)^{\frac{3}{4}}-\sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right)+3 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{4}+1\right)^{\frac{1}{4}} x +2 \RootOf \left(\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) x -\RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{4}+1\right)^{\frac{1}{4}}}{\left(x^{2}-x +1\right)^{2}}\right)}{2}$&$621$\\ \hline \end{longtable}"," ",0,"1/4*RootOf(_Z^2+1)*ln(-2*RootOf(_Z^2+1)*(x^4+1)^(1/2)*x^2+2*RootOf(_Z^2+1)*x^4+2*(x^4+1)^(3/4)*x-2*x^3*(x^4+1)^(1/4)+RootOf(_Z^2+1))-1/4*ln(2*(x^4+1)^(3/4)*x-2*x^2*(x^4+1)^(1/2)+2*x^3*(x^4+1)^(1/4)-2*x^4-1)+1/2*RootOf(_Z^2-RootOf(_Z^2+1))*ln(((x^4+1)^(1/2)*RootOf(_Z^2-RootOf(_Z^2+1))*RootOf(_Z^2+1)*x^2-2*(x^4+1)^(1/2)*RootOf(_Z^2-RootOf(_Z^2+1))*RootOf(_Z^2+1)*x-RootOf(_Z^2+1)*(x^4+1)^(1/4)*x^3+(x^4+1)^(3/4)*x+(x^4+1)^(1/2)*RootOf(_Z^2-RootOf(_Z^2+1))*RootOf(_Z^2+1)+3*RootOf(_Z^2+1)*(x^4+1)^(1/4)*x^2-2*RootOf(_Z^2-RootOf(_Z^2+1))*x^3-(x^4+1)^(3/4)-3*RootOf(_Z^2+1)*(x^4+1)^(1/4)*x+3*RootOf(_Z^2-RootOf(_Z^2+1))*x^2+RootOf(_Z^2+1)*(x^4+1)^(1/4)-2*RootOf(_Z^2-RootOf(_Z^2+1))*x)/(x^2-x+1)^2)-1/2*RootOf(_Z^2+1)*RootOf(_Z^2-RootOf(_Z^2+1))*ln((-(x^4+1)^(1/2)*RootOf(_Z^2-RootOf(_Z^2+1))*x^2+RootOf(_Z^2+1)*(x^4+1)^(1/4)*x^3+2*RootOf(_Z^2-RootOf(_Z^2+1))*RootOf(_Z^2+1)*x^3+(x^4+1)^(3/4)*x+2*(x^4+1)^(1/2)*RootOf(_Z^2-RootOf(_Z^2+1))*x-3*RootOf(_Z^2+1)*(x^4+1)^(1/4)*x^2-3*RootOf(_Z^2-RootOf(_Z^2+1))*RootOf(_Z^2+1)*x^2-(x^4+1)^(3/4)-(x^4+1)^(1/2)*RootOf(_Z^2-RootOf(_Z^2+1))+3*RootOf(_Z^2+1)*(x^4+1)^(1/4)*x+2*RootOf(_Z^2-RootOf(_Z^2+1))*RootOf(_Z^2+1)*x-RootOf(_Z^2+1)*(x^4+1)^(1/4))/(x^2-x+1)^2)","C"
1966,1,559,129,0.139000," ","int((k^4*x^4+1)/((1-x)*x*(-k^2*x+1))^(1/2)/(k^4*x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+1\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+1\right)}-\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}-1\right)}-\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{\left(-1+x \right) k^{2}}{k^{2}-1}}\, \sqrt{k^{2} x}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(k^{2} \textit{\_Z}^{2}+1\right)}{\sum}\EllipticPi \left(\sqrt{-k^{2} x +1}, \frac{k^{2} \underline{\hspace{1.25 ex}}\alpha  +1}{k^{2}+1}, \sqrt{-\frac{1}{k^{2}-1}}\right)\right)}{\left(k^{2}+1\right) \sqrt{x \left(k^{2} x^{2}-k^{2} x -x +1\right)}}-\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{\left(-1+x \right) k^{2}}{k^{2}-1}}\, \sqrt{k^{2} x}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(k^{2} \textit{\_Z}^{2}+1\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-k^{2} x +1}, \frac{k^{2} \underline{\hspace{1.25 ex}}\alpha  +1}{k^{2}+1}, \sqrt{-\frac{1}{k^{2}-1}}\right)}{\underline{\hspace{1.25 ex}}\alpha}\right)}{k^{2} \left(k^{2}+1\right) \sqrt{x \left(k^{2} x^{2}-k^{2} x -x +1\right)}}$&$559$\\ default&$-\frac{2 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{3} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}-\frac{\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{3} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}-\frac{i \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{i}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{3} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}-\frac{i}{k}\right)}+\frac{i \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{i}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{3} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{i}{k}\right)}$&$570$\\ \hline \end{longtable}"," ",0,"-2/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticF((-(x-1/k^2)*k^2)^(1/2),(1/k^2/(1/k^2-1))^(1/2))+1/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+1),(1/k^2/(1/k^2-1))^(1/2))-1/k^2*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-1)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-1),(1/k^2/(1/k^2-1))^(1/2))-1/(k^2+1)*(-k^2*x+1)^(1/2)*(-(-1+x)*k^2/(k^2-1))^(1/2)*(k^2*x)^(1/2)/(x*(k^2*x^2-k^2*x-x+1))^(1/2)*sum(EllipticPi((-k^2*x+1)^(1/2),(_alpha*k^2+1)/(k^2+1),(-1/(k^2-1))^(1/2)),_alpha=RootOf(_Z^2*k^2+1))-1/k^2/(k^2+1)*(-k^2*x+1)^(1/2)*(-(-1+x)*k^2/(k^2-1))^(1/2)*(k^2*x)^(1/2)/(x*(k^2*x^2-k^2*x-x+1))^(1/2)*sum(1/_alpha*EllipticPi((-k^2*x+1)^(1/2),(_alpha*k^2+1)/(k^2+1),(-1/(k^2-1))^(1/2)),_alpha=RootOf(_Z^2*k^2+1))","C"
1967,0,0,60,0.049000," ","int((a*x^8-b)/(a*x^4-b*x^2)^(1/4)/(a*x^8+b),x)","\[\int \frac{a \,x^{8}-b}{\left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}} \left(a \,x^{8}+b \right)}\, dx\]"," ",0,"int((a*x^8-b)/(a*x^4-b*x^2)^(1/4)/(a*x^8+b),x)","F"
1968,0,0,60,0.002000," ","int((a*x^8-b)/(a*x^4-b*x^2)^(1/4)/(a*x^8+b),x)","\[\int \frac{a \,x^{8}-b}{\left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}} \left(a \,x^{8}+b \right)}\, dx\]"," ",0,"int((a*x^8-b)/(a*x^4-b*x^2)^(1/4)/(a*x^8+b),x)","F"
1969,1,287,111,7.930000," ","int((x^8-1)*(x^8+1)/(x^8-x^4-1)^(1/4)/(x^16-3*x^8+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{x}{2 \left(x^{8}-x^{4}-1\right)^{\frac{1}{4}}}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(-\frac{x^{8} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \sqrt{x^{8}-x^{4}-1}\, x^{2}+2 \left(x^{8}-x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{4}+4 \left(x^{8}-x^{4}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)}{x^{8}+x^{4}-1}\right)}{16}+\frac{\RootOf \left(\textit{\_Z}^{4}+8\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}+8\right) x^{8}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} \sqrt{x^{8}-x^{4}-1}\, x^{2}-2 \left(x^{8}-x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{4}+8\right) x^{4}+4 \left(x^{8}-x^{4}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}+8\right)}{x^{8}+x^{4}-1}\right)}{16}$&$287$\\ trager&$-\frac{x}{2 \left(x^{8}-x^{4}-1\right)^{\frac{1}{4}}}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(\frac{x^{8} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \sqrt{x^{8}-x^{4}-1}\, x^{2}-2 \left(x^{8}-x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{4}-4 \left(x^{8}-x^{4}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)}{x^{8}+x^{4}-1}\right)}{16}-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right) x^{8}-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} \sqrt{x^{8}-x^{4}-1}\, x^{2}-2 \left(x^{8}-x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{4}+8\right) x^{4}+4 \left(x^{8}-x^{4}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}+8\right)}{x^{8}+x^{4}-1}\right)}{16}$&$288$\\ \hline \end{longtable}"," ",0,"-1/2*x/(x^8-x^4-1)^(1/4)-1/16*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln(-(x^8*RootOf(_Z^2+RootOf(_Z^4+8)^2)+RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*(x^8-x^4-1)^(1/2)*x^2+2*(x^8-x^4-1)^(1/4)*RootOf(_Z^4+8)^2*x^3-3*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^4+4*(x^8-x^4-1)^(3/4)*x-RootOf(_Z^2+RootOf(_Z^4+8)^2))/(x^8+x^4-1))+1/16*RootOf(_Z^4+8)*ln(-(-RootOf(_Z^4+8)*x^8+RootOf(_Z^4+8)^3*(x^8-x^4-1)^(1/2)*x^2-2*(x^8-x^4-1)^(1/4)*RootOf(_Z^4+8)^2*x^3+3*RootOf(_Z^4+8)*x^4+4*(x^8-x^4-1)^(3/4)*x+RootOf(_Z^4+8))/(x^8+x^4-1))","C"
1970,0,0,112,0.043000," ","int(1/(x^2*(-a+x))^(1/3)/(-a*d+(-1+d)*x),x)","\[\int \frac{1}{\left(x^{2} \left(-a +x \right)\right)^{\frac{1}{3}} \left(-a d +\left(-1+d \right) x \right)}\, dx\]"," ",0,"int(1/(x^2*(-a+x))^(1/3)/(-a*d+(-1+d)*x),x)","F"
1971,1,1277,104,17.381000," ","int((x^2+2*x+6)^(1/3)/(1+x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1277$\\ risch&$\text{Expression too large to display}$&$2698$\\ \hline \end{longtable}"," ",0,"3/2*(x^2+2*x+6)^(1/3)+15/2*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)*ln(-(3600*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)^2*RootOf(_Z^3-5)^3*x^2+255*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)*RootOf(_Z^3-5)^4*x^2+7200*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)^2*RootOf(_Z^3-5)^3*x+510*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)*RootOf(_Z^3-5)^4*x+3825*(x^2+2*x+6)^(2/3)*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)*RootOf(_Z^3-5)^2+2640*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)*RootOf(_Z^3-5)*x^2+187*RootOf(_Z^3-5)^2*x^2+5280*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)*RootOf(_Z^3-5)*x+374*RootOf(_Z^3-5)^2*x+19125*(x^2+2*x+6)^(1/3)*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)+21840*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)*RootOf(_Z^3-5)+1440*(x^2+2*x+6)^(2/3)+1440*(x^2+2*x+6)^(1/3)*RootOf(_Z^3-5)+1547*RootOf(_Z^3-5)^2)/(1+x)^2)-1/2*ln(-(3600*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)^2*RootOf(_Z^3-5)^3*x^2-15*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)*RootOf(_Z^3-5)^4*x^2+7200*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)^2*RootOf(_Z^3-5)^3*x-30*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)*RootOf(_Z^3-5)^4*x-3825*(x^2+2*x+6)^(2/3)*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)*RootOf(_Z^3-5)^2-1440*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)*RootOf(_Z^3-5)*x^2+6*RootOf(_Z^3-5)^2*x^2-2880*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)*RootOf(_Z^3-5)*x+12*RootOf(_Z^3-5)^2*x-19125*(x^2+2*x+6)^(1/3)*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)-21840*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)*RootOf(_Z^3-5)+165*(x^2+2*x+6)^(2/3)+165*(x^2+2*x+6)^(1/3)*RootOf(_Z^3-5)+91*RootOf(_Z^3-5)^2)/(1+x)^2)*RootOf(_Z^3-5)-15/2*ln(-(3600*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)^2*RootOf(_Z^3-5)^3*x^2-15*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)*RootOf(_Z^3-5)^4*x^2+7200*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)^2*RootOf(_Z^3-5)^3*x-30*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)*RootOf(_Z^3-5)^4*x-3825*(x^2+2*x+6)^(2/3)*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)*RootOf(_Z^3-5)^2-1440*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)*RootOf(_Z^3-5)*x^2+6*RootOf(_Z^3-5)^2*x^2-2880*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)*RootOf(_Z^3-5)*x+12*RootOf(_Z^3-5)^2*x-19125*(x^2+2*x+6)^(1/3)*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)-21840*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)*RootOf(_Z^3-5)+165*(x^2+2*x+6)^(2/3)+165*(x^2+2*x+6)^(1/3)*RootOf(_Z^3-5)+91*RootOf(_Z^3-5)^2)/(1+x)^2)*RootOf(RootOf(_Z^3-5)^2+15*_Z*RootOf(_Z^3-5)+225*_Z^2)","C"
1972,1,113,114,8.233000," ","int((-1+x)/x/(x^3-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} \left(\frac{2 \pi  \sqrt{3}\, x^{3} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], x^{3}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+3 \ln \left(x \right)+i \pi \right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{6 \pi  \mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}}}+\frac{\left(-\mathrm{signum}\left(x^{3}-1\right)\right)^{\frac{1}{3}} x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{3}\right)}{\mathrm{signum}\left(x^{3}-1\right)^{\frac{1}{3}}}$&$113$\\ trager&$\text{Expression too large to display}$&$2269$\\ \hline \end{longtable}"," ",0,"-1/6/Pi*3^(1/2)*GAMMA(2/3)/signum(x^3-1)^(1/3)*(-signum(x^3-1))^(1/3)*(2/9*Pi*3^(1/2)/GAMMA(2/3)*x^3*hypergeom([1,1,4/3],[2,2],x^3)+2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)+3*ln(x)+I*Pi)*Pi*3^(1/2)/GAMMA(2/3))+1/signum(x^3-1)^(1/3)*(-signum(x^3-1))^(1/3)*x*hypergeom([1/3,1/3],[4/3],x^3)","C"
1973,1,889,104,18.113000," ","int((x^3-1)^(2/3)*(x^3+1)/x^6/(x^3-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{11 x^{6}-7 x^{3}-4}{40 x^{5} \left(x^{3}-1\right)^{\frac{1}{3}}}+\frac{\RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} x^{3}+27 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}+15 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x +2 \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-3 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{3}-18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) x^{3}+x \left(x^{3}-1\right)^{\frac{2}{3}}+2 \RootOf \left(\textit{\_Z}^{3}-2\right)+18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)}{x^{3}-2}\right)}{8}-\frac{\ln \left(\frac{6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} x^{3}-18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}-30 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x -\RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+24 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right) x^{2}+6 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{3}-18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) x^{3}-8 x \left(x^{3}-1\right)^{\frac{2}{3}}-4 \RootOf \left(\textit{\_Z}^{3}-2\right)+12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)}{x^{3}-2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)}{8}-\frac{3 \ln \left(\frac{6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} x^{3}-18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}-30 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x -\RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+24 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right) x^{2}+6 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{3}-18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) x^{3}-8 x \left(x^{3}-1\right)^{\frac{2}{3}}-4 \RootOf \left(\textit{\_Z}^{3}-2\right)+12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)}{x^{3}-2}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)}{4}$&$889$\\ trager&$\text{Expression too large to display}$&$1116$\\ \hline \end{longtable}"," ",0,"1/40*(11*x^6-7*x^3-4)/x^5/(x^3-1)^(1/3)+1/8*RootOf(_Z^3-2)*ln((3*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^3+27*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^3+15*(x^3-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^2*x+2*RootOf(_Z^3-2)^2*(x^3-1)^(1/3)*x^2-3*(x^3-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)*x^2-2*RootOf(_Z^3-2)*x^3-18*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^3+x*(x^3-1)^(2/3)+2*RootOf(_Z^3-2)+18*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2))/(x^3-2))-1/8*ln((6*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^3-18*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-30*(x^3-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^2*x-RootOf(_Z^3-2)^2*(x^3-1)^(1/3)*x^2+24*(x^3-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)*x^2+6*RootOf(_Z^3-2)*x^3-18*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^3-8*x*(x^3-1)^(2/3)-4*RootOf(_Z^3-2)+12*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2))/(x^3-2))*RootOf(_Z^3-2)-3/4*ln((6*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^3-18*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-30*(x^3-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^2*x-RootOf(_Z^3-2)^2*(x^3-1)^(1/3)*x^2+24*(x^3-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)*x^2+6*RootOf(_Z^3-2)*x^3-18*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^3-8*x*(x^3-1)^(2/3)-4*RootOf(_Z^3-2)+12*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2))/(x^3-2))*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)","C"
1974,1,1101,104,19.530000," ","int((x^2-4)*(x^3+x)^(1/3)/x^4/(x^2+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1101$\\ risch&$\text{Expression too large to display}$&$1570$\\ \hline \end{longtable}"," ",0,"-3/4*(2*x^2-1)*(x^3+x)^(1/3)/x^3-3/8*ln((36*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^3*x^2-6*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^4*x^2-36*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^3+6*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^4+144*(x^3+x)^(2/3)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2+66*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)*x^2-11*RootOf(_Z^3+4)^2*x^2-108*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*(x^3+x)^(1/3)*x-24*(x^3+x)^(1/3)*RootOf(_Z^3+4)*x+60*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)-10*RootOf(_Z^3+4)^2-30*(x^3+x)^(2/3))/(x^2+2))*RootOf(_Z^3+4)-9/2*ln((36*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^3*x^2-6*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^4*x^2-36*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^3+6*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^4+144*(x^3+x)^(2/3)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2+66*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)*x^2-11*RootOf(_Z^3+4)^2*x^2-108*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*(x^3+x)^(1/3)*x-24*(x^3+x)^(1/3)*RootOf(_Z^3+4)*x+60*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)-10*RootOf(_Z^3+4)^2-30*(x^3+x)^(2/3))/(x^2+2))*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)+3/8*RootOf(_Z^3+4)*ln((144*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^3*x^2-6*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^4*x^2-144*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^3+6*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^4-288*(x^3+x)^(2/3)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2-312*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)*x^2+13*RootOf(_Z^3+4)^2*x^2+360*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*(x^3+x)^(1/3)*x+48*(x^3+x)^(1/3)*RootOf(_Z^3+4)*x-192*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)+8*RootOf(_Z^3+4)^2+36*(x^3+x)^(2/3))/(x^2+2))","C"
1975,1,12421,88,25.660000," ","int((x^2+2)/(x^2+1)/(x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$12421$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
1976,1,284,100,0.144000," ","int(x/(a*x^2+b)/(a*x^3-b*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}+\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}$&$284$\\ elliptic&$\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}+\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}$&$284$\\ \hline \end{longtable}"," ",0,"1/2/a^2*(a*b)^(1/2)*(x*a/(a*b)^(1/2)+1)^(1/2)*(-2*x*a/(a*b)^(1/2)+2)^(1/2)*(-x*a/(a*b)^(1/2))^(1/2)/(a*x^3-b*x)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2),-1/a*(a*b)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2)),1/2*2^(1/2))+1/2/a^2*(a*b)^(1/2)*(x*a/(a*b)^(1/2)+1)^(1/2)*(-2*x*a/(a*b)^(1/2)+2)^(1/2)*(-x*a/(a*b)^(1/2))^(1/2)/(a*x^3-b*x)^(1/2)/(-1/a*(a*b)^(1/2)+1/a*(-a*b)^(1/2))*EllipticPi(((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2),-1/a*(a*b)^(1/2)/(-1/a*(a*b)^(1/2)+1/a*(-a*b)^(1/2)),1/2*2^(1/2))","C"
1977,1,380,100,0.145000," ","int((a*x^2-b)/(a*x^2+b)/(a*x^3-b*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}-b x}}-\frac{b \sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{\sqrt{-a b}\, a \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}+\frac{b \sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{\sqrt{-a b}\, a \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}$&$380$\\ default&$\frac{\sqrt{a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}-b x}}-2 b \left(\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{-a b}\, a \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}-\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{-a b}\, a \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}\right)$&$400$\\ \hline \end{longtable}"," ",0,"1/a*(a*b)^(1/2)*(x*a/(a*b)^(1/2)+1)^(1/2)*(-2*x*a/(a*b)^(1/2)+2)^(1/2)*(-x*a/(a*b)^(1/2))^(1/2)/(a*x^3-b*x)^(1/2)*EllipticF(((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2),1/2*2^(1/2))-b/(-a*b)^(1/2)/a*(a*b)^(1/2)*(x*a/(a*b)^(1/2)+1)^(1/2)*(-2*x*a/(a*b)^(1/2)+2)^(1/2)*(-x*a/(a*b)^(1/2))^(1/2)/(a*x^3-b*x)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2),-1/a*(a*b)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2)),1/2*2^(1/2))+b/(-a*b)^(1/2)/a*(a*b)^(1/2)*(x*a/(a*b)^(1/2)+1)^(1/2)*(-2*x*a/(a*b)^(1/2)+2)^(1/2)*(-x*a/(a*b)^(1/2))^(1/2)/(a*x^3-b*x)^(1/2)/(-1/a*(a*b)^(1/2)+1/a*(-a*b)^(1/2))*EllipticPi(((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2),-1/a*(a*b)^(1/2)/(-1/a*(a*b)^(1/2)+1/a*(-a*b)^(1/2)),1/2*2^(1/2))","C"
1978,1,284,100,0.130000," ","int((a*x^3-b*x)^(1/2)/(a^2*x^4-b^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}+\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}$&$284$\\ default&$-\frac{-\frac{2 b \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}-b x}}+\frac{b \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}-b x}}-\frac{b \sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}-\frac{b \sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}}{2 b}+\frac{\sqrt{a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \left(-\frac{2 \sqrt{a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{\sqrt{2}}{2}\right)}{a}+\frac{\sqrt{a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{\sqrt{2}}{2}\right)}{a}\right)}{2 b a \sqrt{a \,x^{3}-b x}}$&$601$\\ \hline \end{longtable}"," ",0,"1/2/a^2*(a*b)^(1/2)*(x*a/(a*b)^(1/2)+1)^(1/2)*(-2*x*a/(a*b)^(1/2)+2)^(1/2)*(-x*a/(a*b)^(1/2))^(1/2)/(a*x^3-b*x)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2),-1/a*(a*b)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2)),1/2*2^(1/2))+1/2/a^2*(a*b)^(1/2)*(x*a/(a*b)^(1/2)+1)^(1/2)*(-2*x*a/(a*b)^(1/2)+2)^(1/2)*(-x*a/(a*b)^(1/2))^(1/2)/(a*x^3-b*x)^(1/2)/(-1/a*(a*b)^(1/2)+1/a*(-a*b)^(1/2))*EllipticPi(((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2),-1/a*(a*b)^(1/2)/(-1/a*(a*b)^(1/2)+1/a*(-a*b)^(1/2)),1/2*2^(1/2))","C"
1979,1,725,109,279.845000," ","int((x^5+1)^(2/3)*(2*x^5-3)*(2*x^5+x^3+2)/x^6/(2*x^5-x^3+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\frac{3}{5} x^{10}+\frac{3}{2} x^{8}+\frac{6}{5} x^{5}+\frac{3}{2} x^{3}+\frac{3}{5}}{x^{5} \left(x^{5}+1\right)^{\frac{1}{3}}}+\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{3}-2\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{3}-2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}+2 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{5}-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{5}+3 \left(x^{5}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{3}-2\right) x^{3}-2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{3}+6 \left(x^{5}+1\right)^{\frac{2}{3}} x +2 \RootOf \left(\textit{\_Z}^{3}-2\right)-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)}{2 x^{5}-x^{3}+2}\right)-\frac{\ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{3}+2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}-4 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{5}-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{5}-3 \left(x^{5}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{2}-6 \left(x^{5}+1\right)^{\frac{2}{3}} x -4 \RootOf \left(\textit{\_Z}^{3}-2\right)-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)}{2 x^{5}-x^{3}+2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)}{2}-\ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{3}+2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}-4 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{5}-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{5}-3 \left(x^{5}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{2}-6 \left(x^{5}+1\right)^{\frac{2}{3}} x -4 \RootOf \left(\textit{\_Z}^{3}-2\right)-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)}{2 x^{5}-x^{3}+2}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)$&$725$\\ trager&$\text{Expression too large to display}$&$1470$\\ \hline \end{longtable}"," ",0,"3/10*(2*x^10+5*x^8+4*x^5+5*x^3+2)/x^5/(x^5+1)^(1/3)+RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*ln(-(RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3-2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3+2*RootOf(_Z^3-2)*x^5-4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^5+3*(x^5+1)^(1/3)*RootOf(_Z^3-2)^2*x^2+RootOf(_Z^3-2)*x^3-2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3+6*(x^5+1)^(2/3)*x+2*RootOf(_Z^3-2)-4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2))/(2*x^5-x^3+2))-1/2*ln((2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3+2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-4*RootOf(_Z^3-2)*x^5-4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^5-3*(x^5+1)^(1/3)*RootOf(_Z^3-2)^2*x^2-6*(x^5+1)^(2/3)*x-4*RootOf(_Z^3-2)-4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2))/(2*x^5-x^3+2))*RootOf(_Z^3-2)-ln((2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3+2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-4*RootOf(_Z^3-2)*x^5-4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^5-3*(x^5+1)^(1/3)*RootOf(_Z^3-2)^2*x^2-6*(x^5+1)^(2/3)*x-4*RootOf(_Z^3-2)-4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2))/(2*x^5-x^3+2))*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)","C"
1980,0,0,124,0.028000," ","int((a*x^6+b)/(a*x^6-b)/(a*x^6+a^3*x^3-b)^(1/3),x)","\[\int \frac{a \,x^{6}+b}{\left(a \,x^{6}-b \right) \left(a \,x^{6}+a^{3} x^{3}-b \right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a*x^6+b)/(a*x^6-b)/(a*x^6+a^3*x^3-b)^(1/3),x)","F"
1981,1,137,124,1.327000," ","int((x^2+1)*(x^8+1)*(x^8+x^6+x^4+x^2+1)^(1/2)/x^7/(x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{8}+x^{6}+x^{4}+x^{2}+1}\, \left(8 x^{8}+26 x^{6}+65 x^{4}+26 x^{2}+8\right)}{48 x^{6}}+\RootOf \left(\textit{\_Z}^{2}-5\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-5\right) x^{4}+\RootOf \left(\textit{\_Z}^{2}-5\right)-2 \sqrt{x^{8}+x^{6}+x^{4}+x^{2}+1}}{\left(-1+x \right)^{2} \left(1+x \right)^{2}}\right)-\frac{65 \ln \left(\frac{-2-x^{2}-2 x^{4}+2 \sqrt{x^{8}+x^{6}+x^{4}+x^{2}+1}}{x^{2}}\right)}{32}$&$137$\\ risch&$\frac{65 x^{12}+91 x^{10}+99 x^{8}+99 x^{6}+99 x^{4}+34 x^{2}+8}{48 x^{6} \sqrt{x^{8}+x^{6}+x^{4}+x^{2}+1}}+\frac{\left(8 x^{2}+26\right) \sqrt{x^{8}+x^{6}+x^{4}+x^{2}+1}}{48}+\RootOf \left(\textit{\_Z}^{2}-5\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-5\right) x^{4}+\RootOf \left(\textit{\_Z}^{2}-5\right)-2 \sqrt{x^{8}+x^{6}+x^{4}+x^{2}+1}}{\left(-1+x \right)^{2} \left(1+x \right)^{2}}\right)-\frac{65 \ln \left(\frac{-2-x^{2}-2 x^{4}+2 \sqrt{x^{8}+x^{6}+x^{4}+x^{2}+1}}{x^{2}}\right)}{32}$&$172$\\ \hline \end{longtable}"," ",0,"1/48*(x^8+x^6+x^4+x^2+1)^(1/2)*(8*x^8+26*x^6+65*x^4+26*x^2+8)/x^6+RootOf(_Z^2-5)*ln(-(RootOf(_Z^2-5)*x^4+RootOf(_Z^2-5)-2*(x^8+x^6+x^4+x^2+1)^(1/2))/(-1+x)^2/(1+x)^2)-65/32*ln((-2-x^2-2*x^4+2*(x^8+x^6+x^4+x^2+1)^(1/2))/x^2)","C"
1982,0,0,60,0.046000," ","int((a*x^8+b)/(a*x^4-b*x^2)^(1/4)/(a*x^8-b),x)","\[\int \frac{a \,x^{8}+b}{\left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}} \left(a \,x^{8}-b \right)}\, dx\]"," ",0,"int((a*x^8+b)/(a*x^4-b*x^2)^(1/4)/(a*x^8-b),x)","F"
1983,0,0,60,0.000000," ","int((a*x^8+b)/(a*x^4-b*x^2)^(1/4)/(a*x^8-b),x)","\[\int \frac{a \,x^{8}+b}{\left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}} \left(a \,x^{8}-b \right)}\, dx\]"," ",0,"int((a*x^8+b)/(a*x^4-b*x^2)^(1/4)/(a*x^8-b),x)","F"
1984,0,0,38,0.021000," ","int((x^4-1)*(x+(x^2+1)^(1/2))^(1/2)/(x^4+1),x)","\[\int \frac{\left(x^{4}-1\right) \sqrt{x +\sqrt{x^{2}+1}}}{x^{4}+1}\, dx\]"," ",0,"int((x^4-1)*(x+(x^2+1)^(1/2))^(1/2)/(x^4+1),x)","F"
1985,0,0,38,0.002000," ","int((x^4-1)*(x+(x^2+1)^(1/2))^(1/2)/(x^4+1),x)","\[\int \frac{\left(x^{4}-1\right) \sqrt{x +\sqrt{x^{2}+1}}}{x^{4}+1}\, dx\]"," ",0,"int((x^4-1)*(x+(x^2+1)^(1/2))^(1/2)/(x^4+1),x)","F"
1986,0,0,109,0.028000," ","int(x^2*(x^2+x)^(1/2)/(x^2+x*(x^2+x)^(1/2))^(1/2),x)","\[\int \frac{x^{2} \sqrt{x^{2}+x}}{\sqrt{x^{2}+x \sqrt{x^{2}+x}}}\, dx\]"," ",0,"int(x^2*(x^2+x)^(1/2)/(x^2+x*(x^2+x)^(1/2))^(1/2),x)","F"
1987,0,0,12,180.000000," ","int(1/(c*x^2+d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{1}{\left(c \,x^{2}+d \right) \sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int(1/(c*x^2+d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","F"
1988,0,0,12,180.000000," ","int(1/(c*x^2+d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{1}{\left(c \,x^{2}+d \right) \sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int(1/(c*x^2+d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","F"
1989,0,0,23,0.043000," ","int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)/(x^2+1)^(1/2),x)","\[\int \frac{\sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right) \sqrt{x^{2}+1}}\, dx\]"," ",0,"int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)/(x^2+1)^(1/2),x)","F"
1990,0,0,23,0.002000," ","int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)/(x^2+1)^(1/2),x)","\[\int \frac{\sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right) \sqrt{x^{2}+1}}\, dx\]"," ",0,"int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)/(x^2+1)^(1/2),x)","F"
1991,0,0,33,0.092000," ","int((a^2*x^2+b)^(1/2)/(x^2-(a*x-(a^2*x^2+b)^(1/2))^(1/3)),x)","\[\int \frac{\sqrt{a^{2} x^{2}+b}}{x^{2}-\left(a x -\sqrt{a^{2} x^{2}+b}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a^2*x^2+b)^(1/2)/(x^2-(a*x-(a^2*x^2+b)^(1/2))^(1/3)),x)","F"
1992,0,0,33,0.146000," ","int((a^2*x^2+b)^(1/2)/(x^2-(a*x-(a^2*x^2+b)^(1/2))^(1/2)),x)","\[\int \frac{\sqrt{a^{2} x^{2}+b}}{x^{2}-\sqrt{a x -\sqrt{a^{2} x^{2}+b}}}\, dx\]"," ",0,"int((a^2*x^2+b)^(1/2)/(x^2-(a*x-(a^2*x^2+b)^(1/2))^(1/2)),x)","F"
1993,1,1819,105,9.402000," ","int((x^2-2*x-6)^(1/3)/(-1+x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$1819$\\ \hline \end{longtable}"," ",0,"3/2*(x^2-2*x-6)^(1/3)+(7/12*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*ln((108*RootOf(_Z^3+7)*x^4-432*RootOf(_Z^3+7)*x^3-2502*RootOf(_Z^3+7)*x^2+5868*RootOf(_Z^3+7)*x+13716*RootOf(_Z^3+7)+21*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)^3*x^4-84*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)^3*x^3-42*RootOf(_Z^3+7)^3*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*x^2-980*RootOf(_Z^3+7)^2*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)^2*x^2+252*RootOf(_Z^3+7)^3*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*x+5880*RootOf(_Z^3+7)^2*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)^2*x+320040*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)-58380*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*x^2+136920*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*x+2520*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*x^4-10080*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*x^3-819*(x^4-4*x^3-8*x^2+24*x+36)^(1/3)*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)*x^2+50274*(x^4-4*x^3-8*x^2+24*x+36)^(2/3)+490*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)^2*RootOf(_Z^3+7)^2*x^4-1960*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)^2*RootOf(_Z^3+7)^2*x^3+1638*(x^4-4*x^3-8*x^2+24*x+36)^(1/3)*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)*x-7560*(x^4-4*x^3-8*x^2+24*x+36)^(2/3)*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)^2+6480*RootOf(_Z^3+7)^2*(x^4-4*x^3-8*x^2+24*x+36)^(1/3)*x^2-12960*RootOf(_Z^3+7)^2*(x^4-4*x^3-8*x^2+24*x+36)^(1/3)*x+4914*(x^4-4*x^3-8*x^2+24*x+36)^(1/3)*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)-38880*RootOf(_Z^3+7)^2*(x^4-4*x^3-8*x^2+24*x+36)^(1/3))/(x^2-2*x-6)/(-1+x)^2)+1/2*RootOf(_Z^3+7)*ln(-(-9360*RootOf(_Z^3+7)*x^4+37440*RootOf(_Z^3+7)*x^3+110160*RootOf(_Z^3+7)*x^2-295200*RootOf(_Z^3+7)*x-548640*RootOf(_Z^3+7)+840*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)^3*x^4-3360*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)^3*x^3-1680*RootOf(_Z^3+7)^3*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*x^2-98*RootOf(_Z^3+7)^2*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)^2*x^2+10080*RootOf(_Z^3+7)^3*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*x+588*RootOf(_Z^3+7)^2*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)^2*x-32004*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)+6426*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*x^2-17220*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*x-546*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*x^4+2184*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*x^3+16758*(x^4-4*x^3-8*x^2+24*x+36)^(1/3)*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)*x^2-9828*(x^4-4*x^3-8*x^2+24*x+36)^(2/3)+49*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)^2*RootOf(_Z^3+7)^2*x^4-196*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)^2*RootOf(_Z^3+7)^2*x^3-33516*(x^4-4*x^3-8*x^2+24*x+36)^(1/3)*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)*x-15120*(x^4-4*x^3-8*x^2+24*x+36)^(2/3)*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)^2+12960*RootOf(_Z^3+7)^2*(x^4-4*x^3-8*x^2+24*x+36)^(1/3)*x^2-25920*RootOf(_Z^3+7)^2*(x^4-4*x^3-8*x^2+24*x+36)^(1/3)*x-100548*(x^4-4*x^3-8*x^2+24*x+36)^(1/3)*RootOf(36*RootOf(_Z^3+7)^2+42*_Z*RootOf(_Z^3+7)+49*_Z^2)*RootOf(_Z^3+7)-77760*RootOf(_Z^3+7)^2*(x^4-4*x^3-8*x^2+24*x+36)^(1/3))/(x^2-2*x-6)/(-1+x)^2))/(x^2-2*x-6)^(2/3)*((x^2-2*x-6)^2)^(1/3)","C"
1994,1,361,105,0.819000," ","int((-1+x)/(x^3-x^2-x+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(-1+x \right) \left(1+x \right)}{\left(\left(-1+x \right)^{2} \left(1+x \right)\right)^{\frac{1}{3}}}+\frac{2 \ln \left(-\frac{-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-x^{2}-x +1\right)^{\frac{2}{3}}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-x^{2}-x +1\right)^{\frac{1}{3}} x +4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x -4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-x^{2}-x +1\right)^{\frac{1}{3}}-3 \left(x^{3}-x^{2}-x +1\right)^{\frac{1}{3}} x +2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x -x^{2}+3 \left(x^{3}-x^{2}-x +1\right)^{\frac{1}{3}}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+1}{-1+x}\right)}{3}+\frac{2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\frac{-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}-x^{2}-x +1\right)^{\frac{2}{3}}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x -5 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+3 \left(x^{3}-x^{2}-x +1\right)^{\frac{2}{3}}-3 \left(x^{3}-x^{2}-x +1\right)^{\frac{1}{3}} x +6 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x -2 x^{2}+3 \left(x^{3}-x^{2}-x +1\right)^{\frac{1}{3}}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+4 x -2}{-1+x}\right)}{3}$&$361$\\ trager&$\frac{\left(x^{3}-x^{2}-x +1\right)^{\frac{2}{3}}}{-1+x}+2 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(-\frac{18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-x^{2}-x +1\right)^{\frac{2}{3}}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-x^{2}-x +1\right)^{\frac{1}{3}} x -18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x +15 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-x^{2}-x +1\right)^{\frac{1}{3}}-12 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x +2 x^{2}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-2}{-1+x}\right)-\frac{2 \ln \left(\frac{-18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-x^{2}-x +1\right)^{\frac{2}{3}}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-x^{2}-x +1\right)^{\frac{1}{3}} x +18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x +3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+3 \left(x^{3}-x^{2}-x +1\right)^{\frac{2}{3}}-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-x^{2}-x +1\right)^{\frac{1}{3}}+3 \left(x^{3}-x^{2}-x +1\right)^{\frac{1}{3}} x +x^{2}-3 \left(x^{3}-x^{2}-x +1\right)^{\frac{1}{3}}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-2 x +1}{-1+x}\right)}{3}-2 \ln \left(\frac{-18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-x^{2}-x +1\right)^{\frac{2}{3}}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-x^{2}-x +1\right)^{\frac{1}{3}} x +18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x +3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+3 \left(x^{3}-x^{2}-x +1\right)^{\frac{2}{3}}-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}-x^{2}-x +1\right)^{\frac{1}{3}}+3 \left(x^{3}-x^{2}-x +1\right)^{\frac{1}{3}} x +x^{2}-3 \left(x^{3}-x^{2}-x +1\right)^{\frac{1}{3}}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-2 x +1}{-1+x}\right) \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)$&$658$\\ \hline \end{longtable}"," ",0,"(-1+x)*(1+x)/((-1+x)^2*(1+x))^(1/3)+2/3*ln(-(-4*RootOf(_Z^2+_Z+1)^2*x^2+3*RootOf(_Z^2+_Z+1)*(x^3-x^2-x+1)^(2/3)-3*RootOf(_Z^2+_Z+1)*(x^3-x^2-x+1)^(1/3)*x+4*RootOf(_Z^2+_Z+1)^2*x-4*RootOf(_Z^2+_Z+1)*x^2+3*RootOf(_Z^2+_Z+1)*(x^3-x^2-x+1)^(1/3)-3*(x^3-x^2-x+1)^(1/3)*x+2*RootOf(_Z^2+_Z+1)*x-x^2+3*(x^3-x^2-x+1)^(1/3)+2*RootOf(_Z^2+_Z+1)+1)/(-1+x))+2/3*RootOf(_Z^2+_Z+1)*ln((-2*RootOf(_Z^2+_Z+1)^2*x^2+3*RootOf(_Z^2+_Z+1)*(x^3-x^2-x+1)^(2/3)+2*RootOf(_Z^2+_Z+1)^2*x-5*RootOf(_Z^2+_Z+1)*x^2+3*(x^3-x^2-x+1)^(2/3)-3*(x^3-x^2-x+1)^(1/3)*x+6*RootOf(_Z^2+_Z+1)*x-2*x^2+3*(x^3-x^2-x+1)^(1/3)-RootOf(_Z^2+_Z+1)+4*x-2)/(-1+x))","C"
1995,1,403,105,0.806000," ","int(x/(x^3+x^2-x-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}}{1+x}+\frac{\ln \left(\frac{-36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x -36 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x -12 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}-9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-3 x \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -x^{2}-3 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}+6 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+1}{1+x}\right)}{3}+\RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(-\frac{-18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{2}+9 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}-18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x -15 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+3 \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}-3 x \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-18 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x -2 x^{2}-3 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-3 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-4 x -2}{1+x}\right)$&$403$\\ risch&$\frac{\left(-1+x \right) \left(1+x \right)}{\left(\left(-1+x \right) \left(1+x \right)^{2}\right)^{\frac{1}{3}}}+\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x +3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x +5 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}+3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}+4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +2 x^{2}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-2}{1+x}\right)}{3}-\frac{\ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x -3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x -\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-3 \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}-3 x \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-3 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-2 x -1}{1+x}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{3}-\frac{\ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x -3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x -\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-3 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-3 \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}-3 x \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-x^{2}+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-3 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-2 x -1}{1+x}\right)}{3}$&$528$\\ \hline \end{longtable}"," ",0,"1/(1+x)*(x^3+x^2-x-1)^(2/3)+1/3*ln((-36*RootOf(9*_Z^2+3*_Z+1)^2*x^2+9*RootOf(9*_Z^2+3*_Z+1)*(x^3+x^2-x-1)^(2/3)-9*RootOf(9*_Z^2+3*_Z+1)*(x^3+x^2-x-1)^(1/3)*x-36*RootOf(9*_Z^2+3*_Z+1)^2*x-12*RootOf(9*_Z^2+3*_Z+1)*x^2-9*RootOf(9*_Z^2+3*_Z+1)*(x^3+x^2-x-1)^(1/3)-3*x*(x^3+x^2-x-1)^(1/3)-6*RootOf(9*_Z^2+3*_Z+1)*x-x^2-3*(x^3+x^2-x-1)^(1/3)+6*RootOf(9*_Z^2+3*_Z+1)+1)/(1+x))+RootOf(9*_Z^2+3*_Z+1)*ln(-(-18*RootOf(9*_Z^2+3*_Z+1)^2*x^2+9*RootOf(9*_Z^2+3*_Z+1)*(x^3+x^2-x-1)^(2/3)-18*RootOf(9*_Z^2+3*_Z+1)^2*x-15*RootOf(9*_Z^2+3*_Z+1)*x^2+3*(x^3+x^2-x-1)^(2/3)-3*x*(x^3+x^2-x-1)^(1/3)-18*RootOf(9*_Z^2+3*_Z+1)*x-2*x^2-3*(x^3+x^2-x-1)^(1/3)-3*RootOf(9*_Z^2+3*_Z+1)-4*x-2)/(1+x))","C"
1996,1,695,112,19.560000," ","int((3+2*x)*(3*x^3+x+1)^(2/3)/x^3/(x^3+x+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{3 \left(3 x^{3}+x +1\right)^{\frac{2}{3}}}{2 x^{2}}+\RootOf \left(\textit{\_Z}^{3}+4\right) \ln \left(-\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}+5 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}+4 \left(3 x^{3}+x +1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +4 \left(3 x^{3}+x +1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{2}+\left(3 x^{3}+x +1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}-5 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}-25 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) x^{3}-7 \left(3 x^{3}+x +1\right)^{\frac{2}{3}} x -\RootOf \left(\textit{\_Z}^{3}+4\right) x -5 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) x -\RootOf \left(\textit{\_Z}^{3}+4\right)-5 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right)}{x^{3}+x +1}\right)+2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) \ln \left(\frac{5 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}+4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}+8 \left(3 x^{3}+x +1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +8 \left(3 x^{3}+x +1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{2}+14 \left(3 x^{3}+x +1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}+15 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}+12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) x^{3}-2 \left(3 x^{3}+x +1\right)^{\frac{2}{3}} x +5 \RootOf \left(\textit{\_Z}^{3}+4\right) x +4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) x +5 \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right)}{x^{3}+x +1}\right)$&$695$\\ trager&$\text{Expression too large to display}$&$1455$\\ \hline \end{longtable}"," ",0,"-3/2*(3*x^3+x+1)^(2/3)/x^2+RootOf(_Z^3+4)*ln(-(RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^3*x^3+5*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+4*(3*x^3+x+1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^2*x+4*(3*x^3+x+1)^(1/3)*RootOf(_Z^3+4)^2*x^2+(3*x^3+x+1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)*x^2-5*RootOf(_Z^3+4)*x^3-25*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^3-7*(3*x^3+x+1)^(2/3)*x-RootOf(_Z^3+4)*x-5*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x-RootOf(_Z^3+4)-5*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2))/(x^3+x+1))+2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*ln((5*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^3*x^3+4*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+8*(3*x^3+x+1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^2*x+8*(3*x^3+x+1)^(1/3)*RootOf(_Z^3+4)^2*x^2+14*(3*x^3+x+1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)*x^2+15*RootOf(_Z^3+4)*x^3+12*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^3-2*(3*x^3+x+1)^(2/3)*x+5*RootOf(_Z^3+4)*x+4*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x+5*RootOf(_Z^3+4)+4*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2))/(x^3+x+1))","C"
1997,0,0,129,0.025000," ","int(x^2*(-3*a*b^3+2*b^2*(3*a+b)*x-3*b*(a+b)*x^2+x^4)/(x*(-a+x)*(-b+x)^3)^(3/4)/(a*b^3-b^2*(3*a+b)*x+3*b*(a+b)*x^2-(a+3*b+d)*x^3+x^4),x)","\[\int \frac{x^{2} \left(-3 a \,b^{3}+2 b^{2} \left(3 a +b \right) x -3 b \left(a +b \right) x^{2}+x^{4}\right)}{\left(x \left(-a +x \right) \left(-b +x \right)^{3}\right)^{\frac{3}{4}} \left(a \,b^{3}-b^{2} \left(3 a +b \right) x +3 b \left(a +b \right) x^{2}-\left(a +3 b +d \right) x^{3}+x^{4}\right)}\, dx\]"," ",0,"int(x^2*(-3*a*b^3+2*b^2*(3*a+b)*x-3*b*(a+b)*x^2+x^4)/(x*(-a+x)*(-b+x)^3)^(3/4)/(a*b^3-b^2*(3*a+b)*x+3*b*(a+b)*x^2-(a+3*b+d)*x^3+x^4),x)","F"
1998,0,0,101,0.047000," ","int(x^6/(a*x^4-b)^(3/4)/(a*x^4+b),x)","\[\int \frac{x^{6}}{\left(a \,x^{4}-b \right)^{\frac{3}{4}} \left(a \,x^{4}+b \right)}\, dx\]"," ",0,"int(x^6/(a*x^4-b)^(3/4)/(a*x^4+b),x)","F"
1999,0,0,109,0.045000," ","int((2*a*x^2-b)/(a*x^2-b)/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{2 a \,x^{2}-b}{\left(a \,x^{2}-b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((2*a*x^2-b)/(a*x^2-b)/(a*x^4+b*x^2)^(1/4),x)","F"
2000,0,0,105,0.046000," ","int((2*a*x^4-3*b)/(a*x^4-2*b)/(a*x^4+b)^(1/4),x)","\[\int \frac{2 a \,x^{4}-3 b}{\left(a \,x^{4}-2 b \right) \left(a \,x^{4}+b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((2*a*x^4-3*b)/(a*x^4-2*b)/(a*x^4+b)^(1/4),x)","F"
2001,0,0,101,0.043000," ","int((a*x^4+b)/(a*x^4-b)^(1/4)/(3*a*x^4+b),x)","\[\int \frac{a \,x^{4}+b}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(3 a \,x^{4}+b \right)}\, dx\]"," ",0,"int((a*x^4+b)/(a*x^4-b)^(1/4)/(3*a*x^4+b),x)","F"
2002,1,308,119,20.673000," ","int((x^6+2)*(x^6-x^4-1)/(-x^6-x^4+1)^(1/4)/(x^6-1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{x \left(-x^{6}-x^{4}+1\right)^{\frac{3}{4}}}{2 \left(x^{6}-1\right)}-\frac{5 \RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \sqrt{-x^{6}-x^{4}+1}\, x^{2}-\RootOf \left(\textit{\_Z}^{4}+1\right) x^{6}-2 \left(-x^{6}-x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}-2 \RootOf \left(\textit{\_Z}^{4}+1\right) x^{4}+2 \left(-x^{6}-x^{4}+1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}+1\right)}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right)}\right)}{8}-\frac{5 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{6}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{4}+2 \left(-x^{6}-x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}-2 \RootOf \left(\textit{\_Z}^{4}+1\right) \sqrt{-x^{6}-x^{4}+1}\, x^{2}+2 \left(-x^{6}-x^{4}+1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right)}\right)}{8}$&$308$\\ risch&$\frac{x \left(x^{6}+x^{4}-1\right)}{2 \left(x^{6}-1\right) \left(-x^{6}-x^{4}+1\right)^{\frac{1}{4}}}+\frac{5 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{6}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{4}+2 \left(-x^{6}-x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}+2 \RootOf \left(\textit{\_Z}^{4}+1\right) \sqrt{-x^{6}-x^{4}+1}\, x^{2}+2 \left(-x^{6}-x^{4}+1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right)}\right)}{8}+\frac{5 \RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{6}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \left(-x^{6}-x^{4}+1\right)^{\frac{1}{4}} x^{3}+2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{4}+2 \left(-x^{6}-x^{4}+1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right) x -2 x^{2} \sqrt{-x^{6}-x^{4}+1}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{2}}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+x +1\right) \left(x^{2}-x +1\right)}\right)}{8}$&$322$\\ \hline \end{longtable}"," ",0,"-1/2*x/(x^6-1)*(-x^6-x^4+1)^(3/4)-5/8*RootOf(_Z^4+1)*ln((-2*RootOf(_Z^4+1)^3*(-x^6-x^4+1)^(1/2)*x^2-RootOf(_Z^4+1)*x^6-2*(-x^6-x^4+1)^(1/4)*RootOf(_Z^4+1)^2*x^3-2*RootOf(_Z^4+1)*x^4+2*(-x^6-x^4+1)^(3/4)*x+RootOf(_Z^4+1))/(-1+x)/(1+x)/(x^2+x+1)/(x^2-x+1))-5/8*RootOf(_Z^4+1)^3*ln((-RootOf(_Z^4+1)^3*x^6-2*RootOf(_Z^4+1)^3*x^4+2*(-x^6-x^4+1)^(1/4)*RootOf(_Z^4+1)^2*x^3-2*RootOf(_Z^4+1)*(-x^6-x^4+1)^(1/2)*x^2+2*(-x^6-x^4+1)^(3/4)*x+RootOf(_Z^4+1)^3)/(-1+x)/(1+x)/(x^2+x+1)/(x^2-x+1))","C"
2003,0,0,111,0.021000," ","int((a*x^6-2*b)*(a*x^6-c*x^4+b)/x^2/(a*x^6+b)^(3/4)/(a*x^6+c*x^4+b),x)","\[\int \frac{\left(a \,x^{6}-2 b \right) \left(a \,x^{6}-c \,x^{4}+b \right)}{x^{2} \left(a \,x^{6}+b \right)^{\frac{3}{4}} \left(a \,x^{6}+c \,x^{4}+b \right)}\, dx\]"," ",0,"int((a*x^6-2*b)*(a*x^6-c*x^4+b)/x^2/(a*x^6+b)^(3/4)/(a*x^6+c*x^4+b),x)","F"
2004,0,0,115,0.012000," ","int((2*x^4+1)^(1/4)*(2*x^8-x^4-1)/x^6/(x^4+2),x)","\[\int \frac{\left(2 x^{4}+1\right)^{\frac{1}{4}} \left(2 x^{8}-x^{4}-1\right)}{x^{6} \left(x^{4}+2\right)}\, dx\]"," ",0,"int((2*x^4+1)^(1/4)*(2*x^8-x^4-1)/x^6/(x^4+2),x)","F"
2005,0,0,11,0.036000," ","int((2*a^4*x^4-b^8)/(a^4*x^4-b^8)^(1/4)/(a^8*x^8-b^8-c*x^4),x)","\[\int \frac{2 a^{4} x^{4}-b^{8}}{\left(a^{4} x^{4}-b^{8}\right)^{\frac{1}{4}} \left(a^{8} x^{8}-b^{8}-c \,x^{4}\right)}\, dx\]"," ",0,"int((2*a^4*x^4-b^8)/(a^4*x^4-b^8)^(1/4)/(a^8*x^8-b^8-c*x^4),x)","F"
2006,0,0,109,0.028000," ","int((x^2-1)/(x^2+1)/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{x^{2}-1}{\left(x^{2}+1\right) \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^2-1)/(x^2+1)/(x+(x^2+1)^(1/2))^(1/2),x)","F"
2007,1,1155,112,20.505000," ","int((x^2+1)*(2*x^3+x)^(1/3)/x^4/(x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1155$\\ risch&$\text{Expression too large to display}$&$1860$\\ \hline \end{longtable}"," ",0,"3/8*(10*x^2+1)*(2*x^3+x)^(1/3)/x^3-ln((102880*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)*RootOf(_Z^3-3)^4*x^2+6755328*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)^2*RootOf(_Z^3-3)^3*x^2+465408*(2*x^3+x)^(2/3)*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)*RootOf(_Z^3-3)^2-411520*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)*RootOf(_Z^3-3)^4-27021312*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)^2*RootOf(_Z^3-3)^3+28935*RootOf(_Z^3-3)^2*x^2+1899936*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)*RootOf(_Z^3-3)*x^2+32883*(2*x^3+x)^(1/3)*RootOf(_Z^3-3)*x+1396224*(2*x^3+x)^(1/3)*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)*x+32883*(2*x^3+x)^(2/3)+3215*RootOf(_Z^3-3)^2+211104*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)*RootOf(_Z^3-3))/(-1+x)/(1+x))*RootOf(_Z^3-3)-288*ln((102880*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)*RootOf(_Z^3-3)^4*x^2+6755328*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)^2*RootOf(_Z^3-3)^3*x^2+465408*(2*x^3+x)^(2/3)*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)*RootOf(_Z^3-3)^2-411520*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)*RootOf(_Z^3-3)^4-27021312*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)^2*RootOf(_Z^3-3)^3+28935*RootOf(_Z^3-3)^2*x^2+1899936*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)*RootOf(_Z^3-3)*x^2+32883*(2*x^3+x)^(1/3)*RootOf(_Z^3-3)*x+1396224*(2*x^3+x)^(1/3)*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)*x+32883*(2*x^3+x)^(2/3)+3215*RootOf(_Z^3-3)^2+211104*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)*RootOf(_Z^3-3))/(-1+x)/(1+x))*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)+288*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)*ln(-(238272*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)*RootOf(_Z^3-3)^4*x^2-20265984*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)^2*RootOf(_Z^3-3)^3*x^2+1396224*(2*x^3+x)^(2/3)*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)*RootOf(_Z^3-3)^2-953088*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)*RootOf(_Z^3-3)^4+81063936*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)^2*RootOf(_Z^3-3)^3-64532*RootOf(_Z^3-3)^2*x^2+5488704*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)*RootOf(_Z^3-3)*x^2-84105*(2*x^3+x)^(1/3)*RootOf(_Z^3-3)*x+4188672*(2*x^3+x)^(1/3)*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)*x-84105*(2*x^3+x)^(2/3)-17374*RootOf(_Z^3-3)^2+1477728*RootOf(RootOf(_Z^3-3)^2+288*_Z*RootOf(_Z^3-3)+82944*_Z^2)*RootOf(_Z^3-3))/(-1+x)/(1+x))","C"
2008,0,0,122,0.010000," ","int((a^3*x^3-b)*(a^3*x^3+b)^(1/3)/x^5,x)","\[\int \frac{\left(a^{3} x^{3}-b \right) \left(a^{3} x^{3}+b \right)^{\frac{1}{3}}}{x^{5}}\, dx\]"," ",0,"int((a^3*x^3-b)*(a^3*x^3+b)^(1/3)/x^5,x)","F"
2009,0,0,109,0.029000," ","int((a*x^2-3*b)/(-2*a*x^2+3*b)^(1/4)/(3*x^4-2*a*x^2+3*b),x)","\[\int \frac{a \,x^{2}-3 b}{\left(-2 a \,x^{2}+3 b \right)^{\frac{1}{4}} \left(3 x^{4}-2 a \,x^{2}+3 b \right)}\, dx\]"," ",0,"int((a*x^2-3*b)/(-2*a*x^2+3*b)^(1/4)/(3*x^4-2*a*x^2+3*b),x)","F"
2010,0,0,112,0.020000," ","int((a*x^5-4*b)*(a*x^5-c*x^4+b)/x^2/(a*x^5+b)^(3/4)/(a*x^5+c*x^4+b),x)","\[\int \frac{\left(a \,x^{5}-4 b \right) \left(a \,x^{5}-c \,x^{4}+b \right)}{x^{2} \left(a \,x^{5}+b \right)^{\frac{3}{4}} \left(a \,x^{5}+c \,x^{4}+b \right)}\, dx\]"," ",0,"int((a*x^5-4*b)*(a*x^5-c*x^4+b)/x^2/(a*x^5+b)^(3/4)/(a*x^5+c*x^4+b),x)","F"
2011,0,0,113,0.019000," ","int((x^3-1)*(x^6+1)^(2/3)*(x^6-x^3+1)/x^6/(x^3+1),x)","\[\int \frac{\left(x^{3}-1\right) \left(x^{6}+1\right)^{\frac{2}{3}} \left(x^{6}-x^{3}+1\right)}{x^{6} \left(x^{3}+1\right)}\, dx\]"," ",0,"int((x^3-1)*(x^6+1)^(2/3)*(x^6-x^3+1)/x^6/(x^3+1),x)","F"
2012,0,0,116,0.047000," ","int((a*x^2-b^2)^2*(b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2)^2,x)","\[\int \frac{\left(a \,x^{2}-b^{2}\right)^{2} \sqrt{b +\sqrt{a \,x^{2}+b^{2}}}}{\left(a \,x^{2}+b^{2}\right)^{2}}\, dx\]"," ",0,"int((a*x^2-b^2)^2*(b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2)^2,x)","F"
2013,1,935,113,19.348000," ","int((x^3+2)*(2*x^3+1)^(2/3)/x^6/(x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{46 x^{6}+31 x^{3}+4}{10 x^{5} \left(2 x^{3}+1\right)^{\frac{1}{3}}}+\RootOf \left(\textit{\_Z}^{3}-9\right) \ln \left(\frac{6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+81 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-9\right)^{3} x^{3}+135 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+81 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-9\right)^{2} x^{3}+21 \left(2 x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}-9\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+81 \textit{\_Z}^{2}\right) x +8 \left(2 x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-9\right)^{2} x^{2}+9 \left(2 x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+81 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-9\right) x^{2}-4 \RootOf \left(\textit{\_Z}^{3}-9\right) x^{3}-90 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+81 \textit{\_Z}^{2}\right) x^{3}-3 \left(2 x^{3}+1\right)^{\frac{2}{3}} x -2 \RootOf \left(\textit{\_Z}^{3}-9\right)-45 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+81 \textit{\_Z}^{2}\right)}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right)-\ln \left(-\frac{-6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+81 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-9\right)^{3} x^{3}+81 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+81 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-9\right)^{2} x^{3}+21 \left(2 x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}-9\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+81 \textit{\_Z}^{2}\right) x -\left(2 x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-9\right)^{2} x^{2}-72 \left(2 x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+81 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-9\right) x^{2}-10 \RootOf \left(\textit{\_Z}^{3}-9\right) x^{3}+135 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+81 \textit{\_Z}^{2}\right) x^{3}+24 \left(2 x^{3}+1\right)^{\frac{2}{3}} x -2 \RootOf \left(\textit{\_Z}^{3}-9\right)+27 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+81 \textit{\_Z}^{2}\right)}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right) \RootOf \left(\textit{\_Z}^{3}-9\right)-9 \ln \left(-\frac{-6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+81 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-9\right)^{3} x^{3}+81 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+81 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-9\right)^{2} x^{3}+21 \left(2 x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}-9\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+81 \textit{\_Z}^{2}\right) x -\left(2 x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-9\right)^{2} x^{2}-72 \left(2 x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+81 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-9\right) x^{2}-10 \RootOf \left(\textit{\_Z}^{3}-9\right) x^{3}+135 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+81 \textit{\_Z}^{2}\right) x^{3}+24 \left(2 x^{3}+1\right)^{\frac{2}{3}} x -2 \RootOf \left(\textit{\_Z}^{3}-9\right)+27 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+81 \textit{\_Z}^{2}\right)}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+9 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+81 \textit{\_Z}^{2}\right)$&$935$\\ trager&$\text{Expression too large to display}$&$1157$\\ \hline \end{longtable}"," ",0,"1/10*(46*x^6+31*x^3+4)/x^5/(2*x^3+1)^(1/3)+RootOf(_Z^3-9)*ln((6*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x^3+135*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x^3+21*(2*x^3+1)^(2/3)*RootOf(_Z^3-9)^2*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x+8*(2*x^3+1)^(1/3)*RootOf(_Z^3-9)^2*x^2+9*(2*x^3+1)^(1/3)*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)*x^2-4*RootOf(_Z^3-9)*x^3-90*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^3-3*(2*x^3+1)^(2/3)*x-2*RootOf(_Z^3-9)-45*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2))/(-1+x)/(x^2+x+1))-ln(-(-6*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x^3+81*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x^3+21*(2*x^3+1)^(2/3)*RootOf(_Z^3-9)^2*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x-(2*x^3+1)^(1/3)*RootOf(_Z^3-9)^2*x^2-72*(2*x^3+1)^(1/3)*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)*x^2-10*RootOf(_Z^3-9)*x^3+135*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^3+24*(2*x^3+1)^(2/3)*x-2*RootOf(_Z^3-9)+27*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2))/(-1+x)/(x^2+x+1))*RootOf(_Z^3-9)-9*ln(-(-6*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x^3+81*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x^3+21*(2*x^3+1)^(2/3)*RootOf(_Z^3-9)^2*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x-(2*x^3+1)^(1/3)*RootOf(_Z^3-9)^2*x^2-72*(2*x^3+1)^(1/3)*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)*x^2-10*RootOf(_Z^3-9)*x^3+135*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^3+24*(2*x^3+1)^(2/3)*x-2*RootOf(_Z^3-9)+27*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2))/(-1+x)/(x^2+x+1))*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)","C"
2014,1,321,123,246.136000," ","int((x^2-4)*(-2*x^4-x^2+2)^(1/4)/x^2/(x^2-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{2 \left(-2 x^{4}-x^{2}+2\right)^{\frac{1}{4}}}{x}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{4}-4 \left(-2 x^{4}-x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{3}-4 \sqrt{-2 x^{4}-x^{2}+2}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{2}+4 \left(-2 x^{4}-x^{2}+2\right)^{\frac{3}{4}} x -2 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right)}{x^{2}-2}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{4}+2\right) \ln \left(-\frac{-4 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} x^{4}+4 \left(-2 x^{4}-x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{3}-4 \sqrt{-2 x^{4}-x^{2}+2}\, \RootOf \left(\textit{\_Z}^{4}+2\right) x^{2}-\RootOf \left(\textit{\_Z}^{4}+2\right)^{3} x^{2}+4 \left(-2 x^{4}-x^{2}+2\right)^{\frac{3}{4}} x +2 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3}}{x^{2}-2}\right)}{2}$&$321$\\ risch&$\frac{4 x^{4}+2 x^{2}-4}{\left(-2 x^{4}-x^{2}+2\right)^{\frac{3}{4}} x}+\frac{\left(\frac{\RootOf \left(\textit{\_Z}^{4}+2\right) \ln \left(\frac{-16 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{12}+8 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} \left(-8 x^{12}-12 x^{10}+18 x^{8}+23 x^{6}-18 x^{4}-12 x^{2}+8\right)^{\frac{1}{4}} x^{9}-20 x^{10} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}+8 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} \left(-8 x^{12}-12 x^{10}+18 x^{8}+23 x^{6}-18 x^{4}-12 x^{2}+8\right)^{\frac{1}{4}} x^{7}+32 x^{8} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}-14 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} \left(-8 x^{12}-12 x^{10}+18 x^{8}+23 x^{6}-18 x^{4}-12 x^{2}+8\right)^{\frac{1}{4}} x^{5}+31 x^{6} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}+8 \sqrt{-8 x^{12}-12 x^{10}+18 x^{8}+23 x^{6}-18 x^{4}-12 x^{2}+8}\, x^{6}-8 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} \left(-8 x^{12}-12 x^{10}+18 x^{8}+23 x^{6}-18 x^{4}-12 x^{2}+8\right)^{\frac{1}{4}} x^{3}-4 \RootOf \left(\textit{\_Z}^{4}+2\right) \left(-8 x^{12}-12 x^{10}+18 x^{8}+23 x^{6}-18 x^{4}-12 x^{2}+8\right)^{\frac{3}{4}} x^{3}-26 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{4}+4 \sqrt{-8 x^{12}-12 x^{10}+18 x^{8}+23 x^{6}-18 x^{4}-12 x^{2}+8}\, x^{4}+8 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} \left(-8 x^{12}-12 x^{10}+18 x^{8}+23 x^{6}-18 x^{4}-12 x^{2}+8\right)^{\frac{1}{4}} x -12 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{2}-8 \sqrt{-8 x^{12}-12 x^{10}+18 x^{8}+23 x^{6}-18 x^{4}-12 x^{2}+8}\, x^{2}+8 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}}{\left(x^{2}-2\right) \left(2 x^{4}+x^{2}-2\right)^{2}}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \ln \left(\frac{16 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{12}+8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \left(-8 x^{12}-12 x^{10}+18 x^{8}+23 x^{6}-18 x^{4}-12 x^{2}+8\right)^{\frac{1}{4}} x^{9}+20 x^{10} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}+8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \left(-8 x^{12}-12 x^{10}+18 x^{8}+23 x^{6}-18 x^{4}-12 x^{2}+8\right)^{\frac{1}{4}} x^{7}-32 x^{8} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}-14 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \left(-8 x^{12}-12 x^{10}+18 x^{8}+23 x^{6}-18 x^{4}-12 x^{2}+8\right)^{\frac{1}{4}} x^{5}-31 x^{6} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}+8 \sqrt{-8 x^{12}-12 x^{10}+18 x^{8}+23 x^{6}-18 x^{4}-12 x^{2}+8}\, x^{6}-8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \left(-8 x^{12}-12 x^{10}+18 x^{8}+23 x^{6}-18 x^{4}-12 x^{2}+8\right)^{\frac{1}{4}} x^{3}+4 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \left(-8 x^{12}-12 x^{10}+18 x^{8}+23 x^{6}-18 x^{4}-12 x^{2}+8\right)^{\frac{3}{4}} x^{3}+26 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{4}+4 \sqrt{-8 x^{12}-12 x^{10}+18 x^{8}+23 x^{6}-18 x^{4}-12 x^{2}+8}\, x^{4}+8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \left(-8 x^{12}-12 x^{10}+18 x^{8}+23 x^{6}-18 x^{4}-12 x^{2}+8\right)^{\frac{1}{4}} x +12 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{2}-8 \sqrt{-8 x^{12}-12 x^{10}+18 x^{8}+23 x^{6}-18 x^{4}-12 x^{2}+8}\, x^{2}-8 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}}{\left(x^{2}-2\right) \left(2 x^{4}+x^{2}-2\right)^{2}}\right)}{2}\right) \left(-\left(2 x^{4}+x^{2}-2\right)^{3}\right)^{\frac{1}{4}}}{\left(-2 x^{4}-x^{2}+2\right)^{\frac{3}{4}}}$&$1168$\\ \hline \end{longtable}"," ",0,"-2*(-2*x^4-x^2+2)^(1/4)/x-1/2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*ln(-(4*RootOf(_Z^4+2)^2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*x^4-4*(-2*x^4-x^2+2)^(1/4)*RootOf(_Z^4+2)^2*x^3-4*(-2*x^4-x^2+2)^(1/2)*RootOf(_Z^2+RootOf(_Z^4+2)^2)*x^2+RootOf(_Z^4+2)^2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*x^2+4*(-2*x^4-x^2+2)^(3/4)*x-2*RootOf(_Z^4+2)^2*RootOf(_Z^2+RootOf(_Z^4+2)^2))/(x^2-2))-1/2*RootOf(_Z^4+2)*ln(-(-4*RootOf(_Z^4+2)^3*x^4+4*(-2*x^4-x^2+2)^(1/4)*RootOf(_Z^4+2)^2*x^3-4*(-2*x^4-x^2+2)^(1/2)*RootOf(_Z^4+2)*x^2-RootOf(_Z^4+2)^3*x^2+4*(-2*x^4-x^2+2)^(3/4)*x+2*RootOf(_Z^4+2)^3)/(x^2-2))","C"
2015,1,118,118,0.357000," ","int(1/(1+x)/(-x^4+x^2+2*x-2)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x^{3}-2 x^{2}-2 x +4}{20 \left(-1+x \right) \sqrt{-\left(x^{2}+2 x +2\right) \left(-1+x \right)^{2}}}-\frac{\left(\frac{7 \sqrt{5}\, \arctan \left(\frac{\left(-6-4 x \right) \sqrt{5}}{10 \sqrt{-\left(-1+x \right)^{2}-1-4 x}}\right)}{200}+\frac{\arctan \left(\frac{1}{\sqrt{-\left(1+x \right)^{2}-1}}\right)}{8}\right) \left(-1+x \right) \sqrt{-x^{2}-2 x -2}}{\sqrt{-\left(x^{2}+2 x +2\right) \left(-1+x \right)^{2}}}$&$118$\\ trager&$-\frac{\left(x^{3}-2 x^{2}-2 x +4\right) \sqrt{-x^{4}+x^{2}+2 x -2}}{20 \left(-1+x \right)^{3} \left(x^{2}+2 x +2\right)}-\frac{7 \RootOf \left(\textit{\_Z}^{2}+5\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+5\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+5\right) x +5 \sqrt{-x^{4}+x^{2}+2 x -2}-3 \RootOf \left(\textit{\_Z}^{2}+5\right)}{\left(-1+x \right)^{2}}\right)}{200}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x +\sqrt{-x^{4}+x^{2}+2 x -2}-\RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(-1+x \right) \left(1+x \right)}\right)}{8}$&$160$\\ default&$\frac{\left(-7 \arctan \left(\frac{\left(3+2 x \right) \sqrt{5}}{5 \sqrt{-x^{2}-2 x -2}}\right) \sqrt{-x^{2}-2 x -2}\, \sqrt{5}\, x^{2}+25 \arctan \left(\frac{1}{\sqrt{-x^{2}-2 x -2}}\right) \sqrt{-x^{2}-2 x -2}\, x^{2}+14 \arctan \left(\frac{\left(3+2 x \right) \sqrt{5}}{5 \sqrt{-x^{2}-2 x -2}}\right) \sqrt{-x^{2}-2 x -2}\, \sqrt{5}\, x -50 \arctan \left(\frac{1}{\sqrt{-x^{2}-2 x -2}}\right) \sqrt{-x^{2}-2 x -2}\, x -7 \sqrt{5}\, \arctan \left(\frac{\left(3+2 x \right) \sqrt{5}}{5 \sqrt{-x^{2}-2 x -2}}\right) \sqrt{-x^{2}-2 x -2}-10 x^{3}+25 \arctan \left(\frac{1}{\sqrt{-x^{2}-2 x -2}}\right) \sqrt{-x^{2}-2 x -2}+20 x^{2}+20 x -40\right) \left(-1+x \right) \left(x^{2}+2 x +2\right)}{200 \left(-x^{4}+x^{2}+2 x -2\right)^{\frac{3}{2}}}$&$253$\\ \hline \end{longtable}"," ",0,"1/20*(x^3-2*x^2-2*x+4)/(-1+x)/(-(x^2+2*x+2)*(-1+x)^2)^(1/2)-(7/200*5^(1/2)*arctan(1/10*(-6-4*x)*5^(1/2)/(-(-1+x)^2-1-4*x)^(1/2))+1/8*arctan(1/(-(1+x)^2-1)^(1/2)))*(-1+x)*(-x^2-2*x-2)^(1/2)/(-(x^2+2*x+2)*(-1+x)^2)^(1/2)","A"
2016,1,664,107,114.843000," ","int((2*x^4-3)*(2*x^4+1)^(2/3)/x^3/(4*x^4-x^3+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 \left(2 x^{4}+1\right)^{\frac{2}{3}}}{4 x^{2}}+\frac{\RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(\frac{2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{3}-2\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{3}-2 \left(2 x^{4}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x -2 \left(2 x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right) x^{2}+8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{4}+\left(2 x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{2}+4 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{4}+2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{3}+\RootOf \left(\textit{\_Z}^{3}-2\right) x^{3}-4 \left(2 x^{4}+1\right)^{\frac{2}{3}} x +4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)+2 \RootOf \left(\textit{\_Z}^{3}-2\right)}{4 x^{4}-x^{3}+2}\right)}{4}+\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) \ln \left(-\frac{2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{3}-2\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{3}-2 \left(2 x^{4}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x +4 \left(2 x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right) x^{2}-8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{4}+\left(2 x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{2}-4 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{4}+2 \left(2 x^{4}+1\right)^{\frac{2}{3}} x -4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)-2 \RootOf \left(\textit{\_Z}^{3}-2\right)}{4 x^{4}-x^{3}+2}\right)}{2}$&$664$\\ trager&$\text{Expression too large to display}$&$1485$\\ \hline \end{longtable}"," ",0,"3/4*(2*x^4+1)^(2/3)/x^2+1/4*RootOf(_Z^3-2)*ln((2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3+RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3-2*(2*x^4+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x-2*(2*x^4+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^2+8*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^4+(2*x^4+1)^(1/3)*RootOf(_Z^3-2)^2*x^2+4*RootOf(_Z^3-2)*x^4+2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3+RootOf(_Z^3-2)*x^3-4*(2*x^4+1)^(2/3)*x+4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)+2*RootOf(_Z^3-2))/(4*x^4-x^3+2))+1/2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*ln(-(2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3+RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3-2*(2*x^4+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x+4*(2*x^4+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^2-8*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^4+(2*x^4+1)^(1/3)*RootOf(_Z^3-2)^2*x^2-4*RootOf(_Z^3-2)*x^4+2*(2*x^4+1)^(2/3)*x-4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)-2*RootOf(_Z^3-2))/(4*x^4-x^3+2))","C"
2017,0,0,115,0.013000," ","int((a*x^3-b)/x^6/(a*x^3+b)/(a*x^4-b*x)^(1/4),x)","\[\int \frac{a \,x^{3}-b}{x^{6} \left(a \,x^{3}+b \right) \left(a \,x^{4}-b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^3-b)/x^6/(a*x^3+b)/(a*x^4-b*x)^(1/4),x)","F"
2018,1,765,110,16.733000," ","int((x^3-1)^(2/3)*(x^6+4*x^3+4)/x^9/(x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(2 x^{6}-2 x^{3}+5\right) \left(x^{3}-1\right)^{\frac{2}{3}}}{10 x^{8}}+512 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+2359296 \textit{\_Z}^{2}\right) \ln \left(\frac{10384382361600 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+2359296 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}+21928657152 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+2359296 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}-394193756160 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+2359296 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x -1588743277056 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+2359296 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-513273120 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{2}-83075058892800 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+2359296 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}-175429257216 \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+2359296 \textit{\_Z}^{2}\right)-743673216000 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+2359296 \textit{\_Z}^{2}\right) x^{3}-1570411645 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}-1042129902 x \left(x^{3}-1\right)^{\frac{2}{3}}+310990617600 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+2359296 \textit{\_Z}^{2}\right)+656717597 \RootOf \left(\textit{\_Z}^{3}+4\right)}{\left(1+x \right) \left(x^{2}-x +1\right)}\right)+\frac{\RootOf \left(\textit{\_Z}^{3}+4\right) \ln \left(-\frac{16841208692736 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+2359296 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}+3380332800 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+2359296 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}-197096878080 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+2359296 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +400177882368 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+2359296 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-256636560 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{2}-134729669541888 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+2359296 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}-27042662400 \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+2359296 \textit{\_Z}^{2}\right)+1162218829056 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+2359296 \textit{\_Z}^{2}\right) x^{3}+233278175 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}+1034338071 x \left(x^{3}-1\right)^{\frac{2}{3}}-153500600064 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+2359296 \textit{\_Z}^{2}\right)-30810325 \RootOf \left(\textit{\_Z}^{3}+4\right)}{\left(1+x \right) \left(x^{2}-x +1\right)}\right)}{3}$&$765$\\ risch&$-\frac{2 x^{9}-4 x^{6}+7 x^{3}-5}{10 x^{8} \left(x^{3}-1\right)^{\frac{1}{3}}}-\frac{\ln \left(-\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}-36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}+12 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +\left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{2}+30 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}-3 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}+36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) x^{3}-10 x \left(x^{3}-1\right)^{\frac{2}{3}}+\RootOf \left(\textit{\_Z}^{3}+4\right)-12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)}{\left(1+x \right) \left(x^{2}-x +1\right)}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)}{3}-2 \ln \left(-\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}-36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}+12 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +\left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{2}+30 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}-3 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}+36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) x^{3}-10 x \left(x^{3}-1\right)^{\frac{2}{3}}+\RootOf \left(\textit{\_Z}^{3}+4\right)-12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)}{\left(1+x \right) \left(x^{2}-x +1\right)}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)+\frac{\RootOf \left(\textit{\_Z}^{3}+4\right) \ln \left(-\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}+54 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}-12 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +5 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{2}+6 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}+\RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}+18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) x^{3}-2 x \left(x^{3}-1\right)^{\frac{2}{3}}-\RootOf \left(\textit{\_Z}^{3}+4\right)-18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)}{\left(1+x \right) \left(x^{2}-x +1\right)}\right)}{3}$&$915$\\ \hline \end{longtable}"," ",0,"-1/10*(2*x^6-2*x^3+5)/x^8*(x^3-1)^(2/3)+512*RootOf(RootOf(_Z^3+4)^2+1536*_Z*RootOf(_Z^3+4)+2359296*_Z^2)*ln((10384382361600*RootOf(RootOf(_Z^3+4)^2+1536*_Z*RootOf(_Z^3+4)+2359296*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+21928657152*RootOf(RootOf(_Z^3+4)^2+1536*_Z*RootOf(_Z^3+4)+2359296*_Z^2)*RootOf(_Z^3+4)^3*x^3-394193756160*(x^3-1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+1536*_Z*RootOf(_Z^3+4)+2359296*_Z^2)*RootOf(_Z^3+4)^2*x-1588743277056*RootOf(RootOf(_Z^3+4)^2+1536*_Z*RootOf(_Z^3+4)+2359296*_Z^2)*RootOf(_Z^3+4)*(x^3-1)^(1/3)*x^2-513273120*(x^3-1)^(1/3)*RootOf(_Z^3+4)^2*x^2-83075058892800*RootOf(RootOf(_Z^3+4)^2+1536*_Z*RootOf(_Z^3+4)+2359296*_Z^2)^2*RootOf(_Z^3+4)^2-175429257216*RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+1536*_Z*RootOf(_Z^3+4)+2359296*_Z^2)-743673216000*RootOf(RootOf(_Z^3+4)^2+1536*_Z*RootOf(_Z^3+4)+2359296*_Z^2)*x^3-1570411645*RootOf(_Z^3+4)*x^3-1042129902*x*(x^3-1)^(2/3)+310990617600*RootOf(RootOf(_Z^3+4)^2+1536*_Z*RootOf(_Z^3+4)+2359296*_Z^2)+656717597*RootOf(_Z^3+4))/(1+x)/(x^2-x+1))+1/3*RootOf(_Z^3+4)*ln(-(16841208692736*RootOf(RootOf(_Z^3+4)^2+1536*_Z*RootOf(_Z^3+4)+2359296*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+3380332800*RootOf(RootOf(_Z^3+4)^2+1536*_Z*RootOf(_Z^3+4)+2359296*_Z^2)*RootOf(_Z^3+4)^3*x^3-197096878080*(x^3-1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+1536*_Z*RootOf(_Z^3+4)+2359296*_Z^2)*RootOf(_Z^3+4)^2*x+400177882368*RootOf(RootOf(_Z^3+4)^2+1536*_Z*RootOf(_Z^3+4)+2359296*_Z^2)*RootOf(_Z^3+4)*(x^3-1)^(1/3)*x^2-256636560*(x^3-1)^(1/3)*RootOf(_Z^3+4)^2*x^2-134729669541888*RootOf(RootOf(_Z^3+4)^2+1536*_Z*RootOf(_Z^3+4)+2359296*_Z^2)^2*RootOf(_Z^3+4)^2-27042662400*RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+1536*_Z*RootOf(_Z^3+4)+2359296*_Z^2)+1162218829056*RootOf(RootOf(_Z^3+4)^2+1536*_Z*RootOf(_Z^3+4)+2359296*_Z^2)*x^3+233278175*RootOf(_Z^3+4)*x^3+1034338071*x*(x^3-1)^(2/3)-153500600064*RootOf(RootOf(_Z^3+4)^2+1536*_Z*RootOf(_Z^3+4)+2359296*_Z^2)-30810325*RootOf(_Z^3+4))/(1+x)/(x^2-x+1))","C"
2019,1,908,110,17.035000," ","int((x^3+1)^(2/3)*(2*x^6-2*x^3-1)/x^9/(x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{41 x^{9}+67 x^{6}+31 x^{3}+5}{40 x^{8} \left(x^{3}+1\right)^{\frac{1}{3}}}+\frac{\RootOf \left(\textit{\_Z}^{3}+4\right) \ln \left(\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}+54 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}-12 \left(x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +5 \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}+6 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}+\RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}+18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) x^{3}-2 x \left(x^{3}+1\right)^{\frac{2}{3}}+\RootOf \left(\textit{\_Z}^{3}+4\right)+18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right)}{3}-\frac{\ln \left(\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}-36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}+12 \left(x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +\RootOf \left(\textit{\_Z}^{3}+4\right)^{2} \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}+30 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}-3 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}+36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) x^{3}-10 x \left(x^{3}+1\right)^{\frac{2}{3}}-\RootOf \left(\textit{\_Z}^{3}+4\right)+12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)}{3}-2 \ln \left(\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}-36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}+12 \left(x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +\RootOf \left(\textit{\_Z}^{3}+4\right)^{2} \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}+30 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}-3 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}+36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) x^{3}-10 x \left(x^{3}+1\right)^{\frac{2}{3}}-\RootOf \left(\textit{\_Z}^{3}+4\right)+12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)$&$908$\\ trager&$\text{Expression too large to display}$&$1121$\\ \hline \end{longtable}"," ",0,"-1/40*(41*x^9+67*x^6+31*x^3+5)/x^8/(x^3+1)^(1/3)+1/3*RootOf(_Z^3+4)*ln((3*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3*x^3+54*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2*x^3-12*(x^3+1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*x+5*RootOf(_Z^3+4)^2*(x^3+1)^(1/3)*x^2+6*(x^3+1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)*x^2+RootOf(_Z^3+4)*x^3+18*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^3-2*x*(x^3+1)^(2/3)+RootOf(_Z^3+4)+18*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2))/(-1+x)/(x^2+x+1))-1/3*ln((3*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3*x^3-36*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+12*(x^3+1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*x+RootOf(_Z^3+4)^2*(x^3+1)^(1/3)*x^2+30*(x^3+1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)*x^2-3*RootOf(_Z^3+4)*x^3+36*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^3-10*x*(x^3+1)^(2/3)-RootOf(_Z^3+4)+12*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2))/(-1+x)/(x^2+x+1))*RootOf(_Z^3+4)-2*ln((3*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3*x^3-36*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+12*(x^3+1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*x+RootOf(_Z^3+4)^2*(x^3+1)^(1/3)*x^2+30*(x^3+1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)*x^2-3*RootOf(_Z^3+4)*x^3+36*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^3-10*x*(x^3+1)^(2/3)-RootOf(_Z^3+4)+12*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2))/(-1+x)/(x^2+x+1))*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)","C"
2020,0,0,14,0.032000," ","int(1/(a^4*x^4-b^4)^(1/4)/(a^8*x^8-b^8-c*x^4),x)","\[\int \frac{1}{\left(a^{4} x^{4}-b^{4}\right)^{\frac{1}{4}} \left(a^{8} x^{8}-b^{8}-c \,x^{4}\right)}\, dx\]"," ",0,"int(1/(a^4*x^4-b^4)^(1/4)/(a^8*x^8-b^8-c*x^4),x)","F"
2021,0,0,14,0.003000," ","int(1/(a^4*x^4-b^4)^(1/4)/(a^8*x^8-b^8-c*x^4),x)","\[\int \frac{1}{\left(a^{4} x^{4}-b^{4}\right)^{\frac{1}{4}} \left(a^{8} x^{8}-b^{8}-c \,x^{4}\right)}\, dx\]"," ",0,"int(1/(a^4*x^4-b^4)^(1/4)/(a^8*x^8-b^8-c*x^4),x)","F"
2022,0,0,104,0.025000," ","int((x-(x^2+1)^(1/2))/(1+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{x -\sqrt{x^{2}+1}}{\sqrt{1+\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x-(x^2+1)^(1/2))/(1+(x^2+1)^(1/2))^(1/2),x)","F"
2023,1,563,110,16.543000," ","int((x^3-4)*(x^3-2)*(x^3-1)^(2/3)/x^9/(3*x^3-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{16 x^{9}-12 x^{6}+x^{3}-5}{10 x^{8} \left(x^{3}-1\right)^{\frac{1}{3}}}+\frac{5 \RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} x^{3}-18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}+18 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x +3 \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+18 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right) x^{2}-\RootOf \left(\textit{\_Z}^{3}-2\right) x^{3}+6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) x^{3}+2 \RootOf \left(\textit{\_Z}^{3}-2\right)-12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)}{3 x^{3}-2}\right)}{6}+5 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \ln \left(\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} x^{3}-18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}-18 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x -3 \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+2 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{3}-12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) x^{3}-6 x \left(x^{3}-1\right)^{\frac{2}{3}}-2 \RootOf \left(\textit{\_Z}^{3}-2\right)+12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)}{3 x^{3}-2}\right)$&$563$\\ trager&$\frac{\left(x^{3}-1\right)^{\frac{2}{3}} \left(16 x^{6}+4 x^{3}+5\right)}{10 x^{8}}+1280 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+2359296 \textit{\_Z}^{2}\right) \ln \left(-\frac{104988672 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+2359296 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}+41088 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+2359296 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} x^{3}+958464 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+2359296 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x +1421568 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+2359296 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+624 \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-839909376 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+2359296 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-328704 \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+2359296 \textit{\_Z}^{2}\right)-1367040 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+2359296 \textit{\_Z}^{2}\right) x^{3}-535 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{3}-603 x \left(x^{3}-1\right)^{\frac{2}{3}}+820224 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+2359296 \textit{\_Z}^{2}\right)+321 \RootOf \left(\textit{\_Z}^{3}-2\right)}{3 x^{3}-2}\right)+\frac{5 \RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(-\frac{43080155136 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+2359296 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}+75406080 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+2359296 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} x^{3}+711751680 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+2359296 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x -891088128 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+2359296 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+463380 \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-344641241088 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+2359296 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-603248640 \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+2359296 \textit{\_Z}^{2}\right)+617033472 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+2359296 \textit{\_Z}^{2}\right) x^{3}+1080035 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{3}+2087031 x \left(x^{3}-1\right)^{\frac{2}{3}}-785315328 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+1536 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+2359296 \textit{\_Z}^{2}\right)-1374590 \RootOf \left(\textit{\_Z}^{3}-2\right)}{3 x^{3}-2}\right)}{6}$&$754$\\ \hline \end{longtable}"," ",0,"1/10*(16*x^9-12*x^6+x^3-5)/x^8/(x^3-1)^(1/3)+5/6*RootOf(_Z^3-2)*ln((3*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^3-18*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^3+18*(x^3-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^2*x+3*RootOf(_Z^3-2)^2*(x^3-1)^(1/3)*x^2+18*(x^3-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)*x^2-RootOf(_Z^3-2)*x^3+6*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^3+2*RootOf(_Z^3-2)-12*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2))/(3*x^3-2))+5*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*ln((3*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^3-18*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-18*(x^3-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^2*x-3*RootOf(_Z^3-2)^2*(x^3-1)^(1/3)*x^2+2*RootOf(_Z^3-2)*x^3-12*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^3-6*x*(x^3-1)^(2/3)-2*RootOf(_Z^3-2)+12*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2))/(3*x^3-2))","C"
2024,1,111,121,0.350000," ","int(1/(-1+x)/(x^4-3*x^3-2*x^2)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{453 x^{3}-1555 x^{2}-238 x +136}{544 x \sqrt{x^{2} \left(x^{2}-3 x -2\right)}}+\frac{\left(-\frac{\arctan \left(\frac{-7-x}{4 \sqrt{\left(-1+x \right)^{2}-3-x}}\right)}{8}+\frac{119 \sqrt{2}\, \arctan \left(\frac{\left(-4-3 x \right) \sqrt{2}}{4 \sqrt{x^{2}-3 x -2}}\right)}{128}\right) x \sqrt{x^{2}-3 x -2}}{\sqrt{x^{2} \left(x^{2}-3 x -2\right)}}$&$111$\\ default&$-\frac{x \left(x^{2}-3 x -2\right) \left(2023 \sqrt{2}\, \arctan \left(\frac{\left(4+3 x \right) \sqrt{2}}{4 \sqrt{x^{2}-3 x -2}}\right) x^{2} \sqrt{x^{2}-3 x -2}-272 \arctan \left(\frac{7+x}{4 \sqrt{x^{2}-3 x -2}}\right) x^{2} \sqrt{x^{2}-3 x -2}+1812 x^{3}-6220 x^{2}-952 x +544\right)}{2176 \left(x^{4}-3 x^{3}-2 x^{2}\right)^{\frac{3}{2}}}$&$113$\\ trager&$-\frac{\left(453 x^{3}-1555 x^{2}-238 x +136\right) \sqrt{x^{4}-3 x^{3}-2 x^{2}}}{544 \left(x^{2}-3 x -2\right) x^{3}}+\frac{119 \RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{3 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{2}+4 \RootOf \left(\textit{\_Z}^{2}+2\right) x +4 \sqrt{x^{4}-3 x^{3}-2 x^{2}}}{x^{2}}\right)}{128}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+7 \RootOf \left(\textit{\_Z}^{2}+1\right) x +4 \sqrt{x^{4}-3 x^{3}-2 x^{2}}}{x \left(-1+x \right)}\right)}{8}$&$156$\\ \hline \end{longtable}"," ",0,"-1/544*(453*x^3-1555*x^2-238*x+136)/x/(x^2*(x^2-3*x-2))^(1/2)+(-1/8*arctan(1/4*(-7-x)/((-1+x)^2-3-x)^(1/2))+119/128*2^(1/2)*arctan(1/4*(-4-3*x)*2^(1/2)/(x^2-3*x-2)^(1/2)))*x*(x^2-3*x-2)^(1/2)/(x^2*(x^2-3*x-2))^(1/2)","A"
2025,0,0,112,0.042000," ","int(1/(2*a*x^3+b)/(a*x^4+b*x)^(1/4),x)","\[\int \frac{1}{\left(2 a \,x^{3}+b \right) \left(a \,x^{4}+b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(2*a*x^3+b)/(a*x^4+b*x)^(1/4),x)","F"
2026,1,1486,108,61.097000," ","int((-x^7+1)^(1/3)*(2*x^7+x^3-2)*(4*x^7+3)/x^2/(x^7-1)/(4*x^7+x^3-4),x)","\[\text{Expression too large to display}\]"," ",0,"-3/2*(x^7-1)/x/(-x^7+1)^(2/3)+(1/4*RootOf(_Z^3+2)*ln((4*RootOf(_Z^3+2)*x^14+4*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^14+RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^10+RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^10-3*(x^14-2*x^7+1)^(1/3)*RootOf(_Z^3+2)^2*x^8-RootOf(_Z^3+2)*x^10-RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^10-8*RootOf(_Z^3+2)*x^7-8*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^7-RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^3-RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^3-3*(x^14-2*x^7+1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x^2+3*(x^14-2*x^7+1)^(1/3)*RootOf(_Z^3+2)^2*x+RootOf(_Z^3+2)*x^3+RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^3+4*RootOf(_Z^3+2)+4*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2))/(-1+x)/(4*x^7+x^3-4)/(x^6+x^5+x^4+x^3+x^2+x+1))-1/4*ln((-4*RootOf(_Z^3+2)*x^14-4*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^14+RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^10+RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^10-6*(x^14-2*x^7+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^8+8*RootOf(_Z^3+2)*x^7+8*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^7-RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^3-RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^3+3*(x^14-2*x^7+1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x^2+6*(x^14-2*x^7+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x-3*(x^14-2*x^7+1)^(2/3)*x^2-4*RootOf(_Z^3+2)-4*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2))/(-1+x)/(4*x^7+x^3-4)/(x^6+x^5+x^4+x^3+x^2+x+1))*RootOf(_Z^3+2)-1/2*ln((-4*RootOf(_Z^3+2)*x^14-4*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^14+RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^10+RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^10-6*(x^14-2*x^7+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^8+8*RootOf(_Z^3+2)*x^7+8*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^7-RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^3-RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^3+3*(x^14-2*x^7+1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x^2+6*(x^14-2*x^7+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x-3*(x^14-2*x^7+1)^(2/3)*x^2-4*RootOf(_Z^3+2)-4*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2))/(-1+x)/(4*x^7+x^3-4)/(x^6+x^5+x^4+x^3+x^2+x+1))*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2))/(-x^7+1)^(2/3)*((x^7-1)^2)^(1/3)","C"
2027,1,110,47,0.128000," ","int((x^2-1)*(x^2+1)^3*((x^2+1)^2)^(1/2)/(x^4+1)/(x^8-x^6+x^4-x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\sqrt{\left(x^{2}+1\right)^{2}}\, \sqrt{2}\, \ln \left(x^{2}+\sqrt{2}\, x +1\right)}{x^{2}+1}-\frac{\sqrt{\left(x^{2}+1\right)^{2}}\, \sqrt{2}\, \ln \left(x^{2}-\sqrt{2}\, x +1\right)}{x^{2}+1}+\frac{\sqrt{\left(x^{2}+1\right)^{2}}\, \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-5 \textit{\_Z}^{2}+5\right)}{\sum}\textit{\_R} \ln \left(-\textit{\_R} x +x^{2}+1\right)\right)}{2 x^{2}+2}$&$110$\\ default&$\frac{\sqrt{\left(x^{2}+1\right)^{2}}\, \left(\sqrt{2}\, \ln \left(-\frac{x^{2}+\sqrt{2}\, x +1}{\sqrt{2}\, x -x^{2}-1}\right)-\sqrt{2}\, \ln \left(-\frac{\sqrt{2}\, x -x^{2}-1}{x^{2}+\sqrt{2}\, x +1}\right)+5 \left(\munderset{\textit{\_R} =\RootOf \left(125 \textit{\_Z}^{4}-25 \textit{\_Z}^{2}+1\right)}{\sum}\textit{\_R} \ln \left(-5 \textit{\_R} x +x^{2}+1\right)\right)\right)}{2 x^{2}+2}$&$113$\\ \hline \end{longtable}"," ",0,"((x^2+1)^2)^(1/2)/(x^2+1)*2^(1/2)*ln(x^2+2^(1/2)*x+1)-((x^2+1)^2)^(1/2)/(x^2+1)*2^(1/2)*ln(x^2-2^(1/2)*x+1)+1/2*((x^2+1)^2)^(1/2)/(x^2+1)*sum(_R*ln(-_R*x+x^2+1),_R=RootOf(_Z^4-5*_Z^2+5))","B"
2028,1,31,107,0.043000," ","int(1/x^2/(b+(a*x^2+b^2)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{2}\, \hypergeom \left(\left[-\frac{1}{2}, \frac{1}{4}, \frac{3}{4}\right], \left[\frac{1}{2}, \frac{3}{2}\right], -\frac{x^{2} a}{b^{2}}\right)}{2 \left(b^{2}\right)^{\frac{1}{4}} x}$&$31$\\ \hline \end{longtable}"," ",0,"-1/2/(b^2)^(1/4)*2^(1/2)/x*hypergeom([-1/2,1/4,3/4],[1/2,3/2],-x^2*a/b^2)","C"
2029,0,0,109,0.027000," ","int((a*x^3-b)^(1/4)/x,x)","\[\int \frac{\left(a \,x^{3}-b \right)^{\frac{1}{4}}}{x}\, dx\]"," ",0,"int((a*x^3-b)^(1/4)/x,x)","F"
2030,0,0,109,0.025000," ","int((a*x^3-b)^(3/4)/x,x)","\[\int \frac{\left(a \,x^{3}-b \right)^{\frac{3}{4}}}{x}\, dx\]"," ",0,"int((a*x^3-b)^(3/4)/x,x)","F"
2031,1,669,109,95.826000," ","int((x^4-1)^(2/3)*(x^4+3)*(x^4-x^3-1)/x^6/(2*x^4-x^3-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\frac{3}{10} x^{8}-\frac{3}{5} x^{4}+\frac{3}{10}-\frac{3}{8} x^{7}+\frac{3}{8} x^{3}}{x^{5} \left(x^{4}-1\right)^{\frac{1}{3}}}+\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right) \ln \left(\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right)^{3} x^{3}+2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+2\right)^{2} x^{3}+2 \left(x^{4}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right)^{2} x +\left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+2\right)^{2} x^{2}+4 \left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right) x^{2}+2 \RootOf \left(\textit{\_Z}^{3}+2\right) x^{4}+4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right) x^{4}+2 \left(x^{4}-1\right)^{\frac{2}{3}} x -2 \RootOf \left(\textit{\_Z}^{3}+2\right)-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right)}{2 x^{4}-x^{3}-2}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{3}+2\right) \ln \left(-\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right)^{3} x^{3}+2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+2\right)^{2} x^{3}+2 \left(x^{4}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right)^{2} x +\left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+2\right)^{2} x^{2}-2 \left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+2\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{3}+2\right) x^{4}-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right) x^{4}-\RootOf \left(\textit{\_Z}^{3}+2\right) x^{3}-2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right) x^{3}-4 \left(x^{4}-1\right)^{\frac{2}{3}} x +2 \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+2\right)+4 \textit{\_Z}^{2}\right)}{2 x^{4}-x^{3}-2}\right)}{8}$&$669$\\ trager&$\text{Expression too large to display}$&$1471$\\ \hline \end{longtable}"," ",0,"3/40*(4*x^8-5*x^7-8*x^4+5*x^3+4)/x^5/(x^4-1)^(1/3)+1/4*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*ln((RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^3+2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^3+2*(x^4-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x+(x^4-1)^(1/3)*RootOf(_Z^3+2)^2*x^2+4*(x^4-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^2+2*RootOf(_Z^3+2)*x^4+4*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^4+2*(x^4-1)^(2/3)*x-2*RootOf(_Z^3+2)-4*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2))/(2*x^4-x^3-2))+1/8*RootOf(_Z^3+2)*ln(-(RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^3+2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^3+2*(x^4-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x+(x^4-1)^(1/3)*RootOf(_Z^3+2)^2*x^2-2*(x^4-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^2-2*RootOf(_Z^3+2)*x^4-4*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^4-RootOf(_Z^3+2)*x^3-2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^3-4*(x^4-1)^(2/3)*x+2*RootOf(_Z^3+2)+4*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2))/(2*x^4-x^3-2))","C"
2032,0,0,109,0.024000," ","int((a*x^4-b)^(3/4)/x,x)","\[\int \frac{\left(a \,x^{4}-b \right)^{\frac{3}{4}}}{x}\, dx\]"," ",0,"int((a*x^4-b)^(3/4)/x,x)","F"
2033,0,0,133,0.022000," ","int((-3*a*b^3+2*b^2*(3*a+b)*x-3*b*(a+b)*x^2+x^4)/(x*(-a+x)*(-b+x)^3)^(1/4)/(a*b^3*d-b^2*(3*a+b)*d*x+3*b*(a+b)*d*x^2-(a*d+3*b*d+1)*x^3+d*x^4),x)","\[\int \frac{-3 a \,b^{3}+2 b^{2} \left(3 a +b \right) x -3 b \left(a +b \right) x^{2}+x^{4}}{\left(x \left(-a +x \right) \left(-b +x \right)^{3}\right)^{\frac{1}{4}} \left(a \,b^{3} d -b^{2} \left(3 a +b \right) d x +3 b \left(a +b \right) d \,x^{2}-\left(a d +3 b d +1\right) x^{3}+d \,x^{4}\right)}\, dx\]"," ",0,"int((-3*a*b^3+2*b^2*(3*a+b)*x-3*b*(a+b)*x^2+x^4)/(x*(-a+x)*(-b+x)^3)^(1/4)/(a*b^3*d-b^2*(3*a+b)*d*x+3*b*(a+b)*d*x^2-(a*d+3*b*d+1)*x^3+d*x^4),x)","F"
2034,0,0,109,0.026000," ","int((a*x^5-b)^(3/4)/x,x)","\[\int \frac{\left(a \,x^{5}-b \right)^{\frac{3}{4}}}{x}\, dx\]"," ",0,"int((a*x^5-b)^(3/4)/x,x)","F"
2035,1,744,109,16.626000," ","int((x^3-1)^(2/3)*(x^6+x^3+4)/x^9/(x^3-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{7 x^{9}+x^{6}+2 x^{3}-10}{40 x^{8} \left(x^{3}-1\right)^{\frac{1}{3}}}-\frac{5 \ln \left(\frac{6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} x^{3}+18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-4 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{3}-12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) x^{3}-6 x \left(x^{3}-1\right)^{\frac{2}{3}}+4 \RootOf \left(\textit{\_Z}^{3}-2\right)+12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)}{x^{3}-2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)}{24}-\frac{5 \ln \left(\frac{6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} x^{3}+18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-4 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{3}-12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) x^{3}-6 x \left(x^{3}-1\right)^{\frac{2}{3}}+4 \RootOf \left(\textit{\_Z}^{3}-2\right)+12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)}{x^{3}-2}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)}{4}+\frac{5 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \ln \left(-\frac{9 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} x^{3}+36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}+30 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x +4 \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+30 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right) x^{2}+9 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{3}+36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) x^{3}+8 x \left(x^{3}-1\right)^{\frac{2}{3}}-6 \RootOf \left(\textit{\_Z}^{3}-2\right)-24 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)}{x^{3}-2}\right)}{4}$&$744$\\ trager&$\text{Expression too large to display}$&$1120$\\ \hline \end{longtable}"," ",0,"1/40*(7*x^9+x^6+2*x^3-10)/x^8/(x^3-1)^(1/3)-5/24*ln((6*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^3+18*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-3*RootOf(_Z^3-2)^2*(x^3-1)^(1/3)*x^2-4*RootOf(_Z^3-2)*x^3-12*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^3-6*x*(x^3-1)^(2/3)+4*RootOf(_Z^3-2)+12*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2))/(x^3-2))*RootOf(_Z^3-2)-5/4*ln((6*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^3+18*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-3*RootOf(_Z^3-2)^2*(x^3-1)^(1/3)*x^2-4*RootOf(_Z^3-2)*x^3-12*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^3-6*x*(x^3-1)^(2/3)+4*RootOf(_Z^3-2)+12*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2))/(x^3-2))*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)+5/4*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*ln(-(9*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^3+36*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^3+30*(x^3-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^2*x+4*RootOf(_Z^3-2)^2*(x^3-1)^(1/3)*x^2+30*(x^3-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)*x^2+9*RootOf(_Z^3-2)*x^3+36*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^3+8*x*(x^3-1)^(2/3)-6*RootOf(_Z^3-2)-24*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2))/(x^3-2))","C"
2036,1,1097,118,32.707000," ","int((3*x^6-4*x-3)/(x^6+2*x+1)/(x^6+2*x^3+2*x+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{3}-\RootOf \left(\textit{\_Z}^{3}-4\right) x^{6}+\left(x^{6}+2 x^{3}+2 x +1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x -\left(x^{6}+2 x^{3}+2 x +1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{2}-4 \left(x^{6}+2 x^{3}+2 x +1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{3}+4 \left(x^{6}+2 x^{3}+2 x +1\right)^{\frac{2}{3}} x -2 \RootOf \left(\textit{\_Z}^{3}-4\right) x -\RootOf \left(\textit{\_Z}^{3}-4\right)}{\left(1+x \right) \left(x^{5}-x^{4}+x^{3}-x^{2}+x +1\right)}\right)}{2}-\frac{\ln \left(-\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{4} x^{3}-2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{3}+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{6}-2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x^{6}+6 \left(x^{6}+2 x^{3}+2 x +1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{2}+4 \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{3}-8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x^{3}-6 \RootOf \left(\textit{\_Z}^{3}-4\right) \left(x^{6}+2 x^{3}+2 x +1\right)^{\frac{2}{3}} x -12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \left(x^{6}+2 x^{3}+2 x +1\right)^{\frac{2}{3}} x +2 \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x -4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x +\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)}{\left(1+x \right) \left(x^{5}-x^{4}+x^{3}-x^{2}+x +1\right)}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)}{2}-\ln \left(-\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{4} x^{3}-2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{3}+\RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{6}-2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x^{6}+6 \left(x^{6}+2 x^{3}+2 x +1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{2}+4 \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{3}-8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x^{3}-6 \RootOf \left(\textit{\_Z}^{3}-4\right) \left(x^{6}+2 x^{3}+2 x +1\right)^{\frac{2}{3}} x -12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \left(x^{6}+2 x^{3}+2 x +1\right)^{\frac{2}{3}} x +2 \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x -4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x +\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)}{\left(1+x \right) \left(x^{5}-x^{4}+x^{3}-x^{2}+x +1\right)}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)$&$1097$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^3-4)*ln((RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x^3-RootOf(_Z^3-4)*x^6+(x^6+2*x^3+2*x+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^2*x-(x^6+2*x^3+2*x+1)^(1/3)*RootOf(_Z^3-4)^2*x^2-4*(x^6+2*x^3+2*x+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)*x^2-2*RootOf(_Z^3-4)*x^3+4*(x^6+2*x^3+2*x+1)^(2/3)*x-2*RootOf(_Z^3-4)*x-RootOf(_Z^3-4))/(1+x)/(x^5-x^4+x^3-x^2+x+1))-1/2*ln(-(RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^4*x^3-2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^3*x^3+RootOf(_Z^3-4)^2*x^6-2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)*x^6+6*(x^6+2*x^3+2*x+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^2*x^2+4*RootOf(_Z^3-4)^2*x^3-8*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)*x^3-6*RootOf(_Z^3-4)*(x^6+2*x^3+2*x+1)^(2/3)*x-12*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*(x^6+2*x^3+2*x+1)^(2/3)*x+2*RootOf(_Z^3-4)^2*x-4*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)*x+RootOf(_Z^3-4)^2-2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4))/(1+x)/(x^5-x^4+x^3-x^2+x+1))*RootOf(_Z^3-4)-ln(-(RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^4*x^3-2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^3*x^3+RootOf(_Z^3-4)^2*x^6-2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)*x^6+6*(x^6+2*x^3+2*x+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^2*x^2+4*RootOf(_Z^3-4)^2*x^3-8*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)*x^3-6*RootOf(_Z^3-4)*(x^6+2*x^3+2*x+1)^(2/3)*x-12*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*(x^6+2*x^3+2*x+1)^(2/3)*x+2*RootOf(_Z^3-4)^2*x-4*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)*x+RootOf(_Z^3-4)^2-2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4))/(1+x)/(x^5-x^4+x^3-x^2+x+1))*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)","C"
2037,0,0,109,0.026000," ","int((a*x^6-b)^(3/4)/x,x)","\[\int \frac{\left(a \,x^{6}-b \right)^{\frac{3}{4}}}{x}\, dx\]"," ",0,"int((a*x^6-b)^(3/4)/x,x)","F"
2038,1,68,121,1.696000," ","int((a*x^6+b)/(x^3-x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 a \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}} x^{\frac{20}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{10}{3}\right], \left[\frac{13}{3}\right], x^{2}\right)}{20 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}}}+\frac{3 b \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}} x^{\frac{2}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{2}\right)}{2 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}}}$&$68$\\ risch&$\frac{a \left(18 x^{4}+21 x^{2}+28\right) x \left(x^{2}-1\right)}{108 \left(x \left(x^{2}-1\right)\right)^{\frac{1}{3}}}+\frac{3 b \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}} x^{\frac{2}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{2}\right)}{2 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}}}+\frac{7 a \left(-\mathrm{signum}\left(x^{2}-1\right)\right)^{\frac{1}{3}} x^{\frac{2}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{1}{3}\right], \left[\frac{4}{3}\right], x^{2}\right)}{27 \mathrm{signum}\left(x^{2}-1\right)^{\frac{1}{3}}}$&$98$\\ trager&$\frac{a \left(18 x^{4}+21 x^{2}+28\right) \left(x^{3}-x \right)^{\frac{2}{3}}}{108}-\frac{\left(14 a +81 b \right) \left(18 \ln \left(-228744 \RootOf \left(324 \textit{\_Z}^{2}-18 \textit{\_Z} +1\right)^{2} x^{2}+40608 \RootOf \left(324 \textit{\_Z}^{2}-18 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}+96390 \RootOf \left(324 \textit{\_Z}^{2}-18 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{1}{3}} x -124290 \RootOf \left(324 \textit{\_Z}^{2}-18 \textit{\_Z} +1\right) x^{2}+914976 \RootOf \left(324 \textit{\_Z}^{2}-18 \textit{\_Z} +1\right)^{2}+5355 \left(x^{3}-x \right)^{\frac{2}{3}}-7611 x \left(x^{3}-x \right)^{\frac{1}{3}}+1550 x^{2}+26964 \RootOf \left(324 \textit{\_Z}^{2}-18 \textit{\_Z} +1\right)-465\right) \RootOf \left(324 \textit{\_Z}^{2}-18 \textit{\_Z} +1\right)+\ln \left(178524 \RootOf \left(324 \textit{\_Z}^{2}-18 \textit{\_Z} +1\right)^{2} x^{2}-40608 \RootOf \left(324 \textit{\_Z}^{2}-18 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}+136998 \RootOf \left(324 \textit{\_Z}^{2}-18 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{1}{3}} x -106308 \RootOf \left(324 \textit{\_Z}^{2}-18 \textit{\_Z} +1\right) x^{2}-714096 \RootOf \left(324 \textit{\_Z}^{2}-18 \textit{\_Z} +1\right)^{2}+7611 \left(x^{3}-x \right)^{\frac{2}{3}}-5355 x \left(x^{3}-x \right)^{\frac{1}{3}}-1705 x^{2}+58266 \RootOf \left(324 \textit{\_Z}^{2}-18 \textit{\_Z} +1\right)+1085\right)-\ln \left(-228744 \RootOf \left(324 \textit{\_Z}^{2}-18 \textit{\_Z} +1\right)^{2} x^{2}+40608 \RootOf \left(324 \textit{\_Z}^{2}-18 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{2}{3}}+96390 \RootOf \left(324 \textit{\_Z}^{2}-18 \textit{\_Z} +1\right) \left(x^{3}-x \right)^{\frac{1}{3}} x -124290 \RootOf \left(324 \textit{\_Z}^{2}-18 \textit{\_Z} +1\right) x^{2}+914976 \RootOf \left(324 \textit{\_Z}^{2}-18 \textit{\_Z} +1\right)^{2}+5355 \left(x^{3}-x \right)^{\frac{2}{3}}-7611 x \left(x^{3}-x \right)^{\frac{1}{3}}+1550 x^{2}+26964 \RootOf \left(324 \textit{\_Z}^{2}-18 \textit{\_Z} +1\right)-465\right)\right)}{162}$&$465$\\ \hline \end{longtable}"," ",0,"3/20*a/signum(x^2-1)^(1/3)*(-signum(x^2-1))^(1/3)*x^(20/3)*hypergeom([1/3,10/3],[13/3],x^2)+3/2*b/signum(x^2-1)^(1/3)*(-signum(x^2-1))^(1/3)*x^(2/3)*hypergeom([1/3,1/3],[4/3],x^2)","C"
2039,0,0,125,0.024000," ","int((a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/4)/(-a/b^2+a^2*x^2/b^2)^(1/2),x)","\[\int \frac{\left(a \,x^{2}+b x \sqrt{-\frac{a}{b^{2}}+\frac{a^{2} x^{2}}{b^{2}}}\right)^{\frac{1}{4}}}{\sqrt{-\frac{a}{b^{2}}+\frac{a^{2} x^{2}}{b^{2}}}}\, dx\]"," ",0,"int((a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/4)/(-a/b^2+a^2*x^2/b^2)^(1/2),x)","F"
2040,0,0,116,0.044000," ","int(1/(x^2*(-a+x))^(1/3)/(a+(-1+d)*x),x)","\[\int \frac{1}{\left(x^{2} \left(-a +x \right)\right)^{\frac{1}{3}} \left(a +\left(-1+d \right) x \right)}\, dx\]"," ",0,"int(1/(x^2*(-a+x))^(1/3)/(a+(-1+d)*x),x)","F"
2041,1,572,128,10.325000," ","int((-x^4-x^3+x+2)^(2/3)*(x^4+2*x+6)*(x^4+x^3-x-2)/x^6/(x^4+2*x^3-x-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{3 \left(-2+x \right) \left(2 x^{3}+x^{2}+2 x +2\right) \left(-x^{4}-x^{3}+x +2\right)^{\frac{2}{3}}}{10 x^{5}}-\ln \left(\frac{-95643648 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x^{4}+143465472 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x^{3}+3100896 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{4}+3680064 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \left(-x^{4}-x^{3}+x +2\right)^{\frac{2}{3}} x -1046304 \left(-x^{4}-x^{3}+x +2\right)^{\frac{1}{3}} \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{2}+81024 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{3}-15890 x^{4}-27435 \left(-x^{4}-x^{3}+x +2\right)^{\frac{2}{3}} x +38334 \left(-x^{4}-x^{3}+x +2\right)^{\frac{1}{3}} x^{2}+95643648 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x -6356 x^{3}+191287296 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2}-3100896 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x -6201792 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)+15890 x +31780}{\left(2+x \right) \left(-1+x \right) \left(x^{2}+x +1\right)}\right)+96 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \ln \left(-\frac{-58576896 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x^{4}+87865344 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x^{3}+81024 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{4}+3680064 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) \left(-x^{4}-x^{3}+x +2\right)^{\frac{2}{3}} x -2633760 \left(-x^{4}-x^{3}+x +2\right)^{\frac{1}{3}} \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{2}-3019872 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x^{3}+15567 x^{4}-10899 \left(-x^{4}-x^{3}+x +2\right)^{\frac{2}{3}} x +38334 \left(-x^{4}-x^{3}+x +2\right)^{\frac{1}{3}} x^{2}+58576896 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2} x +25945 x^{3}+117153792 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)^{2}-81024 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right) x -162048 \RootOf \left(9216 \textit{\_Z}^{2}-96 \textit{\_Z} +1\right)-15567 x -31134}{\left(2+x \right) \left(-1+x \right) \left(x^{2}+x +1\right)}\right)$&$572$\\ risch&$-\frac{3 \left(2 x^{8}-x^{7}-3 x^{6}-4 x^{5}-7 x^{4}+2 x^{3}+2 x^{2}+8 x +8\right)}{10 x^{5} \left(-x^{4}-x^{3}+x +2\right)^{\frac{1}{3}}}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{4}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(-x^{4}-x^{3}+x +2\right)^{\frac{2}{3}} x +\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(-x^{4}-x^{3}+x +2\right)^{\frac{1}{3}} x^{2}+\left(-x^{4}-x^{3}+x +2\right)^{\frac{2}{3}} x +\left(-x^{4}-x^{3}+x +2\right)^{\frac{1}{3}} x^{2}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x +2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)}{\left(-1-x +\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x \right) \left(-1+x \right) \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x +1\right) \left(2+x \right)}\right)-\ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{4}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(-x^{4}-x^{3}+x +2\right)^{\frac{2}{3}} x +\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(-x^{4}-x^{3}+x +2\right)^{\frac{1}{3}} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+x^{4}-2 \left(-x^{4}-x^{3}+x +2\right)^{\frac{2}{3}} x -2 \left(-x^{4}-x^{3}+x +2\right)^{\frac{1}{3}} x^{2}+x^{3}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x +2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-x -2}{\left(-1-x +\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x \right) \left(-1+x \right) \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x +1\right) \left(2+x \right)}\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+\ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{4}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(-x^{4}-x^{3}+x +2\right)^{\frac{2}{3}} x +\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(-x^{4}-x^{3}+x +2\right)^{\frac{1}{3}} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{3}+x^{4}-2 \left(-x^{4}-x^{3}+x +2\right)^{\frac{2}{3}} x -2 \left(-x^{4}-x^{3}+x +2\right)^{\frac{1}{3}} x^{2}+x^{3}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x +2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-x -2}{\left(-1-x +\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x \right) \left(-1+x \right) \left(\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x +1\right) \left(2+x \right)}\right)$&$698$\\ \hline \end{longtable}"," ",0,"3/10*(-2+x)*(2*x^3+x^2+2*x+2)/x^5*(-x^4-x^3+x+2)^(2/3)-ln((-95643648*RootOf(9216*_Z^2-96*_Z+1)^2*x^4+143465472*RootOf(9216*_Z^2-96*_Z+1)^2*x^3+3100896*RootOf(9216*_Z^2-96*_Z+1)*x^4+3680064*RootOf(9216*_Z^2-96*_Z+1)*(-x^4-x^3+x+2)^(2/3)*x-1046304*(-x^4-x^3+x+2)^(1/3)*RootOf(9216*_Z^2-96*_Z+1)*x^2+81024*RootOf(9216*_Z^2-96*_Z+1)*x^3-15890*x^4-27435*(-x^4-x^3+x+2)^(2/3)*x+38334*(-x^4-x^3+x+2)^(1/3)*x^2+95643648*RootOf(9216*_Z^2-96*_Z+1)^2*x-6356*x^3+191287296*RootOf(9216*_Z^2-96*_Z+1)^2-3100896*RootOf(9216*_Z^2-96*_Z+1)*x-6201792*RootOf(9216*_Z^2-96*_Z+1)+15890*x+31780)/(2+x)/(-1+x)/(x^2+x+1))+96*RootOf(9216*_Z^2-96*_Z+1)*ln(-(-58576896*RootOf(9216*_Z^2-96*_Z+1)^2*x^4+87865344*RootOf(9216*_Z^2-96*_Z+1)^2*x^3+81024*RootOf(9216*_Z^2-96*_Z+1)*x^4+3680064*RootOf(9216*_Z^2-96*_Z+1)*(-x^4-x^3+x+2)^(2/3)*x-2633760*(-x^4-x^3+x+2)^(1/3)*RootOf(9216*_Z^2-96*_Z+1)*x^2-3019872*RootOf(9216*_Z^2-96*_Z+1)*x^3+15567*x^4-10899*(-x^4-x^3+x+2)^(2/3)*x+38334*(-x^4-x^3+x+2)^(1/3)*x^2+58576896*RootOf(9216*_Z^2-96*_Z+1)^2*x+25945*x^3+117153792*RootOf(9216*_Z^2-96*_Z+1)^2-81024*RootOf(9216*_Z^2-96*_Z+1)*x-162048*RootOf(9216*_Z^2-96*_Z+1)-15567*x-31134)/(2+x)/(-1+x)/(x^2+x+1))","C"
2042,1,665,110,127.549000," ","int((x^4-3)*(x^4+1)^(2/3)*(2*x^4+x^3+2)/x^6/(4*x^4-x^3+4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\frac{3}{10} x^{8}+\frac{9}{16} x^{7}+\frac{3}{5} x^{4}+\frac{9}{16} x^{3}+\frac{3}{10}}{x^{5} \left(x^{4}+1\right)^{\frac{1}{3}}}-\frac{3 \ln \left(\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{3}+4 \left(x^{4}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x +4 \left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x^{2}-\left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{2}-4 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{4}-4 \left(x^{4}+1\right)^{\frac{2}{3}} x -4 \RootOf \left(\textit{\_Z}^{3}-4\right)}{4 x^{4}-x^{3}+4}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)}{32}-\frac{3 \ln \left(\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{3}+4 \left(x^{4}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x +4 \left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x^{2}-\left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{2}-4 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{4}-4 \left(x^{4}+1\right)^{\frac{2}{3}} x -4 \RootOf \left(\textit{\_Z}^{3}-4\right)}{4 x^{4}-x^{3}+4}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right)}{8}+\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) \ln \left(-\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{3}+4 \left(x^{4}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x +4 \left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x^{2}+2 \left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{2}+4 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{4}+\RootOf \left(\textit{\_Z}^{3}-4\right) x^{3}+8 \left(x^{4}+1\right)^{\frac{2}{3}} x +4 \RootOf \left(\textit{\_Z}^{3}-4\right)}{4 x^{4}-x^{3}+4}\right)}{8}$&$665$\\ trager&$\frac{3 \left(x^{4}+1\right)^{\frac{2}{3}} \left(8 x^{4}+15 x^{3}+8\right)}{80 x^{5}}+\frac{3 \RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(-\frac{-2676 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+144 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{4}-15696 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+144 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{4}+5352 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+144 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{3}+31392 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+144 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{3}+4524 \left(x^{4}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+144 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x -377 \left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{2}-36336 \left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+144 \textit{\_Z}^{2}\right) x^{2}+7136 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{4}+41856 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+144 \textit{\_Z}^{2}\right) x^{4}-2676 \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+144 \textit{\_Z}^{2}\right)-15696 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+144 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2007 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{3}+11772 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+144 \textit{\_Z}^{2}\right) x^{3}-10604 \left(x^{4}+1\right)^{\frac{2}{3}} x +7136 \RootOf \left(\textit{\_Z}^{3}-4\right)+41856 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+144 \textit{\_Z}^{2}\right)}{4 x^{4}-x^{3}+4}\right)}{32}+\frac{9 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+144 \textit{\_Z}^{2}\right) \ln \left(-\frac{208920 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+144 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{4}+2738952 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+144 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{4}-417840 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+144 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{3}-5477904 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+144 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{3}+1269180 \left(x^{4}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+144 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x -105765 \left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{2}-3686922 \left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+144 \textit{\_Z}^{2}\right) x^{2}+626760 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{4}+8216856 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+144 \textit{\_Z}^{2}\right) x^{4}+208920 \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+144 \textit{\_Z}^{2}\right)+2738952 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+144 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+17410 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{3}+228246 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+144 \textit{\_Z}^{2}\right) x^{3}-805914 \left(x^{4}+1\right)^{\frac{2}{3}} x +626760 \RootOf \left(\textit{\_Z}^{3}-4\right)+8216856 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+144 \textit{\_Z}^{2}\right)}{4 x^{4}-x^{3}+4}\right)}{8}$&$996$\\ \hline \end{longtable}"," ",0,"3/80*(8*x^8+15*x^7+16*x^4+15*x^3+8)/x^5/(x^4+1)^(1/3)-3/32*ln((RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*RootOf(_Z^3-4)^3*x^3+4*(x^4+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*RootOf(_Z^3-4)^2*x+4*(x^4+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*RootOf(_Z^3-4)*x^2-(x^4+1)^(1/3)*RootOf(_Z^3-4)^2*x^2-4*RootOf(_Z^3-4)*x^4-4*(x^4+1)^(2/3)*x-4*RootOf(_Z^3-4))/(4*x^4-x^3+4))*RootOf(_Z^3-4)-3/8*ln((RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*RootOf(_Z^3-4)^3*x^3+4*(x^4+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*RootOf(_Z^3-4)^2*x+4*(x^4+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*RootOf(_Z^3-4)*x^2-(x^4+1)^(1/3)*RootOf(_Z^3-4)^2*x^2-4*RootOf(_Z^3-4)*x^4-4*(x^4+1)^(2/3)*x-4*RootOf(_Z^3-4))/(4*x^4-x^3+4))*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)+3/8*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*ln(-(RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*RootOf(_Z^3-4)^3*x^3+4*(x^4+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*RootOf(_Z^3-4)^2*x+4*(x^4+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+4*_Z*RootOf(_Z^3-4)+16*_Z^2)*RootOf(_Z^3-4)*x^2+2*(x^4+1)^(1/3)*RootOf(_Z^3-4)^2*x^2+4*RootOf(_Z^3-4)*x^4+RootOf(_Z^3-4)*x^3+8*(x^4+1)^(2/3)*x+4*RootOf(_Z^3-4))/(4*x^4-x^3+4))","C"
2043,1,774,126,17.270000," ","int((2*x^6-x^4-1)*(x^7-x^5+x)^(1/3)/(x^6-x^4+x^2+1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{x \left(x^{7}-x^{5}+x \right)^{\frac{1}{3}}}{2 \left(x^{6}-x^{4}+x^{2}+1\right)}+2 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \ln \left(-\frac{19423596460464 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{6}+1424454519036 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{6}-19423596460464 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{4}-1424454519036 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{4}-19423596460464 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{2}-1230275999700 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{7}-x^{5}+x \right)^{\frac{2}{3}}+1230275999700 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{7}-x^{5}+x \right)^{\frac{1}{3}} x -3043087557408 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{2}+19423596460464 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}+151067629809 \left(x^{7}-x^{5}+x \right)^{\frac{2}{3}}-151067629809 x \left(x^{7}-x^{5}+x \right)^{\frac{1}{3}}-118704543253 x^{2}+1424454519036 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)}{x^{6}-x^{4}+x^{2}+1}\right)-\frac{\ln \left(-\frac{9711798230232 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{6}+906405778854 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{6}-9711798230232 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{4}+8090771639 x^{6}-906405778854 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{4}-9711798230232 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{2}-8090771639 x^{4}+615137999850 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{7}-x^{5}+x \right)^{\frac{2}{3}}-615137999850 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{7}-x^{5}+x \right)^{\frac{1}{3}} x -97089259668 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{2}+9711798230232 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}+126795314892 \left(x^{7}-x^{5}+x \right)^{\frac{2}{3}}-126795314892 x \left(x^{7}-x^{5}+x \right)^{\frac{1}{3}}+906405778854 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)+8090771639}{x^{6}-x^{4}+x^{2}+1}\right)}{6}-2 \ln \left(-\frac{9711798230232 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{6}+906405778854 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{6}-9711798230232 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{4}+8090771639 x^{6}-906405778854 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{4}-9711798230232 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2} x^{2}-8090771639 x^{4}+615137999850 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{7}-x^{5}+x \right)^{\frac{2}{3}}-615137999850 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \left(x^{7}-x^{5}+x \right)^{\frac{1}{3}} x -97089259668 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) x^{2}+9711798230232 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}+126795314892 \left(x^{7}-x^{5}+x \right)^{\frac{2}{3}}-126795314892 x \left(x^{7}-x^{5}+x \right)^{\frac{1}{3}}+906405778854 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)+8090771639}{x^{6}-x^{4}+x^{2}+1}\right) \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)$&$774$\\ risch&$-\frac{x \left(x \left(x^{6}-x^{4}+1\right)\right)^{\frac{1}{3}}}{2 \left(x^{6}-x^{4}+x^{2}+1\right)}+\frac{\left(-\frac{\ln \left(\frac{4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{12}-8 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{10}-x^{12}+2 x^{10}+2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{8}+12 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{6}+6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{14}-2 x^{12}+x^{10}+2 x^{8}-2 x^{6}+x^{2}\right)^{\frac{1}{3}} x^{6}-x^{8}-2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{6}+3 \left(x^{14}-2 x^{12}+x^{10}+2 x^{8}-2 x^{6}+x^{2}\right)^{\frac{1}{3}} x^{6}-8 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{4}-6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{14}-2 x^{12}+x^{10}+2 x^{8}-2 x^{6}+x^{2}\right)^{\frac{1}{3}} x^{4}-2 x^{6}-3 \left(x^{14}-2 x^{12}+x^{10}+2 x^{8}-2 x^{6}+x^{2}\right)^{\frac{1}{3}} x^{4}-4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{2}+2 x^{4}-6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{14}-2 x^{12}+x^{10}+2 x^{8}-2 x^{6}+x^{2}\right)^{\frac{2}{3}}+2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{2}+4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}+6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{14}-2 x^{12}+x^{10}+2 x^{8}-2 x^{6}+x^{2}\right)^{\frac{1}{3}}-3 \left(x^{14}-2 x^{12}+x^{10}+2 x^{8}-2 x^{6}+x^{2}\right)^{\frac{2}{3}}+3 \left(x^{14}-2 x^{12}+x^{10}+2 x^{8}-2 x^{6}+x^{2}\right)^{\frac{1}{3}}-1}{\left(x^{6}-x^{4}+1\right) \left(x^{6}-x^{4}+x^{2}+1\right)}\right)}{6}-\frac{\ln \left(\frac{4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{12}-8 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{10}-x^{12}+2 x^{10}+2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{8}+12 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{6}+6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{14}-2 x^{12}+x^{10}+2 x^{8}-2 x^{6}+x^{2}\right)^{\frac{1}{3}} x^{6}-x^{8}-2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{6}+3 \left(x^{14}-2 x^{12}+x^{10}+2 x^{8}-2 x^{6}+x^{2}\right)^{\frac{1}{3}} x^{6}-8 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{4}-6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{14}-2 x^{12}+x^{10}+2 x^{8}-2 x^{6}+x^{2}\right)^{\frac{1}{3}} x^{4}-2 x^{6}-3 \left(x^{14}-2 x^{12}+x^{10}+2 x^{8}-2 x^{6}+x^{2}\right)^{\frac{1}{3}} x^{4}-4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{2}+2 x^{4}-6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{14}-2 x^{12}+x^{10}+2 x^{8}-2 x^{6}+x^{2}\right)^{\frac{2}{3}}+2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{2}+4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}+6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{14}-2 x^{12}+x^{10}+2 x^{8}-2 x^{6}+x^{2}\right)^{\frac{1}{3}}-3 \left(x^{14}-2 x^{12}+x^{10}+2 x^{8}-2 x^{6}+x^{2}\right)^{\frac{2}{3}}+3 \left(x^{14}-2 x^{12}+x^{10}+2 x^{8}-2 x^{6}+x^{2}\right)^{\frac{1}{3}}-1}{\left(x^{6}-x^{4}+1\right) \left(x^{6}-x^{4}+x^{2}+1\right)}\right) \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)}{3}+\frac{\RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \ln \left(\frac{2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{12}+2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{12}-4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{10}-4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{10}-\RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{8}+6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{6}-3 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{14}-2 x^{12}+x^{10}+2 x^{8}-2 x^{6}+x^{2}\right)^{\frac{1}{3}} x^{6}-x^{8}+7 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{6}-4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{4}+3 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{14}-2 x^{12}+x^{10}+2 x^{8}-2 x^{6}+x^{2}\right)^{\frac{1}{3}} x^{4}+x^{6}-4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{4}-2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{2}+3 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{14}-2 x^{12}+x^{10}+2 x^{8}-2 x^{6}+x^{2}\right)^{\frac{2}{3}}-3 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{2}+2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}-3 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{14}-2 x^{12}+x^{10}+2 x^{8}-2 x^{6}+x^{2}\right)^{\frac{1}{3}}-x^{2}+2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)}{\left(x^{6}-x^{4}+1\right) \left(x^{6}-x^{4}+x^{2}+1\right)}\right)}{3}\right) \left(x \left(x^{6}-x^{4}+1\right)\right)^{\frac{1}{3}} \left(x^{2} \left(x^{6}-x^{4}+1\right)^{2}\right)^{\frac{1}{3}}}{x \left(x^{6}-x^{4}+1\right)}$&$1528$\\ \hline \end{longtable}"," ",0,"-1/2*x/(x^6-x^4+x^2+1)*(x^7-x^5+x)^(1/3)+2*RootOf(144*_Z^2+12*_Z+1)*ln(-(19423596460464*RootOf(144*_Z^2+12*_Z+1)^2*x^6+1424454519036*RootOf(144*_Z^2+12*_Z+1)*x^6-19423596460464*RootOf(144*_Z^2+12*_Z+1)^2*x^4-1424454519036*RootOf(144*_Z^2+12*_Z+1)*x^4-19423596460464*RootOf(144*_Z^2+12*_Z+1)^2*x^2-1230275999700*RootOf(144*_Z^2+12*_Z+1)*(x^7-x^5+x)^(2/3)+1230275999700*RootOf(144*_Z^2+12*_Z+1)*(x^7-x^5+x)^(1/3)*x-3043087557408*RootOf(144*_Z^2+12*_Z+1)*x^2+19423596460464*RootOf(144*_Z^2+12*_Z+1)^2+151067629809*(x^7-x^5+x)^(2/3)-151067629809*x*(x^7-x^5+x)^(1/3)-118704543253*x^2+1424454519036*RootOf(144*_Z^2+12*_Z+1))/(x^6-x^4+x^2+1))-1/6*ln(-(9711798230232*RootOf(144*_Z^2+12*_Z+1)^2*x^6+906405778854*RootOf(144*_Z^2+12*_Z+1)*x^6-9711798230232*RootOf(144*_Z^2+12*_Z+1)^2*x^4+8090771639*x^6-906405778854*RootOf(144*_Z^2+12*_Z+1)*x^4-9711798230232*RootOf(144*_Z^2+12*_Z+1)^2*x^2-8090771639*x^4+615137999850*RootOf(144*_Z^2+12*_Z+1)*(x^7-x^5+x)^(2/3)-615137999850*RootOf(144*_Z^2+12*_Z+1)*(x^7-x^5+x)^(1/3)*x-97089259668*RootOf(144*_Z^2+12*_Z+1)*x^2+9711798230232*RootOf(144*_Z^2+12*_Z+1)^2+126795314892*(x^7-x^5+x)^(2/3)-126795314892*x*(x^7-x^5+x)^(1/3)+906405778854*RootOf(144*_Z^2+12*_Z+1)+8090771639)/(x^6-x^4+x^2+1))-2*ln(-(9711798230232*RootOf(144*_Z^2+12*_Z+1)^2*x^6+906405778854*RootOf(144*_Z^2+12*_Z+1)*x^6-9711798230232*RootOf(144*_Z^2+12*_Z+1)^2*x^4+8090771639*x^6-906405778854*RootOf(144*_Z^2+12*_Z+1)*x^4-9711798230232*RootOf(144*_Z^2+12*_Z+1)^2*x^2-8090771639*x^4+615137999850*RootOf(144*_Z^2+12*_Z+1)*(x^7-x^5+x)^(2/3)-615137999850*RootOf(144*_Z^2+12*_Z+1)*(x^7-x^5+x)^(1/3)*x-97089259668*RootOf(144*_Z^2+12*_Z+1)*x^2+9711798230232*RootOf(144*_Z^2+12*_Z+1)^2+126795314892*(x^7-x^5+x)^(2/3)-126795314892*x*(x^7-x^5+x)^(1/3)+906405778854*RootOf(144*_Z^2+12*_Z+1)+8090771639)/(x^6-x^4+x^2+1))*RootOf(144*_Z^2+12*_Z+1)","C"
2044,0,0,126,0.044000," ","int(x^4*(a*x^3-4*b)/(a*x^3-b)^(1/4)/(-a^2*x^6+x^8+2*a*b*x^3-b^2),x)","\[\int \frac{x^{4} \left(a \,x^{3}-4 b \right)}{\left(a \,x^{3}-b \right)^{\frac{1}{4}} \left(-a^{2} x^{6}+x^{8}+2 a b \,x^{3}-b^{2}\right)}\, dx\]"," ",0,"int(x^4*(a*x^3-4*b)/(a*x^3-b)^(1/4)/(-a^2*x^6+x^8+2*a*b*x^3-b^2),x)","F"
2045,0,0,110,0.048000," ","int((x^2-1)^(1/2)*(x^2+x*(x^2-1)^(1/2))^(1/2)/(x^2+1),x)","\[\int \frac{\sqrt{x^{2}-1}\, \sqrt{x^{2}+x \sqrt{x^{2}-1}}}{x^{2}+1}\, dx\]"," ",0,"int((x^2-1)^(1/2)*(x^2+x*(x^2-1)^(1/2))^(1/2)/(x^2+1),x)","F"
2046,0,0,117,0.045000," ","int(x/(x^2*(-a+x))^(2/3)/(a+(-1+d)*x),x)","\[\int \frac{x}{\left(x^{2} \left(-a +x \right)\right)^{\frac{2}{3}} \left(a +\left(-1+d \right) x \right)}\, dx\]"," ",0,"int(x/(x^2*(-a+x))^(2/3)/(a+(-1+d)*x),x)","F"
2047,1,12030,80,30.208000," ","int((x^2+x+2)/(x^2+2*x+3)/(x^3+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$12030$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2048,1,10276,80,21.415000," ","int((x^2+x+2)/(x^2+2*x+3)/(x^3+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$10276$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2049,1,691,107,0.147000," ","int((a*x^2-c*x+b)/(a*x^2-b)/(a*x^3+b*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}+b x}}-\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right) c}{2 a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}+\frac{b \sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{\sqrt{a b}\, a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}-\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right) c}{2 a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}-\frac{b \sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{\sqrt{a b}\, a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}$&$691$\\ default&$\frac{\sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}+b x}}-\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right) c}{2 a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}+\frac{b \sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{\sqrt{a b}\, a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}-\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right) c}{2 a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}-\frac{b \sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{\sqrt{a b}\, a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}$&$710$\\ \hline \end{longtable}"," ",0,"1/a*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)*EllipticF(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))-1/2/a^2*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2)),1/2*2^(1/2))*c+b/(a*b)^(1/2)/a*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2)),1/2*2^(1/2))-1/2/a^2*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)+1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)+1/a*(a*b)^(1/2)),1/2*2^(1/2))*c-b/(a*b)^(1/2)/a*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)+1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)+1/a*(a*b)^(1/2)),1/2*2^(1/2))","C"
2050,1,691,107,0.141000," ","int((a*x^2+c*x+b)/(a*x^2-b)/(a*x^3+b*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}+b x}}+\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right) c}{2 a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}+\frac{b \sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{\sqrt{a b}\, a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}+\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right) c}{2 a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}-\frac{b \sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{\sqrt{a b}\, a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}$&$691$\\ default&$\frac{\sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}+b x}}+\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right) c}{2 a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}+\frac{b \sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{\sqrt{a b}\, a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}+\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right) c}{2 a^{2} \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}-\frac{b \sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{\sqrt{a b}\, a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}$&$710$\\ \hline \end{longtable}"," ",0,"1/a*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)*EllipticF(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))+1/2/a^2*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2)),1/2*2^(1/2))*c+b/(a*b)^(1/2)/a*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2)),1/2*2^(1/2))+1/2/a^2*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)+1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)+1/a*(a*b)^(1/2)),1/2*2^(1/2))*c-b/(a*b)^(1/2)/a*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)+1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)+1/a*(a*b)^(1/2)),1/2*2^(1/2))","C"
2051,1,2858,55,46.974000," ","int((1+x)*(x^4-x^3)^(1/4)/(x^2-x+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2858$\\ risch&$\text{Expression too large to display}$&$3741$\\ \hline \end{longtable}"," ",0,"(x^4-x^3)^(1/4)-7/4*RootOf(_Z^2+1)*ln((-2*(x^4-x^3)^(1/2)*RootOf(_Z^2+1)*x+2*RootOf(_Z^2+1)*x^3+2*(x^4-x^3)^(3/4)-2*x^2*(x^4-x^3)^(1/4)-RootOf(_Z^2+1)*x^2)/x^2)+7/4*ln((2*(x^4-x^3)^(3/4)+2*(x^4-x^3)^(1/2)*x+2*x^2*(x^4-x^3)^(1/4)+2*x^3-x^2)/x^2)+RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)*ln((2*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^5*RootOf(_Z^2+1)*x^3-RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*RootOf(_Z^2+1)^2*x^3-4*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^5*RootOf(_Z^2+1)*x^2-10*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*RootOf(_Z^2+1)*(x^4-x^3)^(1/2)*x+2*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*RootOf(_Z^2+1)^2*x^2+10*(x^4-x^3)^(3/4)*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*RootOf(_Z^2+1)+8*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*x^3-6*(x^4-x^3)^(1/4)*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*x^2-4*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)*RootOf(_Z^2+1)*x^3-2*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*x^2+16*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)*(x^4-x^3)^(1/2)*x+10*(x^4-x^3)^(1/4)*RootOf(_Z^2+1)*x^2+RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)*RootOf(_Z^2+1)*x^2-16*(x^4-x^3)^(3/4))/(RootOf(_Z^2+1)*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*x-2*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*RootOf(_Z^2+1)-2*x+1)/x^2)-RootOf(_Z^2+1)*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*ln(-(-3*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^5*RootOf(_Z^2+1)*x^3-RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*RootOf(_Z^2+1)^2*x^3+6*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^5*RootOf(_Z^2+1)*x^2+6*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*RootOf(_Z^2+1)*(x^4-x^3)^(1/2)*x+2*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*RootOf(_Z^2+1)^2*x^2+10*(x^4-x^3)^(3/4)*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*RootOf(_Z^2+1)+15*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*x^3-6*(x^4-x^3)^(1/4)*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*x^2+5*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)*RootOf(_Z^2+1)*x^3-9*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*x^2-16*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)*(x^4-x^3)^(1/2)*x-16*(x^4-x^3)^(1/4)*RootOf(_Z^2+1)*x^2-3*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)*RootOf(_Z^2+1)*x^2+6*(x^4-x^3)^(3/4))/(RootOf(_Z^2+1)*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*x-2*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*RootOf(_Z^2+1)+x+1)/x^2)+RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)*ln(-(-3*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^5*RootOf(_Z^2+1)*x^3-RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*RootOf(_Z^2+1)^2*x^3+6*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^5*RootOf(_Z^2+1)*x^2+6*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*RootOf(_Z^2+1)*(x^4-x^3)^(1/2)*x+2*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*RootOf(_Z^2+1)^2*x^2+10*(x^4-x^3)^(3/4)*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*RootOf(_Z^2+1)+15*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*x^3-6*(x^4-x^3)^(1/4)*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*x^2+5*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)*RootOf(_Z^2+1)*x^3-9*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*x^2-16*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)*(x^4-x^3)^(1/2)*x-16*(x^4-x^3)^(1/4)*RootOf(_Z^2+1)*x^2-3*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)*RootOf(_Z^2+1)*x^2+6*(x^4-x^3)^(3/4))/(RootOf(_Z^2+1)*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*x-2*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*RootOf(_Z^2+1)+x+1)/x^2)+RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*ln(-(3*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^5*RootOf(_Z^2+1)^2*x^3-6*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^5*RootOf(_Z^2+1)^2*x^2-16*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*RootOf(_Z^2+1)*x^3+10*(x^4-x^3)^(3/4)*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*RootOf(_Z^2+1)-6*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*(x^4-x^3)^(1/2)*x+11*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*RootOf(_Z^2+1)*x^2-16*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)*(x^4-x^3)^(1/2)*RootOf(_Z^2+1)*x+6*(x^4-x^3)^(1/4)*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*x^2+16*(x^4-x^3)^(1/4)*RootOf(_Z^2+1)*x^2+5*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)*x^3+6*(x^4-x^3)^(3/4)-3*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)*x^2)/(RootOf(_Z^2+1)*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*x-2*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*RootOf(_Z^2+1)+x+1)/x^2)+RootOf(_Z^2+1)*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)*ln(-(3*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^5*RootOf(_Z^2+1)^2*x^3-6*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^5*RootOf(_Z^2+1)^2*x^2-16*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*RootOf(_Z^2+1)*x^3+10*(x^4-x^3)^(3/4)*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*RootOf(_Z^2+1)-6*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*(x^4-x^3)^(1/2)*x+11*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*RootOf(_Z^2+1)*x^2-16*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)*(x^4-x^3)^(1/2)*RootOf(_Z^2+1)*x+6*(x^4-x^3)^(1/4)*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*x^2+16*(x^4-x^3)^(1/4)*RootOf(_Z^2+1)*x^2+5*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)*x^3+6*(x^4-x^3)^(3/4)-3*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)*x^2)/(RootOf(_Z^2+1)*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*x-2*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*RootOf(_Z^2+1)+x+1)/x^2)+RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)*RootOf(_Z^2+1)*ln((-2*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^5*RootOf(_Z^2+1)^2*x^3+4*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^5*RootOf(_Z^2+1)^2*x^2-9*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*RootOf(_Z^2+1)*x^3+10*(x^4-x^3)^(3/4)*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*RootOf(_Z^2+1)+10*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*(x^4-x^3)^(1/2)*x+4*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^3*RootOf(_Z^2+1)*x^2+16*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)*(x^4-x^3)^(1/2)*RootOf(_Z^2+1)*x+6*(x^4-x^3)^(1/4)*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*x^2-10*(x^4-x^3)^(1/4)*RootOf(_Z^2+1)*x^2-4*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)*x^3-16*(x^4-x^3)^(3/4)+RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)*x^2)/(RootOf(_Z^2+1)*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*x-2*RootOf(_Z^4+RootOf(_Z^2+1)*_Z^2-1)^2*RootOf(_Z^2+1)-2*x+1)/x^2)","B"
2052,1,1746,55,48.667000," ","int((1+x)*(x^4-x^3)^(1/4)/(x^2-x+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1746$\\ risch&$\text{Expression too large to display}$&$5889$\\ \hline \end{longtable}"," ",0,"(x^4-x^3)^(1/4)+RootOf(_Z^8-_Z^4+1)*ln(-(RootOf(_Z^8-_Z^4+1)^11*x^3-2*RootOf(_Z^8-_Z^4+1)^11*x^2-3*RootOf(_Z^8-_Z^4+1)^7*x^3-RootOf(_Z^8-_Z^4+1)^7*x^2+10*RootOf(_Z^8-_Z^4+1)^6*(x^4-x^3)^(1/4)*x^2-10*(x^4-x^3)^(1/2)*RootOf(_Z^8-_Z^4+1)^5*x+10*(x^4-x^3)^(3/4)*RootOf(_Z^8-_Z^4+1)^4-10*RootOf(_Z^8-_Z^4+1)^3*x^3+6*RootOf(_Z^8-_Z^4+1)^3*x^2+6*RootOf(_Z^8-_Z^4+1)^2*(x^4-x^3)^(1/4)*x^2-6*(x^4-x^3)^(1/2)*RootOf(_Z^8-_Z^4+1)*x+6*(x^4-x^3)^(3/4))/(x*RootOf(_Z^8-_Z^4+1)^4-2*RootOf(_Z^8-_Z^4+1)^4+x+1)/x^2)-RootOf(_Z^8-_Z^4+1)^7*ln(-(3*RootOf(_Z^8-_Z^4+1)^9*x^3-6*RootOf(_Z^8-_Z^4+1)^9*x^2+16*(x^4-x^3)^(1/2)*RootOf(_Z^8-_Z^4+1)^7*x-16*RootOf(_Z^8-_Z^4+1)^6*(x^4-x^3)^(1/4)*x^2+10*RootOf(_Z^8-_Z^4+1)^5*x^3+RootOf(_Z^8-_Z^4+1)^5*x^2-10*(x^4-x^3)^(3/4)*RootOf(_Z^8-_Z^4+1)^4-6*(x^4-x^3)^(1/2)*RootOf(_Z^8-_Z^4+1)^3*x+6*RootOf(_Z^8-_Z^4+1)^2*(x^4-x^3)^(1/4)*x^2-8*RootOf(_Z^8-_Z^4+1)*x^3+2*RootOf(_Z^8-_Z^4+1)*x^2+16*(x^4-x^3)^(3/4))/(x*RootOf(_Z^8-_Z^4+1)^4-2*RootOf(_Z^8-_Z^4+1)^4-2*x+1)/x^2)+RootOf(_Z^8-_Z^4+1)^3*ln(-(3*RootOf(_Z^8-_Z^4+1)^9*x^3-6*RootOf(_Z^8-_Z^4+1)^9*x^2+16*(x^4-x^3)^(1/2)*RootOf(_Z^8-_Z^4+1)^7*x-16*RootOf(_Z^8-_Z^4+1)^6*(x^4-x^3)^(1/4)*x^2+10*RootOf(_Z^8-_Z^4+1)^5*x^3+RootOf(_Z^8-_Z^4+1)^5*x^2-10*(x^4-x^3)^(3/4)*RootOf(_Z^8-_Z^4+1)^4-6*(x^4-x^3)^(1/2)*RootOf(_Z^8-_Z^4+1)^3*x+6*RootOf(_Z^8-_Z^4+1)^2*(x^4-x^3)^(1/4)*x^2-8*RootOf(_Z^8-_Z^4+1)*x^3+2*RootOf(_Z^8-_Z^4+1)*x^2+16*(x^4-x^3)^(3/4))/(x*RootOf(_Z^8-_Z^4+1)^4-2*RootOf(_Z^8-_Z^4+1)^4-2*x+1)/x^2)-RootOf(_Z^8-_Z^4+1)^7*ln(-(2*RootOf(_Z^8-_Z^4+1)^9*x^3-4*RootOf(_Z^8-_Z^4+1)^9*x^2+16*(x^4-x^3)^(1/2)*RootOf(_Z^8-_Z^4+1)^7*x-10*RootOf(_Z^8-_Z^4+1)^6*(x^4-x^3)^(1/4)*x^2-13*RootOf(_Z^8-_Z^4+1)^5*x^3+12*RootOf(_Z^8-_Z^4+1)^5*x^2+10*(x^4-x^3)^(3/4)*RootOf(_Z^8-_Z^4+1)^4-10*(x^4-x^3)^(1/2)*RootOf(_Z^8-_Z^4+1)^3*x-6*RootOf(_Z^8-_Z^4+1)^2*(x^4-x^3)^(1/4)*x^2+15*RootOf(_Z^8-_Z^4+1)*x^3-9*RootOf(_Z^8-_Z^4+1)*x^2+6*(x^4-x^3)^(3/4))/(x*RootOf(_Z^8-_Z^4+1)^4-2*RootOf(_Z^8-_Z^4+1)^4+x+1)/x^2)-RootOf(_Z^8-_Z^4+1)^5*ln(-(RootOf(_Z^8-_Z^4+1)^11*x^3-2*RootOf(_Z^8-_Z^4+1)^11*x^2+RootOf(_Z^8-_Z^4+1)^7*x^3+5*RootOf(_Z^8-_Z^4+1)^7*x^2+16*RootOf(_Z^8-_Z^4+1)^6*(x^4-x^3)^(1/4)*x^2+6*(x^4-x^3)^(1/2)*RootOf(_Z^8-_Z^4+1)^5*x-10*(x^4-x^3)^(3/4)*RootOf(_Z^8-_Z^4+1)^4-12*RootOf(_Z^8-_Z^4+1)^3*x^3+3*RootOf(_Z^8-_Z^4+1)^3*x^2-6*RootOf(_Z^8-_Z^4+1)^2*(x^4-x^3)^(1/4)*x^2+10*(x^4-x^3)^(1/2)*RootOf(_Z^8-_Z^4+1)*x+16*(x^4-x^3)^(3/4))/(x*RootOf(_Z^8-_Z^4+1)^4-2*RootOf(_Z^8-_Z^4+1)^4-2*x+1)/x^2)-7/4*ln((2*(x^4-x^3)^(3/4)-2*(x^4-x^3)^(1/2)*x+2*x^2*(x^4-x^3)^(1/4)-2*x^3+x^2)/x^2)-7/4*RootOf(_Z^8-_Z^4+1)^6*ln(-(2*RootOf(_Z^8-_Z^4+1)^6*(x^4-x^3)^(1/2)*x-2*RootOf(_Z^8-_Z^4+1)^6*x^3+RootOf(_Z^8-_Z^4+1)^6*x^2-2*(x^4-x^3)^(3/4)+2*x^2*(x^4-x^3)^(1/4))/x^2)","B"
2053,0,0,114,0.014000," ","int((-a*x^6+b)^(1/3)*(a*x^6+b)/x^2/(a*x^6+c*x^3-b),x)","\[\int \frac{\left(-a \,x^{6}+b \right)^{\frac{1}{3}} \left(a \,x^{6}+b \right)}{x^{2} \left(a \,x^{6}+x^{3} c -b \right)}\, dx\]"," ",0,"int((-a*x^6+b)^(1/3)*(a*x^6+b)/x^2/(a*x^6+c*x^3-b),x)","F"
2054,1,319,123,11.017000," ","int(x^2*(7*x^3+4)/(x^4+x)^(1/3)/(x^7+x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\ln \left(\frac{67419187 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{7}-92588403 x^{7} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-84499942 x^{7}+67419187 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{4}+168096051 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}+x \right)^{\frac{2}{3}} x^{2}-92588403 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}+311926719 x^{2} \left(x^{4}+x \right)^{\frac{2}{3}}-84499942 x^{4}+143830668 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}+x \right)^{\frac{1}{3}} x -134838374 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-168096051 x \left(x^{4}+x \right)^{\frac{1}{3}}-286757503 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-126749913}{x^{7}+x^{4}-1}\right)+\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{42249971 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{7}+194169100 x^{7} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+202257561 x^{7}+42249971 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{4}+168096051 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}+x \right)^{\frac{2}{3}} x^{2}+194169100 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}-143830668 x^{2} \left(x^{4}+x \right)^{\frac{2}{3}}+202257561 x^{4}-311926719 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}+x \right)^{\frac{1}{3}} x -84499942 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}-168096051 x \left(x^{4}+x \right)^{\frac{1}{3}}-92588403 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+67419187}{x^{7}+x^{4}-1}\right)$&$319$\\ \hline \end{longtable}"," ",0,"ln((67419187*RootOf(_Z^2+_Z+1)^2*x^7-92588403*x^7*RootOf(_Z^2+_Z+1)-84499942*x^7+67419187*RootOf(_Z^2+_Z+1)^2*x^4+168096051*RootOf(_Z^2+_Z+1)*(x^4+x)^(2/3)*x^2-92588403*RootOf(_Z^2+_Z+1)*x^4+311926719*x^2*(x^4+x)^(2/3)-84499942*x^4+143830668*RootOf(_Z^2+_Z+1)*(x^4+x)^(1/3)*x-134838374*RootOf(_Z^2+_Z+1)^2-168096051*x*(x^4+x)^(1/3)-286757503*RootOf(_Z^2+_Z+1)-126749913)/(x^7+x^4-1))+RootOf(_Z^2+_Z+1)*ln(-(42249971*RootOf(_Z^2+_Z+1)^2*x^7+194169100*x^7*RootOf(_Z^2+_Z+1)+202257561*x^7+42249971*RootOf(_Z^2+_Z+1)^2*x^4+168096051*RootOf(_Z^2+_Z+1)*(x^4+x)^(2/3)*x^2+194169100*RootOf(_Z^2+_Z+1)*x^4-143830668*x^2*(x^4+x)^(2/3)+202257561*x^4-311926719*RootOf(_Z^2+_Z+1)*(x^4+x)^(1/3)*x-84499942*RootOf(_Z^2+_Z+1)^2-168096051*x*(x^4+x)^(1/3)-92588403*RootOf(_Z^2+_Z+1)+67419187)/(x^7+x^4-1))","C"
2055,0,0,14,0.047000," ","int((c*x^4+2*d)/(a*x^4-b)^(1/4)/(e*x^8-2*f),x)","\[\int \frac{c \,x^{4}+2 d}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(e \,x^{8}-2 f \right)}\, dx\]"," ",0,"int((c*x^4+2*d)/(a*x^4-b)^(1/4)/(e*x^8-2*f),x)","F"
2056,1,217,61,0.177000," ","int((1+x)^(1/2)*(x^2+1)/(x^2-1)/(x+(1+x)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\sqrt{1+x}\, \sqrt{x +\sqrt{1+x}}-\frac{3 \sqrt{x +\sqrt{1+x}}}{2}+\frac{7 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{4}-\frac{\sqrt{2}\, \arctan \left(\frac{2-2 \sqrt{2}+\left(1-2 \sqrt{2}\right) \left(\sqrt{1+x}+\sqrt{2}\right)}{2 \sqrt{\sqrt{2}-1}\, \sqrt{\left(\sqrt{1+x}+\sqrt{2}\right)^{2}+\left(1-2 \sqrt{2}\right) \left(\sqrt{1+x}+\sqrt{2}\right)+1-\sqrt{2}}}\right)}{\sqrt{\sqrt{2}-1}}-\frac{\sqrt{2}\, \arctanh \left(\frac{2+2 \sqrt{2}+\left(1+2 \sqrt{2}\right) \left(\sqrt{1+x}-\sqrt{2}\right)}{2 \sqrt{1+\sqrt{2}}\, \sqrt{\left(\sqrt{1+x}-\sqrt{2}\right)^{2}+\left(1+2 \sqrt{2}\right) \left(\sqrt{1+x}-\sqrt{2}\right)+1+\sqrt{2}}}\right)}{\sqrt{1+\sqrt{2}}}$&$217$\\ default&$\sqrt{1+x}\, \sqrt{x +\sqrt{1+x}}-\frac{3 \sqrt{x +\sqrt{1+x}}}{2}+\frac{7 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{4}-\frac{\sqrt{2}\, \arctan \left(\frac{2-2 \sqrt{2}+\left(1-2 \sqrt{2}\right) \left(\sqrt{1+x}+\sqrt{2}\right)}{2 \sqrt{\sqrt{2}-1}\, \sqrt{\left(\sqrt{1+x}+\sqrt{2}\right)^{2}+\left(1-2 \sqrt{2}\right) \left(\sqrt{1+x}+\sqrt{2}\right)+1-\sqrt{2}}}\right)}{\sqrt{\sqrt{2}-1}}-\frac{\sqrt{2}\, \arctanh \left(\frac{2+2 \sqrt{2}+\left(1+2 \sqrt{2}\right) \left(\sqrt{1+x}-\sqrt{2}\right)}{2 \sqrt{1+\sqrt{2}}\, \sqrt{\left(\sqrt{1+x}-\sqrt{2}\right)^{2}+\left(1+2 \sqrt{2}\right) \left(\sqrt{1+x}-\sqrt{2}\right)+1+\sqrt{2}}}\right)}{\sqrt{1+\sqrt{2}}}$&$217$\\ \hline \end{longtable}"," ",0,"(1+x)^(1/2)*(x+(1+x)^(1/2))^(1/2)-3/2*(x+(1+x)^(1/2))^(1/2)+7/4*ln(1/2+(1+x)^(1/2)+(x+(1+x)^(1/2))^(1/2))-2^(1/2)/(2^(1/2)-1)^(1/2)*arctan(1/2*(2-2*2^(1/2)+(1-2*2^(1/2))*((1+x)^(1/2)+2^(1/2)))/(2^(1/2)-1)^(1/2)/(((1+x)^(1/2)+2^(1/2))^2+(1-2*2^(1/2))*((1+x)^(1/2)+2^(1/2))+1-2^(1/2))^(1/2))-2^(1/2)/(1+2^(1/2))^(1/2)*arctanh(1/2*(2+2*2^(1/2)+(1+2*2^(1/2))*((1+x)^(1/2)-2^(1/2)))/(1+2^(1/2))^(1/2)/(((1+x)^(1/2)-2^(1/2))^2+(1+2*2^(1/2))*((1+x)^(1/2)-2^(1/2))+1+2^(1/2))^(1/2))","B"
2057,1,217,61,0.174000," ","int((1+x)^(1/2)*(x^2+1)/(x^2-1)/(x+(1+x)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\sqrt{1+x}\, \sqrt{x +\sqrt{1+x}}-\frac{3 \sqrt{x +\sqrt{1+x}}}{2}+\frac{7 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{4}-\frac{\sqrt{2}\, \arctan \left(\frac{2-2 \sqrt{2}+\left(1-2 \sqrt{2}\right) \left(\sqrt{1+x}+\sqrt{2}\right)}{2 \sqrt{\sqrt{2}-1}\, \sqrt{\left(\sqrt{1+x}+\sqrt{2}\right)^{2}+\left(1-2 \sqrt{2}\right) \left(\sqrt{1+x}+\sqrt{2}\right)+1-\sqrt{2}}}\right)}{\sqrt{\sqrt{2}-1}}-\frac{\sqrt{2}\, \arctanh \left(\frac{2+2 \sqrt{2}+\left(1+2 \sqrt{2}\right) \left(\sqrt{1+x}-\sqrt{2}\right)}{2 \sqrt{1+\sqrt{2}}\, \sqrt{\left(\sqrt{1+x}-\sqrt{2}\right)^{2}+\left(1+2 \sqrt{2}\right) \left(\sqrt{1+x}-\sqrt{2}\right)+1+\sqrt{2}}}\right)}{\sqrt{1+\sqrt{2}}}$&$217$\\ default&$\sqrt{1+x}\, \sqrt{x +\sqrt{1+x}}-\frac{3 \sqrt{x +\sqrt{1+x}}}{2}+\frac{7 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{4}-\frac{\sqrt{2}\, \arctan \left(\frac{2-2 \sqrt{2}+\left(1-2 \sqrt{2}\right) \left(\sqrt{1+x}+\sqrt{2}\right)}{2 \sqrt{\sqrt{2}-1}\, \sqrt{\left(\sqrt{1+x}+\sqrt{2}\right)^{2}+\left(1-2 \sqrt{2}\right) \left(\sqrt{1+x}+\sqrt{2}\right)+1-\sqrt{2}}}\right)}{\sqrt{\sqrt{2}-1}}-\frac{\sqrt{2}\, \arctanh \left(\frac{2+2 \sqrt{2}+\left(1+2 \sqrt{2}\right) \left(\sqrt{1+x}-\sqrt{2}\right)}{2 \sqrt{1+\sqrt{2}}\, \sqrt{\left(\sqrt{1+x}-\sqrt{2}\right)^{2}+\left(1+2 \sqrt{2}\right) \left(\sqrt{1+x}-\sqrt{2}\right)+1+\sqrt{2}}}\right)}{\sqrt{1+\sqrt{2}}}$&$217$\\ \hline \end{longtable}"," ",0,"(1+x)^(1/2)*(x+(1+x)^(1/2))^(1/2)-3/2*(x+(1+x)^(1/2))^(1/2)+7/4*ln(1/2+(1+x)^(1/2)+(x+(1+x)^(1/2))^(1/2))-2^(1/2)/(2^(1/2)-1)^(1/2)*arctan(1/2*(2-2*2^(1/2)+(1-2*2^(1/2))*((1+x)^(1/2)+2^(1/2)))/(2^(1/2)-1)^(1/2)/(((1+x)^(1/2)+2^(1/2))^2+(1-2*2^(1/2))*((1+x)^(1/2)+2^(1/2))+1-2^(1/2))^(1/2))-2^(1/2)/(1+2^(1/2))^(1/2)*arctanh(1/2*(2+2*2^(1/2)+(1+2*2^(1/2))*((1+x)^(1/2)-2^(1/2)))/(1+2^(1/2))^(1/2)/(((1+x)^(1/2)-2^(1/2))^2+(1+2*2^(1/2))*((1+x)^(1/2)-2^(1/2))+1+2^(1/2))^(1/2))","B"
2058,0,0,117,0.017000," ","int((x-(x^2-1)^(1/2))^(1/2)/x^2,x)","\[\int \frac{\sqrt{x -\sqrt{x^{2}-1}}}{x^{2}}\, dx\]"," ",0,"int((x-(x^2-1)^(1/2))^(1/2)/x^2,x)","F"
2059,0,0,109,180.000000," ","int((a*x+(a^2*x^2-b*x)^(1/2))^(3/4)/(a^2*x^2-b*x)^(1/2),x)","\[\int \frac{\left(a x +\sqrt{a^{2} x^{2}-b x}\right)^{\frac{3}{4}}}{\sqrt{a^{2} x^{2}-b x}}\, dx\]"," ",0,"int((a*x+(a^2*x^2-b*x)^(1/2))^(3/4)/(a^2*x^2-b*x)^(1/2),x)","F"
2060,1,16793,52,101.639000," ","int((1+x)*(x^4+x^3)^(1/4)/x/(x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$16793$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2061,0,0,128,0.011000," ","int((a*x^4-b*x^3)^(1/4)*(c*x^4-d)/x^4,x)","\[\int \frac{\left(a \,x^{4}-b \,x^{3}\right)^{\frac{1}{4}} \left(c \,x^{4}-d \right)}{x^{4}}\, dx\]"," ",0,"int((a*x^4-b*x^3)^(1/4)*(c*x^4-d)/x^4,x)","F"
2062,1,609,111,17.284000," ","int((x^3+1)^(2/3)*(x^3+2)/x^6/(x^3+4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{13 x^{6}+21 x^{3}+8}{80 x^{5} \left(x^{3}+1\right)^{\frac{1}{3}}}+\frac{\RootOf \left(\textit{\_Z}^{3}+36\right) \ln \left(-\frac{756 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+36\right)^{2}+36 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+36\right)+1296 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+36\right)^{2} x^{3}+9 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+36\right)^{2}+36 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+36\right)+1296 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+36\right)^{3} x^{3}+132 \left(x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+36\right)^{2}+36 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+36\right)+1296 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+36\right)^{2} x +36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+36\right)^{2}+36 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+36\right)+1296 \textit{\_Z}^{2}\right) \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+36\right) x^{2}+11 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+36\right)^{2} x^{2}-1764 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+36\right)^{2}+36 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+36\right)+1296 \textit{\_Z}^{2}\right) x^{3}-21 \RootOf \left(\textit{\_Z}^{3}+36\right) x^{3}-120 x \left(x^{3}+1\right)^{\frac{2}{3}}-1008 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+36\right)^{2}+36 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+36\right)+1296 \textit{\_Z}^{2}\right)-12 \RootOf \left(\textit{\_Z}^{3}+36\right)}{x^{3}+4}\right)}{96}+\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+36\right)^{2}+36 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+36\right)+1296 \textit{\_Z}^{2}\right) \ln \left(\frac{324 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+36\right)^{2}+36 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+36\right)+1296 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+36\right)^{2} x^{3}+21 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+36\right)^{2}+36 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+36\right)+1296 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+36\right)^{3} x^{3}+132 \left(x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+36\right)^{2}+36 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+36\right)+1296 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+36\right)^{2} x +360 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+36\right)^{2}+36 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+36\right)+1296 \textit{\_Z}^{2}\right) \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+36\right) x^{2}+11 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+36\right)^{2} x^{2}+432 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+36\right)^{2}+36 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+36\right)+1296 \textit{\_Z}^{2}\right) x^{3}+28 \RootOf \left(\textit{\_Z}^{3}+36\right) x^{3}-12 x \left(x^{3}+1\right)^{\frac{2}{3}}+432 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+36\right)^{2}+36 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+36\right)+1296 \textit{\_Z}^{2}\right)+28 \RootOf \left(\textit{\_Z}^{3}+36\right)}{x^{3}+4}\right)}{8}$&$609$\\ trager&$\text{Expression too large to display}$&$1113$\\ \hline \end{longtable}"," ",0,"-1/80*(13*x^6+21*x^3+8)/x^5/(x^3+1)^(1/3)+1/96*RootOf(_Z^3+36)*ln(-(756*RootOf(RootOf(_Z^3+36)^2+36*_Z*RootOf(_Z^3+36)+1296*_Z^2)^2*RootOf(_Z^3+36)^2*x^3+9*RootOf(RootOf(_Z^3+36)^2+36*_Z*RootOf(_Z^3+36)+1296*_Z^2)*RootOf(_Z^3+36)^3*x^3+132*(x^3+1)^(2/3)*RootOf(RootOf(_Z^3+36)^2+36*_Z*RootOf(_Z^3+36)+1296*_Z^2)*RootOf(_Z^3+36)^2*x+36*RootOf(RootOf(_Z^3+36)^2+36*_Z*RootOf(_Z^3+36)+1296*_Z^2)*(x^3+1)^(1/3)*RootOf(_Z^3+36)*x^2+11*(x^3+1)^(1/3)*RootOf(_Z^3+36)^2*x^2-1764*RootOf(RootOf(_Z^3+36)^2+36*_Z*RootOf(_Z^3+36)+1296*_Z^2)*x^3-21*RootOf(_Z^3+36)*x^3-120*x*(x^3+1)^(2/3)-1008*RootOf(RootOf(_Z^3+36)^2+36*_Z*RootOf(_Z^3+36)+1296*_Z^2)-12*RootOf(_Z^3+36))/(x^3+4))+3/8*RootOf(RootOf(_Z^3+36)^2+36*_Z*RootOf(_Z^3+36)+1296*_Z^2)*ln((324*RootOf(RootOf(_Z^3+36)^2+36*_Z*RootOf(_Z^3+36)+1296*_Z^2)^2*RootOf(_Z^3+36)^2*x^3+21*RootOf(RootOf(_Z^3+36)^2+36*_Z*RootOf(_Z^3+36)+1296*_Z^2)*RootOf(_Z^3+36)^3*x^3+132*(x^3+1)^(2/3)*RootOf(RootOf(_Z^3+36)^2+36*_Z*RootOf(_Z^3+36)+1296*_Z^2)*RootOf(_Z^3+36)^2*x+360*RootOf(RootOf(_Z^3+36)^2+36*_Z*RootOf(_Z^3+36)+1296*_Z^2)*(x^3+1)^(1/3)*RootOf(_Z^3+36)*x^2+11*(x^3+1)^(1/3)*RootOf(_Z^3+36)^2*x^2+432*RootOf(RootOf(_Z^3+36)^2+36*_Z*RootOf(_Z^3+36)+1296*_Z^2)*x^3+28*RootOf(_Z^3+36)*x^3-12*x*(x^3+1)^(2/3)+432*RootOf(RootOf(_Z^3+36)^2+36*_Z*RootOf(_Z^3+36)+1296*_Z^2)+28*RootOf(_Z^3+36))/(x^3+4))","C"
2063,1,643,115,18.030000," ","int((x^3-1)*(3*x^3+1)^(2/3)/x^6/(x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{6 x^{6}-x^{3}-1}{5 x^{5} \left(3 x^{3}+1\right)^{\frac{1}{3}}}+4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \ln \left(\frac{15 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}+36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}+24 \left(3 x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +8 \left(3 x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{2}+42 \left(3 x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) x^{2}+15 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}+36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) x^{3}-2 \left(3 x^{3}+1\right)^{\frac{2}{3}} x +5 \RootOf \left(\textit{\_Z}^{3}+4\right)+12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)}{\left(1+x \right) \left(x^{2}-x +1\right)}\right)+\frac{2 \RootOf \left(\textit{\_Z}^{3}+4\right) \ln \left(-\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}+45 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}+12 \left(3 x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +4 \left(3 x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{2}+3 \left(3 x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) x^{2}-5 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}-75 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) x^{3}-7 \left(3 x^{3}+1\right)^{\frac{2}{3}} x -\RootOf \left(\textit{\_Z}^{3}+4\right)-15 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)}{\left(1+x \right) \left(x^{2}-x +1\right)}\right)}{3}$&$643$\\ trager&$\text{Expression too large to display}$&$1164$\\ \hline \end{longtable}"," ",0,"-1/5*(6*x^6-x^3-1)/x^5/(3*x^3+1)^(1/3)+4*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*ln((15*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3*x^3+36*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+24*(3*x^3+1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*x+8*(3*x^3+1)^(1/3)*RootOf(_Z^3+4)^2*x^2+42*(3*x^3+1)^(1/3)*RootOf(_Z^3+4)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^2+15*RootOf(_Z^3+4)*x^3+36*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^3-2*(3*x^3+1)^(2/3)*x+5*RootOf(_Z^3+4)+12*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2))/(1+x)/(x^2-x+1))+2/3*RootOf(_Z^3+4)*ln(-(3*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3*x^3+45*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+12*(3*x^3+1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*x+4*(3*x^3+1)^(1/3)*RootOf(_Z^3+4)^2*x^2+3*(3*x^3+1)^(1/3)*RootOf(_Z^3+4)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^2-5*RootOf(_Z^3+4)*x^3-75*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^3-7*(3*x^3+1)^(2/3)*x-RootOf(_Z^3+4)-15*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2))/(1+x)/(x^2-x+1))","C"
2064,1,2145,133,5.372000," ","int((-12*x^4+8*x^2-8*x+3)/x/((-2*x^2+1)/(2*x^2+1))^(1/3)/(2*x^2+1)/(2*x^4-6*x^3+7*x^2-7*x+3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2145$\\ \hline \end{longtable}"," ",0,"-2*ln((8-12*x+56*RootOf(4*_Z^2+2*_Z+1)^2*x^2+28*RootOf(4*_Z^2+2*_Z+1)*x^5-84*RootOf(4*_Z^2+2*_Z+1)*x^4+98*RootOf(4*_Z^2+2*_Z+1)*x^3-58*RootOf(4*_Z^2+2*_Z+1)*x^2+42*RootOf(4*_Z^2+2*_Z+1)*x+15*(-(2*x^2-1)/(2*x^2+1))^(1/3)+15*(-(2*x^2-1)/(2*x^2+1))^(2/3)-30*x*(-(2*x^2-1)/(2*x^2+1))^(1/3)-8*x^5+12*x^2-28*x^3+24*x^4-28*RootOf(4*_Z^2+2*_Z+1)^2-20*RootOf(4*_Z^2+2*_Z+1)+12*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(2/3)*x^3-12*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(2/3)*x^2-12*x^4*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3)+24*x^3*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3)-18*x^2*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3)+12*x*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3)+6*x*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(2/3)-30*(-(2*x^2-1)/(2*x^2+1))^(2/3)*x^3-6*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(2/3)-15*(-(2*x^2-1)/(2*x^2+1))^(2/3)*x+45*(-(2*x^2-1)/(2*x^2+1))^(1/3)*x^2+30*(-(2*x^2-1)/(2*x^2+1))^(2/3)*x^2+30*(-(2*x^2-1)/(2*x^2+1))^(1/3)*x^4-60*(-(2*x^2-1)/(2*x^2+1))^(1/3)*x^3-6*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3))/x/(2*x^4-6*x^3+7*x^2-7*x+3))*RootOf(4*_Z^2+2*_Z+1)+2*RootOf(4*_Z^2+2*_Z+1)*ln((11-33*x+56*RootOf(4*_Z^2+2*_Z+1)^2*x^2-28*RootOf(4*_Z^2+2*_Z+1)*x^5+84*RootOf(4*_Z^2+2*_Z+1)*x^4-98*RootOf(4*_Z^2+2*_Z+1)*x^3+114*RootOf(4*_Z^2+2*_Z+1)*x^2-42*RootOf(4*_Z^2+2*_Z+1)*x+18*(-(2*x^2-1)/(2*x^2+1))^(1/3)+18*(-(2*x^2-1)/(2*x^2+1))^(2/3)-36*x*(-(2*x^2-1)/(2*x^2+1))^(1/3)-22*x^5+55*x^2-77*x^3+66*x^4-28*RootOf(4*_Z^2+2*_Z+1)^2-8*RootOf(4*_Z^2+2*_Z+1)-12*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(2/3)*x^3+12*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(2/3)*x^2+12*x^4*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3)-24*x^3*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3)+18*x^2*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3)-12*x*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3)-6*x*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(2/3)-36*(-(2*x^2-1)/(2*x^2+1))^(2/3)*x^3+6*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(2/3)-18*(-(2*x^2-1)/(2*x^2+1))^(2/3)*x+54*(-(2*x^2-1)/(2*x^2+1))^(1/3)*x^2+36*(-(2*x^2-1)/(2*x^2+1))^(2/3)*x^2+36*(-(2*x^2-1)/(2*x^2+1))^(1/3)*x^4-72*(-(2*x^2-1)/(2*x^2+1))^(1/3)*x^3+6*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3))/x/(2*x^4-6*x^3+7*x^2-7*x+3))-ln((8-12*x+56*RootOf(4*_Z^2+2*_Z+1)^2*x^2+28*RootOf(4*_Z^2+2*_Z+1)*x^5-84*RootOf(4*_Z^2+2*_Z+1)*x^4+98*RootOf(4*_Z^2+2*_Z+1)*x^3-58*RootOf(4*_Z^2+2*_Z+1)*x^2+42*RootOf(4*_Z^2+2*_Z+1)*x+15*(-(2*x^2-1)/(2*x^2+1))^(1/3)+15*(-(2*x^2-1)/(2*x^2+1))^(2/3)-30*x*(-(2*x^2-1)/(2*x^2+1))^(1/3)-8*x^5+12*x^2-28*x^3+24*x^4-28*RootOf(4*_Z^2+2*_Z+1)^2-20*RootOf(4*_Z^2+2*_Z+1)+12*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(2/3)*x^3-12*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(2/3)*x^2-12*x^4*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3)+24*x^3*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3)-18*x^2*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3)+12*x*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3)+6*x*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(2/3)-30*(-(2*x^2-1)/(2*x^2+1))^(2/3)*x^3-6*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(2/3)-15*(-(2*x^2-1)/(2*x^2+1))^(2/3)*x+45*(-(2*x^2-1)/(2*x^2+1))^(1/3)*x^2+30*(-(2*x^2-1)/(2*x^2+1))^(2/3)*x^2+30*(-(2*x^2-1)/(2*x^2+1))^(1/3)*x^4-60*(-(2*x^2-1)/(2*x^2+1))^(1/3)*x^3-6*RootOf(4*_Z^2+2*_Z+1)*(-(2*x^2-1)/(2*x^2+1))^(1/3))/x/(2*x^4-6*x^3+7*x^2-7*x+3))","C"
2065,1,421,113,0.156000," ","int(x^2/(a*x^3+b*x)^(1/2)/(a^2*x^4-b^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{x}{2 a b \sqrt{\left(x^{2}+\frac{b}{a}\right) a x}}+\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{4 a^{2} b \sqrt{a \,x^{3}+b x}}+\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{4 a^{2} \sqrt{a b}\, \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}-\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{4 a^{2} \sqrt{a b}\, \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}$&$421$\\ default&$\frac{\frac{x}{b \sqrt{\left(x^{2}+\frac{b}{a}\right) a x}}+\frac{\sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{2 b a \sqrt{a \,x^{3}+b x}}}{2 a}+\frac{\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{a b}\, a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}-\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{a b}\, a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}}{2 a}$&$448$\\ \hline \end{longtable}"," ",0,"1/2/a*x/b/((x^2+b/a)*a*x)^(1/2)+1/4/a^2/b*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)*EllipticF(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))+1/4/a^2/(a*b)^(1/2)*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2)),1/2*2^(1/2))-1/4/a^2/(a*b)^(1/2)*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)+1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)+1/a*(a*b)^(1/2)),1/2*2^(1/2))","C"
2066,0,0,117,0.013000," ","int((a*x^6+b)/x^6/(a*x^3-b)/(a*x^4+b*x)^(1/4),x)","\[\int \frac{a \,x^{6}+b}{x^{6} \left(a \,x^{3}-b \right) \left(a \,x^{4}+b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^6+b)/x^6/(a*x^3-b)/(a*x^4+b*x)^(1/4),x)","F"
2067,1,2498,121,9.580000," ","int((x^8+2*x^3-1)^(1/3)*(5*x^8+3)/x^2/(x^8-1),x)","\[\text{Expression too large to display}\]"," ",0,"3*(x^8+2*x^3-1)^(1/3)/x+(-ln((RootOf(_Z^3-2)*x^16+4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^16+2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x^11+8*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^11+6*(x^16+4*x^11-2*x^8+4*x^6-4*x^3+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^9+6*RootOf(_Z^3-2)*x^11+24*x^11*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)+4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x^6+16*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^6-2*RootOf(_Z^3-2)*x^8-8*x^8*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)-2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3-8*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3+6*(x^16+4*x^11-2*x^8+4*x^6-4*x^3+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x^2+12*(x^16+4*x^11-2*x^8+4*x^6-4*x^3+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^4+8*RootOf(_Z^3-2)*x^6+32*x^6*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)-6*(x^16+4*x^11-2*x^8+4*x^6-4*x^3+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x-6*RootOf(_Z^3-2)*x^3-24*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3+RootOf(_Z^3-2)+4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2))/(x^8+2*x^3-1)/(-1+x)/(1+x)/(x^2+1)/(x^4+1))*RootOf(_Z^3-2)+2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*ln((-4*RootOf(_Z^3-2)*x^11+2*RootOf(_Z^3-2)*x^8-4*RootOf(_Z^3-2)*x^6+4*RootOf(_Z^3-2)*x^3+16*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3-RootOf(_Z^3-2)*x^16-4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)-8*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-RootOf(_Z^3-2)-6*(x^16+4*x^11-2*x^8+4*x^6-4*x^3+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^9-2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3-16*x^6*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)+16*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^6+4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x^6-6*(x^16+4*x^11-2*x^8+4*x^6-4*x^3+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x^2-12*(x^16+4*x^11-2*x^8+4*x^6-4*x^3+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^4+6*(x^16+4*x^11-2*x^8+4*x^6-4*x^3+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x+8*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^11+2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x^11-6*(x^16+4*x^11-2*x^8+4*x^6-4*x^3+1)^(2/3)*x^2-3*(x^16+4*x^11-2*x^8+4*x^6-4*x^3+1)^(1/3)*RootOf(_Z^3-2)^2*x^9-6*(x^16+4*x^11-2*x^8+4*x^6-4*x^3+1)^(1/3)*RootOf(_Z^3-2)^2*x^4+3*(x^16+4*x^11-2*x^8+4*x^6-4*x^3+1)^(1/3)*RootOf(_Z^3-2)^2*x-16*x^11*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)+8*x^8*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)-4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^16)/(x^8+2*x^3-1)/(-1+x)/(1+x)/(x^2+1)/(x^4+1))-2*ln((RootOf(_Z^3-2)*x^16+4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^16+2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x^11+8*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^11+6*(x^16+4*x^11-2*x^8+4*x^6-4*x^3+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^9+6*RootOf(_Z^3-2)*x^11+24*x^11*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)+4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x^6+16*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^6-2*RootOf(_Z^3-2)*x^8-8*x^8*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)-2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3-8*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3+6*(x^16+4*x^11-2*x^8+4*x^6-4*x^3+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x^2+12*(x^16+4*x^11-2*x^8+4*x^6-4*x^3+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^4+8*RootOf(_Z^3-2)*x^6+32*x^6*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)-6*(x^16+4*x^11-2*x^8+4*x^6-4*x^3+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x-6*RootOf(_Z^3-2)*x^3-24*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3+RootOf(_Z^3-2)+4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2))/(x^8+2*x^3-1)/(-1+x)/(1+x)/(x^2+1)/(x^4+1))*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2))/(x^8+2*x^3-1)^(2/3)*((x^8+2*x^3-1)^2)^(1/3)","C"
2068,0,0,112,0.027000," ","int((a*x^2+b^2)^(1/2)/(b+(a*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{a \,x^{2}+b^{2}}}{\sqrt{b +\sqrt{a \,x^{2}+b^{2}}}}\, dx\]"," ",0,"int((a*x^2+b^2)^(1/2)/(b+(a*x^2+b^2)^(1/2))^(1/2),x)","F"
2069,0,0,121,0.030000," ","int((b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2)^3,x)","\[\int \frac{\sqrt{b +\sqrt{a \,x^{2}+b^{2}}}}{\left(a \,x^{2}+b^{2}\right)^{3}}\, dx\]"," ",0,"int((b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2)^3,x)","F"
2070,0,0,114,0.006000," ","int((a*x^2-b)^(3/4)/x^3,x)","\[\int \frac{\left(a \,x^{2}-b \right)^{\frac{3}{4}}}{x^{3}}\, dx\]"," ",0,"int((a*x^2-b)^(3/4)/x^3,x)","F"
2071,1,631,116,17.259000," ","int((x^3+1)*(2*x^3-1)^(2/3)/x^6/(2*x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{18 x^{6}-13 x^{3}+2}{10 x^{5} \left(2 x^{3}-1\right)^{\frac{1}{3}}}+\frac{2 \RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(-\frac{12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} x^{3}+108 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}-12 \left(2 x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x +4 \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \left(2 x^{3}-1\right)^{\frac{1}{3}} x^{2}-6 \RootOf \left(\textit{\_Z}^{3}-2\right) \left(2 x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) x^{2}+6 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{3}+54 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) x^{3}-5 \left(2 x^{3}-1\right)^{\frac{2}{3}} x -\RootOf \left(\textit{\_Z}^{3}-2\right)-9 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)}{2 x^{3}+1}\right)}{3}+4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \ln \left(\frac{36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} x^{3}+144 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}-24 \left(2 x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x +8 \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \left(2 x^{3}-1\right)^{\frac{1}{3}} x^{2}+60 \RootOf \left(\textit{\_Z}^{3}-2\right) \left(2 x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) x^{2}-6 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{3}-24 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) x^{3}+2 \left(2 x^{3}-1\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{3}-2\right)+12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)}{2 x^{3}+1}\right)$&$631$\\ trager&$\frac{\left(2 x^{3}-1\right)^{\frac{2}{3}} \left(9 x^{3}-2\right)}{10 x^{5}}+\frac{2 \RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(\frac{204 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} x^{3}+396 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}-720 \left(2 x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x +240 \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \left(2 x^{3}-1\right)^{\frac{1}{3}} x^{2}+1422 \RootOf \left(\textit{\_Z}^{3}-2\right) \left(2 x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) x^{2}-204 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}-396 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-374 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{3}-726 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) x^{3}-3 \left(2 x^{3}-1\right)^{\frac{2}{3}} x +17 \RootOf \left(\textit{\_Z}^{3}-2\right)+33 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)}{2 x^{3}+1}\right)}{3}+4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \ln \left(\frac{2676 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} x^{3}+96912 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}-64656 \left(2 x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x +21552 \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \left(2 x^{3}-1\right)^{\frac{1}{3}} x^{2}+24372 \RootOf \left(\textit{\_Z}^{3}-2\right) \left(2 x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) x^{2}-2676 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}-96912 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+5798 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{3}+209976 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) x^{3}-17490 \left(2 x^{3}-1\right)^{\frac{2}{3}} x -1115 \RootOf \left(\textit{\_Z}^{3}-2\right)-40380 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)}{2 x^{3}+1}\right)$&$765$\\ \hline \end{longtable}"," ",0,"1/10*(18*x^6-13*x^3+2)/x^5/(2*x^3-1)^(1/3)+2/3*RootOf(_Z^3-2)*ln(-(12*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^3+108*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-12*(2*x^3-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^2*x+4*RootOf(_Z^3-2)^2*(2*x^3-1)^(1/3)*x^2-6*RootOf(_Z^3-2)*(2*x^3-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^2+6*RootOf(_Z^3-2)*x^3+54*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^3-5*(2*x^3-1)^(2/3)*x-RootOf(_Z^3-2)-9*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2))/(2*x^3+1))+4*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*ln((36*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^3+144*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-24*(2*x^3-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^2*x+8*RootOf(_Z^3-2)^2*(2*x^3-1)^(1/3)*x^2+60*RootOf(_Z^3-2)*(2*x^3-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^2-6*RootOf(_Z^3-2)*x^3-24*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^3+2*(2*x^3-1)^(2/3)*x+3*RootOf(_Z^3-2)+12*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2))/(2*x^3+1))","C"
2072,1,791,114,18.041000," ","int((-x^3+1)^(2/3)*(4*x^3-1)/x^6/(3*x^3-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{29 x^{6}-33 x^{3}+4}{40 x^{5} \left(-x^{3}+1\right)^{\frac{1}{3}}}+\frac{5 \RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(-\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} x^{3}+9 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}+9 \left(-x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x -9 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right) x^{2}+2 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{3}+6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) x^{3}+3 \left(-x^{3}+1\right)^{\frac{2}{3}} x -2 \RootOf \left(\textit{\_Z}^{3}-2\right)-6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)}{3 x^{3}-2}\right)}{24}-\frac{5 \ln \left(-\frac{6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} x^{3}+18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}-18 \left(-x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x -3 \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2}-2 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{3}-6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) x^{3}+4 \RootOf \left(\textit{\_Z}^{3}-2\right)+12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)}{3 x^{3}-2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)}{24}-\frac{5 \ln \left(-\frac{6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} x^{3}+18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}-18 \left(-x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x -3 \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \left(-x^{3}+1\right)^{\frac{1}{3}} x^{2}-2 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{3}-6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right) x^{3}+4 \RootOf \left(\textit{\_Z}^{3}-2\right)+12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)}{3 x^{3}-2}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+36 \textit{\_Z}^{2}\right)}{4}$&$791$\\ trager&$\text{Expression too large to display}$&$1147$\\ \hline \end{longtable}"," ",0,"-1/40*(29*x^6-33*x^3+4)/x^5/(-x^3+1)^(1/3)+5/24*RootOf(_Z^3-2)*ln(-(3*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^3+9*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^3+9*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^2*x-9*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)*x^2+2*RootOf(_Z^3-2)*x^3+6*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^3+3*(-x^3+1)^(2/3)*x-2*RootOf(_Z^3-2)-6*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2))/(3*x^3-2))-5/24*ln(-(6*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^3+18*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-18*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^2*x-3*RootOf(_Z^3-2)^2*(-x^3+1)^(1/3)*x^2-2*RootOf(_Z^3-2)*x^3-6*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^3+4*RootOf(_Z^3-2)+12*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2))/(3*x^3-2))*RootOf(_Z^3-2)-5/4*ln(-(6*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x^3+18*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-18*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^2*x-3*RootOf(_Z^3-2)^2*(-x^3+1)^(1/3)*x^2-2*RootOf(_Z^3-2)*x^3-6*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^3+4*RootOf(_Z^3-2)+12*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2))/(3*x^3-2))*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)","C"
2073,0,0,114,0.005000," ","int((a*x^3-b)^(1/4)/x^4,x)","\[\int \frac{\left(a \,x^{3}-b \right)^{\frac{1}{4}}}{x^{4}}\, dx\]"," ",0,"int((a*x^3-b)^(1/4)/x^4,x)","F"
2074,0,0,114,0.005000," ","int((a*x^3-b)^(3/4)/x^4,x)","\[\int \frac{\left(a \,x^{3}-b \right)^{\frac{3}{4}}}{x^{4}}\, dx\]"," ",0,"int((a*x^3-b)^(3/4)/x^4,x)","F"
2075,0,0,136,0.021000," ","int((-a+x)*(-3*a*b+(a+2*b)*x)*(-b^3+3*b^2*x-3*b*x^2+x^3)/x/(x*(-a+x)*(-b+x)^2)^(3/4)/(a*b^2-b*(2*a+b)*x+(a+2*b)*x^2+(-1+d)*x^3),x)","\[\int \frac{\left(-a +x \right) \left(-3 a b +\left(a +2 b \right) x \right) \left(-b^{3}+3 b^{2} x -3 b \,x^{2}+x^{3}\right)}{x \left(x \left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{3}{4}} \left(a \,b^{2}-b \left(2 a +b \right) x +\left(a +2 b \right) x^{2}+\left(-1+d \right) x^{3}\right)}\, dx\]"," ",0,"int((-a+x)*(-3*a*b+(a+2*b)*x)*(-b^3+3*b^2*x-3*b*x^2+x^3)/x/(x*(-a+x)*(-b+x)^2)^(3/4)/(a*b^2-b*(2*a+b)*x+(a+2*b)*x^2+(-1+d)*x^3),x)","F"
2076,0,0,114,0.005000," ","int((a*x^5-b)^(3/4)/x^6,x)","\[\int \frac{\left(a \,x^{5}-b \right)^{\frac{3}{4}}}{x^{6}}\, dx\]"," ",0,"int((a*x^5-b)^(3/4)/x^6,x)","F"
2077,0,0,114,0.006000," ","int((a*x^6-b)^(3/4)/x^7,x)","\[\int \frac{\left(a \,x^{6}-b \right)^{\frac{3}{4}}}{x^{7}}\, dx\]"," ",0,"int((a*x^6-b)^(3/4)/x^7,x)","F"
2078,1,1516,122,410.452000," ","int((5*x^7-4)*(-x^8+2*x^3-2*x)^(1/3)/(x^7+2)/(x^7-2*x^2+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1516$\\ \hline \end{longtable}"," ",0,"-1/2*ln(-(20398661435090962540236945828*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^3*x^7+10729899307170181748674598182*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^4*x^7-10199330717545481270118472914*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^7-5364949653585090874337299091*RootOf(_Z^3+2)^2*x^7-61195984305272887620710837484*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^3*x^2-32189697921510545246023794546*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^4*x^2+40797322870181925080473891656*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^3+21459798614340363497349196364*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^4+30597992152636443810355418742*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*(-x^8+2*x^3-2*x)^(2/3)+61195984305272887620710837484*x^2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)+32189697921510545246023794546*x^2*RootOf(_Z^3+2)^2+3183411537748202871336751608*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*(-x^8+2*x^3-2*x)^(1/3)*x-30597992152636443810355418742*(-x^8+2*x^3-2*x)^(1/3)*RootOf(_Z^3+2)*x-20398661435090962540236945828*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)-10729899307170181748674598182*RootOf(_Z^3+2)^2-32189697921510545246023794546*(-x^8+2*x^3-2*x)^(2/3))/(x^7+2))*RootOf(_Z^3+2)-ln(-(20398661435090962540236945828*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^3*x^7+10729899307170181748674598182*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^4*x^7-10199330717545481270118472914*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^7-5364949653585090874337299091*RootOf(_Z^3+2)^2*x^7-61195984305272887620710837484*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^3*x^2-32189697921510545246023794546*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^4*x^2+40797322870181925080473891656*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^3+21459798614340363497349196364*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^4+30597992152636443810355418742*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*(-x^8+2*x^3-2*x)^(2/3)+61195984305272887620710837484*x^2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)+32189697921510545246023794546*x^2*RootOf(_Z^3+2)^2+3183411537748202871336751608*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*(-x^8+2*x^3-2*x)^(1/3)*x-30597992152636443810355418742*(-x^8+2*x^3-2*x)^(1/3)*RootOf(_Z^3+2)*x-20398661435090962540236945828*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)-10729899307170181748674598182*RootOf(_Z^3+2)^2-32189697921510545246023794546*(-x^8+2*x^3-2*x)^(2/3))/(x^7+2))*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)+1/2*RootOf(_Z^3+2)*ln((207542028224584*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^3*x^7+108187121643730*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^4*x^7-103771014112292*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^7-54093560821865*RootOf(_Z^3+2)^2*x^7-622626084673752*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^3*x^2-324561364931190*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^4*x^2+415084056449168*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^3+216374243287460*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^4+324561364931190*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*(-x^8+2*x^3-2*x)^(2/3)-622626084673752*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*(-x^8+2*x^3-2*x)^(1/3)*x-324561364931190*(-x^8+2*x^3-2*x)^(1/3)*RootOf(_Z^3+2)*x-207542028224584*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)-108187121643730*RootOf(_Z^3+2)^2-13248322594314*(-x^8+2*x^3-2*x)^(2/3))/(x^7+2))","C"
2079,0,0,50,0.031000," ","int((2*x^8-2*a*x^4+b)/(a*x^4+b)^(1/4)/(x^8-a*x^4-2*b),x)","\[\int \frac{2 x^{8}-2 a \,x^{4}+b}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(x^{8}-a \,x^{4}-2 b \right)}\, dx\]"," ",0,"int((2*x^8-2*a*x^4+b)/(a*x^4+b)^(1/4)/(x^8-a*x^4-2*b),x)","F"
2080,0,0,50,0.029000," ","int((2*x^8+2*a*x^4-b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x)","\[\int \frac{2 x^{8}+2 a \,x^{4}-b}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(x^{8}+a \,x^{4}-b \right)}\, dx\]"," ",0,"int((2*x^8+2*a*x^4-b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x)","F"
2081,0,0,50,0.002000," ","int((2*x^8+2*a*x^4-b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x)","\[\int \frac{2 x^{8}+2 a \,x^{4}-b}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(x^{8}+a \,x^{4}-b \right)}\, dx\]"," ",0,"int((2*x^8+2*a*x^4-b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-b),x)","F"
2082,1,284,130,0.129000," ","int((a^4*x^4-b^4)^(1/2)*(a^4*x^4+b^4)/(a^8*x^8+b^8),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(\frac{\ln \left(\frac{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}-\frac{\sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}\, \sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{2 x}+\frac{\sqrt{2}\, \sqrt{a^{4} b^{4}}}{2}}{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}+\frac{\sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}\, \sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{2 x}+\frac{\sqrt{2}\, \sqrt{a^{4} b^{4}}}{2}}\right)}{4 \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}+\frac{\arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{\sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}\, x}+1\right)}{2 \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}+\frac{\arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{\sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}\, x}-1\right)}{2 \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}\right) \sqrt{2}}{2}$&$284$\\ elliptic&$\frac{\left(\frac{\ln \left(\frac{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}-\frac{\sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}\, \sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{2 x}+\frac{\sqrt{2}\, \sqrt{a^{4} b^{4}}}{2}}{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}+\frac{\sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}\, \sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{2 x}+\frac{\sqrt{2}\, \sqrt{a^{4} b^{4}}}{2}}\right)}{4 \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}+\frac{\arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{\sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}\, x}+1\right)}{2 \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}+\frac{\arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{\sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}\, x}-1\right)}{2 \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}\right) \sqrt{2}}{2}$&$284$\\ \hline \end{longtable}"," ",0,"1/2*(1/4/(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*ln((1/2*(a^4*x^4-b^4)/x^2-1/2*(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x+1/2*2^(1/2)*(a^4*b^4)^(1/2))/(1/2*(a^4*x^4-b^4)/x^2+1/2*(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x+1/2*2^(1/2)*(a^4*b^4)^(1/2)))+1/2/(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*arctan(1/(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x+1)+1/2/(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*arctan(1/(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x-1))*2^(1/2)","B"
2083,1,281,130,0.145000," ","int((a^8*x^8-b^8)/(a^4*x^4-b^4)^(1/2)/(a^8*x^8+b^8),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{\sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}-\frac{b^{8} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{8} a^{8}+b^{8}\right)}{\sum}\frac{-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(a^{4} \underline{\hspace{1.25 ex}}\alpha^{6}+b^{4} x^{2}\right) a^{4}}{b^{4} \sqrt{a^{4} \underline{\hspace{1.25 ex}}\alpha^{4}-b^{4}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{\sqrt{a^{4} \underline{\hspace{1.25 ex}}\alpha^{4}-b^{4}}}+\frac{2 \underline{\hspace{1.25 ex}}\alpha^{7} a^{8} \sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{6} a^{6}}{b^{6}}, \frac{\sqrt{\frac{a^{2}}{b^{2}}}}{\sqrt{-\frac{a^{2}}{b^{2}}}}\right)}{\sqrt{-\frac{a^{2}}{b^{2}}}\, b^{8} \sqrt{a^{4} x^{4}-b^{4}}}}{\underline{\hspace{1.25 ex}}\alpha^{7}}\right)}{8 a^{8}}$&$281$\\ elliptic&$\frac{\left(\frac{\ln \left(\frac{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}-\frac{\sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}\, \sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{2 x}+\frac{\sqrt{2}\, \sqrt{a^{4} b^{4}}}{2}}{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}+\frac{\sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}\, \sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{2 x}+\frac{\sqrt{2}\, \sqrt{a^{4} b^{4}}}{2}}\right)}{4 \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}+\frac{\arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{\sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}\, x}+1\right)}{2 \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}+\frac{\arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{\sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}\, x}-1\right)}{2 \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}\right) \sqrt{2}}{2}$&$284$\\ \hline \end{longtable}"," ",0,"1/(-a^2/b^2)^(1/2)*(a^2*x^2/b^2+1)^(1/2)*(1-a^2*x^2/b^2)^(1/2)/(a^4*x^4-b^4)^(1/2)*EllipticF(x*(-a^2/b^2)^(1/2),I)-1/8*b^8/a^8*sum(1/_alpha^7*(-1/(_alpha^4*a^4-b^4)^(1/2)*arctanh(_alpha^2/b^4*(_alpha^6*a^4+b^4*x^2)*a^4/(_alpha^4*a^4-b^4)^(1/2)/(a^4*x^4-b^4)^(1/2))+2/(-a^2/b^2)^(1/2)*_alpha^7*a^8/b^8*(a^2*x^2/b^2+1)^(1/2)*(1-a^2*x^2/b^2)^(1/2)/(a^4*x^4-b^4)^(1/2)*EllipticPi(x*(-a^2/b^2)^(1/2),_alpha^6*a^6/b^6,(a^2/b^2)^(1/2)/(-a^2/b^2)^(1/2))),_alpha=RootOf(_Z^8*a^8+b^8))","C"
2084,0,0,119,0.028000," ","int(x^3*(x^2+x)^(1/2)/(x^2+x*(x^2+x)^(1/2))^(1/2),x)","\[\int \frac{x^{3} \sqrt{x^{2}+x}}{\sqrt{x^{2}+x \sqrt{x^{2}+x}}}\, dx\]"," ",0,"int(x^3*(x^2+x)^(1/2)/(x^2+x*(x^2+x)^(1/2))^(1/2),x)","F"
2085,0,0,119,0.027000," ","int((a*x^2-b)^(3/4)*(2*a*x^2+3*b)/x,x)","\[\int \frac{\left(a \,x^{2}-b \right)^{\frac{3}{4}} \left(2 a \,x^{2}+3 b \right)}{x}\, dx\]"," ",0,"int((a*x^2-b)^(3/4)*(2*a*x^2+3*b)/x,x)","F"
2086,1,735,122,19.801000," ","int((x^2-6)*(x^3-x^2+2)^(2/3)/x^3/(x^3+x^2-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{3 \left(x^{3}-x^{2}+2\right)^{\frac{2}{3}}}{2 x^{2}}+\RootOf \left(\textit{\_Z}^{3}+4\right) \ln \left(\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}+3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}+2 \left(x^{3}-x^{2}+2\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +2 \left(x^{3}-x^{2}+2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{2}-\left(x^{3}-x^{2}+2\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}-3 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}-9 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) x^{3}-5 \left(x^{3}-x^{2}+2\right)^{\frac{2}{3}} x +\RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}+3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{3}+4\right)-6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right)}{\left(-1+x \right) \left(x^{2}+2 x +2\right)}\right)+2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) \ln \left(-\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}+4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}+4 \left(x^{3}-x^{2}+2\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +4 \left(x^{3}-x^{2}+2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{2}+10 \left(x^{3}-x^{2}+2\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}+3 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}+4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) x^{3}+2 \left(x^{3}-x^{2}+2\right)^{\frac{2}{3}} x -3 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right) x^{2}+6 \RootOf \left(\textit{\_Z}^{3}+4\right)+8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+4 \textit{\_Z}^{2}\right)}{\left(-1+x \right) \left(x^{2}+2 x +2\right)}\right)$&$735$\\ trager&$-\frac{3 \left(x^{3}-x^{2}+2\right)^{\frac{2}{3}}}{2 x^{2}}+\RootOf \left(\textit{\_Z}^{3}+4\right) \ln \left(\frac{827472528 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+576 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}-66909540 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+576 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}-3309890112 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+576 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{2}-1753973568 \left(x^{3}-x^{2}+2\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+576 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +267638160 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+576 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{2}-1528686900 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+576 \textit{\_Z}^{2}\right) \left(x^{3}-x^{2}+2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}-146164464 \left(x^{3}-x^{2}+2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{2}+6619780224 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+576 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}-535276320 \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+576 \textit{\_Z}^{2}\right)+1723901100 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+576 \textit{\_Z}^{2}\right) x^{3}-139394875 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}-206868132 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+576 \textit{\_Z}^{2}\right) x^{2}+164938353 \left(x^{3}-x^{2}+2\right)^{\frac{2}{3}} x +16727385 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}+413736264 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+576 \textit{\_Z}^{2}\right)-33454770 \RootOf \left(\textit{\_Z}^{3}+4\right)}{\left(-1+x \right) \left(x^{2}+2 x +2\right)}\right)+24 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+576 \textit{\_Z}^{2}\right) \ln \left(\frac{3211657920 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+576 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}-68956044 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+576 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}-12846631680 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+576 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{2}+3507947136 \left(x^{3}-x^{2}+2\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+576 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +275824176 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+576 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{2}+3958520472 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+576 \textit{\_Z}^{2}\right) \left(x^{3}-x^{2}+2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}+292328928 \left(x^{3}-x^{2}+2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{2}+25693263360 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+576 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}-551648352 \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+576 \textit{\_Z}^{2}\right)-7226230320 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+576 \textit{\_Z}^{2}\right) x^{3}+155151099 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}+2944019760 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+576 \textit{\_Z}^{2}\right) x^{2}-254781150 \left(x^{3}-x^{2}+2\right)^{\frac{2}{3}} x -63209707 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}-5888039520 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+576 \textit{\_Z}^{2}\right)+126419414 \RootOf \left(\textit{\_Z}^{3}+4\right)}{\left(-1+x \right) \left(x^{2}+2 x +2\right)}\right)$&$1028$\\ \hline \end{longtable}"," ",0,"-3/2*(x^3-x^2+2)^(2/3)/x^2+RootOf(_Z^3+4)*ln((RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^3*x^3+3*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+2*(x^3-x^2+2)^(2/3)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^2*x+2*(x^3-x^2+2)^(1/3)*RootOf(_Z^3+4)^2*x^2-(x^3-x^2+2)^(1/3)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)*x^2-3*RootOf(_Z^3+4)*x^3-9*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^3-5*(x^3-x^2+2)^(2/3)*x+RootOf(_Z^3+4)*x^2+3*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^2-2*RootOf(_Z^3+4)-6*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2))/(-1+x)/(x^2+2*x+2))+2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*ln(-(3*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^3*x^3+4*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+4*(x^3-x^2+2)^(2/3)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^2*x+4*(x^3-x^2+2)^(1/3)*RootOf(_Z^3+4)^2*x^2+10*(x^3-x^2+2)^(1/3)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)*x^2+3*RootOf(_Z^3+4)*x^3+4*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^3+2*(x^3-x^2+2)^(2/3)*x-3*RootOf(_Z^3+4)*x^2-4*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^2+6*RootOf(_Z^3+4)+8*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2))/(-1+x)/(x^2+2*x+2))","C"
2087,0,0,123,0.030000," ","int(x^3*(-4*a+3*x)/(x^2*(-a+x))^(2/3)/(x^4+a*d-d*x),x)","\[\int \frac{x^{3} \left(-4 a +3 x \right)}{\left(x^{2} \left(-a +x \right)\right)^{\frac{2}{3}} \left(x^{4}+a d -d x \right)}\, dx\]"," ",0,"int(x^3*(-4*a+3*x)/(x^2*(-a+x))^(2/3)/(x^4+a*d-d*x),x)","F"
2088,1,255,131,0.130000," ","int((k^4*x^4-1)/((1-x)*x*(-k^2*x+1))^(1/2)/(k^4*x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(k^{4} \textit{\_Z}^{4}+1\right)}{\sum}\frac{\left(k^{6} \underline{\hspace{1.25 ex}}\alpha^{3}+k^{4} \underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  \,k^{2}+1\right) \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{k^{6} \underline{\hspace{1.25 ex}}\alpha^{3}+k^{4} \underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  \,k^{2}+1}{k^{4}+1}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\underline{\hspace{1.25 ex}}\alpha^{3} \left(k^{4}+1\right) \sqrt{x \left(k^{2} x^{2}-k^{2} x -x +1\right)}}}{k^{4}}$&$255$\\ elliptic&$-\frac{2 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(k^{4} \textit{\_Z}^{4}+1\right)}{\sum}\frac{\left(k^{6} \underline{\hspace{1.25 ex}}\alpha^{3}+k^{4} \underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  \,k^{2}+1\right) \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{k^{6} \underline{\hspace{1.25 ex}}\alpha^{3}+k^{4} \underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  \,k^{2}+1}{k^{4}+1}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\underline{\hspace{1.25 ex}}\alpha^{3} \left(k^{4}+1\right) \sqrt{x \left(k^{2} x^{2}-k^{2} x -x +1\right)}}}{k^{4}}$&$255$\\ \hline \end{longtable}"," ",0,"-2/k^2*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticF((-(x-1/k^2)*k^2)^(1/2),(1/k^2/(1/k^2-1))^(1/2))+1/k^4*sum(1/_alpha^3*(_alpha^3*k^6+_alpha^2*k^4+_alpha*k^2+1)/(k^4+1)*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(x*(k^2*x^2-k^2*x-x+1))^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),(_alpha^3*k^6+_alpha^2*k^4+_alpha*k^2+1)/(k^4+1),(1/k^2/(1/k^2-1))^(1/2)),_alpha=RootOf(_Z^4*k^4+1))","C"
2089,1,2874,124,52.167000," ","int((-x^4+1)/(x^4+1)/(x^5+x^3)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2874$\\ \hline \end{longtable}"," ",0,"-1/4*RootOf(_Z^8-128)*ln((RootOf(_Z^8-128)^9*x^4-2*RootOf(_Z^8-128)^9*x^3+RootOf(_Z^8-128)^9*x^2-8*(x^5+x^3)^(1/2)*RootOf(_Z^8-128)^7*x+16*(x^5+x^3)^(1/4)*RootOf(_Z^8-128)^6*x^2-16*RootOf(_Z^8-128)^5*x^3-256*RootOf(_Z^8-128)*x^4+256*RootOf(_Z^8-128)*x^3+512*(x^5+x^3)^(3/4)-256*RootOf(_Z^8-128)*x^2)/(RootOf(_Z^8-128)^4*x^2-2*RootOf(_Z^8-128)^4*x+RootOf(_Z^8-128)^4+16*x^2-16*x+16)/x^2)-RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*ln((RootOf(_Z^8-128)^8*x^4*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)-2*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*RootOf(_Z^8-128)^8*x^3+RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*RootOf(_Z^8-128)^8*x^2+8*(x^5+x^3)^(1/2)*RootOf(_Z^8-128)^6*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*x+4*(x^5+x^3)^(1/4)*RootOf(_Z^8-128)^6*x^2+16*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*RootOf(_Z^8-128)^4*x^3+32*(x^5+x^3)^(1/2)*RootOf(_Z^8-128)^3*x+256*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*(x^5+x^3)^(1/4)*RootOf(_Z^8-128)*x^2-256*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*x^4+256*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*x^3-256*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*x^2+128*(x^5+x^3)^(3/4))/(RootOf(_Z^8-128)^4*x^2-2*RootOf(_Z^8-128)^4*x+RootOf(_Z^8-128)^4-16*x^2+16*x-16)/x^2)-1/8*ln((8*RootOf(_Z^8-128)^8*x^4*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)+RootOf(_Z^8-128)^9*x^4-16*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*RootOf(_Z^8-128)^8*x^3-2*RootOf(_Z^8-128)^9*x^3+8*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*RootOf(_Z^8-128)^8*x^2+RootOf(_Z^8-128)^9*x^2+8*(x^5+x^3)^(1/2)*RootOf(_Z^8-128)^7*x-64*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*RootOf(_Z^8-128)^4*x^4-16*(x^5+x^3)^(1/4)*RootOf(_Z^8-128)^6*x^2-16*RootOf(_Z^8-128)^5*x^3-64*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*RootOf(_Z^8-128)^4*x^2+512*(x^5+x^3)^(1/2)*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*RootOf(_Z^8-128)^2*x-1024*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*x^4-256*RootOf(_Z^8-128)*x^4+1024*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*x^3+256*RootOf(_Z^8-128)*x^3-1024*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*x^2+512*(x^5+x^3)^(3/4)-256*RootOf(_Z^8-128)*x^2)/(RootOf(_Z^8-128)^4*x^2-2*RootOf(_Z^8-128)^4*x+RootOf(_Z^8-128)^4+16*x^2-16*x+16)/x^2)*RootOf(_Z^8-128)^4*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)-1/4*ln((8*RootOf(_Z^8-128)^8*x^4*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)+RootOf(_Z^8-128)^9*x^4-16*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*RootOf(_Z^8-128)^8*x^3-2*RootOf(_Z^8-128)^9*x^3+8*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*RootOf(_Z^8-128)^8*x^2+RootOf(_Z^8-128)^9*x^2+8*(x^5+x^3)^(1/2)*RootOf(_Z^8-128)^7*x-64*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*RootOf(_Z^8-128)^4*x^4-16*(x^5+x^3)^(1/4)*RootOf(_Z^8-128)^6*x^2-16*RootOf(_Z^8-128)^5*x^3-64*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*RootOf(_Z^8-128)^4*x^2+512*(x^5+x^3)^(1/2)*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*RootOf(_Z^8-128)^2*x-1024*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*x^4-256*RootOf(_Z^8-128)*x^4+1024*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*x^3+256*RootOf(_Z^8-128)*x^3-1024*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*x^2+512*(x^5+x^3)^(3/4)-256*RootOf(_Z^8-128)*x^2)/(RootOf(_Z^8-128)^4*x^2-2*RootOf(_Z^8-128)^4*x+RootOf(_Z^8-128)^4+16*x^2-16*x+16)/x^2)*RootOf(_Z^8-128)-1/32*ln((2*RootOf(_Z^8-128)^8*x^4*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)-RootOf(_Z^8-128)^9*x^4-4*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*RootOf(_Z^8-128)^8*x^3+2*RootOf(_Z^8-128)^9*x^3+2*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*RootOf(_Z^8-128)^8*x^2-RootOf(_Z^8-128)^9*x^2+16*(x^5+x^3)^(1/2)*RootOf(_Z^8-128)^6*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*x-8*(x^5+x^3)^(1/4)*RootOf(_Z^8-128)^6*x^2-8*RootOf(_Z^8-128)^5*x^4+32*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*RootOf(_Z^8-128)^4*x^3-8*RootOf(_Z^8-128)^5*x^2-512*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*(x^5+x^3)^(1/4)*RootOf(_Z^8-128)*x^2-512*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*x^4+128*RootOf(_Z^8-128)*x^4+512*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*x^3-128*RootOf(_Z^8-128)*x^3-512*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*x^2+256*(x^5+x^3)^(3/4)+128*RootOf(_Z^8-128)*x^2)/(RootOf(_Z^8-128)^4*x^2-2*RootOf(_Z^8-128)^4*x+RootOf(_Z^8-128)^4-16*x^2+16*x-16)/x^2)*RootOf(_Z^8-128)^5-ln((2*RootOf(_Z^8-128)^8*x^4*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)-RootOf(_Z^8-128)^9*x^4-4*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*RootOf(_Z^8-128)^8*x^3+2*RootOf(_Z^8-128)^9*x^3+2*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*RootOf(_Z^8-128)^8*x^2-RootOf(_Z^8-128)^9*x^2+16*(x^5+x^3)^(1/2)*RootOf(_Z^8-128)^6*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*x-8*(x^5+x^3)^(1/4)*RootOf(_Z^8-128)^6*x^2-8*RootOf(_Z^8-128)^5*x^4+32*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*RootOf(_Z^8-128)^4*x^3-8*RootOf(_Z^8-128)^5*x^2-512*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*(x^5+x^3)^(1/4)*RootOf(_Z^8-128)*x^2-512*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*x^4+128*RootOf(_Z^8-128)*x^4+512*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*x^3-128*RootOf(_Z^8-128)*x^3-512*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)*x^2+256*(x^5+x^3)^(3/4)+128*RootOf(_Z^8-128)*x^2)/(RootOf(_Z^8-128)^4*x^2-2*RootOf(_Z^8-128)^4*x+RootOf(_Z^8-128)^4-16*x^2+16*x-16)/x^2)*RootOf(RootOf(_Z^8-128)^5*_Z+2*RootOf(_Z^8-128)^2+32*_Z^2)","C"
2090,1,768,117,16.979000," ","int((x^3+1)^(2/3)*(x^6+2)/x^6/(x^3-1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(17 x^{6}-10 x^{3}-2\right) \left(x^{3}+1\right)^{\frac{2}{3}}}{5 \left(x^{3}-1\right) x^{5}}+2240 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right) \ln \left(\frac{-2544254963712 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}+2045301216 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}+147155162112 \left(x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +194217355584 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}+218980896 \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}+20354039709696 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}-16362409728 \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right)-215807340672 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right) x^{3}+173485371 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}-148947870 x \left(x^{3}+1\right)^{\frac{2}{3}}-94652342400 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right)+76090075 \RootOf \left(\textit{\_Z}^{3}+4\right)}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right)+\frac{5 \RootOf \left(\textit{\_Z}^{3}+4\right) \ln \left(-\frac{1374442417152 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}-946523424 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}+73577581056 \left(x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +50046484320 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}+109490448 \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}-10995539337216 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+7572187392 \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right)-120672771744 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right) x^{3}+83102503 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}-144506961 x \left(x^{3}+1\right)^{\frac{2}{3}}-18407710944 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+1344 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+1806336 \textit{\_Z}^{2}\right)+12676653 \RootOf \left(\textit{\_Z}^{3}+4\right)}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right)}{3}$&$768$\\ risch&$-\frac{17 x^{9}+7 x^{6}-12 x^{3}-2}{5 x^{5} \left(x^{3}+1\right)^{\frac{1}{3}} \left(x^{3}-1\right)}+\frac{5 \RootOf \left(\textit{\_Z}^{3}+4\right) \ln \left(-\frac{-3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}-54 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}+12 \left(x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x -5 \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}-6 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}-\RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}-18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) x^{3}+2 x \left(x^{3}+1\right)^{\frac{2}{3}}-\RootOf \left(\textit{\_Z}^{3}+4\right)-18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right)}{3}-\frac{5 \ln \left(\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}-36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}+12 \left(x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +\RootOf \left(\textit{\_Z}^{3}+4\right)^{2} \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}+30 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}-3 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}+36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) x^{3}-10 x \left(x^{3}+1\right)^{\frac{2}{3}}-\RootOf \left(\textit{\_Z}^{3}+4\right)+12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)}{3}-10 \ln \left(\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}-36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}+12 \left(x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +\RootOf \left(\textit{\_Z}^{3}+4\right)^{2} \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}+30 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}-3 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}+36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) x^{3}-10 x \left(x^{3}+1\right)^{\frac{2}{3}}-\RootOf \left(\textit{\_Z}^{3}+4\right)+12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)$&$919$\\ \hline \end{longtable}"," ",0,"-1/5*(17*x^6-10*x^3-2)/(x^3-1)/x^5*(x^3+1)^(2/3)+2240*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)*ln((-2544254963712*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+2045301216*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)*RootOf(_Z^3+4)^3*x^3+147155162112*(x^3+1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)*RootOf(_Z^3+4)^2*x+194217355584*(x^3+1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)*RootOf(_Z^3+4)*x^2+218980896*RootOf(_Z^3+4)^2*(x^3+1)^(1/3)*x^2+20354039709696*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)^2*RootOf(_Z^3+4)^2-16362409728*RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)-215807340672*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)*x^3+173485371*RootOf(_Z^3+4)*x^3-148947870*x*(x^3+1)^(2/3)-94652342400*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)+76090075*RootOf(_Z^3+4))/(-1+x)/(x^2+x+1))+5/3*RootOf(_Z^3+4)*ln(-(1374442417152*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)^2*RootOf(_Z^3+4)^2*x^3-946523424*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)*RootOf(_Z^3+4)^3*x^3+73577581056*(x^3+1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)*RootOf(_Z^3+4)^2*x+50046484320*(x^3+1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)*RootOf(_Z^3+4)*x^2+109490448*RootOf(_Z^3+4)^2*(x^3+1)^(1/3)*x^2-10995539337216*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)^2*RootOf(_Z^3+4)^2+7572187392*RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)-120672771744*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)*x^3+83102503*RootOf(_Z^3+4)*x^3-144506961*x*(x^3+1)^(2/3)-18407710944*RootOf(RootOf(_Z^3+4)^2+1344*_Z*RootOf(_Z^3+4)+1806336*_Z^2)+12676653*RootOf(_Z^3+4))/(-1+x)/(x^2+x+1))","C"
2091,1,635,117,16.756000," ","int((x^3-1)^(2/3)*(x^6+2*x^3-2)/x^6/(x^3+1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{22 x^{9}-7 x^{6}-17 x^{3}+2}{5 x^{5} \left(x^{3}-1\right)^{\frac{1}{3}} \left(x^{3}+1\right)}+14 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \ln \left(\frac{9 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}+36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}+12 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +4 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{2}+30 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}+3 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}+12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) x^{3}+2 x \left(x^{3}-1\right)^{\frac{2}{3}}-3 \RootOf \left(\textit{\_Z}^{3}+4\right)-12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)}{\left(1+x \right) \left(x^{2}-x +1\right)}\right)+\frac{7 \RootOf \left(\textit{\_Z}^{3}+4\right) \ln \left(-\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{3} x^{3}+27 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{3}+6 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x +2 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+4\right)^{2} x^{2}-3 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+4\right) x^{2}-3 \RootOf \left(\textit{\_Z}^{3}+4\right) x^{3}-27 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right) x^{3}-5 x \left(x^{3}-1\right)^{\frac{2}{3}}+\RootOf \left(\textit{\_Z}^{3}+4\right)+9 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+4\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+4\right)+36 \textit{\_Z}^{2}\right)}{\left(1+x \right) \left(x^{2}-x +1\right)}\right)}{3}$&$635$\\ trager&$\text{Expression too large to display}$&$1132$\\ \hline \end{longtable}"," ",0,"-1/5*(22*x^9-7*x^6-17*x^3+2)/x^5/(x^3-1)^(1/3)/(x^3+1)+14*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*ln((9*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3*x^3+36*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+12*(x^3-1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*x+4*(x^3-1)^(1/3)*RootOf(_Z^3+4)^2*x^2+30*(x^3-1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)*x^2+3*RootOf(_Z^3+4)*x^3+12*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^3+2*x*(x^3-1)^(2/3)-3*RootOf(_Z^3+4)-12*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2))/(1+x)/(x^2-x+1))+7/3*RootOf(_Z^3+4)*ln(-(3*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3*x^3+27*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+6*(x^3-1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*x+2*(x^3-1)^(1/3)*RootOf(_Z^3+4)^2*x^2-3*(x^3-1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)*x^2-3*RootOf(_Z^3+4)*x^3-27*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^3-5*x*(x^3-1)^(2/3)+RootOf(_Z^3+4)+9*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2))/(1+x)/(x^2-x+1))","C"
2092,0,0,121,0.020000," ","int((a*x^6+2*b)*(a*x^6-c*x^4-b)/x^2/(a*x^6-b)^(3/4)/(a*x^6+c*x^4-b),x)","\[\int \frac{\left(a \,x^{6}+2 b \right) \left(a \,x^{6}-c \,x^{4}-b \right)}{x^{2} \left(a \,x^{6}-b \right)^{\frac{3}{4}} \left(a \,x^{6}+c \,x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^6+2*b)*(a*x^6-c*x^4-b)/x^2/(a*x^6-b)^(3/4)/(a*x^6+c*x^4-b),x)","F"
2093,0,0,119,0.011000," ","int((c+d*(a*x^2+b)^(1/2))^(1/2)/x,x)","\[\int \frac{\sqrt{c +d \sqrt{a \,x^{2}+b}}}{x}\, dx\]"," ",0,"int((c+d*(a*x^2+b)^(1/2))^(1/2)/x,x)","F"
2094,0,0,119,180.000000," ","int((a^2*x^4-b)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^4+b)^(1/2),x)","\[\int \frac{\left(a^{2} x^{4}-b \right) \sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}{\sqrt{a^{2} x^{4}+b}}\, dx\]"," ",0,"int((a^2*x^4-b)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^4+b)^(1/2),x)","F"
2095,0,0,119,180.000000," ","int((a^2*x^4+b)^(1/2)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x)","\[\int \sqrt{a^{2} x^{4}+b}\, \sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}\, dx\]"," ",0,"int((a^2*x^4+b)^(1/2)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x)","F"
2096,0,0,116,0.041000," ","int(1/(a*x+2*b)/(a*x^3+b*x^2)^(1/4),x)","\[\int \frac{1}{\left(a x +2 b \right) \left(a \,x^{3}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(a*x+2*b)/(a*x^3+b*x^2)^(1/4),x)","F"
2097,0,0,124,0.029000," ","int(x*(-4*a+3*x)/(x^2*(-a+x))^(1/3)/(x^4+a*d-d*x),x)","\[\int \frac{x \left(-4 a +3 x \right)}{\left(x^{2} \left(-a +x \right)\right)^{\frac{1}{3}} \left(x^{4}+a d -d x \right)}\, dx\]"," ",0,"int(x*(-4*a+3*x)/(x^2*(-a+x))^(1/3)/(x^4+a*d-d*x),x)","F"
2098,0,0,120,0.013000," ","int((a*x^5-b)^(3/4)*(a*x^5+4*b)/x^4/(a*x^5+c*x^4-b),x)","\[\int \frac{\left(a \,x^{5}-b \right)^{\frac{3}{4}} \left(a \,x^{5}+4 b \right)}{x^{4} \left(a \,x^{5}+c \,x^{4}-b \right)}\, dx\]"," ",0,"int((a*x^5-b)^(3/4)*(a*x^5+4*b)/x^4/(a*x^5+c*x^4-b),x)","F"
2099,0,0,112,0.046000," ","int((x^8+1)^(3/4)/(x^8-1),x)","\[\int \frac{\left(x^{8}+1\right)^{\frac{3}{4}}}{x^{8}-1}\, dx\]"," ",0,"int((x^8+1)^(3/4)/(x^8-1),x)","F"
2100,1,998,112,10.857000," ","int(x^4/(x^4-1)^(1/4)/(x^8+2*x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{8}-8\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{8}-8\right)^{9} x^{4}-2 \RootOf \left(\textit{\_Z}^{8}-8\right)^{7} \sqrt{x^{4}-1}\, x^{2}-4 \RootOf \left(\textit{\_Z}^{8}-8\right)^{6} \left(x^{4}-1\right)^{\frac{1}{4}} x^{3}+4 \RootOf \left(\textit{\_Z}^{8}-8\right)^{4} \left(x^{4}-1\right)^{\frac{3}{4}} x +8 \RootOf \left(\textit{\_Z}^{8}-8\right)^{3} \sqrt{x^{4}-1}\, x^{2}+8 \RootOf \left(\textit{\_Z}^{8}-8\right)^{2} \left(x^{4}-1\right)^{\frac{1}{4}} x^{3}-2 \RootOf \left(\textit{\_Z}^{8}-8\right)^{5}-4 \RootOf \left(\textit{\_Z}^{8}-8\right) x^{4}-16 \left(x^{4}-1\right)^{\frac{3}{4}} x +4 \RootOf \left(\textit{\_Z}^{8}-8\right)}{\RootOf \left(\textit{\_Z}^{8}-8\right)^{4} x^{4}-2 x^{4}+2}\right)}{16}+\frac{\ln \left(\frac{3 \RootOf \left(\textit{\_Z}^{8}-8\right)^{9} x^{4}-8 \RootOf \left(\textit{\_Z}^{8}-8\right)^{7} \sqrt{x^{4}-1}\, x^{2}+8 \RootOf \left(\textit{\_Z}^{8}-8\right)^{6} \left(x^{4}-1\right)^{\frac{1}{4}} x^{3}+2 \RootOf \left(\textit{\_Z}^{8}-8\right)^{5} x^{4}-24 \RootOf \left(\textit{\_Z}^{8}-8\right)^{4} \left(x^{4}-1\right)^{\frac{3}{4}} x +48 \RootOf \left(\textit{\_Z}^{8}-8\right)^{3} \sqrt{x^{4}-1}\, x^{2}-48 \RootOf \left(\textit{\_Z}^{8}-8\right)^{2} \left(x^{4}-1\right)^{\frac{1}{4}} x^{3}-6 \RootOf \left(\textit{\_Z}^{8}-8\right)^{5}-8 \RootOf \left(\textit{\_Z}^{8}-8\right) x^{4}+32 \left(x^{4}-1\right)^{\frac{3}{4}} x +8 \RootOf \left(\textit{\_Z}^{8}-8\right)}{\RootOf \left(\textit{\_Z}^{8}-8\right)^{4} x^{4}+2 x^{4}-2}\right) \RootOf \left(\textit{\_Z}^{8}-8\right)^{5}}{64}-\frac{\ln \left(\frac{3 \RootOf \left(\textit{\_Z}^{8}-8\right)^{9} x^{4}-8 \RootOf \left(\textit{\_Z}^{8}-8\right)^{7} \sqrt{x^{4}-1}\, x^{2}+8 \RootOf \left(\textit{\_Z}^{8}-8\right)^{6} \left(x^{4}-1\right)^{\frac{1}{4}} x^{3}+2 \RootOf \left(\textit{\_Z}^{8}-8\right)^{5} x^{4}-24 \RootOf \left(\textit{\_Z}^{8}-8\right)^{4} \left(x^{4}-1\right)^{\frac{3}{4}} x +48 \RootOf \left(\textit{\_Z}^{8}-8\right)^{3} \sqrt{x^{4}-1}\, x^{2}-48 \RootOf \left(\textit{\_Z}^{8}-8\right)^{2} \left(x^{4}-1\right)^{\frac{1}{4}} x^{3}-6 \RootOf \left(\textit{\_Z}^{8}-8\right)^{5}-8 \RootOf \left(\textit{\_Z}^{8}-8\right) x^{4}+32 \left(x^{4}-1\right)^{\frac{3}{4}} x +8 \RootOf \left(\textit{\_Z}^{8}-8\right)}{\RootOf \left(\textit{\_Z}^{8}-8\right)^{4} x^{4}+2 x^{4}-2}\right) \RootOf \left(\textit{\_Z}^{8}-8\right)^{4} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{8}-8\right)^{2}\right)}{64}+\frac{\RootOf \left(\textit{\_Z}^{8}-8\right)^{4} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{8}-8\right)^{2}\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{8}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{8}-8\right)^{6} \sqrt{x^{4}-1}\, x^{2}-\RootOf \left(\textit{\_Z}^{8}-8\right)^{7} \sqrt{x^{4}-1}\, x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{8}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{8}-8\right)^{5} \left(x^{4}-1\right)^{\frac{1}{4}} x^{3}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{8}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{8}-8\right)^{4} x^{4}+\RootOf \left(\textit{\_Z}^{8}-8\right)^{5} x^{4}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{8}-8\right)^{2}\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{8}-8\right) x^{4}+8 \left(x^{4}-1\right)^{\frac{3}{4}} x +2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{8}-8\right)^{2}\right)+2 \RootOf \left(\textit{\_Z}^{8}-8\right)}{\RootOf \left(\textit{\_Z}^{8}-8\right)^{4} x^{4}+2 x^{4}-2}\right)}{32}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{8}-8\right)^{2}\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{8}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{8}-8\right)^{8} x^{4}-4 \RootOf \left(\textit{\_Z}^{8}-8\right)^{6} \left(x^{4}-1\right)^{\frac{1}{4}} x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{8}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{8}-8\right)^{4} x^{4}-8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{8}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{8}-8\right)^{2} \sqrt{x^{4}-1}\, x^{2}-2 \RootOf \left(\textit{\_Z}^{8}-8\right)^{4} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{8}-8\right)^{2}\right)+16 \left(x^{4}-1\right)^{\frac{3}{4}} x}{\RootOf \left(\textit{\_Z}^{8}-8\right)^{4} x^{4}-2 x^{4}+2}\right)}{16}$&$998$\\ \hline \end{longtable}"," ",0,"-1/16*RootOf(_Z^8-8)*ln(-(RootOf(_Z^8-8)^9*x^4-2*RootOf(_Z^8-8)^7*(x^4-1)^(1/2)*x^2-4*RootOf(_Z^8-8)^6*(x^4-1)^(1/4)*x^3+4*RootOf(_Z^8-8)^4*(x^4-1)^(3/4)*x+8*RootOf(_Z^8-8)^3*(x^4-1)^(1/2)*x^2+8*RootOf(_Z^8-8)^2*(x^4-1)^(1/4)*x^3-2*RootOf(_Z^8-8)^5-4*RootOf(_Z^8-8)*x^4-16*(x^4-1)^(3/4)*x+4*RootOf(_Z^8-8))/(RootOf(_Z^8-8)^4*x^4-2*x^4+2))+1/64*ln((3*RootOf(_Z^8-8)^9*x^4-8*RootOf(_Z^8-8)^7*(x^4-1)^(1/2)*x^2+8*RootOf(_Z^8-8)^6*(x^4-1)^(1/4)*x^3+2*RootOf(_Z^8-8)^5*x^4-24*RootOf(_Z^8-8)^4*(x^4-1)^(3/4)*x+48*RootOf(_Z^8-8)^3*(x^4-1)^(1/2)*x^2-48*RootOf(_Z^8-8)^2*(x^4-1)^(1/4)*x^3-6*RootOf(_Z^8-8)^5-8*RootOf(_Z^8-8)*x^4+32*(x^4-1)^(3/4)*x+8*RootOf(_Z^8-8))/(RootOf(_Z^8-8)^4*x^4+2*x^4-2))*RootOf(_Z^8-8)^5-1/64*ln((3*RootOf(_Z^8-8)^9*x^4-8*RootOf(_Z^8-8)^7*(x^4-1)^(1/2)*x^2+8*RootOf(_Z^8-8)^6*(x^4-1)^(1/4)*x^3+2*RootOf(_Z^8-8)^5*x^4-24*RootOf(_Z^8-8)^4*(x^4-1)^(3/4)*x+48*RootOf(_Z^8-8)^3*(x^4-1)^(1/2)*x^2-48*RootOf(_Z^8-8)^2*(x^4-1)^(1/4)*x^3-6*RootOf(_Z^8-8)^5-8*RootOf(_Z^8-8)*x^4+32*(x^4-1)^(3/4)*x+8*RootOf(_Z^8-8))/(RootOf(_Z^8-8)^4*x^4+2*x^4-2))*RootOf(_Z^8-8)^4*RootOf(_Z^2+RootOf(_Z^8-8)^2)+1/32*RootOf(_Z^8-8)^4*RootOf(_Z^2+RootOf(_Z^8-8)^2)*ln((RootOf(_Z^2+RootOf(_Z^8-8)^2)*RootOf(_Z^8-8)^6*(x^4-1)^(1/2)*x^2-RootOf(_Z^8-8)^7*(x^4-1)^(1/2)*x^2-2*RootOf(_Z^2+RootOf(_Z^8-8)^2)*RootOf(_Z^8-8)^5*(x^4-1)^(1/4)*x^3+RootOf(_Z^2+RootOf(_Z^8-8)^2)*RootOf(_Z^8-8)^4*x^4+RootOf(_Z^8-8)^5*x^4-2*RootOf(_Z^2+RootOf(_Z^8-8)^2)*x^4-2*RootOf(_Z^8-8)*x^4+8*(x^4-1)^(3/4)*x+2*RootOf(_Z^2+RootOf(_Z^8-8)^2)+2*RootOf(_Z^8-8))/(RootOf(_Z^8-8)^4*x^4+2*x^4-2))+1/16*RootOf(_Z^2+RootOf(_Z^8-8)^2)*ln((RootOf(_Z^2+RootOf(_Z^8-8)^2)*RootOf(_Z^8-8)^8*x^4-4*RootOf(_Z^8-8)^6*(x^4-1)^(1/4)*x^3+2*RootOf(_Z^2+RootOf(_Z^8-8)^2)*RootOf(_Z^8-8)^4*x^4-8*RootOf(_Z^2+RootOf(_Z^8-8)^2)*RootOf(_Z^8-8)^2*(x^4-1)^(1/2)*x^2-2*RootOf(_Z^8-8)^4*RootOf(_Z^2+RootOf(_Z^8-8)^2)+16*(x^4-1)^(3/4)*x)/(RootOf(_Z^8-8)^4*x^4-2*x^4+2))","C"
2101,1,1570,112,16.554000," ","int((x^4-1)^(3/4)/(x^8+2*x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1570$\\ \hline \end{longtable}"," ",0,"-1/128*ln((RootOf(_Z^8-128)^9*x^4-64*(x^4-1)^(1/2)*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2)*RootOf(_Z^8-128)^6*x^2-8*(x^4-1)^(1/4)*RootOf(_Z^8-128)^6*x^3-8*RootOf(_Z^8-128)^5*x^4-128*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2)*RootOf(_Z^8-128)^4*x^4+2048*(x^4-1)^(1/4)*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2)*RootOf(_Z^8-128)*x^3+8*RootOf(_Z^8-128)^5+1024*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2)*x^4+256*(x^4-1)^(3/4)*x-1024*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2))/(RootOf(_Z^8-128)^4*x^4+8*x^4-8))*RootOf(_Z^8-128)^5+ln((RootOf(_Z^8-128)^9*x^4-64*(x^4-1)^(1/2)*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2)*RootOf(_Z^8-128)^6*x^2-8*(x^4-1)^(1/4)*RootOf(_Z^8-128)^6*x^3-8*RootOf(_Z^8-128)^5*x^4-128*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2)*RootOf(_Z^8-128)^4*x^4+2048*(x^4-1)^(1/4)*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2)*RootOf(_Z^8-128)*x^3+8*RootOf(_Z^8-128)^5+1024*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2)*x^4+256*(x^4-1)^(3/4)*x-1024*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2))/(RootOf(_Z^8-128)^4*x^4+8*x^4-8))*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2)+1/8*ln((4*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2)*RootOf(_Z^8-128)^8*x^4+(x^4-1)^(1/2)*RootOf(_Z^8-128)^7*x^2-2*(x^4-1)^(1/4)*RootOf(_Z^8-128)^6*x^3-2*RootOf(_Z^8-128)^5*x^4+32*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2)*RootOf(_Z^8-128)^4*x^4-256*(x^4-1)^(1/2)*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2)*RootOf(_Z^8-128)^2*x^2-32*RootOf(_Z^8-128)^4*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2)-16*RootOf(_Z^8-128)*x^4+64*(x^4-1)^(3/4)*x+16*RootOf(_Z^8-128))/(RootOf(_Z^8-128)^4*x^4-8*x^4+8))*RootOf(_Z^8-128)^4*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2)-1/16*ln((4*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2)*RootOf(_Z^8-128)^8*x^4+(x^4-1)^(1/2)*RootOf(_Z^8-128)^7*x^2-2*(x^4-1)^(1/4)*RootOf(_Z^8-128)^6*x^3-2*RootOf(_Z^8-128)^5*x^4+32*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2)*RootOf(_Z^8-128)^4*x^4-256*(x^4-1)^(1/2)*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2)*RootOf(_Z^8-128)^2*x^2-32*RootOf(_Z^8-128)^4*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2)-16*RootOf(_Z^8-128)*x^4+64*(x^4-1)^(3/4)*x+16*RootOf(_Z^8-128))/(RootOf(_Z^8-128)^4*x^4-8*x^4+8))*RootOf(_Z^8-128)+RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2)*ln(-(8*(x^4-1)^(1/2)*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2)*RootOf(_Z^8-128)^6*x^2-(x^4-1)^(1/4)*RootOf(_Z^8-128)^6*x^3+16*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2)*RootOf(_Z^8-128)^4*x^4-8*(x^4-1)^(1/2)*RootOf(_Z^8-128)^3*x^2+256*(x^4-1)^(1/4)*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2)*RootOf(_Z^8-128)*x^3-128*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2)*x^4-32*(x^4-1)^(3/4)*x+128*RootOf(-2*RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+256*_Z^2))/(RootOf(_Z^8-128)^4*x^4+8*x^4-8))+1/16*RootOf(_Z^8-128)*ln(((x^4-1)^(1/2)*RootOf(_Z^8-128)^7*x^2+2*(x^4-1)^(1/4)*RootOf(_Z^8-128)^6*x^3+2*RootOf(_Z^8-128)^5*x^4+16*RootOf(_Z^8-128)*x^4+64*(x^4-1)^(3/4)*x-16*RootOf(_Z^8-128))/(RootOf(_Z^8-128)^4*x^4-8*x^4+8))","C"
2102,0,0,113,0.047000," ","int((x^4+1)/(x^4-1)/(1+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{x^{4}+1}{\left(x^{4}-1\right) \sqrt{1+\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^4+1)/(x^4-1)/(1+(x^2+1)^(1/2))^(1/2),x)","F"
2103,0,0,117,0.004000," ","int(1/x^3/(a*x^2-b)^(3/4),x)","\[\int \frac{1}{x^{3} \left(a \,x^{2}-b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x^3/(a*x^2-b)^(3/4),x)","F"
2104,0,0,141,0.121000," ","int((a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^3)^(1/4)/(b-(a*d+1)*x+d*x^2),x)","\[\int \frac{a b -2 b x +x^{2}}{\left(x \left(-a +x \right) \left(-b +x \right)^{3}\right)^{\frac{1}{4}} \left(b -\left(a d +1\right) x +d \,x^{2}\right)}\, dx\]"," ",0,"int((a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^3)^(1/4)/(b-(a*d+1)*x+d*x^2),x)","F"
2105,0,0,117,0.005000," ","int(1/x^4/(a*x^3-b)^(3/4),x)","\[\int \frac{1}{x^{4} \left(a \,x^{3}-b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x^4/(a*x^3-b)^(3/4),x)","F"
2106,0,0,117,0.006000," ","int(1/x^4/(a*x^3-b)^(1/4),x)","\[\int \frac{1}{x^{4} \left(a \,x^{3}-b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/x^4/(a*x^3-b)^(1/4),x)","F"
2107,0,0,56,0.016000," ","int(1/2*(2+x)*(x^2-x-1)*((-2*x^2+x+1)/(4*x^2+x+1))^(1/4)/x/(x^4+x^2+2*x+1),x)","\[\int \frac{\left(2+x \right) \left(x^{2}-x -1\right) \left(\frac{-2 x^{2}+x +1}{4 x^{2}+x +1}\right)^{\frac{1}{4}}}{2 x \left(x^{4}+x^{2}+2 x +1\right)}\, dx\]"," ",0,"int(1/2*(2+x)*(x^2-x-1)*((-2*x^2+x+1)/(4*x^2+x+1))^(1/4)/x/(x^4+x^2+2*x+1),x)","F"
2108,1,620,42,3.366000," ","int((x^4+1)/(x^4-1)/(x^4+x^3-x^2-x+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+676 \RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right)^{2}+78\right) \ln \left(\frac{-9984 \RootOf \left(\textit{\_Z}^{2}+676 \RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right)^{2}+78\right) \RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right)^{4} x +1088 \RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+676 \RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right)^{2}+78\right) x^{2}-1028 \RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+676 \RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right)^{2}+78\right) x +7280 \sqrt{x^{4}+x^{3}-x^{2}-x +1}\, \RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right)^{2}-1088 \RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+676 \RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right)^{2}+78\right)+119 \RootOf \left(\textit{\_Z}^{2}+676 \RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right)^{2}+78\right) x^{2}+7 \RootOf \left(\textit{\_Z}^{2}+676 \RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right)^{2}+78\right) x +78 \sqrt{x^{4}+x^{3}-x^{2}-x +1}-119 \RootOf \left(\textit{\_Z}^{2}+676 \RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right)^{2}+78\right)}{\left(52 x \RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right)^{2}+3 x +2\right)^{2}}\right)}{52}-\frac{\RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right) \ln \left(-\frac{-129792 \RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right)^{5} x -14144 \RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right)^{3} x^{2}-16588 \RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right)^{3} x +3640 \sqrt{x^{4}+x^{3}-x^{2}-x +1}\, \RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right)^{2}+14144 \RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right)^{3}-85 \RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right) x^{2}-95 \RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right) x +381 \sqrt{x^{4}+x^{3}-x^{2}-x +1}+85 \RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right)}{\left(52 x \RootOf \left(208 \textit{\_Z}^{4}+24 \textit{\_Z}^{2}+1\right)^{2}+3 x -2\right)^{2}}\right)}{2}+\frac{\ln \left(-\frac{-x^{2}+2 \sqrt{x^{4}+x^{3}-x^{2}-x +1}-2 x +1}{\left(-1+x \right) \left(1+x \right)}\right)}{2}$&$620$\\ default&$\text{Expression too large to display}$&$95423$\\ elliptic&$\text{Expression too large to display}$&$1418170$\\ \hline \end{longtable}"," ",0,"1/52*RootOf(_Z^2+676*RootOf(208*_Z^4+24*_Z^2+1)^2+78)*ln((-9984*RootOf(_Z^2+676*RootOf(208*_Z^4+24*_Z^2+1)^2+78)*RootOf(208*_Z^4+24*_Z^2+1)^4*x+1088*RootOf(208*_Z^4+24*_Z^2+1)^2*RootOf(_Z^2+676*RootOf(208*_Z^4+24*_Z^2+1)^2+78)*x^2-1028*RootOf(208*_Z^4+24*_Z^2+1)^2*RootOf(_Z^2+676*RootOf(208*_Z^4+24*_Z^2+1)^2+78)*x+7280*(x^4+x^3-x^2-x+1)^(1/2)*RootOf(208*_Z^4+24*_Z^2+1)^2-1088*RootOf(208*_Z^4+24*_Z^2+1)^2*RootOf(_Z^2+676*RootOf(208*_Z^4+24*_Z^2+1)^2+78)+119*RootOf(_Z^2+676*RootOf(208*_Z^4+24*_Z^2+1)^2+78)*x^2+7*RootOf(_Z^2+676*RootOf(208*_Z^4+24*_Z^2+1)^2+78)*x+78*(x^4+x^3-x^2-x+1)^(1/2)-119*RootOf(_Z^2+676*RootOf(208*_Z^4+24*_Z^2+1)^2+78))/(52*x*RootOf(208*_Z^4+24*_Z^2+1)^2+3*x+2)^2)-1/2*RootOf(208*_Z^4+24*_Z^2+1)*ln(-(-129792*RootOf(208*_Z^4+24*_Z^2+1)^5*x-14144*RootOf(208*_Z^4+24*_Z^2+1)^3*x^2-16588*RootOf(208*_Z^4+24*_Z^2+1)^3*x+3640*(x^4+x^3-x^2-x+1)^(1/2)*RootOf(208*_Z^4+24*_Z^2+1)^2+14144*RootOf(208*_Z^4+24*_Z^2+1)^3-85*RootOf(208*_Z^4+24*_Z^2+1)*x^2-95*RootOf(208*_Z^4+24*_Z^2+1)*x+381*(x^4+x^3-x^2-x+1)^(1/2)+85*RootOf(208*_Z^4+24*_Z^2+1))/(52*x*RootOf(208*_Z^4+24*_Z^2+1)^2+3*x-2)^2)+1/2*ln(-(-x^2+2*(x^4+x^3-x^2-x+1)^(1/2)-2*x+1)/(-1+x)/(1+x))","B"
2109,0,0,117,0.006000," ","int(1/x^5/(a*x^4-b)^(3/4),x)","\[\int \frac{1}{x^{5} \left(a \,x^{4}-b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x^5/(a*x^4-b)^(3/4),x)","F"
2110,0,0,141,0.022000," ","int((a*b^3-2*(3*a-b)*b^2*x+3*(3*a-b)*b*x^2-4*a*x^3+x^4)/(x*(-a+x)*(-b+x)^3)^(1/4)/(a^3-(b^3*d+3*a^2)*x+3*(b^2*d+a)*x^2-(3*b*d+1)*x^3+d*x^4),x)","\[\int \frac{a \,b^{3}-2 \left(3 a -b \right) b^{2} x +3 \left(3 a -b \right) b \,x^{2}-4 a \,x^{3}+x^{4}}{\left(x \left(-a +x \right) \left(-b +x \right)^{3}\right)^{\frac{1}{4}} \left(a^{3}-\left(b^{3} d +3 a^{2}\right) x +3 \left(b^{2} d +a \right) x^{2}-\left(3 b d +1\right) x^{3}+d \,x^{4}\right)}\, dx\]"," ",0,"int((a*b^3-2*(3*a-b)*b^2*x+3*(3*a-b)*b*x^2-4*a*x^3+x^4)/(x*(-a+x)*(-b+x)^3)^(1/4)/(a^3-(b^3*d+3*a^2)*x+3*(b^2*d+a)*x^2-(3*b*d+1)*x^3+d*x^4),x)","F"
2111,0,0,117,0.006000," ","int(1/x^6/(a*x^5-b)^(3/4),x)","\[\int \frac{1}{x^{6} \left(a \,x^{5}-b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x^6/(a*x^5-b)^(3/4),x)","F"
2112,0,0,117,0.005000," ","int(1/x^7/(a*x^6-b)^(3/4),x)","\[\int \frac{1}{x^{7} \left(a \,x^{6}-b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x^7/(a*x^6-b)^(3/4),x)","F"
2113,1,111,123,0.174000," ","int((a^6*x^6+b^6)/(a^4*x^4+b^4)^(1/2)/(a^6*x^6-b^6),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\ln \left(-a b +\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{2 x}\right)}{6 a b}+\frac{2 \sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}+b^{4}}}{a b x}\right)}{3 a b}-\frac{\ln \left(a b +\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{2 x}\right)}{6 a b}\right) \sqrt{2}}{2}$&$111$\\ default&$\frac{\sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, i\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}+b^{4}}}-\frac{b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}-\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha  a +2 b \right) \left(-\frac{\arctanh \left(\frac{\left(\underline{\hspace{1.25 ex}}\alpha  a -b \right) a b \left(a \,x^{2}-\underline{\hspace{1.25 ex}}\alpha  b \right)}{\sqrt{-b^{3} \left(\underline{\hspace{1.25 ex}}\alpha  a -b \right)}\, \sqrt{a^{4} x^{4}+b^{4}}}\right)}{\sqrt{-b^{3} \left(\underline{\hspace{1.25 ex}}\alpha  a -b \right)}}+\frac{2 a \left(\underline{\hspace{1.25 ex}}\alpha  a -b \right) \sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, \frac{i \underline{\hspace{1.25 ex}}\alpha  a}{b}, \frac{\sqrt{-\frac{i a^{2}}{b^{2}}}}{\sqrt{\frac{i a^{2}}{b^{2}}}}\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, b^{2} \sqrt{a^{4} x^{4}+b^{4}}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  a -b}\right)}{6 a}-\frac{b \left(-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 a^{2} b^{2} x^{2}+2 b^{4}\right) \sqrt{2}}{4 \sqrt{b^{4}}\, \sqrt{a^{4} x^{4}+b^{4}}}\right)}{4 \sqrt{b^{4}}}+\frac{a \sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, -i, \frac{\sqrt{-\frac{i a^{2}}{b^{2}}}}{\sqrt{\frac{i a^{2}}{b^{2}}}}\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, b \sqrt{a^{4} x^{4}+b^{4}}}\right)}{3 a}+\frac{b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}+\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha  a -2 b \right) \left(\frac{\arctanh \left(\frac{\left(\underline{\hspace{1.25 ex}}\alpha  a +b \right) a b \left(a \,x^{2}+\underline{\hspace{1.25 ex}}\alpha  b \right)}{\sqrt{b^{3} \left(\underline{\hspace{1.25 ex}}\alpha  a +b \right)}\, \sqrt{a^{4} x^{4}+b^{4}}}\right)}{\sqrt{b^{3} \left(\underline{\hspace{1.25 ex}}\alpha  a +b \right)}}+\frac{2 a \left(\underline{\hspace{1.25 ex}}\alpha  a +b \right) \sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, -\frac{i \underline{\hspace{1.25 ex}}\alpha  a}{b}, \frac{\sqrt{-\frac{i a^{2}}{b^{2}}}}{\sqrt{\frac{i a^{2}}{b^{2}}}}\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, b^{2} \sqrt{a^{4} x^{4}+b^{4}}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  a +b}\right)}{6 a}+\frac{b \left(-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 a^{2} b^{2} x^{2}+2 b^{4}\right) \sqrt{2}}{4 \sqrt{b^{4}}\, \sqrt{a^{4} x^{4}+b^{4}}}\right)}{4 \sqrt{b^{4}}}-\frac{a \sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, -i, \frac{\sqrt{-\frac{i a^{2}}{b^{2}}}}{\sqrt{\frac{i a^{2}}{b^{2}}}}\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, b \sqrt{a^{4} x^{4}+b^{4}}}\right)}{3 a}$&$825$\\ \hline \end{longtable}"," ",0,"1/2*(1/6/a/b*ln(-a*b+1/2*(a^4*x^4+b^4)^(1/2)*2^(1/2)/x)+2/3*2^(1/2)/a/b*arctan(1/a/b/x*(a^4*x^4+b^4)^(1/2))-1/6/a/b*ln(a*b+1/2*(a^4*x^4+b^4)^(1/2)*2^(1/2)/x))*2^(1/2)","A"
2114,0,0,117,0.045000," ","int((x^2-1)^(1/2)*(x^2+x*(x^2-1)^(1/2))^(1/2)/(1+x),x)","\[\int \frac{\sqrt{x^{2}-1}\, \sqrt{x^{2}+x \sqrt{x^{2}-1}}}{1+x}\, dx\]"," ",0,"int((x^2-1)^(1/2)*(x^2+x*(x^2-1)^(1/2))^(1/2)/(1+x),x)","F"
2115,0,0,111,0.039000," ","int((x^4+1)*(1+(x^2+1)^(1/2))^(1/2)/(x^4-1),x)","\[\int \frac{\left(x^{4}+1\right) \sqrt{1+\sqrt{x^{2}+1}}}{x^{4}-1}\, dx\]"," ",0,"int((x^4+1)*(1+(x^2+1)^(1/2))^(1/2)/(x^4-1),x)","F"
2116,0,0,114,0.034000," ","int((a*x^2-b^2)/(a*x^2+b^2)/(b+(a*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{a \,x^{2}-b^{2}}{\left(a \,x^{2}+b^{2}\right) \sqrt{b +\sqrt{a \,x^{2}+b^{2}}}}\, dx\]"," ",0,"int((a*x^2-b^2)/(a*x^2+b^2)/(b+(a*x^2+b^2)^(1/2))^(1/2),x)","F"
2117,0,0,130,0.017000," ","int(x/(1+(x+(x^2+1)^(1/2))^(1/2)),x)","\[\int \frac{x}{1+\sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int(x/(1+(x+(x^2+1)^(1/2))^(1/2)),x)","F"
2118,0,0,126,0.130000," ","int((-2*x+(1+k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(b-b*(1+k)*x+(b*k-1)*x^2),x)","\[\int \frac{-2 x +\left(1+k \right) x^{2}}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{2}{3}} \left(b -b \left(1+k \right) x +\left(b k -1\right) x^{2}\right)}\, dx\]"," ",0,"int((-2*x+(1+k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(b-b*(1+k)*x+(b*k-1)*x^2),x)","F"
2119,1,310,116,0.203000," ","int((a*x^2-b)*(a*x^3-b*x)^(1/2)/x^2/(a*x^2+b),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{2 a \,x^{2}-2 b}{\sqrt{x \left(a \,x^{2}-b \right)}}-\frac{2 b \sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}-\frac{2 b \sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}$&$310$\\ risch&$\frac{2 a \,x^{2}-2 b}{\sqrt{x \left(a \,x^{2}-b \right)}}-4 b a \left(\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}+\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}\right)$&$313$\\ default&$2 a \left(-\frac{2 b \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}-b x}}+\frac{b \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}-b x}}-\frac{b \sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}-\frac{b \sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}\right)+\frac{2 a \,x^{2}-2 b}{\sqrt{x \left(a \,x^{2}-b \right)}}-\frac{2 \sqrt{a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \left(-\frac{2 \sqrt{a b}\, \EllipticE \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{\sqrt{2}}{2}\right)}{a}+\frac{\sqrt{a b}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{\sqrt{2}}{2}\right)}{a}\right)}{\sqrt{a \,x^{3}-b x}}$&$617$\\ \hline \end{longtable}"," ",0,"2*(a*x^2-b)/(x*(a*x^2-b))^(1/2)-2*b/a*(a*b)^(1/2)*(x*a/(a*b)^(1/2)+1)^(1/2)*(-2*x*a/(a*b)^(1/2)+2)^(1/2)*(-x*a/(a*b)^(1/2))^(1/2)/(a*x^3-b*x)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2),-1/a*(a*b)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2)),1/2*2^(1/2))-2*b/a*(a*b)^(1/2)*(x*a/(a*b)^(1/2)+1)^(1/2)*(-2*x*a/(a*b)^(1/2)+2)^(1/2)*(-x*a/(a*b)^(1/2))^(1/2)/(a*x^3-b*x)^(1/2)/(-1/a*(a*b)^(1/2)+1/a*(-a*b)^(1/2))*EllipticPi(((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2),-1/a*(a*b)^(1/2)/(-1/a*(a*b)^(1/2)+1/a*(-a*b)^(1/2)),1/2*2^(1/2))","C"
2120,1,16978,56,93.543000," ","int((x^4-x^3)^(1/4)/x/(x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$16978$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2121,1,3097,56,9.030000," ","int((x^4-x^3)^(1/4)/x/(x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$3097$\\ \hline \end{longtable}"," ",0,"-RootOf(6561*_Z^8-81*_Z^4+1)*ln((177147*RootOf(6561*_Z^8-81*_Z^4+1)^11*x^3-354294*RootOf(6561*_Z^8-81*_Z^4+1)^11*x^2+2187*RootOf(6561*_Z^8-81*_Z^4+1)^7*x^3+10935*RootOf(6561*_Z^8-81*_Z^4+1)^7*x^2-11664*RootOf(6561*_Z^8-81*_Z^4+1)^6*(x^4-x^3)^(1/4)*x^2+1458*(x^4-x^3)^(1/2)*RootOf(6561*_Z^8-81*_Z^4+1)^5*x+810*(x^4-x^3)^(3/4)*RootOf(6561*_Z^8-81*_Z^4+1)^4-324*RootOf(6561*_Z^8-81*_Z^4+1)^3*x^3+81*RootOf(6561*_Z^8-81*_Z^4+1)^3*x^2+54*RootOf(6561*_Z^8-81*_Z^4+1)^2*(x^4-x^3)^(1/4)*x^2+30*(x^4-x^3)^(1/2)*RootOf(6561*_Z^8-81*_Z^4+1)*x-16*(x^4-x^3)^(3/4))/(81*RootOf(6561*_Z^8-81*_Z^4+1)^4*x-162*RootOf(6561*_Z^8-81*_Z^4+1)^4-2*x+1)/x^2)-729*RootOf(6561*_Z^8-81*_Z^4+1)^7*ln((13122*x^3*RootOf(6561*_Z^8-81*_Z^4+1)^9-26244*RootOf(6561*_Z^8-81*_Z^4+1)^9*x^2+11664*(x^4-x^3)^(1/2)*RootOf(6561*_Z^8-81*_Z^4+1)^7*x+2430*RootOf(6561*_Z^8-81*_Z^4+1)^6*(x^4-x^3)^(1/4)*x^2-1053*RootOf(6561*_Z^8-81*_Z^4+1)^5*x^3+972*RootOf(6561*_Z^8-81*_Z^4+1)^5*x^2-270*(x^4-x^3)^(3/4)*RootOf(6561*_Z^8-81*_Z^4+1)^4-90*(x^4-x^3)^(1/2)*RootOf(6561*_Z^8-81*_Z^4+1)^3*x+18*RootOf(6561*_Z^8-81*_Z^4+1)^2*(x^4-x^3)^(1/4)*x^2+15*RootOf(6561*_Z^8-81*_Z^4+1)*x^3-9*RootOf(6561*_Z^8-81*_Z^4+1)*x^2-2*(x^4-x^3)^(3/4))/(81*RootOf(6561*_Z^8-81*_Z^4+1)^4*x-162*RootOf(6561*_Z^8-81*_Z^4+1)^4+x+1)/x^2)+9*RootOf(6561*_Z^8-81*_Z^4+1)^3*ln((13122*x^3*RootOf(6561*_Z^8-81*_Z^4+1)^9-26244*RootOf(6561*_Z^8-81*_Z^4+1)^9*x^2+11664*(x^4-x^3)^(1/2)*RootOf(6561*_Z^8-81*_Z^4+1)^7*x+2430*RootOf(6561*_Z^8-81*_Z^4+1)^6*(x^4-x^3)^(1/4)*x^2-1053*RootOf(6561*_Z^8-81*_Z^4+1)^5*x^3+972*RootOf(6561*_Z^8-81*_Z^4+1)^5*x^2-270*(x^4-x^3)^(3/4)*RootOf(6561*_Z^8-81*_Z^4+1)^4-90*(x^4-x^3)^(1/2)*RootOf(6561*_Z^8-81*_Z^4+1)^3*x+18*RootOf(6561*_Z^8-81*_Z^4+1)^2*(x^4-x^3)^(1/4)*x^2+15*RootOf(6561*_Z^8-81*_Z^4+1)*x^3-9*RootOf(6561*_Z^8-81*_Z^4+1)*x^2-2*(x^4-x^3)^(3/4))/(81*RootOf(6561*_Z^8-81*_Z^4+1)^4*x-162*RootOf(6561*_Z^8-81*_Z^4+1)^4+x+1)/x^2)+81*RootOf(6561*_Z^8-81*_Z^4+1)^5*ln((59049*RootOf(6561*_Z^8-81*_Z^4+1)^11*x^3-118098*RootOf(6561*_Z^8-81*_Z^4+1)^11*x^2-2187*RootOf(6561*_Z^8-81*_Z^4+1)^7*x^3-729*RootOf(6561*_Z^8-81*_Z^4+1)^7*x^2-2430*RootOf(6561*_Z^8-81*_Z^4+1)^6*(x^4-x^3)^(1/4)*x^2-810*(x^4-x^3)^(1/2)*RootOf(6561*_Z^8-81*_Z^4+1)^5*x-270*(x^4-x^3)^(3/4)*RootOf(6561*_Z^8-81*_Z^4+1)^4-90*RootOf(6561*_Z^8-81*_Z^4+1)^3*x^3+54*RootOf(6561*_Z^8-81*_Z^4+1)^3*x^2-18*RootOf(6561*_Z^8-81*_Z^4+1)^2*(x^4-x^3)^(1/4)*x^2-6*(x^4-x^3)^(1/2)*RootOf(6561*_Z^8-81*_Z^4+1)*x-2*(x^4-x^3)^(3/4))/(81*RootOf(6561*_Z^8-81*_Z^4+1)^4*x-162*RootOf(6561*_Z^8-81*_Z^4+1)^4+x+1)/x^2)+729*RootOf(6561*_Z^8-81*_Z^4+1)^7*ln(-(59049*x^3*RootOf(6561*_Z^8-81*_Z^4+1)^9-118098*RootOf(6561*_Z^8-81*_Z^4+1)^9*x^2+34992*(x^4-x^3)^(1/2)*RootOf(6561*_Z^8-81*_Z^4+1)^7*x-11664*RootOf(6561*_Z^8-81*_Z^4+1)^6*(x^4-x^3)^(1/4)*x^2+2430*RootOf(6561*_Z^8-81*_Z^4+1)^5*x^3+243*RootOf(6561*_Z^8-81*_Z^4+1)^5*x^2-810*(x^4-x^3)^(3/4)*RootOf(6561*_Z^8-81*_Z^4+1)^4-162*(x^4-x^3)^(1/2)*RootOf(6561*_Z^8-81*_Z^4+1)^3*x+54*RootOf(6561*_Z^8-81*_Z^4+1)^2*(x^4-x^3)^(1/4)*x^2-24*RootOf(6561*_Z^8-81*_Z^4+1)*x^3+6*RootOf(6561*_Z^8-81*_Z^4+1)*x^2+16*(x^4-x^3)^(3/4))/(81*RootOf(6561*_Z^8-81*_Z^4+1)^4*x-162*RootOf(6561*_Z^8-81*_Z^4+1)^4-2*x+1)/x^2)+1/3*RootOf(_Z^2+243*RootOf(6561*_Z^8-81*_Z^4+1)^5-27*RootOf(6561*_Z^8-81*_Z^4+1)^3-3*RootOf(6561*_Z^8-81*_Z^4+1))*ln((729*RootOf(_Z^2+243*RootOf(6561*_Z^8-81*_Z^4+1)^5-27*RootOf(6561*_Z^8-81*_Z^4+1)^3-3*RootOf(6561*_Z^8-81*_Z^4+1))*RootOf(6561*_Z^8-81*_Z^4+1)^5*x^3-243*RootOf(_Z^2+243*RootOf(6561*_Z^8-81*_Z^4+1)^5-27*RootOf(6561*_Z^8-81*_Z^4+1)^3-3*RootOf(6561*_Z^8-81*_Z^4+1))*RootOf(6561*_Z^8-81*_Z^4+1)^5*x^2-972*RootOf(6561*_Z^8-81*_Z^4+1)^5*(x^4-x^3)^(1/4)*x^2-81*RootOf(_Z^2+243*RootOf(6561*_Z^8-81*_Z^4+1)^5-27*RootOf(6561*_Z^8-81*_Z^4+1)^3-3*RootOf(6561*_Z^8-81*_Z^4+1))*RootOf(6561*_Z^8-81*_Z^4+1)^3*x^3+27*RootOf(_Z^2+243*RootOf(6561*_Z^8-81*_Z^4+1)^5-27*RootOf(6561*_Z^8-81*_Z^4+1)^3-3*RootOf(6561*_Z^8-81*_Z^4+1))*RootOf(6561*_Z^8-81*_Z^4+1)^3*x^2+108*RootOf(6561*_Z^8-81*_Z^4+1)^3*(x^4-x^3)^(1/4)*x^2-9*RootOf(_Z^2+243*RootOf(6561*_Z^8-81*_Z^4+1)^5-27*RootOf(6561*_Z^8-81*_Z^4+1)^3-3*RootOf(6561*_Z^8-81*_Z^4+1))*RootOf(6561*_Z^8-81*_Z^4+1)*x^3+3*RootOf(_Z^2+243*RootOf(6561*_Z^8-81*_Z^4+1)^5-27*RootOf(6561*_Z^8-81*_Z^4+1)^3-3*RootOf(6561*_Z^8-81*_Z^4+1))*RootOf(6561*_Z^8-81*_Z^4+1)*x^2-4*(x^4-x^3)^(1/2)*RootOf(_Z^2+243*RootOf(6561*_Z^8-81*_Z^4+1)^5-27*RootOf(6561*_Z^8-81*_Z^4+1)^3-3*RootOf(6561*_Z^8-81*_Z^4+1))*x+12*RootOf(6561*_Z^8-81*_Z^4+1)*(x^4-x^3)^(1/4)*x^2+4*(x^4-x^3)^(3/4))/x^2/(1+x))-243*RootOf(6561*_Z^8-81*_Z^4+1)^6*RootOf(_Z^2+243*RootOf(6561*_Z^8-81*_Z^4+1)^5-27*RootOf(6561*_Z^8-81*_Z^4+1)^3-3*RootOf(6561*_Z^8-81*_Z^4+1))*ln((2916*(x^4-x^3)^(1/2)*RootOf(_Z^2+243*RootOf(6561*_Z^8-81*_Z^4+1)^5-27*RootOf(6561*_Z^8-81*_Z^4+1)^3-3*RootOf(6561*_Z^8-81*_Z^4+1))*RootOf(6561*_Z^8-81*_Z^4+1)^6*x-729*RootOf(_Z^2+243*RootOf(6561*_Z^8-81*_Z^4+1)^5-27*RootOf(6561*_Z^8-81*_Z^4+1)^3-3*RootOf(6561*_Z^8-81*_Z^4+1))*RootOf(6561*_Z^8-81*_Z^4+1)^5*x^3+243*RootOf(_Z^2+243*RootOf(6561*_Z^8-81*_Z^4+1)^5-27*RootOf(6561*_Z^8-81*_Z^4+1)^3-3*RootOf(6561*_Z^8-81*_Z^4+1))*RootOf(6561*_Z^8-81*_Z^4+1)^5*x^2+972*RootOf(6561*_Z^8-81*_Z^4+1)^5*(x^4-x^3)^(1/4)*x^2-81*RootOf(_Z^2+243*RootOf(6561*_Z^8-81*_Z^4+1)^5-27*RootOf(6561*_Z^8-81*_Z^4+1)^3-3*RootOf(6561*_Z^8-81*_Z^4+1))*RootOf(6561*_Z^8-81*_Z^4+1)^3*x^3+27*RootOf(_Z^2+243*RootOf(6561*_Z^8-81*_Z^4+1)^5-27*RootOf(6561*_Z^8-81*_Z^4+1)^3-3*RootOf(6561*_Z^8-81*_Z^4+1))*RootOf(6561*_Z^8-81*_Z^4+1)^3*x^2-108*RootOf(6561*_Z^8-81*_Z^4+1)^3*(x^4-x^3)^(1/4)*x^2+9*RootOf(_Z^2+243*RootOf(6561*_Z^8-81*_Z^4+1)^5-27*RootOf(6561*_Z^8-81*_Z^4+1)^3-3*RootOf(6561*_Z^8-81*_Z^4+1))*RootOf(6561*_Z^8-81*_Z^4+1)*x^3-3*RootOf(_Z^2+243*RootOf(6561*_Z^8-81*_Z^4+1)^5-27*RootOf(6561*_Z^8-81*_Z^4+1)^3-3*RootOf(6561*_Z^8-81*_Z^4+1))*RootOf(6561*_Z^8-81*_Z^4+1)*x^2-12*RootOf(6561*_Z^8-81*_Z^4+1)*(x^4-x^3)^(1/4)*x^2+4*(x^4-x^3)^(3/4))/x^2/(1+x))","B"
2122,1,1089,124,68.682000," ","int((x^4-3)*(x^4-x^3+1)^(2/3)/x^3/(x^4+x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 \left(x^{4}-x^{3}+1\right)^{\frac{2}{3}}}{2 x^{2}}-\ln \left(\frac{2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{3}-2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{3}+4 \left(x^{4}-x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x +\RootOf \left(\textit{\_Z}^{3}-4\right)^{2} \left(x^{4}-x^{3}+1\right)^{\frac{1}{3}} x^{2}-8 \left(x^{4}-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x^{2}+2 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{4}-2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{3}+2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{3}-2 \left(x^{4}-x^{3}+1\right)^{\frac{2}{3}} x +2 \RootOf \left(\textit{\_Z}^{3}-4\right)-2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)}{x^{4}+x^{3}+1}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)+2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \ln \left(-\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{3}+2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{3}+4 \left(x^{4}-x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x -5 \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} \left(x^{4}-x^{3}+1\right)^{\frac{1}{3}} x^{2}-8 \left(x^{4}-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x^{2}-3 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{4}-2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{4}+9 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{3}+6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{3}+10 \left(x^{4}-x^{3}+1\right)^{\frac{2}{3}} x -3 \RootOf \left(\textit{\_Z}^{3}-4\right)-2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)}{x^{4}+x^{3}+1}\right)-2 \ln \left(\frac{2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{3}-2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{3}+4 \left(x^{4}-x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x +\RootOf \left(\textit{\_Z}^{3}-4\right)^{2} \left(x^{4}-x^{3}+1\right)^{\frac{1}{3}} x^{2}-8 \left(x^{4}-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x^{2}+2 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{4}-2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{3}+2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{3}-2 \left(x^{4}-x^{3}+1\right)^{\frac{2}{3}} x +2 \RootOf \left(\textit{\_Z}^{3}-4\right)-2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)}{x^{4}+x^{3}+1}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)$&$1089$\\ trager&$\text{Expression too large to display}$&$1509$\\ \hline \end{longtable}"," ",0,"3/2*(x^4-x^3+1)^(2/3)/x^2-ln((2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x^3-2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+4*(x^4-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^2*x+RootOf(_Z^3-4)^2*(x^4-x^3+1)^(1/3)*x^2-8*(x^4-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)*x^2+2*RootOf(_Z^3-4)*x^4-2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^4-2*RootOf(_Z^3-4)*x^3+2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^3-2*(x^4-x^3+1)^(2/3)*x+2*RootOf(_Z^3-4)-2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2))/(x^4+x^3+1))*RootOf(_Z^3-4)+2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*ln(-(3*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x^3+2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+4*(x^4-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^2*x-5*RootOf(_Z^3-4)^2*(x^4-x^3+1)^(1/3)*x^2-8*(x^4-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)*x^2-3*RootOf(_Z^3-4)*x^4-2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^4+9*RootOf(_Z^3-4)*x^3+6*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^3+10*(x^4-x^3+1)^(2/3)*x-3*RootOf(_Z^3-4)-2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2))/(x^4+x^3+1))-2*ln((2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x^3-2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+4*(x^4-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^2*x+RootOf(_Z^3-4)^2*(x^4-x^3+1)^(1/3)*x^2-8*(x^4-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)*x^2+2*RootOf(_Z^3-4)*x^4-2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^4-2*RootOf(_Z^3-4)*x^3+2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^3-2*(x^4-x^3+1)^(2/3)*x+2*RootOf(_Z^3-4)-2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2))/(x^4+x^3+1))*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)","C"
2123,0,0,116,0.015000," ","int((a*x^5-4*b)*(a*x^5+b)^(3/4)/x^4/(2*a*x^5+c*x^4+2*b),x)","\[\int \frac{\left(a \,x^{5}-4 b \right) \left(a \,x^{5}+b \right)^{\frac{3}{4}}}{x^{4} \left(2 a \,x^{5}+c \,x^{4}+2 b \right)}\, dx\]"," ",0,"int((a*x^5-4*b)*(a*x^5+b)^(3/4)/x^4/(2*a*x^5+c*x^4+2*b),x)","F"
2124,1,4597,124,60.916000," ","int((x^6-1)/(x^4+x^2)^(1/3)/(x^6+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$4597$\\ risch&$\text{Expression too large to display}$&$7488$\\ \hline \end{longtable}"," ",0,"-(x^4+x^2)^(2/3)/x/(x^2+1)+1/9*RootOf(_Z^6-243)*ln((191887380*(x^4+x^2)^(2/3)+171154620*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x^5+49292530560*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x^4-171154620*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x^3+49292530560*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x^2+171154620*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x-4754295*RootOf(_Z^6-243)*x^5-1369236960*RootOf(_Z^6-243)*x^4+4754295*RootOf(_Z^6-243)*x^3-1369236960*RootOf(_Z^6-243)*x^2-4754295*RootOf(_Z^6-243)*x+4226040*RootOf(_Z^6-243)^4*x+4226040*x^5*RootOf(_Z^6-243)^4-2113020*x^2*RootOf(_Z^6-243)^4-4226040*x^3*RootOf(_Z^6-243)^4-2113020*x^4*RootOf(_Z^6-243)^4-16848000*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^6*x^3+16848000*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^6*x^5-8424000*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^6*x^4-79868820096*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^3*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*x^3+779641200*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^3*x^3-5078408400*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^3*x^2-779641200*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^3*x-8424000*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^6*x^2+16848000*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^6*x-779641200*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^3*x^5-5078408400*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^3*x^4-2426112000*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*RootOf(_Z^6-243)^5*x^5+1213056000*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*RootOf(_Z^6-243)^5*x^4+2426112000*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*RootOf(_Z^6-243)^5*x^3+1213056000*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*RootOf(_Z^6-243)^5*x^2+21907791360*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*RootOf(_Z^6-243)^2*x^5-2426112000*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*RootOf(_Z^6-243)^5*x-10953895680*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*RootOf(_Z^6-243)^2*x^4-21907791360*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*RootOf(_Z^6-243)^2*x^3-10953895680*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*RootOf(_Z^6-243)^2*x^2+21907791360*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*RootOf(_Z^6-243)^2*x-29950807536*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x^3-14975403768*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x^2-29950807536*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)*(x^4+x^2)^(1/3)*x+5872464*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^7*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x^3+845634816*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^6*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*x^3-11744928*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^7*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x^2-1691269632*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^6*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*x^2-463255200*(x^4+x^2)^(2/3)*RootOf(_Z^6-243)^5*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x^2+33354374400*(x^4+x^2)^(2/3)*RootOf(_Z^6-243)^4*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*x^2+5872464*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^7*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x+845634816*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^6*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*x+926510400*(x^4+x^2)^(2/3)*RootOf(_Z^6-243)^5*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x-66708748800*(x^4+x^2)^(2/3)*RootOf(_Z^6-243)^4*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*x+1981046808*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^4*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x^3-3169310976*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^4*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x^2+5704395840*(x^4+x^2)^(2/3)*RootOf(_Z^6-243)^2*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x^2+1981046808*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^4*(x^4+x^2)^(1/3)*x+15691637520*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^2*(x^4+x^2)^(2/3)*x+159737640192*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^3*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*x^2-79868820096*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^3*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*x-81562*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^8*x^3+163124*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^8*x^2+1608525*(x^4+x^2)^(2/3)*RootOf(_Z^6-243)^6*x^2-81562*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^8*x-3217050*(x^4+x^2)^(2/3)*RootOf(_Z^6-243)^6*x-3299049*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^5*x^3-463255200*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^5*(x^4+x^2)^(2/3)+33354374400*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*RootOf(_Z^6-243)^4*(x^4+x^2)^(2/3)+17608968*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^5*x^2-39613860*(x^4+x^2)^(2/3)*RootOf(_Z^6-243)^3*x^2-3299049*RootOf(_Z^6-243)^5*(x^4+x^2)^(1/3)*x-108969705*(x^4+x^2)^(2/3)*RootOf(_Z^6-243)^3*x+415983438*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^2*x^3+5704395840*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^2*(x^4+x^2)^(2/3)+207991719*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^2*x^2+415983438*RootOf(_Z^6-243)^2*(x^4+x^2)^(1/3)*x+863493210*(x^4+x^2)^(2/3)*x+1608525*RootOf(_Z^6-243)^6*(x^4+x^2)^(2/3)-39613860*(x^4+x^2)^(2/3)*RootOf(_Z^6-243)^3+191887380*(x^4+x^2)^(2/3)*x^2)/(x^4-x^2+1)/x)-8*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*ln((383774760*(x^4+x^2)^(2/3)+684618480*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x^5+197170122240*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x^4-684618480*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x^3+197170122240*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x^2+684618480*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x-468000*RootOf(_Z^6-243)^7*x^3+468000*RootOf(_Z^6-243)^7*x-4754295*RootOf(_Z^6-243)*x^5-1369236960*RootOf(_Z^6-243)*x^4+4754295*RootOf(_Z^6-243)*x^3-1369236960*RootOf(_Z^6-243)*x^2-4754295*RootOf(_Z^6-243)*x-3699540*RootOf(_Z^6-243)^4*x+468000*RootOf(_Z^6-243)^7*x^5-234000*RootOf(_Z^6-243)^7*x^4-3699540*x^5*RootOf(_Z^6-243)^4+153745020*x^2*RootOf(_Z^6-243)^4+3699540*x^3*RootOf(_Z^6-243)^4+153745020*x^4*RootOf(_Z^6-243)^4-234000*RootOf(_Z^6-243)^7*x^2+67392000*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^6*x^3-67392000*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^6*x^5+33696000*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^6*x^4-1217099520*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^3*x^3-608549760*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^3*x^2+1217099520*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^3*x+33696000*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^6*x^2-67392000*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^6*x+1217099520*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^3*x^5-608549760*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^3*x^4-87631165440*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*RootOf(_Z^6-243)^2*x^5+43815582720*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*RootOf(_Z^6-243)^2*x^4+87631165440*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*RootOf(_Z^6-243)^2*x^3+43815582720*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*RootOf(_Z^6-243)^2*x^2-87631165440*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*RootOf(_Z^6-243)^2*x+46979712*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^7*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x^3-3382539264*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^6*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*x^3-93959424*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^7*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x^2+6765078528*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^6*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*x^2-926510400*(x^4+x^2)^(2/3)*RootOf(_Z^6-243)^5*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x^2+66708748800*(x^4+x^2)^(2/3)*RootOf(_Z^6-243)^4*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*x^2+46979712*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^7*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x-3382539264*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^6*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*x+1853020800*(x^4+x^2)^(2/3)*RootOf(_Z^6-243)^5*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x-133417497600*(x^4+x^2)^(2/3)*RootOf(_Z^6-243)^4*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*x+3487030560*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^4*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x^3-3802930560*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^4*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x^2-11408791680*(x^4+x^2)^(2/3)*RootOf(_Z^6-243)^2*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*x^2+3487030560*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^4*(x^4+x^2)^(1/3)*x-31383275040*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^2*(x^4+x^2)^(2/3)*x-163124*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^8*x^3+326248*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^8*x^2+3217050*(x^4+x^2)^(2/3)*RootOf(_Z^6-243)^6*x^2-163124*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^8*x-6434100*(x^4+x^2)^(2/3)*RootOf(_Z^6-243)^6*x-24215490*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^5*x^3-926510400*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^5*(x^4+x^2)^(2/3)+66708748800*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)^2*RootOf(_Z^6-243)^4*(x^4+x^2)^(2/3)+26409240*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^5*x^2+79227720*(x^4+x^2)^(2/3)*RootOf(_Z^6-243)^3*x^2-24215490*RootOf(_Z^6-243)^5*(x^4+x^2)^(1/3)*x+217939410*(x^4+x^2)^(2/3)*RootOf(_Z^6-243)^3*x-831966876*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^2*x^3-11408791680*RootOf(RootOf(_Z^6-243)^2-72*_Z*RootOf(_Z^6-243)+5184*_Z^2)*RootOf(_Z^6-243)^2*(x^4+x^2)^(2/3)-415983438*(x^4+x^2)^(1/3)*RootOf(_Z^6-243)^2*x^2-831966876*RootOf(_Z^6-243)^2*(x^4+x^2)^(1/3)*x+1726986420*(x^4+x^2)^(2/3)*x+3217050*RootOf(_Z^6-243)^6*(x^4+x^2)^(2/3)+79227720*(x^4+x^2)^(2/3)*RootOf(_Z^6-243)^3+383774760*(x^4+x^2)^(2/3)*x^2)/(x^4-x^2+1)/x)","C"
2125,1,360,122,12.621000," ","int((3*x^4+2)^(1/4)*(x^8+6*x^4+4)/x^6/(x^4+1)/(2*x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(3 x^{4}+2\right)^{\frac{1}{4}} \left(6 x^{4}-1\right)}{5 x^{5}}-\frac{5 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(-\frac{\sqrt{3 x^{4}+2}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}-\left(3 x^{4}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{4}+1\right) x^{4}+\left(3 x^{4}+2\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}+1\right)}{2 x^{4}+1}\right)}{4}-\frac{5 \RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{4}+\left(3 x^{4}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}+\sqrt{3 x^{4}+2}\, \RootOf \left(\textit{\_Z}^{4}+1\right) x^{2}+\left(3 x^{4}+2\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{2 x^{4}+1}\right)}{4}-\frac{\ln \left(-\frac{\left(3 x^{4}+2\right)^{\frac{3}{4}} x +x^{2} \sqrt{3 x^{4}+2}+\left(3 x^{4}+2\right)^{\frac{1}{4}} x^{3}+2 x^{4}+1}{x^{4}+1}\right)}{4}-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} \ln \left(-\frac{\sqrt{3 x^{4}+2}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{4}+\left(3 x^{4}+2\right)^{\frac{3}{4}} x -\left(3 x^{4}+2\right)^{\frac{1}{4}} x^{3}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{2}}{x^{4}+1}\right)}{4}$&$360$\\ risch&$\frac{\frac{36}{5} x^{4}-\frac{8}{5}+\frac{72}{5} x^{8}}{x^{5} \left(3 x^{4}+2\right)^{\frac{3}{4}}}+\frac{\left(\frac{\ln \left(\frac{-18 x^{12}+9 \left(27 x^{12}+54 x^{8}+36 x^{4}+8\right)^{\frac{1}{4}} x^{9}-3 \sqrt{27 x^{12}+54 x^{8}+36 x^{4}+8}\, x^{6}-33 x^{8}+\left(27 x^{12}+54 x^{8}+36 x^{4}+8\right)^{\frac{3}{4}} x^{3}+12 \left(27 x^{12}+54 x^{8}+36 x^{4}+8\right)^{\frac{1}{4}} x^{5}-2 \sqrt{27 x^{12}+54 x^{8}+36 x^{4}+8}\, x^{2}-20 x^{4}+4 \left(27 x^{12}+54 x^{8}+36 x^{4}+8\right)^{\frac{1}{4}} x -4}{\left(x^{4}+1\right) \left(3 x^{4}+2\right)^{2}}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{18 x^{12}-9 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(27 x^{12}+54 x^{8}+36 x^{4}+8\right)^{\frac{1}{4}} x^{9}-3 \sqrt{27 x^{12}+54 x^{8}+36 x^{4}+8}\, x^{6}+33 x^{8}+\RootOf \left(\textit{\_Z}^{2}+1\right) \left(27 x^{12}+54 x^{8}+36 x^{4}+8\right)^{\frac{3}{4}} x^{3}-12 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(27 x^{12}+54 x^{8}+36 x^{4}+8\right)^{\frac{1}{4}} x^{5}-2 \sqrt{27 x^{12}+54 x^{8}+36 x^{4}+8}\, x^{2}+20 x^{4}-4 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(27 x^{12}+54 x^{8}+36 x^{4}+8\right)^{\frac{1}{4}} x +4}{\left(x^{4}+1\right) \left(3 x^{4}+2\right)^{2}}\right)}{4}-\frac{5 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \ln \left(\frac{9 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{12}+9 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) \left(27 x^{12}+54 x^{8}+36 x^{4}+8\right)^{\frac{1}{4}} x^{9}+21 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{8}+12 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) \left(27 x^{12}+54 x^{8}+36 x^{4}+8\right)^{\frac{1}{4}} x^{5}+3 \sqrt{27 x^{12}+54 x^{8}+36 x^{4}+8}\, x^{6}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \left(27 x^{12}+54 x^{8}+36 x^{4}+8\right)^{\frac{3}{4}} x^{3}+16 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+4 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) \left(27 x^{12}+54 x^{8}+36 x^{4}+8\right)^{\frac{1}{4}} x +2 \sqrt{27 x^{12}+54 x^{8}+36 x^{4}+8}\, x^{2}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(2 x^{4}+1\right) \left(3 x^{4}+2\right)^{2}}\right)}{4}-\frac{5 \RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \ln \left(\frac{-9 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{12}+9 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \left(27 x^{12}+54 x^{8}+36 x^{4}+8\right)^{\frac{1}{4}} x^{9}-21 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{8}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) \left(27 x^{12}+54 x^{8}+36 x^{4}+8\right)^{\frac{3}{4}} x^{3}+3 \sqrt{27 x^{12}+54 x^{8}+36 x^{4}+8}\, x^{6}+12 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \left(27 x^{12}+54 x^{8}+36 x^{4}+8\right)^{\frac{1}{4}} x^{5}-16 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \sqrt{27 x^{12}+54 x^{8}+36 x^{4}+8}\, x^{2}+4 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right) \left(27 x^{12}+54 x^{8}+36 x^{4}+8\right)^{\frac{1}{4}} x -4 \RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(2 x^{4}+1\right) \left(3 x^{4}+2\right)^{2}}\right)}{4}\right) \left(\left(3 x^{4}+2\right)^{3}\right)^{\frac{1}{4}}}{\left(3 x^{4}+2\right)^{\frac{3}{4}}}$&$986$\\ \hline \end{longtable}"," ",0,"4/5*(3*x^4+2)^(1/4)*(6*x^4-1)/x^5-5/4*RootOf(_Z^4+1)^3*ln(-((3*x^4+2)^(1/2)*RootOf(_Z^4+1)^3*x^2-(3*x^4+2)^(1/4)*RootOf(_Z^4+1)^2*x^3-RootOf(_Z^4+1)*x^4+(3*x^4+2)^(3/4)*x-RootOf(_Z^4+1))/(2*x^4+1))-5/4*RootOf(_Z^4+1)*ln(-(-RootOf(_Z^4+1)^3*x^4+(3*x^4+2)^(1/4)*RootOf(_Z^4+1)^2*x^3+(3*x^4+2)^(1/2)*RootOf(_Z^4+1)*x^2+(3*x^4+2)^(3/4)*x-RootOf(_Z^4+1)^3)/(2*x^4+1))-1/4*ln(-((3*x^4+2)^(3/4)*x+x^2*(3*x^4+2)^(1/2)+(3*x^4+2)^(1/4)*x^3+2*x^4+1)/(x^4+1))-1/4*RootOf(_Z^4+1)^2*ln(-((3*x^4+2)^(1/2)*RootOf(_Z^4+1)^2*x^2-2*RootOf(_Z^4+1)^2*x^4+(3*x^4+2)^(3/4)*x-(3*x^4+2)^(1/4)*x^3-RootOf(_Z^4+1)^2)/(x^4+1))","C"
2126,0,0,115,0.029000," ","int((x^8-16*x^6+96*x^4-256*x^2+256)^(1/8)/(x^3-1),x)","\[\int \frac{\left(x^{8}-16 x^{6}+96 x^{4}-256 x^{2}+256\right)^{\frac{1}{8}}}{x^{3}-1}\, dx\]"," ",0,"int((x^8-16*x^6+96*x^4-256*x^2+256)^(1/8)/(x^3-1),x)","F"
2127,0,0,132,180.000000," ","int((x^6+6*x^3-6*x^2-36)/x/(x^3-6)/((x^3+6)/(x^3-6))^(1/6)/(x^8-6*x^7+15*x^6-26*x^5+51*x^4-96*x^3+122*x^2-90*x+36),x)","\[\int \frac{x^{6}+6 x^{3}-6 x^{2}-36}{x \left(x^{3}-6\right) \left(\frac{x^{3}+6}{x^{3}-6}\right)^{\frac{1}{6}} \left(x^{8}-6 x^{7}+15 x^{6}-26 x^{5}+51 x^{4}-96 x^{3}+122 x^{2}-90 x +36\right)}\, dx\]"," ",0,"int((x^6+6*x^3-6*x^2-36)/x/(x^3-6)/((x^3+6)/(x^3-6))^(1/6)/(x^8-6*x^7+15*x^6-26*x^5+51*x^4-96*x^3+122*x^2-90*x+36),x)","F"
2128,0,0,50,0.031000," ","int((2*x^8-a*x^4+2*b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-2*b),x)","\[\int \frac{2 x^{8}-a \,x^{4}+2 b}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(x^{8}+a \,x^{4}-2 b \right)}\, dx\]"," ",0,"int((2*x^8-a*x^4+2*b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-2*b),x)","F"
2129,0,0,50,0.002000," ","int((2*x^8-a*x^4+2*b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-2*b),x)","\[\int \frac{2 x^{8}-a \,x^{4}+2 b}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(x^{8}+a \,x^{4}-2 b \right)}\, dx\]"," ",0,"int((2*x^8-a*x^4+2*b)/(a*x^4+b)^(1/4)/(x^8+a*x^4-2*b),x)","F"
2130,0,0,122,0.029000," ","int((a*x^8-b)/(a*x^8+b)/(a*x^8-c*x^4+b)^(1/4),x)","\[\int \frac{a \,x^{8}-b}{\left(a \,x^{8}+b \right) \left(a \,x^{8}-c \,x^{4}+b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^8-b)/(a*x^8+b)/(a*x^8-c*x^4+b)^(1/4),x)","F"
2131,0,0,140,0.050000," ","int(1/x^2/(a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x)","\[\int \frac{1}{x^{2} \sqrt{a^{2} x^{2}-b x}\, \left(a \,x^{2}+x \sqrt{a^{2} x^{2}-b x}\right)^{\frac{3}{2}}}\, dx\]"," ",0,"int(1/x^2/(a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x)","F"
2132,0,0,131,0.032000," ","int((1+(x^2+1)^(1/2))/(1+(x+(x^2+1)^(1/2))^(1/2)),x)","\[\int \frac{1+\sqrt{x^{2}+1}}{1+\sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((1+(x^2+1)^(1/2))/(1+(x+(x^2+1)^(1/2))^(1/2)),x)","F"
2133,0,0,127,0.127000," ","int((-2+(1+k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(b-b*(1+k)*x+(b*k-1)*x^2),x)","\[\int \frac{-2+\left(1+k \right) x}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(b -b \left(1+k \right) x +\left(b k -1\right) x^{2}\right)}\, dx\]"," ",0,"int((-2+(1+k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(b-b*(1+k)*x+(b*k-1)*x^2),x)","F"
2134,0,0,128,0.014000," ","int((a*x^4-b)^(1/4)*(a*x^8-8*b)/x^10/(a*x^4+b),x)","\[\int \frac{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(a \,x^{8}-8 b \right)}{x^{10} \left(a \,x^{4}+b \right)}\, dx\]"," ",0,"int((a*x^4-b)^(1/4)*(a*x^8-8*b)/x^10/(a*x^4+b),x)","F"
2135,1,502,47,0.144000," ","int(x/(x+(x+(1+x)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\sqrt{x +\sqrt{1+x}}+\sqrt{1+x}-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\sum}\frac{\left(2 \textit{\_R}^{3}-3 \textit{\_R}^{2}-\textit{\_R} +6\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +5}\right)+\frac{5}{2 \left(-1-2 \sqrt{1+x}+2 \sqrt{x +\sqrt{1+x}}\right)}+\ln \left(-1-2 \sqrt{1+x}+2 \sqrt{x +\sqrt{1+x}}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+2 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{\sum}\frac{\left(2 \textit{\_R}^{3}+\textit{\_R}^{2}-\textit{\_R} \right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}+6 \textit{\_R}^{2}-10 \textit{\_R} +3}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\textit{\_R} \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)-4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\textit{\_R}^{3} \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)+1+x +2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\left(3 \textit{\_R}^{3}+\textit{\_R}^{2}-2 \textit{\_R} \right) \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\sum}\frac{\left(\textit{\_R}^{3}-\textit{\_R}^{2}+2\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +5}\right)-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+2 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{\sum}\frac{\left(\textit{\_R}^{3}+\textit{\_R}^{2}-2 \textit{\_R} \right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}+6 \textit{\_R}^{2}-10 \textit{\_R} +3}\right)$&$502$\\ default&$-\sqrt{x +\sqrt{1+x}}+\sqrt{1+x}-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\sum}\frac{\left(2 \textit{\_R}^{3}-3 \textit{\_R}^{2}-\textit{\_R} +6\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +5}\right)+\frac{5}{2 \left(-1-2 \sqrt{1+x}+2 \sqrt{x +\sqrt{1+x}}\right)}+\ln \left(-1-2 \sqrt{1+x}+2 \sqrt{x +\sqrt{1+x}}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+2 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{\sum}\frac{\left(2 \textit{\_R}^{3}+\textit{\_R}^{2}-\textit{\_R} \right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}+6 \textit{\_R}^{2}-10 \textit{\_R} +3}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\textit{\_R} \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)-4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\textit{\_R}^{3} \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)+1+x +2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\left(3 \textit{\_R}^{3}+\textit{\_R}^{2}-2 \textit{\_R} \right) \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\sum}\frac{\left(\textit{\_R}^{3}-\textit{\_R}^{2}+2\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +5}\right)-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+2 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{\sum}\frac{\left(\textit{\_R}^{3}+\textit{\_R}^{2}-2 \textit{\_R} \right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}+6 \textit{\_R}^{2}-10 \textit{\_R} +3}\right)$&$502$\\ \hline \end{longtable}"," ",0,"-(x+(1+x)^(1/2))^(1/2)+(1+x)^(1/2)-2*sum((2*_R^3-3*_R^2-_R+6)/(4*_R^3-6*_R^2+2*_R+5)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^4-2*_Z^3+_Z^2+5*_Z-1))+5/2/(-1-2*(1+x)^(1/2)+2*(x+(1+x)^(1/2))^(1/2))+ln(-1-2*(1+x)^(1/2)+2*(x+(1+x)^(1/2))^(1/2))+2*sum((2*_R^3+_R^2-_R)/(4*_R^3+6*_R^2-10*_R+3)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^4+2*_Z^3-5*_Z^2+3*_Z+1))+2*sum(_R/(4*_R^3-6*_R-1)*ln((1+x)^(1/2)-_R),_R=RootOf(_Z^4-3*_Z^2-_Z+2))-4*sum(_R^3/(4*_R^3-6*_R-1)*ln((1+x)^(1/2)-_R),_R=RootOf(_Z^4-3*_Z^2-_Z+2))+1+x+2*sum((3*_R^3+_R^2-2*_R)/(4*_R^3-6*_R-1)*ln((1+x)^(1/2)-_R),_R=RootOf(_Z^4-3*_Z^2-_Z+2))+2*sum((_R^3-_R^2+2)/(4*_R^3-6*_R^2+2*_R+5)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^4-2*_Z^3+_Z^2+5*_Z-1))-2*sum((_R^3+_R^2-2*_R)/(4*_R^3+6*_R^2-10*_R+3)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^4+2*_Z^3-5*_Z^2+3*_Z+1))","B"
2136,1,502,47,0.036000," ","int(x/(x+(x+(1+x)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\sqrt{x +\sqrt{1+x}}+\sqrt{1+x}-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\sum}\frac{\left(2 \textit{\_R}^{3}-3 \textit{\_R}^{2}-\textit{\_R} +6\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +5}\right)+\frac{5}{2 \left(-1-2 \sqrt{1+x}+2 \sqrt{x +\sqrt{1+x}}\right)}+\ln \left(-1-2 \sqrt{1+x}+2 \sqrt{x +\sqrt{1+x}}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+2 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{\sum}\frac{\left(2 \textit{\_R}^{3}+\textit{\_R}^{2}-\textit{\_R} \right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}+6 \textit{\_R}^{2}-10 \textit{\_R} +3}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\textit{\_R} \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)-4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\textit{\_R}^{3} \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)+1+x +2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\left(3 \textit{\_R}^{3}+\textit{\_R}^{2}-2 \textit{\_R} \right) \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\sum}\frac{\left(\textit{\_R}^{3}-\textit{\_R}^{2}+2\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +5}\right)-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+2 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{\sum}\frac{\left(\textit{\_R}^{3}+\textit{\_R}^{2}-2 \textit{\_R} \right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}+6 \textit{\_R}^{2}-10 \textit{\_R} +3}\right)$&$502$\\ default&$-\sqrt{x +\sqrt{1+x}}+\sqrt{1+x}-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\sum}\frac{\left(2 \textit{\_R}^{3}-3 \textit{\_R}^{2}-\textit{\_R} +6\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +5}\right)+\frac{5}{2 \left(-1-2 \sqrt{1+x}+2 \sqrt{x +\sqrt{1+x}}\right)}+\ln \left(-1-2 \sqrt{1+x}+2 \sqrt{x +\sqrt{1+x}}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+2 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{\sum}\frac{\left(2 \textit{\_R}^{3}+\textit{\_R}^{2}-\textit{\_R} \right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}+6 \textit{\_R}^{2}-10 \textit{\_R} +3}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\textit{\_R} \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)-4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\textit{\_R}^{3} \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)+1+x +2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\left(3 \textit{\_R}^{3}+\textit{\_R}^{2}-2 \textit{\_R} \right) \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\sum}\frac{\left(\textit{\_R}^{3}-\textit{\_R}^{2}+2\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +5}\right)-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+2 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{\sum}\frac{\left(\textit{\_R}^{3}+\textit{\_R}^{2}-2 \textit{\_R} \right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}+6 \textit{\_R}^{2}-10 \textit{\_R} +3}\right)$&$502$\\ \hline \end{longtable}"," ",0,"-(x+(1+x)^(1/2))^(1/2)+(1+x)^(1/2)-2*sum((2*_R^3-3*_R^2-_R+6)/(4*_R^3-6*_R^2+2*_R+5)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^4-2*_Z^3+_Z^2+5*_Z-1))+5/2/(-1-2*(1+x)^(1/2)+2*(x+(1+x)^(1/2))^(1/2))+ln(-1-2*(1+x)^(1/2)+2*(x+(1+x)^(1/2))^(1/2))+2*sum((2*_R^3+_R^2-_R)/(4*_R^3+6*_R^2-10*_R+3)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^4+2*_Z^3-5*_Z^2+3*_Z+1))+2*sum(_R/(4*_R^3-6*_R-1)*ln((1+x)^(1/2)-_R),_R=RootOf(_Z^4-3*_Z^2-_Z+2))-4*sum(_R^3/(4*_R^3-6*_R-1)*ln((1+x)^(1/2)-_R),_R=RootOf(_Z^4-3*_Z^2-_Z+2))+1+x+2*sum((3*_R^3+_R^2-2*_R)/(4*_R^3-6*_R-1)*ln((1+x)^(1/2)-_R),_R=RootOf(_Z^4-3*_Z^2-_Z+2))+2*sum((_R^3-_R^2+2)/(4*_R^3-6*_R^2+2*_R+5)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^4-2*_Z^3+_Z^2+5*_Z-1))-2*sum((_R^3+_R^2-2*_R)/(4*_R^3+6*_R^2-10*_R+3)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^4+2*_Z^3-5*_Z^2+3*_Z+1))","B"
2137,1,707,136,4.736000," ","int((x^2-6)*(x^2-2)*(x^3-x^2+2)*(2*x^3+x^2-2)^(1/3)/x^5/(x^3+x^2-2)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(38 x^{6}+27 x^{5}-3 x^{4}-54 x^{3}+12 x^{2}-12\right) \left(2 x^{3}+x^{2}-2\right)^{\frac{1}{3}}}{4 \left(x^{3}+x^{2}-2\right) x^{4}}-\frac{7 \ln \left(-\frac{-26052480000 \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right)^{2} x^{3}+4089968640 \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right) \left(2 x^{3}+x^{2}-2\right)^{\frac{2}{3}} x -6566790240 \left(2 x^{3}+x^{2}-2\right)^{\frac{1}{3}} \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right) x^{2}+104209920000 \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right)^{2} x^{2}+1993381920 \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right) x^{3}+5160045 \left(2 x^{3}+x^{2}-2\right)^{\frac{2}{3}} x +8520768 \left(2 x^{3}+x^{2}-2\right)^{\frac{1}{3}} x^{2}-754819680 \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right) x^{2}-20074174 x^{3}-208419840000 \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right)^{2}-5827986 x^{2}+1509639360 \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right)+11655972}{\left(-1+x \right) \left(x^{2}+2 x +2\right)}\right)}{3}+\frac{7 \ln \left(\frac{-149196441600 \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right)^{2} x^{3}+4089968640 \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right) \left(2 x^{3}+x^{2}-2\right)^{\frac{2}{3}} x +2476821600 \left(2 x^{3}+x^{2}-2\right)^{\frac{1}{3}} \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right) x^{2}+596785766400 \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right)^{2} x^{2}-9270501600 \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right) x^{3}-13680813 \left(2 x^{3}+x^{2}-2\right)^{\frac{2}{3}} x +8520768 \left(2 x^{3}+x^{2}-2\right)^{\frac{1}{3}} x^{2}-4257840960 \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right) x^{2}+3392250 x^{3}-1193571532800 \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right)^{2}+1469975 x^{2}+8515681920 \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right)-2939950}{\left(-1+x \right) \left(x^{2}+2 x +2\right)}\right)}{3}-1120 \ln \left(\frac{-149196441600 \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right)^{2} x^{3}+4089968640 \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right) \left(2 x^{3}+x^{2}-2\right)^{\frac{2}{3}} x +2476821600 \left(2 x^{3}+x^{2}-2\right)^{\frac{1}{3}} \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right) x^{2}+596785766400 \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right)^{2} x^{2}-9270501600 \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right) x^{3}-13680813 \left(2 x^{3}+x^{2}-2\right)^{\frac{2}{3}} x +8520768 \left(2 x^{3}+x^{2}-2\right)^{\frac{1}{3}} x^{2}-4257840960 \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right) x^{2}+3392250 x^{3}-1193571532800 \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right)^{2}+1469975 x^{2}+8515681920 \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right)-2939950}{\left(-1+x \right) \left(x^{2}+2 x +2\right)}\right) \RootOf \left(230400 \textit{\_Z}^{2}-480 \textit{\_Z} +1\right)$&$707$\\ risch&$-\frac{76 x^{9}+92 x^{8}+21 x^{7}-187 x^{6}-84 x^{5}+18 x^{4}+84 x^{3}-36 x^{2}+24}{4 x^{4} \left(x^{3}+x^{2}-2\right) \left(2 x^{3}+x^{2}-2\right)^{\frac{2}{3}}}+\frac{\left(\frac{7 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{6}+\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{5}+6 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{6}+6 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(4 x^{6}+4 x^{5}+x^{4}-8 x^{3}-4 x^{2}+4\right)^{\frac{1}{3}} x^{4}+7 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{5}-8 x^{6}-2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(4 x^{6}+4 x^{5}+x^{4}-8 x^{3}-4 x^{2}+4\right)^{\frac{2}{3}} x^{2}+3 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(4 x^{6}+4 x^{5}+x^{4}-8 x^{3}-4 x^{2}+4\right)^{\frac{1}{3}} x^{3}+2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{4}-12 \left(4 x^{6}+4 x^{5}+x^{4}-8 x^{3}-4 x^{2}+4\right)^{\frac{1}{3}} x^{4}-8 x^{5}-14 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{3}-6 \left(4 x^{6}+4 x^{5}+x^{4}-8 x^{3}-4 x^{2}+4\right)^{\frac{2}{3}} x^{2}-6 \left(4 x^{6}+4 x^{5}+x^{4}-8 x^{3}-4 x^{2}+4\right)^{\frac{1}{3}} x^{3}-2 x^{4}-6 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(4 x^{6}+4 x^{5}+x^{4}-8 x^{3}-4 x^{2}+4\right)^{\frac{1}{3}} x -8 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}+16 x^{3}+12 \left(4 x^{6}+4 x^{5}+x^{4}-8 x^{3}-4 x^{2}+4\right)^{\frac{1}{3}} x +8 x^{2}+8 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)-8}{\left(x^{2}+2 x +2\right) \left(-1+x \right) \left(2 x^{3}+x^{2}-2\right)}\right)}{6}-\frac{7 \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{6}+\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{5}-14 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{6}-6 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(4 x^{6}+4 x^{5}+x^{4}-8 x^{3}-4 x^{2}+4\right)^{\frac{1}{3}} x^{4}-11 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{5}+12 x^{6}-2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(4 x^{6}+4 x^{5}+x^{4}-8 x^{3}-4 x^{2}+4\right)^{\frac{2}{3}} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(4 x^{6}+4 x^{5}+x^{4}-8 x^{3}-4 x^{2}+4\right)^{\frac{1}{3}} x^{3}-2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{4}+10 x^{5}+22 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{3}+2 x^{4}+6 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(4 x^{6}+4 x^{5}+x^{4}-8 x^{3}-4 x^{2}+4\right)^{\frac{1}{3}} x +8 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-20 x^{3}-8 x^{2}-8 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)+8}{\left(x^{2}+2 x +2\right) \left(-1+x \right) \left(2 x^{3}+x^{2}-2\right)}\right) \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)}{6}+\frac{7 \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{6}+\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{5}-14 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{6}-6 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(4 x^{6}+4 x^{5}+x^{4}-8 x^{3}-4 x^{2}+4\right)^{\frac{1}{3}} x^{4}-11 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{5}+12 x^{6}-2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(4 x^{6}+4 x^{5}+x^{4}-8 x^{3}-4 x^{2}+4\right)^{\frac{2}{3}} x^{2}-3 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(4 x^{6}+4 x^{5}+x^{4}-8 x^{3}-4 x^{2}+4\right)^{\frac{1}{3}} x^{3}-2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{4}+10 x^{5}+22 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{3}+2 x^{4}+6 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(4 x^{6}+4 x^{5}+x^{4}-8 x^{3}-4 x^{2}+4\right)^{\frac{1}{3}} x +8 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-20 x^{3}-8 x^{2}-8 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)+8}{\left(x^{2}+2 x +2\right) \left(-1+x \right) \left(2 x^{3}+x^{2}-2\right)}\right)}{3}\right) \left(\left(2 x^{3}+x^{2}-2\right)^{2}\right)^{\frac{1}{3}}}{\left(2 x^{3}+x^{2}-2\right)^{\frac{2}{3}}}$&$1287$\\ \hline \end{longtable}"," ",0,"-1/4*(38*x^6+27*x^5-3*x^4-54*x^3+12*x^2-12)/(x^3+x^2-2)/x^4*(2*x^3+x^2-2)^(1/3)-7/3*ln(-(-26052480000*RootOf(230400*_Z^2-480*_Z+1)^2*x^3+4089968640*RootOf(230400*_Z^2-480*_Z+1)*(2*x^3+x^2-2)^(2/3)*x-6566790240*(2*x^3+x^2-2)^(1/3)*RootOf(230400*_Z^2-480*_Z+1)*x^2+104209920000*RootOf(230400*_Z^2-480*_Z+1)^2*x^2+1993381920*RootOf(230400*_Z^2-480*_Z+1)*x^3+5160045*(2*x^3+x^2-2)^(2/3)*x+8520768*(2*x^3+x^2-2)^(1/3)*x^2-754819680*RootOf(230400*_Z^2-480*_Z+1)*x^2-20074174*x^3-208419840000*RootOf(230400*_Z^2-480*_Z+1)^2-5827986*x^2+1509639360*RootOf(230400*_Z^2-480*_Z+1)+11655972)/(-1+x)/(x^2+2*x+2))+7/3*ln((-149196441600*RootOf(230400*_Z^2-480*_Z+1)^2*x^3+4089968640*RootOf(230400*_Z^2-480*_Z+1)*(2*x^3+x^2-2)^(2/3)*x+2476821600*(2*x^3+x^2-2)^(1/3)*RootOf(230400*_Z^2-480*_Z+1)*x^2+596785766400*RootOf(230400*_Z^2-480*_Z+1)^2*x^2-9270501600*RootOf(230400*_Z^2-480*_Z+1)*x^3-13680813*(2*x^3+x^2-2)^(2/3)*x+8520768*(2*x^3+x^2-2)^(1/3)*x^2-4257840960*RootOf(230400*_Z^2-480*_Z+1)*x^2+3392250*x^3-1193571532800*RootOf(230400*_Z^2-480*_Z+1)^2+1469975*x^2+8515681920*RootOf(230400*_Z^2-480*_Z+1)-2939950)/(-1+x)/(x^2+2*x+2))-1120*ln((-149196441600*RootOf(230400*_Z^2-480*_Z+1)^2*x^3+4089968640*RootOf(230400*_Z^2-480*_Z+1)*(2*x^3+x^2-2)^(2/3)*x+2476821600*(2*x^3+x^2-2)^(1/3)*RootOf(230400*_Z^2-480*_Z+1)*x^2+596785766400*RootOf(230400*_Z^2-480*_Z+1)^2*x^2-9270501600*RootOf(230400*_Z^2-480*_Z+1)*x^3-13680813*(2*x^3+x^2-2)^(2/3)*x+8520768*(2*x^3+x^2-2)^(1/3)*x^2-4257840960*RootOf(230400*_Z^2-480*_Z+1)*x^2+3392250*x^3-1193571532800*RootOf(230400*_Z^2-480*_Z+1)^2+1469975*x^2+8515681920*RootOf(230400*_Z^2-480*_Z+1)-2939950)/(-1+x)/(x^2+2*x+2))*RootOf(230400*_Z^2-480*_Z+1)","C"
2138,1,3100,56,9.045000," ","int((-1+x)*(x^4-x^3)^(1/4)/x/(x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$3100$\\ \hline \end{longtable}"," ",0,"-729*RootOf(6561*_Z^8-81*_Z^4+1)^7*ln(-(13122*x^3*RootOf(6561*_Z^8-81*_Z^4+1)^9-26244*RootOf(6561*_Z^8-81*_Z^4+1)^9*x^2+11664*(x^4-x^3)^(1/2)*RootOf(6561*_Z^8-81*_Z^4+1)^7*x-2430*RootOf(6561*_Z^8-81*_Z^4+1)^6*(x^4-x^3)^(1/4)*x^2-1053*RootOf(6561*_Z^8-81*_Z^4+1)^5*x^3+270*(x^4-x^3)^(3/4)*RootOf(6561*_Z^8-81*_Z^4+1)^4+972*RootOf(6561*_Z^8-81*_Z^4+1)^5*x^2-90*(x^4-x^3)^(1/2)*RootOf(6561*_Z^8-81*_Z^4+1)^3*x-18*RootOf(6561*_Z^8-81*_Z^4+1)^2*(x^4-x^3)^(1/4)*x^2+15*RootOf(6561*_Z^8-81*_Z^4+1)*x^3+2*(x^4-x^3)^(3/4)-9*RootOf(6561*_Z^8-81*_Z^4+1)*x^2)/(81*RootOf(6561*_Z^8-81*_Z^4+1)^4*x-162*RootOf(6561*_Z^8-81*_Z^4+1)^4+x+1)/x^2)-81*RootOf(6561*_Z^8-81*_Z^4+1)^5*ln((-177147*RootOf(6561*_Z^8-81*_Z^4+1)^11*x^3+354294*RootOf(6561*_Z^8-81*_Z^4+1)^11*x^2-2187*RootOf(6561*_Z^8-81*_Z^4+1)^7*x^3-11664*RootOf(6561*_Z^8-81*_Z^4+1)^6*(x^4-x^3)^(1/4)*x^2-10935*RootOf(6561*_Z^8-81*_Z^4+1)^7*x^2-1458*(x^4-x^3)^(1/2)*RootOf(6561*_Z^8-81*_Z^4+1)^5*x+810*(x^4-x^3)^(3/4)*RootOf(6561*_Z^8-81*_Z^4+1)^4+324*RootOf(6561*_Z^8-81*_Z^4+1)^3*x^3+54*RootOf(6561*_Z^8-81*_Z^4+1)^2*(x^4-x^3)^(1/4)*x^2-81*RootOf(6561*_Z^8-81*_Z^4+1)^3*x^2-30*(x^4-x^3)^(1/2)*RootOf(6561*_Z^8-81*_Z^4+1)*x-16*(x^4-x^3)^(3/4))/(81*RootOf(6561*_Z^8-81*_Z^4+1)^4*x-162*RootOf(6561*_Z^8-81*_Z^4+1)^4-2*x+1)/x^2)+729*RootOf(6561*_Z^8-81*_Z^4+1)^7*ln((59049*x^3*RootOf(6561*_Z^8-81*_Z^4+1)^9-118098*RootOf(6561*_Z^8-81*_Z^4+1)^9*x^2+34992*(x^4-x^3)^(1/2)*RootOf(6561*_Z^8-81*_Z^4+1)^7*x+11664*RootOf(6561*_Z^8-81*_Z^4+1)^6*(x^4-x^3)^(1/4)*x^2+2430*RootOf(6561*_Z^8-81*_Z^4+1)^5*x^3+810*(x^4-x^3)^(3/4)*RootOf(6561*_Z^8-81*_Z^4+1)^4+243*RootOf(6561*_Z^8-81*_Z^4+1)^5*x^2-162*(x^4-x^3)^(1/2)*RootOf(6561*_Z^8-81*_Z^4+1)^3*x-54*RootOf(6561*_Z^8-81*_Z^4+1)^2*(x^4-x^3)^(1/4)*x^2-24*RootOf(6561*_Z^8-81*_Z^4+1)*x^3-16*(x^4-x^3)^(3/4)+6*RootOf(6561*_Z^8-81*_Z^4+1)*x^2)/(81*RootOf(6561*_Z^8-81*_Z^4+1)^4*x-162*RootOf(6561*_Z^8-81*_Z^4+1)^4-2*x+1)/x^2)-9*RootOf(6561*_Z^8-81*_Z^4+1)^3*ln((59049*x^3*RootOf(6561*_Z^8-81*_Z^4+1)^9-118098*RootOf(6561*_Z^8-81*_Z^4+1)^9*x^2+34992*(x^4-x^3)^(1/2)*RootOf(6561*_Z^8-81*_Z^4+1)^7*x+11664*RootOf(6561*_Z^8-81*_Z^4+1)^6*(x^4-x^3)^(1/4)*x^2+2430*RootOf(6561*_Z^8-81*_Z^4+1)^5*x^3+810*(x^4-x^3)^(3/4)*RootOf(6561*_Z^8-81*_Z^4+1)^4+243*RootOf(6561*_Z^8-81*_Z^4+1)^5*x^2-162*(x^4-x^3)^(1/2)*RootOf(6561*_Z^8-81*_Z^4+1)^3*x-54*RootOf(6561*_Z^8-81*_Z^4+1)^2*(x^4-x^3)^(1/4)*x^2-24*RootOf(6561*_Z^8-81*_Z^4+1)*x^3-16*(x^4-x^3)^(3/4)+6*RootOf(6561*_Z^8-81*_Z^4+1)*x^2)/(81*RootOf(6561*_Z^8-81*_Z^4+1)^4*x-162*RootOf(6561*_Z^8-81*_Z^4+1)^4-2*x+1)/x^2)-RootOf(6561*_Z^8-81*_Z^4+1)*ln(-(-59049*RootOf(6561*_Z^8-81*_Z^4+1)^11*x^3+118098*RootOf(6561*_Z^8-81*_Z^4+1)^11*x^2+2187*RootOf(6561*_Z^8-81*_Z^4+1)^7*x^3+2430*RootOf(6561*_Z^8-81*_Z^4+1)^6*(x^4-x^3)^(1/4)*x^2+729*RootOf(6561*_Z^8-81*_Z^4+1)^7*x^2+810*(x^4-x^3)^(1/2)*RootOf(6561*_Z^8-81*_Z^4+1)^5*x+270*(x^4-x^3)^(3/4)*RootOf(6561*_Z^8-81*_Z^4+1)^4+90*RootOf(6561*_Z^8-81*_Z^4+1)^3*x^3+18*RootOf(6561*_Z^8-81*_Z^4+1)^2*(x^4-x^3)^(1/4)*x^2-54*RootOf(6561*_Z^8-81*_Z^4+1)^3*x^2+6*(x^4-x^3)^(1/2)*RootOf(6561*_Z^8-81*_Z^4+1)*x+2*(x^4-x^3)^(3/4))/(81*RootOf(6561*_Z^8-81*_Z^4+1)^4*x-162*RootOf(6561*_Z^8-81*_Z^4+1)^4+x+1)/x^2)-1/3*RootOf(_Z^2+972*RootOf(6561*_Z^8-81*_Z^4+1)^5-108*RootOf(6561*_Z^8-81*_Z^4+1)^3-12*RootOf(6561*_Z^8-81*_Z^4+1))*ln((729*RootOf(6561*_Z^8-81*_Z^4+1)^5*RootOf(_Z^2+972*RootOf(6561*_Z^8-81*_Z^4+1)^5-108*RootOf(6561*_Z^8-81*_Z^4+1)^3-12*RootOf(6561*_Z^8-81*_Z^4+1))*x^3-1944*RootOf(6561*_Z^8-81*_Z^4+1)^5*(x^4-x^3)^(1/4)*x^2-243*RootOf(6561*_Z^8-81*_Z^4+1)^5*RootOf(_Z^2+972*RootOf(6561*_Z^8-81*_Z^4+1)^5-108*RootOf(6561*_Z^8-81*_Z^4+1)^3-12*RootOf(6561*_Z^8-81*_Z^4+1))*x^2-81*RootOf(6561*_Z^8-81*_Z^4+1)^3*RootOf(_Z^2+972*RootOf(6561*_Z^8-81*_Z^4+1)^5-108*RootOf(6561*_Z^8-81*_Z^4+1)^3-12*RootOf(6561*_Z^8-81*_Z^4+1))*x^3+216*RootOf(6561*_Z^8-81*_Z^4+1)^3*(x^4-x^3)^(1/4)*x^2+27*RootOf(6561*_Z^8-81*_Z^4+1)^3*RootOf(_Z^2+972*RootOf(6561*_Z^8-81*_Z^4+1)^5-108*RootOf(6561*_Z^8-81*_Z^4+1)^3-12*RootOf(6561*_Z^8-81*_Z^4+1))*x^2-9*RootOf(_Z^2+972*RootOf(6561*_Z^8-81*_Z^4+1)^5-108*RootOf(6561*_Z^8-81*_Z^4+1)^3-12*RootOf(6561*_Z^8-81*_Z^4+1))*RootOf(6561*_Z^8-81*_Z^4+1)*x^3-4*(x^4-x^3)^(1/2)*RootOf(_Z^2+972*RootOf(6561*_Z^8-81*_Z^4+1)^5-108*RootOf(6561*_Z^8-81*_Z^4+1)^3-12*RootOf(6561*_Z^8-81*_Z^4+1))*x+24*RootOf(6561*_Z^8-81*_Z^4+1)*(x^4-x^3)^(1/4)*x^2+3*RootOf(_Z^2+972*RootOf(6561*_Z^8-81*_Z^4+1)^5-108*RootOf(6561*_Z^8-81*_Z^4+1)^3-12*RootOf(6561*_Z^8-81*_Z^4+1))*RootOf(6561*_Z^8-81*_Z^4+1)*x^2+8*(x^4-x^3)^(3/4))/x^2/(1+x))+243*RootOf(6561*_Z^8-81*_Z^4+1)^6*RootOf(_Z^2+972*RootOf(6561*_Z^8-81*_Z^4+1)^5-108*RootOf(6561*_Z^8-81*_Z^4+1)^3-12*RootOf(6561*_Z^8-81*_Z^4+1))*ln((2916*(x^4-x^3)^(1/2)*RootOf(_Z^2+972*RootOf(6561*_Z^8-81*_Z^4+1)^5-108*RootOf(6561*_Z^8-81*_Z^4+1)^3-12*RootOf(6561*_Z^8-81*_Z^4+1))*RootOf(6561*_Z^8-81*_Z^4+1)^6*x-729*RootOf(6561*_Z^8-81*_Z^4+1)^5*RootOf(_Z^2+972*RootOf(6561*_Z^8-81*_Z^4+1)^5-108*RootOf(6561*_Z^8-81*_Z^4+1)^3-12*RootOf(6561*_Z^8-81*_Z^4+1))*x^3+1944*RootOf(6561*_Z^8-81*_Z^4+1)^5*(x^4-x^3)^(1/4)*x^2+243*RootOf(6561*_Z^8-81*_Z^4+1)^5*RootOf(_Z^2+972*RootOf(6561*_Z^8-81*_Z^4+1)^5-108*RootOf(6561*_Z^8-81*_Z^4+1)^3-12*RootOf(6561*_Z^8-81*_Z^4+1))*x^2-81*RootOf(6561*_Z^8-81*_Z^4+1)^3*RootOf(_Z^2+972*RootOf(6561*_Z^8-81*_Z^4+1)^5-108*RootOf(6561*_Z^8-81*_Z^4+1)^3-12*RootOf(6561*_Z^8-81*_Z^4+1))*x^3-216*RootOf(6561*_Z^8-81*_Z^4+1)^3*(x^4-x^3)^(1/4)*x^2+27*RootOf(6561*_Z^8-81*_Z^4+1)^3*RootOf(_Z^2+972*RootOf(6561*_Z^8-81*_Z^4+1)^5-108*RootOf(6561*_Z^8-81*_Z^4+1)^3-12*RootOf(6561*_Z^8-81*_Z^4+1))*x^2+9*RootOf(_Z^2+972*RootOf(6561*_Z^8-81*_Z^4+1)^5-108*RootOf(6561*_Z^8-81*_Z^4+1)^3-12*RootOf(6561*_Z^8-81*_Z^4+1))*RootOf(6561*_Z^8-81*_Z^4+1)*x^3-24*RootOf(6561*_Z^8-81*_Z^4+1)*(x^4-x^3)^(1/4)*x^2-3*RootOf(_Z^2+972*RootOf(6561*_Z^8-81*_Z^4+1)^5-108*RootOf(6561*_Z^8-81*_Z^4+1)^3-12*RootOf(6561*_Z^8-81*_Z^4+1))*RootOf(6561*_Z^8-81*_Z^4+1)*x^2+8*(x^4-x^3)^(3/4))/x^2/(1+x))","B"
2139,1,16806,56,92.963000," ","int((-1+x)*(x^4-x^3)^(1/4)/x/(x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$16806$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2140,1,732,120,12.558000," ","int((1+x)*(x^5+x^3)^(1/4)/x/(x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{4}+2 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{3}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{2}+4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(x^{5}+x^{3}\right)^{\frac{1}{4}} x^{2}+4 \sqrt{x^{5}+x^{3}}\, \RootOf \left(\textit{\_Z}^{4}-2\right) x +4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(-1+x \right)^{2}}\right)}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{4}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}-4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(x^{5}+x^{3}\right)^{\frac{1}{4}} x^{2}-4 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \sqrt{x^{5}+x^{3}}\, x +4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(-1+x \right)^{2}}\right)}{3}+\frac{\ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{4}+4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \sqrt{x^{5}+x^{3}}\, x +\RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}+4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}+4 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} x^{2}}{x^{2} \left(x^{2}+x +1\right)}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}}{6}+\frac{\ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{4}+4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \sqrt{x^{5}+x^{3}}\, x +\RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}+4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}+4 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} x^{2}}{x^{2} \left(x^{2}+x +1\right)}\right) \RootOf \left(\textit{\_Z}^{4}-2\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)}{6}-\frac{\RootOf \left(\textit{\_Z}^{4}-2\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} \left(x^{5}+x^{3}\right)^{\frac{1}{4}} x^{2}-\RootOf \left(\textit{\_Z}^{4}-2\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{4}-\RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{4}+2 \RootOf \left(\textit{\_Z}^{4}-2\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \sqrt{x^{5}+x^{3}}\, x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right) x^{3}-2 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \sqrt{x^{5}+x^{3}}\, x +\RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right) x^{2}-\RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}-4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(x^{2}+x +1\right)}\right)}{3}$&$732$\\ \hline \end{longtable}"," ",0,"-1/3*RootOf(_Z^4-2)*ln((RootOf(_Z^4-2)^3*x^4+2*RootOf(_Z^4-2)^3*x^3+RootOf(_Z^4-2)^3*x^2+4*RootOf(_Z^4-2)^2*(x^5+x^3)^(1/4)*x^2+4*(x^5+x^3)^(1/2)*RootOf(_Z^4-2)*x+4*(x^5+x^3)^(3/4))/x^2/(-1+x)^2)+1/3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln((RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^4+2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*x^3+RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*x^2-4*RootOf(_Z^4-2)^2*(x^5+x^3)^(1/4)*x^2-4*RootOf(_Z^2+RootOf(_Z^4-2)^2)*(x^5+x^3)^(1/2)*x+4*(x^5+x^3)^(3/4))/x^2/(-1+x)^2)+1/6*ln((RootOf(_Z^4-2)^2*x^4+4*RootOf(_Z^4-2)^2*(x^5+x^3)^(1/2)*x+RootOf(_Z^4-2)^2*x^3+RootOf(_Z^4-2)^2*x^2+4*(x^5+x^3)^(3/4)+4*(x^5+x^3)^(1/4)*x^2)/x^2/(x^2+x+1))*RootOf(_Z^4-2)^2+1/6*ln((RootOf(_Z^4-2)^2*x^4+4*RootOf(_Z^4-2)^2*(x^5+x^3)^(1/2)*x+RootOf(_Z^4-2)^2*x^3+RootOf(_Z^4-2)^2*x^2+4*(x^5+x^3)^(3/4)+4*(x^5+x^3)^(1/4)*x^2)/x^2/(x^2+x+1))*RootOf(_Z^4-2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)-1/3*RootOf(_Z^4-2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln(-(2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^3*(x^5+x^3)^(1/4)*x^2-RootOf(_Z^4-2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^4-RootOf(_Z^4-2)^2*x^4+2*RootOf(_Z^4-2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*(x^5+x^3)^(1/2)*x+RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)*x^3-2*RootOf(_Z^4-2)^2*(x^5+x^3)^(1/2)*x+RootOf(_Z^4-2)^2*x^3-RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)*x^2-RootOf(_Z^4-2)^2*x^2-4*(x^5+x^3)^(3/4))/x^2/(x^2+x+1))","C"
2141,0,0,35,0.055000," ","int(x^3/(a*x^3-b*x^2)^(1/3)/(a^2*x^6-b^2),x)","\[\int \frac{x^{3}}{\left(a \,x^{3}-b \,x^{2}\right)^{\frac{1}{3}} \left(a^{2} x^{6}-b^{2}\right)}\, dx\]"," ",0,"int(x^3/(a*x^3-b*x^2)^(1/3)/(a^2*x^6-b^2),x)","F"
2142,1,154,84,0.177000," ","int((x^2+1)/(x^2-1)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{7}{2}}}{7}-\frac{24 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}+\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}+\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+4 \textit{\_Z}^{4}-2\right)}{\sum}\frac{\left(\textit{\_R}^{6}-3 \textit{\_R}^{4}+2 \textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+2 \textit{\_R}^{3}}\right)+2 \sqrt{2}\, \arctanh \left(\frac{\sqrt{1+\sqrt{1+\sqrt{1+x}}}\, \sqrt{2}}{2}\right)+\frac{4}{\sqrt{1+\sqrt{1+\sqrt{1+x}}}}$&$154$\\ default&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{7}{2}}}{7}-\frac{24 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}+\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}+\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+4 \textit{\_Z}^{4}-2\right)}{\sum}\frac{\left(\textit{\_R}^{6}-3 \textit{\_R}^{4}+2 \textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+2 \textit{\_R}^{3}}\right)+2 \sqrt{2}\, \arctanh \left(\frac{\sqrt{1+\sqrt{1+\sqrt{1+x}}}\, \sqrt{2}}{2}\right)+\frac{4}{\sqrt{1+\sqrt{1+\sqrt{1+x}}}}$&$154$\\ \hline \end{longtable}"," ",0,"8/7*(1+(1+(1+x)^(1/2))^(1/2))^(7/2)-24/5*(1+(1+(1+x)^(1/2))^(1/2))^(5/2)+16/3*(1+(1+(1+x)^(1/2))^(1/2))^(3/2)+sum((_R^6-3*_R^4+2*_R^2)/(_R^7-3*_R^5+2*_R^3)*ln((1+(1+(1+x)^(1/2))^(1/2))^(1/2)-_R),_R=RootOf(_Z^8-4*_Z^6+4*_Z^4-2))+2*2^(1/2)*arctanh(1/2*(1+(1+(1+x)^(1/2))^(1/2))^(1/2)*2^(1/2))+4/(1+(1+(1+x)^(1/2))^(1/2))^(1/2)","A"
2143,1,154,84,0.171000," ","int((x^2+1)/(x^2-1)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{7}{2}}}{7}-\frac{24 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}+\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}+\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+4 \textit{\_Z}^{4}-2\right)}{\sum}\frac{\left(\textit{\_R}^{6}-3 \textit{\_R}^{4}+2 \textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+2 \textit{\_R}^{3}}\right)+2 \sqrt{2}\, \arctanh \left(\frac{\sqrt{1+\sqrt{1+\sqrt{1+x}}}\, \sqrt{2}}{2}\right)+\frac{4}{\sqrt{1+\sqrt{1+\sqrt{1+x}}}}$&$154$\\ default&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{7}{2}}}{7}-\frac{24 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}+\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}+\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+4 \textit{\_Z}^{4}-2\right)}{\sum}\frac{\left(\textit{\_R}^{6}-3 \textit{\_R}^{4}+2 \textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+2 \textit{\_R}^{3}}\right)+2 \sqrt{2}\, \arctanh \left(\frac{\sqrt{1+\sqrt{1+\sqrt{1+x}}}\, \sqrt{2}}{2}\right)+\frac{4}{\sqrt{1+\sqrt{1+\sqrt{1+x}}}}$&$154$\\ \hline \end{longtable}"," ",0,"8/7*(1+(1+(1+x)^(1/2))^(1/2))^(7/2)-24/5*(1+(1+(1+x)^(1/2))^(1/2))^(5/2)+16/3*(1+(1+(1+x)^(1/2))^(1/2))^(3/2)+sum((_R^6-3*_R^4+2*_R^2)/(_R^7-3*_R^5+2*_R^3)*ln((1+(1+(1+x)^(1/2))^(1/2))^(1/2)-_R),_R=RootOf(_Z^8-4*_Z^6+4*_Z^4-2))+2*2^(1/2)*arctanh(1/2*(1+(1+(1+x)^(1/2))^(1/2))^(1/2)*2^(1/2))+4/(1+(1+(1+x)^(1/2))^(1/2))^(1/2)","A"
2144,1,189720,88,196.660000," ","int((x^3+x-1)/(x^3-x+1)/(x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$189720$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2145,1,153081,88,170.740000," ","int((x^3+x-1)/(x^3-x+1)/(x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$153081$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2146,1,1174,123,16.628000," ","int((2*x^3+1)^(4/3)*(3*x^3+1)/x^8/(4*x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1174$\\ risch&$\text{Expression too large to display}$&$1409$\\ \hline \end{longtable}"," ",0,"-1/28*(58*x^6+9*x^3+4)/x^7*(2*x^3+1)^(1/3)-2/3*ln((3420*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^3*x^3-462*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^4*x^3-2880*(2*x^3+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^2*x-3420*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^3+462*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^4-2280*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)*x^3+308*RootOf(_Z^3-2)^2*x^3+5760*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*(2*x^3+1)^(1/3)*x^2+1566*(2*x^3+1)^(1/3)*RootOf(_Z^3-2)*x^2-1566*(2*x^3+1)^(2/3)*x-1710*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)+231*RootOf(_Z^3-2)^2)/(4*x^3+1))*RootOf(_Z^3-2)-4*ln((3420*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^3*x^3-462*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^4*x^3-2880*(2*x^3+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^2*x-3420*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^3+462*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^4-2280*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)*x^3+308*RootOf(_Z^3-2)^2*x^3+5760*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*(2*x^3+1)^(1/3)*x^2+1566*(2*x^3+1)^(1/3)*RootOf(_Z^3-2)*x^2-1566*(2*x^3+1)^(2/3)*x-1710*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)+231*RootOf(_Z^3-2)^2)/(4*x^3+1))*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)+4*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*ln((306*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^3*x^3+48*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^4*x^3+36*(2*x^3+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^2*x-306*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^3-48*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^4+306*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)*x^3+48*RootOf(_Z^3-2)^2*x^3-72*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*(2*x^3+1)^(1/3)*x^2+69*(2*x^3+1)^(1/3)*RootOf(_Z^3-2)*x^2-69*(2*x^3+1)^(2/3)*x+51*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)+8*RootOf(_Z^3-2)^2)/(4*x^3+1))","C"
2147,0,0,123,0.047000," ","int((x^2-1)/(x^2+1)/(x^4-x^2)^(1/3),x)","\[\int \frac{x^{2}-1}{\left(x^{2}+1\right) \left(x^{4}-x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((x^2-1)/(x^2+1)/(x^4-x^2)^(1/3),x)","F"
2148,0,0,81,0.010000," ","int((a*x^4-b*x^2)^(1/4)*(2*a*x^4-b)/(a*x^4+b),x)","\[\int \frac{\left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}} \left(2 a \,x^{4}-b \right)}{a \,x^{4}+b}\, dx\]"," ",0,"int((a*x^4-b*x^2)^(1/4)*(2*a*x^4-b)/(a*x^4+b),x)","F"
2149,0,0,81,0.001000," ","int((a*x^4-b*x^2)^(1/4)*(2*a*x^4-b)/(a*x^4+b),x)","\[\int \frac{\left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}} \left(2 a \,x^{4}-b \right)}{a \,x^{4}+b}\, dx\]"," ",0,"int((a*x^4-b*x^2)^(1/4)*(2*a*x^4-b)/(a*x^4+b),x)","F"
2150,0,0,127,0.031000," ","int(x^3*(-4*a+3*x)/(x^2*(-a+x))^(2/3)/(d*x^4+a-x),x)","\[\int \frac{x^{3} \left(-4 a +3 x \right)}{\left(x^{2} \left(-a +x \right)\right)^{\frac{2}{3}} \left(d \,x^{4}+a -x \right)}\, dx\]"," ",0,"int(x^3*(-4*a+3*x)/(x^2*(-a+x))^(2/3)/(d*x^4+a-x),x)","F"
2151,0,0,125,0.014000," ","int((a*x^6+b)/x^6/(a*x^3+b)/(a*x^4-b*x)^(1/4),x)","\[\int \frac{a \,x^{6}+b}{x^{6} \left(a \,x^{3}+b \right) \left(a \,x^{4}-b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^6+b)/x^6/(a*x^3+b)/(a*x^4-b*x)^(1/4),x)","F"
2152,1,125,35,0.104000," ","int((x^2-1)/(1+x)^(1/2)/(x^2+1)/(x+(1+x)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$2 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)+\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)}{\sum}\frac{\left(8 \textit{\_R}^{3}-12 \textit{\_R}^{2}+6 \textit{\_R} -1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+5 \textit{\_R}^{4}+10 \textit{\_R}^{3}-18 \textit{\_R}^{2}+10 \textit{\_R} -1}\right)$&$125$\\ default&$2 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)+\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)}{\sum}\frac{\left(8 \textit{\_R}^{3}-12 \textit{\_R}^{2}+6 \textit{\_R} -1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+5 \textit{\_R}^{4}+10 \textit{\_R}^{3}-18 \textit{\_R}^{2}+10 \textit{\_R} -1}\right)$&$125$\\ \hline \end{longtable}"," ",0,"2*ln(1/2+(1+x)^(1/2)+(x+(1+x)^(1/2))^(1/2))+sum((8*_R^3-12*_R^2+6*_R-1)/(_R^7-3*_R^5+5*_R^4+10*_R^3-18*_R^2+10*_R-1)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^8-4*_Z^6+8*_Z^5+20*_Z^4-48*_Z^3+40*_Z^2-8*_Z+1))","B"
2153,1,125,35,0.105000," ","int((x^2-1)/(1+x)^(1/2)/(x^2+1)/(x+(1+x)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$2 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)+\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)}{\sum}\frac{\left(8 \textit{\_R}^{3}-12 \textit{\_R}^{2}+6 \textit{\_R} -1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+5 \textit{\_R}^{4}+10 \textit{\_R}^{3}-18 \textit{\_R}^{2}+10 \textit{\_R} -1}\right)$&$125$\\ default&$2 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)+\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)}{\sum}\frac{\left(8 \textit{\_R}^{3}-12 \textit{\_R}^{2}+6 \textit{\_R} -1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+5 \textit{\_R}^{4}+10 \textit{\_R}^{3}-18 \textit{\_R}^{2}+10 \textit{\_R} -1}\right)$&$125$\\ \hline \end{longtable}"," ",0,"2*ln(1/2+(1+x)^(1/2)+(x+(1+x)^(1/2))^(1/2))+sum((8*_R^3-12*_R^2+6*_R-1)/(_R^7-3*_R^5+5*_R^4+10*_R^3-18*_R^2+10*_R-1)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^8-4*_Z^6+8*_Z^5+20*_Z^4-48*_Z^3+40*_Z^2-8*_Z+1))","B"
2154,0,0,127,180.000000," ","int(x^2*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x)","\[\int x^{2} \sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}\, dx\]"," ",0,"int(x^2*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x)","F"
2155,0,0,123,180.000000," ","int(1/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/3)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/3))^(1/4),x)","\[\int \frac{1}{\sqrt{a^{2} x^{2}-b}\, \left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{3}} \left(c +\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{3}}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/3)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/3))^(1/4),x)","F"
2156,0,0,144,0.042000," ","int((2*a-3*b+x)*(-a^3+3*a^2*x-3*a*x^2+x^3)/(-b+x)/((-a+x)*(-b+x)^2)^(1/4)/(-a^3-b^2*d+(3*a^2+2*b*d)*x-(3*a+d)*x^2+x^3),x)","\[\int \frac{\left(2 a -3 b +x \right) \left(-a^{3}+3 a^{2} x -3 a \,x^{2}+x^{3}\right)}{\left(-b +x \right) \left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{4}} \left(-a^{3}-b^{2} d +\left(3 a^{2}+2 b d \right) x -\left(3 a +d \right) x^{2}+x^{3}\right)}\, dx\]"," ",0,"int((2*a-3*b+x)*(-a^3+3*a^2*x-3*a*x^2+x^3)/(-b+x)/((-a+x)*(-b+x)^2)^(1/4)/(-a^3-b^2*d+(3*a^2+2*b*d)*x-(3*a+d)*x^2+x^3),x)","F"
2157,1,2789,62,30.380000," ","int((2*x^2-x+2)*(x^4-x^3)^(1/4)/(x^2-2*x-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2789$\\ risch&$\text{Expression too large to display}$&$5736$\\ \hline \end{longtable}"," ",0,"(11/4+x)*(x^4-x^3)^(1/4)+177/16*RootOf(_Z^2+1)*ln((2*(x^4-x^3)^(1/2)*RootOf(_Z^2+1)*x-2*RootOf(_Z^2+1)*x^3+2*(x^4-x^3)^(3/4)-2*x^2*(x^4-x^3)^(1/4)+RootOf(_Z^2+1)*x^2)/x^2)-177/16*ln((2*(x^4-x^3)^(3/4)-2*(x^4-x^3)^(1/2)*x+2*x^2*(x^4-x^3)^(1/4)-2*x^3+x^2)/x^2)+3/4*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*ln(-(11*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(_Z^8-31488*_Z^4+98304)^10*x^3-22*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(_Z^8-31488*_Z^4+98304)^10*x^2+1162240*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(_Z^8-31488*_Z^4+98304)^6*x^3-1308672*RootOf(_Z^8-31488*_Z^4+98304)^6*(x^4-x^3)^(1/4)*x^2+274688*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(_Z^8-31488*_Z^4+98304)^6*x^2+13959168*(x^4-x^3)^(1/2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(_Z^8-31488*_Z^4+98304)^4*x-244285440*(x^4-x^3)^(3/4)*RootOf(_Z^8-31488*_Z^4+98304)^4-50510168064*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(_Z^8-31488*_Z^4+98304)^2*x^3+76105383936*RootOf(_Z^8-31488*_Z^4+98304)^2*(x^4-x^3)^(1/4)*x^2+15003942912*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(_Z^8-31488*_Z^4+98304)^2*x^2+81521541120*(x^4-x^3)^(1/2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*x-86658514944*(x^4-x^3)^(3/4))/(x*RootOf(_Z^8-31488*_Z^4+98304)^4-2*RootOf(_Z^8-31488*_Z^4+98304)^4-6656*x-4864)/x^2)+3/4*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)*ln((11*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^8*x^3-22*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^8*x^2-1854976*x^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^4+1110784*x^2*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^4+1308672*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^2*RootOf(_Z^8-31488*_Z^4+98304)^4*(x^4-x^3)^(1/4)*x^2+13959168*(x^4-x^3)^(1/2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)*RootOf(_Z^8-31488*_Z^4+98304)^4*x-244285440*(x^4-x^3)^(3/4)*RootOf(_Z^8-31488*_Z^4+98304)^4-3007119360*x^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3+1840447488*x^2*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3+34897920000*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^2*(x^4-x^3)^(1/4)*x^2-521067823104*(x^4-x^3)^(1/2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)*x+7778718449664*(x^4-x^3)^(3/4))/(x*RootOf(_Z^8-31488*_Z^4+98304)^4-2*RootOf(_Z^8-31488*_Z^4+98304)^4-24832*x+67840)/x^2)+1/131072*ln(-(23*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^11*x^3-46*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^11*x^2-4641152*x^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^7+3847680*x^2*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^7+678473728*(x^4-x^3)^(1/2)*RootOf(_Z^8-31488*_Z^4+98304)^7*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)*x+123531591680*x^3*RootOf(_Z^8-31488*_Z^4+98304)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)-75605049344*x^2*RootOf(_Z^8-31488*_Z^4+98304)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)+167510016*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^2*RootOf(_Z^8-31488*_Z^4+98304)^4*(x^4-x^3)^(1/4)*x^2-21361993973760*(x^4-x^3)^(1/2)*RootOf(_Z^8-31488*_Z^4+98304)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)*x+31268536320*(x^4-x^3)^(3/4)*RootOf(_Z^8-31488*_Z^4+98304)^4+4466933760000*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^2*(x^4-x^3)^(1/4)*x^2-995675961556992*(x^4-x^3)^(3/4))/(x*RootOf(_Z^8-31488*_Z^4+98304)^4-2*RootOf(_Z^8-31488*_Z^4+98304)^4-24832*x+67840)/x^2)*RootOf(_Z^8-31488*_Z^4+98304)^7*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)-123/512*ln(-(23*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^11*x^3-46*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^11*x^2-4641152*x^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^7+3847680*x^2*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^7+678473728*(x^4-x^3)^(1/2)*RootOf(_Z^8-31488*_Z^4+98304)^7*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)*x+123531591680*x^3*RootOf(_Z^8-31488*_Z^4+98304)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)-75605049344*x^2*RootOf(_Z^8-31488*_Z^4+98304)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)+167510016*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^2*RootOf(_Z^8-31488*_Z^4+98304)^4*(x^4-x^3)^(1/4)*x^2-21361993973760*(x^4-x^3)^(1/2)*RootOf(_Z^8-31488*_Z^4+98304)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)*x+31268536320*(x^4-x^3)^(3/4)*RootOf(_Z^8-31488*_Z^4+98304)^4+4466933760000*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^2*(x^4-x^3)^(1/4)*x^2-995675961556992*(x^4-x^3)^(3/4))/(x*RootOf(_Z^8-31488*_Z^4+98304)^4-2*RootOf(_Z^8-31488*_Z^4+98304)^4-24832*x+67840)/x^2)*RootOf(_Z^8-31488*_Z^4+98304)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)-3/4*RootOf(_Z^8-31488*_Z^4+98304)*ln(-(11*RootOf(_Z^8-31488*_Z^4+98304)^11*x^3-22*RootOf(_Z^8-31488*_Z^4+98304)^11*x^2+1162240*RootOf(_Z^8-31488*_Z^4+98304)^7*x^3+274688*RootOf(_Z^8-31488*_Z^4+98304)^7*x^2+1308672*RootOf(_Z^8-31488*_Z^4+98304)^6*(x^4-x^3)^(1/4)*x^2-13959168*(x^4-x^3)^(1/2)*RootOf(_Z^8-31488*_Z^4+98304)^5*x-244285440*(x^4-x^3)^(3/4)*RootOf(_Z^8-31488*_Z^4+98304)^4-50510168064*RootOf(_Z^8-31488*_Z^4+98304)^3*x^3+15003942912*RootOf(_Z^8-31488*_Z^4+98304)^3*x^2-76105383936*RootOf(_Z^8-31488*_Z^4+98304)^2*(x^4-x^3)^(1/4)*x^2-81521541120*(x^4-x^3)^(1/2)*RootOf(_Z^8-31488*_Z^4+98304)*x-86658514944*(x^4-x^3)^(3/4))/(x*RootOf(_Z^8-31488*_Z^4+98304)^4-2*RootOf(_Z^8-31488*_Z^4+98304)^4-6656*x-4864)/x^2)","B"
2158,1,3305,62,31.109000," ","int((2*x^2-x+2)*(x^4-x^3)^(1/4)/(x^2-2*x-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$3305$\\ risch&$\text{Expression too large to display}$&$6772$\\ \hline \end{longtable}"," ",0,"(11/4+x)*(x^4-x^3)^(1/4)-177/16*ln((2*(x^4-x^3)^(3/4)-2*(x^4-x^3)^(1/2)*x+2*x^2*(x^4-x^3)^(1/4)-2*x^3+x^2)/x^2)+3/4*RootOf(_Z^8-31488*_Z^4+98304)*ln((11*RootOf(_Z^8-31488*_Z^4+98304)^11*x^3-22*RootOf(_Z^8-31488*_Z^4+98304)^11*x^2+1162240*RootOf(_Z^8-31488*_Z^4+98304)^7*x^3+274688*RootOf(_Z^8-31488*_Z^4+98304)^7*x^2-1308672*RootOf(_Z^8-31488*_Z^4+98304)^6*(x^4-x^3)^(1/4)*x^2-13959168*(x^4-x^3)^(1/2)*RootOf(_Z^8-31488*_Z^4+98304)^5*x+244285440*(x^4-x^3)^(3/4)*RootOf(_Z^8-31488*_Z^4+98304)^4-50510168064*RootOf(_Z^8-31488*_Z^4+98304)^3*x^3+15003942912*RootOf(_Z^8-31488*_Z^4+98304)^3*x^2+76105383936*RootOf(_Z^8-31488*_Z^4+98304)^2*(x^4-x^3)^(1/4)*x^2-81521541120*(x^4-x^3)^(1/2)*RootOf(_Z^8-31488*_Z^4+98304)*x+86658514944*(x^4-x^3)^(3/4))/(x*RootOf(_Z^8-31488*_Z^4+98304)^4-2*RootOf(_Z^8-31488*_Z^4+98304)^4-6656*x-4864)/x^2)-3/4*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*ln((11*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(_Z^8-31488*_Z^4+98304)^10*x^3-22*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(_Z^8-31488*_Z^4+98304)^10*x^2+1162240*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(_Z^8-31488*_Z^4+98304)^6*x^3+274688*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(_Z^8-31488*_Z^4+98304)^6*x^2+1308672*RootOf(_Z^8-31488*_Z^4+98304)^6*(x^4-x^3)^(1/4)*x^2+13959168*(x^4-x^3)^(1/2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(_Z^8-31488*_Z^4+98304)^4*x+244285440*(x^4-x^3)^(3/4)*RootOf(_Z^8-31488*_Z^4+98304)^4-50510168064*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(_Z^8-31488*_Z^4+98304)^2*x^3+15003942912*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(_Z^8-31488*_Z^4+98304)^2*x^2-76105383936*RootOf(_Z^8-31488*_Z^4+98304)^2*(x^4-x^3)^(1/4)*x^2+81521541120*(x^4-x^3)^(1/2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*x+86658514944*(x^4-x^3)^(3/4))/(x*RootOf(_Z^8-31488*_Z^4+98304)^4-2*RootOf(_Z^8-31488*_Z^4+98304)^4-6656*x-4864)/x^2)-1/131072*ln((23*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^11*x^3-46*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^11*x^2-4641152*x^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^7+3847680*x^2*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^7+678473728*(x^4-x^3)^(1/2)*RootOf(_Z^8-31488*_Z^4+98304)^7*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)*x+123531591680*x^3*RootOf(_Z^8-31488*_Z^4+98304)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)-75605049344*x^2*RootOf(_Z^8-31488*_Z^4+98304)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)-167510016*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^2*RootOf(_Z^8-31488*_Z^4+98304)^4*(x^4-x^3)^(1/4)*x^2-21361993973760*(x^4-x^3)^(1/2)*RootOf(_Z^8-31488*_Z^4+98304)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)*x-31268536320*(x^4-x^3)^(3/4)*RootOf(_Z^8-31488*_Z^4+98304)^4-4466933760000*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^2*(x^4-x^3)^(1/4)*x^2+995675961556992*(x^4-x^3)^(3/4))/(x*RootOf(_Z^8-31488*_Z^4+98304)^4-2*RootOf(_Z^8-31488*_Z^4+98304)^4-24832*x+67840)/x^2)*RootOf(_Z^8-31488*_Z^4+98304)^7*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)+123/512*ln((23*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^11*x^3-46*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^11*x^2-4641152*x^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^7+3847680*x^2*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^7+678473728*(x^4-x^3)^(1/2)*RootOf(_Z^8-31488*_Z^4+98304)^7*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)*x+123531591680*x^3*RootOf(_Z^8-31488*_Z^4+98304)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)-75605049344*x^2*RootOf(_Z^8-31488*_Z^4+98304)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)-167510016*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^2*RootOf(_Z^8-31488*_Z^4+98304)^4*(x^4-x^3)^(1/4)*x^2-21361993973760*(x^4-x^3)^(1/2)*RootOf(_Z^8-31488*_Z^4+98304)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)*x-31268536320*(x^4-x^3)^(3/4)*RootOf(_Z^8-31488*_Z^4+98304)^4-4466933760000*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^2*(x^4-x^3)^(1/4)*x^2+995675961556992*(x^4-x^3)^(3/4))/(x*RootOf(_Z^8-31488*_Z^4+98304)^4-2*RootOf(_Z^8-31488*_Z^4+98304)^4-24832*x+67840)/x^2)*RootOf(_Z^8-31488*_Z^4+98304)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)+3/4*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)*ln((11*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^8*x^3-22*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^8*x^2-1854976*x^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^4+1110784*x^2*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3*RootOf(_Z^8-31488*_Z^4+98304)^4+1308672*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^2*RootOf(_Z^8-31488*_Z^4+98304)^4*(x^4-x^3)^(1/4)*x^2+13959168*(x^4-x^3)^(1/2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)*RootOf(_Z^8-31488*_Z^4+98304)^4*x-244285440*(x^4-x^3)^(3/4)*RootOf(_Z^8-31488*_Z^4+98304)^4-3007119360*x^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3+1840447488*x^2*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^3+34897920000*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)^2*(x^4-x^3)^(1/4)*x^2-521067823104*(x^4-x^3)^(1/2)*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^4+_Z^4-31488)*x+7778718449664*(x^4-x^3)^(3/4))/(x*RootOf(_Z^8-31488*_Z^4+98304)^4-2*RootOf(_Z^8-31488*_Z^4+98304)^4-24832*x+67840)/x^2)-59/524288*ln(-(2*(x^4-x^3)^(1/2)*RootOf(_Z^8-31488*_Z^4+98304)^7*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*x-2*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(_Z^8-31488*_Z^4+98304)^7*x^3+RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(_Z^8-31488*_Z^4+98304)^7*x^2-62976*(x^4-x^3)^(1/2)*RootOf(_Z^8-31488*_Z^4+98304)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*x+62976*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(_Z^8-31488*_Z^4+98304)^3*x^3-31488*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(_Z^8-31488*_Z^4+98304)^3*x^2-196608*(x^4-x^3)^(3/4)+196608*x^2*(x^4-x^3)^(1/4))/x^2)*RootOf(_Z^8-31488*_Z^4+98304)^7*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)+7257/2048*ln(-(2*(x^4-x^3)^(1/2)*RootOf(_Z^8-31488*_Z^4+98304)^7*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*x-2*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(_Z^8-31488*_Z^4+98304)^7*x^3+RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(_Z^8-31488*_Z^4+98304)^7*x^2-62976*(x^4-x^3)^(1/2)*RootOf(_Z^8-31488*_Z^4+98304)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*x+62976*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(_Z^8-31488*_Z^4+98304)^3*x^3-31488*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)*RootOf(_Z^8-31488*_Z^4+98304)^3*x^2-196608*(x^4-x^3)^(3/4)+196608*x^2*(x^4-x^3)^(1/4))/x^2)*RootOf(_Z^8-31488*_Z^4+98304)^3*RootOf(RootOf(_Z^8-31488*_Z^4+98304)^2+_Z^2)","B"
2159,1,55,134,0.779000," ","int((-2*x^4-3*x^2+1)^(1/2)*(2*x^4+1)/(2*x^4+x^2-1)/(2*x^4+2*x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(-2 \arctan \left(\frac{\sqrt{-2 x^{4}-3 x^{2}+1}\, \sqrt{2}}{2 x}\right)+\sqrt{2}\, \arctan \left(\frac{\sqrt{-2 x^{4}-3 x^{2}+1}}{x}\right)\right) \sqrt{2}}{2}$&$55$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \sqrt{-2 x^{4}-3 x^{2}+1}\, x -\RootOf \left(\textit{\_Z}^{2}+1\right)}{2 x^{4}+2 x^{2}-1}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{4}-5 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{2}+4 \sqrt{-2 x^{4}-3 x^{2}+1}\, x +\RootOf \left(\textit{\_Z}^{2}+2\right)}{\left(x^{2}+1\right) \left(2 x^{2}-1\right)}\right)}{2}$&$148$\\ default&$\frac{8 \sqrt{1-\left(\frac{3}{2}+\frac{\sqrt{17}}{2}\right) x^{2}}\, \sqrt{1-\left(\frac{3}{2}-\frac{\sqrt{17}}{2}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{6+2 \sqrt{17}}}{2}, \frac{i \sqrt{34}}{4}-\frac{3 i \sqrt{2}}{4}\right)}{\sqrt{6+2 \sqrt{17}}\, \sqrt{-2 x^{4}-3 x^{2}+1}}-\frac{16 \sqrt{1-\left(\frac{3}{2}+\frac{\sqrt{17}}{2}\right) x^{2}}\, \sqrt{1-\left(\frac{3}{2}-\frac{\sqrt{17}}{2}\right) x^{2}}\, \left(\EllipticF \left(\frac{x \sqrt{6+2 \sqrt{17}}}{2}, \frac{i \sqrt{34}}{4}-\frac{3 i \sqrt{2}}{4}\right)-\EllipticE \left(\frac{x \sqrt{6+2 \sqrt{17}}}{2}, \frac{i \sqrt{34}}{4}-\frac{3 i \sqrt{2}}{4}\right)\right)}{\sqrt{6+2 \sqrt{17}}\, \sqrt{-2 x^{4}-3 x^{2}+1}\, \left(-3+\sqrt{17}\right)}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(2 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}-1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(\frac{\arctanh \left(\frac{\left(4 \underline{\hspace{1.25 ex}}\alpha^{2}+3\right) \left(-17 \underline{\hspace{1.25 ex}}\alpha^{2}+11 x^{2}+4\right)}{22 \sqrt{-\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{-2 x^{4}-3 x^{2}+1}}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{2}}}-\frac{2 \sqrt{2}\, \left(\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{-3 x^{2}+2-x^{2} \sqrt{17}}\, \sqrt{-3 x^{2}+2+x^{2} \sqrt{17}}\, \EllipticPi \left(\sqrt{\frac{3}{2}+\frac{\sqrt{17}}{2}}\, x , \frac{\underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{17}}{2}-\frac{3 \underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{\sqrt{17}}{2}-\frac{3}{2}, \frac{\sqrt{\frac{3}{2}-\frac{\sqrt{17}}{2}}}{\sqrt{\frac{3}{2}+\frac{\sqrt{17}}{2}}}\right)}{\sqrt{3+\sqrt{17}}\, \sqrt{-2 x^{4}-3 x^{2}+1}}\right)\right)}{4}-\frac{10 \sqrt{1-\frac{3 x^{2}}{2}-\frac{x^{2} \sqrt{17}}{2}}\, \sqrt{1-\frac{3 x^{2}}{2}+\frac{x^{2} \sqrt{17}}{2}}\, \EllipticF \left(\frac{x \sqrt{6+2 \sqrt{17}}}{2}, \frac{i \sqrt{34}}{4}-\frac{3 i \sqrt{2}}{4}\right)}{\sqrt{6+2 \sqrt{17}}\, \sqrt{-2 x^{4}-3 x^{2}+1}}+\frac{16 \sqrt{1-\frac{3 x^{2}}{2}-\frac{x^{2} \sqrt{17}}{2}}\, \sqrt{1-\frac{3 x^{2}}{2}+\frac{x^{2} \sqrt{17}}{2}}\, \EllipticF \left(\frac{x \sqrt{6+2 \sqrt{17}}}{2}, \frac{i \sqrt{34}}{4}-\frac{3 i \sqrt{2}}{4}\right)}{\sqrt{6+2 \sqrt{17}}\, \sqrt{-2 x^{4}-3 x^{2}+1}\, \left(-3+\sqrt{17}\right)}-\frac{16 \sqrt{1-\frac{3 x^{2}}{2}-\frac{x^{2} \sqrt{17}}{2}}\, \sqrt{1-\frac{3 x^{2}}{2}+\frac{x^{2} \sqrt{17}}{2}}\, \EllipticE \left(\frac{x \sqrt{6+2 \sqrt{17}}}{2}, \frac{i \sqrt{34}}{4}-\frac{3 i \sqrt{2}}{4}\right)}{\sqrt{6+2 \sqrt{17}}\, \sqrt{-2 x^{4}-3 x^{2}+1}\, \left(-3+\sqrt{17}\right)}+\frac{2 \sqrt{1-\frac{3 x^{2}}{2}-\frac{x^{2} \sqrt{17}}{2}}\, \sqrt{1-\frac{3 x^{2}}{2}+\frac{x^{2} \sqrt{17}}{2}}\, \EllipticPi \left(\sqrt{\frac{3}{2}+\frac{\sqrt{17}}{2}}\, x , -\frac{1}{\frac{3}{2}+\frac{\sqrt{17}}{2}}, \frac{\sqrt{\frac{3}{2}-\frac{\sqrt{17}}{2}}}{\sqrt{\frac{3}{2}+\frac{\sqrt{17}}{2}}}\right)}{\sqrt{\frac{3}{2}+\frac{\sqrt{17}}{2}}\, \sqrt{-2 x^{4}-3 x^{2}+1}}+\frac{2 \sqrt{1-\frac{3 x^{2}}{2}-\frac{x^{2} \sqrt{17}}{2}}\, \sqrt{1-\frac{3 x^{2}}{2}+\frac{x^{2} \sqrt{17}}{2}}\, \EllipticPi \left(\sqrt{\frac{3}{2}+\frac{\sqrt{17}}{2}}\, x , \frac{2}{\frac{3}{2}+\frac{\sqrt{17}}{2}}, \frac{\sqrt{\frac{3}{2}-\frac{\sqrt{17}}{2}}}{\sqrt{\frac{3}{2}+\frac{\sqrt{17}}{2}}}\right)}{\sqrt{\frac{3}{2}+\frac{\sqrt{17}}{2}}\, \sqrt{-2 x^{4}-3 x^{2}+1}}$&$862$\\ \hline \end{longtable}"," ",0,"1/2*(-2*arctan(1/2*(-2*x^4-3*x^2+1)^(1/2)*2^(1/2)/x)+2^(1/2)*arctan((-2*x^4-3*x^2+1)^(1/2)/x))*2^(1/2)","A"
2160,0,0,78,0.010000," ","int((a*x^4+b*x^2)^(1/4)*(2*a*x^4-b)/(a*x^4-2*b),x)","\[\int \frac{\left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}} \left(2 a \,x^{4}-b \right)}{a \,x^{4}-2 b}\, dx\]"," ",0,"int((a*x^4+b*x^2)^(1/4)*(2*a*x^4-b)/(a*x^4-2*b),x)","F"
2161,0,0,78,0.001000," ","int((a*x^4+b*x^2)^(1/4)*(2*a*x^4-b)/(a*x^4-2*b),x)","\[\int \frac{\left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}} \left(2 a \,x^{4}-b \right)}{a \,x^{4}-2 b}\, dx\]"," ",0,"int((a*x^4+b*x^2)^(1/4)*(2*a*x^4-b)/(a*x^4-2*b),x)","F"
2162,0,0,128,0.027000," ","int(x*(-4*a+3*x)/(x^2*(-a+x))^(1/3)/(d*x^4+a-x),x)","\[\int \frac{x \left(-4 a +3 x \right)}{\left(x^{2} \left(-a +x \right)\right)^{\frac{1}{3}} \left(d \,x^{4}+a -x \right)}\, dx\]"," ",0,"int(x*(-4*a+3*x)/(x^2*(-a+x))^(1/3)/(d*x^4+a-x),x)","F"
2163,0,0,54,0.033000," ","int((2*x^8-2*a*x^4-b)/(a*x^4-b)^(1/4)/(x^8-a*x^4-b),x)","\[\int \frac{2 x^{8}-2 a \,x^{4}-b}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(x^{8}-a \,x^{4}-b \right)}\, dx\]"," ",0,"int((2*x^8-2*a*x^4-b)/(a*x^4-b)^(1/4)/(x^8-a*x^4-b),x)","F"
2164,0,0,54,0.001000," ","int((2*x^8-2*a*x^4-b)/(a*x^4-b)^(1/4)/(x^8-a*x^4-b),x)","\[\int \frac{2 x^{8}-2 a \,x^{4}-b}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(x^{8}-a \,x^{4}-b \right)}\, dx\]"," ",0,"int((2*x^8-2*a*x^4-b)/(a*x^4-b)^(1/4)/(x^8-a*x^4-b),x)","F"
2165,1,1072,123,5.100000," ","int(1/(x^2-1)/(x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$1072$\\ trager&$\text{Expression too large to display}$&$1159$\\ \hline \end{longtable}"," ",0,"-3/2*x/((-1+x)*x^2)^(1/3)-1/4*ln((3*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^2+2*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^2-6*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x-4*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x+24*(x^3-x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2+48*(x^3-x^2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)*x+18*(x^3-x^2)^(1/3)*RootOf(_Z^3-4)^2*x+78*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x^2+52*RootOf(_Z^3-4)*x^2-30*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x-20*RootOf(_Z^3-4)*x+36*(x^3-x^2)^(2/3))/x/(1+x))*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)-1/4*ln((3*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^2+2*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^2-6*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x-4*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x+24*(x^3-x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2+48*(x^3-x^2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)*x+18*(x^3-x^2)^(1/3)*RootOf(_Z^3-4)^2*x+78*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x^2+52*RootOf(_Z^3-4)*x^2-30*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x-20*RootOf(_Z^3-4)*x+36*(x^3-x^2)^(2/3))/x/(1+x))*RootOf(_Z^3-4)+1/4*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*ln((3*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^2+RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^2-6*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x-2*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x-24*(x^3-x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2-48*(x^3-x^2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)*x-30*(x^3-x^2)^(1/3)*RootOf(_Z^3-4)^2*x-66*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x^2-22*RootOf(_Z^3-4)*x^2+6*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x+2*RootOf(_Z^3-4)*x-60*(x^3-x^2)^(2/3))/x/(1+x))","C"
2166,1,374,132,0.162000," ","int((a^2*x^4-b^2)/(a*x^3-b*x)^(1/2)/(a^2*x^4+c*x^2+b^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\sqrt{a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}-b x}}-\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{2} \textit{\_Z}^{4}+c \,\textit{\_Z}^{2}+b^{2}\right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2} c +2 b^{2}\right) \sqrt{a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{\left(x -\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \left(a \left(a^{2} \underline{\hspace{1.25 ex}}\alpha^{3}+a b \underline{\hspace{1.25 ex}}\alpha  +c \underline{\hspace{1.25 ex}}\alpha  \right)-a^{2} \sqrt{a b}\, \underline{\hspace{1.25 ex}}\alpha^{2}-\sqrt{a b}\, a b -\sqrt{a b}\, c \right) \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{-\sqrt{a b}\, \underline{\hspace{1.25 ex}}\alpha^{3} a^{2}+\underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b -\sqrt{a b}\, \underline{\hspace{1.25 ex}}\alpha  a b -\sqrt{a b}\, \underline{\hspace{1.25 ex}}\alpha  c +a \,b^{2}+b c}{b \left(2 a b +c \right)}, \frac{\sqrt{2}}{2}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+c \right) \left(2 a b +c \right) \sqrt{x \left(a \,x^{2}-b \right)}}\right)}{2 a b}$&$374$\\ default&$\frac{\sqrt{a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}-b x}}+\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{2} \textit{\_Z}^{4}+c \,\textit{\_Z}^{2}+b^{2}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{2} c -2 b^{2}\right) \sqrt{a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{\left(x -\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \left(a \left(a^{2} \underline{\hspace{1.25 ex}}\alpha^{3}+a b \underline{\hspace{1.25 ex}}\alpha  +c \underline{\hspace{1.25 ex}}\alpha  \right)-a^{2} \sqrt{a b}\, \underline{\hspace{1.25 ex}}\alpha^{2}-\sqrt{a b}\, a b -\sqrt{a b}\, c \right) \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{-\sqrt{a b}\, \underline{\hspace{1.25 ex}}\alpha^{3} a^{2}+\underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b -\sqrt{a b}\, \underline{\hspace{1.25 ex}}\alpha  a b -\sqrt{a b}\, \underline{\hspace{1.25 ex}}\alpha  c +a \,b^{2}+b c}{b \left(2 a b +c \right)}, \frac{\sqrt{2}}{2}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+c \right) \left(2 a b +c \right) \sqrt{x \left(a \,x^{2}-b \right)}}\right)}{2 a b}$&$375$\\ \hline \end{longtable}"," ",0,"1/a*(a*b)^(1/2)*((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2)*(-2*(x-1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2)*(-x*a/(a*b)^(1/2))^(1/2)/(a*x^3-b*x)^(1/2)*EllipticF(((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2),1/2*2^(1/2))-1/2/a/b*2^(1/2)*sum((_alpha^2*c+2*b^2)/_alpha/(2*_alpha^2*a^2+c)/(2*a*b+c)*(a*b)^(1/2)*((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2)*(-(x-1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2)*(-x*a/(a*b)^(1/2))^(1/2)/(x*(a*x^2-b))^(1/2)*(a*(_alpha^3*a^2+_alpha*a*b+_alpha*c)-a^2*(a*b)^(1/2)*_alpha^2-(a*b)^(1/2)*a*b-(a*b)^(1/2)*c)*EllipticPi(((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2),(-(a*b)^(1/2)*_alpha^3*a^2+_alpha^2*a^2*b-(a*b)^(1/2)*_alpha*a*b-(a*b)^(1/2)*_alpha*c+a*b^2+b*c)/b/(2*a*b+c),1/2*2^(1/2)),_alpha=RootOf(_Z^4*a^2+_Z^2*c+b^2))","C"
2167,0,0,147,0.023000," ","int((2*p*x^3-q)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)/x/(b*x^2+a*(p*x^3+q)^2),x)","\[\int \frac{\left(2 p \,x^{3}-q \right) \sqrt{p^{2} x^{6}+2 p q \,x^{3}-2 p q \,x^{2}+q^{2}}}{x \left(b \,x^{2}+a \left(p \,x^{3}+q \right)^{2}\right)}\, dx\]"," ",0,"int((2*p*x^3-q)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)/x/(b*x^2+a*(p*x^3+q)^2),x)","F"
2168,0,0,147,0.023000," ","int((p*x^3-2*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)/x/(b*x^4+a*(p*x^3+q)^2),x)","\[\int \frac{\left(p \,x^{3}-2 q \right) \sqrt{p^{2} x^{6}-2 p q \,x^{4}+2 p q \,x^{3}+q^{2}}}{x \left(b \,x^{4}+a \left(p \,x^{3}+q \right)^{2}\right)}\, dx\]"," ",0,"int((p*x^3-2*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)/x/(b*x^4+a*(p*x^3+q)^2),x)","F"
2169,0,0,25,0.073000," ","int((x^2-(x^2+1)^(1/2))/(x^2+(x+(x^2+1)^(1/2))^(1/2)),x)","\[\int \frac{x^{2}-\sqrt{x^{2}+1}}{x^{2}+\sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^2-(x^2+1)^(1/2))/(x^2+(x+(x^2+1)^(1/2))^(1/2)),x)","F"
2170,0,0,25,0.000000," ","int((x^2-(x^2+1)^(1/2))/(x^2+(x+(x^2+1)^(1/2))^(1/2)),x)","\[\int \frac{x^{2}-\sqrt{x^{2}+1}}{x^{2}+\sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^2-(x^2+1)^(1/2))/(x^2+(x+(x^2+1)^(1/2))^(1/2)),x)","F"
2171,0,0,120,0.068000," ","int((1+(1-(1+1/x^2)^(1/2))^(1/2))^(1/2)/x,x)","\[\int \frac{\sqrt{1+\sqrt{1-\sqrt{1+\frac{1}{x^{2}}}}}}{x}\, dx\]"," ",0,"int((1+(1-(1+1/x^2)^(1/2))^(1/2))^(1/2)/x,x)","F"
2172,0,0,130,0.119000," ","int((-2*x+(1+k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(1-(1+k)*x+(-b+k)*x^2),x)","\[\int \frac{-2 x +\left(1+k \right) x^{2}}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{2}{3}} \left(1-\left(1+k \right) x +\left(-b +k \right) x^{2}\right)}\, dx\]"," ",0,"int((-2*x+(1+k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(1-(1+k)*x+(-b+k)*x^2),x)","F"
2173,0,0,131,0.029000," ","int((2-(1+k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(1-(1+k)*x),x)","\[\int \frac{2-\left(1+k \right) x}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(1-\left(1+k \right) x \right)}\, dx\]"," ",0,"int((2-(1+k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(1-(1+k)*x),x)","F"
2174,0,0,131,0.107000," ","int((-2+(1+k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(1-(1+k)*x+(-b+k)*x^2),x)","\[\int \frac{-2+\left(1+k \right) x}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(1-\left(1+k \right) x +\left(-b +k \right) x^{2}\right)}\, dx\]"," ",0,"int((-2+(1+k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(1-(1+k)*x+(-b+k)*x^2),x)","F"
2175,1,749,131,19.475000," ","int((2*x^2+3)*(2*x^3+2*x^2+1)^(2/3)/x^3/(x^3-2*x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 \left(2 x^{3}+2 x^{2}+1\right)^{\frac{2}{3}}}{2 x^{2}}+3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+9 \textit{\_Z}^{2}\right) \ln \left(\frac{-5 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+9 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-9\right)^{3} x^{3}-9 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+9 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-9\right)^{2} x^{3}+7 \left(2 x^{3}+2 x^{2}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}-9\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+9 \textit{\_Z}^{2}\right) x -7 \left(2 x^{3}+2 x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-9\right)^{2} x^{2}-24 \left(2 x^{3}+2 x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+9 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-9\right) x^{2}+10 \RootOf \left(\textit{\_Z}^{3}-9\right) x^{3}+18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+9 \textit{\_Z}^{2}\right) x^{3}-3 \left(2 x^{3}+2 x^{2}+1\right)^{\frac{2}{3}} x +10 \RootOf \left(\textit{\_Z}^{3}-9\right) x^{2}+18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+9 \textit{\_Z}^{2}\right) x^{2}+5 \RootOf \left(\textit{\_Z}^{3}-9\right)+9 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+9 \textit{\_Z}^{2}\right)}{x^{3}-2 x^{2}-1}\right)+\RootOf \left(\textit{\_Z}^{3}-9\right) \ln \left(-\frac{-3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+9 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-9\right)^{3} x^{3}-15 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+9 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-9\right)^{2} x^{3}+7 \left(2 x^{3}+2 x^{2}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}-9\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+9 \textit{\_Z}^{2}\right) x -7 \left(2 x^{3}+2 x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-9\right)^{2} x^{2}+3 \left(2 x^{3}+2 x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+9 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-9\right) x^{2}-15 \RootOf \left(\textit{\_Z}^{3}-9\right) x^{3}-75 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+9 \textit{\_Z}^{2}\right) x^{3}+24 \left(2 x^{3}+2 x^{2}+1\right)^{\frac{2}{3}} x -6 \RootOf \left(\textit{\_Z}^{3}-9\right) x^{2}-30 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+9 \textit{\_Z}^{2}\right) x^{2}-3 \RootOf \left(\textit{\_Z}^{3}-9\right)-15 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-9\right)^{2}+3 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-9\right)+9 \textit{\_Z}^{2}\right)}{x^{3}-2 x^{2}-1}\right)$&$749$\\ trager&$\text{Expression too large to display}$&$1561$\\ \hline \end{longtable}"," ",0,"3/2*(2*x^3+2*x^2+1)^(2/3)/x^2+3*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*ln((-5*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x^3-9*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x^3+7*(2*x^3+2*x^2+1)^(2/3)*RootOf(_Z^3-9)^2*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x-7*(2*x^3+2*x^2+1)^(1/3)*RootOf(_Z^3-9)^2*x^2-24*(2*x^3+2*x^2+1)^(1/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)*x^2+10*RootOf(_Z^3-9)*x^3+18*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x^3-3*(2*x^3+2*x^2+1)^(2/3)*x+10*RootOf(_Z^3-9)*x^2+18*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x^2+5*RootOf(_Z^3-9)+9*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2))/(x^3-2*x^2-1))+RootOf(_Z^3-9)*ln(-(-3*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x^3-15*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x^3+7*(2*x^3+2*x^2+1)^(2/3)*RootOf(_Z^3-9)^2*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x-7*(2*x^3+2*x^2+1)^(1/3)*RootOf(_Z^3-9)^2*x^2+3*(2*x^3+2*x^2+1)^(1/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)*x^2-15*RootOf(_Z^3-9)*x^3-75*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x^3+24*(2*x^3+2*x^2+1)^(2/3)*x-6*RootOf(_Z^3-9)*x^2-30*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x^2-3*RootOf(_Z^3-9)-15*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2))/(x^3-2*x^2-1))","C"
2176,1,664,119,0.149000," ","int((a*x^2+c*x-b)/(a*x^2+b)/(a*x^3-b*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}-b x}}+\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right) c}{2 a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}-\frac{b \sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{\sqrt{-a b}\, a \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}+\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right) c}{2 a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}+\frac{b \sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{\sqrt{-a b}\, a \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}$&$664$\\ default&$\frac{\sqrt{a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}-b x}}+\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right) c}{2 a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}-\frac{b \sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{\sqrt{-a b}\, a \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}+\frac{\sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right) c}{2 a^{2} \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}+\frac{b \sqrt{a b}\, \sqrt{\frac{x a}{\sqrt{a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{a b}}{a}\right) a}{\sqrt{a b}}}, -\frac{\sqrt{a b}}{a \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{\sqrt{-a b}\, a \sqrt{a \,x^{3}-b x}\, \left(-\frac{\sqrt{a b}}{a}+\frac{\sqrt{-a b}}{a}\right)}$&$681$\\ \hline \end{longtable}"," ",0,"1/a*(a*b)^(1/2)*(x*a/(a*b)^(1/2)+1)^(1/2)*(-2*x*a/(a*b)^(1/2)+2)^(1/2)*(-x*a/(a*b)^(1/2))^(1/2)/(a*x^3-b*x)^(1/2)*EllipticF(((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2),1/2*2^(1/2))+1/2/a^2*(a*b)^(1/2)*(x*a/(a*b)^(1/2)+1)^(1/2)*(-2*x*a/(a*b)^(1/2)+2)^(1/2)*(-x*a/(a*b)^(1/2))^(1/2)/(a*x^3-b*x)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2),-1/a*(a*b)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2)),1/2*2^(1/2))*c-b/(-a*b)^(1/2)/a*(a*b)^(1/2)*(x*a/(a*b)^(1/2)+1)^(1/2)*(-2*x*a/(a*b)^(1/2)+2)^(1/2)*(-x*a/(a*b)^(1/2))^(1/2)/(a*x^3-b*x)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2),-1/a*(a*b)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2)),1/2*2^(1/2))+1/2/a^2*(a*b)^(1/2)*(x*a/(a*b)^(1/2)+1)^(1/2)*(-2*x*a/(a*b)^(1/2)+2)^(1/2)*(-x*a/(a*b)^(1/2))^(1/2)/(a*x^3-b*x)^(1/2)/(-1/a*(a*b)^(1/2)+1/a*(-a*b)^(1/2))*EllipticPi(((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2),-1/a*(a*b)^(1/2)/(-1/a*(a*b)^(1/2)+1/a*(-a*b)^(1/2)),1/2*2^(1/2))*c+b/(-a*b)^(1/2)/a*(a*b)^(1/2)*(x*a/(a*b)^(1/2)+1)^(1/2)*(-2*x*a/(a*b)^(1/2)+2)^(1/2)*(-x*a/(a*b)^(1/2))^(1/2)/(a*x^3-b*x)^(1/2)/(-1/a*(a*b)^(1/2)+1/a*(-a*b)^(1/2))*EllipticPi(((x+1/a*(a*b)^(1/2))*a/(a*b)^(1/2))^(1/2),-1/a*(a*b)^(1/2)/(-1/a*(a*b)^(1/2)+1/a*(-a*b)^(1/2)),1/2*2^(1/2))","C"
2177,1,1065,134,6.789000," ","int((x^4+2*x^2-2*x-4)/x/(x^2-2)/((x^2+2)/(x^2-2))^(1/4)/(x^5-4*x^4+4*x^3+4*x^2-10*x+8),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{-2 \sqrt{-\frac{-x^{2}-2}{x^{2}-2}}\, x^{4} \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+4 \sqrt{-\frac{-x^{2}-2}{x^{2}-2}}\, x^{3} \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}-2 \left(-\frac{-x^{2}-2}{x^{2}-2}\right)^{\frac{1}{4}} x^{5} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+2 \sqrt{-\frac{-x^{2}-2}{x^{2}-2}}\, x^{2} \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+6 \left(-\frac{-x^{2}-2}{x^{2}-2}\right)^{\frac{1}{4}} x^{4} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-\RootOf \left(\textit{\_Z}^{4}+1\right) x^{6}+2 \left(-\frac{-x^{2}-2}{x^{2}-2}\right)^{\frac{3}{4}} x^{3}-8 \sqrt{-\frac{-x^{2}-2}{x^{2}-2}}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x -2 \left(-\frac{-x^{2}-2}{x^{2}-2}\right)^{\frac{1}{4}} x^{3} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+4 \RootOf \left(\textit{\_Z}^{4}+1\right) x^{5}-2 \left(-\frac{-x^{2}-2}{x^{2}-2}\right)^{\frac{3}{4}} x^{2}+4 \sqrt{-\frac{-x^{2}-2}{x^{2}-2}}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}-10 \left(-\frac{-x^{2}-2}{x^{2}-2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}-4 \RootOf \left(\textit{\_Z}^{4}+1\right) x^{4}-4 \left(-\frac{-x^{2}-2}{x^{2}-2}\right)^{\frac{3}{4}} x +12 \left(-\frac{-x^{2}-2}{x^{2}-2}\right)^{\frac{1}{4}} x \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-4 \RootOf \left(\textit{\_Z}^{4}+1\right) x^{3}+4 \left(-\frac{-x^{2}-2}{x^{2}-2}\right)^{\frac{3}{4}}-4 \left(-\frac{-x^{2}-2}{x^{2}-2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+12 \RootOf \left(\textit{\_Z}^{4}+1\right) x^{2}-8 \RootOf \left(\textit{\_Z}^{4}+1\right) x +4 \RootOf \left(\textit{\_Z}^{4}+1\right)}{x \left(x^{5}-4 x^{4}+4 x^{3}+4 x^{2}-10 x +8\right)}\right)}{4}-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{6}+2 \left(-\frac{-x^{2}-2}{x^{2}-2}\right)^{\frac{1}{4}} x^{5} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-4 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{5}+2 x^{4} \sqrt{-\frac{-x^{2}-2}{x^{2}-2}}\, \RootOf \left(\textit{\_Z}^{4}+1\right)-6 \left(-\frac{-x^{2}-2}{x^{2}-2}\right)^{\frac{1}{4}} x^{4} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+4 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{4}+2 \left(-\frac{-x^{2}-2}{x^{2}-2}\right)^{\frac{3}{4}} x^{3}-4 x^{3} \sqrt{-\frac{-x^{2}-2}{x^{2}-2}}\, \RootOf \left(\textit{\_Z}^{4}+1\right)+2 \left(-\frac{-x^{2}-2}{x^{2}-2}\right)^{\frac{1}{4}} x^{3} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+4 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{3}-2 \left(-\frac{-x^{2}-2}{x^{2}-2}\right)^{\frac{3}{4}} x^{2}-2 x^{2} \sqrt{-\frac{-x^{2}-2}{x^{2}-2}}\, \RootOf \left(\textit{\_Z}^{4}+1\right)+10 \left(-\frac{-x^{2}-2}{x^{2}-2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}-12 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}-4 \left(-\frac{-x^{2}-2}{x^{2}-2}\right)^{\frac{3}{4}} x +8 \sqrt{-\frac{-x^{2}-2}{x^{2}-2}}\, \RootOf \left(\textit{\_Z}^{4}+1\right) x -12 \left(-\frac{-x^{2}-2}{x^{2}-2}\right)^{\frac{1}{4}} x \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+8 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x +4 \left(-\frac{-x^{2}-2}{x^{2}-2}\right)^{\frac{3}{4}}-4 \sqrt{-\frac{-x^{2}-2}{x^{2}-2}}\, \RootOf \left(\textit{\_Z}^{4}+1\right)+4 \left(-\frac{-x^{2}-2}{x^{2}-2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-4 \RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{x \left(x^{5}-4 x^{4}+4 x^{3}+4 x^{2}-10 x +8\right)}\right)}{4}$&$1065$\\ \hline \end{longtable}"," ",0,"1/4*RootOf(_Z^4+1)*ln((-2*(-(-x^2-2)/(x^2-2))^(1/2)*x^4*RootOf(_Z^4+1)^3+4*(-(-x^2-2)/(x^2-2))^(1/2)*x^3*RootOf(_Z^4+1)^3-2*(-(-x^2-2)/(x^2-2))^(1/4)*x^5*RootOf(_Z^4+1)^2+2*(-(-x^2-2)/(x^2-2))^(1/2)*x^2*RootOf(_Z^4+1)^3+6*(-(-x^2-2)/(x^2-2))^(1/4)*x^4*RootOf(_Z^4+1)^2-RootOf(_Z^4+1)*x^6+2*(-(-x^2-2)/(x^2-2))^(3/4)*x^3-8*(-(-x^2-2)/(x^2-2))^(1/2)*RootOf(_Z^4+1)^3*x-2*(-(-x^2-2)/(x^2-2))^(1/4)*x^3*RootOf(_Z^4+1)^2+4*RootOf(_Z^4+1)*x^5-2*(-(-x^2-2)/(x^2-2))^(3/4)*x^2+4*(-(-x^2-2)/(x^2-2))^(1/2)*RootOf(_Z^4+1)^3-10*(-(-x^2-2)/(x^2-2))^(1/4)*RootOf(_Z^4+1)^2*x^2-4*RootOf(_Z^4+1)*x^4-4*(-(-x^2-2)/(x^2-2))^(3/4)*x+12*(-(-x^2-2)/(x^2-2))^(1/4)*x*RootOf(_Z^4+1)^2-4*RootOf(_Z^4+1)*x^3+4*(-(-x^2-2)/(x^2-2))^(3/4)-4*(-(-x^2-2)/(x^2-2))^(1/4)*RootOf(_Z^4+1)^2+12*RootOf(_Z^4+1)*x^2-8*RootOf(_Z^4+1)*x+4*RootOf(_Z^4+1))/x/(x^5-4*x^4+4*x^3+4*x^2-10*x+8))-1/4*RootOf(_Z^4+1)^3*ln((RootOf(_Z^4+1)^3*x^6+2*(-(-x^2-2)/(x^2-2))^(1/4)*x^5*RootOf(_Z^4+1)^2-4*RootOf(_Z^4+1)^3*x^5+2*x^4*(-(-x^2-2)/(x^2-2))^(1/2)*RootOf(_Z^4+1)-6*(-(-x^2-2)/(x^2-2))^(1/4)*x^4*RootOf(_Z^4+1)^2+4*RootOf(_Z^4+1)^3*x^4+2*(-(-x^2-2)/(x^2-2))^(3/4)*x^3-4*x^3*(-(-x^2-2)/(x^2-2))^(1/2)*RootOf(_Z^4+1)+2*(-(-x^2-2)/(x^2-2))^(1/4)*x^3*RootOf(_Z^4+1)^2+4*RootOf(_Z^4+1)^3*x^3-2*(-(-x^2-2)/(x^2-2))^(3/4)*x^2-2*x^2*(-(-x^2-2)/(x^2-2))^(1/2)*RootOf(_Z^4+1)+10*(-(-x^2-2)/(x^2-2))^(1/4)*RootOf(_Z^4+1)^2*x^2-12*RootOf(_Z^4+1)^3*x^2-4*(-(-x^2-2)/(x^2-2))^(3/4)*x+8*(-(-x^2-2)/(x^2-2))^(1/2)*RootOf(_Z^4+1)*x-12*(-(-x^2-2)/(x^2-2))^(1/4)*x*RootOf(_Z^4+1)^2+8*RootOf(_Z^4+1)^3*x+4*(-(-x^2-2)/(x^2-2))^(3/4)-4*(-(-x^2-2)/(x^2-2))^(1/2)*RootOf(_Z^4+1)+4*(-(-x^2-2)/(x^2-2))^(1/4)*RootOf(_Z^4+1)^2-4*RootOf(_Z^4+1)^3)/x/(x^5-4*x^4+4*x^3+4*x^2-10*x+8))","C"
2178,1,119,49,0.111000," ","int((1+x)^(1/2)*(x^4-1)*(1+(1+x)^(1/2))^(1/2)/(x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{7}{2}}}{7}-\frac{8 \left(1+\sqrt{1+x}\right)^{\frac{5}{2}}}{5}+\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}-\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+16 \textit{\_Z}^{8}+1\right)}{\sum}\frac{\left(\textit{\_R}^{6}-2 \textit{\_R}^{4}+\textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+8 \textit{\_R}^{7}}\right)}{2}$&$119$\\ default&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{7}{2}}}{7}-\frac{8 \left(1+\sqrt{1+x}\right)^{\frac{5}{2}}}{5}+\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}-\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+16 \textit{\_Z}^{8}+1\right)}{\sum}\frac{\left(\textit{\_R}^{6}-2 \textit{\_R}^{4}+\textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+8 \textit{\_R}^{7}}\right)}{2}$&$119$\\ \hline \end{longtable}"," ",0,"4/7*(1+(1+x)^(1/2))^(7/2)-8/5*(1+(1+x)^(1/2))^(5/2)+4/3*(1+(1+x)^(1/2))^(3/2)-1/2*sum((_R^6-2*_R^4+_R^2)/(_R^15-7*_R^13+18*_R^11-20*_R^9+8*_R^7)*ln((1+(1+x)^(1/2))^(1/2)-_R),_R=RootOf(_Z^16-8*_Z^14+24*_Z^12-32*_Z^10+16*_Z^8+1))","B"
2179,1,119,49,0.102000," ","int((1+x)^(1/2)*(x^4-1)*(1+(1+x)^(1/2))^(1/2)/(x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{7}{2}}}{7}-\frac{8 \left(1+\sqrt{1+x}\right)^{\frac{5}{2}}}{5}+\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}-\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+16 \textit{\_Z}^{8}+1\right)}{\sum}\frac{\left(\textit{\_R}^{6}-2 \textit{\_R}^{4}+\textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+8 \textit{\_R}^{7}}\right)}{2}$&$119$\\ default&$\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{7}{2}}}{7}-\frac{8 \left(1+\sqrt{1+x}\right)^{\frac{5}{2}}}{5}+\frac{4 \left(1+\sqrt{1+x}\right)^{\frac{3}{2}}}{3}-\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+16 \textit{\_Z}^{8}+1\right)}{\sum}\frac{\left(\textit{\_R}^{6}-2 \textit{\_R}^{4}+\textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+8 \textit{\_R}^{7}}\right)}{2}$&$119$\\ \hline \end{longtable}"," ",0,"4/7*(1+(1+x)^(1/2))^(7/2)-8/5*(1+(1+x)^(1/2))^(5/2)+4/3*(1+(1+x)^(1/2))^(3/2)-1/2*sum((_R^6-2*_R^4+_R^2)/(_R^15-7*_R^13+18*_R^11-20*_R^9+8*_R^7)*ln((1+(1+x)^(1/2))^(1/2)-_R),_R=RootOf(_Z^16-8*_Z^14+24*_Z^12-32*_Z^10+16*_Z^8+1))","B"
2180,0,0,126,0.012000," ","int((c*x-d)/x^4/(a*x^3-b)^(1/3),x)","\[\int \frac{c x -d}{x^{4} \left(a \,x^{3}-b \right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((c*x-d)/x^4/(a*x^3-b)^(1/3),x)","F"
2181,0,0,142,0.011000," ","int((a*x^4-b*x^3)^(1/4)*(c*x^4-d)/x^2,x)","\[\int \frac{\left(a \,x^{4}-b \,x^{3}\right)^{\frac{1}{4}} \left(c \,x^{4}-d \right)}{x^{2}}\, dx\]"," ",0,"int((a*x^4-b*x^3)^(1/4)*(c*x^4-d)/x^2,x)","F"
2182,0,0,134,0.019000," ","int(x^3*(5-4*(1+k)*x+3*k*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(-b+b*(1+k)*x-b*k*x^2+x^5),x)","\[\int \frac{x^{3} \left(5-4 \left(1+k \right) x +3 k \,x^{2}\right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{2}{3}} \left(-b +b \left(1+k \right) x -b k \,x^{2}+x^{5}\right)}\, dx\]"," ",0,"int(x^3*(5-4*(1+k)*x+3*k*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(-b+b*(1+k)*x-b*k*x^2+x^5),x)","F"
2183,0,0,130,180.000000," ","int((x^5-8)*(x^5+2)*(x^5-3*x^4+2)^(1/4)/x^6/(2*x^5-3*x^4+4),x)","\[\int \frac{\left(x^{5}-8\right) \left(x^{5}+2\right) \left(x^{5}-3 x^{4}+2\right)^{\frac{1}{4}}}{x^{6} \left(2 x^{5}-3 x^{4}+4\right)}\, dx\]"," ",0,"int((x^5-8)*(x^5+2)*(x^5-3*x^4+2)^(1/4)/x^6/(2*x^5-3*x^4+4),x)","F"
2184,1,635,124,22.025000," ","int(x^2/(x^4-1)/(x^6+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{4}-8\right) x^{5}+2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}-8\right) x}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{16}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{5}-2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{16}-\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(x^{2}+1\right)}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{3}}{32}-\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(x^{2}+1\right)}\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2}}{32}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{5}-\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{5}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}+2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{3}+8 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right) x^{2}-8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \sqrt{x^{6}+x^{2}}\, x -8 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}-8\right) x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x -\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x +16 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{x \left(x^{2}+1\right)^{2}}\right)}{32}$&$635$\\ \hline \end{longtable}"," ",0,"1/16*RootOf(_Z^4-8)*ln((-RootOf(_Z^4-8)^3*(x^6+x^2)^(1/2)*x-RootOf(_Z^4-8)*x^5+2*(x^6+x^2)^(1/4)*RootOf(_Z^4-8)^2*x^2-2*RootOf(_Z^4-8)*x^3+4*(x^6+x^2)^(3/4)-RootOf(_Z^4-8)*x)/(-1+x)^2/(1+x)^2/x)+1/16*RootOf(_Z^2+RootOf(_Z^4-8)^2)*ln((RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*(x^6+x^2)^(1/2)*x-RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^5-2*(x^6+x^2)^(1/4)*RootOf(_Z^4-8)^2*x^2-2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^3+4*(x^6+x^2)^(3/4)-RootOf(_Z^2+RootOf(_Z^4-8)^2)*x)/(-1+x)^2/(1+x)^2/x)-1/32*ln(-(RootOf(_Z^4-8)^2*x^2-2*RootOf(_Z^4-8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(x^2+1))*RootOf(_Z^4-8)^3-1/32*ln(-(RootOf(_Z^4-8)^2*x^2-2*RootOf(_Z^4-8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(x^2+1))*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2+1/32*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*ln((RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x^5-RootOf(_Z^4-8)^3*x^5-2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x^3+2*RootOf(_Z^4-8)^3*x^3+8*(x^6+x^2)^(1/4)*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)*x^2-8*RootOf(_Z^2+RootOf(_Z^4-8)^2)*(x^6+x^2)^(1/2)*x-8*(x^6+x^2)^(1/2)*RootOf(_Z^4-8)*x+RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x-RootOf(_Z^4-8)^3*x+16*(x^6+x^2)^(3/4))/x/(x^2+1)^2)","C"
2185,1,639,124,21.640000," ","int(x^2/(x^4-1)/(x^6+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{4}+8\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{4}+8\right) x^{5}-2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+8\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}+8\right) x}{x \left(x^{2}+1\right)^{2}}\right)}{16}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{5}+2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x}{x \left(x^{2}+1\right)^{2}}\right)}{16}-\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{3}}{32}-\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)}{32}+\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{5}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{5}+2 \RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{3}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{3}+8 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{2}-8 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}+8\right) x -8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x -\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x +16 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{32}$&$639$\\ \hline \end{longtable}"," ",0,"1/16*RootOf(_Z^4+8)*ln(-(-RootOf(_Z^4+8)^3*(x^6+x^2)^(1/2)*x+RootOf(_Z^4+8)*x^5-2*(x^6+x^2)^(1/4)*RootOf(_Z^4+8)^2*x^2-2*RootOf(_Z^4+8)*x^3+4*(x^6+x^2)^(3/4)+RootOf(_Z^4+8)*x)/x/(x^2+1)^2)-1/16*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln(-(-RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*(x^6+x^2)^(1/2)*x-RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^5+2*(x^6+x^2)^(1/4)*RootOf(_Z^4+8)^2*x^2+2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^3+4*(x^6+x^2)^(3/4)-RootOf(_Z^2+RootOf(_Z^4+8)^2)*x)/x/(x^2+1)^2)-1/32*ln(-(RootOf(_Z^4+8)^2*x^2-2*RootOf(_Z^4+8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(-1+x)/(1+x))*RootOf(_Z^4+8)^3-1/32*ln(-(RootOf(_Z^4+8)^2*x^2-2*RootOf(_Z^4+8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(-1+x)/(1+x))*RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)+1/32*RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln((RootOf(_Z^4+8)^3*x^5-RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*x^5+2*RootOf(_Z^4+8)^3*x^3-2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*x^3+8*(x^6+x^2)^(1/4)*RootOf(_Z^4+8)*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^2-8*(x^6+x^2)^(1/2)*RootOf(_Z^4+8)*x-8*RootOf(_Z^2+RootOf(_Z^4+8)^2)*(x^6+x^2)^(1/2)*x+RootOf(_Z^4+8)^3*x-RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x+16*(x^6+x^2)^(3/4))/(-1+x)^2/(1+x)^2/x)","C"
2186,1,635,124,20.870000," ","int((x^4+1)/(x^4-1)/(x^6+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{5}+2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{3}-4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{8}+\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{4}-8\right) x^{5}-2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{3}-4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}-8\right) x}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{8}+\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(x^{2}+1\right)}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{3}}{16}+\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(x^{2}+1\right)}\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2}}{16}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{5}-\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{5}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}+2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{3}+8 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right) x^{2}-8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \sqrt{x^{6}+x^{2}}\, x -8 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}-8\right) x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x -\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x +16 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{x \left(x^{2}+1\right)^{2}}\right)}{16}$&$635$\\ \hline \end{longtable}"," ",0,"-1/8*RootOf(_Z^2+RootOf(_Z^4-8)^2)*ln(-(RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*(x^6+x^2)^(1/2)*x-RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^5+2*RootOf(_Z^4-8)^2*(x^6+x^2)^(1/4)*x^2-2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^3-4*(x^6+x^2)^(3/4)-RootOf(_Z^2+RootOf(_Z^4-8)^2)*x)/(-1+x)^2/(1+x)^2/x)+1/8*RootOf(_Z^4-8)*ln(-(RootOf(_Z^4-8)^3*(x^6+x^2)^(1/2)*x+RootOf(_Z^4-8)*x^5-2*RootOf(_Z^4-8)^2*(x^6+x^2)^(1/4)*x^2+2*RootOf(_Z^4-8)*x^3-4*(x^6+x^2)^(3/4)+RootOf(_Z^4-8)*x)/(-1+x)^2/(1+x)^2/x)+1/16*ln(-(RootOf(_Z^4-8)^2*x^2-2*RootOf(_Z^4-8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(x^2+1))*RootOf(_Z^4-8)^3+1/16*ln(-(RootOf(_Z^4-8)^2*x^2-2*RootOf(_Z^4-8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(x^2+1))*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2-1/16*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*ln(-(RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x^5-RootOf(_Z^4-8)^3*x^5-2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x^3+2*RootOf(_Z^4-8)^3*x^3+8*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)*(x^6+x^2)^(1/4)*x^2+RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x-8*RootOf(_Z^2+RootOf(_Z^4-8)^2)*(x^6+x^2)^(1/2)*x-RootOf(_Z^4-8)^3*x-8*(x^6+x^2)^(1/2)*RootOf(_Z^4-8)*x+16*(x^6+x^2)^(3/4))/x/(x^2+1)^2)","C"
2187,1,633,124,19.203000," ","int((x^4+1)/(x^4-1)/(x^6+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{4}-8\right) x^{5}-2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{3}-4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}-8\right) x}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{8}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{5}-2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{8}+\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(x^{2}+1\right)}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{3}}{16}+\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(x^{2}+1\right)}\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2}}{16}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{5}-\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{5}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}+2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{3}+8 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right) x^{2}-8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \sqrt{x^{6}+x^{2}}\, x -8 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}-8\right) x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x -\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x +16 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{x \left(x^{2}+1\right)^{2}}\right)}{16}$&$633$\\ \hline \end{longtable}"," ",0,"1/8*RootOf(_Z^4-8)*ln(-(RootOf(_Z^4-8)^3*(x^6+x^2)^(1/2)*x+RootOf(_Z^4-8)*x^5-2*RootOf(_Z^4-8)^2*(x^6+x^2)^(1/4)*x^2+2*RootOf(_Z^4-8)*x^3-4*(x^6+x^2)^(3/4)+RootOf(_Z^4-8)*x)/(-1+x)^2/(1+x)^2/x)-1/8*RootOf(_Z^2+RootOf(_Z^4-8)^2)*ln((-RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*(x^6+x^2)^(1/2)*x+RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^5-2*RootOf(_Z^4-8)^2*(x^6+x^2)^(1/4)*x^2+2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^3+4*(x^6+x^2)^(3/4)+RootOf(_Z^2+RootOf(_Z^4-8)^2)*x)/(-1+x)^2/(1+x)^2/x)+1/16*ln(-(RootOf(_Z^4-8)^2*x^2-2*RootOf(_Z^4-8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(x^2+1))*RootOf(_Z^4-8)^3+1/16*ln(-(RootOf(_Z^4-8)^2*x^2-2*RootOf(_Z^4-8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(x^2+1))*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2-1/16*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*ln(-(RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x^5-RootOf(_Z^4-8)^3*x^5-2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x^3+2*RootOf(_Z^4-8)^3*x^3+8*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)*(x^6+x^2)^(1/4)*x^2+RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x-8*RootOf(_Z^2+RootOf(_Z^4-8)^2)*(x^6+x^2)^(1/2)*x-RootOf(_Z^4-8)^3*x-8*(x^6+x^2)^(1/2)*RootOf(_Z^4-8)*x+16*(x^6+x^2)^(3/4))/x/(x^2+1)^2)","C"
2188,1,637,124,22.800000," ","int((x^4-x^2+1)/(x^4-1)/(x^6+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{5}+2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x}{x \left(x^{2}+1\right)^{2}}\right)}{16}+\frac{3 \RootOf \left(\textit{\_Z}^{4}+8\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{4}+8\right) x^{5}-2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}+8\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}+8\right) x}{x \left(x^{2}+1\right)^{2}}\right)}{16}-\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{3}}{32}-\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)}{32}+\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{5}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{5}+2 \RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{3}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{3}+8 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{2}-8 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}+8\right) x -8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x -\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x +16 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{32}$&$637$\\ \hline \end{longtable}"," ",0,"-3/16*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln(-(RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*(x^6+x^2)^(1/2)*x+RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^5+2*(x^6+x^2)^(1/4)*RootOf(_Z^4+8)^2*x^2-2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^3+4*(x^6+x^2)^(3/4)+RootOf(_Z^2+RootOf(_Z^4+8)^2)*x)/x/(x^2+1)^2)+3/16*RootOf(_Z^4+8)*ln(-(RootOf(_Z^4+8)^3*(x^6+x^2)^(1/2)*x-RootOf(_Z^4+8)*x^5-2*(x^6+x^2)^(1/4)*RootOf(_Z^4+8)^2*x^2+2*RootOf(_Z^4+8)*x^3+4*(x^6+x^2)^(3/4)-RootOf(_Z^4+8)*x)/x/(x^2+1)^2)-1/32*ln(-(RootOf(_Z^4+8)^2*x^2-2*RootOf(_Z^4+8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(-1+x)/(1+x))*RootOf(_Z^4+8)^3-1/32*ln(-(RootOf(_Z^4+8)^2*x^2-2*RootOf(_Z^4+8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(-1+x)/(1+x))*RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)+1/32*RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln((RootOf(_Z^4+8)^3*x^5-RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*x^5+2*RootOf(_Z^4+8)^3*x^3-2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*x^3+8*(x^6+x^2)^(1/4)*RootOf(_Z^4+8)*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^2-8*(x^6+x^2)^(1/2)*RootOf(_Z^4+8)*x-8*RootOf(_Z^2+RootOf(_Z^4+8)^2)*(x^6+x^2)^(1/2)*x+RootOf(_Z^4+8)^3*x-RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x+16*(x^6+x^2)^(3/4))/(-1+x)^2/(1+x)^2/x)","C"
2189,1,639,124,21.273000," ","int((x^4-x^2+1)/(x^4-1)/(x^6+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{3 \RootOf \left(\textit{\_Z}^{4}+8\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{4}+8\right) x^{5}-2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+8\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}+8\right) x}{x \left(x^{2}+1\right)^{2}}\right)}{16}+\frac{3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{5}+2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x}{x \left(x^{2}+1\right)^{2}}\right)}{16}-\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{3}}{32}-\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)}{32}+\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{5}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{5}+2 \RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{3}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{3}+8 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{2}-8 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}+8\right) x -8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x -\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x +16 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{32}$&$639$\\ \hline \end{longtable}"," ",0,"-3/16*RootOf(_Z^4+8)*ln(-(-RootOf(_Z^4+8)^3*(x^6+x^2)^(1/2)*x+RootOf(_Z^4+8)*x^5-2*(x^6+x^2)^(1/4)*RootOf(_Z^4+8)^2*x^2-2*RootOf(_Z^4+8)*x^3+4*(x^6+x^2)^(3/4)+RootOf(_Z^4+8)*x)/x/(x^2+1)^2)+3/16*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln(-(-RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*(x^6+x^2)^(1/2)*x-RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^5+2*(x^6+x^2)^(1/4)*RootOf(_Z^4+8)^2*x^2+2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^3+4*(x^6+x^2)^(3/4)-RootOf(_Z^2+RootOf(_Z^4+8)^2)*x)/x/(x^2+1)^2)-1/32*ln(-(RootOf(_Z^4+8)^2*x^2-2*RootOf(_Z^4+8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(-1+x)/(1+x))*RootOf(_Z^4+8)^3-1/32*ln(-(RootOf(_Z^4+8)^2*x^2-2*RootOf(_Z^4+8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(-1+x)/(1+x))*RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)+1/32*RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln((RootOf(_Z^4+8)^3*x^5-RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*x^5+2*RootOf(_Z^4+8)^3*x^3-2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*x^3+8*(x^6+x^2)^(1/4)*RootOf(_Z^4+8)*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^2-8*(x^6+x^2)^(1/2)*RootOf(_Z^4+8)*x-8*RootOf(_Z^2+RootOf(_Z^4+8)^2)*(x^6+x^2)^(1/2)*x+RootOf(_Z^4+8)^3*x-RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x+16*(x^6+x^2)^(3/4))/(-1+x)^2/(1+x)^2/x)","C"
2190,1,633,124,22.890000," ","int((x^4+x^2+1)/(x^4-1)/(x^6+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{5}-2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{16}-\frac{3 \RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{4}-8\right) x^{5}+2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}-8\right) x}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{16}+\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(x^{2}+1\right)}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{3}}{32}+\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(x^{2}+1\right)}\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2}}{32}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{5}-\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{5}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}+2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{3}+8 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right) x^{2}-8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \sqrt{x^{6}+x^{2}}\, x -8 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}-8\right) x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x -\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x +16 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{x \left(x^{2}+1\right)^{2}}\right)}{32}$&$633$\\ \hline \end{longtable}"," ",0,"-3/16*RootOf(_Z^2+RootOf(_Z^4-8)^2)*ln(-(-RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*(x^6+x^2)^(1/2)*x+RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^5-2*RootOf(_Z^4-8)^2*(x^6+x^2)^(1/4)*x^2+2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^3+4*(x^6+x^2)^(3/4)+RootOf(_Z^2+RootOf(_Z^4-8)^2)*x)/(-1+x)^2/(1+x)^2/x)-3/16*RootOf(_Z^4-8)*ln((RootOf(_Z^4-8)^3*(x^6+x^2)^(1/2)*x+RootOf(_Z^4-8)*x^5+2*RootOf(_Z^4-8)^2*(x^6+x^2)^(1/4)*x^2+2*RootOf(_Z^4-8)*x^3+4*(x^6+x^2)^(3/4)+RootOf(_Z^4-8)*x)/(-1+x)^2/(1+x)^2/x)+1/32*ln(-(RootOf(_Z^4-8)^2*x^2-2*RootOf(_Z^4-8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(x^2+1))*RootOf(_Z^4-8)^3+1/32*ln(-(RootOf(_Z^4-8)^2*x^2-2*RootOf(_Z^4-8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(x^2+1))*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2-1/32*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*ln(-(RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x^5-RootOf(_Z^4-8)^3*x^5-2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x^3+2*RootOf(_Z^4-8)^3*x^3+8*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)*(x^6+x^2)^(1/4)*x^2+RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x-8*RootOf(_Z^2+RootOf(_Z^4-8)^2)*(x^6+x^2)^(1/2)*x-RootOf(_Z^4-8)^3*x-8*(x^6+x^2)^(1/2)*RootOf(_Z^4-8)*x+16*(x^6+x^2)^(3/4))/x/(x^2+1)^2)","C"
2191,1,636,124,22.272000," ","int((x^4+x^2+1)/(x^4-1)/(x^6+x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{5}+2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{3}-4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{16}+\frac{3 \RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{4}-8\right) x^{5}+2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}-8\right) x}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{16}+\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(x^{2}+1\right)}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{3}}{32}+\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(x^{2}+1\right)}\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2}}{32}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{5}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{5}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}-2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{3}-8 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right) x^{2}+8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x +8 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}-8\right) x +\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x -16 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{x \left(x^{2}+1\right)^{2}}\right)}{32}$&$636$\\ \hline \end{longtable}"," ",0,"-3/16*RootOf(_Z^2+RootOf(_Z^4-8)^2)*ln(-(RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*(x^6+x^2)^(1/2)*x-RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^5+2*RootOf(_Z^4-8)^2*(x^6+x^2)^(1/4)*x^2-2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^3-4*(x^6+x^2)^(3/4)-RootOf(_Z^2+RootOf(_Z^4-8)^2)*x)/(-1+x)^2/(1+x)^2/x)+3/16*RootOf(_Z^4-8)*ln((-RootOf(_Z^4-8)^3*(x^6+x^2)^(1/2)*x-RootOf(_Z^4-8)*x^5+2*RootOf(_Z^4-8)^2*(x^6+x^2)^(1/4)*x^2-2*RootOf(_Z^4-8)*x^3+4*(x^6+x^2)^(3/4)-RootOf(_Z^4-8)*x)/(-1+x)^2/(1+x)^2/x)+1/32*ln(-(RootOf(_Z^4-8)^2*x^2-2*RootOf(_Z^4-8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(x^2+1))*RootOf(_Z^4-8)^3+1/32*ln(-(RootOf(_Z^4-8)^2*x^2-2*RootOf(_Z^4-8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(x^2+1))*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2-1/32*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*ln((-RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x^5+RootOf(_Z^4-8)^3*x^5+2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x^3-2*RootOf(_Z^4-8)^3*x^3-8*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)*(x^6+x^2)^(1/4)*x^2+8*RootOf(_Z^2+RootOf(_Z^4-8)^2)*(x^6+x^2)^(1/2)*x-RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x+8*(x^6+x^2)^(1/2)*RootOf(_Z^4-8)*x+RootOf(_Z^4-8)^3*x-16*(x^6+x^2)^(3/4))/x/(x^2+1)^2)","C"
2192,1,890,124,17.702000," ","int((x^3-4)*(x^3-2)*(x^3-1)^(2/3)/x^6/(x^6+x^3-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{13 x^{6}-21 x^{3}+8}{10 x^{5} \left(x^{3}-1\right)^{\frac{1}{3}}}-\frac{\ln \left(-\frac{6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{3} x^{3}-162 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{3}+42 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x +\left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{2}+144 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x^{2}-10 \RootOf \left(\textit{\_Z}^{3}+18\right) x^{3}+270 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x^{3}-48 x \left(x^{3}-1\right)^{\frac{2}{3}}+4 \RootOf \left(\textit{\_Z}^{3}+18\right)-108 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right)}{x^{3}+2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)}{3}-6 \ln \left(-\frac{6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{3} x^{3}-162 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{3}+42 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x +\left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{2}+144 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x^{2}-10 \RootOf \left(\textit{\_Z}^{3}+18\right) x^{3}+270 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x^{3}-48 x \left(x^{3}-1\right)^{\frac{2}{3}}+4 \RootOf \left(\textit{\_Z}^{3}+18\right)-108 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right)}{x^{3}+2}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right)+\frac{\RootOf \left(\textit{\_Z}^{3}+18\right) \ln \left(\frac{-3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{3} x^{3}-135 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{3}+21 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x -4 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{2}-9 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{3}+18\right) x^{3}-90 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x^{3}+3 x \left(x^{3}-1\right)^{\frac{2}{3}}+2 \RootOf \left(\textit{\_Z}^{3}+18\right)+90 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right)}{x^{3}+2}\right)}{3}$&$890$\\ trager&$\text{Expression too large to display}$&$1096$\\ \hline \end{longtable}"," ",0,"-1/10*(13*x^6-21*x^3+8)/x^5/(x^3-1)^(1/3)-1/3*ln(-(6*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*RootOf(_Z^3+18)^3*x^3-162*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)^2*RootOf(_Z^3+18)^2*x^3+42*(x^3-1)^(2/3)*RootOf(_Z^3+18)^2*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x+(x^3-1)^(1/3)*RootOf(_Z^3+18)^2*x^2+144*(x^3-1)^(1/3)*RootOf(_Z^3+18)*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x^2-10*RootOf(_Z^3+18)*x^3+270*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x^3-48*x*(x^3-1)^(2/3)+4*RootOf(_Z^3+18)-108*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2))/(x^3+2))*RootOf(_Z^3+18)-6*ln(-(6*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*RootOf(_Z^3+18)^3*x^3-162*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)^2*RootOf(_Z^3+18)^2*x^3+42*(x^3-1)^(2/3)*RootOf(_Z^3+18)^2*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x+(x^3-1)^(1/3)*RootOf(_Z^3+18)^2*x^2+144*(x^3-1)^(1/3)*RootOf(_Z^3+18)*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x^2-10*RootOf(_Z^3+18)*x^3+270*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x^3-48*x*(x^3-1)^(2/3)+4*RootOf(_Z^3+18)-108*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2))/(x^3+2))*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)+1/3*RootOf(_Z^3+18)*ln((-3*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*RootOf(_Z^3+18)^3*x^3-135*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)^2*RootOf(_Z^3+18)^2*x^3+21*(x^3-1)^(2/3)*RootOf(_Z^3+18)^2*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x-4*(x^3-1)^(1/3)*RootOf(_Z^3+18)^2*x^2-9*(x^3-1)^(1/3)*RootOf(_Z^3+18)*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x^2-2*RootOf(_Z^3+18)*x^3-90*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x^3+3*x*(x^3-1)^(2/3)+2*RootOf(_Z^3+18)+90*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2))/(x^3+2))","C"
2193,1,2862,124,108.446000," ","int((x^4-1)*(x^6+x^2)^(1/4)/(x^8+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2862$\\ \hline \end{longtable}"," ",0,"RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*ln(-(4*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x^5-RootOf(_Z^8-32)^11*x^5-8*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x^3+2*RootOf(_Z^8-32)^11*x^3+4*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x-RootOf(_Z^8-32)^11*x-4*x^5*RootOf(_Z^8-32)^7+32*RootOf(_Z^8-32)^6*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x^3-128*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*(x^6+x^2)^(1/4)*RootOf(_Z^8-32)^5*x^2+128*(x^6+x^2)^(1/2)*RootOf(_Z^8-32)^4*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x-256*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x^5-4*x*RootOf(_Z^8-32)^7+32*x^5*RootOf(_Z^8-32)^3+256*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x^3-32*x^3*RootOf(_Z^8-32)^3-64*(x^6+x^2)^(1/4)*RootOf(_Z^8-32)^2*x^2-256*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x+32*x*RootOf(_Z^8-32)^3+128*(x^6+x^2)^(3/4))/x/(RootOf(_Z^8-32)^4*x^4-2*RootOf(_Z^8-32)^4*x^2+RootOf(_Z^8-32)^4-8*x^4+8*x^2-8))+1/32*ln(-(RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x^5-2*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x^3+RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x+8*RootOf(_Z^8-32)^6*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x^3+32*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*(x^6+x^2)^(1/4)*RootOf(_Z^8-32)^5*x^2+32*(x^6+x^2)^(1/2)*RootOf(_Z^8-32)^4*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x-64*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x^5+64*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x^3+16*(x^6+x^2)^(1/4)*RootOf(_Z^8-32)^2*x^2-64*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x+32*RootOf(_Z^8-32)*(x^6+x^2)^(1/2)*x+32*(x^6+x^2)^(3/4))/x/(RootOf(_Z^8-32)^4*x^4-2*RootOf(_Z^8-32)^4*x^2+RootOf(_Z^8-32)^4-8*x^4+8*x^2-8))*RootOf(_Z^8-32)^5+ln(-(RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x^5-2*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x^3+RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x+8*RootOf(_Z^8-32)^6*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x^3+32*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*(x^6+x^2)^(1/4)*RootOf(_Z^8-32)^5*x^2+32*(x^6+x^2)^(1/2)*RootOf(_Z^8-32)^4*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x-64*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x^5+64*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x^3+16*(x^6+x^2)^(1/4)*RootOf(_Z^8-32)^2*x^2-64*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x+32*RootOf(_Z^8-32)*(x^6+x^2)^(1/2)*x+32*(x^6+x^2)^(3/4))/x/(RootOf(_Z^8-32)^4*x^4-2*RootOf(_Z^8-32)^4*x^2+RootOf(_Z^8-32)^4-8*x^4+8*x^2-8))*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)-1/8*RootOf(_Z^8-32)*ln(-(-RootOf(_Z^8-32)^11*x^5+2*RootOf(_Z^8-32)^11*x^3-RootOf(_Z^8-32)^11*x+8*x^3*RootOf(_Z^8-32)^7+32*RootOf(_Z^8-32)^5*(x^6+x^2)^(1/2)*x+64*x^5*RootOf(_Z^8-32)^3-64*x^3*RootOf(_Z^8-32)^3+128*(x^6+x^2)^(1/4)*RootOf(_Z^8-32)^2*x^2+64*x*RootOf(_Z^8-32)^3+256*(x^6+x^2)^(3/4))/(RootOf(_Z^8-32)^4*x^4-2*RootOf(_Z^8-32)^4*x^2+RootOf(_Z^8-32)^4+8*x^4-8*x^2+8)/x)+1/4*ln((16*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x^5+RootOf(_Z^8-32)^11*x^5-32*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x^3-2*RootOf(_Z^8-32)^11*x^3+16*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x-64*RootOf(_Z^8-32)^6*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x^5+RootOf(_Z^8-32)^11*x-8*x^3*RootOf(_Z^8-32)^7-64*RootOf(_Z^8-32)^6*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x-512*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x^5+32*RootOf(_Z^8-32)^5*(x^6+x^2)^(1/2)*x-64*x^5*RootOf(_Z^8-32)^3+512*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x^3+64*x^3*RootOf(_Z^8-32)^3+128*(x^6+x^2)^(1/4)*RootOf(_Z^8-32)^2*x^2+2048*(x^6+x^2)^(1/2)*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x-512*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x-64*x*RootOf(_Z^8-32)^3-256*(x^6+x^2)^(3/4))/(RootOf(_Z^8-32)^4*x^4-2*RootOf(_Z^8-32)^4*x^2+RootOf(_Z^8-32)^4+8*x^4-8*x^2+8)/x)*RootOf(_Z^8-32)^4*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)+1/8*ln((16*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x^5+RootOf(_Z^8-32)^11*x^5-32*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x^3-2*RootOf(_Z^8-32)^11*x^3+16*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x-64*RootOf(_Z^8-32)^6*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x^5+RootOf(_Z^8-32)^11*x-8*x^3*RootOf(_Z^8-32)^7-64*RootOf(_Z^8-32)^6*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x-512*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x^5+32*RootOf(_Z^8-32)^5*(x^6+x^2)^(1/2)*x-64*x^5*RootOf(_Z^8-32)^3+512*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x^3+64*x^3*RootOf(_Z^8-32)^3+128*(x^6+x^2)^(1/4)*RootOf(_Z^8-32)^2*x^2+2048*(x^6+x^2)^(1/2)*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x-512*RootOf(2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x-64*x*RootOf(_Z^8-32)^3-256*(x^6+x^2)^(3/4))/(RootOf(_Z^8-32)^4*x^4-2*RootOf(_Z^8-32)^4*x^2+RootOf(_Z^8-32)^4+8*x^4-8*x^2+8)/x)*RootOf(_Z^8-32)","C"
2194,1,2863,124,111.183000," ","int((x^4-1)*(x^6+x^2)^(1/4)/(x^8+1),x)","\[\text{output too large to display}\]"," ",0,"1/8*RootOf(_Z^8-32)*ln(-(RootOf(_Z^8-32)^11*x^5-2*RootOf(_Z^8-32)^11*x^3+RootOf(_Z^8-32)^11*x-8*x^3*RootOf(_Z^8-32)^7-32*RootOf(_Z^8-32)^5*(x^6+x^2)^(1/2)*x-64*x^5*RootOf(_Z^8-32)^3+64*x^3*RootOf(_Z^8-32)^3+128*(x^6+x^2)^(1/4)*RootOf(_Z^8-32)^2*x^2-64*x*RootOf(_Z^8-32)^3+256*(x^6+x^2)^(3/4))/(RootOf(_Z^8-32)^4*x^4-2*RootOf(_Z^8-32)^4*x^2+RootOf(_Z^8-32)^4+8*x^4-8*x^2+8)/x)-1/32*ln(-(RootOf(_Z^8-32)^10*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x^5-2*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x^3+RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x+8*RootOf(_Z^8-32)^6*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x^3-32*(x^6+x^2)^(1/4)*RootOf(_Z^8-32)^5*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x^2+32*(x^6+x^2)^(1/2)*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^4*x-64*RootOf(_Z^8-32)^2*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x^5+64*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x^3+16*(x^6+x^2)^(1/4)*RootOf(_Z^8-32)^2*x^2-32*RootOf(_Z^8-32)*(x^6+x^2)^(1/2)*x-64*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x+32*(x^6+x^2)^(3/4))/x/(RootOf(_Z^8-32)^4*x^4-2*RootOf(_Z^8-32)^4*x^2+RootOf(_Z^8-32)^4-8*x^4+8*x^2-8))*RootOf(_Z^8-32)^5+ln(-(RootOf(_Z^8-32)^10*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x^5-2*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x^3+RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x+8*RootOf(_Z^8-32)^6*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x^3-32*(x^6+x^2)^(1/4)*RootOf(_Z^8-32)^5*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x^2+32*(x^6+x^2)^(1/2)*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^4*x-64*RootOf(_Z^8-32)^2*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x^5+64*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x^3+16*(x^6+x^2)^(1/4)*RootOf(_Z^8-32)^2*x^2-32*RootOf(_Z^8-32)*(x^6+x^2)^(1/2)*x-64*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x+32*(x^6+x^2)^(3/4))/x/(RootOf(_Z^8-32)^4*x^4-2*RootOf(_Z^8-32)^4*x^2+RootOf(_Z^8-32)^4-8*x^4+8*x^2-8))*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)-RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*ln(-(-RootOf(_Z^8-32)^11*x^5-4*RootOf(_Z^8-32)^10*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x^5+2*RootOf(_Z^8-32)^11*x^3+8*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x^3-RootOf(_Z^8-32)^11*x-4*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x-4*x^5*RootOf(_Z^8-32)^7-32*RootOf(_Z^8-32)^6*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x^3+128*(x^6+x^2)^(1/4)*RootOf(_Z^8-32)^5*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x^2-128*(x^6+x^2)^(1/2)*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^4*x-4*x*RootOf(_Z^8-32)^7+32*x^5*RootOf(_Z^8-32)^3+256*RootOf(_Z^8-32)^2*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x^5-32*x^3*RootOf(_Z^8-32)^3-256*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x^3-64*(x^6+x^2)^(1/4)*RootOf(_Z^8-32)^2*x^2+32*x*RootOf(_Z^8-32)^3+256*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x+128*(x^6+x^2)^(3/4))/x/(RootOf(_Z^8-32)^4*x^4-2*RootOf(_Z^8-32)^4*x^2+RootOf(_Z^8-32)^4-8*x^4+8*x^2-8))+1/4*ln(-(RootOf(_Z^8-32)^11*x^5-16*RootOf(_Z^8-32)^10*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x^5-2*RootOf(_Z^8-32)^11*x^3+32*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x^3+RootOf(_Z^8-32)^11*x-16*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x+64*RootOf(_Z^8-32)^6*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x^5-8*x^3*RootOf(_Z^8-32)^7+32*RootOf(_Z^8-32)^5*(x^6+x^2)^(1/2)*x+64*RootOf(_Z^8-32)^6*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x-64*x^5*RootOf(_Z^8-32)^3+512*RootOf(_Z^8-32)^2*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x^5+64*x^3*RootOf(_Z^8-32)^3-512*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x^3-128*(x^6+x^2)^(1/4)*RootOf(_Z^8-32)^2*x^2-2048*(x^6+x^2)^(1/2)*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x-64*x*RootOf(_Z^8-32)^3+512*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x+256*(x^6+x^2)^(3/4))/(RootOf(_Z^8-32)^4*x^4-2*RootOf(_Z^8-32)^4*x^2+RootOf(_Z^8-32)^4+8*x^4-8*x^2+8)/x)*RootOf(_Z^8-32)^4*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)-1/8*ln(-(RootOf(_Z^8-32)^11*x^5-16*RootOf(_Z^8-32)^10*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x^5-2*RootOf(_Z^8-32)^11*x^3+32*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x^3+RootOf(_Z^8-32)^11*x-16*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^10*x+64*RootOf(_Z^8-32)^6*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x^5-8*x^3*RootOf(_Z^8-32)^7+32*RootOf(_Z^8-32)^5*(x^6+x^2)^(1/2)*x+64*RootOf(_Z^8-32)^6*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x-64*x^5*RootOf(_Z^8-32)^3+512*RootOf(_Z^8-32)^2*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x^5+64*x^3*RootOf(_Z^8-32)^3-512*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x^3-128*(x^6+x^2)^(1/4)*RootOf(_Z^8-32)^2*x^2-2048*(x^6+x^2)^(1/2)*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*x-64*x*RootOf(_Z^8-32)^3+512*RootOf(-2*RootOf(_Z^8-32)^5*_Z+RootOf(_Z^8-32)^2+64*_Z^2)*RootOf(_Z^8-32)^2*x+256*(x^6+x^2)^(3/4))/(RootOf(_Z^8-32)^4*x^4-2*RootOf(_Z^8-32)^4*x^2+RootOf(_Z^8-32)^4+8*x^4-8*x^2+8)/x)*RootOf(_Z^8-32)","C"
2195,1,2802,124,134.563000," ","int((x^8-1)/(x^6+x^2)^(1/4)/(x^8+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2802$\\ \hline \end{longtable}"," ",0,"-1/8*RootOf(_Z^8-128)*ln((RootOf(_Z^8-128)^9*x^5-2*RootOf(_Z^8-128)^9*x^3+RootOf(_Z^8-128)^9*x-8*(x^6+x^2)^(1/2)*RootOf(_Z^8-128)^7*x-16*RootOf(_Z^8-128)^6*(x^6+x^2)^(1/4)*x^2-16*RootOf(_Z^8-128)^5*x^3-256*RootOf(_Z^8-128)*x^5+256*RootOf(_Z^8-128)*x^3-512*(x^6+x^2)^(3/4)-256*RootOf(_Z^8-128)*x)/x/(RootOf(_Z^8-128)^4*x^4-2*RootOf(_Z^8-128)^4*x^2+RootOf(_Z^8-128)^4+16*x^4-16*x^2+16))+1/64*ln((4*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x^5+RootOf(_Z^8-128)^9*x^5-8*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x^3-2*RootOf(_Z^8-128)^9*x^3+4*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x+32*(x^6+x^2)^(1/2)*RootOf(_Z^8-128)^6*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x+RootOf(_Z^8-128)^9*x+8*RootOf(_Z^8-128)^5*x^5+8*RootOf(_Z^8-128)^6*(x^6+x^2)^(1/4)*x^2+64*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^4*x^3-1024*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x^5+8*RootOf(_Z^8-128)^5*x-128*RootOf(_Z^8-128)*x^5-1024*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)*(x^6+x^2)^(1/4)*x^2+1024*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x^3+128*RootOf(_Z^8-128)*x^3-256*(x^6+x^2)^(3/4)-1024*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x-128*RootOf(_Z^8-128)*x)/x/(RootOf(_Z^8-128)^4*x^4-2*RootOf(_Z^8-128)^4*x^2+RootOf(_Z^8-128)^4-16*x^4+16*x^2-16))*RootOf(_Z^8-128)^5-ln((4*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x^5+RootOf(_Z^8-128)^9*x^5-8*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x^3-2*RootOf(_Z^8-128)^9*x^3+4*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x+32*(x^6+x^2)^(1/2)*RootOf(_Z^8-128)^6*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x+RootOf(_Z^8-128)^9*x+8*RootOf(_Z^8-128)^5*x^5+8*RootOf(_Z^8-128)^6*(x^6+x^2)^(1/4)*x^2+64*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^4*x^3-1024*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x^5+8*RootOf(_Z^8-128)^5*x-128*RootOf(_Z^8-128)*x^5-1024*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)*(x^6+x^2)^(1/4)*x^2+1024*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x^3+128*RootOf(_Z^8-128)*x^3-256*(x^6+x^2)^(3/4)-1024*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x-128*RootOf(_Z^8-128)*x)/x/(RootOf(_Z^8-128)^4*x^4-2*RootOf(_Z^8-128)^4*x^2+RootOf(_Z^8-128)^4-16*x^4+16*x^2-16))*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)-1/8*ln((16*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x^5-RootOf(_Z^8-128)^9*x^5-32*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x^3+2*RootOf(_Z^8-128)^9*x^3+16*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x-128*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^4*x^5-RootOf(_Z^8-128)^9*x-8*(x^6+x^2)^(1/2)*RootOf(_Z^8-128)^7*x+16*RootOf(_Z^8-128)^6*(x^6+x^2)^(1/4)*x^2+16*RootOf(_Z^8-128)^5*x^3-128*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^4*x+1024*(x^6+x^2)^(1/2)*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^2*x-2048*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x^5+256*RootOf(_Z^8-128)*x^5+2048*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x^3-256*RootOf(_Z^8-128)*x^3-512*(x^6+x^2)^(3/4)-2048*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x+256*RootOf(_Z^8-128)*x)/x/(RootOf(_Z^8-128)^4*x^4-2*RootOf(_Z^8-128)^4*x^2+RootOf(_Z^8-128)^4+16*x^4-16*x^2+16))*RootOf(_Z^8-128)^4*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)+1/8*ln((16*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x^5-RootOf(_Z^8-128)^9*x^5-32*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x^3+2*RootOf(_Z^8-128)^9*x^3+16*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x-128*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^4*x^5-RootOf(_Z^8-128)^9*x-8*(x^6+x^2)^(1/2)*RootOf(_Z^8-128)^7*x+16*RootOf(_Z^8-128)^6*(x^6+x^2)^(1/4)*x^2+16*RootOf(_Z^8-128)^5*x^3-128*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^4*x+1024*(x^6+x^2)^(1/2)*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^2*x-2048*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x^5+256*RootOf(_Z^8-128)*x^5+2048*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x^3-256*RootOf(_Z^8-128)*x^3-512*(x^6+x^2)^(3/4)-2048*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x+256*RootOf(_Z^8-128)*x)/x/(RootOf(_Z^8-128)^4*x^4-2*RootOf(_Z^8-128)^4*x^2+RootOf(_Z^8-128)^4+16*x^4-16*x^2+16))*RootOf(_Z^8-128)+RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*ln(-(RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x^5-2*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x^3+RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x+8*(x^6+x^2)^(1/2)*RootOf(_Z^8-128)^6*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x+2*RootOf(_Z^8-128)^6*(x^6+x^2)^(1/4)*x^2+16*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^4*x^3-256*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x^5-16*(x^6+x^2)^(1/2)*RootOf(_Z^8-128)^3*x-256*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)*(x^6+x^2)^(1/4)*x^2+256*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x^3+64*(x^6+x^2)^(3/4)-256*RootOf(-RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x)/x/(RootOf(_Z^8-128)^4*x^4-2*RootOf(_Z^8-128)^4*x^2+RootOf(_Z^8-128)^4-16*x^4+16*x^2-16))","C"
2196,1,2757,124,127.975000," ","int((x^8-1)/(x^6+x^2)^(1/4)/(x^8+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2757$\\ \hline \end{longtable}"," ",0,"-1/64*ln(-(RootOf(_Z^8-128)^9*x^5-4*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x^5-2*RootOf(_Z^8-128)^9*x^3+8*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x^3-32*(x^6+x^2)^(1/2)*RootOf(_Z^8-128)^6*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x+RootOf(_Z^8-128)^9*x-4*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x+8*RootOf(_Z^8-128)^5*x^5-8*RootOf(_Z^8-128)^6*(x^6+x^2)^(1/4)*x^2-64*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^4*x^3+8*RootOf(_Z^8-128)^5*x-128*RootOf(_Z^8-128)*x^5+1024*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x^5-1024*(x^6+x^2)^(1/4)*RootOf(_Z^8-128)*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x^2+128*RootOf(_Z^8-128)*x^3-1024*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x^3+256*(x^6+x^2)^(3/4)-128*RootOf(_Z^8-128)*x+1024*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x)/x/(RootOf(_Z^8-128)^4*x^4-2*RootOf(_Z^8-128)^4*x^2+RootOf(_Z^8-128)^4-16*x^4+16*x^2-16))*RootOf(_Z^8-128)^5-ln(-(RootOf(_Z^8-128)^9*x^5-4*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x^5-2*RootOf(_Z^8-128)^9*x^3+8*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x^3-32*(x^6+x^2)^(1/2)*RootOf(_Z^8-128)^6*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x+RootOf(_Z^8-128)^9*x-4*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x+8*RootOf(_Z^8-128)^5*x^5-8*RootOf(_Z^8-128)^6*(x^6+x^2)^(1/4)*x^2-64*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^4*x^3+8*RootOf(_Z^8-128)^5*x-128*RootOf(_Z^8-128)*x^5+1024*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x^5-1024*(x^6+x^2)^(1/4)*RootOf(_Z^8-128)*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x^2+128*RootOf(_Z^8-128)*x^3-1024*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x^3+256*(x^6+x^2)^(3/4)-128*RootOf(_Z^8-128)*x+1024*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x)/x/(RootOf(_Z^8-128)^4*x^4-2*RootOf(_Z^8-128)^4*x^2+RootOf(_Z^8-128)^4-16*x^4+16*x^2-16))*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)+RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*ln(-(RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x^5-2*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x^3+8*(x^6+x^2)^(1/2)*RootOf(_Z^8-128)^6*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x+RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x+2*RootOf(_Z^8-128)^6*(x^6+x^2)^(1/4)*x^2+16*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^4*x^3+16*(x^6+x^2)^(1/2)*RootOf(_Z^8-128)^3*x-256*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x^5+256*(x^6+x^2)^(1/4)*RootOf(_Z^8-128)*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x^2+256*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x^3+64*(x^6+x^2)^(3/4)-256*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x)/x/(RootOf(_Z^8-128)^4*x^4-2*RootOf(_Z^8-128)^4*x^2+RootOf(_Z^8-128)^4-16*x^4+16*x^2-16))+1/8*ln(-(RootOf(_Z^8-128)^9*x^5+16*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x^5-2*RootOf(_Z^8-128)^9*x^3-32*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x^3+8*(x^6+x^2)^(1/2)*RootOf(_Z^8-128)^7*x+RootOf(_Z^8-128)^9*x+16*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x-128*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^4*x^5-16*RootOf(_Z^8-128)^6*(x^6+x^2)^(1/4)*x^2-16*RootOf(_Z^8-128)^5*x^3+1024*(x^6+x^2)^(1/2)*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^2*x-128*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^4*x-256*RootOf(_Z^8-128)*x^5-2048*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x^5+256*RootOf(_Z^8-128)*x^3+2048*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x^3+512*(x^6+x^2)^(3/4)-256*RootOf(_Z^8-128)*x-2048*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x)/x/(RootOf(_Z^8-128)^4*x^4-2*RootOf(_Z^8-128)^4*x^2+RootOf(_Z^8-128)^4+16*x^4-16*x^2+16))*RootOf(_Z^8-128)^4*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)+1/8*ln(-(RootOf(_Z^8-128)^9*x^5+16*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x^5-2*RootOf(_Z^8-128)^9*x^3-32*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x^3+8*(x^6+x^2)^(1/2)*RootOf(_Z^8-128)^7*x+RootOf(_Z^8-128)^9*x+16*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^8*x-128*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^4*x^5-16*RootOf(_Z^8-128)^6*(x^6+x^2)^(1/4)*x^2-16*RootOf(_Z^8-128)^5*x^3+1024*(x^6+x^2)^(1/2)*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^2*x-128*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*RootOf(_Z^8-128)^4*x-256*RootOf(_Z^8-128)*x^5-2048*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x^5+256*RootOf(_Z^8-128)*x^3+2048*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x^3+512*(x^6+x^2)^(3/4)-256*RootOf(_Z^8-128)*x-2048*RootOf(RootOf(_Z^8-128)^5*_Z+RootOf(_Z^8-128)^2+64*_Z^2)*x)/x/(RootOf(_Z^8-128)^4*x^4-2*RootOf(_Z^8-128)^4*x^2+RootOf(_Z^8-128)^4+16*x^4-16*x^2+16))*RootOf(_Z^8-128)-1/8*RootOf(_Z^8-128)*ln(-(-RootOf(_Z^8-128)^9*x^5+2*RootOf(_Z^8-128)^9*x^3+8*(x^6+x^2)^(1/2)*RootOf(_Z^8-128)^7*x-RootOf(_Z^8-128)^9*x+16*RootOf(_Z^8-128)^6*(x^6+x^2)^(1/4)*x^2+16*RootOf(_Z^8-128)^5*x^3+256*RootOf(_Z^8-128)*x^5-256*RootOf(_Z^8-128)*x^3+512*(x^6+x^2)^(3/4)+256*RootOf(_Z^8-128)*x)/x/(RootOf(_Z^8-128)^4*x^4-2*RootOf(_Z^8-128)^4*x^2+RootOf(_Z^8-128)^4+16*x^4-16*x^2+16))","C"
2197,0,0,134,0.016000," ","int(x^5*(8-7*(1+k)*x+6*k*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(-b+b*(1+k)*x-b*k*x^2+x^8),x)","\[\int \frac{x^{5} \left(8-7 \left(1+k \right) x +6 k \,x^{2}\right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{2}{3}} \left(-b +b \left(1+k \right) x -b k \,x^{2}+x^{8}\right)}\, dx\]"," ",0,"int(x^5*(8-7*(1+k)*x+6*k*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(-b+b*(1+k)*x-b*k*x^2+x^8),x)","F"
2198,0,0,54,0.034000," ","int((2*x^8-a*x^4-2*b)/(a*x^4-b)^(1/4)/(x^8-a*x^4-2*b),x)","\[\int \frac{2 x^{8}-a \,x^{4}-2 b}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(x^{8}-a \,x^{4}-2 b \right)}\, dx\]"," ",0,"int((2*x^8-a*x^4-2*b)/(a*x^4-b)^(1/4)/(x^8-a*x^4-2*b),x)","F"
2199,1,31,123,0.041000," ","int((b+(a*x^2+b^2)^(1/2))^(1/2)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \hypergeom \left(\left[-\frac{3}{2}, -\frac{1}{4}, \frac{1}{4}\right], \left[-\frac{1}{2}, \frac{1}{2}\right], -\frac{x^{2} a}{b^{2}}\right)}{3 x^{3}}$&$31$\\ \hline \end{longtable}"," ",0,"-1/3*(b^2)^(1/4)*2^(1/2)/x^3*hypergeom([-3/2,-1/4,1/4],[-1/2,1/2],-x^2*a/b^2)","C"
2200,0,0,123,0.029000," ","int((b+(a*x^2+b^2)^(1/2))^(1/2)/x^4/(a*x^2+b^2)^(1/2),x)","\[\int \frac{\sqrt{b +\sqrt{a \,x^{2}+b^{2}}}}{x^{4} \sqrt{a \,x^{2}+b^{2}}}\, dx\]"," ",0,"int((b+(a*x^2+b^2)^(1/2))^(1/2)/x^4/(a*x^2+b^2)^(1/2),x)","F"
2201,1,5190,97,79.492000," ","int(1/(x^3+x)^(1/3)/(x^6-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$5190$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2202,0,0,97,0.055000," ","int(1/(x^3+x)^(1/3)/(x^6-1),x)","\[\int \frac{1}{\left(x^{3}+x \right)^{\frac{1}{3}} \left(x^{6}-1\right)}\, dx\]"," ",0,"int(1/(x^3+x)^(1/3)/(x^6-1),x)","F"
2203,0,0,130,0.017000," ","int((x^3+1)*(x^6-x^3-2)^(1/2)/x^4/(x^6-2*x^3-1),x)","\[\int \frac{\left(x^{3}+1\right) \sqrt{x^{6}-x^{3}-2}}{x^{4} \left(x^{6}-2 x^{3}-1\right)}\, dx\]"," ",0,"int((x^3+1)*(x^6-x^3-2)^(1/2)/x^4/(x^6-2*x^3-1),x)","F"
2204,1,516,139,17.805000," ","int(x^2*(7*x^3-4)/(x^4-x)^(1/3)/(x^7-x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(-\frac{2750978024320396805141 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{7}-397640531996478951563644 x^{7} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+10027471246530585051439424 x^{7}-2750978024320396805141 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{4}+9624328758485465306265498 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}-x \right)^{\frac{2}{3}} x^{2}+397640531996478951563644 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}+20449832047033328657637351 x^{2} \left(x^{4}-x \right)^{\frac{2}{3}}-10027471246530585051439424 x^{4}+9624328758485465306265498 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}-x \right)^{\frac{1}{3}} x -308109538723884442175792 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+20449832047033328657637351 x \left(x^{4}-x \right)^{\frac{1}{3}}+9716610729782380212458491 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+10117002239803179560827276}{x^{7}-x^{4}-1}\right)-\ln \left(-\frac{2750978024320396805141 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{7}+403142488045119745173926 x^{7} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+10427862756551384399808209 x^{7}-2750978024320396805141 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{4}-9624328758485465306265498 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}-x \right)^{\frac{2}{3}} x^{2}-403142488045119745173926 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}+10825503288547863351371853 x^{2} \left(x^{4}-x \right)^{\frac{2}{3}}-10427862756551384399808209 x^{4}-9624328758485465306265498 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}-x \right)^{\frac{1}{3}} x -308109538723884442175792 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+10825503288547863351371853 x \left(x^{4}-x \right)^{\frac{1}{3}}-10332829807230149096810075 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+92281971296914906192993}{x^{7}-x^{4}-1}\right) \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-\ln \left(-\frac{2750978024320396805141 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{7}+403142488045119745173926 x^{7} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+10427862756551384399808209 x^{7}-2750978024320396805141 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2} x^{4}-9624328758485465306265498 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}-x \right)^{\frac{2}{3}} x^{2}-403142488045119745173926 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}+10825503288547863351371853 x^{2} \left(x^{4}-x \right)^{\frac{2}{3}}-10427862756551384399808209 x^{4}-9624328758485465306265498 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{4}-x \right)^{\frac{1}{3}} x -308109538723884442175792 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)^{2}+10825503288547863351371853 x \left(x^{4}-x \right)^{\frac{1}{3}}-10332829807230149096810075 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+92281971296914906192993}{x^{7}-x^{4}-1}\right)$&$516$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2+_Z+1)*ln(-(2750978024320396805141*RootOf(_Z^2+_Z+1)^2*x^7-397640531996478951563644*x^7*RootOf(_Z^2+_Z+1)+10027471246530585051439424*x^7-2750978024320396805141*RootOf(_Z^2+_Z+1)^2*x^4+9624328758485465306265498*RootOf(_Z^2+_Z+1)*(x^4-x)^(2/3)*x^2+397640531996478951563644*RootOf(_Z^2+_Z+1)*x^4+20449832047033328657637351*x^2*(x^4-x)^(2/3)-10027471246530585051439424*x^4+9624328758485465306265498*RootOf(_Z^2+_Z+1)*(x^4-x)^(1/3)*x-308109538723884442175792*RootOf(_Z^2+_Z+1)^2+20449832047033328657637351*x*(x^4-x)^(1/3)+9716610729782380212458491*RootOf(_Z^2+_Z+1)+10117002239803179560827276)/(x^7-x^4-1))-ln(-(2750978024320396805141*RootOf(_Z^2+_Z+1)^2*x^7+403142488045119745173926*x^7*RootOf(_Z^2+_Z+1)+10427862756551384399808209*x^7-2750978024320396805141*RootOf(_Z^2+_Z+1)^2*x^4-9624328758485465306265498*RootOf(_Z^2+_Z+1)*(x^4-x)^(2/3)*x^2-403142488045119745173926*RootOf(_Z^2+_Z+1)*x^4+10825503288547863351371853*x^2*(x^4-x)^(2/3)-10427862756551384399808209*x^4-9624328758485465306265498*RootOf(_Z^2+_Z+1)*(x^4-x)^(1/3)*x-308109538723884442175792*RootOf(_Z^2+_Z+1)^2+10825503288547863351371853*x*(x^4-x)^(1/3)-10332829807230149096810075*RootOf(_Z^2+_Z+1)+92281971296914906192993)/(x^7-x^4-1))*RootOf(_Z^2+_Z+1)-ln(-(2750978024320396805141*RootOf(_Z^2+_Z+1)^2*x^7+403142488045119745173926*x^7*RootOf(_Z^2+_Z+1)+10427862756551384399808209*x^7-2750978024320396805141*RootOf(_Z^2+_Z+1)^2*x^4-9624328758485465306265498*RootOf(_Z^2+_Z+1)*(x^4-x)^(2/3)*x^2-403142488045119745173926*RootOf(_Z^2+_Z+1)*x^4+10825503288547863351371853*x^2*(x^4-x)^(2/3)-10427862756551384399808209*x^4-9624328758485465306265498*RootOf(_Z^2+_Z+1)*(x^4-x)^(1/3)*x-308109538723884442175792*RootOf(_Z^2+_Z+1)^2+10825503288547863351371853*x*(x^4-x)^(1/3)-10332829807230149096810075*RootOf(_Z^2+_Z+1)+92281971296914906192993)/(x^7-x^4-1))","C"
2205,0,0,60,0.033000," ","int((x^8+a*x^4)/(a*x^4-b*x^2)^(1/4)/(x^8+2*a*x^4-b),x)","\[\int \frac{x^{8}+a \,x^{4}}{\left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}} \left(x^{8}+2 a \,x^{4}-b \right)}\, dx\]"," ",0,"int((x^8+a*x^4)/(a*x^4-b*x^2)^(1/4)/(x^8+2*a*x^4-b),x)","F"
2206,0,0,60,0.001000," ","int((x^8+a*x^4)/(a*x^4-b*x^2)^(1/4)/(x^8+2*a*x^4-b),x)","\[\int \frac{x^{8}+a \,x^{4}}{\left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}} \left(x^{8}+2 a \,x^{4}-b \right)}\, dx\]"," ",0,"int((x^8+a*x^4)/(a*x^4-b*x^2)^(1/4)/(x^8+2*a*x^4-b),x)","F"
2207,1,112,132,3.300000," ","int((-x^4+2*x^2+1)^(1/2)*(x^4-1)*(x^4+1)/(x^4-x^2-1)/(x^8-3*x^6-x^4+3*x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(-\frac{2 \sqrt{5}\, \arctan \left(\frac{\sqrt{-x^{4}+2 x^{2}+1}\, \sqrt{2}}{x \sqrt{\sqrt{5}-1}}\right)}{5 \sqrt{\sqrt{5}-1}}-\frac{2 \sqrt{5}\, \arctanh \left(\frac{\sqrt{-x^{4}+2 x^{2}+1}\, \sqrt{2}}{x \sqrt{\sqrt{5}+1}}\right)}{5 \sqrt{\sqrt{5}+1}}+\sqrt{2}\, \arctanh \left(\frac{\sqrt{-x^{4}+2 x^{2}+1}}{x}\right)\right) \sqrt{2}}{2}$&$112$\\ default&$-\frac{\sqrt{1-\left(\sqrt{2}-1\right) x^{2}}\, \sqrt{1-\left(-1-\sqrt{2}\right) x^{2}}\, \EllipticF \left(x \sqrt{\sqrt{2}-1}, i+i \sqrt{2}\right)}{\sqrt{\sqrt{2}-1}\, \sqrt{-x^{4}+2 x^{2}+1}}-\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{8}-3 \textit{\_Z}^{6}-\textit{\_Z}^{4}+3 \textit{\_Z}^{2}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{6}-6 \underline{\hspace{1.25 ex}}\alpha^{4}+3\right) \left(\frac{\arctanh \left(\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \left(2 \underline{\hspace{1.25 ex}}\alpha^{6}-4 \underline{\hspace{1.25 ex}}\alpha^{4}-6 \underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}-1\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{4}+2 \underline{\hspace{1.25 ex}}\alpha^{2}+1}\, \sqrt{-x^{4}+2 x^{2}+1}}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{4}+2 \underline{\hspace{1.25 ex}}\alpha^{2}+1}}-\frac{2 \left(-\underline{\hspace{1.25 ex}}\alpha^{7}+3 \underline{\hspace{1.25 ex}}\alpha^{5}+\underline{\hspace{1.25 ex}}\alpha^{3}-3 \underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{-\sqrt{2}\, x^{2}+x^{2}+1}\, \sqrt{\sqrt{2}\, x^{2}+x^{2}+1}\, \EllipticPi \left(x \sqrt{\sqrt{2}-1}, -\underline{\hspace{1.25 ex}}\alpha^{6} \sqrt{2}-\underline{\hspace{1.25 ex}}\alpha^{6}+3 \underline{\hspace{1.25 ex}}\alpha^{4} \sqrt{2}+3 \underline{\hspace{1.25 ex}}\alpha^{4}+\underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{2}+\underline{\hspace{1.25 ex}}\alpha^{2}-3 \sqrt{2}-3, \frac{\sqrt{-1-\sqrt{2}}}{\sqrt{\sqrt{2}-1}}\right)}{\sqrt{\sqrt{2}-1}\, \sqrt{-x^{4}+2 x^{2}+1}}\right)\right)}{20}-\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}-\textit{\_Z}^{2}-1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(\frac{\arctanh \left(\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \left(-2 \underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}-1\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{-x^{4}+2 x^{2}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}}-\frac{2 \left(\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{-\sqrt{2}\, x^{2}+x^{2}+1}\, \sqrt{\sqrt{2}\, x^{2}+x^{2}+1}\, \EllipticPi \left(x \sqrt{\sqrt{2}-1}, \underline{\hspace{1.25 ex}}\alpha^{2} \sqrt{2}+\underline{\hspace{1.25 ex}}\alpha^{2}-\sqrt{2}-1, \frac{\sqrt{-1-\sqrt{2}}}{\sqrt{\sqrt{2}-1}}\right)}{\sqrt{\sqrt{2}-1}\, \sqrt{-x^{4}+2 x^{2}+1}}\right)\right)}{4}$&$488$\\ trager&$\frac{\ln \left(-\frac{-x^{4}+2 \sqrt{-x^{4}+2 x^{2}+1}\, x +3 x^{2}+1}{x^{4}-x^{2}-1}\right)}{2}-\RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right) \ln \left(\frac{600 x^{2} \RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right)^{5}-30 \RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right)^{3} x^{4}+130 \RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right)^{3} x^{2}-2 \RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right) x^{4}+10 \RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right)^{2} \sqrt{-x^{4}+2 x^{2}+1}\, x +30 \RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right)^{3}+6 \RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right) x^{2}+\sqrt{-x^{4}+2 x^{2}+1}\, x +2 \RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right)}{20 x^{2} \RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right)^{2}+x^{4}-x^{2}-1}\right)+\frac{\RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right)^{2}+5\right) \ln \left(-\frac{1200 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right)^{2}+5\right) \RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right)^{4} x^{2}+60 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right)^{2}+5\right) \RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right)^{2} x^{4}-140 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right)^{2}+5\right) \RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right)^{2} x^{2}-\RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right)^{2}+5\right) x^{4}+200 \RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right)^{2} \sqrt{-x^{4}+2 x^{2}+1}\, x -60 \RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right)^{2}+5\right)+2 \RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right)^{2}+5\right) x^{2}-10 \sqrt{-x^{4}+2 x^{2}+1}\, x +\RootOf \left(\textit{\_Z}^{2}+100 \RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right)^{2}+5\right)}{20 x^{2} \RootOf \left(400 \textit{\_Z}^{4}+20 \textit{\_Z}^{2}-1\right)^{2}-x^{4}+2 x^{2}+1}\right)}{10}$&$634$\\ \hline \end{longtable}"," ",0,"1/2*(-2/5*5^(1/2)/(5^(1/2)-1)^(1/2)*arctan((-x^4+2*x^2+1)^(1/2)*2^(1/2)/x/(5^(1/2)-1)^(1/2))-2/5*5^(1/2)/(5^(1/2)+1)^(1/2)*arctanh((-x^4+2*x^2+1)^(1/2)*2^(1/2)/x/(5^(1/2)+1)^(1/2))+2^(1/2)*arctanh((-x^4+2*x^2+1)^(1/2)/x))*2^(1/2)","A"
2208,0,0,115,0.041000," ","int(1/(x^2-1)/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{1}{\left(x^{2}-1\right) \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int(1/(x^2-1)/(x+(x^2+1)^(1/2))^(1/2),x)","F"
2209,0,0,139,0.046000," ","int((-a/b^2+a^2*x^2/b^2)^(1/2)/(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{-\frac{a}{b^{2}}+\frac{a^{2} x^{2}}{b^{2}}}}{\sqrt{a \,x^{2}+b x \sqrt{-\frac{a}{b^{2}}+\frac{a^{2} x^{2}}{b^{2}}}}}\, dx\]"," ",0,"int((-a/b^2+a^2*x^2/b^2)^(1/2)/(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2),x)","F"
2210,0,0,139,0.025000," ","int((-a/b^2+a^2*x^2/b^2)^(1/2)*(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2),x)","\[\int \sqrt{-\frac{a}{b^{2}}+\frac{a^{2} x^{2}}{b^{2}}}\, \sqrt{a \,x^{2}+b x \sqrt{-\frac{a}{b^{2}}+\frac{a^{2} x^{2}}{b^{2}}}}\, dx\]"," ",0,"int((-a/b^2+a^2*x^2/b^2)^(1/2)*(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2),x)","F"
2211,1,671,134,19.081000," ","int((-3+x)*(-2+x)*(2*x^3-x+2)^(2/3)/x^6/(2*x^3+x-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{-\frac{6}{5} x +\frac{6}{5}+\frac{21}{5} x^{6}+\frac{3}{10} x^{2}+\frac{27}{5} x^{3}-\frac{27}{10} x^{4}}{x^{5} \left(2 x^{3}-x +2\right)^{\frac{1}{3}}}+8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+16 \textit{\_Z}^{2}\right) \ln \left(-\frac{24 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} x^{3}+64 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+16 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}-16 \left(2 x^{3}-x +2\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x +8 \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \left(2 x^{3}-x +2\right)^{\frac{1}{3}} x^{2}+40 \left(2 x^{3}-x +2\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right) x^{2}-6 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{3}-16 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+16 \textit{\_Z}^{2}\right) x^{3}+2 \left(2 x^{3}-x +2\right)^{\frac{2}{3}} x +3 \RootOf \left(\textit{\_Z}^{3}-2\right) x +8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+16 \textit{\_Z}^{2}\right) x -6 \RootOf \left(\textit{\_Z}^{3}-2\right)-16 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+16 \textit{\_Z}^{2}\right)}{2 x^{3}+x -2}\right)+2 \RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(\frac{8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} x^{3}+16 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+16 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}-12 \left(2 x^{3}-x +2\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+16 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right) x^{2}+6 \RootOf \left(\textit{\_Z}^{3}-2\right) x^{3}+12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+16 \textit{\_Z}^{2}\right) x^{3}-3 \left(2 x^{3}-x +2\right)^{\frac{2}{3}} x -\RootOf \left(\textit{\_Z}^{3}-2\right) x -2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+16 \textit{\_Z}^{2}\right) x +2 \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+16 \textit{\_Z}^{2}\right)}{2 x^{3}+x -2}\right)$&$671$\\ trager&$\text{Expression too large to display}$&$1499$\\ \hline \end{longtable}"," ",0,"3/10*(14*x^6-9*x^4+18*x^3+x^2-4*x+4)/x^5/(2*x^3-x+2)^(1/3)+8*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*ln(-(24*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*RootOf(_Z^3-2)^3*x^3+64*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-16*(2*x^3-x+2)^(2/3)*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*RootOf(_Z^3-2)^2*x+8*RootOf(_Z^3-2)^2*(2*x^3-x+2)^(1/3)*x^2+40*(2*x^3-x+2)^(1/3)*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*RootOf(_Z^3-2)*x^2-6*RootOf(_Z^3-2)*x^3-16*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*x^3+2*(2*x^3-x+2)^(2/3)*x+3*RootOf(_Z^3-2)*x+8*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*x-6*RootOf(_Z^3-2)-16*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2))/(2*x^3+x-2))+2*RootOf(_Z^3-2)*ln((8*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*RootOf(_Z^3-2)^3*x^3+16*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-12*(2*x^3-x+2)^(1/3)*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*RootOf(_Z^3-2)*x^2+6*RootOf(_Z^3-2)*x^3+12*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*x^3-3*(2*x^3-x+2)^(2/3)*x-RootOf(_Z^3-2)*x-2*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2)*x+2*RootOf(_Z^3-2)+4*RootOf(RootOf(_Z^3-2)^2+4*_Z*RootOf(_Z^3-2)+16*_Z^2))/(2*x^3+x-2))","C"
2212,1,886,118,18.086000," ","int((x^3+1)^(2/3)*(x^3+2)/x^6/(x^6-x^3-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x^{6}+2 x^{3}+1}{5 x^{5} \left(x^{3}+1\right)^{\frac{1}{3}}}-\frac{\ln \left(\frac{6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+324 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-18\right)^{3} x^{3}-162 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+324 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-18\right)^{2} x^{3}-42 \left(x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}-18\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+324 \textit{\_Z}^{2}\right) x +\RootOf \left(\textit{\_Z}^{3}-18\right)^{2} \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}+144 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-18\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+324 \textit{\_Z}^{2}\right) x^{2}+10 \RootOf \left(\textit{\_Z}^{3}-18\right) x^{3}-270 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+324 \textit{\_Z}^{2}\right) x^{3}-48 x \left(x^{3}+1\right)^{\frac{2}{3}}+4 \RootOf \left(\textit{\_Z}^{3}-18\right)-108 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+324 \textit{\_Z}^{2}\right)}{x^{3}-2}\right) \RootOf \left(\textit{\_Z}^{3}-18\right)}{18}-\ln \left(\frac{6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+324 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-18\right)^{3} x^{3}-162 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+324 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-18\right)^{2} x^{3}-42 \left(x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}-18\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+324 \textit{\_Z}^{2}\right) x +\RootOf \left(\textit{\_Z}^{3}-18\right)^{2} \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}+144 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-18\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+324 \textit{\_Z}^{2}\right) x^{2}+10 \RootOf \left(\textit{\_Z}^{3}-18\right) x^{3}-270 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+324 \textit{\_Z}^{2}\right) x^{3}-48 x \left(x^{3}+1\right)^{\frac{2}{3}}+4 \RootOf \left(\textit{\_Z}^{3}-18\right)-108 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+324 \textit{\_Z}^{2}\right)}{x^{3}-2}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+324 \textit{\_Z}^{2}\right)+\frac{\RootOf \left(\textit{\_Z}^{3}-18\right) \ln \left(\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+324 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-18\right)^{3} x^{3}+135 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+324 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-18\right)^{2} x^{3}+21 \left(x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}-18\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+324 \textit{\_Z}^{2}\right) x +4 \RootOf \left(\textit{\_Z}^{3}-18\right)^{2} \left(x^{3}+1\right)^{\frac{1}{3}} x^{2}+9 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-18\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+324 \textit{\_Z}^{2}\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{3}-18\right) x^{3}-90 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+324 \textit{\_Z}^{2}\right) x^{3}-3 x \left(x^{3}+1\right)^{\frac{2}{3}}-2 \RootOf \left(\textit{\_Z}^{3}-18\right)-90 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+324 \textit{\_Z}^{2}\right)}{x^{3}-2}\right)}{18}$&$886$\\ trager&$\text{Expression too large to display}$&$1108$\\ \hline \end{longtable}"," ",0,"1/5*(x^6+2*x^3+1)/x^5/(x^3+1)^(1/3)-1/18*ln((6*RootOf(RootOf(_Z^3-18)^2+18*_Z*RootOf(_Z^3-18)+324*_Z^2)*RootOf(_Z^3-18)^3*x^3-162*RootOf(RootOf(_Z^3-18)^2+18*_Z*RootOf(_Z^3-18)+324*_Z^2)^2*RootOf(_Z^3-18)^2*x^3-42*(x^3+1)^(2/3)*RootOf(_Z^3-18)^2*RootOf(RootOf(_Z^3-18)^2+18*_Z*RootOf(_Z^3-18)+324*_Z^2)*x+RootOf(_Z^3-18)^2*(x^3+1)^(1/3)*x^2+144*(x^3+1)^(1/3)*RootOf(_Z^3-18)*RootOf(RootOf(_Z^3-18)^2+18*_Z*RootOf(_Z^3-18)+324*_Z^2)*x^2+10*RootOf(_Z^3-18)*x^3-270*RootOf(RootOf(_Z^3-18)^2+18*_Z*RootOf(_Z^3-18)+324*_Z^2)*x^3-48*x*(x^3+1)^(2/3)+4*RootOf(_Z^3-18)-108*RootOf(RootOf(_Z^3-18)^2+18*_Z*RootOf(_Z^3-18)+324*_Z^2))/(x^3-2))*RootOf(_Z^3-18)-ln((6*RootOf(RootOf(_Z^3-18)^2+18*_Z*RootOf(_Z^3-18)+324*_Z^2)*RootOf(_Z^3-18)^3*x^3-162*RootOf(RootOf(_Z^3-18)^2+18*_Z*RootOf(_Z^3-18)+324*_Z^2)^2*RootOf(_Z^3-18)^2*x^3-42*(x^3+1)^(2/3)*RootOf(_Z^3-18)^2*RootOf(RootOf(_Z^3-18)^2+18*_Z*RootOf(_Z^3-18)+324*_Z^2)*x+RootOf(_Z^3-18)^2*(x^3+1)^(1/3)*x^2+144*(x^3+1)^(1/3)*RootOf(_Z^3-18)*RootOf(RootOf(_Z^3-18)^2+18*_Z*RootOf(_Z^3-18)+324*_Z^2)*x^2+10*RootOf(_Z^3-18)*x^3-270*RootOf(RootOf(_Z^3-18)^2+18*_Z*RootOf(_Z^3-18)+324*_Z^2)*x^3-48*x*(x^3+1)^(2/3)+4*RootOf(_Z^3-18)-108*RootOf(RootOf(_Z^3-18)^2+18*_Z*RootOf(_Z^3-18)+324*_Z^2))/(x^3-2))*RootOf(RootOf(_Z^3-18)^2+18*_Z*RootOf(_Z^3-18)+324*_Z^2)+1/18*RootOf(_Z^3-18)*ln((3*RootOf(RootOf(_Z^3-18)^2+18*_Z*RootOf(_Z^3-18)+324*_Z^2)*RootOf(_Z^3-18)^3*x^3+135*RootOf(RootOf(_Z^3-18)^2+18*_Z*RootOf(_Z^3-18)+324*_Z^2)^2*RootOf(_Z^3-18)^2*x^3+21*(x^3+1)^(2/3)*RootOf(_Z^3-18)^2*RootOf(RootOf(_Z^3-18)^2+18*_Z*RootOf(_Z^3-18)+324*_Z^2)*x+4*RootOf(_Z^3-18)^2*(x^3+1)^(1/3)*x^2+9*(x^3+1)^(1/3)*RootOf(_Z^3-18)*RootOf(RootOf(_Z^3-18)^2+18*_Z*RootOf(_Z^3-18)+324*_Z^2)*x^2-2*RootOf(_Z^3-18)*x^3-90*RootOf(RootOf(_Z^3-18)^2+18*_Z*RootOf(_Z^3-18)+324*_Z^2)*x^3-3*x*(x^3+1)^(2/3)-2*RootOf(_Z^3-18)-90*RootOf(RootOf(_Z^3-18)^2+18*_Z*RootOf(_Z^3-18)+324*_Z^2))/(x^3-2))","C"
2213,0,0,99,0.045000," ","int((a*x^6+b)/(x^3+x)^(1/3)/(c*x^6+d),x)","\[\int \frac{a \,x^{6}+b}{\left(x^{3}+x \right)^{\frac{1}{3}} \left(c \,x^{6}+d \right)}\, dx\]"," ",0,"int((a*x^6+b)/(x^3+x)^(1/3)/(c*x^6+d),x)","F"
2214,0,0,99,0.002000," ","int((a*x^6+b)/(x^3+x)^(1/3)/(c*x^6+d),x)","\[\int \frac{a \,x^{6}+b}{\left(x^{3}+x \right)^{\frac{1}{3}} \left(c \,x^{6}+d \right)}\, dx\]"," ",0,"int((a*x^6+b)/(x^3+x)^(1/3)/(c*x^6+d),x)","F"
2215,1,2074,122,14.965000," ","int(1/(2+x)/(x^2+x+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2074$\\ \hline \end{longtable}"," ",0,"1/3*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*ln((14529*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x^3+4257*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x^3-29058*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x^2-8514*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x^2+131841*(x^2+x+1)^(2/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^2*x+58116*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x+17028*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x-131841*(x^2+x+1)^(2/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^2-88233*(x^2+x+1)^(1/3)*RootOf(_Z^3-9)^2*x^2-131841*(x^2+x+1)^(1/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)*x^2+176466*(x^2+x+1)^(1/3)*RootOf(_Z^3-9)^2*x+263682*(x^2+x+1)^(1/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)*x+48430*RootOf(_Z^3-9)*x^3+14190*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x^3-88233*(x^2+x+1)^(1/3)*RootOf(_Z^3-9)^2-131841*(x^2+x+1)^(1/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)-537573*RootOf(_Z^3-9)*x^2-157509*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x^2+794097*(x^2+x+1)^(2/3)*x-246993*RootOf(_Z^3-9)*x-72369*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x-794097*(x^2+x+1)^(2/3)-440713*RootOf(_Z^3-9)-129129*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2))/(2+x)^3)-1/9*ln(-(13110*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x^3-4257*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x^3-26220*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x^2+8514*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x^2+131841*(x^2+x+1)^(2/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^2*x+52440*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x-17028*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x-131841*(x^2+x+1)^(2/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^2+44286*(x^2+x+1)^(1/3)*RootOf(_Z^3-9)^2*x^2-131841*(x^2+x+1)^(1/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)*x^2-88572*(x^2+x+1)^(1/3)*RootOf(_Z^3-9)^2*x+263682*(x^2+x+1)^(1/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)*x-4370*RootOf(_Z^3-9)*x^3+1419*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x^3+44286*(x^2+x+1)^(1/3)*RootOf(_Z^3-9)^2-131841*(x^2+x+1)^(1/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)+406410*RootOf(_Z^3-9)*x^2-131967*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x^2-398574*(x^2+x+1)^(2/3)*x+380190*RootOf(_Z^3-9)*x-123453*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x+398574*(x^2+x+1)^(2/3)+397670*RootOf(_Z^3-9)-129129*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2))/(2+x)^3)*RootOf(_Z^3-9)-1/3*ln(-(13110*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x^3-4257*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x^3-26220*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x^2+8514*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x^2+131841*(x^2+x+1)^(2/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^2*x+52440*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x-17028*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x-131841*(x^2+x+1)^(2/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^2+44286*(x^2+x+1)^(1/3)*RootOf(_Z^3-9)^2*x^2-131841*(x^2+x+1)^(1/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)*x^2-88572*(x^2+x+1)^(1/3)*RootOf(_Z^3-9)^2*x+263682*(x^2+x+1)^(1/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)*x-4370*RootOf(_Z^3-9)*x^3+1419*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x^3+44286*(x^2+x+1)^(1/3)*RootOf(_Z^3-9)^2-131841*(x^2+x+1)^(1/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)+406410*RootOf(_Z^3-9)*x^2-131967*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x^2-398574*(x^2+x+1)^(2/3)*x+380190*RootOf(_Z^3-9)*x-123453*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x+398574*(x^2+x+1)^(2/3)+397670*RootOf(_Z^3-9)-129129*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2))/(2+x)^3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)","C"
2216,1,1275,123,18.693000," ","int((-3+2*x)*(x^3+x-1)^(1/3)/x^2/(x^3-2*x+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1275$\\ risch&$\text{Expression too large to display}$&$1561$\\ \hline \end{longtable}"," ",0,"3/2*(x^3+x-1)^(1/3)/x-1/4*ln(-(11502*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)^2*RootOf(_Z^3-12)^3*x-22842*(x^3+x-1)^(2/3)*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)*RootOf(_Z^3-12)^2*x-6309*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)*RootOf(_Z^3-12)^4*x-11502*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)^2*RootOf(_Z^3-12)^3+6309*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)*RootOf(_Z^3-12)^4-24282*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)*RootOf(_Z^3-12)*x^3+13319*RootOf(_Z^3-12)^2*x^3-137052*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)*(x^3+x-1)^(1/3)*x^2+29016*(x^3+x-1)^(1/3)*RootOf(_Z^3-12)*x^2-5112*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)*RootOf(_Z^3-12)*x+58032*(x^3+x-1)^(2/3)*x+2804*RootOf(_Z^3-12)^2*x+5112*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)*RootOf(_Z^3-12)-2804*RootOf(_Z^3-12)^2)/(x^3-2*x+2))*RootOf(_Z^3-12)-9/2*ln(-(11502*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)^2*RootOf(_Z^3-12)^3*x-22842*(x^3+x-1)^(2/3)*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)*RootOf(_Z^3-12)^2*x-6309*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)*RootOf(_Z^3-12)^4*x-11502*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)^2*RootOf(_Z^3-12)^3+6309*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)*RootOf(_Z^3-12)^4-24282*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)*RootOf(_Z^3-12)*x^3+13319*RootOf(_Z^3-12)^2*x^3-137052*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)*(x^3+x-1)^(1/3)*x^2+29016*(x^3+x-1)^(1/3)*RootOf(_Z^3-12)*x^2-5112*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)*RootOf(_Z^3-12)*x+58032*(x^3+x-1)^(2/3)*x+2804*RootOf(_Z^3-12)^2*x+5112*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)*RootOf(_Z^3-12)-2804*RootOf(_Z^3-12)^2)/(x^3-2*x+2))*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)+9/2*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)*ln(-(5751*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)^2*RootOf(_Z^3-12)^3*x+11421*(x^3+x-1)^(2/3)*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)*RootOf(_Z^3-12)^2*x+3474*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)*RootOf(_Z^3-12)^4*x-5751*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)^2*RootOf(_Z^3-12)^3-3474*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)*RootOf(_Z^3-12)^4+12141*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)*RootOf(_Z^3-12)*x^3+7334*RootOf(_Z^3-12)^2*x^3+68526*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)*(x^3+x-1)^(1/3)*x^2+18315*(x^3+x-1)^(1/3)*RootOf(_Z^3-12)*x^2+6390*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)*RootOf(_Z^3-12)*x+36630*(x^3+x-1)^(2/3)*x+3860*RootOf(_Z^3-12)^2*x-6390*RootOf(RootOf(_Z^3-12)^2+18*_Z*RootOf(_Z^3-12)+324*_Z^2)*RootOf(_Z^3-12)-3860*RootOf(_Z^3-12)^2)/(x^3-2*x+2))","C"
2217,0,0,151,0.127000," ","int((-(2*a-b)*b^2+(4*a-b)*b*x-(2*a+b)*x^2+x^3)/(-a+x)/((-a+x)*(-b+x)^2)^(1/4)/(b^2+a*d-(2*b+d)*x+x^2),x)","\[\int \frac{-\left(2 a -b \right) b^{2}+\left(4 a -b \right) b x -\left(2 a +b \right) x^{2}+x^{3}}{\left(-a +x \right) \left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{4}} \left(b^{2}+a d -\left(2 b +d \right) x +x^{2}\right)}\, dx\]"," ",0,"int((-(2*a-b)*b^2+(4*a-b)*b*x-(2*a+b)*x^2+x^3)/(-a+x)/((-a+x)*(-b+x)^2)^(1/4)/(b^2+a*d-(2*b+d)*x+x^2),x)","F"
2218,0,0,67,0.057000," ","int(x^4/(a*x^4+b)^2/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{x^{4}}{\left(a \,x^{4}+b \right)^{2} \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(x^4/(a*x^4+b)^2/(a*x^4+b*x^2)^(1/4),x)","F"
2219,0,0,67,0.003000," ","int(x^4/(a*x^4+b)^2/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{x^{4}}{\left(a \,x^{4}+b \right)^{2} \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(x^4/(a*x^4+b)^2/(a*x^4+b*x^2)^(1/4),x)","F"
2220,0,0,67,0.001000," ","int(x^4/(a*x^4+b)^2/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{x^{4}}{\left(a \,x^{4}+b \right)^{2} \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(x^4/(a*x^4+b)^2/(a*x^4+b*x^2)^(1/4),x)","F"
2221,0,0,129,0.013000," ","int((a*x^4-b)*(a*x^4+b)^(3/4)/x^8/(2*a*x^4+b),x)","\[\int \frac{\left(a \,x^{4}-b \right) \left(a \,x^{4}+b \right)^{\frac{3}{4}}}{x^{8} \left(2 a \,x^{4}+b \right)}\, dx\]"," ",0,"int((a*x^4-b)*(a*x^4+b)^(3/4)/x^8/(2*a*x^4+b),x)","F"
2222,1,129,58,0.118000," ","int(x*(a*x+b)^(1/2)/(x+(c+(a*x+b)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\frac{2 \left(c +\sqrt{a x +b}\right)^{3}}{3}-2 c \left(c +\sqrt{a x +b}\right)^{2}-\frac{4 a \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}+2 c^{2} \left(c +\sqrt{a x +b}\right)+4 a \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 c \,\textit{\_Z}^{2}+a \textit{\_Z} +c^{2}-b \right)}{\sum}\frac{\left(\textit{\_R}^{3} a -\textit{\_R}^{2} b \right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-4 \textit{\_R} c +a}\right)}{a}$&$129$\\ default&$\frac{\frac{2 \left(c +\sqrt{a x +b}\right)^{3}}{3}-2 c \left(c +\sqrt{a x +b}\right)^{2}-\frac{4 a \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}+2 c^{2} \left(c +\sqrt{a x +b}\right)+4 a \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 c \,\textit{\_Z}^{2}+a \textit{\_Z} +c^{2}-b \right)}{\sum}\frac{\left(\textit{\_R}^{3} a -\textit{\_R}^{2} b \right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-4 \textit{\_R} c +a}\right)}{a}$&$129$\\ \hline \end{longtable}"," ",0,"2/a*(1/3*(c+(a*x+b)^(1/2))^3-c*(c+(a*x+b)^(1/2))^2-2/3*a*(c+(a*x+b)^(1/2))^(3/2)+c^2*(c+(a*x+b)^(1/2))+2*a*sum((_R^3*a-_R^2*b)/(4*_R^3-4*_R*c+a)*ln((c+(a*x+b)^(1/2))^(1/2)-_R),_R=RootOf(_Z^4-2*_Z^2*c+_Z*a+c^2-b)))","B"
2223,1,129,58,0.106000," ","int(x*(a*x+b)^(1/2)/(x+(c+(a*x+b)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\frac{2 \left(c +\sqrt{a x +b}\right)^{3}}{3}-2 c \left(c +\sqrt{a x +b}\right)^{2}-\frac{4 a \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}+2 c^{2} \left(c +\sqrt{a x +b}\right)+4 a \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 c \,\textit{\_Z}^{2}+a \textit{\_Z} +c^{2}-b \right)}{\sum}\frac{\left(\textit{\_R}^{3} a -\textit{\_R}^{2} b \right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-4 \textit{\_R} c +a}\right)}{a}$&$129$\\ default&$\frac{\frac{2 \left(c +\sqrt{a x +b}\right)^{3}}{3}-2 c \left(c +\sqrt{a x +b}\right)^{2}-\frac{4 a \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}+2 c^{2} \left(c +\sqrt{a x +b}\right)+4 a \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 c \,\textit{\_Z}^{2}+a \textit{\_Z} +c^{2}-b \right)}{\sum}\frac{\left(\textit{\_R}^{3} a -\textit{\_R}^{2} b \right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-4 \textit{\_R} c +a}\right)}{a}$&$129$\\ \hline \end{longtable}"," ",0,"2/a*(1/3*(c+(a*x+b)^(1/2))^3-c*(c+(a*x+b)^(1/2))^2-2/3*a*(c+(a*x+b)^(1/2))^(3/2)+c^2*(c+(a*x+b)^(1/2))+2*a*sum((_R^3*a-_R^2*b)/(4*_R^3-4*_R*c+a)*ln((c+(a*x+b)^(1/2))^(1/2)-_R),_R=RootOf(_Z^4-2*_Z^2*c+_Z*a+c^2-b)))","B"
2224,0,0,126,0.065000," ","int((1-(1-(1-1/x)^(1/2))^(1/2))^(1/2)/x,x)","\[\int \frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}}{x}\, dx\]"," ",0,"int((1-(1-(1-1/x)^(1/2))^(1/2))^(1/2)/x,x)","F"
2225,0,0,138,0.135000," ","int((-2*a*b*x+(a+b)*x^2)/(x*(-a+x)*(-b+x))^(2/3)/(a*b*d-(a+b)*d*x+(-1+d)*x^2),x)","\[\int \frac{-2 a b x +\left(a +b \right) x^{2}}{\left(x \left(-a +x \right) \left(-b +x \right)\right)^{\frac{2}{3}} \left(a b d -\left(a +b \right) d x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((-2*a*b*x+(a+b)*x^2)/(x*(-a+x)*(-b+x))^(2/3)/(a*b*d-(a+b)*d*x+(-1+d)*x^2),x)","F"
2226,0,0,130,0.005000," ","int((a*x^3-b)^(1/4)/x^7,x)","\[\int \frac{\left(a \,x^{3}-b \right)^{\frac{1}{4}}}{x^{7}}\, dx\]"," ",0,"int((a*x^3-b)^(1/4)/x^7,x)","F"
2227,0,0,128,0.009000," ","int((2*a*x^2+b)*(a*x^4+b*x^2)^(1/4)/(a*x^2-b),x)","\[\int \frac{\left(2 a \,x^{2}+b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}{a \,x^{2}-b}\, dx\]"," ",0,"int((2*a*x^2+b)*(a*x^4+b*x^2)^(1/4)/(a*x^2-b),x)","F"
2228,1,247,127,0.166000," ","int((a^4*x^4-b^4)/(a^2*x^3-b^2*x)^(1/2)/(a^4*x^4+b^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{b \sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{2 \left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}-b^{2} x}}-\frac{b \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{4} \textit{\_Z}^{4}+b^{4}\right)}{\sum}\frac{\left(a^{3} \underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b +\underline{\hspace{1.25 ex}}\alpha  a \,b^{2}-b^{3}\right) \sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{\left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, -\frac{a^{3} \underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b +\underline{\hspace{1.25 ex}}\alpha  a \,b^{2}-b^{3}}{2 b^{3}}, \frac{\sqrt{2}}{2}\right)}{\underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{x \left(a^{2} x^{2}-b^{2}\right)}}\right)}{4 a^{4}}$&$247$\\ elliptic&$\frac{b \sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{2 \left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}-b^{2} x}}-\frac{b \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{4} \textit{\_Z}^{4}+b^{4}\right)}{\sum}\frac{\left(a^{3} \underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b +\underline{\hspace{1.25 ex}}\alpha  a \,b^{2}-b^{3}\right) \sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{\left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, -\frac{a^{3} \underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b +\underline{\hspace{1.25 ex}}\alpha  a \,b^{2}-b^{3}}{2 b^{3}}, \frac{\sqrt{2}}{2}\right)}{\underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{x \left(a^{2} x^{2}-b^{2}\right)}}\right)}{4 a^{4}}$&$247$\\ \hline \end{longtable}"," ",0,"b/a*((x+b/a)/b*a)^(1/2)*(-2*(x-b/a)/b*a)^(1/2)*(-a*x/b)^(1/2)/(a^2*x^3-b^2*x)^(1/2)*EllipticF(((x+b/a)/b*a)^(1/2),1/2*2^(1/2))-1/4*b/a^4*2^(1/2)*sum(1/_alpha^3*(_alpha^3*a^3-_alpha^2*a^2*b+_alpha*a*b^2-b^3)*((x+b/a)/b*a)^(1/2)*(-(x-b/a)/b*a)^(1/2)*(-a*x/b)^(1/2)/(x*(a^2*x^2-b^2))^(1/2)*EllipticPi(((x+b/a)/b*a)^(1/2),-1/2*(_alpha^3*a^3-_alpha^2*a^2*b+_alpha*a*b^2-b^3)/b^3,1/2*2^(1/2)),_alpha=RootOf(_Z^4*a^4+b^4))","C"
2229,1,206,40,3.181000," ","int((x^5-1)/(x^4+1)^(1/2)/(x^5+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4 \sqrt{\left(x^{2}-1\right)^{2}+2 x^{2}}}\right)}{10}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-\textit{\_Z}^{2}-1\right)}{\sum}\textit{\_R} \ln \left(\left(-x^{2}+\sqrt{x^{4}+1}\right)^{2}+\left(\textit{\_R}^{2}-\textit{\_R} -1\right) \left(-x^{2}+\sqrt{x^{4}+1}\right)+\textit{\_R}^{2}-\textit{\_R} \right)\right)}{5}+\frac{\left(\frac{\ln \left(-1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{10}-\frac{\ln \left(1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{10}+\frac{4 \arctan \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{x \sqrt{\sqrt{5}+1}}\right)}{5 \sqrt{\sqrt{5}+1}}-\frac{4 \arctanh \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{x \sqrt{\sqrt{5}-1}}\right)}{5 \sqrt{\sqrt{5}-1}}\right) \sqrt{2}}{2}$&$206$\\ default&$\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4 \sqrt{x^{4}+1}}\right)}{10}+\frac{2 \left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{5 \sqrt{x^{4}+1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-\textit{\_Z} +1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{3}+x^{2}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha }\, \sqrt{x^{4}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha }}+\frac{2 \left(-1\right)^{\frac{3}{4}} \left(-\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +1\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \underline{\hspace{1.25 ex}}\alpha^{3}, i\right)}{\sqrt{x^{4}+1}}\right)\right)}{5}$&$267$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}-2\right) x +\sqrt{x^{4}+1}-\RootOf \left(\textit{\_Z}^{2}-2\right)}{\left(1+x \right)^{2}}\right)}{10}-\frac{\RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right) \ln \left(-\frac{-625 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right) \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{4} x -50 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right) \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2} x^{2}-50 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right) \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2} x +150 \sqrt{x^{4}+1}\, \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-50 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2} \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right)-4 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right) x^{2}+16 \sqrt{x^{4}+1}-4 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right)}{4 x^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2} x -4 x +4}\right)}{5}+\RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right) \ln \left(\frac{-625 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{5} x +50 x^{2} \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{3}+250 x \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{3}+30 \sqrt{x^{4}+1}\, \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}+50 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{3}-12 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right) x^{2}-24 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right) x -8 \sqrt{x^{4}+1}-12 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)}{25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2} x -4 x^{2}-4}\right)$&$563$\\ \hline \end{longtable}"," ",0,"1/10*2^(1/2)*arctanh(1/4*(2*x^2+2)*2^(1/2)/((x^2-1)^2+2*x^2)^(1/2))+1/5*sum(_R*ln((-x^2+(x^4+1)^(1/2))^2+(_R^2-_R-1)*(-x^2+(x^4+1)^(1/2))+_R^2-_R),_R=RootOf(_Z^4-_Z^2-1))+1/2*(1/10*ln(-1+1/2*2^(1/2)/x*(x^4+1)^(1/2))-1/10*ln(1+1/2*2^(1/2)/x*(x^4+1)^(1/2))+4/5/(5^(1/2)+1)^(1/2)*arctan(2^(1/2)/x*(x^4+1)^(1/2)/(5^(1/2)+1)^(1/2))-4/5/(5^(1/2)-1)^(1/2)*arctanh(2^(1/2)/x*(x^4+1)^(1/2)/(5^(1/2)-1)^(1/2)))*2^(1/2)","B"
2230,1,206,40,2.702000," ","int((x^5-1)/(x^4+1)^(1/2)/(x^5+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4 \sqrt{\left(x^{2}-1\right)^{2}+2 x^{2}}}\right)}{10}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-\textit{\_Z}^{2}-1\right)}{\sum}\textit{\_R} \ln \left(\left(-x^{2}+\sqrt{x^{4}+1}\right)^{2}+\left(\textit{\_R}^{2}-\textit{\_R} -1\right) \left(-x^{2}+\sqrt{x^{4}+1}\right)+\textit{\_R}^{2}-\textit{\_R} \right)\right)}{5}+\frac{\left(\frac{\ln \left(-1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{10}-\frac{\ln \left(1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{10}+\frac{4 \arctan \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{x \sqrt{\sqrt{5}+1}}\right)}{5 \sqrt{\sqrt{5}+1}}-\frac{4 \arctanh \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{x \sqrt{\sqrt{5}-1}}\right)}{5 \sqrt{\sqrt{5}-1}}\right) \sqrt{2}}{2}$&$206$\\ default&$\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4 \sqrt{x^{4}+1}}\right)}{10}+\frac{2 \left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{5 \sqrt{x^{4}+1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}-\textit{\_Z}^{3}+\textit{\_Z}^{2}-\textit{\_Z} +1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{3}+x^{2}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha }\, \sqrt{x^{4}+1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha }}+\frac{2 \left(-1\right)^{\frac{3}{4}} \left(-\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +1\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i \underline{\hspace{1.25 ex}}\alpha^{3}, i\right)}{\sqrt{x^{4}+1}}\right)\right)}{5}$&$267$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}-2\right) x +\RootOf \left(\textit{\_Z}^{2}-2\right)+\sqrt{x^{4}+1}}{\left(1+x \right)^{2}}\right)}{10}+\frac{\RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right) \ln \left(-\frac{625 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right) \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{4} x +50 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right) \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2} x^{2}+50 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right) \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2} x +50 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2} \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right)+4 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right) x^{2}+150 \sqrt{x^{4}+1}\, \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}+4 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right)+16 \sqrt{x^{4}+1}}{4 x^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2} x -4 x +4}\right)}{5}+\RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right) \ln \left(-\frac{625 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{5} x -50 x^{2} \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{3}-250 x \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{3}-50 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{3}-30 \sqrt{x^{4}+1}\, \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}+12 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right) x^{2}+24 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right) x +12 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)+8 \sqrt{x^{4}+1}}{25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2} x -4 x^{2}-4}\right)$&$560$\\ \hline \end{longtable}"," ",0,"1/10*2^(1/2)*arctanh(1/4*(2*x^2+2)*2^(1/2)/((x^2-1)^2+2*x^2)^(1/2))+1/5*sum(_R*ln((-x^2+(x^4+1)^(1/2))^2+(_R^2-_R-1)*(-x^2+(x^4+1)^(1/2))+_R^2-_R),_R=RootOf(_Z^4-_Z^2-1))+1/2*(1/10*ln(-1+1/2*2^(1/2)/x*(x^4+1)^(1/2))-1/10*ln(1+1/2*2^(1/2)/x*(x^4+1)^(1/2))+4/5/(5^(1/2)+1)^(1/2)*arctan(2^(1/2)/x*(x^4+1)^(1/2)/(5^(1/2)+1)^(1/2))-4/5/(5^(1/2)-1)^(1/2)*arctanh(2^(1/2)/x*(x^4+1)^(1/2)/(5^(1/2)-1)^(1/2)))*2^(1/2)","B"
2231,1,206,40,2.793000," ","int((x^5+1)/(x^4+1)^(1/2)/(x^5-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4 \sqrt{\left(x^{2}-1\right)^{2}+2 x^{2}}}\right)}{10}-\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-\textit{\_Z}^{2}-1\right)}{\sum}\textit{\_R} \ln \left(\left(-x^{2}+\sqrt{x^{4}+1}\right)^{2}+\left(\textit{\_R}^{2}-\textit{\_R} -1\right) \left(-x^{2}+\sqrt{x^{4}+1}\right)+\textit{\_R}^{2}-\textit{\_R} \right)\right)}{5}+\frac{\left(\frac{\ln \left(-1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{10}-\frac{\ln \left(1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{10}+\frac{4 \arctan \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{x \sqrt{\sqrt{5}+1}}\right)}{5 \sqrt{\sqrt{5}+1}}-\frac{4 \arctanh \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{x \sqrt{\sqrt{5}-1}}\right)}{5 \sqrt{\sqrt{5}-1}}\right) \sqrt{2}}{2}$&$206$\\ default&$\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4 \sqrt{x^{4}+1}}\right)}{10}+\frac{2 \left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{5 \sqrt{x^{4}+1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+\textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{3}+x^{2}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha }\, \sqrt{x^{4}+1}}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha }}+\frac{2 \left(-1\right)^{\frac{3}{4}} \left(-\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  -1\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i \underline{\hspace{1.25 ex}}\alpha^{3}, i\right)}{\sqrt{x^{4}+1}}\right)\right)}{5}$&$271$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}-2\right) x +\sqrt{x^{4}+1}-\RootOf \left(\textit{\_Z}^{2}-2\right)}{\left(-1+x \right)^{2}}\right)}{10}+\RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right) \ln \left(\frac{-625 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{5} x -50 x^{2} \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{3}+250 x \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{3}+30 \sqrt{x^{4}+1}\, \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-50 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{3}+12 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right) x^{2}-24 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right) x -8 \sqrt{x^{4}+1}+12 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)}{4 x^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2} x +4}\right)-\frac{\RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right) \ln \left(-\frac{-625 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right) \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{4} x +50 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right) \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2} x^{2}-50 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right) \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2} x +150 \sqrt{x^{4}+1}\, \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}+50 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2} \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right)+4 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right) x^{2}+16 \sqrt{x^{4}+1}+4 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right)}{25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2} x -4 x^{2}-4 x -4}\right)}{5}$&$562$\\ \hline \end{longtable}"," ",0,"-1/10*2^(1/2)*arctanh(1/4*(2*x^2+2)*2^(1/2)/((x^2-1)^2+2*x^2)^(1/2))-1/5*sum(_R*ln((-x^2+(x^4+1)^(1/2))^2+(_R^2-_R-1)*(-x^2+(x^4+1)^(1/2))+_R^2-_R),_R=RootOf(_Z^4-_Z^2-1))+1/2*(1/10*ln(-1+1/2*2^(1/2)/x*(x^4+1)^(1/2))-1/10*ln(1+1/2*2^(1/2)/x*(x^4+1)^(1/2))+4/5/(5^(1/2)+1)^(1/2)*arctan(2^(1/2)/x*(x^4+1)^(1/2)/(5^(1/2)+1)^(1/2))-4/5/(5^(1/2)-1)^(1/2)*arctanh(2^(1/2)/x*(x^4+1)^(1/2)/(5^(1/2)-1)^(1/2)))*2^(1/2)","B"
2232,1,206,40,2.725000," ","int((x^5+1)/(x^4+1)^(1/2)/(x^5-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4 \sqrt{\left(x^{2}-1\right)^{2}+2 x^{2}}}\right)}{10}-\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-\textit{\_Z}^{2}-1\right)}{\sum}\textit{\_R} \ln \left(\left(-x^{2}+\sqrt{x^{4}+1}\right)^{2}+\left(\textit{\_R}^{2}-\textit{\_R} -1\right) \left(-x^{2}+\sqrt{x^{4}+1}\right)+\textit{\_R}^{2}-\textit{\_R} \right)\right)}{5}+\frac{\left(\frac{\ln \left(-1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{10}-\frac{\ln \left(1+\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{2 x}\right)}{10}+\frac{4 \arctan \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{x \sqrt{\sqrt{5}+1}}\right)}{5 \sqrt{\sqrt{5}+1}}-\frac{4 \arctanh \left(\frac{\sqrt{2}\, \sqrt{x^{4}+1}}{x \sqrt{\sqrt{5}-1}}\right)}{5 \sqrt{\sqrt{5}-1}}\right) \sqrt{2}}{2}$&$206$\\ default&$\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(x \left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right), i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4 \sqrt{x^{4}+1}}\right)}{10}+\frac{2 \left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{5 \sqrt{x^{4}+1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+\textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{3}+x^{2}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha }\, \sqrt{x^{4}+1}}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha }}+\frac{2 \left(-1\right)^{\frac{3}{4}} \left(-\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  -1\right) \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i \underline{\hspace{1.25 ex}}\alpha^{3}, i\right)}{\sqrt{x^{4}+1}}\right)\right)}{5}$&$271$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}-2\right) x +\sqrt{x^{4}+1}+\RootOf \left(\textit{\_Z}^{2}-2\right)}{\left(-1+x \right)^{2}}\right)}{10}+\frac{\RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right) \ln \left(-\frac{625 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right) \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{4} x -50 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right) \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2} x^{2}+50 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right) \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2} x -50 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2} \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right)-4 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right) x^{2}+150 \sqrt{x^{4}+1}\, \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4 \RootOf \left(\textit{\_Z}^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-4\right)+16 \sqrt{x^{4}+1}}{25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2} x -4 x^{2}-4 x -4}\right)}{5}-\RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right) \ln \left(\frac{625 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{5} x +50 x^{2} \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{3}-250 x \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{3}+50 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{3}+30 \sqrt{x^{4}+1}\, \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2}-12 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right) x^{2}+24 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right) x -12 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)-8 \sqrt{x^{4}+1}}{4 x^{2}+25 \RootOf \left(625 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}-16\right)^{2} x +4}\right)$&$561$\\ \hline \end{longtable}"," ",0,"-1/10*2^(1/2)*arctanh(1/4*(2*x^2+2)*2^(1/2)/((x^2-1)^2+2*x^2)^(1/2))-1/5*sum(_R*ln((-x^2+(x^4+1)^(1/2))^2+(_R^2-_R-1)*(-x^2+(x^4+1)^(1/2))+_R^2-_R),_R=RootOf(_Z^4-_Z^2-1))+1/2*(1/10*ln(-1+1/2*2^(1/2)/x*(x^4+1)^(1/2))-1/10*ln(1+1/2*2^(1/2)/x*(x^4+1)^(1/2))+4/5/(5^(1/2)+1)^(1/2)*arctan(2^(1/2)/x*(x^4+1)^(1/2)/(5^(1/2)+1)^(1/2))-4/5/(5^(1/2)-1)^(1/2)*arctanh(2^(1/2)/x*(x^4+1)^(1/2)/(5^(1/2)-1)^(1/2)))*2^(1/2)","B"
2233,1,78,134,0.208000," ","int((a^6*x^6-b^6)/(a^4*x^4+b^4)^(1/2)/(a^6*x^6+b^6),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(-\frac{2 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a^{4} x^{4}+b^{4}}}{a b x}\right)}{3 a b}+\frac{\arctan \left(\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{2 x a b}\right)}{3 a b}\right) \sqrt{2}}{2}$&$78$\\ default&$\frac{\sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, i\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}+b^{4}}}-\frac{2 \sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, i, \frac{\sqrt{-\frac{i a^{2}}{b^{2}}}}{\sqrt{\frac{i a^{2}}{b^{2}}}}\right)}{3 \sqrt{\frac{i a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}+b^{4}}}-\frac{b^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{4} \textit{\_Z}^{4}-a^{2} b^{2} \textit{\_Z}^{2}+b^{4}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+2 b^{2}\right) \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+a^{2} x^{2}+b^{2}\right) a^{2}}{\sqrt{a^{2} b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{a^{4} x^{4}+b^{4}}}\right)}{\sqrt{a^{2} b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{2 a^{2} \underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-b^{2}\right) \sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, \frac{i \left(\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-b^{2}\right)}{b^{2}}, \frac{\sqrt{-\frac{i a^{2}}{b^{2}}}}{\sqrt{\frac{i a^{2}}{b^{2}}}}\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, b^{4} \sqrt{a^{4} x^{4}+b^{4}}}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-b^{2}\right)}\right)}{6 a^{2}}$&$441$\\ \hline \end{longtable}"," ",0,"1/2*(-2/3*2^(1/2)/a/b*arctanh(1/a/b/x*(a^4*x^4+b^4)^(1/2))+1/3/a/b*arctan(1/2*(a^4*x^4+b^4)^(1/2)*2^(1/2)/x/a/b))*2^(1/2)","A"
2234,0,0,139,0.129000," ","int((-2*a*b+(a+b)*x)/(x*(-a+x)*(-b+x))^(1/3)/(a*b*d-(a+b)*d*x+(-1+d)*x^2),x)","\[\int \frac{-2 a b +\left(a +b \right) x}{\left(x \left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{3}} \left(a b d -\left(a +b \right) d x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((-2*a*b+(a+b)*x)/(x*(-a+x)*(-b+x))^(1/3)/(a*b*d-(a+b)*d*x+(-1+d)*x^2),x)","F"
2235,0,0,131,0.005000," ","int(1/x^7/(a*x^3-b)^(3/4),x)","\[\int \frac{1}{x^{7} \left(a \,x^{3}-b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x^7/(a*x^3-b)^(3/4),x)","F"
2236,0,0,131,0.005000," ","int(1/x^7/(a*x^3-b)^(1/4),x)","\[\int \frac{1}{x^{7} \left(a \,x^{3}-b \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/x^7/(a*x^3-b)^(1/4),x)","F"
2237,1,3893,126,27.198000," ","int((x^2+1)/(x^2-1)/(x^4+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$3893$\\ \hline \end{longtable}"," ",0,"-1/4*ln((103270595614550*RootOf(_Z^3-4)*x^5+4019307231787848*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x^2+193570532266839*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x+2144315288715600*RootOf(_Z^3-4)*x^4-206541191229100*RootOf(_Z^3-4)*x^3+2144315288715600*RootOf(_Z^3-4)*x^2+103270595614550*RootOf(_Z^3-4)*x+1106640125761716*(x^4+x^2)^(2/3)+4019307231787848*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x^4-387141064533678*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x^3+193570532266839*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x^5+86997992030040*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x+46413750838000*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x-78298192827036*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^4-41772375754200*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^4-173995984060080*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^3-92827501676000*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^3+112141044506364*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^4*x^3-78298192827036*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^2-41772375754200*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^2-548711573636490*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^3*x^2-280352611265910*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^4*x^2+219484629454596*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^3*(x^4+x^2)^(1/3)*x+797336343950328*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*(x^4+x^2)^(2/3)*RootOf(_Z^3-4)^2*x^2+112141044506364*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^4*(x^4+x^2)^(1/3)*x+242958643915260*(x^4+x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2*x+2085103979818662*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)*x^3-219484629454596*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)*x^2+2085103979818662*(x^4+x^2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)*x+122536959111840*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*(x^4+x^2)^(2/3)*RootOf(_Z^3-4)^4*x^2-306342397779600*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^4*(x^4+x^2)^(2/3)*x+219484629454596*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^3*x^3+86997992030040*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^5+46413750838000*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^5+1065339922810458*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^2*x+122536959111840*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^4*(x^4+x^2)^(2/3)+1065339922810458*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^2*x^3+797336343950328*(x^4+x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2-112141044506364*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^2*x^2+1721440195629336*(x^4+x^2)^(2/3)*x+1106640125761716*(x^4+x^2)^(2/3)*x^2)/(-1+x)^2/(1+x)^2/x)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)-1/4*ln((103270595614550*RootOf(_Z^3-4)*x^5+4019307231787848*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x^2+193570532266839*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x+2144315288715600*RootOf(_Z^3-4)*x^4-206541191229100*RootOf(_Z^3-4)*x^3+2144315288715600*RootOf(_Z^3-4)*x^2+103270595614550*RootOf(_Z^3-4)*x+1106640125761716*(x^4+x^2)^(2/3)+4019307231787848*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x^4-387141064533678*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x^3+193570532266839*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x^5+86997992030040*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x+46413750838000*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x-78298192827036*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^4-41772375754200*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^4-173995984060080*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^3-92827501676000*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^3+112141044506364*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^4*x^3-78298192827036*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^2-41772375754200*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^2-548711573636490*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^3*x^2-280352611265910*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^4*x^2+219484629454596*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^3*(x^4+x^2)^(1/3)*x+797336343950328*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*(x^4+x^2)^(2/3)*RootOf(_Z^3-4)^2*x^2+112141044506364*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^4*(x^4+x^2)^(1/3)*x+242958643915260*(x^4+x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2*x+2085103979818662*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)*x^3-219484629454596*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)*x^2+2085103979818662*(x^4+x^2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)*x+122536959111840*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*(x^4+x^2)^(2/3)*RootOf(_Z^3-4)^4*x^2-306342397779600*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^4*(x^4+x^2)^(2/3)*x+219484629454596*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^3*x^3+86997992030040*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^5+46413750838000*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^5+1065339922810458*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^2*x+122536959111840*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^4*(x^4+x^2)^(2/3)+1065339922810458*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^2*x^3+797336343950328*(x^4+x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2-112141044506364*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^2*x^2+1721440195629336*(x^4+x^2)^(2/3)*x+1106640125761716*(x^4+x^2)^(2/3)*x^2)/(-1+x)^2/(1+x)^2/x)*RootOf(_Z^3-4)+1/4*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*ln((72037028115871*RootOf(_Z^3-4)*x^5-4332500003095992*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x^2+154421435853321*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x-2021095211363592*RootOf(_Z^3-4)*x^4-144074056231742*RootOf(_Z^3-4)*x^3-2021095211363592*RootOf(_Z^3-4)*x^2+72037028115871*RootOf(_Z^3-4)*x-122113904250156*(x^4+x^2)^(2/3)-4332500003095992*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x^4-308842871706642*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x^3+154421435853321*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x^5+86997992030040*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x+40584241192040*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x-78298192827036*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^4-36525817072836*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^4-173995984060080*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^3-81168482384080*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^3+107343584948232*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^4*x^3-78298192827036*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^2-36525817072836*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^2-548711573636490*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^3*x^2-268358962370580*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^4*x^2+219484629454596*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^3*(x^4+x^2)^(1/3)*x+182959328944392*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*(x^4+x^2)^(2/3)*RootOf(_Z^3-4)^2*x^2+107343584948232*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^4*(x^4+x^2)^(1/3)*x-2693697826152060*(x^4+x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2*x-1207165462000278*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)*x^3-1975361665091364*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)*x^2-1207165462000278*(x^4+x^2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)*x+122536959111840*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*(x^4+x^2)^(2/3)*RootOf(_Z^3-4)^4*x^2-306342397779600*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^4*(x^4+x^2)^(2/3)*x+219484629454596*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^3*x^3+86997992030040*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^5+40584241192040*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^5-590389717215276*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^2*x+122536959111840*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^4*(x^4+x^2)^(2/3)-590389717215276*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^2*x^3+182959328944392*(x^4+x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2-966092264534088*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^2*x^2-4151872744505304*(x^4+x^2)^(2/3)*x-122113904250156*(x^4+x^2)^(2/3)*x^2)/(-1+x)^2/(1+x)^2/x)","C"
2238,1,808,129,123.727000," ","int((x^4-1)^(2/3)*(x^4+3)*(2*x^4-x^3-2)/x^6/(2*x^4+3*x^3-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\frac{3}{5} x^{8}-3 x^{7}-\frac{6}{5} x^{4}+3 x^{3}+\frac{3}{5}}{x^{5} \left(x^{4}-1\right)^{\frac{1}{3}}}-\ln \left(-\frac{-6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{3}+2 \left(x^{4}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x -\left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{2}-12 \left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right) x^{2}-12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right) x^{4}+18 x^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right)-12 \left(x^{4}-1\right)^{\frac{2}{3}} x +12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right)}{2 x^{4}+3 x^{3}-2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)-6 \ln \left(-\frac{-6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{3}+2 \left(x^{4}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x -\left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{2}-12 \left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right) x^{2}-12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right) x^{4}+18 x^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right)-12 \left(x^{4}-1\right)^{\frac{2}{3}} x +12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right)}{2 x^{4}+3 x^{3}-2}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right)+\RootOf \left(\textit{\_Z}^{3}+18\right) \ln \left(\frac{-3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{3}+\left(x^{4}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x +\left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{2}+3 \left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right) x^{2}+6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right) x^{4}+3 \left(x^{4}-1\right)^{\frac{2}{3}} x -6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right)}{2 x^{4}+3 x^{3}-2}\right)$&$808$\\ trager&$\frac{3 \left(x^{4}-1\right)^{\frac{2}{3}} \left(x^{4}-5 x^{3}-1\right)}{5 x^{5}}+576 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+576 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+331776 \textit{\_Z}^{2}\right) \ln \left(-\frac{86999040 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+576 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+331776 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{4}-96896 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+576 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+331776 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{3} x^{4}-163123200 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+576 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+331776 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{3}+181680 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+576 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+331776 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{3} x^{3}+96192 \left(x^{4}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+576 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+331776 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x +3712608 \left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+576 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+331776 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right) x^{2}-501 \left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{2}+679680 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+576 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+331776 \textit{\_Z}^{2}\right) x^{4}-757 \RootOf \left(\textit{\_Z}^{3}+18\right) x^{4}-86999040 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+576 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+331776 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+96896 \RootOf \left(\textit{\_Z}^{3}+18\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+576 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+331776 \textit{\_Z}^{2}\right)+4078080 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+576 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+331776 \textit{\_Z}^{2}\right) x^{3}-4542 \RootOf \left(\textit{\_Z}^{3}+18\right) x^{3}-41679 \left(x^{4}-1\right)^{\frac{2}{3}} x -679680 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+576 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+331776 \textit{\_Z}^{2}\right)+757 \RootOf \left(\textit{\_Z}^{3}+18\right)}{2 x^{4}+3 x^{3}-2}\right)+\RootOf \left(\textit{\_Z}^{3}+18\right) \ln \left(\frac{-55812096 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+576 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+331776 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{4}+151040 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+576 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+331776 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{3} x^{4}+104647680 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+576 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+331776 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{3}-283200 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+576 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+331776 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{3} x^{3}+96192 \left(x^{4}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+576 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+331776 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x -4001184 \left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+576 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+331776 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right) x^{2}-501 \left(x^{4}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{2}+2180160 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+576 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+331776 \textit{\_Z}^{2}\right) x^{4}-5900 \RootOf \left(\textit{\_Z}^{3}+18\right) x^{4}+55812096 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+576 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+331776 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2}-151040 \RootOf \left(\textit{\_Z}^{3}+18\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+576 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+331776 \textit{\_Z}^{2}\right)-654048 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+576 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+331776 \textit{\_Z}^{2}\right) x^{3}+1770 \RootOf \left(\textit{\_Z}^{3}+18\right) x^{3}+38673 \left(x^{4}-1\right)^{\frac{2}{3}} x -2180160 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+576 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+331776 \textit{\_Z}^{2}\right)+5900 \RootOf \left(\textit{\_Z}^{3}+18\right)}{2 x^{4}+3 x^{3}-2}\right)$&$992$\\ \hline \end{longtable}"," ",0,"3/5*(x^8-5*x^7-2*x^4+5*x^3+1)/x^5/(x^4-1)^(1/3)-ln(-(-6*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)^2*RootOf(_Z^3+18)^2*x^3+2*(x^4-1)^(2/3)*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)*RootOf(_Z^3+18)^2*x-(x^4-1)^(1/3)*RootOf(_Z^3+18)^2*x^2-12*(x^4-1)^(1/3)*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)*RootOf(_Z^3+18)*x^2-12*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)*x^4+18*x^3*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)-12*(x^4-1)^(2/3)*x+12*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2))/(2*x^4+3*x^3-2))*RootOf(_Z^3+18)-6*ln(-(-6*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)^2*RootOf(_Z^3+18)^2*x^3+2*(x^4-1)^(2/3)*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)*RootOf(_Z^3+18)^2*x-(x^4-1)^(1/3)*RootOf(_Z^3+18)^2*x^2-12*(x^4-1)^(1/3)*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)*RootOf(_Z^3+18)*x^2-12*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)*x^4+18*x^3*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)-12*(x^4-1)^(2/3)*x+12*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2))/(2*x^4+3*x^3-2))*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)+RootOf(_Z^3+18)*ln((-3*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)^2*RootOf(_Z^3+18)^2*x^3+(x^4-1)^(2/3)*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)*RootOf(_Z^3+18)^2*x+(x^4-1)^(1/3)*RootOf(_Z^3+18)^2*x^2+3*(x^4-1)^(1/3)*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)*RootOf(_Z^3+18)*x^2+6*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)*x^4+3*(x^4-1)^(2/3)*x-6*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2))/(2*x^4+3*x^3-2))","C"
2239,0,0,131,0.006000," ","int(1/x^9/(a*x^4-b)^(3/4),x)","\[\int \frac{1}{x^{9} \left(a \,x^{4}-b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x^9/(a*x^4-b)^(3/4),x)","F"
2240,1,567,131,0.174000," ","int((a^2*x^4+c*x^2+b^2)/(a*x^3+b*x)^(1/2)/(a^2*x^4-b^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a \,x^{3}+b x}}+\frac{\left(-2 a b +c \right) \left(\frac{x}{b \sqrt{\left(x^{2}+\frac{b}{a}\right) a x}}+\frac{\sqrt{-a b}\, \sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{2 \left(x -\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{2 b a \sqrt{a \,x^{3}+b x}}\right)}{2 a}+\frac{\left(2 a b +c \right) \left(\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{a b}\, a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}-\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{a b}\, a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}\right)}{2 a}$&$567$\\ elliptic&$-\frac{x \left(2 a b -c \right)}{2 a b \sqrt{\left(x^{2}+\frac{b}{a}\right) a x}}+\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right)}{2 a \sqrt{a \,x^{3}+b x}}+\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, \frac{\sqrt{2}}{2}\right) c}{4 a^{2} \sqrt{a \,x^{3}+b x}\, b}+\frac{b \sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{a b}\, a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}+\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right) c}{4 a^{2} \sqrt{a b}\, \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}-\frac{\sqrt{a b}}{a}\right)}-\frac{b \sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 \sqrt{a b}\, a \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}-\frac{\sqrt{-a b}\, \sqrt{\frac{x a}{\sqrt{-a b}}+1}\, \sqrt{-\frac{2 x a}{\sqrt{-a b}}+2}\, \sqrt{-\frac{x a}{\sqrt{-a b}}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{\sqrt{-a b}}{a}\right) a}{\sqrt{-a b}}}, -\frac{\sqrt{-a b}}{a \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}, \frac{\sqrt{2}}{2}\right) c}{4 a^{2} \sqrt{a b}\, \sqrt{a \,x^{3}+b x}\, \left(-\frac{\sqrt{-a b}}{a}+\frac{\sqrt{a b}}{a}\right)}$&$827$\\ \hline \end{longtable}"," ",0,"1/a*(-a*b)^(1/2)*((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2)*(-2*(x-1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)*EllipticF(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),1/2*2^(1/2))+1/2*(-2*a*b+c)/a*(x/b/((x^2+b/a)*a*x)^(1/2)+1/2/b/a*(-a*b)^(1/2)*((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2)*(-2*(x-1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)*EllipticF(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),1/2*2^(1/2)))+1/2*(2*a*b+c)/a*(1/2/(a*b)^(1/2)/a*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)-1/a*(a*b)^(1/2)),1/2*2^(1/2))-1/2/(a*b)^(1/2)/a*(-a*b)^(1/2)*(x*a/(-a*b)^(1/2)+1)^(1/2)*(-2*x*a/(-a*b)^(1/2)+2)^(1/2)*(-x*a/(-a*b)^(1/2))^(1/2)/(a*x^3+b*x)^(1/2)/(-1/a*(-a*b)^(1/2)+1/a*(a*b)^(1/2))*EllipticPi(((x+1/a*(-a*b)^(1/2))*a/(-a*b)^(1/2))^(1/2),-1/a*(-a*b)^(1/2)/(-1/a*(-a*b)^(1/2)+1/a*(a*b)^(1/2)),1/2*2^(1/2)))","C"
2241,0,0,131,0.006000," ","int(1/x^11/(a*x^5-b)^(3/4),x)","\[\int \frac{1}{x^{11} \left(a \,x^{5}-b \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(1/x^11/(a*x^5-b)^(3/4),x)","F"
2242,1,758,137,11.180000," ","int((x^6+1)/(x^4-x^2)^(1/3)/(x^6-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{x}{\left(x^{2} \left(x^{2}-1\right)\right)^{\frac{1}{3}}}-\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{5}+12 \RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{4}+\RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{3}-54 \left(x^{4}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}+243\right)^{2} x^{3}-12 \RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{2}-54 \left(x^{4}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}+243\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x +162 x^{2} \left(x^{4}-x^{2}\right)^{\frac{2}{3}}+54 \RootOf \left(\textit{\_Z}^{6}+243\right)^{2} \left(x^{4}-x^{2}\right)^{\frac{1}{3}} x +486 \left(x^{4}-x^{2}\right)^{\frac{2}{3}} x -162 \left(x^{4}-x^{2}\right)^{\frac{2}{3}}}{\left(x^{2}-x +1\right) x \left(x^{2}+x +1\right)}\right) \RootOf \left(\textit{\_Z}^{6}+243\right)^{4}}{162}+\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{5}+12 \RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{4}+\RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{3}-54 \left(x^{4}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}+243\right)^{2} x^{3}-12 \RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{2}-54 \left(x^{4}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}+243\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x +162 x^{2} \left(x^{4}-x^{2}\right)^{\frac{2}{3}}+54 \RootOf \left(\textit{\_Z}^{6}+243\right)^{2} \left(x^{4}-x^{2}\right)^{\frac{1}{3}} x +486 \left(x^{4}-x^{2}\right)^{\frac{2}{3}} x -162 \left(x^{4}-x^{2}\right)^{\frac{2}{3}}}{\left(x^{2}-x +1\right) x \left(x^{2}+x +1\right)}\right) \RootOf \left(\textit{\_Z}^{6}+243\right)}{18}-\frac{\RootOf \left(\textit{\_Z}^{6}+243\right) \ln \left(\frac{-6 \left(x^{4}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}+243\right)^{5} x^{3}+\RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{5}+6 \left(x^{4}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}+243\right)^{5} x^{2}-12 \RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{4}+6 \RootOf \left(\textit{\_Z}^{6}+243\right)^{5} \left(x^{4}-x^{2}\right)^{\frac{1}{3}} x +\RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{3}-54 \left(x^{4}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}+243\right)^{2} x^{3}+12 \RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{2}+27 \RootOf \left(\textit{\_Z}^{6}+243\right) x^{5}+54 \left(x^{4}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}+243\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x -324 \RootOf \left(\textit{\_Z}^{6}+243\right) x^{4}+324 x^{2} \left(x^{4}-x^{2}\right)^{\frac{2}{3}}+54 \RootOf \left(\textit{\_Z}^{6}+243\right)^{2} \left(x^{4}-x^{2}\right)^{\frac{1}{3}} x +27 \RootOf \left(\textit{\_Z}^{6}+243\right) x^{3}-972 \left(x^{4}-x^{2}\right)^{\frac{2}{3}} x +324 \RootOf \left(\textit{\_Z}^{6}+243\right) x^{2}-324 \left(x^{4}-x^{2}\right)^{\frac{2}{3}}+27 \RootOf \left(\textit{\_Z}^{6}+243\right) x}{\left(x^{2}-x +1\right) x \left(x^{2}+x +1\right)}\right)}{9}$&$758$\\ trager&$-\frac{\left(x^{4}-x^{2}\right)^{\frac{2}{3}}}{x \left(x^{2}-1\right)}+\frac{\ln \left(\frac{-\RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{5}+12 \RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{4}-\RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{3}+54 \left(x^{4}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}+243\right)^{2} x^{3}-12 \RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{2}-54 \left(x^{4}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}+243\right)^{2} x^{2}-\RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x +162 x^{2} \left(x^{4}-x^{2}\right)^{\frac{2}{3}}-54 \RootOf \left(\textit{\_Z}^{6}+243\right)^{2} \left(x^{4}-x^{2}\right)^{\frac{1}{3}} x -486 \left(x^{4}-x^{2}\right)^{\frac{2}{3}} x -162 \left(x^{4}-x^{2}\right)^{\frac{2}{3}}}{\left(x^{2}-x +1\right) x \left(x^{2}+x +1\right)}\right) \RootOf \left(\textit{\_Z}^{6}+243\right)^{4}}{162}+\frac{\ln \left(\frac{-\RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{5}+12 \RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{4}-\RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{3}+54 \left(x^{4}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}+243\right)^{2} x^{3}-12 \RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{2}-54 \left(x^{4}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}+243\right)^{2} x^{2}-\RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x +162 x^{2} \left(x^{4}-x^{2}\right)^{\frac{2}{3}}-54 \RootOf \left(\textit{\_Z}^{6}+243\right)^{2} \left(x^{4}-x^{2}\right)^{\frac{1}{3}} x -486 \left(x^{4}-x^{2}\right)^{\frac{2}{3}} x -162 \left(x^{4}-x^{2}\right)^{\frac{2}{3}}}{\left(x^{2}-x +1\right) x \left(x^{2}+x +1\right)}\right) \RootOf \left(\textit{\_Z}^{6}+243\right)}{18}+\frac{\RootOf \left(\textit{\_Z}^{6}+243\right) \ln \left(\frac{6 \left(x^{4}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}+243\right)^{5} x^{3}+\RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{5}-6 \left(x^{4}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}+243\right)^{5} x^{2}-12 \RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{4}-6 \RootOf \left(\textit{\_Z}^{6}+243\right)^{5} \left(x^{4}-x^{2}\right)^{\frac{1}{3}} x +\RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{3}-54 \left(x^{4}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}+243\right)^{2} x^{3}+12 \RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x^{2}-27 \RootOf \left(\textit{\_Z}^{6}+243\right) x^{5}+54 \left(x^{4}-x^{2}\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}+243\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{6}+243\right)^{4} x +324 \RootOf \left(\textit{\_Z}^{6}+243\right) x^{4}+324 x^{2} \left(x^{4}-x^{2}\right)^{\frac{2}{3}}+54 \RootOf \left(\textit{\_Z}^{6}+243\right)^{2} \left(x^{4}-x^{2}\right)^{\frac{1}{3}} x -27 \RootOf \left(\textit{\_Z}^{6}+243\right) x^{3}-972 \left(x^{4}-x^{2}\right)^{\frac{2}{3}} x -324 \RootOf \left(\textit{\_Z}^{6}+243\right) x^{2}-324 \left(x^{4}-x^{2}\right)^{\frac{2}{3}}-27 \RootOf \left(\textit{\_Z}^{6}+243\right) x}{\left(x^{2}-x +1\right) x \left(x^{2}+x +1\right)}\right)}{9}$&$771$\\ \hline \end{longtable}"," ",0,"-x/(x^2*(x^2-1))^(1/3)-1/162*ln(-(RootOf(_Z^6+243)^4*x^5+12*RootOf(_Z^6+243)^4*x^4+RootOf(_Z^6+243)^4*x^3-54*(x^4-x^2)^(1/3)*RootOf(_Z^6+243)^2*x^3-12*RootOf(_Z^6+243)^4*x^2-54*(x^4-x^2)^(1/3)*RootOf(_Z^6+243)^2*x^2+RootOf(_Z^6+243)^4*x+162*x^2*(x^4-x^2)^(2/3)+54*RootOf(_Z^6+243)^2*(x^4-x^2)^(1/3)*x+486*(x^4-x^2)^(2/3)*x-162*(x^4-x^2)^(2/3))/(x^2-x+1)/x/(x^2+x+1))*RootOf(_Z^6+243)^4+1/18*ln(-(RootOf(_Z^6+243)^4*x^5+12*RootOf(_Z^6+243)^4*x^4+RootOf(_Z^6+243)^4*x^3-54*(x^4-x^2)^(1/3)*RootOf(_Z^6+243)^2*x^3-12*RootOf(_Z^6+243)^4*x^2-54*(x^4-x^2)^(1/3)*RootOf(_Z^6+243)^2*x^2+RootOf(_Z^6+243)^4*x+162*x^2*(x^4-x^2)^(2/3)+54*RootOf(_Z^6+243)^2*(x^4-x^2)^(1/3)*x+486*(x^4-x^2)^(2/3)*x-162*(x^4-x^2)^(2/3))/(x^2-x+1)/x/(x^2+x+1))*RootOf(_Z^6+243)-1/9*RootOf(_Z^6+243)*ln((-6*(x^4-x^2)^(1/3)*RootOf(_Z^6+243)^5*x^3+RootOf(_Z^6+243)^4*x^5+6*(x^4-x^2)^(1/3)*RootOf(_Z^6+243)^5*x^2-12*RootOf(_Z^6+243)^4*x^4+6*RootOf(_Z^6+243)^5*(x^4-x^2)^(1/3)*x+RootOf(_Z^6+243)^4*x^3-54*(x^4-x^2)^(1/3)*RootOf(_Z^6+243)^2*x^3+12*RootOf(_Z^6+243)^4*x^2+27*RootOf(_Z^6+243)*x^5+54*(x^4-x^2)^(1/3)*RootOf(_Z^6+243)^2*x^2+RootOf(_Z^6+243)^4*x-324*RootOf(_Z^6+243)*x^4+324*x^2*(x^4-x^2)^(2/3)+54*RootOf(_Z^6+243)^2*(x^4-x^2)^(1/3)*x+27*RootOf(_Z^6+243)*x^3-972*(x^4-x^2)^(2/3)*x+324*RootOf(_Z^6+243)*x^2-324*(x^4-x^2)^(2/3)+27*RootOf(_Z^6+243)*x)/(x^2-x+1)/x/(x^2+x+1))","C"
2243,1,341,134,0.288000," ","int((a^6*x^6-b^6)/(a^2*x^3+b^2*x)^(1/2)/(a^6*x^6+b^6),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\frac{2 x}{3 \sqrt{\left(x^{2}+\frac{b^{2}}{a^{2}}\right) a^{2} x}}+\frac{2 i b \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticF \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{3 a \sqrt{a^{2} x^{3}+b^{2} x}}+\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4} a^{4}-a^{2} b^{2} \textit{\_Z}^{2}+b^{4}\right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-2 b^{2}\right) \left(\underline{\hspace{1.25 ex}}\alpha^{3} a^{3}-i \underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b -2 \underline{\hspace{1.25 ex}}\alpha  a \,b^{2}+2 i b^{3}\right) \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, -\frac{i \underline{\hspace{1.25 ex}}\alpha^{3} a^{3}+\underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b -2 i \underline{\hspace{1.25 ex}}\alpha  a \,b^{2}-2 b^{3}}{3 b^{3}}, \frac{\sqrt{2}}{2}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-b^{2}\right) \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}\right)}{9 b \,a^{2}}$&$341$\\ default&$\frac{i b \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticF \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}+b^{2} x}}-\frac{2 b^{2} \left(\frac{x}{b^{2} \sqrt{\left(x^{2}+\frac{b^{2}}{a^{2}}\right) a^{2} x}}+\frac{i \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticF \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{2 b a \sqrt{a^{2} x^{3}+b^{2} x}}\right)}{3}-\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4} a^{4}-a^{2} b^{2} \textit{\_Z}^{2}+b^{4}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+2 b^{2}\right) \left(\underline{\hspace{1.25 ex}}\alpha^{3} a^{3}-i \underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b -2 \underline{\hspace{1.25 ex}}\alpha  a \,b^{2}+2 i b^{3}\right) \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, -\frac{i \underline{\hspace{1.25 ex}}\alpha^{3} a^{3}+\underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b -2 i \underline{\hspace{1.25 ex}}\alpha  a \,b^{2}-2 b^{3}}{3 b^{3}}, \frac{\sqrt{2}}{2}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-b^{2}\right) \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}\right)}{9 b \,a^{2}}$&$447$\\ \hline \end{longtable}"," ",0,"-2/3*x/((x^2+b^2/a^2)*a^2*x)^(1/2)+2/3*I*b/a*(-I*(x+I*b/a)/b*a)^(1/2)*2^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(a^2*x^3+b^2*x)^(1/2)*EllipticF((-I*(x+I*b/a)/b*a)^(1/2),1/2*2^(1/2))+1/9*I/b/a^2*2^(1/2)*sum((_alpha^2*a^2-2*b^2)/_alpha/(2*_alpha^2*a^2-b^2)*(-I*_alpha^2*a^2*b+_alpha^3*a^3+2*I*b^3-2*_alpha*a*b^2)*(-I*(x+I*b/a)/b*a)^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(x*(a^2*x^2+b^2))^(1/2)*EllipticPi((-I*(x+I*b/a)/b*a)^(1/2),-1/3*(I*_alpha^3*a^3+_alpha^2*a^2*b-2*I*_alpha*a*b^2-2*b^3)/b^3,1/2*2^(1/2)),_alpha=RootOf(_Z^4*a^4-_Z^2*a^2*b^2+b^4))","C"
2244,0,0,54,180.000000," ","int((a*x^2+1)/(a*x^2-1)/(a*x+(a^2*x^2+b)^(1/2))^(1/2),x)","\[\int \frac{a \,x^{2}+1}{\left(a \,x^{2}-1\right) \sqrt{a x +\sqrt{a^{2} x^{2}+b}}}\, dx\]"," ",0,"int((a*x^2+1)/(a*x^2-1)/(a*x+(a^2*x^2+b)^(1/2))^(1/2),x)","F"
2245,0,0,145,0.044000," ","int((-a/b^2+a^2*x^2/b^2)^(1/2)/x^2/(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{-\frac{a}{b^{2}}+\frac{a^{2} x^{2}}{b^{2}}}}{x^{2} \sqrt{a \,x^{2}+b x \sqrt{-\frac{a}{b^{2}}+\frac{a^{2} x^{2}}{b^{2}}}}}\, dx\]"," ",0,"int((-a/b^2+a^2*x^2/b^2)^(1/2)/x^2/(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2),x)","F"
2246,1,1164,124,0.382000," ","int((p*x^3-2*q)*(p*x^3+q)^(1/2)/(b*x^4+a*(p*x^3+q)^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}}{-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{p \left(-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right)}}\right)}{3 a p \sqrt{p \,x^{3}+q}}-\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,p^{2} \textit{\_Z}^{6}+2 a q p \,\textit{\_Z}^{3}+b \,\textit{\_Z}^{4}+a \,q^{2}\right)}{\sum}\frac{\left(3 \underline{\hspace{1.25 ex}}\alpha^{3} a p q +\underline{\hspace{1.25 ex}}\alpha^{4} b +3 a \,q^{2}\right) \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i p \left(2 x +\frac{-i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}+\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{p \left(x -\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{-3 \left(-q \,p^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i p \left(2 x +\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}+\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{2 \left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \left(2 q \,p^{2} \left(a \,p^{2} \underline{\hspace{1.25 ex}}\alpha^{4}+a q p \underline{\hspace{1.25 ex}}\alpha  +b \,\underline{\hspace{1.25 ex}}\alpha^{2}\right)+i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a q \,p^{2}+\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{5} a \,p^{3}+i \left(-q \,p^{2}\right)^{\frac{2}{3}} p^{3} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5} a -i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, q b +i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} p b -\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{3} a \,p^{3} q +\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a \,p^{2} q +i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, a \,q^{2} p^{2}+\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{3} b p +i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  q p b +i \left(-q \,p^{2}\right)^{\frac{1}{3}} p^{3} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} a q -\left(-q \,p^{2}\right)^{\frac{1}{3}} a \,p^{2} q^{2}-\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  b p q -\left(-q \,p^{2}\right)^{\frac{2}{3}} b q \right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a \,p^{3} q +i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  b -2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} b p -3 p^{4} \underline{\hspace{1.25 ex}}\alpha^{5} a +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5} a \,p^{4}+3 \left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{3} a \,p^{2}-2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a \,p^{2} q +i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, a p q -i \sqrt{3}\, b p q +i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} a \,p^{2}-3 p^{3} \underline{\hspace{1.25 ex}}\alpha^{2} a q -2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{4} a \,p^{3}-3 \underline{\hspace{1.25 ex}}\alpha^{3} p^{2} b +3 \left(-q \,p^{2}\right)^{\frac{2}{3}} a q p +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} b \,p^{2}+3 \left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  b +3 b p q}{2 p q b}, \sqrt{\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{p \left(-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right)}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha^{2} \left(3 \underline{\hspace{1.25 ex}}\alpha^{3} a \,p^{2}+3 a q p +2 \underline{\hspace{1.25 ex}}\alpha  b \right) \sqrt{p \,x^{3}+q}}\right)}{2 a \,p^{2} q^{2} b}$&$1164$\\ elliptic&$-\frac{2 i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}}{-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{p \left(-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right)}}\right)}{3 a p \sqrt{p \,x^{3}+q}}-\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,p^{2} \textit{\_Z}^{6}+2 a q p \,\textit{\_Z}^{3}+b \,\textit{\_Z}^{4}+a \,q^{2}\right)}{\sum}\frac{\left(3 \underline{\hspace{1.25 ex}}\alpha^{3} a p q +\underline{\hspace{1.25 ex}}\alpha^{4} b +3 a \,q^{2}\right) \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i p \left(2 x +\frac{-i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}+\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{p \left(x -\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{-3 \left(-q \,p^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i p \left(2 x +\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}+\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{2 \left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \left(2 q \,p^{2} \left(a \,p^{2} \underline{\hspace{1.25 ex}}\alpha^{4}+a q p \underline{\hspace{1.25 ex}}\alpha  +b \,\underline{\hspace{1.25 ex}}\alpha^{2}\right)+i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a q \,p^{2}+\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{5} a \,p^{3}+i \left(-q \,p^{2}\right)^{\frac{2}{3}} p^{3} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5} a -i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, q b +i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} p b -\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{3} a \,p^{3} q +\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a \,p^{2} q +i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, a \,q^{2} p^{2}+\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{3} b p +i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  q p b +i \left(-q \,p^{2}\right)^{\frac{1}{3}} p^{3} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} a q -\left(-q \,p^{2}\right)^{\frac{1}{3}} a \,p^{2} q^{2}-\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  b p q -\left(-q \,p^{2}\right)^{\frac{2}{3}} b q \right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a \,p^{3} q +i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  b -2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} b p -3 p^{4} \underline{\hspace{1.25 ex}}\alpha^{5} a +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5} a \,p^{4}+3 \left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{3} a \,p^{2}-2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a \,p^{2} q +i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, a p q -i \sqrt{3}\, b p q +i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} a \,p^{2}-3 p^{3} \underline{\hspace{1.25 ex}}\alpha^{2} a q -2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{4} a \,p^{3}-3 \underline{\hspace{1.25 ex}}\alpha^{3} p^{2} b +3 \left(-q \,p^{2}\right)^{\frac{2}{3}} a q p +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} b \,p^{2}+3 \left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  b +3 b p q}{2 p q b}, \sqrt{\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{p \left(-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right)}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha^{2} \left(3 \underline{\hspace{1.25 ex}}\alpha^{3} a \,p^{2}+3 a q p +2 \underline{\hspace{1.25 ex}}\alpha  b \right) \sqrt{p \,x^{3}+q}}\right)}{2 a \,p^{2} q^{2} b}$&$1164$\\ \hline \end{longtable}"," ",0,"-2/3*I/a*3^(1/2)/p*(-q*p^2)^(1/3)*(I*(x+1/2/p*(-q*p^2)^(1/3)-1/2*I*3^(1/2)/p*(-q*p^2)^(1/3))*3^(1/2)*p/(-q*p^2)^(1/3))^(1/2)*((x-1/p*(-q*p^2)^(1/3))/(-3/2/p*(-q*p^2)^(1/3)+1/2*I*3^(1/2)/p*(-q*p^2)^(1/3)))^(1/2)*(-I*(x+1/2/p*(-q*p^2)^(1/3)+1/2*I*3^(1/2)/p*(-q*p^2)^(1/3))*3^(1/2)*p/(-q*p^2)^(1/3))^(1/2)/(p*x^3+q)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2/p*(-q*p^2)^(1/3)-1/2*I*3^(1/2)/p*(-q*p^2)^(1/3))*3^(1/2)*p/(-q*p^2)^(1/3))^(1/2),(I*3^(1/2)/p*(-q*p^2)^(1/3)/(-3/2/p*(-q*p^2)^(1/3)+1/2*I*3^(1/2)/p*(-q*p^2)^(1/3)))^(1/2))-1/2*I/a/p^2/q^2/b*2^(1/2)*sum((3*_alpha^3*a*p*q+_alpha^4*b+3*a*q^2)/_alpha^2/(3*_alpha^3*a*p^2+3*a*p*q+2*_alpha*b)*(-q*p^2)^(1/3)*(1/2*I*p*(2*x+1/p*(-I*3^(1/2)*(-q*p^2)^(1/3)+(-q*p^2)^(1/3)))/(-q*p^2)^(1/3))^(1/2)*(p*(x-1/p*(-q*p^2)^(1/3))/(-3*(-q*p^2)^(1/3)+I*3^(1/2)*(-q*p^2)^(1/3)))^(1/2)*(-1/2*I*p*(2*x+1/p*(I*3^(1/2)*(-q*p^2)^(1/3)+(-q*p^2)^(1/3)))/(-q*p^2)^(1/3))^(1/2)/(p*x^3+q)^(1/2)*(2*q*p^2*(_alpha^4*a*p^2+_alpha*a*p*q+_alpha^2*b)+I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^2*a*q*p^2+(-q*p^2)^(2/3)*_alpha^5*a*p^3+I*(-q*p^2)^(2/3)*p^3*3^(1/2)*_alpha^5*a-I*(-q*p^2)^(2/3)*3^(1/2)*q*b+I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^3*p*b-(-q*p^2)^(1/3)*_alpha^3*a*p^3*q+(-q*p^2)^(2/3)*_alpha^2*a*p^2*q+I*(-q*p^2)^(1/3)*3^(1/2)*a*q^2*p^2+(-q*p^2)^(2/3)*_alpha^3*b*p+I*(-q*p^2)^(1/3)*3^(1/2)*_alpha*q*p*b+I*(-q*p^2)^(1/3)*p^3*3^(1/2)*_alpha^3*a*q-(-q*p^2)^(1/3)*a*p^2*q^2-(-q*p^2)^(1/3)*_alpha*b*p*q-(-q*p^2)^(2/3)*b*q)*EllipticPi(1/3*3^(1/2)*(I*(x+1/2/p*(-q*p^2)^(1/3)-1/2*I*3^(1/2)/p*(-q*p^2)^(1/3))*3^(1/2)*p/(-q*p^2)^(1/3))^(1/2),1/2/p/q*(I*3^(1/2)*_alpha^2*a*p^3*q+I*(-q*p^2)^(2/3)*3^(1/2)*_alpha*b-2*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha^2*b*p-3*p^4*_alpha^5*a+I*3^(1/2)*_alpha^5*a*p^4+3*(-q*p^2)^(2/3)*_alpha^3*a*p^2-2*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha*a*p^2*q+I*(-q*p^2)^(2/3)*3^(1/2)*a*p*q-I*3^(1/2)*b*p*q+I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^3*a*p^2-3*p^3*_alpha^2*a*q-2*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha^4*a*p^3-3*_alpha^3*p^2*b+3*(-q*p^2)^(2/3)*a*q*p+I*3^(1/2)*_alpha^3*b*p^2+3*(-q*p^2)^(2/3)*_alpha*b+3*b*p*q)/b,(I*3^(1/2)/p*(-q*p^2)^(1/3)/(-3/2/p*(-q*p^2)^(1/3)+1/2*I*3^(1/2)/p*(-q*p^2)^(1/3)))^(1/2)),_alpha=RootOf(_Z^6*a*p^2+2*_Z^3*a*p*q+_Z^4*b+a*q^2))","C"
2247,0,0,140,0.021000," ","int(x^4*(x^4+1)^(1/2)*(x^2+(x^4+1)^(1/2))^(1/2),x)","\[\int x^{4} \sqrt{x^{4}+1}\, \sqrt{x^{2}+\sqrt{x^{4}+1}}\, dx\]"," ",0,"int(x^4*(x^4+1)^(1/2)*(x^2+(x^4+1)^(1/2))^(1/2),x)","F"
2248,0,0,124,0.033000," ","int((p*x^5+q)^(1/2)*(3*p*x^5-2*q)/(b*x^4+a*(p*x^5+q)^2),x)","\[\int \frac{\sqrt{p \,x^{5}+q}\, \left(3 p \,x^{5}-2 q \right)}{b \,x^{4}+a \left(p \,x^{5}+q \right)^{2}}\, dx\]"," ",0,"int((p*x^5+q)^(1/2)*(3*p*x^5-2*q)/(b*x^4+a*(p*x^5+q)^2),x)","F"
2249,1,1552,128,8.262000," ","int((-3+x)/(-x^2+1)^(1/3)/(x^2+3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1552$\\ \hline \end{longtable}"," ",0,"RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*ln((-6*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^2-8*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^2+18*(-x^2+1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2-18*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x-24*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x+3*(-x^2+1)^(1/3)*RootOf(_Z^3+2)^2*x+18*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x+3*(-x^2+1)^(1/3)*RootOf(_Z^3+2)^2+18*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)+3*RootOf(_Z^3+2)*x^2+4*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^2-6*(-x^2+1)^(2/3)+18*RootOf(_Z^3+2)*x+24*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x-9*RootOf(_Z^3+2)-12*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2))/(2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x-x+3)/(2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x-x-3))-1/2*ln(-(-2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^2+8*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^2+18*(-x^2+1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2-6*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x+24*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x+6*(-x^2+1)^(1/3)*RootOf(_Z^3+2)^2*x+18*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x+6*(-x^2+1)^(1/3)*RootOf(_Z^3+2)^2+18*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)+RootOf(_Z^3+2)*x^2-4*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^2-12*(-x^2+1)^(2/3)+3*RootOf(_Z^3+2)-12*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2))/(2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x-x+3)/(2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x-x-3))*RootOf(_Z^3+2)-ln(-(-2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^2+8*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^2+18*(-x^2+1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2-6*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x+24*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x+6*(-x^2+1)^(1/3)*RootOf(_Z^3+2)^2*x+18*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x+6*(-x^2+1)^(1/3)*RootOf(_Z^3+2)^2+18*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)+RootOf(_Z^3+2)*x^2-4*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^2-12*(-x^2+1)^(2/3)+3*RootOf(_Z^3+2)-12*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2))/(2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x-x+3)/(2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x-x-3))*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)","C"
2250,0,0,154,0.062000," ","int(x^3*(-3*a*b+(a+2*b)*x)/(-a+x)/(-b+x)/(x*(-a+x)*(-b+x)^2)^(1/4)/(-a*b^2*d+b*(2*a+b)*d*x-(a+2*b)*d*x^2+(-1+d)*x^3),x)","\[\int \frac{x^{3} \left(-3 a b +\left(a +2 b \right) x \right)}{\left(-a +x \right) \left(-b +x \right) \left(x \left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{4}} \left(-a \,b^{2} d +b \left(2 a +b \right) d x -\left(a +2 b \right) d \,x^{2}+\left(-1+d \right) x^{3}\right)}\, dx\]"," ",0,"int(x^3*(-3*a*b+(a+2*b)*x)/(-a+x)/(-b+x)/(x*(-a+x)*(-b+x)^2)^(1/4)/(-a*b^2*d+b*(2*a+b)*d*x-(a+2*b)*d*x^2+(-1+d)*x^3),x)","F"
2251,0,0,142,0.047000," ","int((a*x+(a^2*x^2+b^2)^(1/2))/(b+(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)),x)","\[\int \frac{a x +\sqrt{a^{2} x^{2}+b^{2}}}{b +\sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int((a*x+(a^2*x^2+b^2)^(1/2))/(b+(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)),x)","F"
2252,1,445,136,2.838000," ","int(1/(x^2+3)/(3*x^2+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\ln \left(-\frac{12 \RootOf \left(48 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) \left(3 x^{2}+1\right)^{\frac{1}{3}} x +6 \RootOf \left(48 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) x^{2}+\left(3 x^{2}+1\right)^{\frac{2}{3}}-12 \RootOf \left(48 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) \left(3 x^{2}+1\right)^{\frac{1}{3}}-\left(3 x^{2}+1\right)^{\frac{1}{3}} x -24 \RootOf \left(48 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) x -x^{2}+\left(3 x^{2}+1\right)^{\frac{1}{3}}-6 \RootOf \left(48 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)+4 x +1}{x^{2}+3}\right)}{4}-\ln \left(-\frac{12 \RootOf \left(48 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) \left(3 x^{2}+1\right)^{\frac{1}{3}} x +6 \RootOf \left(48 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) x^{2}+\left(3 x^{2}+1\right)^{\frac{2}{3}}-12 \RootOf \left(48 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) \left(3 x^{2}+1\right)^{\frac{1}{3}}-\left(3 x^{2}+1\right)^{\frac{1}{3}} x -24 \RootOf \left(48 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) x -x^{2}+\left(3 x^{2}+1\right)^{\frac{1}{3}}-6 \RootOf \left(48 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)+4 x +1}{x^{2}+3}\right) \RootOf \left(48 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)+\RootOf \left(48 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) \ln \left(-\frac{-24 \RootOf \left(48 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) \left(3 x^{2}+1\right)^{\frac{1}{3}} x -12 \RootOf \left(48 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) x^{2}+2 \left(3 x^{2}+1\right)^{\frac{2}{3}}+24 \RootOf \left(48 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) \left(3 x^{2}+1\right)^{\frac{1}{3}}+4 \left(3 x^{2}+1\right)^{\frac{1}{3}} x +48 \RootOf \left(48 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) x +x^{2}-4 \left(3 x^{2}+1\right)^{\frac{1}{3}}+12 \RootOf \left(48 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)-4 x -1}{x^{2}+3}\right)$&$445$\\ \hline \end{longtable}"," ",0,"1/4*ln(-(12*RootOf(48*_Z^2-12*_Z+1)*(3*x^2+1)^(1/3)*x+6*RootOf(48*_Z^2-12*_Z+1)*x^2+(3*x^2+1)^(2/3)-12*RootOf(48*_Z^2-12*_Z+1)*(3*x^2+1)^(1/3)-(3*x^2+1)^(1/3)*x-24*RootOf(48*_Z^2-12*_Z+1)*x-x^2+(3*x^2+1)^(1/3)-6*RootOf(48*_Z^2-12*_Z+1)+4*x+1)/(x^2+3))-ln(-(12*RootOf(48*_Z^2-12*_Z+1)*(3*x^2+1)^(1/3)*x+6*RootOf(48*_Z^2-12*_Z+1)*x^2+(3*x^2+1)^(2/3)-12*RootOf(48*_Z^2-12*_Z+1)*(3*x^2+1)^(1/3)-(3*x^2+1)^(1/3)*x-24*RootOf(48*_Z^2-12*_Z+1)*x-x^2+(3*x^2+1)^(1/3)-6*RootOf(48*_Z^2-12*_Z+1)+4*x+1)/(x^2+3))*RootOf(48*_Z^2-12*_Z+1)+RootOf(48*_Z^2-12*_Z+1)*ln(-(-24*RootOf(48*_Z^2-12*_Z+1)*(3*x^2+1)^(1/3)*x-12*RootOf(48*_Z^2-12*_Z+1)*x^2+2*(3*x^2+1)^(2/3)+24*RootOf(48*_Z^2-12*_Z+1)*(3*x^2+1)^(1/3)+4*(3*x^2+1)^(1/3)*x+48*RootOf(48*_Z^2-12*_Z+1)*x+x^2-4*(3*x^2+1)^(1/3)+12*RootOf(48*_Z^2-12*_Z+1)-4*x-1)/(x^2+3))","C"
2253,1,721,137,28.947000," ","int((x^2+1)*(x^5+x^3)^(1/4)/x^2/(x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{5}+x^{3}\right)^{\frac{1}{4}}}{x}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{4}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}-4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(x^{5}+x^{3}\right)^{\frac{1}{4}} x^{2}-4 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \sqrt{x^{5}+x^{3}}\, x +4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(-1+x \right)^{2}}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{4}+2 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{3}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{2}+4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(x^{5}+x^{3}\right)^{\frac{1}{4}} x^{2}+4 \sqrt{x^{5}+x^{3}}\, \RootOf \left(\textit{\_Z}^{4}-2\right) x +4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(-1+x \right)^{2}}\right)}{2}-\frac{\ln \left(\frac{4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} \sqrt{x^{5}+x^{3}}\, x +4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(x^{5}+x^{3}\right)^{\frac{1}{4}} x^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right) x^{4}+2 \RootOf \left(\textit{\_Z}^{4}-2\right) x^{3}+4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}-2\right) x^{2}}{\left(1+x \right)^{2} x^{2}}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}}{4}-\frac{\ln \left(\frac{4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} \sqrt{x^{5}+x^{3}}\, x +4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \left(x^{5}+x^{3}\right)^{\frac{1}{4}} x^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right) x^{4}+2 \RootOf \left(\textit{\_Z}^{4}-2\right) x^{3}+4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}-2\right) x^{2}}{\left(1+x \right)^{2} x^{2}}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \sqrt{x^{5}+x^{3}}\, x +2 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} \sqrt{x^{5}+x^{3}}\, x -4 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right) x^{2}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{4}+\RootOf \left(\textit{\_Z}^{4}-2\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{3}-2 \RootOf \left(\textit{\_Z}^{4}-2\right) x^{3}+4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right) x^{2}}{\left(1+x \right)^{2} x^{2}}\right)}{2}$&$721$\\ risch&$\text{Expression too large to display}$&$1752$\\ \hline \end{longtable}"," ",0,"4*(x^5+x^3)^(1/4)/x+1/2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln((RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^4+2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*x^3+RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*x^2-4*RootOf(_Z^4-2)^2*(x^5+x^3)^(1/4)*x^2-4*RootOf(_Z^2+RootOf(_Z^4-2)^2)*(x^5+x^3)^(1/2)*x+4*(x^5+x^3)^(3/4))/x^2/(-1+x)^2)-1/2*RootOf(_Z^4-2)*ln((RootOf(_Z^4-2)^3*x^4+2*RootOf(_Z^4-2)^3*x^3+RootOf(_Z^4-2)^3*x^2+4*RootOf(_Z^4-2)^2*(x^5+x^3)^(1/4)*x^2+4*(x^5+x^3)^(1/2)*RootOf(_Z^4-2)*x+4*(x^5+x^3)^(3/4))/x^2/(-1+x)^2)-1/4*ln((4*RootOf(_Z^4-2)^3*(x^5+x^3)^(1/2)*x+4*RootOf(_Z^4-2)^2*(x^5+x^3)^(1/4)*x^2+RootOf(_Z^4-2)*x^4+2*RootOf(_Z^4-2)*x^3+4*(x^5+x^3)^(3/4)+RootOf(_Z^4-2)*x^2)/(1+x)^2/x^2)*RootOf(_Z^4-2)^3-1/4*ln((4*RootOf(_Z^4-2)^3*(x^5+x^3)^(1/2)*x+4*RootOf(_Z^4-2)^2*(x^5+x^3)^(1/4)*x^2+RootOf(_Z^4-2)*x^4+2*RootOf(_Z^4-2)*x^3+4*(x^5+x^3)^(3/4)+RootOf(_Z^4-2)*x^2)/(1+x)^2/x^2)*RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)+1/2*RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln(-(-2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*(x^5+x^3)^(1/2)*x+2*RootOf(_Z^4-2)^3*(x^5+x^3)^(1/2)*x-4*(x^5+x^3)^(1/4)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)*x^2+RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^4+RootOf(_Z^4-2)*x^4-2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^3-2*RootOf(_Z^4-2)*x^3+4*(x^5+x^3)^(3/4)+RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^2+RootOf(_Z^4-2)*x^2)/(1+x)^2/x^2)","C"
2254,0,0,148,180.000000," ","int((x^5+x^2+4)*(2*x^5-2*x^4-x^2-2)^(1/4)/x^2/(2*x^5-x^2-2),x)","\[\int \frac{\left(x^{5}+x^{2}+4\right) \left(2 x^{5}-2 x^{4}-x^{2}-2\right)^{\frac{1}{4}}}{x^{2} \left(2 x^{5}-x^{2}-2\right)}\, dx\]"," ",0,"int((x^5+x^2+4)*(2*x^5-2*x^4-x^2-2)^(1/4)/x^2/(2*x^5-x^2-2),x)","F"
2255,0,0,139,0.058000," ","int((x^4-1)^2*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^2,x)","\[\int \frac{\left(x^{4}-1\right)^{2} \sqrt{x^{2}+\sqrt{x^{4}+1}}}{\left(x^{4}+1\right)^{2}}\, dx\]"," ",0,"int((x^4-1)^2*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^2,x)","F"
2256,1,133,51,0.200000," ","int((x^2-1)/(1+x)^(1/2)/(x^2+1)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}-8 \sqrt{1+\sqrt{1+\sqrt{1+x}}}+\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+14 \textit{\_Z}^{8}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{4}+2\right)}{\sum}\frac{\left(-\textit{\_R}^{2}+1\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+7 \textit{\_R}^{7}+3 \textit{\_R}^{5}-2 \textit{\_R}^{3}}\right)$&$133$\\ default&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}-8 \sqrt{1+\sqrt{1+\sqrt{1+x}}}+\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+14 \textit{\_Z}^{8}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{4}+2\right)}{\sum}\frac{\left(-\textit{\_R}^{2}+1\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+7 \textit{\_R}^{7}+3 \textit{\_R}^{5}-2 \textit{\_R}^{3}}\right)$&$133$\\ \hline \end{longtable}"," ",0,"8/3*(1+(1+(1+x)^(1/2))^(1/2))^(3/2)-8*(1+(1+(1+x)^(1/2))^(1/2))^(1/2)+sum((-_R^2+1)/(_R^15-7*_R^13+18*_R^11-20*_R^9+7*_R^7+3*_R^5-2*_R^3)*ln((1+(1+(1+x)^(1/2))^(1/2))^(1/2)-_R),_R=RootOf(_Z^16-8*_Z^14+24*_Z^12-32*_Z^10+14*_Z^8+8*_Z^6-8*_Z^4+2))","B"
2257,1,133,51,0.193000," ","int((x^2-1)/(1+x)^(1/2)/(x^2+1)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}-8 \sqrt{1+\sqrt{1+\sqrt{1+x}}}+\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+14 \textit{\_Z}^{8}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{4}+2\right)}{\sum}\frac{\left(-\textit{\_R}^{2}+1\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+7 \textit{\_R}^{7}+3 \textit{\_R}^{5}-2 \textit{\_R}^{3}}\right)$&$133$\\ default&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}-8 \sqrt{1+\sqrt{1+\sqrt{1+x}}}+\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+14 \textit{\_Z}^{8}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{4}+2\right)}{\sum}\frac{\left(-\textit{\_R}^{2}+1\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+7 \textit{\_R}^{7}+3 \textit{\_R}^{5}-2 \textit{\_R}^{3}}\right)$&$133$\\ \hline \end{longtable}"," ",0,"8/3*(1+(1+(1+x)^(1/2))^(1/2))^(3/2)-8*(1+(1+(1+x)^(1/2))^(1/2))^(1/2)+sum((-_R^2+1)/(_R^15-7*_R^13+18*_R^11-20*_R^9+7*_R^7+3*_R^5-2*_R^3)*ln((1+(1+(1+x)^(1/2))^(1/2))^(1/2)-_R),_R=RootOf(_Z^16-8*_Z^14+24*_Z^12-32*_Z^10+14*_Z^8+8*_Z^6-8*_Z^4+2))","B"
2258,1,72,119,0.123000," ","int(1/(1-x^(1/2))^(1/2)-(1-x^(1/2)-x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{2 \left(1-\sqrt{x}-x \right)^{\frac{3}{2}}}{3}-\frac{\left(-2 \sqrt{x}-1\right) \sqrt{1-\sqrt{x}-x}}{4}+\frac{5 \arcsin \left(\frac{2 \sqrt{5}\, \left(\sqrt{x}+\frac{1}{2}\right)}{5}\right)}{8}+\frac{4 \left(1-\sqrt{x}\right)^{\frac{3}{2}}}{3}-4 \sqrt{1-\sqrt{x}}$&$72$\\ default&$\frac{2 \left(1-\sqrt{x}-x \right)^{\frac{3}{2}}}{3}-\frac{\left(-2 \sqrt{x}-1\right) \sqrt{1-\sqrt{x}-x}}{4}+\frac{5 \arcsin \left(\frac{2 \sqrt{5}\, \left(\sqrt{x}+\frac{1}{2}\right)}{5}\right)}{8}+\frac{4 \left(1-\sqrt{x}\right)^{\frac{3}{2}}}{3}-4 \sqrt{1-\sqrt{x}}$&$72$\\ \hline \end{longtable}"," ",0,"2/3*(1-x^(1/2)-x)^(3/2)-1/4*(-2*x^(1/2)-1)*(1-x^(1/2)-x)^(1/2)+5/8*arcsin(2/5*5^(1/2)*(x^(1/2)+1/2))+4/3*(1-x^(1/2))^(3/2)-4*(1-x^(1/2))^(1/2)","A"
2259,1,1404,133,9.610000," ","int((-5+x)/(x^2-x-2)^(1/3)/(x^2+4*x-3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1404$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^3-2)*ln(-(452*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x^2+192*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^2+1500*(x^2-x-2)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2+1130*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x+480*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x+123*(x^2-x-2)^(1/3)*RootOf(_Z^3-2)^2*x+1746*(x^2-x-2)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x+123*(x^2-x-2)^(1/3)*RootOf(_Z^3-2)^2+1746*(x^2-x-2)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)-113*RootOf(_Z^3-2)*x^2-48*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^2+1746*(x^2-x-2)^(2/3)+904*RootOf(_Z^3-2)*x+384*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x-2373*RootOf(_Z^3-2)-1008*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2))/(x^2+4*x-3))-1/2*ln((-452*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x^2-712*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^2+1500*(x^2-x-2)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2-1130*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x-1780*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x-873*(x^2-x-2)^(1/3)*RootOf(_Z^3-2)^2*x-246*(x^2-x-2)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x-873*(x^2-x-2)^(1/3)*RootOf(_Z^3-2)^2-246*(x^2-x-2)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)-565*RootOf(_Z^3-2)*x^2-890*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^2-246*(x^2-x-2)^(2/3)-226*RootOf(_Z^3-2)*x-356*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x-2373*RootOf(_Z^3-2)-3738*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2))/(x^2+4*x-3))*RootOf(_Z^3-2)-ln((-452*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x^2-712*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^2+1500*(x^2-x-2)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2-1130*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x-1780*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x-873*(x^2-x-2)^(1/3)*RootOf(_Z^3-2)^2*x-246*(x^2-x-2)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x-873*(x^2-x-2)^(1/3)*RootOf(_Z^3-2)^2-246*(x^2-x-2)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)-565*RootOf(_Z^3-2)*x^2-890*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^2-246*(x^2-x-2)^(2/3)-226*RootOf(_Z^3-2)*x-356*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x-2373*RootOf(_Z^3-2)-3738*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2))/(x^2+4*x-3))*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)","C"
2260,0,0,157,0.119000," ","int((-a+x)*(-2*a+b+x)/((-a+x)*(-b+x)^2)^(3/4)/(a+b^2*d-(2*b*d+1)*x+d*x^2),x)","\[\int \frac{\left(-a +x \right) \left(-2 a +b +x \right)}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{3}{4}} \left(a +b^{2} d -\left(2 b d +1\right) x +d \,x^{2}\right)}\, dx\]"," ",0,"int((-a+x)*(-2*a+b+x)/((-a+x)*(-b+x)^2)^(3/4)/(a+b^2*d-(2*b*d+1)*x+d*x^2),x)","F"
2261,1,1157,130,9.214000," ","int((1+x)/(x^2+4*x+1)/(-x^3+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1157$\\ \hline \end{longtable}"," ",0,"-1/6*ln((90*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x+756*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x+108*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^2-33*(-x^3+1)^(1/3)*RootOf(_Z^3-2)^2*x-90*(-x^3+1)^(1/3)*RootOf(_Z^3-2)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x+33*(-x^3+1)^(1/3)*RootOf(_Z^3-2)^2+90*(-x^3+1)^(1/3)*RootOf(_Z^3-2)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)-35*RootOf(_Z^3-2)*x^2-294*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^2+10*RootOf(_Z^3-2)*x+84*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x-30*(-x^3+1)^(2/3)-35*RootOf(_Z^3-2)-294*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2))/(x^2+4*x+1))*RootOf(_Z^3-2)-ln((90*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x+756*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x+108*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^2-33*(-x^3+1)^(1/3)*RootOf(_Z^3-2)^2*x-90*(-x^3+1)^(1/3)*RootOf(_Z^3-2)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x+33*(-x^3+1)^(1/3)*RootOf(_Z^3-2)^2+90*(-x^3+1)^(1/3)*RootOf(_Z^3-2)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)-35*RootOf(_Z^3-2)*x^2-294*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^2+10*RootOf(_Z^3-2)*x+84*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x-30*(-x^3+1)^(2/3)-35*RootOf(_Z^3-2)-294*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2))/(x^2+4*x+1))*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)+1/6*RootOf(_Z^3-2)*ln((90*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^3*x-216*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)^2*RootOf(_Z^3-2)^2*x-108*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*RootOf(_Z^3-2)^2-15*(-x^3+1)^(1/3)*RootOf(_Z^3-2)^2*x-198*(-x^3+1)^(1/3)*RootOf(_Z^3-2)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x+15*(-x^3+1)^(1/3)*RootOf(_Z^3-2)^2+198*(-x^3+1)^(1/3)*RootOf(_Z^3-2)*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)+35*RootOf(_Z^3-2)*x^2-84*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x^2+20*RootOf(_Z^3-2)*x-48*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2)*x-66*(-x^3+1)^(2/3)+35*RootOf(_Z^3-2)-84*RootOf(RootOf(_Z^3-2)^2+6*_Z*RootOf(_Z^3-2)+36*_Z^2))/(x^2+4*x+1))","C"
2262,0,0,72,0.050000," ","int(x^4/(a*x^4-b)^2/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{x^{4}}{\left(a \,x^{4}-b \right)^{2} \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(x^4/(a*x^4-b)^2/(a*x^4+b*x^2)^(1/4),x)","F"
2263,0,0,72,0.003000," ","int(x^4/(a*x^4-b)^2/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{x^{4}}{\left(a \,x^{4}-b \right)^{2} \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(x^4/(a*x^4-b)^2/(a*x^4+b*x^2)^(1/4),x)","F"
2264,0,0,72,0.003000," ","int(x^4/(a*x^4-b)^2/(a*x^4+b*x^2)^(1/4),x)","\[\int \frac{x^{4}}{\left(a \,x^{4}-b \right)^{2} \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(x^4/(a*x^4-b)^2/(a*x^4+b*x^2)^(1/4),x)","F"
2265,1,214,132,1.079000," ","int(x^8/(x^4-1)^(1/2)/(x^16-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{x}{8 \sqrt{x^{4}-1}}+\frac{i \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticF \left(i x , i\right)}{8 \sqrt{x^{4}-1}}+\frac{i \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\sqrt{2}\, \arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}\right) \sqrt{-2}}{2 \sqrt{x^{4}-1}}\right)-\frac{4 \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticPi \left(i x , \underline{\hspace{1.25 ex}}\alpha^{2}, i\right)}{\sqrt{x^{4}-1}}\right)\right)}{64}-\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{8}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{6}+x^{2}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}-1}\, \sqrt{x^{4}-1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}-1}}-\frac{2 i \underline{\hspace{1.25 ex}}\alpha^{7} \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticPi \left(i x , \underline{\hspace{1.25 ex}}\alpha^{6}, i\right)}{\sqrt{x^{4}-1}}\right)\right)}{32}$&$214$\\ elliptic&$\frac{\left(\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{x^{4}-1}}{x}+1\right)}{32}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{x^{4}-1}}{x}-1\right)}{32}+\frac{\sqrt{2}\, \ln \left(\frac{\frac{x^{4}-1}{2 x^{2}}-\frac{\sqrt{x^{4}-1}}{x}+1}{\frac{x^{4}-1}{2 x^{2}}+\frac{\sqrt{x^{4}-1}}{x}+1}\right)}{64}-\frac{\sqrt{2}\, x}{8 \sqrt{x^{4}-1}}-\frac{2^{\frac{3}{4}} \arctan \left(\frac{\sqrt{x^{4}-1}\, 2^{\frac{1}{4}}}{x}+1\right)}{16}-\frac{2^{\frac{3}{4}} \arctan \left(\frac{\sqrt{x^{4}-1}\, 2^{\frac{1}{4}}}{x}-1\right)}{16}-\frac{2^{\frac{3}{4}} \ln \left(\frac{\frac{x^{4}-1}{2 x^{2}}-\frac{2^{\frac{3}{4}} \sqrt{x^{4}-1}}{2 x}+\frac{\sqrt{2}}{2}}{\frac{x^{4}-1}{2 x^{2}}+\frac{2^{\frac{3}{4}} \sqrt{x^{4}-1}}{2 x}+\frac{\sqrt{2}}{2}}\right)}{32}\right) \sqrt{2}}{2}$&$229$\\ default&$-\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{8}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{6}+x^{2}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}-1}\, \sqrt{x^{4}-1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}-1}}-\frac{2 i \underline{\hspace{1.25 ex}}\alpha^{7} \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticPi \left(i x , \underline{\hspace{1.25 ex}}\alpha^{6}, i\right)}{\sqrt{x^{4}-1}}\right)\right)}{32}+\frac{\left(x^{2}-1\right) x}{16 \sqrt{\left(x^{2}+1\right) \left(x^{2}-1\right)}}+\frac{i \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticF \left(i x , i\right)}{8 \sqrt{x^{4}-1}}-\frac{x^{3}-x^{2}+x -1}{32 \sqrt{\left(1+x \right) \left(x^{3}-x^{2}+x -1\right)}}-\frac{x^{3}+x^{2}+x +1}{32 \sqrt{\left(-1+x \right) \left(x^{3}+x^{2}+x +1\right)}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-i \sqrt{2}\, \arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}\right) \sqrt{-2}}{2 \sqrt{x^{4}-1}}\right)-\frac{4 i \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticPi \left(i x , \underline{\hspace{1.25 ex}}\alpha^{2}, i\right)}{\sqrt{x^{4}-1}}\right)\right)}{64}$&$282$\\ \hline \end{longtable}"," ",0,"-1/8*x/(x^4-1)^(1/2)+1/8*I*(x^2+1)^(1/2)*(-x^2+1)^(1/2)/(x^4-1)^(1/2)*EllipticF(I*x,I)+1/64*I*sum(_alpha*(-2^(1/2)*arctanh(1/2*_alpha^2*(_alpha^2+x^2)*(-2)^(1/2)/(x^4-1)^(1/2))-4*_alpha^3*(x^2+1)^(1/2)*(-x^2+1)^(1/2)/(x^4-1)^(1/2)*EllipticPi(I*x,_alpha^2,I)),_alpha=RootOf(_Z^4+1))-1/32*sum(_alpha*(-1/(_alpha^4-1)^(1/2)*arctanh(_alpha^2*(_alpha^6+x^2)/(_alpha^4-1)^(1/2)/(x^4-1)^(1/2))-2*I*_alpha^7*(x^2+1)^(1/2)*(-x^2+1)^(1/2)/(x^4-1)^(1/2)*EllipticPi(I*x,_alpha^6,I)),_alpha=RootOf(_Z^8+1))","C"
2266,0,0,143,0.030000," ","int((b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2)^4,x)","\[\int \frac{\sqrt{b +\sqrt{a \,x^{2}+b^{2}}}}{\left(a \,x^{2}+b^{2}\right)^{4}}\, dx\]"," ",0,"int((b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2+b^2)^4,x)","F"
2267,0,0,133,0.019000," ","int((x^2+(x^4+1)^(1/2))^(1/2)/(x^2+1),x)","\[\int \frac{\sqrt{x^{2}+\sqrt{x^{4}+1}}}{x^{2}+1}\, dx\]"," ",0,"int((x^2+(x^4+1)^(1/2))^(1/2)/(x^2+1),x)","F"
2268,0,0,132,0.068000," ","int((1-(1-(1-1/x^2)^(1/2))^(1/2))^(1/2)/x,x)","\[\int \frac{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x^{2}}}}}}{x}\, dx\]"," ",0,"int((1-(1-(1-1/x^2)^(1/2))^(1/2))^(1/2)/x,x)","F"
2269,1,769,128,8.282000," ","int(1/(1+x)/(-x^3+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \ln \left(\frac{2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x +10 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x -4 \left(-x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-2 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x +9 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x +2 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-9 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)+7 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{2}+35 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{2}+6 \RootOf \left(\textit{\_Z}^{3}-4\right) x +30 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x -26 \left(-x^{3}+1\right)^{\frac{2}{3}}+7 \RootOf \left(\textit{\_Z}^{3}-4\right)+35 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)}{\left(1+x \right)^{2}}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(-\frac{10 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x +8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x -8 \left(-x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-4 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x -26 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x +4 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+26 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)-35 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{2}-28 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{2}-10 \RootOf \left(\textit{\_Z}^{3}-4\right) x -8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x +36 \left(-x^{3}+1\right)^{\frac{2}{3}}-35 \RootOf \left(\textit{\_Z}^{3}-4\right)-28 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)}{\left(1+x \right)^{2}}\right)}{4}$&$769$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*ln((2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x+10*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x-4*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^2-2*(-x^3+1)^(1/3)*RootOf(_Z^3-4)^2*x+9*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)*x+2*(-x^3+1)^(1/3)*RootOf(_Z^3-4)^2-9*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)+7*RootOf(_Z^3-4)*x^2+35*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^2+6*RootOf(_Z^3-4)*x+30*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x-26*(-x^3+1)^(2/3)+7*RootOf(_Z^3-4)+35*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2))/(1+x)^2)+1/4*RootOf(_Z^3-4)*ln(-(10*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x+8*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x-8*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^2-4*(-x^3+1)^(1/3)*RootOf(_Z^3-4)^2*x-26*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)*x+4*(-x^3+1)^(1/3)*RootOf(_Z^3-4)^2+26*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)-35*RootOf(_Z^3-4)*x^2-28*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^2-10*RootOf(_Z^3-4)*x-8*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x+36*(-x^3+1)^(2/3)-35*RootOf(_Z^3-4)-28*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2))/(1+x)^2)","C"
2270,0,0,161,0.106000," ","int((a*b-2*b*x+x^2)*(b^2-2*b*x+x^2)/(x*(-a+x)*(-b+x)^3)^(3/4)/(b*d-(a+d)*x+x^2),x)","\[\int \frac{\left(a b -2 b x +x^{2}\right) \left(b^{2}-2 b x +x^{2}\right)}{\left(x \left(-a +x \right) \left(-b +x \right)^{3}\right)^{\frac{3}{4}} \left(b d -\left(a +d \right) x +x^{2}\right)}\, dx\]"," ",0,"int((a*b-2*b*x+x^2)*(b^2-2*b*x+x^2)/(x*(-a+x)*(-b+x)^3)^(3/4)/(b*d-(a+d)*x+x^2),x)","F"
2271,0,0,143,0.129000," ","int((-2*a*b+(a+b)*x)/(x*(-a+x)*(-b+x))^(1/3)/(-a*b+(a+b)*x+(-1+d)*x^2),x)","\[\int \frac{-2 a b +\left(a +b \right) x}{\left(x \left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{3}} \left(-a b +\left(a +b \right) x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((-2*a*b+(a+b)*x)/(x*(-a+x)*(-b+x))^(1/3)/(-a*b+(a+b)*x+(-1+d)*x^2),x)","F"
2272,1,888,125,16.269000," ","int((x^3-1)^(2/3)*(x^3+1)/x^6/(x^3+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{x^{6}+3 x^{3}-4}{40 x^{5} \left(x^{3}-1\right)^{\frac{1}{3}}}-\frac{\ln \left(-\frac{6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{3} x^{3}-162 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{3}+42 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x +\left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{2}+144 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x^{2}-10 \RootOf \left(\textit{\_Z}^{3}+18\right) x^{3}+270 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x^{3}-48 x \left(x^{3}-1\right)^{\frac{2}{3}}+4 \RootOf \left(\textit{\_Z}^{3}+18\right)-108 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right)}{x^{3}+2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)}{24}-\frac{3 \ln \left(-\frac{6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{3} x^{3}-162 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{3}+42 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x +\left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{2}+144 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x^{2}-10 \RootOf \left(\textit{\_Z}^{3}+18\right) x^{3}+270 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x^{3}-48 x \left(x^{3}-1\right)^{\frac{2}{3}}+4 \RootOf \left(\textit{\_Z}^{3}+18\right)-108 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right)}{x^{3}+2}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{3}+18\right) \ln \left(\frac{-3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{3} x^{3}-135 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{3}+21 \left(x^{3}-1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x -4 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{2}-9 \left(x^{3}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{3}+18\right) x^{3}-90 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x^{3}+3 x \left(x^{3}-1\right)^{\frac{2}{3}}+2 \RootOf \left(\textit{\_Z}^{3}+18\right)+90 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right)}{x^{3}+2}\right)}{24}$&$888$\\ trager&$\text{Expression too large to display}$&$1113$\\ \hline \end{longtable}"," ",0,"-1/40*(x^6+3*x^3-4)/x^5/(x^3-1)^(1/3)-1/24*ln(-(6*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*RootOf(_Z^3+18)^3*x^3-162*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)^2*RootOf(_Z^3+18)^2*x^3+42*(x^3-1)^(2/3)*RootOf(_Z^3+18)^2*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x+(x^3-1)^(1/3)*RootOf(_Z^3+18)^2*x^2+144*(x^3-1)^(1/3)*RootOf(_Z^3+18)*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x^2-10*RootOf(_Z^3+18)*x^3+270*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x^3-48*x*(x^3-1)^(2/3)+4*RootOf(_Z^3+18)-108*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2))/(x^3+2))*RootOf(_Z^3+18)-3/4*ln(-(6*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*RootOf(_Z^3+18)^3*x^3-162*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)^2*RootOf(_Z^3+18)^2*x^3+42*(x^3-1)^(2/3)*RootOf(_Z^3+18)^2*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x+(x^3-1)^(1/3)*RootOf(_Z^3+18)^2*x^2+144*(x^3-1)^(1/3)*RootOf(_Z^3+18)*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x^2-10*RootOf(_Z^3+18)*x^3+270*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x^3-48*x*(x^3-1)^(2/3)+4*RootOf(_Z^3+18)-108*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2))/(x^3+2))*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)+1/24*RootOf(_Z^3+18)*ln((-3*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*RootOf(_Z^3+18)^3*x^3-135*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)^2*RootOf(_Z^3+18)^2*x^3+21*(x^3-1)^(2/3)*RootOf(_Z^3+18)^2*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x-4*(x^3-1)^(1/3)*RootOf(_Z^3+18)^2*x^2-9*(x^3-1)^(1/3)*RootOf(_Z^3+18)*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x^2-2*RootOf(_Z^3+18)*x^3-90*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x^3+3*x*(x^3-1)^(2/3)+2*RootOf(_Z^3+18)+90*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2))/(x^3+2))","C"
2273,1,134,135,0.352000," ","int(1/(1+x)/(-2*x^4+3*x^3-2*x^2+3*x-2)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{22 x^{3}+73 x^{2}-107 x -18}{600 \left(-1+x \right) \sqrt{-\left(-1+x \right)^{2} \left(2 x^{2}+x +2\right)}}-\frac{\left(\frac{91 \sqrt{5}\, \arctan \left(\frac{\left(-5-5 x \right) \sqrt{5}}{10 \sqrt{-2 \left(-1+x \right)^{2}-5 x}}\right)}{2000}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(-3+3 x \right) \sqrt{3}}{6 \sqrt{-2 \left(1+x \right)^{2}+3 x}}\right)}{72}\right) \left(-1+x \right) \sqrt{-2 x^{2}-x -2}}{\sqrt{-\left(-1+x \right)^{2} \left(2 x^{2}+x +2\right)}}$&$134$\\ trager&$\frac{\left(22 x^{3}+73 x^{2}-107 x -18\right) \sqrt{-2 x^{4}+3 x^{3}-2 x^{2}+3 x -2}}{600 \left(-1+x \right)^{3} \left(2 x^{2}+x +2\right)}+\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+3\right) x +\RootOf \left(\textit{\_Z}^{2}+3\right)-2 \sqrt{-2 x^{4}+3 x^{3}-2 x^{2}+3 x -2}}{\left(-1+x \right) \left(1+x \right)}\right)}{72}-\frac{91 \RootOf \left(\textit{\_Z}^{2}+5\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+5\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}+5\right)+2 \sqrt{-2 x^{4}+3 x^{3}-2 x^{2}+3 x -2}}{\left(-1+x \right)^{2}}\right)}{2000}$&$184$\\ default&$-\frac{\left(250 \sqrt{3}\, \arctan \left(\frac{\left(-1+x \right) \sqrt{3}}{2 \sqrt{-2 x^{2}-x -2}}\right) \sqrt{-2 x^{2}-x -2}\, x^{2}+819 \sqrt{5}\, \arctan \left(\frac{\left(1+x \right) \sqrt{5}}{2 \sqrt{-2 x^{2}-x -2}}\right) \sqrt{-2 x^{2}-x -2}\, x^{2}-500 \sqrt{3}\, \arctan \left(\frac{\left(-1+x \right) \sqrt{3}}{2 \sqrt{-2 x^{2}-x -2}}\right) \sqrt{-2 x^{2}-x -2}\, x -1638 \sqrt{5}\, \arctan \left(\frac{\left(1+x \right) \sqrt{5}}{2 \sqrt{-2 x^{2}-x -2}}\right) \sqrt{-2 x^{2}-x -2}\, x +250 \sqrt{3}\, \arctan \left(\frac{\left(-1+x \right) \sqrt{3}}{2 \sqrt{-2 x^{2}-x -2}}\right) \sqrt{-2 x^{2}-x -2}+819 \sqrt{5}\, \arctan \left(\frac{\left(1+x \right) \sqrt{5}}{2 \sqrt{-2 x^{2}-x -2}}\right) \sqrt{-2 x^{2}-x -2}-660 x^{3}-2190 x^{2}+3210 x +540\right) \left(-1+x \right) \left(2 x^{2}+x +2\right)}{18000 \left(-2 x^{4}+3 x^{3}-2 x^{2}+3 x -2\right)^{\frac{3}{2}}}$&$287$\\ \hline \end{longtable}"," ",0,"-1/600*(22*x^3+73*x^2-107*x-18)/(-1+x)/(-(-1+x)^2*(2*x^2+x+2))^(1/2)-(91/2000*5^(1/2)*arctan(1/10*(-5-5*x)*5^(1/2)/(-2*(-1+x)^2-5*x)^(1/2))-1/72*3^(1/2)*arctan(1/6*(-3+3*x)*3^(1/2)/(-2*(1+x)^2+3*x)^(1/2)))*(-1+x)*(-2*x^2-x-2)^(1/2)/(-(-1+x)^2*(2*x^2+x+2))^(1/2)","A"
2274,1,1932,80,13.617000," ","int(x^2*(x^4+x^3)^(1/4)/(x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1932$\\ \hline \end{longtable}"," ",0,"ln((2*(x^4+x^3)^(3/4)+2*(x^4+x^3)^(1/2)*x+2*x^2*(x^4+x^3)^(1/4)+2*x^3+x^2)/x^2)+RootOf(_Z^2+1)*ln((2*RootOf(_Z^2+1)*(x^4+x^3)^(1/2)*x-2*RootOf(_Z^2+1)*x^3+2*(x^4+x^3)^(3/4)-2*x^2*(x^4+x^3)^(1/4)-RootOf(_Z^2+1)*x^2)/x^2)+1/4*RootOf(_Z^2+1)*RootOf(_Z^4-RootOf(_Z^2+1)-1)*ln((-33*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)^2*x^3+66*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)^2*x^2-415*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)*x^3-68*(x^4+x^3)^(1/4)*RootOf(_Z^2+1)*RootOf(_Z^4-RootOf(_Z^2+1)-1)^2*x^2-127*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)*x^2-228*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*x^3+576*RootOf(_Z^4-RootOf(_Z^2+1)-1)*RootOf(_Z^2+1)*(x^4+x^3)^(1/2)*x+576*(x^4+x^3)^(1/4)*RootOf(_Z^4-RootOf(_Z^2+1)-1)^2*x^2-95*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*x^2+68*RootOf(_Z^2+1)*(x^4+x^3)^(3/4)+68*RootOf(_Z^4-RootOf(_Z^2+1)-1)*(x^4+x^3)^(1/2)*x-576*(x^4+x^3)^(3/4))/(RootOf(_Z^2+1)*x-2*RootOf(_Z^2+1)-2*x-1)/x^2)-1/4*RootOf(_Z^4-RootOf(_Z^2+1)-1)*ln((19*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)^2*x^3-38*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)^2*x^2+195*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)*x^3+68*(x^4+x^3)^(1/4)*RootOf(_Z^2+1)*RootOf(_Z^4-RootOf(_Z^2+1)-1)^2*x^2+161*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)*x^2-396*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*x^3+68*RootOf(_Z^4-RootOf(_Z^2+1)-1)*RootOf(_Z^2+1)*(x^4+x^3)^(1/2)*x-576*(x^4+x^3)^(1/4)*RootOf(_Z^4-RootOf(_Z^2+1)-1)^2*x^2-165*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*x^2+68*RootOf(_Z^2+1)*(x^4+x^3)^(3/4)-576*RootOf(_Z^4-RootOf(_Z^2+1)-1)*(x^4+x^3)^(1/2)*x-576*(x^4+x^3)^(3/4))/(RootOf(_Z^2+1)*x-2*RootOf(_Z^2+1)-2*x-1)/x^2)-1/4*RootOf(_Z^4+RootOf(_Z^2+1)-1)*ln(-(-19*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)^2*x^3+38*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)^2*x^2+195*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)*x^3+68*(x^4+x^3)^(1/4)*RootOf(_Z^2+1)*RootOf(_Z^4+RootOf(_Z^2+1)-1)^2*x^2+161*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)*x^2+396*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*x^3+68*RootOf(_Z^4+RootOf(_Z^2+1)-1)*RootOf(_Z^2+1)*(x^4+x^3)^(1/2)*x+576*(x^4+x^3)^(1/4)*RootOf(_Z^4+RootOf(_Z^2+1)-1)^2*x^2+165*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*x^2+68*RootOf(_Z^2+1)*(x^4+x^3)^(3/4)+576*RootOf(_Z^4+RootOf(_Z^2+1)-1)*(x^4+x^3)^(1/2)*x+576*(x^4+x^3)^(3/4))/(RootOf(_Z^2+1)*x-2*RootOf(_Z^2+1)+2*x+1)/x^2)+1/4*RootOf(_Z^2+1)*RootOf(_Z^4+RootOf(_Z^2+1)-1)*ln(-(-33*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)^2*x^3+66*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)^2*x^2+415*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)*x^3-68*(x^4+x^3)^(1/4)*RootOf(_Z^2+1)*RootOf(_Z^4+RootOf(_Z^2+1)-1)^2*x^2+127*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)*x^2-228*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*x^3-576*RootOf(_Z^4+RootOf(_Z^2+1)-1)*RootOf(_Z^2+1)*(x^4+x^3)^(1/2)*x-576*(x^4+x^3)^(1/4)*RootOf(_Z^4+RootOf(_Z^2+1)-1)^2*x^2-95*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*x^2+68*RootOf(_Z^2+1)*(x^4+x^3)^(3/4)+68*RootOf(_Z^4+RootOf(_Z^2+1)-1)*(x^4+x^3)^(1/2)*x+576*(x^4+x^3)^(3/4))/(RootOf(_Z^2+1)*x-2*RootOf(_Z^2+1)+2*x+1)/x^2)-1/4*RootOf(_Z^4+RootOf(_Z^2+1)-1)*RootOf(_Z^4-RootOf(_Z^2+1)-1)*ln((3*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*x^3+RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*x^2+4*(x^4+x^3)^(1/4)*RootOf(_Z^4+RootOf(_Z^2+1)-1)^2*RootOf(_Z^4-RootOf(_Z^2+1)-1)^2*x^2+4*(x^4+x^3)^(1/2)*RootOf(_Z^4-RootOf(_Z^2+1)-1)*RootOf(_Z^4+RootOf(_Z^2+1)-1)*x+4*(x^4+x^3)^(3/4))/(-1+x)/x^2)-1/4*RootOf(_Z^2+1)*RootOf(_Z^4-RootOf(_Z^2+1)-1)*RootOf(_Z^4+RootOf(_Z^2+1)-1)*ln((-3*RootOf(_Z^2+1)*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*x^3-RootOf(_Z^2+1)*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*x^2-4*(x^4+x^3)^(1/4)*RootOf(_Z^4+RootOf(_Z^2+1)-1)^2*RootOf(_Z^4-RootOf(_Z^2+1)-1)^2*x^2+4*(x^4+x^3)^(1/2)*RootOf(_Z^4-RootOf(_Z^2+1)-1)*RootOf(_Z^4+RootOf(_Z^2+1)-1)*RootOf(_Z^2+1)*x+4*(x^4+x^3)^(3/4))/(-1+x)/x^2)","B"
2275,1,1934,80,12.327000," ","int(x^2*(x^4+x^3)^(1/4)/(x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1934$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^2+1)*ln((2*RootOf(_Z^2+1)*(x^4+x^3)^(1/2)*x-2*RootOf(_Z^2+1)*x^3+2*(x^4+x^3)^(3/4)-2*x^2*(x^4+x^3)^(1/4)-RootOf(_Z^2+1)*x^2)/x^2)-ln((2*(x^4+x^3)^(3/4)-2*(x^4+x^3)^(1/2)*x+2*x^2*(x^4+x^3)^(1/4)-2*x^3-x^2)/x^2)-1/4*RootOf(_Z^2+1)*RootOf(_Z^4+RootOf(_Z^2+1)-1)*ln(-(33*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)^2*x^3-66*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)^2*x^2-415*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)*x^3-127*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)*x^2-68*(x^4+x^3)^(1/4)*RootOf(_Z^2+1)*RootOf(_Z^4+RootOf(_Z^2+1)-1)^2*x^2+228*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*x^3+576*RootOf(_Z^4+RootOf(_Z^2+1)-1)*RootOf(_Z^2+1)*(x^4+x^3)^(1/2)*x+95*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*x^2-576*(x^4+x^3)^(1/4)*RootOf(_Z^4+RootOf(_Z^2+1)-1)^2*x^2+68*RootOf(_Z^2+1)*(x^4+x^3)^(3/4)-68*RootOf(_Z^4+RootOf(_Z^2+1)-1)*(x^4+x^3)^(1/2)*x+576*(x^4+x^3)^(3/4))/(RootOf(_Z^2+1)*x-2*RootOf(_Z^2+1)+2*x+1)/x^2)-1/4*RootOf(_Z^4+RootOf(_Z^2+1)-1)*ln((19*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)^2*x^3-38*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)^2*x^2-195*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)*x^3-161*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)*x^2-68*(x^4+x^3)^(1/4)*RootOf(_Z^2+1)*RootOf(_Z^4+RootOf(_Z^2+1)-1)^2*x^2-396*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*x^3-68*RootOf(_Z^4+RootOf(_Z^2+1)-1)*RootOf(_Z^2+1)*(x^4+x^3)^(1/2)*x-165*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*x^2-576*(x^4+x^3)^(1/4)*RootOf(_Z^4+RootOf(_Z^2+1)-1)^2*x^2-68*RootOf(_Z^2+1)*(x^4+x^3)^(3/4)-576*RootOf(_Z^4+RootOf(_Z^2+1)-1)*(x^4+x^3)^(1/2)*x-576*(x^4+x^3)^(3/4))/(RootOf(_Z^2+1)*x-2*RootOf(_Z^2+1)+2*x+1)/x^2)-1/4*RootOf(_Z^4-RootOf(_Z^2+1)-1)*ln((19*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)^2*x^3-38*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)^2*x^2+195*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)*x^3+68*(x^4+x^3)^(1/4)*RootOf(_Z^2+1)*RootOf(_Z^4-RootOf(_Z^2+1)-1)^2*x^2+161*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)*x^2-396*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*x^3+68*RootOf(_Z^4-RootOf(_Z^2+1)-1)*RootOf(_Z^2+1)*(x^4+x^3)^(1/2)*x-576*(x^4+x^3)^(1/4)*RootOf(_Z^4-RootOf(_Z^2+1)-1)^2*x^2-165*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*x^2+68*RootOf(_Z^2+1)*(x^4+x^3)^(3/4)-576*RootOf(_Z^4-RootOf(_Z^2+1)-1)*(x^4+x^3)^(1/2)*x-576*(x^4+x^3)^(3/4))/(RootOf(_Z^2+1)*x-2*RootOf(_Z^2+1)-2*x-1)/x^2)-1/4*RootOf(_Z^2+1)*RootOf(_Z^4-RootOf(_Z^2+1)-1)*ln((33*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)^2*x^3-66*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)^2*x^2+415*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)*x^3+127*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*RootOf(_Z^2+1)*x^2-68*(x^4+x^3)^(1/4)*RootOf(_Z^2+1)*RootOf(_Z^4-RootOf(_Z^2+1)-1)^2*x^2+228*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*x^3-576*RootOf(_Z^4-RootOf(_Z^2+1)-1)*RootOf(_Z^2+1)*(x^4+x^3)^(1/2)*x+95*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*x^2+576*(x^4+x^3)^(1/4)*RootOf(_Z^4-RootOf(_Z^2+1)-1)^2*x^2+68*RootOf(_Z^2+1)*(x^4+x^3)^(3/4)-68*RootOf(_Z^4-RootOf(_Z^2+1)-1)*(x^4+x^3)^(1/2)*x-576*(x^4+x^3)^(3/4))/(RootOf(_Z^2+1)*x-2*RootOf(_Z^2+1)-2*x-1)/x^2)-1/4*RootOf(_Z^4+RootOf(_Z^2+1)-1)*RootOf(_Z^4-RootOf(_Z^2+1)-1)*ln((3*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*x^3+RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*x^2+4*(x^4+x^3)^(1/4)*RootOf(_Z^4+RootOf(_Z^2+1)-1)^2*RootOf(_Z^4-RootOf(_Z^2+1)-1)^2*x^2+4*(x^4+x^3)^(1/2)*RootOf(_Z^4-RootOf(_Z^2+1)-1)*RootOf(_Z^4+RootOf(_Z^2+1)-1)*x+4*(x^4+x^3)^(3/4))/(-1+x)/x^2)+1/4*RootOf(_Z^2+1)*RootOf(_Z^4-RootOf(_Z^2+1)-1)*RootOf(_Z^4+RootOf(_Z^2+1)-1)*ln((3*RootOf(_Z^2+1)*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*x^3+RootOf(_Z^2+1)*RootOf(_Z^4+RootOf(_Z^2+1)-1)^3*RootOf(_Z^4-RootOf(_Z^2+1)-1)^3*x^2-4*(x^4+x^3)^(1/4)*RootOf(_Z^4+RootOf(_Z^2+1)-1)^2*RootOf(_Z^4-RootOf(_Z^2+1)-1)^2*x^2-4*(x^4+x^3)^(1/2)*RootOf(_Z^4-RootOf(_Z^2+1)-1)*RootOf(_Z^4+RootOf(_Z^2+1)-1)*RootOf(_Z^2+1)*x+4*(x^4+x^3)^(3/4))/(-1+x)/x^2)","B"
2276,1,4395,105,75.294000," ","int(1/(x^3-x)^(1/3)/(x^6+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$4395$\\ \hline \end{longtable}"," ",0,"-1/12*ln(-(-4380*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^3*x^2+504*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^2*x^2+21312*(x^3-x)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)-13905*(x^3-x)^(1/3)*RootOf(_Z^3+4)^2*x-42624*(x^3-x)^(1/3)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)*x+17520*RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)-2016*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^2+19710*RootOf(_Z^3+4)*x^2-2268*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*x^2-27810*(x^3-x)^(2/3)-8030*RootOf(_Z^3+4)+924*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2))/(x^2+1))*RootOf(_Z^3+4)-ln(-(-4380*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^3*x^2+504*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^2*x^2+21312*(x^3-x)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)-13905*(x^3-x)^(1/3)*RootOf(_Z^3+4)^2*x-42624*(x^3-x)^(1/3)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)*x+17520*RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)-2016*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^2+19710*RootOf(_Z^3+4)*x^2-2268*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*x^2-27810*(x^3-x)^(2/3)-8030*RootOf(_Z^3+4)+924*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2))/(x^2+1))*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)+RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*ln((-4422*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^3*x^2-504*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^2*x^2+21312*(x^3-x)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)+10353*(x^3-x)^(1/3)*RootOf(_Z^3+4)^2*x-42624*(x^3-x)^(1/3)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)*x+17688*RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)+2016*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^2-18425*RootOf(_Z^3+4)*x^2-2100*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*x^2+20706*(x^3-x)^(2/3)+2211*RootOf(_Z^3+4)+252*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2))/(x^2+1))+1/2*ln(-(45*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^4*x^2+195*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2*(x^3-x)^(1/3)*x-180*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^4+63*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2*x^2+39*(x^3-x)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)-13*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*(x^3-x)^(1/3)*x-57*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)+18*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*x^2+52*(x^3-x)^(2/3)+6*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2))/(3*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*x^2-12*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2-4*x^2+3))*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)-1/6*ln(-(45*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^4*x^2+195*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2*(x^3-x)^(1/3)*x-180*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^4+63*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2*x^2+39*(x^3-x)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)-13*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*(x^3-x)^(1/3)*x-57*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)+18*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*x^2+52*(x^3-x)^(2/3)+6*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2))/(3*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*x^2-12*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2-4*x^2+3))*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)+1/6*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*ln(-(75*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2*(x^3-x)^(1/3)*x-36*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2*x^2-129*(x^3-x)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)+43*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*(x^3-x)^(1/3)*x+18*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)+74*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*x^2+68*(x^3-x)^(2/3)-37*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2))/(3*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*x^2-12*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2-4*x^2+3))+1/6*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*ln(-(36*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2*x^2-129*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2*(x^3-x)^(1/3)*x-18*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2+129*(x^3-x)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)+62*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*x^2-25*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*(x^3-x)^(1/3)*x-31*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2+25*(x^3-x)^(2/3))/(3*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*x^2-12*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2+3*x^2+1))-1/2*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2*ln(-(45*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^4*x^2-180*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^4-93*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2*x^2+39*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2*(x^3-x)^(1/3)*x+177*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2-39*(x^3-x)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)+44*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*x^2-65*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*(x^3-x)^(1/3)*x-33*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2+65*(x^3-x)^(2/3))/(3*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*x^2-12*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2+3*x^2+1))","B"
2277,1,3898,105,70.151000," ","int(1/(x^3-x)^(1/3)/(x^6+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$3898$\\ \hline \end{longtable}"," ",0,"1/12*RootOf(_Z^3+4)*ln((2190*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^3*x^2+26532*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^2*x^2+10656*(x^3-x)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)+1776*(x^3-x)^(1/3)*RootOf(_Z^3+4)^2*x+83430*(x^3-x)^(1/3)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)*x-8760*RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)-106128*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^2+9125*RootOf(_Z^3+4)*x^2+110550*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*x^2+10353*(x^3-x)^(2/3)-1095*RootOf(_Z^3+4)-13266*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2))/(x^2+1))+RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*ln(-(4422*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^3*x^2+52560*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^2*x^2+21312*(x^3-x)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)+3552*(x^3-x)^(1/3)*RootOf(_Z^3+4)^2*x-124236*(x^3-x)^(1/3)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)*x-17688*RootOf(_Z^3+4)^3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)-210240*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^2-19899*RootOf(_Z^3+4)*x^2-236520*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*x^2-27810*(x^3-x)^(2/3)+8107*RootOf(_Z^3+4)+96360*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2))/(x^2+1))-1/2*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*ln(-(54*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^4*x^2-156*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2*(x^3-x)^(1/3)*x-216*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^4+21*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2*x^2+39*(x^3-x)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)+65*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*(x^3-x)^(1/3)*x+150*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)-33*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*x^2+52*(x^3-x)^(2/3)-11*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2))/(3*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*x^2-12*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2-4*x^2+3))+1/2*ln((204*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2*(x^3-x)^(1/3)*x-222*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2*x^2+129*(x^3-x)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)-25*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*(x^3-x)^(1/3)*x+111*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)+62*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*x^2-68*(x^3-x)^(2/3)-31*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2))/(3*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*x^2-12*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2-4*x^2+3))*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)-1/6*ln((204*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2*(x^3-x)^(1/3)*x-222*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2*x^2+129*(x^3-x)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)-25*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*(x^3-x)^(1/3)*x+111*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)+62*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*x^2-68*(x^3-x)^(2/3)-31*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2))/(3*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*x^2-12*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2-4*x^2+3))*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)+1/6*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*ln(-(36*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2*x^2-129*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2*(x^3-x)^(1/3)*x-18*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2+129*(x^3-x)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)+62*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*x^2-25*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*(x^3-x)^(1/3)*x-31*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2+25*(x^3-x)^(2/3))/(3*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*x^2-12*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2+3*x^2+1))-1/2*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2*ln((-45*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^4*x^2+180*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)^2*RootOf(_Z^3+4)^4+93*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2*x^2-39*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2*(x^3-x)^(1/3)*x+39*(x^3-x)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)-177*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2-44*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2*x^2+65*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)*(x^3-x)^(1/3)*x-65*(x^3-x)^(2/3)+33*RootOf(_Z^3+3*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2)^2)/(3*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*x^2-12*RootOf(RootOf(_Z^3+4)^2+12*_Z*RootOf(_Z^3+4)+144*_Z^2)*RootOf(_Z^3+4)^2+3*x^2+1))","B"
2278,1,365,129,0.544000," ","int((x^4-x)^(1/2)/(a*x^6-b),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{6}-b \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{3}+1\right) \left(-1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{5}+\underline{\hspace{1.25 ex}}\alpha^{4}+\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(1-i \sqrt{3}\right) \sqrt{\frac{x \left(-3+i \sqrt{3}\right)}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{\left(-1+x \right) \left(-1-i \sqrt{3}\right)}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\frac{\underline{\hspace{1.25 ex}}\alpha^{5} a \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{i \underline{\hspace{1.25 ex}}\alpha^{5} \sqrt{3}\, a -3 \underline{\hspace{1.25 ex}}\alpha^{5} a -i \sqrt{3}\, b +3 b}{6 b}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{b}\right)}{\underline{\hspace{1.25 ex}}\alpha^{4} \left(a -b \right) \left(-3+i \sqrt{3}\right) \sqrt{x \left(-1+x \right) \left(i \sqrt{3}+2 x +1\right) \left(1+2 x -i \sqrt{3}\right)}}\right)}{3}$&$365$\\ elliptic&$-\frac{\sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{6}-b \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{3}+1\right) \left(-1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{5}+\underline{\hspace{1.25 ex}}\alpha^{4}+\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(1-i \sqrt{3}\right) \sqrt{\frac{x \left(-3+i \sqrt{3}\right)}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{\left(-1+x \right) \left(-1-i \sqrt{3}\right)}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\frac{\underline{\hspace{1.25 ex}}\alpha^{5} a \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{i \underline{\hspace{1.25 ex}}\alpha^{5} \sqrt{3}\, a -3 \underline{\hspace{1.25 ex}}\alpha^{5} a -i \sqrt{3}\, b +3 b}{6 b}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{b}\right)}{\underline{\hspace{1.25 ex}}\alpha^{4} \left(a -b \right) \left(-3+i \sqrt{3}\right) \sqrt{x \left(-1+x \right) \left(i \sqrt{3}+2 x +1\right) \left(1+2 x -i \sqrt{3}\right)}}\right)}{3}$&$365$\\ \hline \end{longtable}"," ",0,"-1/3*4^(1/2)*sum((-_alpha^3+1)/_alpha^4*(-1+x)^2*(_alpha^5+_alpha^4+_alpha^3+_alpha^2+_alpha+1)/(a-b)*(1-I*3^(1/2))*(x/(-1+x)*(-3+I*3^(1/2))/(-1+I*3^(1/2)))^(1/2)*(1/(-1+x)*(I*3^(1/2)+2*x+1)/(-1-I*3^(1/2)))^(1/2)*(1/(-1+x)*(1+2*x-I*3^(1/2))/(-1+I*3^(1/2)))^(1/2)/(-3+I*3^(1/2))/(x*(-1+x)*(I*3^(1/2)+2*x+1)*(1+2*x-I*3^(1/2)))^(1/2)*(EllipticF(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-_alpha^5*a/b*EllipticPi(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),1/6*(I*_alpha^5*3^(1/2)*a-3*_alpha^5*a-I*3^(1/2)*b+3*b)/b,((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))),_alpha=RootOf(_Z^6*a-b))","C"
2279,1,347,145,620.105000," ","int((2*x^8+1)*(2*x^8-2*x^4-1)^(1/4)*(4*x^16-3*x^8+1)/x^10/(2*x^8-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(2 x^{8}-2 x^{4}-1\right)^{\frac{1}{4}} \left(20 x^{16}-4 x^{12}+9 x^{8}+2 x^{4}+5\right)}{45 x^{9}}+\frac{\RootOf \left(\textit{\_Z}^{4}+2\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} x^{8}-4 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} x^{4}+4 \left(2 x^{8}-2 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{3}-4 \sqrt{2 x^{8}-2 x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}+2\right) x^{2}+4 \left(2 x^{8}-2 x^{4}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}+2\right)^{3}}{2 x^{8}-1}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{8}+4 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{4}-4 \left(2 x^{8}-2 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{3}-4 \sqrt{2 x^{8}-2 x^{4}-1}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{2}+4 \left(2 x^{8}-2 x^{4}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right)}{2 x^{8}-1}\right)}{4}$&$347$\\ risch&$\frac{40 x^{24}-48 x^{20}+6 x^{16}-10 x^{12}-3 x^{8}-12 x^{4}-5}{45 x^{9} \left(2 x^{8}-2 x^{4}-1\right)^{\frac{3}{4}}}+\frac{\left(-\frac{\RootOf \left(\textit{\_Z}^{4}+2\right) \ln \left(-\frac{-8 x^{24} \RootOf \left(\textit{\_Z}^{4}+2\right)+32 \RootOf \left(\textit{\_Z}^{4}+2\right) x^{20}-8 \left(8 x^{24}-24 x^{20}+12 x^{16}+16 x^{12}-6 x^{8}-6 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{17}-28 \RootOf \left(\textit{\_Z}^{4}+2\right) x^{16}+16 \left(8 x^{24}-24 x^{20}+12 x^{16}+16 x^{12}-6 x^{8}-6 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{13}-4 \sqrt{8 x^{24}-24 x^{20}+12 x^{16}+16 x^{12}-6 x^{8}-6 x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} x^{10}-16 \RootOf \left(\textit{\_Z}^{4}+2\right) x^{12}+4 \sqrt{8 x^{24}-24 x^{20}+12 x^{16}+16 x^{12}-6 x^{8}-6 x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} x^{6}+14 \RootOf \left(\textit{\_Z}^{4}+2\right) x^{8}-8 \left(8 x^{24}-24 x^{20}+12 x^{16}+16 x^{12}-6 x^{8}-6 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{5}+2 \sqrt{8 x^{24}-24 x^{20}+12 x^{16}+16 x^{12}-6 x^{8}-6 x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} x^{2}+4 \left(8 x^{24}-24 x^{20}+12 x^{16}+16 x^{12}-6 x^{8}-6 x^{4}-1\right)^{\frac{3}{4}} x^{3}+8 \RootOf \left(\textit{\_Z}^{4}+2\right) x^{4}-2 \left(8 x^{24}-24 x^{20}+12 x^{16}+16 x^{12}-6 x^{8}-6 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x +\RootOf \left(\textit{\_Z}^{4}+2\right)}{\left(2 x^{8}-1\right) \left(2 x^{8}-2 x^{4}-1\right)^{2}}\right)}{4}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \ln \left(-\frac{-8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{24}+32 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{20}+8 \left(8 x^{24}-24 x^{20}+12 x^{16}+16 x^{12}-6 x^{8}-6 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{17}-28 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{16}-16 \left(8 x^{24}-24 x^{20}+12 x^{16}+16 x^{12}-6 x^{8}-6 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{13}+4 \sqrt{8 x^{24}-24 x^{20}+12 x^{16}+16 x^{12}-6 x^{8}-6 x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{10}-16 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{12}-4 \sqrt{8 x^{24}-24 x^{20}+12 x^{16}+16 x^{12}-6 x^{8}-6 x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{6}+14 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{8}+8 \left(8 x^{24}-24 x^{20}+12 x^{16}+16 x^{12}-6 x^{8}-6 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{5}-2 \sqrt{8 x^{24}-24 x^{20}+12 x^{16}+16 x^{12}-6 x^{8}-6 x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{2}+4 \left(8 x^{24}-24 x^{20}+12 x^{16}+16 x^{12}-6 x^{8}-6 x^{4}-1\right)^{\frac{3}{4}} x^{3}+8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{4}+2 \left(8 x^{24}-24 x^{20}+12 x^{16}+16 x^{12}-6 x^{8}-6 x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right)}{\left(2 x^{8}-1\right) \left(2 x^{8}-2 x^{4}-1\right)^{2}}\right)}{4}\right) \left(\left(2 x^{8}-2 x^{4}-1\right)^{3}\right)^{\frac{1}{4}}}{\left(2 x^{8}-2 x^{4}-1\right)^{\frac{3}{4}}}$&$1126$\\ \hline \end{longtable}"," ",0,"1/45*(2*x^8-2*x^4-1)^(1/4)*(20*x^16-4*x^12+9*x^8+2*x^4+5)/x^9+1/4*RootOf(_Z^4+2)*ln(-(2*RootOf(_Z^4+2)^3*x^8-4*RootOf(_Z^4+2)^3*x^4+4*(2*x^8-2*x^4-1)^(1/4)*RootOf(_Z^4+2)^2*x^3-4*(2*x^8-2*x^4-1)^(1/2)*RootOf(_Z^4+2)*x^2+4*(2*x^8-2*x^4-1)^(3/4)*x-RootOf(_Z^4+2)^3)/(2*x^8-1))+1/4*RootOf(_Z^2+RootOf(_Z^4+2)^2)*ln(-(-2*RootOf(_Z^4+2)^2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*x^8+4*RootOf(_Z^4+2)^2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*x^4-4*(2*x^8-2*x^4-1)^(1/4)*RootOf(_Z^4+2)^2*x^3-4*(2*x^8-2*x^4-1)^(1/2)*RootOf(_Z^2+RootOf(_Z^4+2)^2)*x^2+4*(2*x^8-2*x^4-1)^(3/4)*x+RootOf(_Z^4+2)^2*RootOf(_Z^2+RootOf(_Z^4+2)^2))/(2*x^8-1))","C"
2280,0,0,136,0.029000," ","int((a*x^2+b^2)^(3/2)/(b+(a*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{\left(a \,x^{2}+b^{2}\right)^{\frac{3}{2}}}{\sqrt{b +\sqrt{a \,x^{2}+b^{2}}}}\, dx\]"," ",0,"int((a*x^2+b^2)^(3/2)/(b+(a*x^2+b^2)^(1/2))^(1/2),x)","F"
2281,0,0,126,0.031000," ","int(x*(p*x^6-2*q)*(p*x^6+q)^(1/2)/(b*x^8+a*(p*x^6+q)^2),x)","\[\int \frac{x \left(p \,x^{6}-2 q \right) \sqrt{p \,x^{6}+q}}{b \,x^{8}+a \left(p \,x^{6}+q \right)^{2}}\, dx\]"," ",0,"int(x*(p*x^6-2*q)*(p*x^6+q)^(1/2)/(b*x^8+a*(p*x^6+q)^2),x)","F"
2282,1,1308,136,16.078000," ","int((6*x^2-2*x-1)^(1/3)/(-1+6*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1308$\\ risch&$\text{Expression too large to display}$&$2660$\\ \hline \end{longtable}"," ",0,"1/4*(6*x^2-2*x-1)^(1/3)+7/4*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)*ln((-2394*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)*RootOf(_Z^3+252)^4*x^2-317520*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)^2*RootOf(_Z^3+252)^3*x^2+798*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)*RootOf(_Z^3+252)^4*x+105840*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)^2*RootOf(_Z^3+252)^3*x+50274*(6*x^2-2*x-1)^(2/3)*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)*RootOf(_Z^3+252)^2+8892*RootOf(_Z^3+252)^2*x^2+1179360*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)*RootOf(_Z^3+252)*x^2-2964*RootOf(_Z^3+252)^2*x-393120*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)*RootOf(_Z^3+252)*x-90720*(6*x^2-2*x-1)^(2/3)-15120*(6*x^2-2*x-1)^(1/3)*RootOf(_Z^3+252)-2111508*(6*x^2-2*x-1)^(1/3)*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)-2413*RootOf(_Z^3+252)^2-320040*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)*RootOf(_Z^3+252))/(-1+6*x)^2)-1/72*ln(-(126*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)*RootOf(_Z^3+252)^4*x^2+317520*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)^2*RootOf(_Z^3+252)^3*x^2-42*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)*RootOf(_Z^3+252)^4*x-105840*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)^2*RootOf(_Z^3+252)^3*x+50274*(6*x^2-2*x-1)^(2/3)*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)*RootOf(_Z^3+252)^2+216*RootOf(_Z^3+252)^2*x^2+544320*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)*RootOf(_Z^3+252)*x^2-72*RootOf(_Z^3+252)^2*x-181440*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)*RootOf(_Z^3+252)*x-9828*(6*x^2-2*x-1)^(2/3)-1638*(6*x^2-2*x-1)^(1/3)*RootOf(_Z^3+252)-2111508*(6*x^2-2*x-1)^(1/3)*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)-127*RootOf(_Z^3+252)^2-320040*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)*RootOf(_Z^3+252))/(-1+6*x)^2)*RootOf(_Z^3+252)-7/4*ln(-(126*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)*RootOf(_Z^3+252)^4*x^2+317520*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)^2*RootOf(_Z^3+252)^3*x^2-42*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)*RootOf(_Z^3+252)^4*x-105840*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)^2*RootOf(_Z^3+252)^3*x+50274*(6*x^2-2*x-1)^(2/3)*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)*RootOf(_Z^3+252)^2+216*RootOf(_Z^3+252)^2*x^2+544320*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)*RootOf(_Z^3+252)*x^2-72*RootOf(_Z^3+252)^2*x-181440*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)*RootOf(_Z^3+252)*x-9828*(6*x^2-2*x-1)^(2/3)-1638*(6*x^2-2*x-1)^(1/3)*RootOf(_Z^3+252)-2111508*(6*x^2-2*x-1)^(1/3)*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)-127*RootOf(_Z^3+252)^2-320040*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)*RootOf(_Z^3+252))/(-1+6*x)^2)*RootOf(RootOf(_Z^3+252)^2+126*_Z*RootOf(_Z^3+252)+15876*_Z^2)","C"
2283,0,0,144,0.133000," ","int((-2*a*b*x+(a+b)*x^2)/(x*(-a+x)*(-b+x))^(2/3)/(-a*b+(a+b)*x+(-1+d)*x^2),x)","\[\int \frac{-2 a b x +\left(a +b \right) x^{2}}{\left(x \left(-a +x \right) \left(-b +x \right)\right)^{\frac{2}{3}} \left(-a b +\left(a +b \right) x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((-2*a*b*x+(a+b)*x^2)/(x*(-a+x)*(-b+x))^(2/3)/(-a*b+(a+b)*x+(-1+d)*x^2),x)","F"
2284,0,0,146,0.142000," ","int(x*(-a*b+x^2)/(x^2*(-a+x)*(-b+x))^(2/3)/(a*b*d-(a*d+b*d+1)*x+d*x^2),x)","\[\int \frac{x \left(-a b +x^{2}\right)}{\left(x^{2} \left(-a +x \right) \left(-b +x \right)\right)^{\frac{2}{3}} \left(a b d -\left(a d +b d +1\right) x +d \,x^{2}\right)}\, dx\]"," ",0,"int(x*(-a*b+x^2)/(x^2*(-a+x)*(-b+x))^(2/3)/(a*b*d-(a*d+b*d+1)*x+d*x^2),x)","F"
2285,1,835,136,23.727000," ","int((x^3-2)*(x^3-1)^(2/3)/x^3/(2*x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(x^{3}-1\right)^{\frac{2}{3}}}{x^{2}}-\frac{\ln \left(\frac{33016196884989482270840140 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}+279393921796415422876156 x \left(x^{3}-1\right)^{\frac{2}{3}}+8254049221247370567710035 x^{11} \left(x^{3}-1\right)^{\frac{1}{3}}-24762147663742111703130105 x^{8} \left(x^{3}-1\right)^{\frac{1}{3}}+18700889327124136369949940 x^{9}-49803421050130594753656156 x^{6}+39403101898028224175982242 x^{3}-7250695686481463399577082 x^{12}+18845785825826111769772760 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)+28300298612496775796977664 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{2}-139696960898207711438078 \left(x^{3}-1\right)^{\frac{2}{3}} x^{10}+419090882694623134314234 \left(x^{3}-1\right)^{\frac{2}{3}} x^{4}+3100410598970580503439069-48860088729938611858127568 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) x^{3}+129827490572386253096509632 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) x^{6}+1002891832080354492305395968 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{2} x^{6}-611993957495242776609641984 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{2} x^{3}-8026828278127257345063624 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) x^{12}+66032393769978964541680280 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x^{10}-64914818082793302850175656 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{11}+194744454248379908550526968 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{8}-198097181309936893625040840 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x^{4}-132064787539957929083360560 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x -259659272331173211400702624 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-558046513265170797746653312 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{2} x^{9}-102605316937845350087800336 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) x^{9}+55274020727532765228472000 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{2} x^{12}}{\left(2 x^{3}-1\right)^{3}}\right)}{6}+\frac{4 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) \ln \left(\frac{-33016196884989482270840140 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-16228704520698325712543914 x \left(x^{3}-1\right)^{\frac{2}{3}}-8254049221247370567710035 x^{11} \left(x^{3}-1\right)^{\frac{1}{3}}+24762147663742111703130105 x^{8} \left(x^{3}-1\right)^{\frac{1}{3}}+842928816094874669734198 x^{9}+5306305989843145461933312 x^{6}-7033619137578544375323062 x^{3}+2190233071328485822178203 x^{12}-29664743373524966194481896 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)+67191967266579353132732416 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{2}+8114352260349162856271957 \left(x^{3}-1\right)^{\frac{2}{3}} x^{10}-24343056781047488568815871 \left(x^{3}-1\right)^{\frac{2}{3}} x^{4}-210095773353658826547145872 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) x^{3}+226149429909913341237273120 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) x^{6}+2381115340009405826641204992 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{2} x^{6}-1453026292139778511495338496 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{2} x^{3}+48510529199351077964254656 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) x^{12}-66032393769978964541680280 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x^{10}+1117575687185661691504624 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{11}-3352727061556985074513872 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{8}+198097181309936893625040840 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x^{4}+132064787539957929083360560 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +4470302748742646766018496 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}-1324941604537861619586067328 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{2} x^{9}-53745228207906738229672768 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right) x^{9}+131234311067537799087368000 \RootOf \left(64 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)^{2} x^{12}-1748040905508223700350427}{\left(2 x^{3}-1\right)^{3}}\right)}{3}$&$835$\\ risch&$-\frac{\left(x^{3}-1\right)^{\frac{2}{3}}}{x^{2}}+\frac{\ln \left(-\frac{-11+12 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-6 x \left(x^{3}-1\right)^{\frac{2}{3}}+3 x^{11} \left(x^{3}-1\right)^{\frac{1}{3}}-9 x^{8} \left(x^{3}-1\right)^{\frac{1}{3}}+22 x^{9}-22 x^{3}+11 x^{12}-16 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)+3 \left(x^{3}-1\right)^{\frac{2}{3}} x^{10}-9 \left(x^{3}-1\right)^{\frac{2}{3}} x^{4}-108 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +216 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+54 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x^{10}+54 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{11}-162 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{8}-162 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x^{4}-256 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x^{3}+264 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x^{6}-208 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x^{3}+32 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x^{12}+38 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x^{12}-192 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x^{9}-100 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x^{9}+384 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x^{6}}{\left(2 x^{3}-1\right)^{3}}\right)}{6}-\frac{\ln \left(-\frac{-11+12 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}-6 x \left(x^{3}-1\right)^{\frac{2}{3}}+3 x^{11} \left(x^{3}-1\right)^{\frac{1}{3}}-9 x^{8} \left(x^{3}-1\right)^{\frac{1}{3}}+22 x^{9}-22 x^{3}+11 x^{12}-16 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)+3 \left(x^{3}-1\right)^{\frac{2}{3}} x^{10}-9 \left(x^{3}-1\right)^{\frac{2}{3}} x^{4}-108 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +216 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+54 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x^{10}+54 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{11}-162 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{8}-162 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x^{4}-256 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x^{3}+264 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x^{6}-208 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x^{3}+32 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x^{12}+38 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x^{12}-192 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x^{9}-100 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x^{9}+384 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x^{6}}{\left(2 x^{3}-1\right)^{3}}\right) \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)}{3}+\frac{\RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \ln \left(\frac{19-120 x^{2} \left(x^{3}-1\right)^{\frac{1}{3}}+60 x \left(x^{3}-1\right)^{\frac{2}{3}}-30 x^{11} \left(x^{3}-1\right)^{\frac{1}{3}}+90 x^{8} \left(x^{3}-1\right)^{\frac{1}{3}}+76 x^{9}-228 x^{6}+190 x^{3}-38 x^{12}-16 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)-30 \left(x^{3}-1\right)^{\frac{2}{3}} x^{10}+90 \left(x^{3}-1\right)^{\frac{2}{3}} x^{4}-108 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x +216 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{2}+54 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x^{10}+54 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{11}-162 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{1}{3}} x^{8}-162 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \left(x^{3}-1\right)^{\frac{2}{3}} x^{4}+256 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x^{3}+648 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x^{6}-464 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x^{3}-32 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x^{12}+70 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x^{12}+192 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x^{9}-292 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) x^{9}-384 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2} x^{6}}{\left(2 x^{3}-1\right)^{3}}\right)}{3}$&$1198$\\ \hline \end{longtable}"," ",0,"-(x^3-1)^(2/3)/x^2-1/6*ln((33016196884989482270840140*x^2*(x^3-1)^(1/3)+279393921796415422876156*x*(x^3-1)^(2/3)-48860088729938611858127568*RootOf(64*_Z^2-8*_Z+1)*x^3+8254049221247370567710035*x^11*(x^3-1)^(1/3)-24762147663742111703130105*x^8*(x^3-1)^(1/3)+18700889327124136369949940*x^9-49803421050130594753656156*x^6+39403101898028224175982242*x^3-7250695686481463399577082*x^12+129827490572386253096509632*RootOf(64*_Z^2-8*_Z+1)*x^6+1002891832080354492305395968*RootOf(64*_Z^2-8*_Z+1)^2*x^6-611993957495242776609641984*RootOf(64*_Z^2-8*_Z+1)^2*x^3+28300298612496775796977664*RootOf(64*_Z^2-8*_Z+1)^2+18845785825826111769772760*RootOf(64*_Z^2-8*_Z+1)-8026828278127257345063624*RootOf(64*_Z^2-8*_Z+1)*x^12-558046513265170797746653312*RootOf(64*_Z^2-8*_Z+1)^2*x^9-102605316937845350087800336*RootOf(64*_Z^2-8*_Z+1)*x^9+55274020727532765228472000*RootOf(64*_Z^2-8*_Z+1)^2*x^12-139696960898207711438078*(x^3-1)^(2/3)*x^10+419090882694623134314234*(x^3-1)^(2/3)*x^4+66032393769978964541680280*RootOf(64*_Z^2-8*_Z+1)*(x^3-1)^(2/3)*x^10-64914818082793302850175656*RootOf(64*_Z^2-8*_Z+1)*(x^3-1)^(1/3)*x^11+194744454248379908550526968*RootOf(64*_Z^2-8*_Z+1)*(x^3-1)^(1/3)*x^8-198097181309936893625040840*RootOf(64*_Z^2-8*_Z+1)*(x^3-1)^(2/3)*x^4-132064787539957929083360560*RootOf(64*_Z^2-8*_Z+1)*(x^3-1)^(2/3)*x-259659272331173211400702624*RootOf(64*_Z^2-8*_Z+1)*(x^3-1)^(1/3)*x^2+3100410598970580503439069)/(2*x^3-1)^3)+4/3*RootOf(64*_Z^2-8*_Z+1)*ln((-33016196884989482270840140*x^2*(x^3-1)^(1/3)-16228704520698325712543914*x*(x^3-1)^(2/3)-210095773353658826547145872*RootOf(64*_Z^2-8*_Z+1)*x^3-8254049221247370567710035*x^11*(x^3-1)^(1/3)+24762147663742111703130105*x^8*(x^3-1)^(1/3)+842928816094874669734198*x^9+5306305989843145461933312*x^6-7033619137578544375323062*x^3+2190233071328485822178203*x^12+226149429909913341237273120*RootOf(64*_Z^2-8*_Z+1)*x^6+2381115340009405826641204992*RootOf(64*_Z^2-8*_Z+1)^2*x^6-1453026292139778511495338496*RootOf(64*_Z^2-8*_Z+1)^2*x^3+67191967266579353132732416*RootOf(64*_Z^2-8*_Z+1)^2-29664743373524966194481896*RootOf(64*_Z^2-8*_Z+1)+48510529199351077964254656*RootOf(64*_Z^2-8*_Z+1)*x^12-1324941604537861619586067328*RootOf(64*_Z^2-8*_Z+1)^2*x^9-53745228207906738229672768*RootOf(64*_Z^2-8*_Z+1)*x^9+131234311067537799087368000*RootOf(64*_Z^2-8*_Z+1)^2*x^12+8114352260349162856271957*(x^3-1)^(2/3)*x^10-24343056781047488568815871*(x^3-1)^(2/3)*x^4-66032393769978964541680280*RootOf(64*_Z^2-8*_Z+1)*(x^3-1)^(2/3)*x^10+1117575687185661691504624*RootOf(64*_Z^2-8*_Z+1)*(x^3-1)^(1/3)*x^11-3352727061556985074513872*RootOf(64*_Z^2-8*_Z+1)*(x^3-1)^(1/3)*x^8+198097181309936893625040840*RootOf(64*_Z^2-8*_Z+1)*(x^3-1)^(2/3)*x^4+132064787539957929083360560*RootOf(64*_Z^2-8*_Z+1)*(x^3-1)^(2/3)*x+4470302748742646766018496*RootOf(64*_Z^2-8*_Z+1)*(x^3-1)^(1/3)*x^2-1748040905508223700350427)/(2*x^3-1)^3)","C"
2286,0,0,134,0.010000," ","int((a*x^2-b)*(a*x^4-b*x^2)^(1/4)/(a*x^2+b),x)","\[\int \frac{\left(a \,x^{2}-b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}{a \,x^{2}+b}\, dx\]"," ",0,"int((a*x^2-b)*(a*x^4-b*x^2)^(1/4)/(a*x^2+b),x)","F"
2287,0,0,148,0.123000," ","int((x^3+1)/(x^3-1)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x)","\[\int \frac{x^{3}+1}{\left(x^{3}-1\right) \sqrt{a \,x^{4}+b \,x^{3}+c \,x^{2}+b x +a}}\, dx\]"," ",0,"int((x^3+1)/(x^3-1)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x)","F"
2288,0,0,107,0.059000," ","int((a*x^6-b)/(x^3-x)^(1/3)/(c*x^6-d),x)","\[\int \frac{a \,x^{6}-b}{\left(x^{3}-x \right)^{\frac{1}{3}} \left(c \,x^{6}-d \right)}\, dx\]"," ",0,"int((a*x^6-b)/(x^3-x)^(1/3)/(c*x^6-d),x)","F"
2289,0,0,107,0.001000," ","int((a*x^6-b)/(x^3-x)^(1/3)/(c*x^6-d),x)","\[\int \frac{a \,x^{6}-b}{\left(x^{3}-x \right)^{\frac{1}{3}} \left(c \,x^{6}-d \right)}\, dx\]"," ",0,"int((a*x^6-b)/(x^3-x)^(1/3)/(c*x^6-d),x)","F"
2290,1,93,132,0.125000," ","int(1/(d+(c+(a*x+b)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\frac{8 \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{7}{2}}}{7}-\frac{24 d \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{5}{2}}}{5}+\frac{8 \left(3 d^{2}-c \right) \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{3}{2}}}{3}-8 \left(d^{2}-c \right) d \sqrt{d +\sqrt{c +\sqrt{a x +b}}}}{a}$&$93$\\ default&$\frac{\frac{8 \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{7}{2}}}{7}-\frac{24 d \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{5}{2}}}{5}+\frac{8 \left(3 d^{2}-c \right) \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{3}{2}}}{3}-8 \left(d^{2}-c \right) d \sqrt{d +\sqrt{c +\sqrt{a x +b}}}}{a}$&$93$\\ \hline \end{longtable}"," ",0,"2/a*(4/7*(d+(c+(a*x+b)^(1/2))^(1/2))^(7/2)-12/5*d*(d+(c+(a*x+b)^(1/2))^(1/2))^(5/2)+4/3*(3*d^2-c)*(d+(c+(a*x+b)^(1/2))^(1/2))^(3/2)-4*(d^2-c)*d*(d+(c+(a*x+b)^(1/2))^(1/2))^(1/2))","A"
2291,1,2339,134,14.562000," ","int(1/x/(x^2+3*x+3)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2339$\\ \hline \end{longtable}"," ",0,"-1/9*ln(-(-232188818352256*RootOf(_Z^3-9)*x^3-6236446542930126*RootOf(_Z^3-9)*x^2-18709339628790378*RootOf(_Z^3-9)*x-18684300290294655*(x^2+3*x+3)^(2/3)-18709339628790378*RootOf(_Z^3-9)-8346446165241*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x^2-10883850860262*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x^2-25039338495723*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x-32651552580786*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x-539492107992192*(x^2+3*x+3)^(2/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^2*x-539492107992192*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)*(x^2+3*x+3)^(1/3)*x^2-3236952647953152*(x^2+3*x+3)^(1/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)*x-1618476323976576*(x^2+3*x+3)^(2/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^2-692011121862765*RootOf(_Z^3-9)^2*(x^2+3*x+3)^(1/3)*x^2-4152066731176590*(x^2+3*x+3)^(1/3)*RootOf(_Z^3-9)^2*x-4855428971929728*(x^2+3*x+3)^(1/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)-178057518191808*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x^3-4782513652683093*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x^2-14347540958049279*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x-14347540958049279*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)-25039338495723*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2-6228100096764885*(x^2+3*x+3)^(1/3)*RootOf(_Z^3-9)^2-6228100096764885*(x^2+3*x+3)^(2/3)*x-32651552580786*RootOf(_Z^3-9)^3*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)+76186956021834*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x^3+58425123156687*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x^3)/x^3)*RootOf(_Z^3-9)-1/3*ln(-(-232188818352256*RootOf(_Z^3-9)*x^3-6236446542930126*RootOf(_Z^3-9)*x^2-18709339628790378*RootOf(_Z^3-9)*x-18684300290294655*(x^2+3*x+3)^(2/3)-18709339628790378*RootOf(_Z^3-9)-8346446165241*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x^2-10883850860262*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x^2-25039338495723*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x-32651552580786*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x-539492107992192*(x^2+3*x+3)^(2/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^2*x-539492107992192*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)*(x^2+3*x+3)^(1/3)*x^2-3236952647953152*(x^2+3*x+3)^(1/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)*x-1618476323976576*(x^2+3*x+3)^(2/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^2-692011121862765*RootOf(_Z^3-9)^2*(x^2+3*x+3)^(1/3)*x^2-4152066731176590*(x^2+3*x+3)^(1/3)*RootOf(_Z^3-9)^2*x-4855428971929728*(x^2+3*x+3)^(1/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)-178057518191808*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x^3-4782513652683093*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x^2-14347540958049279*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x-14347540958049279*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)-25039338495723*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2-6228100096764885*(x^2+3*x+3)^(1/3)*RootOf(_Z^3-9)^2-6228100096764885*(x^2+3*x+3)^(2/3)*x-32651552580786*RootOf(_Z^3-9)^3*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)+76186956021834*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x^3+58425123156687*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x^3)/x^3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)+1/3*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*ln(-(-342972057197135*RootOf(_Z^3-9)*x^3-4617970218953550*RootOf(_Z^3-9)*x^2-13853910656860650*RootOf(_Z^3-9)*x-13828871318364927*(x^2+3*x+3)^(2/3)-13853910656860650*RootOf(_Z^3-9)-8346446165241*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x^2+8101702138515*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x^2-25039338495723*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x+24305106415545*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x+539492107992192*(x^2+3*x+3)^(2/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^2*x+539492107992192*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)*(x^2+3*x+3)^(1/3)*x^2+3236952647953152*(x^2+3*x+3)^(1/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)*x+1618476323976576*(x^2+3*x+3)^(2/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^2-512180419198701*RootOf(_Z^3-9)^2*(x^2+3*x+3)^(1/3)*x^2-3073082515192206*(x^2+3*x+3)^(1/3)*RootOf(_Z^3-9)^2*x+4855428971929728*(x^2+3*x+3)^(1/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)+353332887661869*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x^3+4757474314187370*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x^2+14272422942562110*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x+14272422942562110*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)-25039338495723*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2-4609623772788309*(x^2+3*x+3)^(1/3)*RootOf(_Z^3-9)^2-4609623772788309*(x^2+3*x+3)^(2/3)*x+24305106415545*RootOf(_Z^3-9)^3*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)-56711914969605*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x^3+58425123156687*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x^3)/x^3)","C"
2292,0,0,147,0.138000," ","int((-a*b+x^2)/(x^2*(-a+x)*(-b+x))^(1/3)/(a*b*d-(a*d+b*d+1)*x+d*x^2),x)","\[\int \frac{-a b +x^{2}}{\left(x^{2} \left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{3}} \left(a b d -\left(a d +b d +1\right) x +d \,x^{2}\right)}\, dx\]"," ",0,"int((-a*b+x^2)/(x^2*(-a+x)*(-b+x))^(1/3)/(a*b*d-(a*d+b*d+1)*x+d*x^2),x)","F"
2293,1,635,133,18.880000," ","int((-3+2*x)*(x^3-x+1)^(2/3)/x^3/(x^3+2*x-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{3 \left(x^{3}-x +1\right)^{\frac{2}{3}}}{4 x^{2}}+\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right) \ln \left(-\frac{5 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{3} x^{3}+18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{3}+14 \left(x^{3}-x +1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x +7 \left(x^{3}-x +1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{2}+48 \left(x^{3}-x +1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right) x^{2}+10 \RootOf \left(\textit{\_Z}^{3}+18\right) x^{3}+36 x^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right)+6 \left(x^{3}-x +1\right)^{\frac{2}{3}} x -10 \RootOf \left(\textit{\_Z}^{3}+18\right) x -36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right) x +10 \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right)}{x^{3}+2 x -2}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{3}+18\right) \ln \left(-\frac{-\RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{3} x^{3}-3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{3}+9 \left(x^{3}-x +1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right) x^{2}+5 \RootOf \left(\textit{\_Z}^{3}+18\right) x^{3}+15 x^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right)+9 \left(x^{3}-x +1\right)^{\frac{2}{3}} x -2 \RootOf \left(\textit{\_Z}^{3}+18\right) x -6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right) x +2 \RootOf \left(\textit{\_Z}^{3}+18\right)+6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+36 \textit{\_Z}^{2}\right)}{x^{3}+2 x -2}\right)}{4}$&$635$\\ trager&$\text{Expression too large to display}$&$1234$\\ \hline \end{longtable}"," ",0,"-3/4*(x^3-x+1)^(2/3)/x^2+3/2*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)*ln(-(5*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)*RootOf(_Z^3+18)^3*x^3+18*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)^2*RootOf(_Z^3+18)^2*x^3+14*(x^3-x+1)^(2/3)*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)*RootOf(_Z^3+18)^2*x+7*(x^3-x+1)^(1/3)*RootOf(_Z^3+18)^2*x^2+48*(x^3-x+1)^(1/3)*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)*RootOf(_Z^3+18)*x^2+10*RootOf(_Z^3+18)*x^3+36*x^3*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)+6*(x^3-x+1)^(2/3)*x-10*RootOf(_Z^3+18)*x-36*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)*x+10*RootOf(_Z^3+18)+36*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2))/(x^3+2*x-2))+1/4*RootOf(_Z^3+18)*ln(-(-RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)*RootOf(_Z^3+18)^3*x^3-3*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)^2*RootOf(_Z^3+18)^2*x^3+9*(x^3-x+1)^(1/3)*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)*RootOf(_Z^3+18)*x^2+5*RootOf(_Z^3+18)*x^3+15*x^3*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)+9*(x^3-x+1)^(2/3)*x-2*RootOf(_Z^3+18)*x-6*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2)*x+2*RootOf(_Z^3+18)+6*RootOf(RootOf(_Z^3+18)^2+6*_Z*RootOf(_Z^3+18)+36*_Z^2))/(x^3+2*x-2))","C"
2294,1,1054,133,18.985000," ","int((-3+4*x)*(x^3+2*x-1)^(2/3)/x^3/(x^3-4*x+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 \left(x^{3}+2 x -1\right)^{\frac{2}{3}}}{4 x^{2}}-\frac{\ln \left(-\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-18\right)^{3} x^{3}-12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-18\right)^{2} x^{3}+14 \left(x^{3}+2 x -1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-18\right)^{2} x -\left(x^{3}+2 x -1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-18\right)^{2} x^{2}+42 \left(x^{3}+2 x -1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-18\right) x^{2}-6 \RootOf \left(\textit{\_Z}^{3}-18\right) x^{3}+24 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+36 \textit{\_Z}^{2}\right) x^{3}-6 \left(x^{3}+2 x -1\right)^{\frac{2}{3}} x -12 \RootOf \left(\textit{\_Z}^{3}-18\right) x +48 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+36 \textit{\_Z}^{2}\right) x +6 \RootOf \left(\textit{\_Z}^{3}-18\right)-24 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+36 \textit{\_Z}^{2}\right)}{x^{3}-4 x +2}\right) \RootOf \left(\textit{\_Z}^{3}-18\right)}{4}-\frac{3 \ln \left(-\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-18\right)^{3} x^{3}-12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-18\right)^{2} x^{3}+14 \left(x^{3}+2 x -1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-18\right)^{2} x -\left(x^{3}+2 x -1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-18\right)^{2} x^{2}+42 \left(x^{3}+2 x -1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-18\right) x^{2}-6 \RootOf \left(\textit{\_Z}^{3}-18\right) x^{3}+24 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+36 \textit{\_Z}^{2}\right) x^{3}-6 \left(x^{3}+2 x -1\right)^{\frac{2}{3}} x -12 \RootOf \left(\textit{\_Z}^{3}-18\right) x +48 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+36 \textit{\_Z}^{2}\right) x +6 \RootOf \left(\textit{\_Z}^{3}-18\right)-24 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+36 \textit{\_Z}^{2}\right)}{x^{3}-4 x +2}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+36 \textit{\_Z}^{2}\right)}{2}+\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+36 \textit{\_Z}^{2}\right) \ln \left(\frac{5 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-18\right)^{3} x^{3}+12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-18\right)^{2} x^{3}+14 \left(x^{3}+2 x -1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-18\right)^{2} x +8 \left(x^{3}+2 x -1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-18\right)^{2} x^{2}+42 \left(x^{3}+2 x -1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-18\right) x^{2}+25 \RootOf \left(\textit{\_Z}^{3}-18\right) x^{3}+60 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+36 \textit{\_Z}^{2}\right) x^{3}+48 \left(x^{3}+2 x -1\right)^{\frac{2}{3}} x +20 \RootOf \left(\textit{\_Z}^{3}-18\right) x +48 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+36 \textit{\_Z}^{2}\right) x -10 \RootOf \left(\textit{\_Z}^{3}-18\right)-24 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-18\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-18\right)+36 \textit{\_Z}^{2}\right)}{x^{3}-4 x +2}\right)}{2}$&$1054$\\ trager&$\text{Expression too large to display}$&$1480$\\ \hline \end{longtable}"," ",0,"3/4*(x^3+2*x-1)^(2/3)/x^2-1/4*ln(-(3*RootOf(RootOf(_Z^3-18)^2+6*_Z*RootOf(_Z^3-18)+36*_Z^2)*RootOf(_Z^3-18)^3*x^3-12*RootOf(RootOf(_Z^3-18)^2+6*_Z*RootOf(_Z^3-18)+36*_Z^2)^2*RootOf(_Z^3-18)^2*x^3+14*(x^3+2*x-1)^(2/3)*RootOf(RootOf(_Z^3-18)^2+6*_Z*RootOf(_Z^3-18)+36*_Z^2)*RootOf(_Z^3-18)^2*x-(x^3+2*x-1)^(1/3)*RootOf(_Z^3-18)^2*x^2+42*(x^3+2*x-1)^(1/3)*RootOf(RootOf(_Z^3-18)^2+6*_Z*RootOf(_Z^3-18)+36*_Z^2)*RootOf(_Z^3-18)*x^2-6*RootOf(_Z^3-18)*x^3+24*RootOf(RootOf(_Z^3-18)^2+6*_Z*RootOf(_Z^3-18)+36*_Z^2)*x^3-6*(x^3+2*x-1)^(2/3)*x-12*RootOf(_Z^3-18)*x+48*RootOf(RootOf(_Z^3-18)^2+6*_Z*RootOf(_Z^3-18)+36*_Z^2)*x+6*RootOf(_Z^3-18)-24*RootOf(RootOf(_Z^3-18)^2+6*_Z*RootOf(_Z^3-18)+36*_Z^2))/(x^3-4*x+2))*RootOf(_Z^3-18)-3/2*ln(-(3*RootOf(RootOf(_Z^3-18)^2+6*_Z*RootOf(_Z^3-18)+36*_Z^2)*RootOf(_Z^3-18)^3*x^3-12*RootOf(RootOf(_Z^3-18)^2+6*_Z*RootOf(_Z^3-18)+36*_Z^2)^2*RootOf(_Z^3-18)^2*x^3+14*(x^3+2*x-1)^(2/3)*RootOf(RootOf(_Z^3-18)^2+6*_Z*RootOf(_Z^3-18)+36*_Z^2)*RootOf(_Z^3-18)^2*x-(x^3+2*x-1)^(1/3)*RootOf(_Z^3-18)^2*x^2+42*(x^3+2*x-1)^(1/3)*RootOf(RootOf(_Z^3-18)^2+6*_Z*RootOf(_Z^3-18)+36*_Z^2)*RootOf(_Z^3-18)*x^2-6*RootOf(_Z^3-18)*x^3+24*RootOf(RootOf(_Z^3-18)^2+6*_Z*RootOf(_Z^3-18)+36*_Z^2)*x^3-6*(x^3+2*x-1)^(2/3)*x-12*RootOf(_Z^3-18)*x+48*RootOf(RootOf(_Z^3-18)^2+6*_Z*RootOf(_Z^3-18)+36*_Z^2)*x+6*RootOf(_Z^3-18)-24*RootOf(RootOf(_Z^3-18)^2+6*_Z*RootOf(_Z^3-18)+36*_Z^2))/(x^3-4*x+2))*RootOf(RootOf(_Z^3-18)^2+6*_Z*RootOf(_Z^3-18)+36*_Z^2)+3/2*RootOf(RootOf(_Z^3-18)^2+6*_Z*RootOf(_Z^3-18)+36*_Z^2)*ln((5*RootOf(RootOf(_Z^3-18)^2+6*_Z*RootOf(_Z^3-18)+36*_Z^2)*RootOf(_Z^3-18)^3*x^3+12*RootOf(RootOf(_Z^3-18)^2+6*_Z*RootOf(_Z^3-18)+36*_Z^2)^2*RootOf(_Z^3-18)^2*x^3+14*(x^3+2*x-1)^(2/3)*RootOf(RootOf(_Z^3-18)^2+6*_Z*RootOf(_Z^3-18)+36*_Z^2)*RootOf(_Z^3-18)^2*x+8*(x^3+2*x-1)^(1/3)*RootOf(_Z^3-18)^2*x^2+42*(x^3+2*x-1)^(1/3)*RootOf(RootOf(_Z^3-18)^2+6*_Z*RootOf(_Z^3-18)+36*_Z^2)*RootOf(_Z^3-18)*x^2+25*RootOf(_Z^3-18)*x^3+60*RootOf(RootOf(_Z^3-18)^2+6*_Z*RootOf(_Z^3-18)+36*_Z^2)*x^3+48*(x^3+2*x-1)^(2/3)*x+20*RootOf(_Z^3-18)*x+48*RootOf(RootOf(_Z^3-18)^2+6*_Z*RootOf(_Z^3-18)+36*_Z^2)*x-10*RootOf(_Z^3-18)-24*RootOf(RootOf(_Z^3-18)^2+6*_Z*RootOf(_Z^3-18)+36*_Z^2))/(x^3-4*x+2))","C"
2295,1,102,163,0.306000," ","int((x^6-13*x^5+65*x^4-150*x^3+135*x^2+27*x-81)^(1/2)/(-1+x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(8 x^{2}-62 x +115\right) \sqrt{\left(x^{2}-x -1\right) \left(-3+x \right)^{4}}}{24 \left(-3+x \right)^{2}}+\frac{\left(\frac{77 \ln \left(x -\frac{1}{2}+\sqrt{x^{2}-x -1}\right)}{16}-4 \arctan \left(\frac{-3+x}{2 \sqrt{\left(-1+x \right)^{2}-2+x}}\right)\right) \sqrt{\left(x^{2}-x -1\right) \left(-3+x \right)^{4}}}{\left(-3+x \right)^{2} \sqrt{x^{2}-x -1}}$&$102$\\ default&$\frac{\sqrt{x^{6}-13 x^{5}+65 x^{4}-150 x^{3}+135 x^{2}+27 x -81}\, \left(16 \left(x^{2}-x -1\right)^{\frac{3}{2}}-108 x \sqrt{x^{2}-x -1}+246 \sqrt{x^{2}-x -1}+231 \ln \left(x -\frac{1}{2}+\sqrt{x^{2}-x -1}\right)-192 \arctan \left(\frac{-3+x}{2 \sqrt{x^{2}-x -1}}\right)\right)}{48 \left(-3+x \right)^{2} \sqrt{x^{2}-x -1}}$&$120$\\ trager&$\frac{\left(8 x^{2}-62 x +115\right) \sqrt{x^{6}-13 x^{5}+65 x^{4}-150 x^{3}+135 x^{2}+27 x -81}}{24 \left(-3+x \right)^{2}}+\frac{77 \ln \left(\frac{2 x^{3}-13 x^{2}+2 \sqrt{x^{6}-13 x^{5}+65 x^{4}-150 x^{3}+135 x^{2}+27 x -81}+24 x -9}{\left(-3+x \right)^{2}}\right)}{16}+4 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}-9 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+27 \RootOf \left(\textit{\_Z}^{2}+1\right) x -27 \RootOf \left(\textit{\_Z}^{2}+1\right)+2 \sqrt{x^{6}-13 x^{5}+65 x^{4}-150 x^{3}+135 x^{2}+27 x -81}}{\left(-1+x \right) \left(-3+x \right)^{2}}\right)$&$197$\\ \hline \end{longtable}"," ",0,"1/24*(8*x^2-62*x+115)*((x^2-x-1)*(-3+x)^4)^(1/2)/(-3+x)^2+(77/16*ln(x-1/2+(x^2-x-1)^(1/2))-4*arctan(1/2*(-3+x)/((-1+x)^2-2+x)^(1/2)))*((x^2-x-1)*(-3+x)^4)^(1/2)/(-3+x)^2/(x^2-x-1)^(1/2)","A"
2296,0,0,165,0.019000," ","int((2*p*x^3-q)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)/x^2/(a*p*x^3+a*q+b*x),x)","\[\int \frac{\left(2 p \,x^{3}-q \right) \sqrt{p^{2} x^{6}+2 p q \,x^{3}-2 p q \,x^{2}+q^{2}}}{x^{2} \left(a p \,x^{3}+a q +b x \right)}\, dx\]"," ",0,"int((2*p*x^3-q)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)/x^2/(a*p*x^3+a*q+b*x),x)","F"
2297,1,11794,97,43.435000," ","int(1/x^2/(x^8+x^7-5*x^6-2*x^5+10*x^4-2*x^3-7*x^2+5*x-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$11794$\\ trager&$\text{Expression too large to display}$&$106745$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2298,0,0,137,0.043000," ","int((x^2+1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^2-1)/(x^4+1)^(1/2),x)","\[\int \frac{\left(x^{2}+1\right) \sqrt{x^{2}+\sqrt{x^{4}+1}}}{\left(x^{2}-1\right) \sqrt{x^{4}+1}}\, dx\]"," ",0,"int((x^2+1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^2-1)/(x^4+1)^(1/2),x)","F"
2299,1,403,134,4.880000," ","int((2+x)/(-3+x)/(-x^2+1)^(1/4)/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{4}+2\right) \ln \left(\frac{2 \sqrt{-x^{2}+1}\, \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} x -2 \sqrt{-x^{2}+1}\, \RootOf \left(\textit{\_Z}^{4}+2\right)^{3}-2 \left(-x^{2}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{2}+4 \left(-x^{2}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x +\RootOf \left(\textit{\_Z}^{4}+2\right) x^{3}+4 \left(-x^{2}+1\right)^{\frac{3}{4}}-2 \left(-x^{2}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}-3 \RootOf \left(\textit{\_Z}^{4}+2\right) x^{2}+5 \RootOf \left(\textit{\_Z}^{4}+2\right) x +\RootOf \left(\textit{\_Z}^{4}+2\right)}{\left(-3+x \right) \left(x^{2}+1\right)}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \ln \left(\frac{-2 \sqrt{-x^{2}+1}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x +2 \sqrt{-x^{2}+1}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}+2 \left(-x^{2}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{2}-4 \left(-x^{2}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{3}+4 \left(-x^{2}+1\right)^{\frac{3}{4}}+2 \left(-x^{2}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2}-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{2}+5 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right)}{\left(-3+x \right) \left(x^{2}+1\right)}\right)}{4}$&$403$\\ \hline \end{longtable}"," ",0,"1/4*RootOf(_Z^4+2)*ln((2*(-x^2+1)^(1/2)*RootOf(_Z^4+2)^3*x-2*(-x^2+1)^(1/2)*RootOf(_Z^4+2)^3-2*(-x^2+1)^(1/4)*RootOf(_Z^4+2)^2*x^2+4*(-x^2+1)^(1/4)*RootOf(_Z^4+2)^2*x+RootOf(_Z^4+2)*x^3+4*(-x^2+1)^(3/4)-2*(-x^2+1)^(1/4)*RootOf(_Z^4+2)^2-3*RootOf(_Z^4+2)*x^2+5*RootOf(_Z^4+2)*x+RootOf(_Z^4+2))/(-3+x)/(x^2+1))+1/4*RootOf(_Z^2+RootOf(_Z^4+2)^2)*ln((-2*(-x^2+1)^(1/2)*RootOf(_Z^2+RootOf(_Z^4+2)^2)*RootOf(_Z^4+2)^2*x+2*(-x^2+1)^(1/2)*RootOf(_Z^2+RootOf(_Z^4+2)^2)*RootOf(_Z^4+2)^2+2*(-x^2+1)^(1/4)*RootOf(_Z^4+2)^2*x^2-4*(-x^2+1)^(1/4)*RootOf(_Z^4+2)^2*x+RootOf(_Z^2+RootOf(_Z^4+2)^2)*x^3+4*(-x^2+1)^(3/4)+2*(-x^2+1)^(1/4)*RootOf(_Z^4+2)^2-3*RootOf(_Z^2+RootOf(_Z^4+2)^2)*x^2+5*RootOf(_Z^2+RootOf(_Z^4+2)^2)*x+RootOf(_Z^2+RootOf(_Z^4+2)^2))/(-3+x)/(x^2+1))","C"
2300,1,943,140,0.787000," ","int((a^2*x^3+b^2)^(1/2)*(a^2*x^6+c*x^3+2*b^2)/x/(a^2*x^6-b^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(3 a b +c \right) \left(\frac{2 \sqrt{a^{2} x^{3}+b^{2}}}{3 a}+\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}-b \right)}{\sum}\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i a \left(2 x +\frac{-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{a \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i a \left(2 x +\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(i \left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  \sqrt{3}\, a -i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}}+2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-\left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  a -\left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  +i \sqrt{3}\, b^{2}-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  -3 b^{2}}{2 b \left(a +b \right)}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{2 \sqrt{a^{2} x^{3}+b^{2}}}\right)}{3 a^{2}}\right)}{2 b}+\frac{\left(3 a b -c \right) \left(\frac{2 \sqrt{a^{2} x^{3}+b^{2}}}{3 a}+\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}+b \right)}{\sum}\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i a \left(2 x +\frac{-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{a \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i a \left(2 x +\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(i \left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  \sqrt{3}\, a -i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}}+2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-\left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  a -\left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  +i \sqrt{3}\, b^{2}-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  -3 b^{2}}{2 b \left(a -b \right)}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{2 \sqrt{a^{2} x^{3}+b^{2}}}\right)}{3 a^{2}}\right)}{2 b}-\frac{4 \sqrt{a^{2} x^{3}+b^{2}}}{3}+\frac{4 b^{2} \arctanh \left(\frac{\sqrt{a^{2} x^{3}+b^{2}}}{\sqrt{b^{2}}}\right)}{3 \sqrt{b^{2}}}$&$943$\\ elliptic&$\text{Expression too large to display}$&$3175$\\ \hline \end{longtable}"," ",0,"1/2*(3*a*b+c)/b*(2/3/a*(a^2*x^3+b^2)^(1/2)+1/3*I/a^2*2^(1/2)*sum((-a*b^2)^(1/3)*(1/2*I*a*(2*x+1/a*(-I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3)))/(-a*b^2)^(1/3))^(1/2)*(a*(x-1/a*(-a*b^2)^(1/3))/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3)))^(1/2)*(-1/2*I*a*(2*x+1/a*(I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3)))/(-a*b^2)^(1/3))^(1/2)/(a^2*x^3+b^2)^(1/2)*(I*(-a*b^2)^(1/3)*_alpha*3^(1/2)*a-I*3^(1/2)*(-a*b^2)^(2/3)+2*_alpha^2*a^2-(-a*b^2)^(1/3)*_alpha*a-(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2/a*(-a*b^2)^(1/3)-1/2*I*3^(1/2)/a*(-a*b^2)^(1/3))*3^(1/2)*a/(-a*b^2)^(1/3))^(1/2),-1/2*(2*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha^2*a-I*(-a*b^2)^(2/3)*3^(1/2)*_alpha+I*3^(1/2)*b^2-3*(-a*b^2)^(2/3)*_alpha-3*b^2)/b/(a+b),(I*3^(1/2)/a*(-a*b^2)^(1/3)/(-3/2/a*(-a*b^2)^(1/3)+1/2*I*3^(1/2)/a*(-a*b^2)^(1/3)))^(1/2)),_alpha=RootOf(_Z^3*a-b)))+1/2*(3*a*b-c)/b*(2/3/a*(a^2*x^3+b^2)^(1/2)+1/3*I/a^2*2^(1/2)*sum((-a*b^2)^(1/3)*(1/2*I*a*(2*x+1/a*(-I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3)))/(-a*b^2)^(1/3))^(1/2)*(a*(x-1/a*(-a*b^2)^(1/3))/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3)))^(1/2)*(-1/2*I*a*(2*x+1/a*(I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3)))/(-a*b^2)^(1/3))^(1/2)/(a^2*x^3+b^2)^(1/2)*(I*(-a*b^2)^(1/3)*_alpha*3^(1/2)*a-I*3^(1/2)*(-a*b^2)^(2/3)+2*_alpha^2*a^2-(-a*b^2)^(1/3)*_alpha*a-(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2/a*(-a*b^2)^(1/3)-1/2*I*3^(1/2)/a*(-a*b^2)^(1/3))*3^(1/2)*a/(-a*b^2)^(1/3))^(1/2),1/2*(2*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha^2*a-I*(-a*b^2)^(2/3)*3^(1/2)*_alpha+I*3^(1/2)*b^2-3*(-a*b^2)^(2/3)*_alpha-3*b^2)/b/(a-b),(I*3^(1/2)/a*(-a*b^2)^(1/3)/(-3/2/a*(-a*b^2)^(1/3)+1/2*I*3^(1/2)/a*(-a*b^2)^(1/3)))^(1/2)),_alpha=RootOf(_Z^3*a+b)))-4/3*(a^2*x^3+b^2)^(1/2)+4/3*b^2*arctanh((a^2*x^3+b^2)^(1/2)/(b^2)^(1/2))/(b^2)^(1/2)","C"
2301,0,0,132,0.023000," ","int((2*x^8-x^4+1)/(x^4+1)^(1/4)/(x^8-2*x^4-1),x)","\[\int \frac{2 x^{8}-x^{4}+1}{\left(x^{4}+1\right)^{\frac{1}{4}} \left(x^{8}-2 x^{4}-1\right)}\, dx\]"," ",0,"int((2*x^8-x^4+1)/(x^4+1)^(1/4)/(x^8-2*x^4-1),x)","F"
2302,0,0,138,0.037000," ","int((x^2-1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^2+1)/(x^4+1)^(1/2),x)","\[\int \frac{\left(x^{2}-1\right) \sqrt{x^{2}+\sqrt{x^{4}+1}}}{\left(x^{2}+1\right) \sqrt{x^{4}+1}}\, dx\]"," ",0,"int((x^2-1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^2+1)/(x^4+1)^(1/2),x)","F"
2303,1,118,29,0.084000," ","int(x/(x+(c+(a*x+b)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\left(c +\sqrt{a x +b}\right)^{2}-2 c \left(c +\sqrt{a x +b}\right)-4 a \sqrt{c +\sqrt{a x +b}}+4 a \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 c \,\textit{\_Z}^{2}+a \textit{\_Z} +c^{2}-b \right)}{\sum}\frac{\left(-\textit{\_R}^{2} c +\textit{\_R} a +c^{2}-b \right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-4 \textit{\_R} c +a}\right)}{a}$&$118$\\ default&$\frac{\left(c +\sqrt{a x +b}\right)^{2}-2 c \left(c +\sqrt{a x +b}\right)-4 a \sqrt{c +\sqrt{a x +b}}+4 a \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 c \,\textit{\_Z}^{2}+a \textit{\_Z} +c^{2}-b \right)}{\sum}\frac{\left(-\textit{\_R}^{2} c +\textit{\_R} a +c^{2}-b \right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-4 \textit{\_R} c +a}\right)}{a}$&$118$\\ \hline \end{longtable}"," ",0,"2/a*(1/2*(c+(a*x+b)^(1/2))^2-c*(c+(a*x+b)^(1/2))-2*a*(c+(a*x+b)^(1/2))^(1/2)+2*a*sum((-_R^2*c+_R*a+c^2-b)/(4*_R^3-4*_R*c+a)*ln((c+(a*x+b)^(1/2))^(1/2)-_R),_R=RootOf(_Z^4-2*_Z^2*c+_Z*a+c^2-b)))","B"
2304,1,118,29,0.084000," ","int(x/(x+(c+(a*x+b)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\left(c +\sqrt{a x +b}\right)^{2}-2 c \left(c +\sqrt{a x +b}\right)-4 a \sqrt{c +\sqrt{a x +b}}+4 a \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 c \,\textit{\_Z}^{2}+a \textit{\_Z} +c^{2}-b \right)}{\sum}\frac{\left(-\textit{\_R}^{2} c +\textit{\_R} a +c^{2}-b \right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-4 \textit{\_R} c +a}\right)}{a}$&$118$\\ default&$\frac{\left(c +\sqrt{a x +b}\right)^{2}-2 c \left(c +\sqrt{a x +b}\right)-4 a \sqrt{c +\sqrt{a x +b}}+4 a \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 c \,\textit{\_Z}^{2}+a \textit{\_Z} +c^{2}-b \right)}{\sum}\frac{\left(-\textit{\_R}^{2} c +\textit{\_R} a +c^{2}-b \right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-4 \textit{\_R} c +a}\right)}{a}$&$118$\\ \hline \end{longtable}"," ",0,"2/a*(1/2*(c+(a*x+b)^(1/2))^2-c*(c+(a*x+b)^(1/2))-2*a*(c+(a*x+b)^(1/2))^(1/2)+2*a*sum((-_R^2*c+_R*a+c^2-b)/(4*_R^3-4*_R*c+a)*ln((c+(a*x+b)^(1/2))^(1/2)-_R),_R=RootOf(_Z^4-2*_Z^2*c+_Z*a+c^2-b)))","B"
2305,1,1416,134,14.083000," ","int(1/(1+x)/(x^2-x+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1416$\\ \hline \end{longtable}"," ",0,"1/9*RootOf(_Z^3-9)*ln((61590*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x^3+65997*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x^3+123180*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x^2+131994*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x^2+967776*(x^2-x+1)^(2/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^2*x+246360*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x+263988*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x-1935552*(x^2-x+1)^(2/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^2+322592*(x^2-x+1)^(1/3)*RootOf(_Z^3-9)^2*x^2+1579341*(x^2-x+1)^(1/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)*x^2-1290368*(x^2-x+1)^(1/3)*RootOf(_Z^3-9)^2*x-6317364*(x^2-x+1)^(1/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)*x+349010*RootOf(_Z^3-9)*x^3+373983*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x^3+1290368*(x^2-x+1)^(1/3)*RootOf(_Z^3-9)^2+6317364*(x^2-x+1)^(1/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)-3756990*RootOf(_Z^3-9)*x^2-4025817*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x^2-1834695*(x^2-x+1)^(2/3)*x+5851050*RootOf(_Z^3-9)*x+6269715*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x+3669390*(x^2-x+1)^(2/3)-4455010*RootOf(_Z^3-9)-4773783*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2))/(1+x)^3)+1/3*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*ln((3*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x^3+234*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x^3+6*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x^2+468*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x^2+1872*(x^2-x+1)^(2/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^2*x+12*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^3*x+936*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)^2*RootOf(_Z^3-9)^2*x-3744*(x^2-x+1)^(2/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)^2+624*(x^2-x+1)^(1/3)*RootOf(_Z^3-9)^2*x^2-153*(x^2-x+1)^(1/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)*x^2-2496*(x^2-x+1)^(1/3)*RootOf(_Z^3-9)^2*x+612*(x^2-x+1)^(1/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)*x-8*RootOf(_Z^3-9)*x^3-624*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x^3+2496*(x^2-x+1)^(1/3)*RootOf(_Z^3-9)^2-612*(x^2-x+1)^(1/3)*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*RootOf(_Z^3-9)+201*RootOf(_Z^3-9)*x^2+15678*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x^2+6075*(x^2-x+1)^(2/3)*x-249*RootOf(_Z^3-9)*x-19422*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2)*x-12150*(x^2-x+1)^(2/3)+217*RootOf(_Z^3-9)+16926*RootOf(RootOf(_Z^3-9)^2+3*_Z*RootOf(_Z^3-9)+9*_Z^2))/(1+x)^3)","C"
2306,1,4009,79,58.941000," ","int((x^4+1)*(x^4-x^3)^(1/4)/x^4/(x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$4009$\\ risch&$\text{Expression too large to display}$&$7765$\\ \hline \end{longtable}"," ",0,"-4/45*(4*x^2+x-5)*(x^4-x^3)^(1/4)/x^3-1/2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln((-3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*x^3-4*RootOf(_Z^4-2)^2*(x^4-x^3)^(1/4)*x^2+RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*x^2+4*(x^4-x^3)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x+4*(x^4-x^3)^(3/4))/x^2/(1+x))+1/2*RootOf(_Z^4-2)*ln((-3*RootOf(_Z^4-2)^3*x^3+4*RootOf(_Z^4-2)^2*(x^4-x^3)^(1/4)*x^2+RootOf(_Z^4-2)^3*x^2-4*(x^4-x^3)^(1/2)*RootOf(_Z^4-2)*x+4*(x^4-x^3)^(3/4))/x^2/(1+x))+1/4*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*ln((23*RootOf(_Z^2+RootOf(_Z^4-2)^2)^2*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^3*RootOf(_Z^4-2)^6*x^3-46*RootOf(_Z^2+RootOf(_Z^4-2)^2)^2*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^3*RootOf(_Z^4-2)^6*x^2-346*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^3*x^3+94*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^3*x^2-1008*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^2*(x^4-x^3)^(1/4)*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^2-2016*(x^4-x^3)^(1/2)*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*x-4032*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^3*(x^4-x^3)^(3/4)-352*x^3*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^3+132*x^2*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^3-512*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^2*(x^4-x^3)^(1/4)*x^2-1024*(x^4-x^3)^(1/2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*x-2048*(x^4-x^3)^(3/4))/(RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^3*x-2*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)+4*x+2)/x^2)+1/8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*ln(-(11*RootOf(_Z^2+RootOf(_Z^4-2)^2)^2*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^3*RootOf(_Z^4-2)^6*x^3-22*RootOf(_Z^2+RootOf(_Z^4-2)^2)^2*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^3*RootOf(_Z^4-2)^6*x^2-222*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^3*x^3+158*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^3*x^2-1008*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^2*(x^4-x^3)^(1/4)*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^2+512*(x^4-x^3)^(1/2)*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*x+4032*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^3*(x^4-x^3)^(3/4)+736*x^3*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^3-276*x^2*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^3-512*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^2*(x^4-x^3)^(1/4)*x^2-4032*(x^4-x^3)^(1/2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*x+2048*(x^4-x^3)^(3/4))/(RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^3*x-2*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)+4*x+2)/x^2)+1/32*ln((-37*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^6*x^3-9*RootOf(_Z^2+RootOf(_Z^4-2)^2)^2*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^5*x^3+74*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^6*x^2+18*RootOf(_Z^2+RootOf(_Z^4-2)^2)^2*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^5*x^2+128*(x^4-x^3)^(1/2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^3*RootOf(_Z^4-2)*x-204*(x^4-x^3)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^3*x+332*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^2*(x^4-x^3)^(1/4)*RootOf(_Z^4-2)^2*x^2-76*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^2*(x^4-x^3)^(1/4)*RootOf(_Z^4-2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^2+148*x^3*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^3+36*x^3*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)-816*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^3*(x^4-x^3)^(3/4)+74*x^2*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^3+18*x^2*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)+1024*(x^4-x^3)^(3/4))/(RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^3*x-2*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-4*x-2)/x^2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^3*RootOf(_Z^4-2)+1/32*ln((-37*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^6*x^3-9*RootOf(_Z^2+RootOf(_Z^4-2)^2)^2*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^5*x^3+74*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^6*x^2+18*RootOf(_Z^2+RootOf(_Z^4-2)^2)^2*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^5*x^2+128*(x^4-x^3)^(1/2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^3*RootOf(_Z^4-2)*x-204*(x^4-x^3)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^3*x+332*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^2*(x^4-x^3)^(1/4)*RootOf(_Z^4-2)^2*x^2-76*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^2*(x^4-x^3)^(1/4)*RootOf(_Z^4-2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^2+148*x^3*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^3+36*x^3*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)-816*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^3*(x^4-x^3)^(3/4)+74*x^2*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^3+18*x^2*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)+1024*(x^4-x^3)^(3/4))/(RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^3*x-2*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-4*x-2)/x^2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^3-1/16*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^3*ln((6*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^6*x^3+17*RootOf(_Z^2+RootOf(_Z^4-2)^2)^2*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^5*x^3-12*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^6*x^2-34*RootOf(_Z^2+RootOf(_Z^4-2)^2)^2*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^5*x^2+47*(x^4-x^3)^(1/2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^3*RootOf(_Z^4-2)*x+79*(x^4-x^3)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^3*x+94*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^2*(x^4-x^3)^(1/4)*RootOf(_Z^4-2)^2*x^2+158*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)^2*(x^4-x^3)^(1/4)*RootOf(_Z^4-2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^2+96*x^3*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^3+272*x^3*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)+504*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^3*(x^4-x^3)^(3/4)-36*x^2*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^3-102*x^2*RootOf(_Z^4-8*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-16)*RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)-256*(x^4-x^3)^(3/4))/(RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^3*x-2*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)-4*x-2)/x^2)","B"
2307,1,3747,79,61.744000," ","int((x^4+1)*(x^4-x^3)^(1/4)/x^4/(x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$3747$\\ risch&$\text{Expression too large to display}$&$8062$\\ \hline \end{longtable}"," ",0,"-4/45*(4*x^2+x-5)*(x^4-x^3)^(1/4)/x^3+536870912*ln((50728546202701266944*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^8*x^3-101457092405402533888*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^8*x^2+95563022336*x^3*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3-1082331758592*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4*(x^4-x^3)^(1/4)*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^2*x^2-37580963840*x^2*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3-1099511627776*(x^4-x^3)^(1/2)*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)*x+17317308137472*(x^4-x^3)^(3/4)*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4+21*x^3*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3+316*(x^4-x^3)^(1/4)*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^2*x^2-3*x^2*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3-752*(x^4-x^3)^(1/2)*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)*x-5056*(x^4-x^3)^(3/4))/(4294967296*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4*x-8589934592*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-3*x+1)/x^2)*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)-1/8*ln((50728546202701266944*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^8*x^3-101457092405402533888*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^8*x^2+95563022336*x^3*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3-1082331758592*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4*(x^4-x^3)^(1/4)*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^2*x^2-37580963840*x^2*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3-1099511627776*(x^4-x^3)^(1/2)*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)*x+17317308137472*(x^4-x^3)^(3/4)*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4+21*x^3*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3+316*(x^4-x^3)^(1/4)*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^2*x^2-3*x^2*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3-752*(x^4-x^3)^(1/2)*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)*x-5056*(x^4-x^3)^(3/4))/(4294967296*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4*x-8589934592*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-3*x+1)/x^2)*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)-1/8*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)*ln(-(212137556847659843584*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^8*x^3-424275113695319687168*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^8*x^2+272730423296*x^3*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3-2164663517184*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4*(x^4-x^3)^(1/4)*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^2*x^2+96636764160*x^2*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3+8658654068736*(x^4-x^3)^(1/2)*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)*x-34634616274944*(x^4-x^3)^(3/4)*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-119*x^3*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3+632*(x^4-x^3)^(1/4)*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^2*x^2+17*x^2*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3-2528*(x^4-x^3)^(1/2)*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)*x+10112*(x^4-x^3)^(3/4))/(4294967296*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4*x-8589934592*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-3*x+1)/x^2)+549755813888*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^5*ln(-(851083777008698938993147904*x^3*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^11-1702167554017397877986295808*x^2*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^11-2395915001761103872*x^3*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^7+2215771016666284032*x^2*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^7-17732923532771328*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^6*(x^4-x^3)^(1/4)*x^2+17592186044416*(x^4-x^3)^(1/2)*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^5*x+270582939648*(x^4-x^3)^(3/4)*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4+1283457024*x^3*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^3-713031680*x^2*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^3+3080192*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^2*(x^4-x^3)^(1/4)*x^2-20224*(x^4-x^3)^(1/2)*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)*x-47*(x^4-x^3)^(3/4))/(4294967296*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4*x-8589934592*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4+x+3)/x^2)-128*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)*ln(-(851083777008698938993147904*x^3*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^11-1702167554017397877986295808*x^2*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^11-2395915001761103872*x^3*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^7+2215771016666284032*x^2*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^7-17732923532771328*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^6*(x^4-x^3)^(1/4)*x^2+17592186044416*(x^4-x^3)^(1/2)*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^5*x+270582939648*(x^4-x^3)^(3/4)*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4+1283457024*x^3*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^3-713031680*x^2*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^3+3080192*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^2*(x^4-x^3)^(1/4)*x^2-20224*(x^4-x^3)^(1/2)*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)*x-47*(x^4-x^3)^(3/4))/(4294967296*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4*x-8589934592*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4+x+3)/x^2)-128*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)*ln(-(1779538806472734145167491072*x^3*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^11-3559077612945468290334982144*x^2*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^11-3945153273576554496*x^3*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^7+2504001392817995776*x^2*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^7+17732923532771328*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^6*(x^4-x^3)^(1/4)*x^2-69269232549888*(x^4-x^3)^(1/2)*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^5*x+270582939648*(x^4-x^3)^(3/4)*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4+452984832*x^3*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^3-251658240*x^2*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^3-3080192*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^2*(x^4-x^3)^(1/4)*x^2+12032*(x^4-x^3)^(1/2)*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)*x-47*(x^4-x^3)^(3/4))/(4294967296*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4*x-8589934592*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4+x+3)/x^2)-137438953472*ln(-(844424930131968*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^7*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3*x^3-281474976710656*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^7*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3*x^2-274877906944*(x^4-x^3)^(1/2)*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^5*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)*x-196608*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^3*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3*x^3+65536*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^3*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3*x^2+4096*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^2*(x^4-x^3)^(1/4)*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^2*x^2+64*(x^4-x^3)^(1/2)*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)*x-(x^4-x^3)^(3/4))/x^2/(1+x))*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^5*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)+32*ln(-(844424930131968*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^7*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3*x^3-281474976710656*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^7*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3*x^2-274877906944*(x^4-x^3)^(1/2)*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^5*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)*x-196608*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^3*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3*x^3+65536*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^3*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3*x^2+4096*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^2*(x^4-x^3)^(1/4)*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^2*x^2+64*(x^4-x^3)^(1/2)*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)*x-(x^4-x^3)^(3/4))/x^2/(1+x))*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)-32*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)*ln((196608*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^3*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3*x^3-65536*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^3*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^3*x^2+4096*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^2*(x^4-x^3)^(1/4)*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)^2*x^2+64*(x^4-x^3)^(1/2)*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)*RootOf(_Z^4+1099511627776*RootOf(9223372036854775808*_Z^8-4294967296*_Z^4+1)^4-512)*x+(x^4-x^3)^(3/4))/x^2/(1+x))","B"
2308,0,0,139,0.009000," ","int((a*x^3+b*x)^(1/3)*(a*x^4+b)/x^4,x)","\[\int \frac{\left(a \,x^{3}+b x \right)^{\frac{1}{3}} \left(a \,x^{4}+b \right)}{x^{4}}\, dx\]"," ",0,"int((a*x^3+b*x)^(1/3)*(a*x^4+b)/x^4,x)","F"
2309,1,322,139,0.225000," ","int((a^4*x^4+b^4)/(a^2*x^3-b^2*x)^(1/2)/(a^4*x^4-b^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\frac{x}{\sqrt{\left(x^{2}-\frac{b^{2}}{a^{2}}\right) a^{2} x}}+\frac{b \sqrt{1+\frac{a x}{b}}\, \sqrt{2-\frac{2 a x}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{2 a \sqrt{a^{2} x^{3}-b^{2} x}}+\frac{i b^{2} \sqrt{1+\frac{a x}{b}}\, \sqrt{2-\frac{2 a x}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, -\frac{b}{a \left(-\frac{i b}{a}-\frac{b}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a^{2} x^{3}-b^{2} x}\, \left(-\frac{i b}{a}-\frac{b}{a}\right)}-\frac{i b^{2} \sqrt{1+\frac{a x}{b}}\, \sqrt{2-\frac{2 a x}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, -\frac{b}{a \left(-\frac{b}{a}+\frac{i b}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a^{2} x^{3}-b^{2} x}\, \left(-\frac{b}{a}+\frac{i b}{a}\right)}$&$322$\\ default&$\frac{b \sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{2 \left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}-b^{2} x}}-\frac{b \left(-\frac{a^{2} x^{2}-a b x}{b^{2} a \sqrt{\left(x +\frac{b}{a}\right) \left(a^{2} x^{2}-a b x \right)}}+\frac{\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{2 \left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{2 a \sqrt{a^{2} x^{3}-b^{2} x}}+\frac{\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{2 \left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \left(-\frac{2 b \EllipticE \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a}+\frac{b \EllipticF \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a}\right)}{2 b \sqrt{a^{2} x^{3}-b^{2} x}}\right)}{2}+\frac{b \left(-\frac{a^{2} x^{2}+a b x}{b^{2} a \sqrt{\left(x -\frac{b}{a}\right) \left(a^{2} x^{2}+a b x \right)}}-\frac{\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{2 \left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{2 a \sqrt{a^{2} x^{3}-b^{2} x}}+\frac{\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{2 \left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \left(-\frac{2 b \EllipticE \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a}+\frac{b \EllipticF \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a}\right)}{2 b \sqrt{a^{2} x^{3}-b^{2} x}}\right)}{2}-b^{2} \left(-\frac{i \sqrt{1+\frac{a x}{b}}\, \sqrt{2-\frac{2 a x}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, -\frac{b}{a \left(-\frac{i b}{a}-\frac{b}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a^{2} x^{3}-b^{2} x}\, \left(-\frac{i b}{a}-\frac{b}{a}\right)}+\frac{i \sqrt{1+\frac{a x}{b}}\, \sqrt{2-\frac{2 a x}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, -\frac{b}{a \left(-\frac{b}{a}+\frac{i b}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a^{2} x^{3}-b^{2} x}\, \left(-\frac{b}{a}+\frac{i b}{a}\right)}\right)$&$787$\\ \hline \end{longtable}"," ",0,"-x/((x^2-b^2/a^2)*a^2*x)^(1/2)+1/2*b/a*(1+a*x/b)^(1/2)*(2-2*a*x/b)^(1/2)*(-a*x/b)^(1/2)/(a^2*x^3-b^2*x)^(1/2)*EllipticF(((x+b/a)/b*a)^(1/2),1/2*2^(1/2))+1/2*I*b^2/a^2*(1+a*x/b)^(1/2)*(2-2*a*x/b)^(1/2)*(-a*x/b)^(1/2)/(a^2*x^3-b^2*x)^(1/2)/(-I*b/a-b/a)*EllipticPi(((x+b/a)/b*a)^(1/2),-b/a/(-I*b/a-b/a),1/2*2^(1/2))-1/2*I*b^2/a^2*(1+a*x/b)^(1/2)*(2-2*a*x/b)^(1/2)*(-a*x/b)^(1/2)/(a^2*x^3-b^2*x)^(1/2)/(-b/a+I*b/a)*EllipticPi(((x+b/a)/b*a)^(1/2),-b/a/(-b/a+I*b/a),1/2*2^(1/2))","C"
2310,0,0,59,0.035000," ","int((1+x)/(x^3-1)/(x^8-16*x^6+96*x^4-256*x^2+256)^(1/8),x)","\[\int \frac{1+x}{\left(x^{3}-1\right) \left(x^{8}-16 x^{6}+96 x^{4}-256 x^{2}+256\right)^{\frac{1}{8}}}\, dx\]"," ",0,"int((1+x)/(x^3-1)/(x^8-16*x^6+96*x^4-256*x^2+256)^(1/8),x)","F"
2311,1,16709,103,46.646000," ","int(1/x^2/(x^8-5*x^7+7*x^6+2*x^5-10*x^4+2*x^3+5*x^2-x-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$16709$\\ trager&$\text{Expression too large to display}$&$93820$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2312,0,0,136,0.059000," ","int(c*x^6*(a*x^5-4*b)/(a*x^5+b)^(3/4)/(a^2*x^10-c^2*x^8+2*a*b*x^5+b^2),x)","\[\int \frac{c \,x^{6} \left(a \,x^{5}-4 b \right)}{\left(a \,x^{5}+b \right)^{\frac{3}{4}} \left(a^{2} x^{10}-c^{2} x^{8}+2 a b \,x^{5}+b^{2}\right)}\, dx\]"," ",0,"int(c*x^6*(a*x^5-4*b)/(a*x^5+b)^(3/4)/(a^2*x^10-c^2*x^8+2*a*b*x^5+b^2),x)","F"
2313,1,565,155,0.117000," ","int(x^2*(a*x+(a*x-b)^(1/2))^(1/2)/(a*x-b)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\frac{\left(a x -b \right)^{\frac{3}{2}} \left(a x +\sqrt{a x -b}\right)^{\frac{3}{2}}}{3}-\frac{3 \left(a x -b \right) \left(a x +\sqrt{a x -b}\right)^{\frac{3}{2}}}{10}+\frac{21 \sqrt{a x -b}\, \left(a x +\sqrt{a x -b}\right)^{\frac{3}{2}}}{80}-\frac{7 \left(a x +\sqrt{a x -b}\right)^{\frac{3}{2}}}{32}+\frac{21 \left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{256}+\frac{21 \left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{512}-\frac{21 b \left(\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{4}+\frac{\left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{8}\right)}{80}+\frac{3 b \left(\frac{\left(a x +\sqrt{a x -b}\right)^{\frac{3}{2}}}{3}-\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{8}-\frac{\left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{16}\right)}{5}+3 b \left(\frac{\sqrt{a x -b}\, \left(a x +\sqrt{a x -b}\right)^{\frac{3}{2}}}{4}-\frac{5 \left(a x +\sqrt{a x -b}\right)^{\frac{3}{2}}}{24}+\frac{5 \left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{64}+\frac{5 \left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{128}-\frac{b \left(\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{4}+\frac{\left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{8}\right)}{4}\right)+2 b^{2} \left(\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{4}+\frac{\left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{8}\right)}{a^{3}}$&$565$\\ default&$\frac{\frac{\left(a x -b \right)^{\frac{3}{2}} \left(a x +\sqrt{a x -b}\right)^{\frac{3}{2}}}{3}-\frac{3 \left(a x -b \right) \left(a x +\sqrt{a x -b}\right)^{\frac{3}{2}}}{10}+\frac{21 \sqrt{a x -b}\, \left(a x +\sqrt{a x -b}\right)^{\frac{3}{2}}}{80}-\frac{7 \left(a x +\sqrt{a x -b}\right)^{\frac{3}{2}}}{32}+\frac{21 \left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{256}+\frac{21 \left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{512}-\frac{21 b \left(\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{4}+\frac{\left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{8}\right)}{80}+\frac{3 b \left(\frac{\left(a x +\sqrt{a x -b}\right)^{\frac{3}{2}}}{3}-\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{8}-\frac{\left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{16}\right)}{5}+3 b \left(\frac{\sqrt{a x -b}\, \left(a x +\sqrt{a x -b}\right)^{\frac{3}{2}}}{4}-\frac{5 \left(a x +\sqrt{a x -b}\right)^{\frac{3}{2}}}{24}+\frac{5 \left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{64}+\frac{5 \left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{128}-\frac{b \left(\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{4}+\frac{\left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{8}\right)}{4}\right)+2 b^{2} \left(\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{4}+\frac{\left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{8}\right)}{a^{3}}$&$565$\\ \hline \end{longtable}"," ",0,"2/a^3*(1/6*(a*x-b)^(3/2)*(a*x+(a*x-b)^(1/2))^(3/2)-3/20*(a*x-b)*(a*x+(a*x-b)^(1/2))^(3/2)+21/160*(a*x-b)^(1/2)*(a*x+(a*x-b)^(1/2))^(3/2)-7/64*(a*x+(a*x-b)^(1/2))^(3/2)+21/512*(2*(a*x-b)^(1/2)+1)*(a*x+(a*x-b)^(1/2))^(1/2)+21/1024*(4*b-1)*ln(1/2+(a*x-b)^(1/2)+(a*x+(a*x-b)^(1/2))^(1/2))-21/160*b*(1/4*(2*(a*x-b)^(1/2)+1)*(a*x+(a*x-b)^(1/2))^(1/2)+1/8*(4*b-1)*ln(1/2+(a*x-b)^(1/2)+(a*x+(a*x-b)^(1/2))^(1/2)))+3/10*b*(1/3*(a*x+(a*x-b)^(1/2))^(3/2)-1/8*(2*(a*x-b)^(1/2)+1)*(a*x+(a*x-b)^(1/2))^(1/2)-1/16*(4*b-1)*ln(1/2+(a*x-b)^(1/2)+(a*x+(a*x-b)^(1/2))^(1/2)))+3/2*b*(1/4*(a*x-b)^(1/2)*(a*x+(a*x-b)^(1/2))^(3/2)-5/24*(a*x+(a*x-b)^(1/2))^(3/2)+5/64*(2*(a*x-b)^(1/2)+1)*(a*x+(a*x-b)^(1/2))^(1/2)+5/128*(4*b-1)*ln(1/2+(a*x-b)^(1/2)+(a*x+(a*x-b)^(1/2))^(1/2))-1/4*b*(1/4*(2*(a*x-b)^(1/2)+1)*(a*x+(a*x-b)^(1/2))^(1/2)+1/8*(4*b-1)*ln(1/2+(a*x-b)^(1/2)+(a*x+(a*x-b)^(1/2))^(1/2))))+b^2*(1/4*(2*(a*x-b)^(1/2)+1)*(a*x+(a*x-b)^(1/2))^(1/2)+1/8*(4*b-1)*ln(1/2+(a*x-b)^(1/2)+(a*x+(a*x-b)^(1/2))^(1/2))))","B"
2314,1,604,162,0.176000," ","int((a*k^4*x^4+b*x^2+a)/((1-x)*x*(-k^2*x+1))^(1/2)/(k^4*x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 a \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}-\frac{\left(-2 a \,k^{2}-b \right) \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{2 k^{5} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{1}{k}\right)}-\frac{\left(2 a \,k^{2}+b \right) \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{2 k^{5} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}-\frac{1}{k}\right)}+\frac{\left(-2 a \,k^{2}+b \right) \left(\frac{i \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{i}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{3} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}-\frac{i}{k}\right)}-\frac{i \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{i}{k}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{3} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+\frac{i}{k}\right)}\right)}{2 k^{2}}$&$604$\\ elliptic&$-\frac{2 a \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+1\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) a}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+1\right)}+\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+1\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{2 k^{4} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}+1\right)}-\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) a}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}-1\right)}-\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{2 k^{4} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, \left(\frac{1}{k^{2}}-1\right)}-\frac{\left(2 a \,k^{2}-b \right) \sqrt{-k^{2} x +1}\, \sqrt{-\frac{\left(-1+x \right) k^{2}}{k^{2}-1}}\, \sqrt{k^{2} x}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} k^{2}+1\right)}{\sum}\EllipticPi \left(\sqrt{-k^{2} x +1}, \frac{\underline{\hspace{1.25 ex}}\alpha  \,k^{2}+1}{k^{2}+1}, \sqrt{-\frac{1}{k^{2}-1}}\right)\right)}{2 k^{2} \left(k^{2}+1\right) \sqrt{x \left(k^{2} x^{2}-k^{2} x -x +1\right)}}-\frac{\left(2 a \,k^{2}-b \right) \sqrt{-k^{2} x +1}\, \sqrt{-\frac{\left(-1+x \right) k^{2}}{k^{2}-1}}\, \sqrt{k^{2} x}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} k^{2}+1\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-k^{2} x +1}, \frac{\underline{\hspace{1.25 ex}}\alpha  \,k^{2}+1}{k^{2}+1}, \sqrt{-\frac{1}{k^{2}-1}}\right)}{\underline{\hspace{1.25 ex}}\alpha}\right)}{2 k^{4} \left(k^{2}+1\right) \sqrt{x \left(k^{2} x^{2}-k^{2} x -x +1\right)}}$&$813$\\ \hline \end{longtable}"," ",0,"-2*a/k^2*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticF((-(x-1/k^2)*k^2)^(1/2),(1/k^2/(1/k^2-1))^(1/2))-1/2*(-2*a*k^2-b)/k^5*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+1/k)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+1/k),(1/k^2/(1/k^2-1))^(1/2))-1/2*(2*a*k^2+b)/k^5*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-1/k)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-1/k),(1/k^2/(1/k^2-1))^(1/2))+1/2/k^2*(-2*a*k^2+b)*(I/k^3*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2-I/k)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-I/k),(1/k^2/(1/k^2-1))^(1/2))-I/k^3*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)/(1/k^2+I/k)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+I/k),(1/k^2/(1/k^2-1))^(1/2)))","C"
2315,0,0,170,0.020000," ","int((p*x^3-2*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)*(a*p^2*x^6+2*a*p*q*x^3+b*x^4+a*q^2)/x^9,x)","\[\int \frac{\left(p \,x^{3}-2 q \right) \sqrt{p^{2} x^{6}-2 p q \,x^{4}+2 p q \,x^{3}+q^{2}}\, \left(a \,p^{2} x^{6}+2 a p q \,x^{3}+b \,x^{4}+a \,q^{2}\right)}{x^{9}}\, dx\]"," ",0,"int((p*x^3-2*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)*(a*p^2*x^6+2*a*p*q*x^3+b*x^4+a*q^2)/x^9,x)","F"
2316,0,0,153,0.106000," ","int((x^3-1)/(x^3+1)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x)","\[\int \frac{x^{3}-1}{\left(x^{3}+1\right) \sqrt{a \,x^{4}+b \,x^{3}+c \,x^{2}+b x +a}}\, dx\]"," ",0,"int((x^3-1)/(x^3+1)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x)","F"
2317,0,0,149,0.014000," ","int((5*x-4*(1+k)*x^2+3*k*x^3)/((1-x)*x*(-k*x+1))^(1/3)/(-1+(1+k)*x-k*x^2+b*x^5),x)","\[\int \frac{5 x -4 \left(1+k \right) x^{2}+3 k \,x^{3}}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(-1+\left(1+k \right) x -k \,x^{2}+b \,x^{5}\right)}\, dx\]"," ",0,"int((5*x-4*(1+k)*x^2+3*k*x^3)/((1-x)*x*(-k*x+1))^(1/3)/(-1+(1+k)*x-k*x^2+b*x^5),x)","F"
2318,0,0,149,0.014000," ","int(x^2*(8-7*(1+k)*x+6*k*x^2)/((1-x)*x*(-k*x+1))^(1/3)/(-1+(1+k)*x-k*x^2+b*x^8),x)","\[\int \frac{x^{2} \left(8-7 \left(1+k \right) x +6 k \,x^{2}\right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(-1+\left(1+k \right) x -k \,x^{2}+b \,x^{8}\right)}\, dx\]"," ",0,"int(x^2*(8-7*(1+k)*x+6*k*x^2)/((1-x)*x*(-k*x+1))^(1/3)/(-1+(1+k)*x-k*x^2+b*x^8),x)","F"
2319,0,0,150,0.119000," ","int(x*(-a*b+x^2)/(x^2*(-a+x)*(-b+x))^(2/3)/(a*b-(a+b+d)*x+x^2),x)","\[\int \frac{x \left(-a b +x^{2}\right)}{\left(x^{2} \left(-a +x \right) \left(-b +x \right)\right)^{\frac{2}{3}} \left(a b -\left(a +b +d \right) x +x^{2}\right)}\, dx\]"," ",0,"int(x*(-a*b+x^2)/(x^2*(-a+x)*(-b+x))^(2/3)/(a*b-(a+b+d)*x+x^2),x)","F"
2320,0,0,152,0.005000," ","int((x^3+b)*(x^3+c)/(x^3+a)^(1/3),x)","\[\int \frac{\left(x^{3}+b \right) \left(x^{3}+c \right)}{\left(x^{3}+a \right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((x^3+b)*(x^3+c)/(x^3+a)^(1/3),x)","F"
2321,1,1895,113,5.263000," ","int(1/(x^3+1)/(x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1895$\\ \hline \end{longtable}"," ",0,"81/32*RootOf(729*_Z^6+216*_Z^3+64)^5*ln((81*RootOf(729*_Z^6+216*_Z^3+64)^5*x^2-162*RootOf(729*_Z^6+216*_Z^3+64)^5*x+48*x^2*RootOf(729*_Z^6+216*_Z^3+64)^2-24*x*RootOf(729*_Z^6+216*_Z^3+64)^2-48*RootOf(729*_Z^6+216*_Z^3+64)*(x^3-x^2)^(1/3)*x+32*(x^3-x^2)^(2/3))/(27*RootOf(729*_Z^6+216*_Z^3+64)^3*x-54*RootOf(729*_Z^6+216*_Z^3+64)^3-8*x-8)/x)+3/4*RootOf(729*_Z^6+216*_Z^3+64)^2*ln((162*RootOf(729*_Z^6+216*_Z^3+64)^5*x^2-81*RootOf(729*_Z^6+216*_Z^3+64)^5*x-81*RootOf(729*_Z^6+216*_Z^3+64)^4*(x^3-x^2)^(1/3)*x+54*RootOf(729*_Z^6+216*_Z^3+64)^3*(x^3-x^2)^(2/3)+24*x^2*RootOf(729*_Z^6+216*_Z^3+64)^2-12*x*RootOf(729*_Z^6+216*_Z^3+64)^2-24*RootOf(729*_Z^6+216*_Z^3+64)*(x^3-x^2)^(1/3)*x+16*(x^3-x^2)^(2/3))/(27*RootOf(729*_Z^6+216*_Z^3+64)^3*x-54*RootOf(729*_Z^6+216*_Z^3+64)^3-8*x-8)/x)+27/16*RootOf(729*_Z^6+216*_Z^3+64)^4*ln((243*RootOf(729*_Z^6+216*_Z^3+64)^4*(x^3-x^2)^(1/3)*x+108*RootOf(729*_Z^6+216*_Z^3+64)^3*x^2-54*RootOf(729*_Z^6+216*_Z^3+64)^3*x-108*(x^3-x^2)^(2/3)*RootOf(729*_Z^6+216*_Z^3+64)^2+64*x^2-32*x)/(27*RootOf(729*_Z^6+216*_Z^3+64)^3*x-54*RootOf(729*_Z^6+216*_Z^3+64)^3+16*x-8)/x)+1/2*RootOf(729*_Z^6+216*_Z^3+64)*ln((729*RootOf(729*_Z^6+216*_Z^3+64)^6*x^2-1458*RootOf(729*_Z^6+216*_Z^3+64)^6*x-972*RootOf(729*_Z^6+216*_Z^3+64)^4*(x^3-x^2)^(1/3)*x-648*RootOf(729*_Z^6+216*_Z^3+64)^3*x+432*(x^3-x^2)^(2/3)*RootOf(729*_Z^6+216*_Z^3+64)^2-64*x^2-64*x)/(27*RootOf(729*_Z^6+216*_Z^3+64)^3*x-54*RootOf(729*_Z^6+216*_Z^3+64)^3+16*x-8)/x)+1/6*RootOf(_Z^3+4)*ln(-(3*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^3*x^2+3*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)^2*RootOf(_Z^3+4)^2*x^2-6*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^3*x-6*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)^2*RootOf(_Z^3+4)^2*x+24*(x^3-x^2)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)-10*(x^3-x^2)^(1/3)*RootOf(_Z^3+4)^2*x+18*(x^3-x^2)^(1/3)*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)*x-26*RootOf(_Z^3+4)*x^2-26*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*x^2+10*RootOf(_Z^3+4)*x+10*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*x-12*(x^3-x^2)^(2/3))/x/(1+x))-1/6*ln(-(3*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^3*x^2+6*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)^2*RootOf(_Z^3+4)^2*x^2-6*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^3*x-12*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)^2*RootOf(_Z^3+4)^2*x-24*(x^3-x^2)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)+6*(x^3-x^2)^(1/3)*RootOf(_Z^3+4)^2*x-30*(x^3-x^2)^(1/3)*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)*x+22*RootOf(_Z^3+4)*x^2+44*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*x^2-2*RootOf(_Z^3+4)*x-4*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*x+20*(x^3-x^2)^(2/3))/x/(1+x))*RootOf(_Z^3+4)-1/2*ln(-(3*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^3*x^2+6*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)^2*RootOf(_Z^3+4)^2*x^2-6*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^3*x-12*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)^2*RootOf(_Z^3+4)^2*x-24*(x^3-x^2)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)+6*(x^3-x^2)^(1/3)*RootOf(_Z^3+4)^2*x-30*(x^3-x^2)^(1/3)*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)*x+22*RootOf(_Z^3+4)*x^2+44*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*x^2-2*RootOf(_Z^3+4)*x-4*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*x+20*(x^3-x^2)^(2/3))/x/(1+x))*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)","B"
2322,1,3979,113,18.883000," ","int(1/(x^3+1)/(x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$3979$\\ \hline \end{longtable}"," ",0,"-1/6*ln((6*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^3*x^2+27*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)^2*RootOf(_Z^3+4)^2*x^2-12*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^3*x-54*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)^2*RootOf(_Z^3+4)^2*x-72*(x^3-x^2)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)+18*(x^3-x^2)^(1/3)*RootOf(_Z^3+4)^2*x+144*(x^3-x^2)^(1/3)*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)*x-52*RootOf(_Z^3+4)*x^2-234*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*x^2+20*RootOf(_Z^3+4)*x+90*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*x+36*(x^3-x^2)^(2/3))/x/(1+x))*RootOf(_Z^3+4)-1/2*ln((6*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^3*x^2+27*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)^2*RootOf(_Z^3+4)^2*x^2-12*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^3*x-54*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)^2*RootOf(_Z^3+4)^2*x-72*(x^3-x^2)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)+18*(x^3-x^2)^(1/3)*RootOf(_Z^3+4)^2*x+144*(x^3-x^2)^(1/3)*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)*x-52*RootOf(_Z^3+4)*x^2-234*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*x^2+20*RootOf(_Z^3+4)*x+90*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*x+36*(x^3-x^2)^(2/3))/x/(1+x))*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)+1/2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*ln((3*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^3*x^2+27*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)^2*RootOf(_Z^3+4)^2*x^2-6*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^3*x-54*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)^2*RootOf(_Z^3+4)^2*x+72*(x^3-x^2)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)-30*(x^3-x^2)^(1/3)*RootOf(_Z^3+4)^2*x-144*(x^3-x^2)^(1/3)*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)*x+22*RootOf(_Z^3+4)*x^2+198*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*x^2-2*RootOf(_Z^3+4)*x-18*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*x-60*(x^3-x^2)^(2/3))/x/(1+x))+1/6*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))*ln((9*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^2*(x^3-x^2)^(1/3)*x+24*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^2*x^2+36*(x^3-x^2)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)-12*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^2*x-12*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))^2*(x^3-x^2)^(1/3)*x-16*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))*x^2+8*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))*x)/(3*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*x-6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)-8*x+4)/x)+1/8*ln((3*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)^2*RootOf(_Z^3+4)^4*x^2-6*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)^2*RootOf(_Z^3+4)^4*x+6*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^2*(x^3-x^2)^(1/3)*x+4*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^2*x^2+24*(x^3-x^2)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)+4*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^2*x-8*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))^2*(x^3-x^2)^(1/3)*x)/(3*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*x-6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)-8*x+4)/x)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))-1/6*ln((3*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)^2*RootOf(_Z^3+4)^4*x^2-6*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)^2*RootOf(_Z^3+4)^4*x+6*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^2*(x^3-x^2)^(1/3)*x+4*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^2*x^2+24*(x^3-x^2)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)+4*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^2*x-8*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))^2*(x^3-x^2)^(1/3)*x)/(3*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*x-6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)-8*x+4)/x)*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))-1/16*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))^2*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*ln(-(3*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^2*x^2-6*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^2*x-8*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))^2*x^2+24*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))*(x^3-x^2)^(1/3)*x+4*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))^2*x-48*(x^3-x^2)^(2/3))/(3*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*x-6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)+4*x+4)/x)+1/12*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))^2*ln(-(6*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^2*x^2-9*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^2*(x^3-x^2)^(1/3)*x-3*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^2*x+18*(x^3-x^2)^(2/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)-4*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))^2*x^2+12*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))*(x^3-x^2)^(1/3)*x+2*RootOf(_Z^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2))^2*x-24*(x^3-x^2)^(2/3))/(3*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)*x-6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+3*_Z*RootOf(_Z^3+4)+9*_Z^2)+4*x+4)/x)","B"
2323,0,0,170,0.029000," ","int((p*x^3-2*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)/x^3/(a*p*x^3+b*x^2+a*q),x)","\[\int \frac{\left(p \,x^{3}-2 q \right) \sqrt{p^{2} x^{6}-2 p q \,x^{4}+2 p q \,x^{3}+q^{2}}}{x^{3} \left(a p \,x^{3}+b \,x^{2}+a q \right)}\, dx\]"," ",0,"int((p*x^3-2*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)/x^3/(a*p*x^3+b*x^2+a*q),x)","F"
2324,1,658,143,53.887000," ","int((x^6+x^2)^(1/4)*(x^8+1)/x^4/(x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{4}+1\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}}}{5 x^{3}}-\frac{\RootOf \left(\textit{\_Z}^{4}+2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+2\right)^{3} x^{5}-2 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{2}-4 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}+2\right) x +\RootOf \left(\textit{\_Z}^{4}+2\right)^{3} x +4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{x \left(x^{2}+1\right)^{2}}\right)}{4}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{5}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{3}-4 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{2}-4 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x +4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{x \left(x^{2}+1\right)^{2}}\right)}{4}-\frac{\ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \sqrt{x^{6}+x^{2}}-2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right) x +2 x^{2}}{x \left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{3}}{4}-\frac{\ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \sqrt{x^{6}+x^{2}}-2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right) x +2 x^{2}}{x \left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} \sqrt{x^{6}+x^{2}}\, x -2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{4}+2\right) x^{5}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{5}+4 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+2\right) x^{3}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}+2\right) x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{4}$&$658$\\ risch&$\text{Expression too large to display}$&$1589$\\ \hline \end{longtable}"," ",0,"2/5*(x^4+1)*(x^6+x^2)^(1/4)/x^3-1/4*RootOf(_Z^4+2)*ln(-(RootOf(_Z^4+2)^3*x^5-2*RootOf(_Z^4+2)^3*x^3+4*(x^6+x^2)^(1/4)*RootOf(_Z^4+2)^2*x^2-4*(x^6+x^2)^(1/2)*RootOf(_Z^4+2)*x+RootOf(_Z^4+2)^3*x+4*(x^6+x^2)^(3/4))/x/(x^2+1)^2)-1/4*RootOf(_Z^2+RootOf(_Z^4+2)^2)*ln(-(-RootOf(_Z^2+RootOf(_Z^4+2)^2)*RootOf(_Z^4+2)^2*x^5+2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*RootOf(_Z^4+2)^2*x^3-4*(x^6+x^2)^(1/4)*RootOf(_Z^4+2)^2*x^2-4*RootOf(_Z^2+RootOf(_Z^4+2)^2)*(x^6+x^2)^(1/2)*x-RootOf(_Z^4+2)^2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*x+4*(x^6+x^2)^(3/4))/x/(x^2+1)^2)-1/4*ln((RootOf(_Z^4+2)^2*(x^6+x^2)^(1/2)-2*(x^6+x^2)^(1/4)*RootOf(_Z^4+2)*x+2*x^2)/x/(-1+x)/(1+x))*RootOf(_Z^4+2)^3-1/4*ln((RootOf(_Z^4+2)^2*(x^6+x^2)^(1/2)-2*(x^6+x^2)^(1/4)*RootOf(_Z^4+2)*x+2*x^2)/x/(-1+x)/(1+x))*RootOf(_Z^4+2)^2*RootOf(_Z^2+RootOf(_Z^4+2)^2)+1/4*RootOf(_Z^4+2)^2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*ln((2*RootOf(_Z^4+2)^3*(x^6+x^2)^(1/2)*x-2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*RootOf(_Z^4+2)^2*(x^6+x^2)^(1/2)*x-RootOf(_Z^4+2)*x^5-RootOf(_Z^2+RootOf(_Z^4+2)^2)*x^5+4*(x^6+x^2)^(1/4)*RootOf(_Z^4+2)*RootOf(_Z^2+RootOf(_Z^4+2)^2)*x^2-2*RootOf(_Z^4+2)*x^3-2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*x^3+4*(x^6+x^2)^(3/4)-RootOf(_Z^4+2)*x-RootOf(_Z^2+RootOf(_Z^4+2)^2)*x)/(-1+x)^2/(1+x)^2/x)","C"
2325,1,658,143,51.108000," ","int((x^6+x^2)^(1/4)*(x^8+1)/x^4/(x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{2 \left(x^{4}+1\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}}}{5 x^{3}}+\frac{\RootOf \left(\textit{\_Z}^{4}+2\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}+2\right)^{3} x^{5}+2 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{2}+4 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}+2\right) x -\RootOf \left(\textit{\_Z}^{4}+2\right)^{3} x +4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{x \left(x^{2}+1\right)^{2}}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{5}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{3}-4 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{2}+4 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x +4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{x \left(x^{2}+1\right)^{2}}\right)}{4}-\frac{\ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \sqrt{x^{6}+x^{2}}-2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right) x +2 x^{2}}{x \left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{3}}{4}-\frac{\ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \sqrt{x^{6}+x^{2}}-2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right) x +2 x^{2}}{x \left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} \sqrt{x^{6}+x^{2}}\, x -2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{4}+2\right) x^{5}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{5}+4 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+2\right) x^{3}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}+2\right) x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{4}$&$658$\\ risch&$\text{Expression too large to display}$&$1587$\\ \hline \end{longtable}"," ",0,"2/5*(x^4+1)*(x^6+x^2)^(1/4)/x^3+1/4*RootOf(_Z^4+2)*ln(-(-RootOf(_Z^4+2)^3*x^5+2*RootOf(_Z^4+2)^3*x^3+4*(x^6+x^2)^(1/4)*RootOf(_Z^4+2)^2*x^2+4*(x^6+x^2)^(1/2)*RootOf(_Z^4+2)*x-RootOf(_Z^4+2)^3*x+4*(x^6+x^2)^(3/4))/x/(x^2+1)^2)+1/4*RootOf(_Z^2+RootOf(_Z^4+2)^2)*ln(-(RootOf(_Z^2+RootOf(_Z^4+2)^2)*RootOf(_Z^4+2)^2*x^5-2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*RootOf(_Z^4+2)^2*x^3-4*(x^6+x^2)^(1/4)*RootOf(_Z^4+2)^2*x^2+4*RootOf(_Z^2+RootOf(_Z^4+2)^2)*(x^6+x^2)^(1/2)*x+RootOf(_Z^4+2)^2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*x+4*(x^6+x^2)^(3/4))/x/(x^2+1)^2)-1/4*ln((RootOf(_Z^4+2)^2*(x^6+x^2)^(1/2)-2*(x^6+x^2)^(1/4)*RootOf(_Z^4+2)*x+2*x^2)/x/(-1+x)/(1+x))*RootOf(_Z^4+2)^3-1/4*ln((RootOf(_Z^4+2)^2*(x^6+x^2)^(1/2)-2*(x^6+x^2)^(1/4)*RootOf(_Z^4+2)*x+2*x^2)/x/(-1+x)/(1+x))*RootOf(_Z^4+2)^2*RootOf(_Z^2+RootOf(_Z^4+2)^2)+1/4*RootOf(_Z^4+2)^2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*ln((2*RootOf(_Z^4+2)^3*(x^6+x^2)^(1/2)*x-2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*RootOf(_Z^4+2)^2*(x^6+x^2)^(1/2)*x-RootOf(_Z^4+2)*x^5-RootOf(_Z^2+RootOf(_Z^4+2)^2)*x^5+4*(x^6+x^2)^(1/4)*RootOf(_Z^4+2)*RootOf(_Z^2+RootOf(_Z^4+2)^2)*x^2-2*RootOf(_Z^4+2)*x^3-2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*x^3+4*(x^6+x^2)^(3/4)-RootOf(_Z^4+2)*x-RootOf(_Z^2+RootOf(_Z^4+2)^2)*x)/(-1+x)^2/(1+x)^2/x)","C"
2326,1,1069,137,8.572000," ","int(1/x/(x^2-3*x+2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \ln \left(-\frac{-28 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{2}-68 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{2}+108 \left(x^{2}-3 x +2\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+126 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x +306 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x +54 \left(x^{2}-3 x +2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x +237 \left(x^{2}-3 x +2\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x -126 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}-306 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-108 \left(x^{2}-3 x +2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-474 \left(x^{2}-3 x +2\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)-7 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{2}-17 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{2}-258 \left(x^{2}-3 x +2\right)^{\frac{2}{3}}-168 \RootOf \left(\textit{\_Z}^{3}-4\right) x -408 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x +168 \RootOf \left(\textit{\_Z}^{3}-4\right)+408 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)}{x^{2}}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(\frac{-68 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{2}-112 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{2}+216 \left(x^{2}-3 x +2\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+306 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x +504 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x +108 \left(x^{2}-3 x +2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x -258 \left(x^{2}-3 x +2\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) x -306 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3}-504 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-216 \left(x^{2}-3 x +2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+516 \left(x^{2}-3 x +2\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)-119 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{2}-196 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x^{2}+948 \left(x^{2}-3 x +2\right)^{\frac{2}{3}}+1020 \RootOf \left(\textit{\_Z}^{3}-4\right) x +1680 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right) x -1020 \RootOf \left(\textit{\_Z}^{3}-4\right)-1680 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+4 \textit{\_Z}^{2}\right)}{x^{2}}\right)}{4}$&$1069$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*ln(-(-28*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x^2-68*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x^2+108*(x^2-3*x+2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^2+126*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x+306*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x+54*(x^2-3*x+2)^(1/3)*RootOf(_Z^3-4)^2*x+237*(x^2-3*x+2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)*x-126*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3-306*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2-108*(x^2-3*x+2)^(1/3)*RootOf(_Z^3-4)^2-474*(x^2-3*x+2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)-7*RootOf(_Z^3-4)*x^2-17*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^2-258*(x^2-3*x+2)^(2/3)-168*RootOf(_Z^3-4)*x-408*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x+168*RootOf(_Z^3-4)+408*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2))/x^2)+1/4*RootOf(_Z^3-4)*ln((-68*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x^2-112*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x^2+216*(x^2-3*x+2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^2+306*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3*x+504*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2*x+108*(x^2-3*x+2)^(1/3)*RootOf(_Z^3-4)^2*x-258*(x^2-3*x+2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)*x-306*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)^3-504*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)^2*RootOf(_Z^3-4)^2-216*(x^2-3*x+2)^(1/3)*RootOf(_Z^3-4)^2+516*(x^2-3*x+2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*RootOf(_Z^3-4)-119*RootOf(_Z^3-4)*x^2-196*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x^2+948*(x^2-3*x+2)^(2/3)+1020*RootOf(_Z^3-4)*x+1680*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2)*x-1020*RootOf(_Z^3-4)-1680*RootOf(RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+4*_Z^2))/x^2)","C"
2327,0,0,151,0.117000," ","int((a*b-x^2)/(x^2*(-a+x)*(-b+x))^(1/3)/(a*b-(a+b+d)*x+x^2),x)","\[\int \frac{a b -x^{2}}{\left(x^{2} \left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{3}} \left(a b -\left(a +b +d \right) x +x^{2}\right)}\, dx\]"," ",0,"int((a*b-x^2)/(x^2*(-a+x)*(-b+x))^(1/3)/(a*b-(a+b+d)*x+x^2),x)","F"
2328,0,0,171,0.020000," ","int((2*p*x^3-q)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)*(b*x^2+a*(p*x^3+q)^2)/x^5,x)","\[\int \frac{\left(2 p \,x^{3}-q \right) \sqrt{p^{2} x^{6}+2 p q \,x^{3}-2 p q \,x^{2}+q^{2}}\, \left(b \,x^{2}+a \left(p \,x^{3}+q \right)^{2}\right)}{x^{5}}\, dx\]"," ",0,"int((2*p*x^3-q)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)*(b*x^2+a*(p*x^3+q)^2)/x^5,x)","F"
2329,1,117,97,0.175000," ","int((1+x)/(-1+x)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{7}{2}}}{7}-\frac{24 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}+\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+4 \textit{\_Z}^{4}-2\right)}{\sum}\frac{\left(\textit{\_R}^{6}-3 \textit{\_R}^{4}+2 \textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+2 \textit{\_R}^{3}}\right)$&$117$\\ default&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{7}{2}}}{7}-\frac{24 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}+\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+4 \textit{\_Z}^{4}-2\right)}{\sum}\frac{\left(\textit{\_R}^{6}-3 \textit{\_R}^{4}+2 \textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+2 \textit{\_R}^{3}}\right)$&$117$\\ \hline \end{longtable}"," ",0,"8/7*(1+(1+(1+x)^(1/2))^(1/2))^(7/2)-24/5*(1+(1+(1+x)^(1/2))^(1/2))^(5/2)+16/3*(1+(1+(1+x)^(1/2))^(1/2))^(3/2)+2*sum((_R^6-3*_R^4+2*_R^2)/(_R^7-3*_R^5+2*_R^3)*ln((1+(1+(1+x)^(1/2))^(1/2))^(1/2)-_R),_R=RootOf(_Z^8-4*_Z^6+4*_Z^4-2))","A"
2330,1,117,97,0.171000," ","int((1+x)/(-1+x)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{7}{2}}}{7}-\frac{24 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}+\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+4 \textit{\_Z}^{4}-2\right)}{\sum}\frac{\left(\textit{\_R}^{6}-3 \textit{\_R}^{4}+2 \textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+2 \textit{\_R}^{3}}\right)$&$117$\\ default&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{7}{2}}}{7}-\frac{24 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}+\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+4 \textit{\_Z}^{4}-2\right)}{\sum}\frac{\left(\textit{\_R}^{6}-3 \textit{\_R}^{4}+2 \textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+2 \textit{\_R}^{3}}\right)$&$117$\\ \hline \end{longtable}"," ",0,"8/7*(1+(1+(1+x)^(1/2))^(1/2))^(7/2)-24/5*(1+(1+(1+x)^(1/2))^(1/2))^(5/2)+16/3*(1+(1+(1+x)^(1/2))^(1/2))^(3/2)+2*sum((_R^6-3*_R^4+2*_R^2)/(_R^7-3*_R^5+2*_R^3)*ln((1+(1+(1+x)^(1/2))^(1/2))^(1/2)-_R),_R=RootOf(_Z^8-4*_Z^6+4*_Z^4-2))","A"
2331,0,0,38,0.180000," ","int(1/(d+c*x+(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)),x)","\[\int \frac{1}{d +c x +\sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int(1/(d+c*x+(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)),x)","F"
2332,0,0,38,0.003000," ","int(1/(d+c*x+(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)),x)","\[\int \frac{1}{d +c x +\sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int(1/(d+c*x+(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)),x)","F"
2333,0,0,148,0.012000," ","int((c*x-d)/x^7/(a*x^3-b)^(1/3),x)","\[\int \frac{c x -d}{x^{7} \left(a \,x^{3}-b \right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((c*x-d)/x^7/(a*x^3-b)^(1/3),x)","F"
2334,1,733,144,31.231000," ","int((x^4+x^2+1)/(-x^4+1)/(x^5+x^3)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x}{\left(x^{3} \left(x^{2}+1\right)\right)^{\frac{1}{4}}}+\frac{3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \sqrt{x^{5}+x^{3}}\, \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x -2 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{4}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{3}+4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{2}}{x^{2} \left(-1+x \right)^{2}}\right)}{16}+\frac{3 \RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} \sqrt{x^{5}+x^{3}}\, x +2 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+x^{4} \RootOf \left(\textit{\_Z}^{4}-8\right)+2 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{3}+4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}-8\right) x^{2}}{x^{2} \left(-1+x \right)^{2}}\right)}{16}-\frac{3 \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{4}-2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{3}+8 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{2}-16 \sqrt{x^{5}+x^{3}}\, \RootOf \left(\textit{\_Z}^{4}-8\right) x +16 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}}{\left(1+x \right)^{2} x^{2}}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{3}}{64}-\frac{3 \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{4}-2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{3}+8 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{2}-16 \sqrt{x^{5}+x^{3}}\, \RootOf \left(\textit{\_Z}^{4}-8\right) x +16 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}}{\left(1+x \right)^{2} x^{2}}\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2}}{64}+\frac{3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{4}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{4}+2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{3}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}+8 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{2}-\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{2} \RootOf \left(\textit{\_Z}^{4}-8\right)^{2}-8 \sqrt{x^{5}+x^{3}}\, \RootOf \left(\textit{\_Z}^{4}-8\right) x -8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \sqrt{x^{5}+x^{3}}\, x +16 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}}{\left(1+x \right)^{2} x^{2}}\right)}{32}$&$733$\\ trager&$\frac{\left(x^{5}+x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(x^{2}+1\right)}+\frac{3 \RootOf \left(\textit{\_Z}^{4}+8\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} \sqrt{x^{5}+x^{3}}\, x -2 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{4}+8\right) x^{3}+4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}+8\right) x^{2}}{\left(1+x \right)^{2} x^{2}}\right)}{16}+\frac{3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(-\frac{\sqrt{x^{5}+x^{3}}\, \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x +2 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{3}+4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{2}}{\left(1+x \right)^{2} x^{2}}\right)}{16}+\frac{3 \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{4}-2 \RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{3}+8 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{2}-16 \sqrt{x^{5}+x^{3}}\, \RootOf \left(\textit{\_Z}^{4}+8\right) x +16 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(-1+x \right)^{2}}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{3}}{64}+\frac{3 \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{4}-2 \RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{3}+8 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{2}-16 \sqrt{x^{5}+x^{3}}\, \RootOf \left(\textit{\_Z}^{4}+8\right) x +16 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(-1+x \right)^{2}}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)}{64}-\frac{3 \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{4}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{4}+2 \RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{3}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{3}+8 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{2}-\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{2}-8 \sqrt{x^{5}+x^{3}}\, \RootOf \left(\textit{\_Z}^{4}+8\right) x -8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \sqrt{x^{5}+x^{3}}\, x +16 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(-1+x \right)^{2}}\right)}{32}$&$739$\\ \hline \end{longtable}"," ",0,"x/(x^3*(x^2+1))^(1/4)+3/16*RootOf(_Z^2+RootOf(_Z^4-8)^2)*ln((-RootOf(_Z^2+RootOf(_Z^4-8)^2)*(x^5+x^3)^(1/2)*RootOf(_Z^4-8)^2*x-2*(x^5+x^3)^(1/4)*RootOf(_Z^4-8)^2*x^2+RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^4+2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^3+4*(x^5+x^3)^(3/4)+RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^2)/x^2/(-1+x)^2)+3/16*RootOf(_Z^4-8)*ln((RootOf(_Z^4-8)^3*(x^5+x^3)^(1/2)*x+2*(x^5+x^3)^(1/4)*RootOf(_Z^4-8)^2*x^2+x^4*RootOf(_Z^4-8)+2*RootOf(_Z^4-8)*x^3+4*(x^5+x^3)^(3/4)+RootOf(_Z^4-8)*x^2)/x^2/(-1+x)^2)-3/64*ln((-RootOf(_Z^4-8)^3*x^4-2*RootOf(_Z^4-8)^3*x^3+8*(x^5+x^3)^(1/4)*RootOf(_Z^4-8)^2*x^2-RootOf(_Z^4-8)^3*x^2-16*(x^5+x^3)^(1/2)*RootOf(_Z^4-8)*x+16*(x^5+x^3)^(3/4))/(1+x)^2/x^2)*RootOf(_Z^4-8)^3-3/64*ln((-RootOf(_Z^4-8)^3*x^4-2*RootOf(_Z^4-8)^3*x^3+8*(x^5+x^3)^(1/4)*RootOf(_Z^4-8)^2*x^2-RootOf(_Z^4-8)^3*x^2-16*(x^5+x^3)^(1/2)*RootOf(_Z^4-8)*x+16*(x^5+x^3)^(3/4))/(1+x)^2/x^2)*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2+3/32*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*ln(-(-RootOf(_Z^4-8)^3*x^4+RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x^4+2*RootOf(_Z^4-8)^3*x^3-2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x^3+8*(x^5+x^3)^(1/4)*RootOf(_Z^4-8)*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^2-RootOf(_Z^4-8)^3*x^2+RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^2*RootOf(_Z^4-8)^2-8*(x^5+x^3)^(1/2)*RootOf(_Z^4-8)*x-8*RootOf(_Z^2+RootOf(_Z^4-8)^2)*(x^5+x^3)^(1/2)*x+16*(x^5+x^3)^(3/4))/(1+x)^2/x^2)","C"
2335,1,241,35,7.710000," ","int((2*x^4-1)^(1/2)*(2*x^8-1)/x^7/(x^8+2*x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{8 x^{8}-2 x^{4}-1}{6 x^{6} \sqrt{2 x^{4}-1}}-\frac{\arctan \left(\frac{2 \left(\sqrt{2 x^{4}-1}-\sqrt{2}\, x^{2}\right)^{2}-8 \sqrt{2}+10}{4 \sqrt{-14+10 \sqrt{2}}}\right) \sqrt{2}}{\sqrt{-14+10 \sqrt{2}}}+\frac{5 \arctan \left(\frac{2 \left(\sqrt{2 x^{4}-1}-\sqrt{2}\, x^{2}\right)^{2}-8 \sqrt{2}+10}{4 \sqrt{-14+10 \sqrt{2}}}\right)}{4 \sqrt{-14+10 \sqrt{2}}}+\frac{\arctanh \left(\frac{2 \left(\sqrt{2 x^{4}-1}-\sqrt{2}\, x^{2}\right)^{2}+10+8 \sqrt{2}}{4 \sqrt{14+10 \sqrt{2}}}\right) \sqrt{2}}{\sqrt{14+10 \sqrt{2}}}+\frac{5 \arctanh \left(\frac{2 \left(\sqrt{2 x^{4}-1}-\sqrt{2}\, x^{2}\right)^{2}+10+8 \sqrt{2}}{4 \sqrt{14+10 \sqrt{2}}}\right)}{4 \sqrt{14+10 \sqrt{2}}}$&$241$\\ elliptic&$-\frac{\arctan \left(\frac{2 \left(\sqrt{2 x^{4}-1}-\sqrt{2}\, x^{2}\right)^{2}-8 \sqrt{2}+10}{4 \sqrt{-14+10 \sqrt{2}}}\right) \sqrt{2}}{\sqrt{-14+10 \sqrt{2}}}+\frac{5 \arctan \left(\frac{2 \left(\sqrt{2 x^{4}-1}-\sqrt{2}\, x^{2}\right)^{2}-8 \sqrt{2}+10}{4 \sqrt{-14+10 \sqrt{2}}}\right)}{4 \sqrt{-14+10 \sqrt{2}}}+\frac{\arctanh \left(\frac{2 \left(\sqrt{2 x^{4}-1}-\sqrt{2}\, x^{2}\right)^{2}+10+8 \sqrt{2}}{4 \sqrt{14+10 \sqrt{2}}}\right) \sqrt{2}}{\sqrt{14+10 \sqrt{2}}}+\frac{5 \arctanh \left(\frac{2 \left(\sqrt{2 x^{4}-1}-\sqrt{2}\, x^{2}\right)^{2}+10+8 \sqrt{2}}{4 \sqrt{14+10 \sqrt{2}}}\right)}{4 \sqrt{14+10 \sqrt{2}}}-\frac{\sqrt{2 x^{4}-1}}{6 x^{6}}-\frac{2 \sqrt{2 x^{4}-1}}{3 x^{2}}$&$243$\\ default&$-\frac{\arctan \left(\frac{2 \left(\sqrt{2 x^{4}-1}-\sqrt{2}\, x^{2}\right)^{2}-8 \sqrt{2}+10}{4 \sqrt{-14+10 \sqrt{2}}}\right) \sqrt{2}}{\sqrt{-14+10 \sqrt{2}}}+\frac{5 \arctan \left(\frac{2 \left(\sqrt{2 x^{4}-1}-\sqrt{2}\, x^{2}\right)^{2}-8 \sqrt{2}+10}{4 \sqrt{-14+10 \sqrt{2}}}\right)}{4 \sqrt{-14+10 \sqrt{2}}}+\frac{\arctanh \left(\frac{2 \left(\sqrt{2 x^{4}-1}-\sqrt{2}\, x^{2}\right)^{2}+10+8 \sqrt{2}}{4 \sqrt{14+10 \sqrt{2}}}\right) \sqrt{2}}{\sqrt{14+10 \sqrt{2}}}+\frac{5 \arctanh \left(\frac{2 \left(\sqrt{2 x^{4}-1}-\sqrt{2}\, x^{2}\right)^{2}+10+8 \sqrt{2}}{4 \sqrt{14+10 \sqrt{2}}}\right)}{4 \sqrt{14+10 \sqrt{2}}}+\frac{\left(2 x^{4}-1\right)^{\frac{3}{2}}}{6 x^{6}}+\frac{\left(2 x^{4}-1\right)^{\frac{3}{2}}}{x^{2}}-2 \sqrt{2 x^{4}-1}\, x^{2}$&$256$\\ trager&$-\frac{\left(4 x^{4}+1\right) \sqrt{2 x^{4}-1}}{6 x^{6}}+\frac{\RootOf \left(\textit{\_Z}^{2}+64 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{2}-1\right) \ln \left(-\frac{490 \left(49152 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{4} \RootOf \left(\textit{\_Z}^{2}+64 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{2}-1\right) x^{4}+6400 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{2} \RootOf \left(\textit{\_Z}^{2}+64 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{2}-1\right) x^{4}-49152 \RootOf \left(\textit{\_Z}^{2}+64 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{2}-1\right) \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{4}-133 \RootOf \left(\textit{\_Z}^{2}+64 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{2}-1\right) x^{4}-1792 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{2} \sqrt{2 x^{4}-1}\, x^{2}-2560 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{2} \RootOf \left(\textit{\_Z}^{2}+64 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{2}-1\right)-546 \sqrt{2 x^{4}-1}\, x^{2}+63 \RootOf \left(\textit{\_Z}^{2}+64 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{2}-1\right)\right)}{\left(4096 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{3} x^{2}+896 x^{2} \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{2}-4096 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{3}+48 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right) x^{2}-896 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{2}+63 x^{2}-48 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)+7\right) \left(4096 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{3} x^{2}-896 x^{2} \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{2}-4096 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{3}+48 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right) x^{2}+896 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{2}-63 x^{2}-48 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)-7\right)}\right)}{8}-\RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right) \ln \left(-\frac{196608 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{5} x^{4}-31744 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{3} x^{4}-196608 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{5}-896 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{2} \sqrt{2 x^{4}-1}\, x^{2}-84 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right) x^{4}+16384 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{3}+287 \sqrt{2 x^{4}-1}\, x^{2}+44 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)}{128 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{2} x^{4}-11 x^{4}-128 \RootOf \left(16384 \textit{\_Z}^{4}-256 \textit{\_Z}^{2}-49\right)^{2}+1}\right)$&$761$\\ \hline \end{longtable}"," ",0,"-1/6*(8*x^8-2*x^4-1)/x^6/(2*x^4-1)^(1/2)-1/(-14+10*2^(1/2))^(1/2)*arctan(1/4*(2*((2*x^4-1)^(1/2)-2^(1/2)*x^2)^2-8*2^(1/2)+10)/(-14+10*2^(1/2))^(1/2))*2^(1/2)+5/4/(-14+10*2^(1/2))^(1/2)*arctan(1/4*(2*((2*x^4-1)^(1/2)-2^(1/2)*x^2)^2-8*2^(1/2)+10)/(-14+10*2^(1/2))^(1/2))+1/(14+10*2^(1/2))^(1/2)*arctanh(1/4*(2*((2*x^4-1)^(1/2)-2^(1/2)*x^2)^2+10+8*2^(1/2))/(14+10*2^(1/2))^(1/2))*2^(1/2)+5/4/(14+10*2^(1/2))^(1/2)*arctanh(1/4*(2*((2*x^4-1)^(1/2)-2^(1/2)*x^2)^2+10+8*2^(1/2))/(14+10*2^(1/2))^(1/2))","B"
2336,1,115,126,0.197000," ","int((1+x)^(1/2)*(1+(1+x)^(1/2))^(1/2)/x/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}-\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}+8 \sqrt{1+\sqrt{1+\sqrt{1+x}}}-\frac{2 \sqrt{2}\, \arctanh \left(\frac{\sqrt{1+\sqrt{1+\sqrt{1+x}}}}{\sqrt{1+\sqrt{2}}}\right)}{\sqrt{1+\sqrt{2}}}-\frac{2 \sqrt{2}\, \arctan \left(\frac{\sqrt{1+\sqrt{1+\sqrt{1+x}}}}{\sqrt{\sqrt{2}-1}}\right)}{\sqrt{\sqrt{2}-1}}$&$115$\\ default&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}-\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}+8 \sqrt{1+\sqrt{1+\sqrt{1+x}}}-\frac{2 \sqrt{2}\, \arctanh \left(\frac{\sqrt{1+\sqrt{1+\sqrt{1+x}}}}{\sqrt{1+\sqrt{2}}}\right)}{\sqrt{1+\sqrt{2}}}-\frac{2 \sqrt{2}\, \arctan \left(\frac{\sqrt{1+\sqrt{1+\sqrt{1+x}}}}{\sqrt{\sqrt{2}-1}}\right)}{\sqrt{\sqrt{2}-1}}$&$115$\\ \hline \end{longtable}"," ",0,"8/5*(1+(1+(1+x)^(1/2))^(1/2))^(5/2)-16/3*(1+(1+(1+x)^(1/2))^(1/2))^(3/2)+8*(1+(1+(1+x)^(1/2))^(1/2))^(1/2)-2*2^(1/2)/(1+2^(1/2))^(1/2)*arctanh((1+(1+(1+x)^(1/2))^(1/2))^(1/2)/(1+2^(1/2))^(1/2))-2*2^(1/2)/(2^(1/2)-1)^(1/2)*arctan((1+(1+(1+x)^(1/2))^(1/2))^(1/2)/(2^(1/2)-1)^(1/2))","A"
2337,1,1370,134,16.424000," ","int((1+x)/(3+x)/(1+2*x)/(x^2+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1370$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)*ln((17440696250*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)^2*RootOf(_Z^3-100)^2*x^3-2389977875*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)*RootOf(_Z^3-100)^3*x^3+34881392500*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)^2*RootOf(_Z^3-100)^2*x^2-4779955750*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)*RootOf(_Z^3-100)^3*x^2+197503327200*(x^2+1)^(2/3)*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)*RootOf(_Z^3-100)^2*x+209288355000*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)^2*RootOf(_Z^3-100)^2*x-28679734500*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)*RootOf(_Z^3-100)^3*x-395006654400*(x^2+1)^(2/3)*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)*RootOf(_Z^3-100)^2+259900176450*(x^2+1)^(1/3)*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)*RootOf(_Z^3-100)*x^2+15800266176*(x^2+1)^(1/3)*RootOf(_Z^3-100)^2*x^2-1039600705800*(x^2+1)^(1/3)*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)*RootOf(_Z^3-100)*x-44648182400*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)*x^3-63201064704*(x^2+1)^(1/3)*RootOf(_Z^3-100)^2*x+6118343360*RootOf(_Z^3-100)*x^3+1039600705800*(x^2+1)^(1/3)*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)*RootOf(_Z^3-100)+1698026186900*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)*x^2+63201064704*(x^2+1)^(1/3)*RootOf(_Z^3-100)^2-232688245910*RootOf(_Z^3-100)*x^2+270212955900*(x^2+1)^(2/3)*x-535778188800*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)*x+73420120320*RootOf(_Z^3-100)*x-540425911800*(x^2+1)^(2/3)+1787322551700*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)-244924932630*RootOf(_Z^3-100))/(3+x)^2/(1+2*x))+1/50*RootOf(_Z^3-100)*ln((393125*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)^2*RootOf(_Z^3-100)^2*x^3+1450*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)*RootOf(_Z^3-100)^3*x^3+786250*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)^2*RootOf(_Z^3-100)^2*x^2+2900*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)*RootOf(_Z^3-100)^3*x^2-955200*(x^2+1)^(2/3)*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)*RootOf(_Z^3-100)^2*x+4717500*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)^2*RootOf(_Z^3-100)^2*x+17400*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)*RootOf(_Z^3-100)^3*x+1910400*(x^2+1)^(2/3)*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)*RootOf(_Z^3-100)^2-91650*(x^2+1)^(1/3)*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)*RootOf(_Z^3-100)*x^2-76416*(x^2+1)^(1/3)*RootOf(_Z^3-100)^2*x^2+366600*(x^2+1)^(1/3)*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)*RootOf(_Z^3-100)*x+2578900*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)*x^3+305664*(x^2+1)^(1/3)*RootOf(_Z^3-100)^2*x+9512*RootOf(_Z^3-100)*x^3-366600*(x^2+1)^(1/3)*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)*RootOf(_Z^3-100)-35129650*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)*x^2-305664*(x^2+1)^(1/3)*RootOf(_Z^3-100)^2-129572*RootOf(_Z^3-100)*x^2-3637500*(x^2+1)^(2/3)*x+30946800*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)*x+114144*RootOf(_Z^3-100)*x+7275000*(x^2+1)^(2/3)-40287450*RootOf(RootOf(_Z^3-100)^2+25*_Z*RootOf(_Z^3-100)+625*_Z^2)-148596*RootOf(_Z^3-100))/(3+x)^2/(1+2*x))","C"
2338,1,2446,89,4.350000," ","int((x^3-x^2)^(1/3)/(x^2+x+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2446$\\ \hline \end{longtable}"," ",0,"RootOf(9*_Z^6+3*_Z^3+1)*ln((279*x^2*RootOf(9*_Z^6+3*_Z^3+1)^8-558*RootOf(9*_Z^6+3*_Z^3+1)^8*x+1206*RootOf(9*_Z^6+3*_Z^3+1)^5*x^2-645*RootOf(9*_Z^6+3*_Z^3+1)^5*x-654*(x^3-x^2)^(1/3)*RootOf(9*_Z^6+3*_Z^3+1)^4*x+195*(x^3-x^2)^(2/3)*RootOf(9*_Z^6+3*_Z^3+1)^3+360*RootOf(9*_Z^6+3*_Z^3+1)^2*x^2-150*RootOf(9*_Z^6+3*_Z^3+1)^2*x-241*(x^3-x^2)^(1/3)*RootOf(9*_Z^6+3*_Z^3+1)*x+153*(x^3-x^2)^(2/3))/(3*x*RootOf(9*_Z^6+3*_Z^3+1)^3-6*RootOf(9*_Z^6+3*_Z^3+1)^3+3*x+1)/x)+RootOf(9*_Z^6+3*_Z^3+1)^3*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)*ln(-(306*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)^2*RootOf(9*_Z^6+3*_Z^3+1)^6*x^2-612*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)^2*RootOf(9*_Z^6+3*_Z^3+1)^6*x+582*x^2*RootOf(9*_Z^6+3*_Z^3+1)^3*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)^2+549*(x^3-x^2)^(1/3)*RootOf(9*_Z^6+3*_Z^3+1)^3*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)*x-501*x*RootOf(9*_Z^6+3*_Z^3+1)^3*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)^2-513*(x^3-x^2)^(2/3)*RootOf(9*_Z^6+3*_Z^3+1)^3+232*x^2*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)^2+537*(x^3-x^2)^(1/3)*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)*x-87*x*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)^2+720*(x^3-x^2)^(2/3))/(3*x*RootOf(9*_Z^6+3*_Z^3+1)^3-6*RootOf(9*_Z^6+3*_Z^3+1)^3-2*x-3)/x)+3*RootOf(9*_Z^6+3*_Z^3+1)^4*ln((522*x^2*RootOf(9*_Z^6+3*_Z^3+1)^8-1044*RootOf(9*_Z^6+3*_Z^3+1)^8*x-420*RootOf(9*_Z^6+3*_Z^3+1)^5*x^2-291*RootOf(9*_Z^6+3*_Z^3+1)^5*x+354*(x^3-x^2)^(1/3)*RootOf(9*_Z^6+3*_Z^3+1)^4*x-57*(x^3-x^2)^(2/3)*RootOf(9*_Z^6+3*_Z^3+1)^3-102*RootOf(9*_Z^6+3*_Z^3+1)^2*x^2-17*RootOf(9*_Z^6+3*_Z^3+1)^2*x+179*(x^3-x^2)^(1/3)*RootOf(9*_Z^6+3*_Z^3+1)*x-99*(x^3-x^2)^(2/3))/(3*x*RootOf(9*_Z^6+3*_Z^3+1)^3-6*RootOf(9*_Z^6+3*_Z^3+1)^3+3*x+1)/x)-ln(-(270*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)^2*RootOf(9*_Z^6+3*_Z^3+1)^6*x^2-540*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)^2*RootOf(9*_Z^6+3*_Z^3+1)^6*x-897*x^2*RootOf(9*_Z^6+3*_Z^3+1)^3*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)^2-207*(x^3-x^2)^(1/3)*RootOf(9*_Z^6+3*_Z^3+1)^3*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)*x+84*x*RootOf(9*_Z^6+3*_Z^3+1)^3*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)^2+1755*(x^3-x^2)^(2/3)*RootOf(9*_Z^6+3*_Z^3+1)^3-341*x^2*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)^2-723*(x^3-x^2)^(1/3)*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)*x+93*x*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)^2-792*(x^3-x^2)^(2/3))/(3*x*RootOf(9*_Z^6+3*_Z^3+1)^3-6*RootOf(9*_Z^6+3*_Z^3+1)^3-2*x-3)/x)*RootOf(9*_Z^6+3*_Z^3+1)^3*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)-1/3*ln(-(270*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)^2*RootOf(9*_Z^6+3*_Z^3+1)^6*x^2-540*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)^2*RootOf(9*_Z^6+3*_Z^3+1)^6*x-897*x^2*RootOf(9*_Z^6+3*_Z^3+1)^3*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)^2-207*(x^3-x^2)^(1/3)*RootOf(9*_Z^6+3*_Z^3+1)^3*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)*x+84*x*RootOf(9*_Z^6+3*_Z^3+1)^3*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)^2+1755*(x^3-x^2)^(2/3)*RootOf(9*_Z^6+3*_Z^3+1)^3-341*x^2*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)^2-723*(x^3-x^2)^(1/3)*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)*x+93*x*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)^2-792*(x^3-x^2)^(2/3))/(3*x*RootOf(9*_Z^6+3*_Z^3+1)^3-6*RootOf(9*_Z^6+3*_Z^3+1)^3-2*x-3)/x)*RootOf(_Z^3+27*RootOf(9*_Z^6+3*_Z^3+1)^3+9)+3*RootOf(9*_Z^6+3*_Z^3+1)^3*ln((45*RootOf(9*_Z^6+3*_Z^3+1)^6*x^2-90*RootOf(9*_Z^6+3*_Z^3+1)^6*x-72*(x^3-x^2)^(2/3)*RootOf(9*_Z^6+3*_Z^3+1)^3-72*(x^3-x^2)^(1/3)*RootOf(9*_Z^6+3*_Z^3+1)^3*x-57*x^2*RootOf(9*_Z^6+3*_Z^3+1)^3+9*x*RootOf(9*_Z^6+3*_Z^3+1)^3-9*(x^3-x^2)^(2/3)-9*x*(x^3-x^2)^(1/3)-4*x^2+x)/x)+ln((45*RootOf(9*_Z^6+3*_Z^3+1)^6*x^2-90*RootOf(9*_Z^6+3*_Z^3+1)^6*x-72*(x^3-x^2)^(2/3)*RootOf(9*_Z^6+3*_Z^3+1)^3-72*(x^3-x^2)^(1/3)*RootOf(9*_Z^6+3*_Z^3+1)^3*x-57*x^2*RootOf(9*_Z^6+3*_Z^3+1)^3+9*x*RootOf(9*_Z^6+3*_Z^3+1)^3-9*(x^3-x^2)^(2/3)-9*x*(x^3-x^2)^(1/3)-4*x^2+x)/x)-3*RootOf(9*_Z^6+3*_Z^3+1)^3*ln((45*RootOf(9*_Z^6+3*_Z^3+1)^6*x^2-90*RootOf(9*_Z^6+3*_Z^3+1)^6*x+72*(x^3-x^2)^(2/3)*RootOf(9*_Z^6+3*_Z^3+1)^3+72*(x^3-x^2)^(1/3)*RootOf(9*_Z^6+3*_Z^3+1)^3*x+87*x^2*RootOf(9*_Z^6+3*_Z^3+1)^3-69*x*RootOf(9*_Z^6+3*_Z^3+1)^3+15*(x^3-x^2)^(2/3)+15*x*(x^3-x^2)^(1/3)+20*x^2-12*x)/x)","B"
2339,1,2319,89,4.665000," ","int((x^3-x^2)^(1/3)/(x^2+x+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2319$\\ \hline \end{longtable}"," ",0,"-ln(-(RootOf(_Z^2-_Z+1)^2*x^2-2*RootOf(_Z^2-_Z+1)^2*x+24*RootOf(_Z^2-_Z+1)*(x^3-x^2)^(2/3)-15*RootOf(_Z^2-_Z+1)*(x^3-x^2)^(1/3)*x-10*RootOf(_Z^2-_Z+1)*x^2+13*RootOf(_Z^2-_Z+1)*x-15*(x^3-x^2)^(2/3)-9*x*(x^3-x^2)^(1/3)+25*x^2-15*x)/x)+RootOf(_Z^2-_Z+1)*ln(-(4*RootOf(_Z^2-_Z+1)^2*x^2-8*RootOf(_Z^2-_Z+1)^2*x-24*RootOf(_Z^2-_Z+1)*(x^3-x^2)^(2/3)+9*RootOf(_Z^2-_Z+1)*(x^3-x^2)^(1/3)*x+11*RootOf(_Z^2-_Z+1)*x^2+6*RootOf(_Z^2-_Z+1)*x+9*(x^3-x^2)^(2/3)+15*x*(x^3-x^2)^(1/3)-20*x^2+5*x)/x)+1/3*ln(-(RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)^2*x^2-2*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)^2*x-43*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)*x^2+67*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)*x+723*(x^3-x^2)^(1/3)*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))*RootOf(_Z^2-_Z+1)*x+372*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))^2*x^2+585*RootOf(_Z^2-_Z+1)*(x^3-x^2)^(2/3)-155*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))^2*x-69*(x^3-x^2)^(1/3)*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))*x-1377*(x^3-x^2)^(2/3))/(RootOf(_Z^2-_Z+1)*x-2*RootOf(_Z^2-_Z+1)-3*x-1)/x)*RootOf(_Z^2-_Z+1)*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))-1/3*ln(-(RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)^2*x^2-2*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)^2*x-43*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)*x^2+67*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)*x+723*(x^3-x^2)^(1/3)*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))*RootOf(_Z^2-_Z+1)*x+372*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))^2*x^2+585*RootOf(_Z^2-_Z+1)*(x^3-x^2)^(2/3)-155*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))^2*x-69*(x^3-x^2)^(1/3)*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))*x-1377*(x^3-x^2)^(2/3))/(RootOf(_Z^2-_Z+1)*x-2*RootOf(_Z^2-_Z+1)-3*x-1)/x)*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))+1/3*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))*ln(-(24*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)^2*x^2-48*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)^2*x+14*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)*x^2+128*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)*x-537*(x^3-x^2)^(1/3)*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))*RootOf(_Z^2-_Z+1)*x-174*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))^2*x^2-171*RootOf(_Z^2-_Z+1)*(x^3-x^2)^(2/3)-29*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))^2*x+183*(x^3-x^2)^(1/3)*RootOf(_Z^3+9*RootOf(_Z^2-_Z+1))*x+891*(x^3-x^2)^(2/3))/(RootOf(_Z^2-_Z+1)*x-2*RootOf(_Z^2-_Z+1)-3*x-1)/x)+1/3*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))*ln((31*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)^2*x^2-62*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)^2*x+340*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)*x^2-91*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)*x-654*(x^3-x^2)^(1/3)*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))*RootOf(_Z^2-_Z+1)*x-11*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))^2*x^2+585*RootOf(_Z^2-_Z+1)*(x^3-x^2)^(2/3)+3*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))^2*x-69*(x^3-x^2)^(1/3)*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))*x+792*(x^3-x^2)^(2/3))/(RootOf(_Z^2-_Z+1)*x-2*RootOf(_Z^2-_Z+1)+2*x+3)/x)+1/3*ln((58*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)^2*x^2-116*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)^2*x-256*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)*x^2+135*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)*x+354*(x^3-x^2)^(1/3)*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))*RootOf(_Z^2-_Z+1)*x+96*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))^2*x^2-171*RootOf(_Z^2-_Z+1)*(x^3-x^2)^(2/3)-36*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))^2*x+183*(x^3-x^2)^(1/3)*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))*x-720*(x^3-x^2)^(2/3))/(RootOf(_Z^2-_Z+1)*x-2*RootOf(_Z^2-_Z+1)+2*x+3)/x)*RootOf(_Z^2-_Z+1)*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))-1/3*ln((58*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)^2*x^2-116*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)^2*x-256*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)*x^2+135*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))^2*RootOf(_Z^2-_Z+1)*x+354*(x^3-x^2)^(1/3)*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))*RootOf(_Z^2-_Z+1)*x+96*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))^2*x^2-171*RootOf(_Z^2-_Z+1)*(x^3-x^2)^(2/3)-36*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))^2*x+183*(x^3-x^2)^(1/3)*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))*x-720*(x^3-x^2)^(2/3))/(RootOf(_Z^2-_Z+1)*x-2*RootOf(_Z^2-_Z+1)+2*x+3)/x)*RootOf(_Z^3+9-9*RootOf(_Z^2-_Z+1))","B"
2340,0,0,153,0.014000," ","int(x*(5-4*(1+k)*x+3*k*x^2)/((1-x)*x*(-k*x+1))^(1/3)/(-b+(b*k+b)*x-b*k*x^2+x^5),x)","\[\int \frac{x \left(5-4 \left(1+k \right) x +3 k \,x^{2}\right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(-b +\left(b k +b \right) x -b k \,x^{2}+x^{5}\right)}\, dx\]"," ",0,"int(x*(5-4*(1+k)*x+3*k*x^2)/((1-x)*x*(-k*x+1))^(1/3)/(-b+(b*k+b)*x-b*k*x^2+x^5),x)","F"
2341,1,737,145,23.975000," ","int((x^4+1)/(-x^4+1)/(x^5+x^3)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{2 x}{\left(x^{3} \left(x^{2}+1\right)\right)^{\frac{1}{4}}}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(-\frac{\sqrt{x^{5}+x^{3}}\, \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x +2 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{3}+4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{2}}{\left(1+x \right)^{2} x^{2}}\right)}{8}+\frac{\RootOf \left(\textit{\_Z}^{4}+8\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} \sqrt{x^{5}+x^{3}}\, x -2 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{4}+8\right) x^{3}+4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}+8\right) x^{2}}{\left(1+x \right)^{2} x^{2}}\right)}{8}-\frac{\ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{4}+2 \RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{3}+8 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{2}+16 \sqrt{x^{5}+x^{3}}\, \RootOf \left(\textit{\_Z}^{4}+8\right) x +16 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(-1+x \right)^{2}}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)}{32}-\frac{\ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{4}+2 \RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{3}+8 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{2}+16 \sqrt{x^{5}+x^{3}}\, \RootOf \left(\textit{\_Z}^{4}+8\right) x +16 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(-1+x \right)^{2}}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{3}}{32}+\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{4}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{4}-2 \RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{3}+8 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{2}-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{2}+8 \sqrt{x^{5}+x^{3}}\, \RootOf \left(\textit{\_Z}^{4}+8\right) x +8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \sqrt{x^{5}+x^{3}}\, x +16 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(-1+x \right)^{2}}\right)}{16}$&$737$\\ trager&$\frac{2 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(x^{2}+1\right)}+\frac{\RootOf \left(\textit{\_Z}^{4}+8\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} \sqrt{x^{5}+x^{3}}\, x -2 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{4}+8\right) x^{3}+4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}+8\right) x^{2}}{\left(1+x \right)^{2} x^{2}}\right)}{8}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(-\frac{\sqrt{x^{5}+x^{3}}\, \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x +2 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{3}+4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{2}}{\left(1+x \right)^{2} x^{2}}\right)}{8}-\frac{\ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{4}+2 \RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{3}+8 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{2}+16 \sqrt{x^{5}+x^{3}}\, \RootOf \left(\textit{\_Z}^{4}+8\right) x +16 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(-1+x \right)^{2}}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{3}}{32}-\frac{\ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{4}+2 \RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{3}+8 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{2}+16 \sqrt{x^{5}+x^{3}}\, \RootOf \left(\textit{\_Z}^{4}+8\right) x +16 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(-1+x \right)^{2}}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)}{32}+\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{4}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{4}-2 \RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{3}+8 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{2}-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{2}+8 \sqrt{x^{5}+x^{3}}\, \RootOf \left(\textit{\_Z}^{4}+8\right) x +8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \sqrt{x^{5}+x^{3}}\, x +16 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(-1+x \right)^{2}}\right)}{16}$&$744$\\ \hline \end{longtable}"," ",0,"2*x/(x^3*(x^2+1))^(1/4)+1/8*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln(-((x^5+x^3)^(1/2)*RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x+2*(x^5+x^3)^(1/4)*RootOf(_Z^4+8)^2*x^2+RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^4-2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^3+4*(x^5+x^3)^(3/4)+RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^2)/(1+x)^2/x^2)+1/8*RootOf(_Z^4+8)*ln(-(-RootOf(_Z^4+8)^3*(x^5+x^3)^(1/2)*x-2*(x^5+x^3)^(1/4)*RootOf(_Z^4+8)^2*x^2+RootOf(_Z^4+8)*x^4-2*RootOf(_Z^4+8)*x^3+4*(x^5+x^3)^(3/4)+RootOf(_Z^4+8)*x^2)/(1+x)^2/x^2)-1/32*ln(-(-RootOf(_Z^4+8)^3*x^4+2*RootOf(_Z^4+8)^3*x^3+8*(x^5+x^3)^(1/4)*RootOf(_Z^4+8)^2*x^2-RootOf(_Z^4+8)^3*x^2+16*(x^5+x^3)^(1/2)*RootOf(_Z^4+8)*x+16*(x^5+x^3)^(3/4))/x^2/(-1+x)^2)*RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)-1/32*ln(-(-RootOf(_Z^4+8)^3*x^4+2*RootOf(_Z^4+8)^3*x^3+8*(x^5+x^3)^(1/4)*RootOf(_Z^4+8)^2*x^2-RootOf(_Z^4+8)^3*x^2+16*(x^5+x^3)^(1/2)*RootOf(_Z^4+8)*x+16*(x^5+x^3)^(3/4))/x^2/(-1+x)^2)*RootOf(_Z^4+8)^3+1/16*RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln((-RootOf(_Z^4+8)^3*x^4+RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*x^4-2*RootOf(_Z^4+8)^3*x^3+2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*x^3+8*(x^5+x^3)^(1/4)*RootOf(_Z^4+8)*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^2-RootOf(_Z^4+8)^3*x^2+RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^2+8*(x^5+x^3)^(1/2)*RootOf(_Z^4+8)*x+8*RootOf(_Z^2+RootOf(_Z^4+8)^2)*(x^5+x^3)^(1/2)*x+16*(x^5+x^3)^(3/4))/x^2/(-1+x)^2)","C"
2342,1,901,137,17.347000," ","int((x^3+1)^(2/3)*(x^6+x^3+2)/x^6/(x^3-2)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{97 x^{9}-5 x^{6}-126 x^{3}-24}{120 x^{5} \left(x^{3}+1\right)^{\frac{1}{3}} \left(x^{3}-2\right)}+\frac{35 \RootOf \left(\textit{\_Z}^{3}+18\right) \ln \left(-\frac{-3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{3} x^{3}-135 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{3}+21 \left(x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x -4 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{2}-9 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{3}+18\right) x^{3}-90 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x^{3}+3 x \left(x^{3}+1\right)^{\frac{2}{3}}-2 \RootOf \left(\textit{\_Z}^{3}+18\right)-90 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right)}{x^{3}-2}\right)}{216}-\frac{35 \ln \left(\frac{6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{3} x^{3}-162 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{3}+42 \left(x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x +\left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{2}+144 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x^{2}-10 \RootOf \left(\textit{\_Z}^{3}+18\right) x^{3}+270 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x^{3}-48 x \left(x^{3}+1\right)^{\frac{2}{3}}-4 \RootOf \left(\textit{\_Z}^{3}+18\right)+108 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right)}{x^{3}-2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)}{216}-\frac{35 \ln \left(\frac{6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{3} x^{3}-162 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{3}+42 \left(x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x +\left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right)^{2} x^{2}+144 \left(x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}+18\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x^{2}-10 \RootOf \left(\textit{\_Z}^{3}+18\right) x^{3}+270 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right) x^{3}-48 x \left(x^{3}+1\right)^{\frac{2}{3}}-4 \RootOf \left(\textit{\_Z}^{3}+18\right)+108 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right)}{x^{3}-2}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}+18\right)^{2}+18 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}+18\right)+324 \textit{\_Z}^{2}\right)}{12}$&$901$\\ trager&$\text{Expression too large to display}$&$1108$\\ \hline \end{longtable}"," ",0,"-1/120*(97*x^9-5*x^6-126*x^3-24)/x^5/(x^3+1)^(1/3)/(x^3-2)+35/216*RootOf(_Z^3+18)*ln(-(-3*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*RootOf(_Z^3+18)^3*x^3-135*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)^2*RootOf(_Z^3+18)^2*x^3+21*(x^3+1)^(2/3)*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*RootOf(_Z^3+18)^2*x-4*(x^3+1)^(1/3)*RootOf(_Z^3+18)^2*x^2-9*(x^3+1)^(1/3)*RootOf(_Z^3+18)*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x^2-2*RootOf(_Z^3+18)*x^3-90*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x^3+3*x*(x^3+1)^(2/3)-2*RootOf(_Z^3+18)-90*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2))/(x^3-2))-35/216*ln((6*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*RootOf(_Z^3+18)^3*x^3-162*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)^2*RootOf(_Z^3+18)^2*x^3+42*(x^3+1)^(2/3)*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*RootOf(_Z^3+18)^2*x+(x^3+1)^(1/3)*RootOf(_Z^3+18)^2*x^2+144*(x^3+1)^(1/3)*RootOf(_Z^3+18)*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x^2-10*RootOf(_Z^3+18)*x^3+270*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x^3-48*x*(x^3+1)^(2/3)-4*RootOf(_Z^3+18)+108*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2))/(x^3-2))*RootOf(_Z^3+18)-35/12*ln((6*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*RootOf(_Z^3+18)^3*x^3-162*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)^2*RootOf(_Z^3+18)^2*x^3+42*(x^3+1)^(2/3)*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*RootOf(_Z^3+18)^2*x+(x^3+1)^(1/3)*RootOf(_Z^3+18)^2*x^2+144*(x^3+1)^(1/3)*RootOf(_Z^3+18)*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x^2-10*RootOf(_Z^3+18)*x^3+270*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)*x^3-48*x*(x^3+1)^(2/3)-4*RootOf(_Z^3+18)+108*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2))/(x^3-2))*RootOf(RootOf(_Z^3+18)^2+18*_Z*RootOf(_Z^3+18)+324*_Z^2)","C"
2343,1,652,145,43.149000," ","int((x^8+1)/(x^6+x^2)^(1/4)/(x^8-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{x \left(x^{4}+1\right)}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{5}+2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{3}-4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{16}-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{4}-8\right) x^{5}+2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}-8\right) x}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{16}-\frac{\ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(x^{2}+1\right)}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{3}}{32}-\frac{\ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(x^{2}+1\right)}\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2}}{32}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{5}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{5}-2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}+8 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x +8 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}-8\right) x +8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \sqrt{x^{6}+x^{2}}\, x +16 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{x \left(x^{2}+1\right)^{2}}\right)}{32}$&$652$\\ risch&$-\frac{x}{\left(x^{2} \left(x^{4}+1\right)\right)^{\frac{1}{4}}}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{5}+2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x}{x \left(x^{2}+1\right)^{2}}\right)}{16}+\frac{\RootOf \left(\textit{\_Z}^{4}+8\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{4}+8\right) x^{5}-2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}+8\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}+8\right) x}{x \left(x^{2}+1\right)^{2}}\right)}{16}-\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{3}}{32}-\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)}{32}+\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{5}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{5}+2 \RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{3}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{3}+8 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{2}-8 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}+8\right) x -8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x -\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x +16 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{32}$&$654$\\ \hline \end{longtable}"," ",0,"-(x^6+x^2)^(3/4)/x/(x^4+1)-1/16*RootOf(_Z^2+RootOf(_Z^4-8)^2)*ln(-(RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*(x^6+x^2)^(1/2)*x-RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^5+2*RootOf(_Z^4-8)^2*(x^6+x^2)^(1/4)*x^2-2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^3-4*(x^6+x^2)^(3/4)-RootOf(_Z^2+RootOf(_Z^4-8)^2)*x)/(-1+x)^2/(1+x)^2/x)-1/16*RootOf(_Z^4-8)*ln((RootOf(_Z^4-8)^3*(x^6+x^2)^(1/2)*x+RootOf(_Z^4-8)*x^5+2*RootOf(_Z^4-8)^2*(x^6+x^2)^(1/4)*x^2+2*RootOf(_Z^4-8)*x^3+4*(x^6+x^2)^(3/4)+RootOf(_Z^4-8)*x)/(-1+x)^2/(1+x)^2/x)-1/32*ln((RootOf(_Z^4-8)^2*x^2+2*RootOf(_Z^4-8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(x^2+1))*RootOf(_Z^4-8)^3-1/32*ln((RootOf(_Z^4-8)^2*x^2+2*RootOf(_Z^4-8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(x^2+1))*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2+1/32*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*ln((RootOf(_Z^4-8)^3*x^5-RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x^5-2*RootOf(_Z^4-8)^3*x^3+2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x^3+8*RootOf(_Z^4-8)*(x^6+x^2)^(1/4)*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^2+RootOf(_Z^4-8)^3*x-RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x+8*(x^6+x^2)^(1/2)*RootOf(_Z^4-8)*x+8*RootOf(_Z^2+RootOf(_Z^4-8)^2)*(x^6+x^2)^(1/2)*x+16*(x^6+x^2)^(3/4))/x/(x^2+1)^2)","C"
2344,1,627,145,44.851000," ","int((x^8+1)/(x^6+x^2)^(1/4)/(x^8-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{x}{\left(x^{2} \left(x^{4}+1\right)\right)^{\frac{1}{4}}}+\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{4}-8\right) x^{5}+2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}-8\right) x}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{16}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{5}-2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{16}-\frac{\ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(x^{2}+1\right)}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{3}}{32}-\frac{\ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(x^{2}+1\right)}\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2}}{32}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right) x^{5}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right) x^{3}-4 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{2}-4 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right) x^{2}-8 \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right) x}{x \left(x^{2}+1\right)^{2}}\right)}{32}$&$627$\\ trager&$-\frac{\left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{x \left(x^{4}+1\right)}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{5}+2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x}{x \left(x^{2}+1\right)^{2}}\right)}{16}-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{4}+8\right) x^{5}+2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}+8\right) x^{3}-4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}+8\right) x}{x \left(x^{2}+1\right)^{2}}\right)}{16}-\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{3}}{32}-\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)}{32}+\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right) x^{5}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \left(x^{6}+x^{2}\right)^{\frac{3}{4}}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right) x^{3}-4 \RootOf \left(\textit{\_Z}^{4}+8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x^{2}-4 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{2}+x \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)+8 \sqrt{x^{6}+x^{2}}\, x}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{32}$&$637$\\ \hline \end{longtable}"," ",0,"-x/(x^2*(x^4+1))^(1/4)+1/16*RootOf(_Z^4-8)*ln(-(-RootOf(_Z^4-8)^3*(x^6+x^2)^(1/2)*x-RootOf(_Z^4-8)*x^5+2*RootOf(_Z^4-8)^2*(x^6+x^2)^(1/4)*x^2-2*RootOf(_Z^4-8)*x^3+4*(x^6+x^2)^(3/4)-RootOf(_Z^4-8)*x)/(-1+x)^2/(1+x)^2/x)-1/16*RootOf(_Z^2+RootOf(_Z^4-8)^2)*ln((-RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*(x^6+x^2)^(1/2)*x+RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^5-2*RootOf(_Z^4-8)^2*(x^6+x^2)^(1/4)*x^2+2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^3+4*(x^6+x^2)^(3/4)+RootOf(_Z^2+RootOf(_Z^4-8)^2)*x)/(-1+x)^2/(1+x)^2/x)-1/32*ln((RootOf(_Z^4-8)^2*x^2+2*RootOf(_Z^4-8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(x^2+1))*RootOf(_Z^4-8)^3-1/32*ln((RootOf(_Z^4-8)^2*x^2+2*RootOf(_Z^4-8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(x^2+1))*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2+1/32*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*ln(-(RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)*x^5+RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*(x^6+x^2)^(3/4)-RootOf(_Z^4-8)^3*(x^6+x^2)^(3/4)-2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)*x^3-4*(x^6+x^2)^(1/4)*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^2-4*(x^6+x^2)^(1/4)*RootOf(_Z^4-8)*x^2-8*(x^6+x^2)^(1/2)*x+RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)*x)/x/(x^2+1)^2)","C"
2345,0,0,153,0.017000," ","int(x^2*(8-7*(1+k)*x+6*k*x^2)/((1-x)*x*(-k*x+1))^(1/3)/(-b+b*(1+k)*x-b*k*x^2+x^8),x)","\[\int \frac{x^{2} \left(8-7 \left(1+k \right) x +6 k \,x^{2}\right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(-b +b \left(1+k \right) x -b k \,x^{2}+x^{8}\right)}\, dx\]"," ",0,"int(x^2*(8-7*(1+k)*x+6*k*x^2)/((1-x)*x*(-k*x+1))^(1/3)/(-b+b*(1+k)*x-b*k*x^2+x^8),x)","F"
2346,0,0,143,0.028000," ","int(1/(x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{1}{\left(x^{2}+1\right)^{2} \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int(1/(x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x)","F"
2347,0,0,172,0.187000," ","int(x*(-a+x)*(a*b+(a-2*b)*x)/(x*(-a+x)*(-b+x)^2)^(3/4)/(b^2*d+(-2*b*d+a)*x+(-1+d)*x^2),x)","\[\int \frac{x \left(-a +x \right) \left(a b +\left(a -2 b \right) x \right)}{\left(x \left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{3}{4}} \left(b^{2} d +\left(-2 b d +a \right) x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int(x*(-a+x)*(a*b+(a-2*b)*x)/(x*(-a+x)*(-b+x)^2)^(3/4)/(b^2*d+(-2*b*d+a)*x+(-1+d)*x^2),x)","F"
2348,1,1372,145,6.127000," ","int((x^2+1)*(x^4-3*x^2+1)/x^2/((2*x^2+x-2)/(x^2+x-1))^(1/2)/(x^4+x^3-3*x^2-x+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(x^{2}+x -1\right) \sqrt{-\frac{-2 x^{2}-x +2}{x^{2}+x -1}}}{2 x}-\frac{\RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right) \ln \left(\frac{614375 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{5} x^{2}+497600 \sqrt{-\frac{-2 x^{2}-x +2}{x^{2}+x -1}}\, \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{2} x^{2}-614375 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{5}-2032100 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{3} x^{2}+497600 \sqrt{-\frac{-2 x^{2}-x +2}{x^{2}+x -1}}\, \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{2} x -1081300 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{3} x -497600 \sqrt{-\frac{-2 x^{2}-x +2}{x^{2}+x -1}}\, \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{2}-293952 \sqrt{-\frac{-2 x^{2}-x +2}{x^{2}+x -1}}\, x^{2}+2032100 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{3}+981920 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right) x^{2}-293952 \sqrt{-\frac{-2 x^{2}-x +2}{x^{2}+x -1}}\, x +635360 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right) x +293952 \sqrt{-\frac{-2 x^{2}-x +2}{x^{2}+x -1}}-981920 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)}{25 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{2} x^{2}-25 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{2}-12 x^{2}+4 x +12}\right)}{2}+\frac{25 \ln \left(-\frac{413125 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{5} x^{2}+497600 \sqrt{-\frac{-2 x^{2}-x +2}{x^{2}+x -1}}\, \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{2} x^{2}-413125 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{5}+693200 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{3} x^{2}+497600 \sqrt{-\frac{-2 x^{2}-x +2}{x^{2}+x -1}}\, \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{2} x +727100 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{3} x -497600 \sqrt{-\frac{-2 x^{2}-x +2}{x^{2}+x -1}}\, \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{2}-104128 \sqrt{-\frac{-2 x^{2}-x +2}{x^{2}+x -1}}\, x^{2}-693200 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{3}-192000 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right) x^{2}-104128 \sqrt{-\frac{-2 x^{2}-x +2}{x^{2}+x -1}}\, x -176000 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right) x +104128 \sqrt{-\frac{-2 x^{2}-x +2}{x^{2}+x -1}}+192000 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)}{25 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{2} x^{2}-25 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{2}-8 x^{2}-4 x +8}\right) \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{3}}{8}-\frac{3 \ln \left(-\frac{413125 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{5} x^{2}+497600 \sqrt{-\frac{-2 x^{2}-x +2}{x^{2}+x -1}}\, \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{2} x^{2}-413125 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{5}+693200 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{3} x^{2}+497600 \sqrt{-\frac{-2 x^{2}-x +2}{x^{2}+x -1}}\, \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{2} x +727100 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{3} x -497600 \sqrt{-\frac{-2 x^{2}-x +2}{x^{2}+x -1}}\, \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{2}-104128 \sqrt{-\frac{-2 x^{2}-x +2}{x^{2}+x -1}}\, x^{2}-693200 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{3}-192000 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right) x^{2}-104128 \sqrt{-\frac{-2 x^{2}-x +2}{x^{2}+x -1}}\, x -176000 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right) x +104128 \sqrt{-\frac{-2 x^{2}-x +2}{x^{2}+x -1}}+192000 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)}{25 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{2} x^{2}-25 \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)^{2}-8 x^{2}-4 x +8}\right) \RootOf \left(125 \textit{\_Z}^{4}-100 \textit{\_Z}^{2}+16\right)}{2}+\frac{3 \RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{4 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}-4 \sqrt{-\frac{-2 x^{2}-x +2}{x^{2}+x -1}}\, x^{2}+3 \RootOf \left(\textit{\_Z}^{2}-2\right) x -4 \sqrt{-\frac{-2 x^{2}-x +2}{x^{2}+x -1}}\, x -4 \RootOf \left(\textit{\_Z}^{2}-2\right)+4 \sqrt{-\frac{-2 x^{2}-x +2}{x^{2}+x -1}}}{x}\right)}{8}$&$1372$\\ risch&$\text{Expression too large to display}$&$1635$\\ default&$\text{Expression too large to display}$&$14835$\\ \hline \end{longtable}"," ",0,"1/2*(x^2+x-1)/x*(-(-2*x^2-x+2)/(x^2+x-1))^(1/2)-1/2*RootOf(125*_Z^4-100*_Z^2+16)*ln((614375*RootOf(125*_Z^4-100*_Z^2+16)^5*x^2+497600*(-(-2*x^2-x+2)/(x^2+x-1))^(1/2)*RootOf(125*_Z^4-100*_Z^2+16)^2*x^2-614375*RootOf(125*_Z^4-100*_Z^2+16)^5-2032100*RootOf(125*_Z^4-100*_Z^2+16)^3*x^2+497600*(-(-2*x^2-x+2)/(x^2+x-1))^(1/2)*RootOf(125*_Z^4-100*_Z^2+16)^2*x-1081300*RootOf(125*_Z^4-100*_Z^2+16)^3*x-497600*(-(-2*x^2-x+2)/(x^2+x-1))^(1/2)*RootOf(125*_Z^4-100*_Z^2+16)^2-293952*(-(-2*x^2-x+2)/(x^2+x-1))^(1/2)*x^2+2032100*RootOf(125*_Z^4-100*_Z^2+16)^3+981920*RootOf(125*_Z^4-100*_Z^2+16)*x^2-293952*(-(-2*x^2-x+2)/(x^2+x-1))^(1/2)*x+635360*RootOf(125*_Z^4-100*_Z^2+16)*x+293952*(-(-2*x^2-x+2)/(x^2+x-1))^(1/2)-981920*RootOf(125*_Z^4-100*_Z^2+16))/(25*RootOf(125*_Z^4-100*_Z^2+16)^2*x^2-25*RootOf(125*_Z^4-100*_Z^2+16)^2-12*x^2+4*x+12))+25/8*ln(-(413125*RootOf(125*_Z^4-100*_Z^2+16)^5*x^2+497600*(-(-2*x^2-x+2)/(x^2+x-1))^(1/2)*RootOf(125*_Z^4-100*_Z^2+16)^2*x^2-413125*RootOf(125*_Z^4-100*_Z^2+16)^5+693200*RootOf(125*_Z^4-100*_Z^2+16)^3*x^2+497600*(-(-2*x^2-x+2)/(x^2+x-1))^(1/2)*RootOf(125*_Z^4-100*_Z^2+16)^2*x+727100*RootOf(125*_Z^4-100*_Z^2+16)^3*x-497600*(-(-2*x^2-x+2)/(x^2+x-1))^(1/2)*RootOf(125*_Z^4-100*_Z^2+16)^2-104128*(-(-2*x^2-x+2)/(x^2+x-1))^(1/2)*x^2-693200*RootOf(125*_Z^4-100*_Z^2+16)^3-192000*RootOf(125*_Z^4-100*_Z^2+16)*x^2-104128*(-(-2*x^2-x+2)/(x^2+x-1))^(1/2)*x-176000*RootOf(125*_Z^4-100*_Z^2+16)*x+104128*(-(-2*x^2-x+2)/(x^2+x-1))^(1/2)+192000*RootOf(125*_Z^4-100*_Z^2+16))/(25*RootOf(125*_Z^4-100*_Z^2+16)^2*x^2-25*RootOf(125*_Z^4-100*_Z^2+16)^2-8*x^2-4*x+8))*RootOf(125*_Z^4-100*_Z^2+16)^3-3/2*ln(-(413125*RootOf(125*_Z^4-100*_Z^2+16)^5*x^2+497600*(-(-2*x^2-x+2)/(x^2+x-1))^(1/2)*RootOf(125*_Z^4-100*_Z^2+16)^2*x^2-413125*RootOf(125*_Z^4-100*_Z^2+16)^5+693200*RootOf(125*_Z^4-100*_Z^2+16)^3*x^2+497600*(-(-2*x^2-x+2)/(x^2+x-1))^(1/2)*RootOf(125*_Z^4-100*_Z^2+16)^2*x+727100*RootOf(125*_Z^4-100*_Z^2+16)^3*x-497600*(-(-2*x^2-x+2)/(x^2+x-1))^(1/2)*RootOf(125*_Z^4-100*_Z^2+16)^2-104128*(-(-2*x^2-x+2)/(x^2+x-1))^(1/2)*x^2-693200*RootOf(125*_Z^4-100*_Z^2+16)^3-192000*RootOf(125*_Z^4-100*_Z^2+16)*x^2-104128*(-(-2*x^2-x+2)/(x^2+x-1))^(1/2)*x-176000*RootOf(125*_Z^4-100*_Z^2+16)*x+104128*(-(-2*x^2-x+2)/(x^2+x-1))^(1/2)+192000*RootOf(125*_Z^4-100*_Z^2+16))/(25*RootOf(125*_Z^4-100*_Z^2+16)^2*x^2-25*RootOf(125*_Z^4-100*_Z^2+16)^2-8*x^2-4*x+8))*RootOf(125*_Z^4-100*_Z^2+16)+3/8*RootOf(_Z^2-2)*ln((4*RootOf(_Z^2-2)*x^2-4*(-(-2*x^2-x+2)/(x^2+x-1))^(1/2)*x^2+3*RootOf(_Z^2-2)*x-4*(-(-2*x^2-x+2)/(x^2+x-1))^(1/2)*x-4*RootOf(_Z^2-2)+4*(-(-2*x^2-x+2)/(x^2+x-1))^(1/2))/x)","C"
2349,0,0,156,0.020000," ","int(x^3*(5-4*(1+k)*x+3*k*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(-1+(1+k)*x-k*x^2+b*x^5),x)","\[\int \frac{x^{3} \left(5-4 \left(1+k \right) x +3 k \,x^{2}\right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{2}{3}} \left(-1+\left(1+k \right) x -k \,x^{2}+b \,x^{5}\right)}\, dx\]"," ",0,"int(x^3*(5-4*(1+k)*x+3*k*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(-1+(1+k)*x-k*x^2+b*x^5),x)","F"
2350,1,41,14,0.616000," ","int((x^4-2)*(x^4+2)^(1/2)/(x^8+3*x^4+4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{x^{4}+2}}{x}\right)}{2}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{x^{4}+2}}{x}\right)}{2}\right) \sqrt{2}}{2}$&$41$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \sqrt{x^{4}+2}\, x +2 \RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{4}+x^{2}+2}\right)}{4}-\frac{\ln \left(-\frac{x^{4}+2 \sqrt{x^{4}+2}\, x +x^{2}+2}{x^{4}-x^{2}+2}\right)}{4}$&$98$\\ default&$\frac{\sqrt{2}\, \sqrt{4-2 i \sqrt{2}\, x^{2}}\, \sqrt{4+2 i \sqrt{2}\, x^{2}}\, \EllipticF \left(\frac{x \sqrt{2}\, \sqrt{i \sqrt{2}}}{2}, i\right)}{4 \sqrt{i \sqrt{2}}\, \sqrt{x^{4}+2}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}-\textit{\_Z}^{2}+2\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{4 \arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}+1\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{x^{4}+2}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}}}-\frac{2 \,2^{\frac{1}{4}} \left(-\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{2-i \sqrt{2}\, x^{2}}\, \sqrt{2+i \sqrt{2}\, x^{2}}\, \EllipticPi \left(\frac{x \sqrt{2}\, \sqrt{i \sqrt{2}}}{2}, \frac{i \sqrt{2}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{2}-\frac{i \sqrt{2}}{2}, \frac{\sqrt{-\frac{i \sqrt{2}}{2}}\, \sqrt{2}}{\sqrt{i \sqrt{2}}}\right)}{\sqrt{i}\, \sqrt{x^{4}+2}}\right)\right)}{32}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+\textit{\_Z}^{2}+2\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{4 \arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}-1\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{x^{4}+2}}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{2}}}-\frac{2 \,2^{\frac{1}{4}} \left(-\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{2-i \sqrt{2}\, x^{2}}\, \sqrt{2+i \sqrt{2}\, x^{2}}\, \EllipticPi \left(\frac{x \sqrt{2}\, \sqrt{i \sqrt{2}}}{2}, \frac{i \sqrt{2}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{i \sqrt{2}}{2}, \frac{\sqrt{-\frac{i \sqrt{2}}{2}}\, \sqrt{2}}{\sqrt{i \sqrt{2}}}\right)}{\sqrt{i}\, \sqrt{x^{4}+2}}\right)\right)}{32}$&$361$\\ \hline \end{longtable}"," ",0,"1/2*(1/2*2^(1/2)*arctan((x^4+2)^(1/2)/x)-1/2*2^(1/2)*arctanh((x^4+2)^(1/2)/x))*2^(1/2)","B"
2351,1,137,152,0.777000," ","int((x^8-5*x^7+7*x^6+2*x^5-10*x^4+2*x^3+5*x^2-x-1)^(1/3)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(6 x^{3}-27 x^{2}+31 x -10\right) \left(\left(-1+x \right)^{2} \left(x^{2}-x -1\right)^{3}\right)^{\frac{1}{3}}}{10 x \left(-1+x \right) \left(x^{2}-x -1\right)}+\frac{\left(-\frac{\ln \left(1+\left(-1+x \right)^{\frac{1}{3}}\right)}{3}+\frac{\ln \left(1-\left(-1+x \right)^{\frac{1}{3}}+\left(-1+x \right)^{\frac{2}{3}}\right)}{6}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 \left(-1+x \right)^{\frac{1}{3}}-1\right) \sqrt{3}}{3}\right)}{3}\right) \left(\left(-1+x \right)^{2} \left(x^{2}-x -1\right)^{3}\right)^{\frac{1}{3}}}{\left(-1+x \right)^{\frac{2}{3}} \left(x^{2}-x -1\right)}$&$137$\\ trager&$\frac{\left(6 x^{2}-21 x +10\right) \left(x^{8}-5 x^{7}+7 x^{6}+2 x^{5}-10 x^{4}+2 x^{3}+5 x^{2}-x -1\right)^{\frac{1}{3}}}{10 x \left(x^{2}-x -1\right)}-\frac{\ln \left(-\frac{1+x +6 x^{2} \left(x^{8}-5 x^{7}+7 x^{6}+2 x^{5}-10 x^{4}+2 x^{3}+5 x^{2}-x -1\right)^{\frac{1}{3}}-x^{5}-3 x^{2}-x^{3}+3 x^{4}-3 \left(x^{8}-5 x^{7}+7 x^{6}+2 x^{5}-10 x^{4}+2 x^{3}+5 x^{2}-x -1\right)^{\frac{1}{3}}+18 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{8}-5 x^{7}+7 x^{6}+2 x^{5}-10 x^{4}+2 x^{3}+5 x^{2}-x -1\right)^{\frac{2}{3}}+18 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{8}-5 x^{7}+7 x^{6}+2 x^{5}-10 x^{4}+2 x^{3}+5 x^{2}-x -1\right)^{\frac{1}{3}}+18 \left(x^{8}-5 x^{7}+7 x^{6}+2 x^{5}-10 x^{4}+2 x^{3}+5 x^{2}-x -1\right)^{\frac{1}{3}} \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{3}-36 \left(x^{8}-5 x^{7}+7 x^{6}+2 x^{5}-10 x^{4}+2 x^{3}+5 x^{2}-x -1\right)^{\frac{1}{3}} \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}+72 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{6}-6 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{6}-78 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{4}+504 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{4}+42 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{5}-360 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{5}+72 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x -504 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{2}+78 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}-18 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x -24 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)+144 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2}+72 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{3}+6 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{3}-3 \left(x^{8}-5 x^{7}+7 x^{6}+2 x^{5}-10 x^{4}+2 x^{3}+5 x^{2}-x -1\right)^{\frac{1}{3}} x^{3}}{\left(x^{2}-x -1\right)^{2} x \left(-1+x \right)}\right)}{3}+\frac{\ln \left(\frac{2+6 x^{2} \left(x^{8}-5 x^{7}+7 x^{6}+2 x^{5}-10 x^{4}+2 x^{3}+5 x^{2}-x -1\right)^{\frac{1}{3}}-8 x^{5}+2 x^{6}-8 x^{2}+4 x^{3}+8 x^{4}-3 \left(x^{8}-5 x^{7}+7 x^{6}+2 x^{5}-10 x^{4}+2 x^{3}+5 x^{2}-x -1\right)^{\frac{1}{3}}+18 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{8}-5 x^{7}+7 x^{6}+2 x^{5}-10 x^{4}+2 x^{3}+5 x^{2}-x -1\right)^{\frac{2}{3}}+36 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{6}-18 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{6}-108 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{4}+252 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{4}+84 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{5}-180 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{5}+36 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x -252 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{2}+108 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}-12 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x -30 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)+72 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2}+36 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{3}-24 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{3}-3 \left(x^{8}-5 x^{7}+7 x^{6}+2 x^{5}-10 x^{4}+2 x^{3}+5 x^{2}-x -1\right)^{\frac{2}{3}}-3 \left(x^{8}-5 x^{7}+7 x^{6}+2 x^{5}-10 x^{4}+2 x^{3}+5 x^{2}-x -1\right)^{\frac{1}{3}} x^{3}}{\left(x^{2}-x -1\right)^{2} x \left(-1+x \right)}\right)}{3}-2 \ln \left(\frac{2+6 x^{2} \left(x^{8}-5 x^{7}+7 x^{6}+2 x^{5}-10 x^{4}+2 x^{3}+5 x^{2}-x -1\right)^{\frac{1}{3}}-8 x^{5}+2 x^{6}-8 x^{2}+4 x^{3}+8 x^{4}-3 \left(x^{8}-5 x^{7}+7 x^{6}+2 x^{5}-10 x^{4}+2 x^{3}+5 x^{2}-x -1\right)^{\frac{1}{3}}+18 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) \left(x^{8}-5 x^{7}+7 x^{6}+2 x^{5}-10 x^{4}+2 x^{3}+5 x^{2}-x -1\right)^{\frac{2}{3}}+36 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{6}-18 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{6}-108 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{4}+252 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{4}+84 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{5}-180 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{5}+36 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x -252 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{2}+108 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{2}-12 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x -30 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)+72 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2}+36 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)^{2} x^{3}-24 \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right) x^{3}-3 \left(x^{8}-5 x^{7}+7 x^{6}+2 x^{5}-10 x^{4}+2 x^{3}+5 x^{2}-x -1\right)^{\frac{2}{3}}-3 \left(x^{8}-5 x^{7}+7 x^{6}+2 x^{5}-10 x^{4}+2 x^{3}+5 x^{2}-x -1\right)^{\frac{1}{3}} x^{3}}{\left(x^{2}-x -1\right)^{2} x \left(-1+x \right)}\right) \RootOf \left(36 \textit{\_Z}^{2}-6 \textit{\_Z} +1\right)$&$1710$\\ \hline \end{longtable}"," ",0,"1/10*(6*x^3-27*x^2+31*x-10)/x/(-1+x)*((-1+x)^2*(x^2-x-1)^3)^(1/3)/(x^2-x-1)+(-1/3*ln(1+(-1+x)^(1/3))+1/6*ln(1-(-1+x)^(1/3)+(-1+x)^(2/3))+1/3*3^(1/2)*arctan(1/3*(2*(-1+x)^(1/3)-1)*3^(1/2)))*((-1+x)^2*(x^2-x-1)^3)^(1/3)/(-1+x)^(2/3)/(x^2-x-1)","A"
2352,0,0,144,180.000000," ","int((a^2*x^2-b)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^4+b)^(1/2),x)","\[\int \frac{\left(a^{2} x^{2}-b \right) \sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}{\sqrt{a^{2} x^{4}+b}}\, dx\]"," ",0,"int((a^2*x^2-b)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^4+b)^(1/2),x)","F"
2353,1,271,42,0.125000," ","int((1+x)^(1/2)/(x+(x+(1+x)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\textit{\_R}^{2} \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+2 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{\sum}\frac{\left(-3 \textit{\_R}^{2}+2 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}+6 \textit{\_R}^{2}-10 \textit{\_R} +3}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\sum}\frac{\left(\textit{\_R}^{2}-2 \textit{\_R} -3\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +5}\right)+2 \ln \left(-1-2 \sqrt{1+x}+2 \sqrt{x +\sqrt{1+x}}\right)+2 \sqrt{1+x}-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\left(-3 \textit{\_R}^{2}-\textit{\_R} +2\right) \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)$&$271$\\ default&$-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\textit{\_R}^{2} \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+2 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{\sum}\frac{\left(-3 \textit{\_R}^{2}+2 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}+6 \textit{\_R}^{2}-10 \textit{\_R} +3}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\sum}\frac{\left(\textit{\_R}^{2}-2 \textit{\_R} -3\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +5}\right)+2 \ln \left(-1-2 \sqrt{1+x}+2 \sqrt{x +\sqrt{1+x}}\right)+2 \sqrt{1+x}-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\left(-3 \textit{\_R}^{2}-\textit{\_R} +2\right) \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)$&$271$\\ \hline \end{longtable}"," ",0,"-2*sum(_R^2/(4*_R^3-6*_R-1)*ln((1+x)^(1/2)-_R),_R=RootOf(_Z^4-3*_Z^2-_Z+2))+2*sum((-3*_R^2+2*_R+1)/(4*_R^3+6*_R^2-10*_R+3)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^4+2*_Z^3-5*_Z^2+3*_Z+1))+2*sum((_R^2-2*_R-3)/(4*_R^3-6*_R^2+2*_R+5)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^4-2*_Z^3+_Z^2+5*_Z-1))+2*ln(-1-2*(1+x)^(1/2)+2*(x+(1+x)^(1/2))^(1/2))+2*(1+x)^(1/2)-2*sum((-3*_R^2-_R+2)/(4*_R^3-6*_R-1)*ln((1+x)^(1/2)-_R),_R=RootOf(_Z^4-3*_Z^2-_Z+2))","B"
2354,1,271,42,0.117000," ","int((1+x)^(1/2)/(x+(x+(1+x)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\textit{\_R}^{2} \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+2 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{\sum}\frac{\left(-3 \textit{\_R}^{2}+2 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}+6 \textit{\_R}^{2}-10 \textit{\_R} +3}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\sum}\frac{\left(\textit{\_R}^{2}-2 \textit{\_R} -3\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +5}\right)+2 \ln \left(-1-2 \sqrt{1+x}+2 \sqrt{x +\sqrt{1+x}}\right)+2 \sqrt{1+x}-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\left(-3 \textit{\_R}^{2}-\textit{\_R} +2\right) \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)$&$271$\\ default&$-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\textit{\_R}^{2} \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+2 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{\sum}\frac{\left(-3 \textit{\_R}^{2}+2 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}+6 \textit{\_R}^{2}-10 \textit{\_R} +3}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\sum}\frac{\left(\textit{\_R}^{2}-2 \textit{\_R} -3\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +5}\right)+2 \ln \left(-1-2 \sqrt{1+x}+2 \sqrt{x +\sqrt{1+x}}\right)+2 \sqrt{1+x}-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\left(-3 \textit{\_R}^{2}-\textit{\_R} +2\right) \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)$&$271$\\ \hline \end{longtable}"," ",0,"-2*sum(_R^2/(4*_R^3-6*_R-1)*ln((1+x)^(1/2)-_R),_R=RootOf(_Z^4-3*_Z^2-_Z+2))+2*sum((-3*_R^2+2*_R+1)/(4*_R^3+6*_R^2-10*_R+3)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^4+2*_Z^3-5*_Z^2+3*_Z+1))+2*sum((_R^2-2*_R-3)/(4*_R^3-6*_R^2+2*_R+5)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^4-2*_Z^3+_Z^2+5*_Z-1))+2*ln(-1-2*(1+x)^(1/2)+2*(x+(1+x)^(1/2))^(1/2))+2*(1+x)^(1/2)-2*sum((-3*_R^2-_R+2)/(4*_R^3-6*_R-1)*ln((1+x)^(1/2)-_R),_R=RootOf(_Z^4-3*_Z^2-_Z+2))","B"
2355,1,145,172,0.287000," ","int((-I+k^(1/2)*x)/(I+k^(1/2)*x)/((-x^2+1)*(-k^2*x^2+1))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\arctan \left(\frac{\sqrt{\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)}}{x \left(1+k \right)}\right)}{1+k}+\frac{i \ln \left(\frac{2 k^{2}+4 k +2+\left(-k^{3}-2 k^{2}-k \right) \left(x^{2}+\frac{1}{k}\right)+2 \sqrt{\left(1+k \right)^{2}}\, \sqrt{k^{3} \left(x^{2}+\frac{1}{k}\right)^{2}+\left(-k^{3}-2 k^{2}-k \right) \left(x^{2}+\frac{1}{k}\right)+k^{2}+2 k +1}}{x^{2}+\frac{1}{k}}\right)}{\sqrt{\left(1+k \right)^{2}}}$&$145$\\ default&$\frac{\sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticF \left(x , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}-2 i \left(-\frac{i \sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticPi \left(x , -k , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}-\frac{\ln \left(\frac{2 k^{2}+4 k +2+\left(-k^{3}-2 k^{2}-k \right) \left(x^{2}+\frac{1}{k}\right)+2 \sqrt{\left(1+k \right)^{2}}\, \sqrt{k^{3} \left(x^{2}+\frac{1}{k}\right)^{2}+\left(-k^{3}-2 k^{2}-k \right) \left(x^{2}+\frac{1}{k}\right)+k^{2}+2 k +1}}{x^{2}+\frac{1}{k}}\right)}{2 \sqrt{\left(1+k \right)^{2}}}\right)$&$215$\\ \hline \end{longtable}"," ",0,"1/(1+k)*arctan(((-x^2+1)*(-k^2*x^2+1))^(1/2)/x/(1+k))+I/((1+k)^2)^(1/2)*ln((2*k^2+4*k+2+(-k^3-2*k^2-k)*(x^2+1/k)+2*((1+k)^2)^(1/2)*(k^3*(x^2+1/k)^2+(-k^3-2*k^2-k)*(x^2+1/k)+k^2+2*k+1)^(1/2))/(x^2+1/k))","A"
2356,1,145,172,0.253000," ","int((I+k^(1/2)*x)/(-I+k^(1/2)*x)/((-x^2+1)*(-k^2*x^2+1))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\arctan \left(\frac{\sqrt{\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)}}{x \left(1+k \right)}\right)}{1+k}-\frac{i \ln \left(\frac{2 k^{2}+4 k +2+\left(-k^{3}-2 k^{2}-k \right) \left(x^{2}+\frac{1}{k}\right)+2 \sqrt{\left(1+k \right)^{2}}\, \sqrt{k^{3} \left(x^{2}+\frac{1}{k}\right)^{2}+\left(-k^{3}-2 k^{2}-k \right) \left(x^{2}+\frac{1}{k}\right)+k^{2}+2 k +1}}{x^{2}+\frac{1}{k}}\right)}{\sqrt{\left(1+k \right)^{2}}}$&$145$\\ default&$\frac{\sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticF \left(x , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}+2 i \left(\frac{i \sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticPi \left(x , -k , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}-\frac{\ln \left(\frac{2 k^{2}+4 k +2+\left(-k^{3}-2 k^{2}-k \right) \left(x^{2}+\frac{1}{k}\right)+2 \sqrt{\left(1+k \right)^{2}}\, \sqrt{k^{3} \left(x^{2}+\frac{1}{k}\right)^{2}+\left(-k^{3}-2 k^{2}-k \right) \left(x^{2}+\frac{1}{k}\right)+k^{2}+2 k +1}}{x^{2}+\frac{1}{k}}\right)}{2 \sqrt{\left(1+k \right)^{2}}}\right)$&$215$\\ \hline \end{longtable}"," ",0,"1/(1+k)*arctan(((-x^2+1)*(-k^2*x^2+1))^(1/2)/x/(1+k))-I/((1+k)^2)^(1/2)*ln((2*k^2+4*k+2+(-k^3-2*k^2-k)*(x^2+1/k)+2*((1+k)^2)^(1/2)*(k^3*(x^2+1/k)^2+(-k^3-2*k^2-k)*(x^2+1/k)+k^2+2*k+1)^(1/2))/(x^2+1/k))","A"
2357,0,0,87,180.000000," ","int(1/(x^3-3*x^2+3*x-1)^(1/4)/(3*x^3+x^2-2*x-1)^4,x)","\[\int \frac{1}{\left(x^{3}-3 x^{2}+3 x -1\right)^{\frac{1}{4}} \left(3 x^{3}+x^{2}-2 x -1\right)^{4}}\, dx\]"," ",0,"int(1/(x^3-3*x^2+3*x-1)^(1/4)/(3*x^3+x^2-2*x-1)^4,x)","F"
2358,0,0,36,0.011000," ","int((a*x^4+b*x^3)^(1/4)/x^2/(c*x^2-d),x)","\[\int \frac{\left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}}{x^{2} \left(c \,x^{2}-d \right)}\, dx\]"," ",0,"int((a*x^4+b*x^3)^(1/4)/x^2/(c*x^2-d),x)","F"
2359,0,0,36,0.003000," ","int((a*x^4+b*x^3)^(1/4)/x^2/(c*x^2-d),x)","\[\int \frac{\left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}}{x^{2} \left(c \,x^{2}-d \right)}\, dx\]"," ",0,"int((a*x^4+b*x^3)^(1/4)/x^2/(c*x^2-d),x)","F"
2360,1,653,145,46.012000," ","int(x^4/(x^6+x^2)^(1/4)/(x^8-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x}{2 \left(x^{2} \left(x^{4}+1\right)\right)^{\frac{1}{4}}}-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{4}+8\right) x^{5}-2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+8\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}+8\right) x}{x \left(x^{2}+1\right)^{2}}\right)}{32}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{5}+2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x}{x \left(x^{2}+1\right)^{2}}\right)}{32}-\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{3}}{64}-\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)}{64}+\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{5}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{5}+2 \RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{3}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{3}+8 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{2}-8 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}+8\right) x -8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x -\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x +16 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{64}$&$653$\\ trager&$\frac{\left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{2 x \left(x^{4}+1\right)}+\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{4}-8\right) x^{5}+2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}-8\right) x}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{32}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{5}-2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{32}-\frac{\ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(x^{2}+1\right)}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{3}}{64}-\frac{\ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(x^{2}+1\right)}\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2}}{64}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{5}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{5}-2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}+8 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x +8 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}-8\right) x +8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \sqrt{x^{6}+x^{2}}\, x +16 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{x \left(x^{2}+1\right)^{2}}\right)}{64}$&$655$\\ \hline \end{longtable}"," ",0,"1/2*x/(x^2*(x^4+1))^(1/4)-1/32*RootOf(_Z^4+8)*ln(-(-RootOf(_Z^4+8)^3*(x^6+x^2)^(1/2)*x+RootOf(_Z^4+8)*x^5-2*(x^6+x^2)^(1/4)*RootOf(_Z^4+8)^2*x^2-2*RootOf(_Z^4+8)*x^3+4*(x^6+x^2)^(3/4)+RootOf(_Z^4+8)*x)/x/(x^2+1)^2)+1/32*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln(-(-RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*(x^6+x^2)^(1/2)*x-RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^5+2*(x^6+x^2)^(1/4)*RootOf(_Z^4+8)^2*x^2+2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^3+4*(x^6+x^2)^(3/4)-RootOf(_Z^2+RootOf(_Z^4+8)^2)*x)/x/(x^2+1)^2)-1/64*ln(-(RootOf(_Z^4+8)^2*x^2-2*RootOf(_Z^4+8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(-1+x)/(1+x))*RootOf(_Z^4+8)^3-1/64*ln(-(RootOf(_Z^4+8)^2*x^2-2*RootOf(_Z^4+8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(-1+x)/(1+x))*RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)+1/64*RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln((RootOf(_Z^4+8)^3*x^5-RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*x^5+2*RootOf(_Z^4+8)^3*x^3-2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*x^3+8*(x^6+x^2)^(1/4)*RootOf(_Z^4+8)*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^2-8*(x^6+x^2)^(1/2)*RootOf(_Z^4+8)*x-8*RootOf(_Z^2+RootOf(_Z^4+8)^2)*(x^6+x^2)^(1/2)*x+RootOf(_Z^4+8)^3*x-RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x+16*(x^6+x^2)^(3/4))/(-1+x)^2/(1+x)^2/x)","C"
2361,1,653,145,48.439000," ","int(x^4/(x^6+x^2)^(1/4)/(x^8-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x}{2 \left(x^{2} \left(x^{4}+1\right)\right)^{\frac{1}{4}}}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{5}-2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{32}-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{5}+2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{4}-8\right)+8 \sqrt{x^{6}+x^{2}}\, x +x \RootOf \left(\textit{\_Z}^{4}-8\right)^{2}}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{32}+\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(x^{2}+1\right)}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{3}}{64}+\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(x^{2}+1\right)}\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2}}{64}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{5}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{5}+2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{3}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}+8 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{2}-8 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}-8\right) x -8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x +16 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{x \left(x^{2}+1\right)^{2}}\right)}{64}$&$653$\\ trager&$\frac{\left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{2 x \left(x^{4}+1\right)}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{5}+2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x}{x \left(x^{2}+1\right)^{2}}\right)}{32}+\frac{\RootOf \left(\textit{\_Z}^{4}+8\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{4}+8\right) x^{5}-2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}+8\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}+8\right) x}{x \left(x^{2}+1\right)^{2}}\right)}{32}+\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}+8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{\left(1+x \right) x \left(-1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{3}}{64}+\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}+8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{\left(1+x \right) x \left(-1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)}{64}-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{5}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{5}-2 \RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{3}+8 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{2}+8 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}+8\right) x +8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x +\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x +16 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{64}$&$658$\\ \hline \end{longtable}"," ",0,"1/2*x/(x^2*(x^4+1))^(1/4)+1/32*RootOf(_Z^2+RootOf(_Z^4-8)^2)*ln((RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*(x^6+x^2)^(1/2)*x-RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^5-2*RootOf(_Z^4-8)^2*(x^6+x^2)^(1/4)*x^2-2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*x^3+4*(x^6+x^2)^(3/4)-RootOf(_Z^2+RootOf(_Z^4-8)^2)*x)/(-1+x)^2/(1+x)^2/x)-1/32*RootOf(_Z^4-8)*ln(-(RootOf(_Z^4-8)^2*x^5+2*(x^6+x^2)^(1/4)*RootOf(_Z^4-8)^3*x^2+2*RootOf(_Z^4-8)^2*x^3+4*(x^6+x^2)^(3/4)*RootOf(_Z^4-8)+8*(x^6+x^2)^(1/2)*x+x*RootOf(_Z^4-8)^2)/(-1+x)^2/(1+x)^2/x)+1/64*ln(-(RootOf(_Z^4-8)^2*x^2-2*RootOf(_Z^4-8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(x^2+1))*RootOf(_Z^4-8)^3+1/64*ln(-(RootOf(_Z^4-8)^2*x^2-2*RootOf(_Z^4-8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(x^2+1))*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2-1/64*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*ln(-(-RootOf(_Z^4-8)^3*x^5+RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x^5+2*RootOf(_Z^4-8)^3*x^3-2*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x^3+8*(x^6+x^2)^(1/4)*RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)*x^2-8*(x^6+x^2)^(1/2)*RootOf(_Z^4-8)*x-8*RootOf(_Z^2+RootOf(_Z^4-8)^2)*(x^6+x^2)^(1/2)*x-RootOf(_Z^4-8)^3*x+RootOf(_Z^2+RootOf(_Z^4-8)^2)*RootOf(_Z^4-8)^2*x+16*(x^6+x^2)^(3/4))/x/(x^2+1)^2)","C"
2362,1,1512,139,84.991000," ","int((x^4-1)*(x^6+x^2)^(1/4)/(x^8-x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1512$\\ \hline \end{longtable}"," ",0,"1/2916*RootOf(_Z^8-243)^7*RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^2-RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*ln(-(RootOf(_Z^2-RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)^10*x^5-2*RootOf(_Z^2-RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)^10*x^3+RootOf(_Z^2-RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)^10*x+9*RootOf(_Z^2-RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)^6*x^3+54*(x^6+x^2)^(1/2)*RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^2-RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)^3*x-324*RootOf(_Z^2-RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)^2*x^5+486*RootOf(_Z^2-RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)^2*x^3-486*RootOf(_Z^2+RootOf(_Z^8-243)^2)*(x^6+x^2)^(1/4)*RootOf(_Z^8-243)*x^2-324*RootOf(_Z^2-RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)^2*x+1458*(x^6+x^2)^(3/4))/(RootOf(_Z^8-243)^4*x^4-2*RootOf(_Z^8-243)^4*x^2+RootOf(_Z^8-243)^4-18*x^4+27*x^2-18)/x)+1/12*RootOf(_Z^2-RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*ln(-(RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^2-RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)^9*x^5-2*RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^2-RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)^9*x^3+RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^2-RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)^9*x+9*RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^8-243)^5*RootOf(_Z^2-RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*x^3-324*x^5*RootOf(_Z^2-RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^8-243)+54*(x^6+x^2)^(1/2)*RootOf(_Z^2-RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)^4*x+486*RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^2-RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)*x^3+486*RootOf(_Z^2+RootOf(_Z^8-243)^2)*(x^6+x^2)^(1/4)*RootOf(_Z^8-243)*x^2-324*RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^2-RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)*x+1458*(x^6+x^2)^(3/4))/(RootOf(_Z^8-243)^4*x^4-2*RootOf(_Z^8-243)^4*x^2+RootOf(_Z^8-243)^4-18*x^4+27*x^2-18)/x)-1/12*RootOf(_Z^8-243)*ln(-(-RootOf(_Z^8-243)^11*x^5+2*RootOf(_Z^8-243)^11*x^3-RootOf(_Z^8-243)^11*x+9*RootOf(_Z^8-243)^7*x^3+54*RootOf(_Z^8-243)^5*(x^6+x^2)^(1/2)*x+324*RootOf(_Z^8-243)^3*x^5-486*RootOf(_Z^8-243)^3*x^3+486*(x^6+x^2)^(1/4)*RootOf(_Z^8-243)^2*x^2+324*RootOf(_Z^8-243)^3*x+1458*(x^6+x^2)^(3/4))/(RootOf(_Z^8-243)^4*x^4-2*RootOf(_Z^8-243)^4*x^2+RootOf(_Z^8-243)^4+18*x^4-27*x^2+18)/x)-1/12*RootOf(_Z^2+RootOf(_Z^8-243)^2)*ln(-(RootOf(_Z^8-243)^10*RootOf(_Z^2+RootOf(_Z^8-243)^2)*x^5-2*RootOf(_Z^8-243)^10*RootOf(_Z^2+RootOf(_Z^8-243)^2)*x^3+RootOf(_Z^8-243)^10*RootOf(_Z^2+RootOf(_Z^8-243)^2)*x-9*RootOf(_Z^8-243)^6*RootOf(_Z^2+RootOf(_Z^8-243)^2)*x^3+54*RootOf(_Z^2+RootOf(_Z^8-243)^2)*(x^6+x^2)^(1/2)*RootOf(_Z^8-243)^4*x-324*RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^8-243)^2*x^5+486*RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^8-243)^2*x^3-486*(x^6+x^2)^(1/4)*RootOf(_Z^8-243)^2*x^2-324*RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^8-243)^2*x+1458*(x^6+x^2)^(3/4))/(RootOf(_Z^8-243)^4*x^4-2*RootOf(_Z^8-243)^4*x^2+RootOf(_Z^8-243)^4+18*x^4-27*x^2+18)/x)","C"
2363,1,1496,139,76.987000," ","int((x^4-1)*(x^6+x^2)^(1/4)/(x^8-x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1496$\\ \hline \end{longtable}"," ",0,"-1/12*RootOf(_Z^2+RootOf(_Z^8-243)^2)*ln(-(RootOf(_Z^8-243)^10*RootOf(_Z^2+RootOf(_Z^8-243)^2)*x^5-2*RootOf(_Z^8-243)^10*RootOf(_Z^2+RootOf(_Z^8-243)^2)*x^3+RootOf(_Z^8-243)^10*RootOf(_Z^2+RootOf(_Z^8-243)^2)*x-9*RootOf(_Z^8-243)^6*RootOf(_Z^2+RootOf(_Z^8-243)^2)*x^3+54*RootOf(_Z^2+RootOf(_Z^8-243)^2)*(x^6+x^2)^(1/2)*RootOf(_Z^8-243)^4*x-324*RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^8-243)^2*x^5+486*RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^8-243)^2*x^3-486*(x^6+x^2)^(1/4)*RootOf(_Z^8-243)^2*x^2-324*RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^8-243)^2*x+1458*(x^6+x^2)^(3/4))/(RootOf(_Z^8-243)^4*x^4-2*RootOf(_Z^8-243)^4*x^2+RootOf(_Z^8-243)^4+18*x^4-27*x^2+18)/x)-1/12*RootOf(_Z^2+RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*ln((-RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^2+RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)^9*x^5+2*RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^2+RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)^9*x^3-RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^2+RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)^9*x-9*RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^8-243)^5*RootOf(_Z^2+RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*x^3+324*RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^2+RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)*x^5+54*(x^6+x^2)^(1/2)*RootOf(_Z^8-243)^4*RootOf(_Z^2+RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*x-486*RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^2+RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)*x^3+486*RootOf(_Z^2+RootOf(_Z^8-243)^2)*(x^6+x^2)^(1/4)*RootOf(_Z^8-243)*x^2+324*RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^2+RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)*x-1458*(x^6+x^2)^(3/4))/(RootOf(_Z^8-243)^4*x^4-2*RootOf(_Z^8-243)^4*x^2+RootOf(_Z^8-243)^4-18*x^4+27*x^2-18)/x)-1/2916*RootOf(_Z^8-243)^7*RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^2+RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*ln((-RootOf(_Z^2+RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)^10*x^5+2*RootOf(_Z^2+RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)^10*x^3-RootOf(_Z^2+RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)^10*x-9*RootOf(_Z^2+RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)^6*x^3+54*(x^6+x^2)^(1/2)*RootOf(_Z^2+RootOf(_Z^8-243)^2)*RootOf(_Z^2+RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)^3*x+324*RootOf(_Z^2+RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)^2*x^5-486*RootOf(_Z^2+RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)^2*x^3-486*RootOf(_Z^2+RootOf(_Z^8-243)^2)*(x^6+x^2)^(1/4)*RootOf(_Z^8-243)*x^2+324*RootOf(_Z^2+RootOf(_Z^8-243)*RootOf(_Z^2+RootOf(_Z^8-243)^2))*RootOf(_Z^8-243)^2*x-1458*(x^6+x^2)^(3/4))/(RootOf(_Z^8-243)^4*x^4-2*RootOf(_Z^8-243)^4*x^2+RootOf(_Z^8-243)^4-18*x^4+27*x^2-18)/x)-1/12*RootOf(_Z^8-243)*ln(-(-RootOf(_Z^8-243)^11*x^5+2*RootOf(_Z^8-243)^11*x^3-RootOf(_Z^8-243)^11*x+9*RootOf(_Z^8-243)^7*x^3+54*RootOf(_Z^8-243)^5*(x^6+x^2)^(1/2)*x+324*RootOf(_Z^8-243)^3*x^5-486*RootOf(_Z^8-243)^3*x^3+486*(x^6+x^2)^(1/4)*RootOf(_Z^8-243)^2*x^2+324*RootOf(_Z^8-243)^3*x+1458*(x^6+x^2)^(3/4))/(RootOf(_Z^8-243)^4*x^4-2*RootOf(_Z^8-243)^4*x^2+RootOf(_Z^8-243)^4+18*x^4-27*x^2+18)/x)","C"
2364,1,650,145,41.748000," ","int((x^8-x^4+1)/(x^6+x^2)^(1/4)/(x^8-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{3 x}{2 \left(x^{2} \left(x^{4}+1\right)\right)^{\frac{1}{4}}}-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{4}+8\right) x^{5}-2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+8\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}+8\right) x}{x \left(x^{2}+1\right)^{2}}\right)}{32}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{5}+2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x}{x \left(x^{2}+1\right)^{2}}\right)}{32}+\frac{\ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}+8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{\left(1+x \right) x \left(-1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{3}}{64}+\frac{\ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}+8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{\left(1+x \right) x \left(-1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)}{64}-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{5}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{5}-2 \RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{3}+8 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{2}+8 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}+8\right) x +8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x +\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x +16 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{64}$&$650$\\ trager&$-\frac{3 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{2 x \left(x^{4}+1\right)}-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{4}+8\right) x^{5}-2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+8\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}+8\right) x}{x \left(x^{2}+1\right)^{2}}\right)}{32}-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{5}+2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x}{x \left(x^{2}+1\right)^{2}}\right)}{32}+\frac{\ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}+8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{\left(1+x \right) x \left(-1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{3}}{64}+\frac{\ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}+8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{\left(1+x \right) x \left(-1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)}{64}-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{5}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{5}-2 \RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{3}+8 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{2}+8 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}+8\right) x +8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x +\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x +16 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{64}$&$654$\\ \hline \end{longtable}"," ",0,"-3/2*x/(x^2*(x^4+1))^(1/4)-1/32*RootOf(_Z^4+8)*ln((-RootOf(_Z^4+8)^3*(x^6+x^2)^(1/2)*x+RootOf(_Z^4+8)*x^5-2*(x^6+x^2)^(1/4)*RootOf(_Z^4+8)^2*x^2-2*RootOf(_Z^4+8)*x^3+4*(x^6+x^2)^(3/4)+RootOf(_Z^4+8)*x)/x/(x^2+1)^2)+1/32*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln(-(-RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*(x^6+x^2)^(1/2)*x-RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^5+2*(x^6+x^2)^(1/4)*RootOf(_Z^4+8)^2*x^2+2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^3+4*(x^6+x^2)^(3/4)-RootOf(_Z^2+RootOf(_Z^4+8)^2)*x)/x/(x^2+1)^2)+1/64*ln((RootOf(_Z^4+8)^2*x^2+2*RootOf(_Z^4+8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/(1+x)/x/(-1+x))*RootOf(_Z^4+8)^3+1/64*ln((RootOf(_Z^4+8)^2*x^2+2*RootOf(_Z^4+8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/(1+x)/x/(-1+x))*RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)-1/64*RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln((-RootOf(_Z^4+8)^3*x^5+RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*x^5-2*RootOf(_Z^4+8)^3*x^3+2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*x^3+8*(x^6+x^2)^(1/4)*RootOf(_Z^4+8)*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^2+8*(x^6+x^2)^(1/2)*RootOf(_Z^4+8)*x+8*RootOf(_Z^2+RootOf(_Z^4+8)^2)*(x^6+x^2)^(1/2)*x-RootOf(_Z^4+8)^3*x+RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x+16*(x^6+x^2)^(3/4))/(-1+x)^2/(1+x)^2/x)","C"
2365,1,653,145,45.960000," ","int((x^8-x^4+1)/(x^6+x^2)^(1/4)/(x^8-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{3 x}{2 \left(x^{2} \left(x^{4}+1\right)\right)^{\frac{1}{4}}}-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{4}+8\right) x^{5}-2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+8\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}+\RootOf \left(\textit{\_Z}^{4}+8\right) x}{x \left(x^{2}+1\right)^{2}}\right)}{32}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{5}+2 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x}{x \left(x^{2}+1\right)^{2}}\right)}{32}-\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{3}}{64}-\frac{\ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}+8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(-1+x \right) \left(1+x \right)}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right)}{64}+\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{5}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{5}+2 \RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x^{3}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+8\right)^{2} x^{3}+8 \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+8\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x^{2}-8 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}+8\right) x -8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{4}+8\right)^{3} x -\RootOf \left(\textit{\_Z}^{4}+8\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+8\right)^{2}\right) x +16 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{64}$&$653$\\ trager&$-\frac{3 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{2 x \left(x^{4}+1\right)}+\frac{\RootOf \left(\textit{\_Z}^{4}-8\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{4}-8\right) x^{5}+2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x^{2}-2 \RootOf \left(\textit{\_Z}^{4}-8\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}-8\right) x}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{32}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \sqrt{x^{6}+x^{2}}\, x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{5}-2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{3}+4 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x}{\left(-1+x \right)^{2} \left(1+x \right)^{2} x}\right)}{32}-\frac{\ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(x^{2}+1\right)}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{3}}{64}-\frac{\ln \left(\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{2}+2 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} x +2 \sqrt{x^{6}+x^{2}}}{x \left(x^{2}+1\right)}\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2}}{64}+\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{5}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{5}-2 \RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x^{3}+2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x^{3}+8 \RootOf \left(\textit{\_Z}^{4}-8\right) \left(x^{6}+x^{2}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) x^{2}+8 \sqrt{x^{6}+x^{2}}\, \RootOf \left(\textit{\_Z}^{4}-8\right) x +8 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \sqrt{x^{6}+x^{2}}\, x +\RootOf \left(\textit{\_Z}^{4}-8\right)^{3} x -\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-8\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-8\right)^{2} x +16 \left(x^{6}+x^{2}\right)^{\frac{3}{4}}}{x \left(x^{2}+1\right)^{2}}\right)}{64}$&$655$\\ \hline \end{longtable}"," ",0,"-3/2*x/(x^2*(x^4+1))^(1/4)-1/32*RootOf(_Z^4+8)*ln(-(-RootOf(_Z^4+8)^3*(x^6+x^2)^(1/2)*x+RootOf(_Z^4+8)*x^5-2*(x^6+x^2)^(1/4)*RootOf(_Z^4+8)^2*x^2-2*RootOf(_Z^4+8)*x^3+4*(x^6+x^2)^(3/4)+RootOf(_Z^4+8)*x)/x/(x^2+1)^2)+1/32*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln(-(-RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*(x^6+x^2)^(1/2)*x-RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^5+2*(x^6+x^2)^(1/4)*RootOf(_Z^4+8)^2*x^2+2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^3+4*(x^6+x^2)^(3/4)-RootOf(_Z^2+RootOf(_Z^4+8)^2)*x)/x/(x^2+1)^2)-1/64*ln(-(RootOf(_Z^4+8)^2*x^2-2*RootOf(_Z^4+8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(-1+x)/(1+x))*RootOf(_Z^4+8)^3-1/64*ln(-(RootOf(_Z^4+8)^2*x^2-2*RootOf(_Z^4+8)*(x^6+x^2)^(1/4)*x+2*(x^6+x^2)^(1/2))/x/(-1+x)/(1+x))*RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)+1/64*RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln((RootOf(_Z^4+8)^3*x^5-RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*x^5+2*RootOf(_Z^4+8)^3*x^3-2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*x^3+8*(x^6+x^2)^(1/4)*RootOf(_Z^4+8)*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^2-8*(x^6+x^2)^(1/2)*RootOf(_Z^4+8)*x-8*RootOf(_Z^2+RootOf(_Z^4+8)^2)*(x^6+x^2)^(1/2)*x+RootOf(_Z^4+8)^3*x-RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x+16*(x^6+x^2)^(3/4))/(-1+x)^2/(1+x)^2/x)","C"
2366,0,0,148,0.063000," ","int(1/(a*x-b)/(x^4-x^3)^(1/4),x)","\[\int \frac{1}{\left(a x -b \right) \left(x^{4}-x^{3}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(a*x-b)/(x^4-x^3)^(1/4),x)","F"
2367,1,1121,155,0.285000," ","int((x^2-x)/((1-x)*x*(-k^2*x+1))^(1/2)/(k^2*x^2-2*x+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{4} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{2}}-\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\sqrt{-k^{2}+1}\, \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\sqrt{-k^{2}+1}\, \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{2}}-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{-1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{-1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{2}}+\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{-1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\sqrt{-k^{2}+1}\, \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{-1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\sqrt{-k^{2}+1}\, \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{2}}}{k^{2}}$&$1121$\\ elliptic&$-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{4} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{2}}+\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{4}}-\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\sqrt{-k^{2}+1}\, \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{2}}+\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\sqrt{-k^{2}+1}\, \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{4}}-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{-1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{2}}+\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{-1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{4}}+\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{-1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\sqrt{-k^{2}+1}\, \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{2}}-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{-1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\sqrt{-k^{2}+1}\, \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{4}}$&$1132$\\ \hline \end{longtable}"," ",0,"-2/k^4*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticF((-(x-1/k^2)*k^2)^(1/2),(1/k^2/(1/k^2-1))^(1/2))+1/k^2*(-2/(-k^2+1)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-(1+(-k^2+1)^(1/2))/k^2),(1/k^2/(1/k^2-1))^(1/2))+2/(-k^2+1)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-(1+(-k^2+1)^(1/2))/k^2),(1/k^2/(1/k^2-1))^(1/2))/k^2-1/(-k^2+1)^(1/2)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-(1+(-k^2+1)^(1/2))/k^2),(1/k^2/(1/k^2-1))^(1/2))+2/(-k^2+1)^(1/2)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-(1+(-k^2+1)^(1/2))/k^2),(1/k^2/(1/k^2-1))^(1/2))/k^2-2/(-k^2+1)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+(-1+(-k^2+1)^(1/2))/k^2),(1/k^2/(1/k^2-1))^(1/2))+2/(-k^2+1)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+(-1+(-k^2+1)^(1/2))/k^2),(1/k^2/(1/k^2-1))^(1/2))/k^2+1/(-k^2+1)^(1/2)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+(-1+(-k^2+1)^(1/2))/k^2),(1/k^2/(1/k^2-1))^(1/2))-2/(-k^2+1)^(1/2)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+(-1+(-k^2+1)^(1/2))/k^2),(1/k^2/(1/k^2-1))^(1/2))/k^2)","C"
2368,0,0,124,0.057000," ","int((a^3*x^2-b)/(a^3*x^2+b)/(a^3*x^3-b*x^2)^(1/3),x)","\[\int \frac{a^{3} x^{2}-b}{\left(a^{3} x^{2}+b \right) \left(a^{3} x^{3}-b \,x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a^3*x^2-b)/(a^3*x^2+b)/(a^3*x^3-b*x^2)^(1/3),x)","F"
2369,0,0,124,0.002000," ","int((a^3*x^2-b)/(a^3*x^2+b)/(a^3*x^3-b*x^2)^(1/3),x)","\[\int \frac{a^{3} x^{2}-b}{\left(a^{3} x^{2}+b \right) \left(a^{3} x^{3}-b \,x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a^3*x^2-b)/(a^3*x^2+b)/(a^3*x^3-b*x^2)^(1/3),x)","F"
2370,1,4541,165,0.233000," ","int((x^2+1)/(x^2-1)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$4541$\\ elliptic&$\text{Expression too large to display}$&$90178$\\ \hline \end{longtable}"," ",0,"2*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))^2*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2)*EllipticF(((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2),((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2))-2*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))^2*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)+1)*(EllipticF(((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2),((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2))+(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1)+1)*EllipticPi(((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2),(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)+1)*(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1)+1)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)),((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)))+2*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))^2*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-1)*(EllipticF(((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2),((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2))+(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1)-1)*EllipticPi(((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2),(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-1)*(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1)-1)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)),((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)))","C"
2371,1,6392,23,168.770000," ","int(x^4*(x^4-x^2)^(1/4)/(x^8+x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$6392$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2372,1,6395,23,159.802000," ","int(x^4*(x^4-x^2)^(1/4)/(x^8+x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$6395$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2373,1,1362,149,0.634000," ","int((p*x^3-2*q)*(p*x^3+q)^(1/2)/(c*x^4+b*x^2*(p*x^3+q)+a*(p*x^3+q)^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}}{-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{p \left(-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right)}}\right)}{3 a p \sqrt{p \,x^{3}+q}}-\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,p^{2} \textit{\_Z}^{6}+b p \,\textit{\_Z}^{5}+2 a q p \,\textit{\_Z}^{3}+c \,\textit{\_Z}^{4}+b q \,\textit{\_Z}^{2}+a \,q^{2}\right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{5} b p +3 \underline{\hspace{1.25 ex}}\alpha^{3} a p q +\underline{\hspace{1.25 ex}}\alpha^{4} c +\underline{\hspace{1.25 ex}}\alpha^{2} b q +3 a \,q^{2}\right) \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i p \left(2 x +\frac{-i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}+\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{p \left(x -\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{-3 \left(-q \,p^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i p \left(2 x +\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}+\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{2 \left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \left(2 q \,p^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{4} a \,p^{2}+\underline{\hspace{1.25 ex}}\alpha^{3} b p +\underline{\hspace{1.25 ex}}\alpha  a p q +\underline{\hspace{1.25 ex}}\alpha^{2} c \right)+i \left(-q \,p^{2}\right)^{\frac{1}{3}} p^{3} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} a q +i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, a \,q^{2} p^{2}+\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{5} a \,p^{3}+i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} p c +i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  q p c -i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, q c +\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{4} b \,p^{2}+i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} b q \,p^{2}-\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{3} a \,p^{3} q +\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a \,p^{2} q +i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a q \,p^{2}+\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{3} c p +i \left(-q \,p^{2}\right)^{\frac{2}{3}} p^{3} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5} a -\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} b \,p^{2} q +i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{4} b \,p^{2}-\left(-q \,p^{2}\right)^{\frac{1}{3}} a \,p^{2} q^{2}-\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  c p q -\left(-q \,p^{2}\right)^{\frac{2}{3}} c q \right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, a p q -2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{4} a \,p^{3}+i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{4} b \,p^{3}+i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a \,p^{3} q -3 p^{4} \underline{\hspace{1.25 ex}}\alpha^{5} a +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5} a \,p^{4}+i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} b p +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} c \,p^{2}+3 \left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{3} a \,p^{2}-2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} b \,p^{2}+i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  c -3 b \,p^{3} \underline{\hspace{1.25 ex}}\alpha^{4}+i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} a \,p^{2}-i \sqrt{3}\, c p q -3 p^{3} \underline{\hspace{1.25 ex}}\alpha^{2} a q -2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a \,p^{2} q +3 \left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} b p -3 \underline{\hspace{1.25 ex}}\alpha^{3} p^{2} c +3 \left(-q \,p^{2}\right)^{\frac{2}{3}} a q p -2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} c p +3 \left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  c +3 q c p}{2 p q c}, \sqrt{\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{p \left(-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right)}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  \left(6 \underline{\hspace{1.25 ex}}\alpha^{4} a \,p^{2}+5 \underline{\hspace{1.25 ex}}\alpha^{3} b p +6 \underline{\hspace{1.25 ex}}\alpha  a p q +4 \underline{\hspace{1.25 ex}}\alpha^{2} c +2 b q \right) \sqrt{p \,x^{3}+q}}\right)}{a \,p^{2} q^{2} c}$&$1362$\\ elliptic&$-\frac{2 i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}}{-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{p \left(-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right)}}\right)}{3 a p \sqrt{p \,x^{3}+q}}-\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,p^{2} \textit{\_Z}^{6}+b p \,\textit{\_Z}^{5}+2 a q p \,\textit{\_Z}^{3}+c \,\textit{\_Z}^{4}+b q \,\textit{\_Z}^{2}+a \,q^{2}\right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{5} b p +3 \underline{\hspace{1.25 ex}}\alpha^{3} a p q +\underline{\hspace{1.25 ex}}\alpha^{4} c +\underline{\hspace{1.25 ex}}\alpha^{2} b q +3 a \,q^{2}\right) \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i p \left(2 x +\frac{-i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}+\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{p \left(x -\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{-3 \left(-q \,p^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i p \left(2 x +\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}+\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{2 \left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \left(2 q \,p^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{4} a \,p^{2}+\underline{\hspace{1.25 ex}}\alpha^{3} b p +\underline{\hspace{1.25 ex}}\alpha  a p q +\underline{\hspace{1.25 ex}}\alpha^{2} c \right)+i \left(-q \,p^{2}\right)^{\frac{1}{3}} p^{3} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} a q +i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, a \,q^{2} p^{2}+\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{5} a \,p^{3}+i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} p c +i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  q p c -i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, q c +\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{4} b \,p^{2}+i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} b q \,p^{2}-\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{3} a \,p^{3} q +\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a \,p^{2} q +i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a q \,p^{2}+\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{3} c p +i \left(-q \,p^{2}\right)^{\frac{2}{3}} p^{3} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5} a -\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} b \,p^{2} q +i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{4} b \,p^{2}-\left(-q \,p^{2}\right)^{\frac{1}{3}} a \,p^{2} q^{2}-\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  c p q -\left(-q \,p^{2}\right)^{\frac{2}{3}} c q \right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, a p q -2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{4} a \,p^{3}+i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{4} b \,p^{3}+i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a \,p^{3} q -3 p^{4} \underline{\hspace{1.25 ex}}\alpha^{5} a +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5} a \,p^{4}+i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} b p +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} c \,p^{2}+3 \left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{3} a \,p^{2}-2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} b \,p^{2}+i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  c -3 b \,p^{3} \underline{\hspace{1.25 ex}}\alpha^{4}+i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} a \,p^{2}-i \sqrt{3}\, c p q -3 p^{3} \underline{\hspace{1.25 ex}}\alpha^{2} a q -2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a \,p^{2} q +3 \left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} b p -3 \underline{\hspace{1.25 ex}}\alpha^{3} p^{2} c +3 \left(-q \,p^{2}\right)^{\frac{2}{3}} a q p -2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} c p +3 \left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  c +3 q c p}{2 p q c}, \sqrt{\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{p \left(-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right)}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  \left(6 \underline{\hspace{1.25 ex}}\alpha^{4} a \,p^{2}+5 \underline{\hspace{1.25 ex}}\alpha^{3} b p +6 \underline{\hspace{1.25 ex}}\alpha  a p q +4 \underline{\hspace{1.25 ex}}\alpha^{2} c +2 b q \right) \sqrt{p \,x^{3}+q}}\right)}{a \,p^{2} q^{2} c}$&$1362$\\ \hline \end{longtable}"," ",0,"-2/3*I/a*3^(1/2)/p*(-q*p^2)^(1/3)*(I*(x+1/2/p*(-q*p^2)^(1/3)-1/2*I*3^(1/2)/p*(-q*p^2)^(1/3))*3^(1/2)*p/(-q*p^2)^(1/3))^(1/2)*((x-1/p*(-q*p^2)^(1/3))/(-3/2/p*(-q*p^2)^(1/3)+1/2*I*3^(1/2)/p*(-q*p^2)^(1/3)))^(1/2)*(-I*(x+1/2/p*(-q*p^2)^(1/3)+1/2*I*3^(1/2)/p*(-q*p^2)^(1/3))*3^(1/2)*p/(-q*p^2)^(1/3))^(1/2)/(p*x^3+q)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2/p*(-q*p^2)^(1/3)-1/2*I*3^(1/2)/p*(-q*p^2)^(1/3))*3^(1/2)*p/(-q*p^2)^(1/3))^(1/2),(I*3^(1/2)/p*(-q*p^2)^(1/3)/(-3/2/p*(-q*p^2)^(1/3)+1/2*I*3^(1/2)/p*(-q*p^2)^(1/3)))^(1/2))-I/a/p^2/q^2/c*2^(1/2)*sum((_alpha^5*b*p+3*_alpha^3*a*p*q+_alpha^4*c+_alpha^2*b*q+3*a*q^2)/_alpha/(6*_alpha^4*a*p^2+5*_alpha^3*b*p+6*_alpha*a*p*q+4*_alpha^2*c+2*b*q)*(-q*p^2)^(1/3)*(1/2*I*p*(2*x+1/p*(-I*3^(1/2)*(-q*p^2)^(1/3)+(-q*p^2)^(1/3)))/(-q*p^2)^(1/3))^(1/2)*(p*(x-1/p*(-q*p^2)^(1/3))/(-3*(-q*p^2)^(1/3)+I*3^(1/2)*(-q*p^2)^(1/3)))^(1/2)*(-1/2*I*p*(2*x+1/p*(I*3^(1/2)*(-q*p^2)^(1/3)+(-q*p^2)^(1/3)))/(-q*p^2)^(1/3))^(1/2)/(p*x^3+q)^(1/2)*(2*q*p^2*(_alpha^4*a*p^2+_alpha^3*b*p+_alpha*a*p*q+_alpha^2*c)+I*(-q*p^2)^(1/3)*p^3*3^(1/2)*_alpha^3*a*q+I*(-q*p^2)^(1/3)*3^(1/2)*a*q^2*p^2+(-q*p^2)^(2/3)*_alpha^5*a*p^3+I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^3*p*c+I*(-q*p^2)^(1/3)*3^(1/2)*_alpha*q*p*c-I*(-q*p^2)^(2/3)*3^(1/2)*q*c+(-q*p^2)^(2/3)*_alpha^4*b*p^2+I*(-q*p^2)^(1/3)*3^(1/2)*_alpha^2*b*q*p^2-(-q*p^2)^(1/3)*_alpha^3*a*p^3*q+(-q*p^2)^(2/3)*_alpha^2*a*p^2*q+I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^2*a*q*p^2+(-q*p^2)^(2/3)*_alpha^3*c*p+I*(-q*p^2)^(2/3)*p^3*3^(1/2)*_alpha^5*a-(-q*p^2)^(1/3)*_alpha^2*b*p^2*q+I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^4*b*p^2-(-q*p^2)^(1/3)*a*p^2*q^2-(-q*p^2)^(1/3)*_alpha*c*p*q-(-q*p^2)^(2/3)*c*q)*EllipticPi(1/3*3^(1/2)*(I*(x+1/2/p*(-q*p^2)^(1/3)-1/2*I*3^(1/2)/p*(-q*p^2)^(1/3))*3^(1/2)*p/(-q*p^2)^(1/3))^(1/2),1/2/p/q*(I*(-q*p^2)^(2/3)*3^(1/2)*a*p*q-2*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha^4*a*p^3+I*3^(1/2)*_alpha^4*b*p^3+I*3^(1/2)*_alpha^2*a*p^3*q-3*p^4*_alpha^5*a+I*3^(1/2)*_alpha^5*a*p^4+I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^2*b*p+I*3^(1/2)*_alpha^3*c*p^2+3*(-q*p^2)^(2/3)*_alpha^3*a*p^2-2*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha^3*b*p^2+I*(-q*p^2)^(2/3)*3^(1/2)*_alpha*c-3*b*p^3*_alpha^4+I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^3*a*p^2-I*3^(1/2)*c*p*q-3*p^3*_alpha^2*a*q-2*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha*a*p^2*q+3*(-q*p^2)^(2/3)*_alpha^2*b*p-3*_alpha^3*p^2*c+3*(-q*p^2)^(2/3)*a*q*p-2*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha^2*c*p+3*(-q*p^2)^(2/3)*_alpha*c+3*q*c*p)/c,(I*3^(1/2)/p*(-q*p^2)^(1/3)/(-3/2/p*(-q*p^2)^(1/3)+1/2*I*3^(1/2)/p*(-q*p^2)^(1/3)))^(1/2)),_alpha=RootOf(_Z^6*a*p^2+_Z^5*b*p+2*_Z^3*a*p*q+_Z^4*c+_Z^2*b*q+a*q^2))","C"
2374,0,0,162,0.075000," ","int((x^4-1)^2/(x^4+1)^2/(x^2+(x^4+1)^(1/2))^(1/2),x)","\[\int \frac{\left(x^{4}-1\right)^{2}}{\left(x^{4}+1\right)^{2} \sqrt{x^{2}+\sqrt{x^{4}+1}}}\, dx\]"," ",0,"int((x^4-1)^2/(x^4+1)^2/(x^2+(x^4+1)^(1/2))^(1/2),x)","F"
2375,0,0,149,0.038000," ","int((x^2+(x^4+1)^(1/2))^(1/2)/(x^2+1)^2/(x^4+1)^(1/2),x)","\[\int \frac{\sqrt{x^{2}+\sqrt{x^{4}+1}}}{\left(x^{2}+1\right)^{2} \sqrt{x^{4}+1}}\, dx\]"," ",0,"int((x^2+(x^4+1)^(1/2))^(1/2)/(x^2+1)^2/(x^4+1)^(1/2),x)","F"
2376,0,0,149,10.168000," ","int((p*x^5+q)^(1/2)*(3*p*x^5-2*q)/(c*x^4+b*x^2*(p*x^5+q)+a*(p*x^5+q)^2),x)","\[\int \frac{\sqrt{p \,x^{5}+q}\, \left(3 p \,x^{5}-2 q \right)}{c \,x^{4}+b \,x^{2} \left(p \,x^{5}+q \right)+a \left(p \,x^{5}+q \right)^{2}}\, dx\]"," ",0,"int((p*x^5+q)^(1/2)*(3*p*x^5-2*q)/(c*x^4+b*x^2*(p*x^5+q)+a*(p*x^5+q)^2),x)","F"
2377,0,0,92,180.000000," ","int(1/x/(a*x+(a^2*x^2-b)^(1/2))^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/2))^(1/2),x)","\[\int \frac{1}{x \sqrt{a x +\sqrt{a^{2} x^{2}-b}}\, \sqrt{c +\sqrt{a x +\sqrt{a^{2} x^{2}-b}}}}\, dx\]"," ",0,"int(1/x/(a*x+(a^2*x^2-b)^(1/2))^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/2))^(1/2),x)","F"
2378,1,622,145,6.517000," ","int(1/(x^2+1)^(1/3)/(x^2+9),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-144 \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{3} \ln \left(-\frac{-497664 \left(x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{5} x +995328 \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{5} x +6912 \left(x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{3} x -20736 \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{3} x +144 \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2} x^{2}-864 \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2} \left(x^{2}+1\right)^{\frac{1}{3}}+6 \left(x^{2}+1\right)^{\frac{2}{3}}-432 \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2}+96 \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right) x -x^{2}+3}{x^{2}+9}\right)+\RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right) \ln \left(-\frac{82944 \left(x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{5} x -165888 \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{5} x -1728 \left(x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{3} x +2304 \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{3} x -24 \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2} x^{2}+144 \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2} \left(x^{2}+1\right)^{\frac{1}{3}}+8 \left(x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right) x +\left(x^{2}+1\right)^{\frac{2}{3}}+72 \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2}-\left(x^{2}+1\right)^{\frac{1}{3}}}{x^{2}+9}\right)+\RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right) \ln \left(-\frac{-497664 \left(x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{5} x +995328 \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{5} x +6912 \left(x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{3} x -20736 \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{3} x +144 \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2} x^{2}-864 \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2} \left(x^{2}+1\right)^{\frac{1}{3}}+6 \left(x^{2}+1\right)^{\frac{2}{3}}-432 \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2}+96 \RootOf \left(20736 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right) x -x^{2}+3}{x^{2}+9}\right)$&$622$\\ \hline \end{longtable}"," ",0,"-144*RootOf(20736*_Z^4-144*_Z^2+1)^3*ln(-(-497664*(x^2+1)^(1/3)*RootOf(20736*_Z^4-144*_Z^2+1)^5*x+995328*RootOf(20736*_Z^4-144*_Z^2+1)^5*x+6912*(x^2+1)^(1/3)*RootOf(20736*_Z^4-144*_Z^2+1)^3*x-20736*RootOf(20736*_Z^4-144*_Z^2+1)^3*x+144*RootOf(20736*_Z^4-144*_Z^2+1)^2*x^2-864*RootOf(20736*_Z^4-144*_Z^2+1)^2*(x^2+1)^(1/3)+6*(x^2+1)^(2/3)-432*RootOf(20736*_Z^4-144*_Z^2+1)^2+96*RootOf(20736*_Z^4-144*_Z^2+1)*x-x^2+3)/(x^2+9))+RootOf(20736*_Z^4-144*_Z^2+1)*ln(-(82944*(x^2+1)^(1/3)*RootOf(20736*_Z^4-144*_Z^2+1)^5*x-165888*RootOf(20736*_Z^4-144*_Z^2+1)^5*x-1728*(x^2+1)^(1/3)*RootOf(20736*_Z^4-144*_Z^2+1)^3*x+2304*RootOf(20736*_Z^4-144*_Z^2+1)^3*x-24*RootOf(20736*_Z^4-144*_Z^2+1)^2*x^2+144*RootOf(20736*_Z^4-144*_Z^2+1)^2*(x^2+1)^(1/3)+8*(x^2+1)^(1/3)*RootOf(20736*_Z^4-144*_Z^2+1)*x+(x^2+1)^(2/3)+72*RootOf(20736*_Z^4-144*_Z^2+1)^2-(x^2+1)^(1/3))/(x^2+9))+RootOf(20736*_Z^4-144*_Z^2+1)*ln(-(-497664*(x^2+1)^(1/3)*RootOf(20736*_Z^4-144*_Z^2+1)^5*x+995328*RootOf(20736*_Z^4-144*_Z^2+1)^5*x+6912*(x^2+1)^(1/3)*RootOf(20736*_Z^4-144*_Z^2+1)^3*x-20736*RootOf(20736*_Z^4-144*_Z^2+1)^3*x+144*RootOf(20736*_Z^4-144*_Z^2+1)^2*x^2-864*RootOf(20736*_Z^4-144*_Z^2+1)^2*(x^2+1)^(1/3)+6*(x^2+1)^(2/3)-432*RootOf(20736*_Z^4-144*_Z^2+1)^2+96*RootOf(20736*_Z^4-144*_Z^2+1)*x-x^2+3)/(x^2+9))","C"
2379,0,0,124,0.055000," ","int((a^3*x^2+b)/(a^3*x^2-b)/(a^3*x^3-b*x^2)^(1/3),x)","\[\int \frac{a^{3} x^{2}+b}{\left(a^{3} x^{2}-b \right) \left(a^{3} x^{3}-b \,x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a^3*x^2+b)/(a^3*x^2-b)/(a^3*x^3-b*x^2)^(1/3),x)","F"
2380,0,0,124,0.001000," ","int((a^3*x^2+b)/(a^3*x^2-b)/(a^3*x^3-b*x^2)^(1/3),x)","\[\int \frac{a^{3} x^{2}+b}{\left(a^{3} x^{2}-b \right) \left(a^{3} x^{3}-b \,x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a^3*x^2+b)/(a^3*x^2-b)/(a^3*x^3-b*x^2)^(1/3),x)","F"
2381,0,0,158,0.027000," ","int((-3-2*(k^2+1)*x+(k^2+1)*x^2+4*k^2*x^3+k^2*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(-1+d-(2+d)*x-(d*k^2+1)*x^2+d*k^2*x^3),x)","\[\int \frac{-3-2 \left(k^{2}+1\right) x +\left(k^{2}+1\right) x^{2}+4 k^{2} x^{3}+k^{2} x^{4}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{2}{3}} \left(-1+d -\left(2+d \right) x -\left(d \,k^{2}+1\right) x^{2}+d \,k^{2} x^{3}\right)}\, dx\]"," ",0,"int((-3-2*(k^2+1)*x+(k^2+1)*x^2+4*k^2*x^3+k^2*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(-1+d-(2+d)*x-(d*k^2+1)*x^2+d*k^2*x^3),x)","F"
2382,1,742,148,29.585000," ","int((x^5+x^3)^(1/4)*(x^8+x^4+1)/x^4/(x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{4 \left(x^{4}+2 x^{2}+1\right) \left(x^{5}+x^{3}\right)^{\frac{1}{4}}}{9 x^{3}}+\frac{3 \RootOf \left(\textit{\_Z}^{4}+2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+2\right)^{3} x^{4}-2 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} x^{3}+4 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{3} x^{2}-4 \sqrt{x^{5}+x^{3}}\, \RootOf \left(\textit{\_Z}^{4}+2\right) x +4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}}{\left(1+x \right)^{2} x^{2}}\right)}{8}-\frac{3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{3}-4 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{2}+4 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \sqrt{x^{5}+x^{3}}\, x +4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}}{\left(1+x \right)^{2} x^{2}}\right)}{8}-\frac{3 \ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} \sqrt{x^{5}+x^{3}}\, x -4 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{2}-\RootOf \left(\textit{\_Z}^{4}+2\right) x^{4}+2 \RootOf \left(\textit{\_Z}^{4}+2\right) x^{3}+4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}+2\right) x^{2}}{x^{2} \left(-1+x \right)^{2}}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{3}}{16}-\frac{3 \ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} \sqrt{x^{5}+x^{3}}\, x -4 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} x^{2}-\RootOf \left(\textit{\_Z}^{4}+2\right) x^{4}+2 \RootOf \left(\textit{\_Z}^{4}+2\right) x^{3}+4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{4}+2\right) x^{2}}{x^{2} \left(-1+x \right)^{2}}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right)}{16}+\frac{3 \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \ln \left(\frac{-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+2\right)^{2} \sqrt{x^{5}+x^{3}}\, x +2 \RootOf \left(\textit{\_Z}^{4}+2\right)^{3} \sqrt{x^{5}+x^{3}}\, x +4 \left(x^{5}+x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+2\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{4}-\RootOf \left(\textit{\_Z}^{4}+2\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{3}-2 \RootOf \left(\textit{\_Z}^{4}+2\right) x^{3}+4 \left(x^{5}+x^{3}\right)^{\frac{3}{4}}-\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+2\right)^{2}\right) x^{2}-\RootOf \left(\textit{\_Z}^{4}+2\right) x^{2}}{x^{2} \left(-1+x \right)^{2}}\right)}{8}$&$742$\\ risch&$\text{Expression too large to display}$&$1784$\\ \hline \end{longtable}"," ",0,"4/9*(x^4+2*x^2+1)*(x^5+x^3)^(1/4)/x^3+3/8*RootOf(_Z^4+2)*ln(-(RootOf(_Z^4+2)^3*x^4-2*RootOf(_Z^4+2)^3*x^3+4*(x^5+x^3)^(1/4)*RootOf(_Z^4+2)^2*x^2+RootOf(_Z^4+2)^3*x^2-4*(x^5+x^3)^(1/2)*RootOf(_Z^4+2)*x+4*(x^5+x^3)^(3/4))/(1+x)^2/x^2)-3/8*RootOf(_Z^2+RootOf(_Z^4+2)^2)*ln(-(RootOf(_Z^4+2)^2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*x^4-2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*RootOf(_Z^4+2)^2*x^3-4*(x^5+x^3)^(1/4)*RootOf(_Z^4+2)^2*x^2+RootOf(_Z^4+2)^2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*x^2+4*RootOf(_Z^2+RootOf(_Z^4+2)^2)*(x^5+x^3)^(1/2)*x+4*(x^5+x^3)^(3/4))/(1+x)^2/x^2)-3/16*ln(-(4*RootOf(_Z^4+2)^3*(x^5+x^3)^(1/2)*x-4*(x^5+x^3)^(1/4)*RootOf(_Z^4+2)^2*x^2-RootOf(_Z^4+2)*x^4+2*RootOf(_Z^4+2)*x^3+4*(x^5+x^3)^(3/4)-RootOf(_Z^4+2)*x^2)/x^2/(-1+x)^2)*RootOf(_Z^4+2)^3-3/16*ln(-(4*RootOf(_Z^4+2)^3*(x^5+x^3)^(1/2)*x-4*(x^5+x^3)^(1/4)*RootOf(_Z^4+2)^2*x^2-RootOf(_Z^4+2)*x^4+2*RootOf(_Z^4+2)*x^3+4*(x^5+x^3)^(3/4)-RootOf(_Z^4+2)*x^2)/x^2/(-1+x)^2)*RootOf(_Z^4+2)^2*RootOf(_Z^2+RootOf(_Z^4+2)^2)+3/8*RootOf(_Z^4+2)^2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*ln((-2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*RootOf(_Z^4+2)^2*(x^5+x^3)^(1/2)*x+2*RootOf(_Z^4+2)^3*(x^5+x^3)^(1/2)*x+4*(x^5+x^3)^(1/4)*RootOf(_Z^2+RootOf(_Z^4+2)^2)*RootOf(_Z^4+2)*x^2-RootOf(_Z^2+RootOf(_Z^4+2)^2)*x^4-RootOf(_Z^4+2)*x^4-2*RootOf(_Z^2+RootOf(_Z^4+2)^2)*x^3-2*RootOf(_Z^4+2)*x^3+4*(x^5+x^3)^(3/4)-RootOf(_Z^2+RootOf(_Z^4+2)^2)*x^2-RootOf(_Z^4+2)*x^2)/x^2/(-1+x)^2)","C"
2383,0,0,143,0.045000," ","int(1/(a*x^2+b)/(x^3+x)^(1/3),x)","\[\int \frac{1}{\left(a \,x^{2}+b \right) \left(x^{3}+x \right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(a*x^2+b)/(x^3+x)^(1/3),x)","F"
2384,0,0,37,0.012000," ","int((a*x^4-b*x^3)^(1/4)/x^2/(c*x^2-d),x)","\[\int \frac{\left(a \,x^{4}-b \,x^{3}\right)^{\frac{1}{4}}}{x^{2} \left(c \,x^{2}-d \right)}\, dx\]"," ",0,"int((a*x^4-b*x^3)^(1/4)/x^2/(c*x^2-d),x)","F"
2385,0,0,37,0.003000," ","int((a*x^4-b*x^3)^(1/4)/x^2/(c*x^2-d),x)","\[\int \frac{\left(a \,x^{4}-b \,x^{3}\right)^{\frac{1}{4}}}{x^{2} \left(c \,x^{2}-d \right)}\, dx\]"," ",0,"int((a*x^4-b*x^3)^(1/4)/x^2/(c*x^2-d),x)","F"
2386,0,0,113,0.012000," ","int((x^3+x)^(1/3)*(a*x^6+b)/(c*x^6+d),x)","\[\int \frac{\left(x^{3}+x \right)^{\frac{1}{3}} \left(a \,x^{6}+b \right)}{c \,x^{6}+d}\, dx\]"," ",0,"int((x^3+x)^(1/3)*(a*x^6+b)/(c*x^6+d),x)","F"
2387,0,0,113,0.002000," ","int((x^3+x)^(1/3)*(a*x^6+b)/(c*x^6+d),x)","\[\int \frac{\left(x^{3}+x \right)^{\frac{1}{3}} \left(a \,x^{6}+b \right)}{c \,x^{6}+d}\, dx\]"," ",0,"int((x^3+x)^(1/3)*(a*x^6+b)/(c*x^6+d),x)","F"
2388,0,0,147,2.209000," ","int((2*x^6-1)*(x^7+x)^(1/3)/(x^6-2*x^2+1)/(x^6-x^2+1),x)","\[\int \frac{\left(2 x^{6}-1\right) \left(x^{7}+x \right)^{\frac{1}{3}}}{\left(x^{6}-2 x^{2}+1\right) \left(x^{6}-x^{2}+1\right)}\, dx\]"," ",0,"int((2*x^6-1)*(x^7+x)^(1/3)/(x^6-2*x^2+1)/(x^6-x^2+1),x)","F"
2389,0,0,185,0.023000," ","int((2*p*x^3-q)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)*(b*x^3+a*(p*x^3+q)^3)/x^6,x)","\[\int \frac{\left(2 p \,x^{3}-q \right) \sqrt{p^{2} x^{6}+2 p q \,x^{3}-2 p q \,x^{2}+q^{2}}\, \left(b \,x^{3}+a \left(p \,x^{3}+q \right)^{3}\right)}{x^{6}}\, dx\]"," ",0,"int((2*p*x^3-q)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)*(b*x^3+a*(p*x^3+q)^3)/x^6,x)","F"
2390,0,0,158,0.141000," ","int((-1+(-1+2*k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(1-(2+b)*x+(b*k+1)*x^2),x)","\[\int \frac{-1+\left(-1+2 k \right) x}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(1-\left(2+b \right) x +\left(b k +1\right) x^{2}\right)}\, dx\]"," ",0,"int((-1+(-1+2*k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(1-(2+b)*x+(b*k+1)*x^2),x)","F"
2391,0,0,160,0.026000," ","int((-3+2*(k^2+1)*x+(k^2+1)*x^2-4*k^2*x^3+k^2*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(1-d-(2+d)*x+(d*k^2+1)*x^2+d*k^2*x^3),x)","\[\int \frac{-3+2 \left(k^{2}+1\right) x +\left(k^{2}+1\right) x^{2}-4 k^{2} x^{3}+k^{2} x^{4}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{2}{3}} \left(1-d -\left(2+d \right) x +\left(d \,k^{2}+1\right) x^{2}+d \,k^{2} x^{3}\right)}\, dx\]"," ",0,"int((-3+2*(k^2+1)*x+(k^2+1)*x^2-4*k^2*x^3+k^2*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(1-d-(2+d)*x+(d*k^2+1)*x^2+d*k^2*x^3),x)","F"
2392,0,0,157,0.016000," ","int((3*x^6-3*a*x^3+b)/x^6/(2*a*x^3-b)/(a*x^4-b*x)^(1/4),x)","\[\int \frac{3 x^{6}-3 a \,x^{3}+b}{x^{6} \left(2 a \,x^{3}-b \right) \left(a \,x^{4}-b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((3*x^6-3*a*x^3+b)/x^6/(2*a*x^3-b)/(a*x^4-b*x)^(1/4),x)","F"
2393,0,0,186,0.023000," ","int((p*x^3-2*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)*(b*x^6+a*(p*x^3+q)^3)/x^11,x)","\[\int \frac{\left(p \,x^{3}-2 q \right) \sqrt{p^{2} x^{6}-2 p q \,x^{4}+2 p q \,x^{3}+q^{2}}\, \left(b \,x^{6}+a \left(p \,x^{3}+q \right)^{3}\right)}{x^{11}}\, dx\]"," ",0,"int((p*x^3-2*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)*(b*x^6+a*(p*x^3+q)^3)/x^11,x)","F"
2394,1,526,68,0.161000," ","int(x*(1+x)^(1/2)/(x+(x+(1+x)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\left(2 \sqrt{1+x}+1\right) \sqrt{x +\sqrt{1+x}}}{2}+\frac{5 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{4}+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\sum}\frac{\left(-\textit{\_R}^{3}+2 \textit{\_R}^{2}-4 \textit{\_R} -9\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +5}\right)+4 \ln \left(-1-2 \sqrt{1+x}+2 \sqrt{x +\sqrt{1+x}}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+2 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{\sum}\frac{\left(\textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}+6 \textit{\_R}^{2}-10 \textit{\_R} +3}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\textit{\_R}^{2} \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)+2 \sqrt{1+x}+4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\left(-3 \textit{\_R}^{2}-\textit{\_R} +2\right) \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)+\frac{2 \left(1+x \right)^{\frac{3}{2}}}{3}-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\left(-\textit{\_R}^{3}-7 \textit{\_R}^{2}-3 \textit{\_R} +6\right) \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\sum}\frac{\left(\textit{\_R}^{2}-2 \textit{\_R} -3\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +5}\right)-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+2 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{\sum}\frac{\left(-3 \textit{\_R}^{2}+2 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}+6 \textit{\_R}^{2}-10 \textit{\_R} +3}\right)$&$526$\\ default&$-\frac{\left(2 \sqrt{1+x}+1\right) \sqrt{x +\sqrt{1+x}}}{2}+\frac{5 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{4}+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\sum}\frac{\left(-\textit{\_R}^{3}+2 \textit{\_R}^{2}-4 \textit{\_R} -9\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +5}\right)+4 \ln \left(-1-2 \sqrt{1+x}+2 \sqrt{x +\sqrt{1+x}}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+2 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{\sum}\frac{\left(\textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}+6 \textit{\_R}^{2}-10 \textit{\_R} +3}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\textit{\_R}^{2} \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)+2 \sqrt{1+x}+4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\left(-3 \textit{\_R}^{2}-\textit{\_R} +2\right) \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)+\frac{2 \left(1+x \right)^{\frac{3}{2}}}{3}-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\left(-\textit{\_R}^{3}-7 \textit{\_R}^{2}-3 \textit{\_R} +6\right) \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\sum}\frac{\left(\textit{\_R}^{2}-2 \textit{\_R} -3\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +5}\right)-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+2 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{\sum}\frac{\left(-3 \textit{\_R}^{2}+2 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}+6 \textit{\_R}^{2}-10 \textit{\_R} +3}\right)$&$526$\\ \hline \end{longtable}"," ",0,"-1/2*(2*(1+x)^(1/2)+1)*(x+(1+x)^(1/2))^(1/2)+5/4*ln(1/2+(1+x)^(1/2)+(x+(1+x)^(1/2))^(1/2))+2*sum((-_R^3+2*_R^2-4*_R-9)/(4*_R^3-6*_R^2+2*_R+5)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^4-2*_Z^3+_Z^2+5*_Z-1))+4*ln(-1-2*(1+x)^(1/2)+2*(x+(1+x)^(1/2))^(1/2))+2*sum((_R^3-6*_R^2+2*_R+1)/(4*_R^3+6*_R^2-10*_R+3)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^4+2*_Z^3-5*_Z^2+3*_Z+1))+2*sum(_R^2/(4*_R^3-6*_R-1)*ln((1+x)^(1/2)-_R),_R=RootOf(_Z^4-3*_Z^2-_Z+2))+2*(1+x)^(1/2)+4*sum((-3*_R^2-_R+2)/(4*_R^3-6*_R-1)*ln((1+x)^(1/2)-_R),_R=RootOf(_Z^4-3*_Z^2-_Z+2))+2/3*(1+x)^(3/2)-2*sum((-_R^3-7*_R^2-3*_R+6)/(4*_R^3-6*_R-1)*ln((1+x)^(1/2)-_R),_R=RootOf(_Z^4-3*_Z^2-_Z+2))-2*sum((_R^2-2*_R-3)/(4*_R^3-6*_R^2+2*_R+5)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^4-2*_Z^3+_Z^2+5*_Z-1))-2*sum((-3*_R^2+2*_R+1)/(4*_R^3+6*_R^2-10*_R+3)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^4+2*_Z^3-5*_Z^2+3*_Z+1))","B"
2395,1,526,68,0.115000," ","int(x*(1+x)^(1/2)/(x+(x+(1+x)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\left(2 \sqrt{1+x}+1\right) \sqrt{x +\sqrt{1+x}}}{2}+\frac{5 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{4}+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\sum}\frac{\left(-\textit{\_R}^{3}+2 \textit{\_R}^{2}-4 \textit{\_R} -9\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +5}\right)+4 \ln \left(-1-2 \sqrt{1+x}+2 \sqrt{x +\sqrt{1+x}}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+2 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{\sum}\frac{\left(\textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}+6 \textit{\_R}^{2}-10 \textit{\_R} +3}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\textit{\_R}^{2} \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)+2 \sqrt{1+x}+4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\left(-3 \textit{\_R}^{2}-\textit{\_R} +2\right) \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)+\frac{2 \left(1+x \right)^{\frac{3}{2}}}{3}-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\left(-\textit{\_R}^{3}-7 \textit{\_R}^{2}-3 \textit{\_R} +6\right) \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\sum}\frac{\left(\textit{\_R}^{2}-2 \textit{\_R} -3\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +5}\right)-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+2 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{\sum}\frac{\left(-3 \textit{\_R}^{2}+2 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}+6 \textit{\_R}^{2}-10 \textit{\_R} +3}\right)$&$526$\\ default&$-\frac{\left(2 \sqrt{1+x}+1\right) \sqrt{x +\sqrt{1+x}}}{2}+\frac{5 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{4}+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\sum}\frac{\left(-\textit{\_R}^{3}+2 \textit{\_R}^{2}-4 \textit{\_R} -9\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +5}\right)+4 \ln \left(-1-2 \sqrt{1+x}+2 \sqrt{x +\sqrt{1+x}}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+2 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{\sum}\frac{\left(\textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}+6 \textit{\_R}^{2}-10 \textit{\_R} +3}\right)+2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\textit{\_R}^{2} \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)+2 \sqrt{1+x}+4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\left(-3 \textit{\_R}^{2}-\textit{\_R} +2\right) \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)+\frac{2 \left(1+x \right)^{\frac{3}{2}}}{3}-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-3 \textit{\_Z}^{2}-\textit{\_Z} +2\right)}{\sum}\frac{\left(-\textit{\_R}^{3}-7 \textit{\_R}^{2}-3 \textit{\_R} +6\right) \ln \left(\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R} -1}\right)-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\sum}\frac{\left(\textit{\_R}^{2}-2 \textit{\_R} -3\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-6 \textit{\_R}^{2}+2 \textit{\_R} +5}\right)-2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+2 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)}{\sum}\frac{\left(-3 \textit{\_R}^{2}+2 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{3}+6 \textit{\_R}^{2}-10 \textit{\_R} +3}\right)$&$526$\\ \hline \end{longtable}"," ",0,"-1/2*(2*(1+x)^(1/2)+1)*(x+(1+x)^(1/2))^(1/2)+5/4*ln(1/2+(1+x)^(1/2)+(x+(1+x)^(1/2))^(1/2))+2*sum((-_R^3+2*_R^2-4*_R-9)/(4*_R^3-6*_R^2+2*_R+5)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^4-2*_Z^3+_Z^2+5*_Z-1))+4*ln(-1-2*(1+x)^(1/2)+2*(x+(1+x)^(1/2))^(1/2))+2*sum((_R^3-6*_R^2+2*_R+1)/(4*_R^3+6*_R^2-10*_R+3)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^4+2*_Z^3-5*_Z^2+3*_Z+1))+2*sum(_R^2/(4*_R^3-6*_R-1)*ln((1+x)^(1/2)-_R),_R=RootOf(_Z^4-3*_Z^2-_Z+2))+2*(1+x)^(1/2)+4*sum((-3*_R^2-_R+2)/(4*_R^3-6*_R-1)*ln((1+x)^(1/2)-_R),_R=RootOf(_Z^4-3*_Z^2-_Z+2))+2/3*(1+x)^(3/2)-2*sum((-_R^3-7*_R^2-3*_R+6)/(4*_R^3-6*_R-1)*ln((1+x)^(1/2)-_R),_R=RootOf(_Z^4-3*_Z^2-_Z+2))-2*sum((_R^2-2*_R-3)/(4*_R^3-6*_R^2+2*_R+5)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^4-2*_Z^3+_Z^2+5*_Z-1))-2*sum((-3*_R^2+2*_R+1)/(4*_R^3+6*_R^2-10*_R+3)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^4+2*_Z^3-5*_Z^2+3*_Z+1))","B"
2396,1,588,177,0.106000," ","int(x^2/((a*x+b)/(c*x+d))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(a x +b \right) \left(-12 \sqrt{x^{2} a c +a d x +c x b +b d}\, \sqrt{a c}\, a^{2} c d x -36 \sqrt{x^{2} a c +a d x +c x b +b d}\, \sqrt{a c}\, a b \,c^{2} x +3 \ln \left(\frac{2 a c x +2 \sqrt{x^{2} a c +a d x +c x b +b d}\, \sqrt{a c}+a d +b c}{2 \sqrt{a c}}\right) a^{3} d^{3}+3 \ln \left(\frac{2 a c x +2 \sqrt{x^{2} a c +a d x +c x b +b d}\, \sqrt{a c}+a d +b c}{2 \sqrt{a c}}\right) a^{2} b c \,d^{2}-15 \ln \left(\frac{2 a c x +2 \sqrt{x^{2} a c +a d x +c x b +b d}\, \sqrt{a c}+a d +b c}{2 \sqrt{a c}}\right) a \,b^{2} c^{2} d +9 \ln \left(\frac{2 a c x +2 \sqrt{x^{2} a c +a d x +c x b +b d}\, \sqrt{a c}+a d +b c}{2 \sqrt{a c}}\right) b^{3} c^{3}+24 \ln \left(\frac{2 a c x +2 \sqrt{\left(c x +d \right) \left(a x +b \right)}\, \sqrt{a c}+a d +b c}{2 \sqrt{a c}}\right) a \,b^{2} c^{2} d -24 \ln \left(\frac{2 a c x +2 \sqrt{\left(c x +d \right) \left(a x +b \right)}\, \sqrt{a c}+a d +b c}{2 \sqrt{a c}}\right) b^{3} c^{3}+16 \left(x^{2} a c +a d x +c x b +b d \right)^{\frac{3}{2}} a c \sqrt{a c}-6 \sqrt{x^{2} a c +a d x +c x b +b d}\, \sqrt{a c}\, a^{2} d^{2}-24 \sqrt{x^{2} a c +a d x +c x b +b d}\, \sqrt{a c}\, a b c d -18 \sqrt{x^{2} a c +a d x +c x b +b d}\, \sqrt{a c}\, b^{2} c^{2}+48 \sqrt{a c}\, \sqrt{\left(c x +d \right) \left(a x +b \right)}\, b^{2} c^{2}\right)}{48 a^{3} \sqrt{\frac{a x +b}{c x +d}}\, \sqrt{\left(c x +d \right) \left(a x +b \right)}\, c^{2} \sqrt{a c}}$&$588$\\ \hline \end{longtable}"," ",0,"1/48*(a*x+b)/a^3*(-12*(a*c*x^2+a*d*x+b*c*x+b*d)^(1/2)*(a*c)^(1/2)*a^2*c*d*x-36*(a*c*x^2+a*d*x+b*c*x+b*d)^(1/2)*(a*c)^(1/2)*a*b*c^2*x+3*ln(1/2*(2*a*c*x+2*(a*c*x^2+a*d*x+b*c*x+b*d)^(1/2)*(a*c)^(1/2)+a*d+b*c)/(a*c)^(1/2))*a^3*d^3+3*ln(1/2*(2*a*c*x+2*(a*c*x^2+a*d*x+b*c*x+b*d)^(1/2)*(a*c)^(1/2)+a*d+b*c)/(a*c)^(1/2))*a^2*b*c*d^2-15*ln(1/2*(2*a*c*x+2*(a*c*x^2+a*d*x+b*c*x+b*d)^(1/2)*(a*c)^(1/2)+a*d+b*c)/(a*c)^(1/2))*a*b^2*c^2*d+9*ln(1/2*(2*a*c*x+2*(a*c*x^2+a*d*x+b*c*x+b*d)^(1/2)*(a*c)^(1/2)+a*d+b*c)/(a*c)^(1/2))*b^3*c^3+24*ln(1/2*(2*a*c*x+2*((c*x+d)*(a*x+b))^(1/2)*(a*c)^(1/2)+a*d+b*c)/(a*c)^(1/2))*a*b^2*c^2*d-24*ln(1/2*(2*a*c*x+2*((c*x+d)*(a*x+b))^(1/2)*(a*c)^(1/2)+a*d+b*c)/(a*c)^(1/2))*b^3*c^3+16*(a*c*x^2+a*d*x+b*c*x+b*d)^(3/2)*a*c*(a*c)^(1/2)-6*(a*c*x^2+a*d*x+b*c*x+b*d)^(1/2)*(a*c)^(1/2)*a^2*d^2-24*(a*c*x^2+a*d*x+b*c*x+b*d)^(1/2)*(a*c)^(1/2)*a*b*c*d-18*(a*c*x^2+a*d*x+b*c*x+b*d)^(1/2)*(a*c)^(1/2)*b^2*c^2+48*(a*c)^(1/2)*((c*x+d)*(a*x+b))^(1/2)*b^2*c^2)/((a*x+b)/(c*x+d))^(1/2)/((c*x+d)*(a*x+b))^(1/2)/c^2/(a*c)^(1/2)","B"
2397,0,0,153,0.149000," ","int((2*a*x+b)/(a*x-b)/(a*x+2*b)/(a*x^2+b*x-1)^(1/4),x)","\[\int \frac{2 a x +b}{\left(a x -b \right) \left(a x +2 b \right) \left(a \,x^{2}+b x -1\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((2*a*x+b)/(a*x-b)/(a*x+2*b)/(a*x^2+b*x-1)^(1/4),x)","F"
2398,1,160,177,0.156000," ","int((a*k*x+k*x^2-1)/(k*x^2+1)/((-x^2+1)*(-k^2*x^2+1))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\frac{a \ln \left(\frac{\frac{2 k^{2}+4 k +2}{k}+\left(-k^{2}-2 k -1\right) \left(x^{2}+\frac{1}{k}\right)+2 \sqrt{\frac{k^{2}+2 k +1}{k}}\, \sqrt{k^{2} \left(x^{2}+\frac{1}{k}\right)^{2}+\left(-k^{2}-2 k -1\right) \left(x^{2}+\frac{1}{k}\right)+\frac{k^{2}+2 k +1}{k}}}{x^{2}+\frac{1}{k}}\right)}{2 \sqrt{\frac{k^{2}+2 k +1}{k}}}+\frac{\arctan \left(\frac{\sqrt{\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)}}{x \left(1+k \right)}\right)}{1+k}$&$160$\\ default&$\frac{\sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticF \left(x , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}+\frac{a \arctanh \left(\frac{k \,x^{2}}{\sqrt{\frac{1}{k}+2+k}\, \sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}-\frac{k}{2 \sqrt{\frac{1}{k}+2+k}\, \sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}+\frac{k^{2} x^{2}}{2 \sqrt{\frac{1}{k}+2+k}\, \sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}-\frac{1}{2 \sqrt{\frac{1}{k}+2+k}\, \sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}\, k}+\frac{x^{2}}{2 \sqrt{\frac{1}{k}+2+k}\, \sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}-\frac{1}{\sqrt{\frac{1}{k}+2+k}\, \sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}\right)}{2 \sqrt{\frac{1}{k}+2+k}}-\frac{2 \sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticPi \left(x , -k , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}$&$337$\\ \hline \end{longtable}"," ",0,"-1/2*a/((k^2+2*k+1)/k)^(1/2)*ln((2*(k^2+2*k+1)/k+(-k^2-2*k-1)*(x^2+1/k)+2*((k^2+2*k+1)/k)^(1/2)*(k^2*(x^2+1/k)^2+(-k^2-2*k-1)*(x^2+1/k)+(k^2+2*k+1)/k)^(1/2))/(x^2+1/k))+1/(1+k)*arctan(((-x^2+1)*(-k^2*x^2+1))^(1/2)/x/(1+k))","A"
2399,0,0,169,0.007000," ","int((x^3-b)*(x^3+b)/(a*x^2+x^3)^(1/3),x)","\[\int \frac{\left(x^{3}-b \right) \left(x^{3}+b \right)}{\left(a \,x^{2}+x^{3}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((x^3-b)*(x^3+b)/(a*x^2+x^3)^(1/3),x)","F"
2400,1,3458,168,0.219000," ","int(x/(-x^2+1)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$3458$\\ elliptic&$\text{Expression too large to display}$&$78106$\\ \hline \end{longtable}"," ",0,"-(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))^2*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)+1)*(EllipticF(((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2),((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2))+(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1)+1)*EllipticPi(((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2),(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)+1)*(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1)+1)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)),((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)))-(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))^2*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)*((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-1)*(EllipticF(((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2),((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2))+(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1)-1)*EllipticPi(((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2))*(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(x-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2),(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-1)*(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1)-1)/(RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)),((RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3))*(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=3)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=1))/(-RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=4)+RootOf(_Z^4*a+_Z^3*b+_Z^2*c+_Z*b+a,index=2)))^(1/2)))","C"
2401,1,1671,125,11.167000," ","int(1/(x^4-1)^(1/4)/(x^8-x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1671$\\ \hline \end{longtable}"," ",0,"-1/20*RootOf(_Z^2+400*RootOf(6400*_Z^4+80*_Z^2-1)^2+5)*ln((3200*RootOf(_Z^2+400*RootOf(6400*_Z^4+80*_Z^2-1)^2+5)*RootOf(6400*_Z^4+80*_Z^2-1)^4*x^4-160*(x^4-1)^(1/2)*RootOf(_Z^2+400*RootOf(6400*_Z^4+80*_Z^2-1)^2+5)*RootOf(6400*_Z^4+80*_Z^2-1)^2*x^2+200*RootOf(_Z^2+400*RootOf(6400*_Z^4+80*_Z^2-1)^2+5)*RootOf(6400*_Z^4+80*_Z^2-1)^2*x^4+320*RootOf(6400*_Z^4+80*_Z^2-1)^2*(x^4-1)^(3/4)*x-560*(x^4-1)^(1/4)*RootOf(6400*_Z^4+80*_Z^2-1)^2*x^3-3*(x^4-1)^(1/2)*RootOf(_Z^2+400*RootOf(6400*_Z^4+80*_Z^2-1)^2+5)*x^2+3*RootOf(_Z^2+400*RootOf(6400*_Z^4+80*_Z^2-1)^2+5)*x^4+7*(x^4-1)^(3/4)*x-11*x^3*(x^4-1)^(1/4)-40*RootOf(6400*_Z^4+80*_Z^2-1)^2*RootOf(_Z^2+400*RootOf(6400*_Z^4+80*_Z^2-1)^2+5)-RootOf(_Z^2+400*RootOf(6400*_Z^4+80*_Z^2-1)^2+5))/(80*RootOf(6400*_Z^4+80*_Z^2-1)^2*x^4+x^4+1))+RootOf(6400*_Z^4+80*_Z^2-1)*ln(-(64000*RootOf(6400*_Z^4+80*_Z^2-1)^5*x^4+1600*RootOf(6400*_Z^4+80*_Z^2-1)^3*(x^4-1)^(1/2)*x^2-1600*x^4*RootOf(6400*_Z^4+80*_Z^2-1)^3+240*RootOf(6400*_Z^4+80*_Z^2-1)^2*(x^4-1)^(3/4)*x-320*(x^4-1)^(1/4)*RootOf(6400*_Z^4+80*_Z^2-1)^2*x^3-20*(x^4-1)^(1/2)*RootOf(6400*_Z^4+80*_Z^2-1)*x^2-(x^4-1)^(3/4)*x+3*x^3*(x^4-1)^(1/4)+800*RootOf(6400*_Z^4+80*_Z^2-1)^3)/(640*RootOf(6400*_Z^4+80*_Z^2-1)^3*x^2+4*RootOf(6400*_Z^4+80*_Z^2-1)*x^2+1)/(640*RootOf(6400*_Z^4+80*_Z^2-1)^3*x^2+4*RootOf(6400*_Z^4+80*_Z^2-1)*x^2-1))-4*RootOf(6400*_Z^4+80*_Z^2-1)^2*RootOf(_Z^2+400*RootOf(6400*_Z^4+80*_Z^2-1)^2+5)*ln(-(6400*RootOf(_Z^2+400*RootOf(6400*_Z^4+80*_Z^2-1)^2+5)*RootOf(6400*_Z^4+80*_Z^2-1)^4*x^4-320*(x^4-1)^(1/2)*RootOf(_Z^2+400*RootOf(6400*_Z^4+80*_Z^2-1)^2+5)*RootOf(6400*_Z^4+80*_Z^2-1)^2*x^2-240*RootOf(_Z^2+400*RootOf(6400*_Z^4+80*_Z^2-1)^2+5)*RootOf(6400*_Z^4+80*_Z^2-1)^2*x^4+480*RootOf(6400*_Z^4+80*_Z^2-1)^2*(x^4-1)^(3/4)*x+640*(x^4-1)^(1/4)*RootOf(6400*_Z^4+80*_Z^2-1)^2*x^3+2*(x^4-1)^(1/2)*RootOf(_Z^2+400*RootOf(6400*_Z^4+80*_Z^2-1)^2+5)*x^2+2*RootOf(_Z^2+400*RootOf(6400*_Z^4+80*_Z^2-1)^2+5)*x^4-2*(x^4-1)^(3/4)*x-6*x^3*(x^4-1)^(1/4)+80*RootOf(6400*_Z^4+80*_Z^2-1)^2*RootOf(_Z^2+400*RootOf(6400*_Z^4+80*_Z^2-1)^2+5)-RootOf(_Z^2+400*RootOf(6400*_Z^4+80*_Z^2-1)^2+5))/(640*RootOf(6400*_Z^4+80*_Z^2-1)^3*x^2+4*RootOf(6400*_Z^4+80*_Z^2-1)*x^2+1)/(640*RootOf(6400*_Z^4+80*_Z^2-1)^3*x^2+4*RootOf(6400*_Z^4+80*_Z^2-1)*x^2-1))+80*RootOf(6400*_Z^4+80*_Z^2-1)^3*ln(-(704000*RootOf(6400*_Z^4+80*_Z^2-1)^5*x^4+27200*RootOf(6400*_Z^4+80*_Z^2-1)^3*(x^4-1)^(1/2)*x^2+40000*x^4*RootOf(6400*_Z^4+80*_Z^2-1)^3-1840*RootOf(6400*_Z^4+80*_Z^2-1)^2*(x^4-1)^(3/4)*x-3120*(x^4-1)^(1/4)*RootOf(6400*_Z^4+80*_Z^2-1)^2*x^3+560*(x^4-1)^(1/2)*RootOf(6400*_Z^4+80*_Z^2-1)*x^2+510*RootOf(6400*_Z^4+80*_Z^2-1)*x^4-39*(x^4-1)^(3/4)*x-62*x^3*(x^4-1)^(1/4)-8800*RootOf(6400*_Z^4+80*_Z^2-1)^3-170*RootOf(6400*_Z^4+80*_Z^2-1))/(80*RootOf(6400*_Z^4+80*_Z^2-1)^2*x^4+x^4+1))+RootOf(6400*_Z^4+80*_Z^2-1)*ln(-(704000*RootOf(6400*_Z^4+80*_Z^2-1)^5*x^4+27200*RootOf(6400*_Z^4+80*_Z^2-1)^3*(x^4-1)^(1/2)*x^2+40000*x^4*RootOf(6400*_Z^4+80*_Z^2-1)^3-1840*RootOf(6400*_Z^4+80*_Z^2-1)^2*(x^4-1)^(3/4)*x-3120*(x^4-1)^(1/4)*RootOf(6400*_Z^4+80*_Z^2-1)^2*x^3+560*(x^4-1)^(1/2)*RootOf(6400*_Z^4+80*_Z^2-1)*x^2+510*RootOf(6400*_Z^4+80*_Z^2-1)*x^4-39*(x^4-1)^(3/4)*x-62*x^3*(x^4-1)^(1/4)-8800*RootOf(6400*_Z^4+80*_Z^2-1)^3-170*RootOf(6400*_Z^4+80*_Z^2-1))/(80*RootOf(6400*_Z^4+80*_Z^2-1)^2*x^4+x^4+1))","C"
2402,1,1750,125,11.144000," ","int((2*x^4-1)/(x^4-1)^(1/4)/(x^8-x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1750$\\ \hline \end{longtable}"," ",0,"RootOf(256*_Z^4-16*_Z^2-1)*ln((512*RootOf(256*_Z^4-16*_Z^2-1)^5*x^4+192*RootOf(256*_Z^4-16*_Z^2-1)^3*(x^4-1)^(1/2)*x^2+128*x^4*RootOf(256*_Z^4-16*_Z^2-1)^3+48*RootOf(256*_Z^4-16*_Z^2-1)^2*(x^4-1)^(3/4)*x+64*(x^4-1)^(1/4)*RootOf(256*_Z^4-16*_Z^2-1)^2*x^3+4*RootOf(256*_Z^4-16*_Z^2-1)*(x^4-1)^(1/2)*x^2+8*x^4*RootOf(256*_Z^4-16*_Z^2-1)+(x^4-1)^(3/4)*x+3*x^3*(x^4-1)^(1/4)-32*RootOf(256*_Z^4-16*_Z^2-1)^3-4*RootOf(256*_Z^4-16*_Z^2-1))/(16*RootOf(256*_Z^4-16*_Z^2-1)^2*x^4+1))+1/4*RootOf(_Z^2+16*RootOf(256*_Z^4-16*_Z^2-1)^2-1)*ln((256*RootOf(_Z^2+16*RootOf(256*_Z^4-16*_Z^2-1)^2-1)*RootOf(256*_Z^4-16*_Z^2-1)^4*x^4-96*(x^4-1)^(1/2)*RootOf(_Z^2+16*RootOf(256*_Z^4-16*_Z^2-1)^2-1)*RootOf(256*_Z^4-16*_Z^2-1)^2*x^2-96*RootOf(_Z^2+16*RootOf(256*_Z^4-16*_Z^2-1)^2-1)*RootOf(256*_Z^4-16*_Z^2-1)^2*x^4-96*RootOf(256*_Z^4-16*_Z^2-1)^2*(x^4-1)^(3/4)*x-128*(x^4-1)^(1/4)*RootOf(256*_Z^4-16*_Z^2-1)^2*x^3+8*(x^4-1)^(1/2)*RootOf(_Z^2+16*RootOf(256*_Z^4-16*_Z^2-1)^2-1)*x^2+9*RootOf(_Z^2+16*RootOf(256*_Z^4-16*_Z^2-1)^2-1)*x^4+8*(x^4-1)^(3/4)*x+14*x^3*(x^4-1)^(1/4)+16*RootOf(256*_Z^4-16*_Z^2-1)^2*RootOf(_Z^2+16*RootOf(256*_Z^4-16*_Z^2-1)^2-1)-3*RootOf(_Z^2+16*RootOf(256*_Z^4-16*_Z^2-1)^2-1))/(64*RootOf(256*_Z^4-16*_Z^2-1)^3*x^2-4*RootOf(256*_Z^4-16*_Z^2-1)*x^2-1)/(64*RootOf(256*_Z^4-16*_Z^2-1)^3*x^2-4*RootOf(256*_Z^4-16*_Z^2-1)*x^2+1))+4*RootOf(256*_Z^4-16*_Z^2-1)^2*RootOf(_Z^2+16*RootOf(256*_Z^4-16*_Z^2-1)^2-1)*ln((768*RootOf(_Z^2+16*RootOf(256*_Z^4-16*_Z^2-1)^2-1)*RootOf(256*_Z^4-16*_Z^2-1)^4*x^4-128*(x^4-1)^(1/2)*RootOf(_Z^2+16*RootOf(256*_Z^4-16*_Z^2-1)^2-1)*RootOf(256*_Z^4-16*_Z^2-1)^2*x^2+112*RootOf(_Z^2+16*RootOf(256*_Z^4-16*_Z^2-1)^2-1)*RootOf(256*_Z^4-16*_Z^2-1)^2*x^4+96*RootOf(256*_Z^4-16*_Z^2-1)^2*(x^4-1)^(3/4)*x-128*(x^4-1)^(1/4)*RootOf(256*_Z^4-16*_Z^2-1)^2*x^3-6*(x^4-1)^(1/2)*RootOf(_Z^2+16*RootOf(256*_Z^4-16*_Z^2-1)^2-1)*x^2+2*RootOf(_Z^2+16*RootOf(256*_Z^4-16*_Z^2-1)^2-1)*x^4+2*(x^4-1)^(3/4)*x-6*x^3*(x^4-1)^(1/4)-48*RootOf(256*_Z^4-16*_Z^2-1)^2*RootOf(_Z^2+16*RootOf(256*_Z^4-16*_Z^2-1)^2-1)-RootOf(_Z^2+16*RootOf(256*_Z^4-16*_Z^2-1)^2-1))/(16*RootOf(256*_Z^4-16*_Z^2-1)^2*x^4+1))-16*RootOf(256*_Z^4-16*_Z^2-1)^3*ln((2048*RootOf(256*_Z^4-16*_Z^2-1)^5*x^4+448*RootOf(256*_Z^4-16*_Z^2-1)^3*(x^4-1)^(1/2)*x^2-608*x^4*RootOf(256*_Z^4-16*_Z^2-1)^3-64*RootOf(256*_Z^4-16*_Z^2-1)^2*(x^4-1)^(3/4)*x+112*(x^4-1)^(1/4)*RootOf(256*_Z^4-16*_Z^2-1)^2*x^3-44*RootOf(256*_Z^4-16*_Z^2-1)*(x^4-1)^(1/2)*x^2+42*x^4*RootOf(256*_Z^4-16*_Z^2-1)+7*(x^4-1)^(3/4)*x-11*x^3*(x^4-1)^(1/4)+128*RootOf(256*_Z^4-16*_Z^2-1)^3-14*RootOf(256*_Z^4-16*_Z^2-1))/(64*RootOf(256*_Z^4-16*_Z^2-1)^3*x^2-4*RootOf(256*_Z^4-16*_Z^2-1)*x^2-1)/(64*RootOf(256*_Z^4-16*_Z^2-1)^3*x^2-4*RootOf(256*_Z^4-16*_Z^2-1)*x^2+1))+RootOf(256*_Z^4-16*_Z^2-1)*ln((2048*RootOf(256*_Z^4-16*_Z^2-1)^5*x^4+448*RootOf(256*_Z^4-16*_Z^2-1)^3*(x^4-1)^(1/2)*x^2-608*x^4*RootOf(256*_Z^4-16*_Z^2-1)^3-64*RootOf(256*_Z^4-16*_Z^2-1)^2*(x^4-1)^(3/4)*x+112*(x^4-1)^(1/4)*RootOf(256*_Z^4-16*_Z^2-1)^2*x^3-44*RootOf(256*_Z^4-16*_Z^2-1)*(x^4-1)^(1/2)*x^2+42*x^4*RootOf(256*_Z^4-16*_Z^2-1)+7*(x^4-1)^(3/4)*x-11*x^3*(x^4-1)^(1/4)+128*RootOf(256*_Z^4-16*_Z^2-1)^3-14*RootOf(256*_Z^4-16*_Z^2-1))/(64*RootOf(256*_Z^4-16*_Z^2-1)^3*x^2-4*RootOf(256*_Z^4-16*_Z^2-1)*x^2-1)/(64*RootOf(256*_Z^4-16*_Z^2-1)^3*x^2-4*RootOf(256*_Z^4-16*_Z^2-1)*x^2+1))","C"
2403,1,1705,125,11.493000," ","int(1/(x^4+1)^(1/4)/(x^8+x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1705$\\ \hline \end{longtable}"," ",0,"RootOf(6400*_Z^4-80*_Z^2-1)*ln(-(64000*RootOf(6400*_Z^4-80*_Z^2-1)^5*x^4+3200*RootOf(6400*_Z^4-80*_Z^2-1)^3*(x^4+1)^(1/2)*x^2+2400*x^4*RootOf(6400*_Z^4-80*_Z^2-1)^3-320*RootOf(6400*_Z^4-80*_Z^2-1)^2*(x^4+1)^(3/4)*x-560*(x^4+1)^(1/4)*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^3+20*RootOf(6400*_Z^4-80*_Z^2-1)*(x^4+1)^(1/2)*x^2+20*RootOf(6400*_Z^4-80*_Z^2-1)*x^4-3*(x^4+1)^(3/4)*x-4*x^3*(x^4+1)^(1/4)+800*RootOf(6400*_Z^4-80*_Z^2-1)^3+10*RootOf(6400*_Z^4-80*_Z^2-1))/(640*RootOf(6400*_Z^4-80*_Z^2-1)^3*x^2-4*RootOf(6400*_Z^4-80*_Z^2-1)*x^2+1)/(640*RootOf(6400*_Z^4-80*_Z^2-1)^3*x^2-4*RootOf(6400*_Z^4-80*_Z^2-1)*x^2-1))+1/20*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*ln(-(6400*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*RootOf(6400*_Z^4-80*_Z^2-1)^4*x^4-160*(x^4+1)^(1/2)*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^2-320*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^4+480*RootOf(6400*_Z^4-80*_Z^2-1)^2*(x^4+1)^(3/4)*x+640*(x^4+1)^(1/4)*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^3+4*(x^4+1)^(1/2)*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*x^2+3*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*x^4-8*(x^4+1)^(3/4)*x-14*x^3*(x^4+1)^(1/4)-80*RootOf(6400*_Z^4-80*_Z^2-1)^2*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)+RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5))/(80*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^4-x^4+1))-4*RootOf(6400*_Z^4-80*_Z^2-1)^2*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*ln((6400*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*RootOf(6400*_Z^4-80*_Z^2-1)^4*x^4-320*(x^4+1)^(1/2)*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^2+240*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^4+480*RootOf(6400*_Z^4-80*_Z^2-1)^2*(x^4+1)^(3/4)*x-640*(x^4+1)^(1/4)*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^3-2*(x^4+1)^(1/2)*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*x^2+2*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*x^4+2*(x^4+1)^(3/4)*x-6*x^3*(x^4+1)^(1/4)+80*RootOf(6400*_Z^4-80*_Z^2-1)^2*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)+RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5))/(640*RootOf(6400*_Z^4-80*_Z^2-1)^3*x^2-4*RootOf(6400*_Z^4-80*_Z^2-1)*x^2+1)/(640*RootOf(6400*_Z^4-80*_Z^2-1)^3*x^2-4*RootOf(6400*_Z^4-80*_Z^2-1)*x^2-1))+80*RootOf(6400*_Z^4-80*_Z^2-1)^3*ln((64000*RootOf(6400*_Z^4-80*_Z^2-1)^5*x^4+3200*RootOf(6400*_Z^4-80*_Z^2-1)^3*(x^4+1)^(1/2)*x^2-4000*x^4*RootOf(6400*_Z^4-80*_Z^2-1)^3-240*RootOf(6400*_Z^4-80*_Z^2-1)^2*(x^4+1)^(3/4)*x+320*(x^4+1)^(1/4)*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^3-60*RootOf(6400*_Z^4-80*_Z^2-1)*(x^4+1)^(1/2)*x^2+60*RootOf(6400*_Z^4-80*_Z^2-1)*x^4+4*(x^4+1)^(3/4)*x-7*x^3*(x^4+1)^(1/4)-800*RootOf(6400*_Z^4-80*_Z^2-1)^3+20*RootOf(6400*_Z^4-80*_Z^2-1))/(80*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^4-x^4+1))-RootOf(6400*_Z^4-80*_Z^2-1)*ln((64000*RootOf(6400*_Z^4-80*_Z^2-1)^5*x^4+3200*RootOf(6400*_Z^4-80*_Z^2-1)^3*(x^4+1)^(1/2)*x^2-4000*x^4*RootOf(6400*_Z^4-80*_Z^2-1)^3-240*RootOf(6400*_Z^4-80*_Z^2-1)^2*(x^4+1)^(3/4)*x+320*(x^4+1)^(1/4)*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^3-60*RootOf(6400*_Z^4-80*_Z^2-1)*(x^4+1)^(1/2)*x^2+60*RootOf(6400*_Z^4-80*_Z^2-1)*x^4+4*(x^4+1)^(3/4)*x-7*x^3*(x^4+1)^(1/4)-800*RootOf(6400*_Z^4-80*_Z^2-1)^3+20*RootOf(6400*_Z^4-80*_Z^2-1))/(80*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^4-x^4+1))","C"
2404,1,1696,125,10.984000," ","int((x^4-2)/(x^4+1)^(1/4)/(x^8+x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1696$\\ \hline \end{longtable}"," ",0,"-RootOf(256*_Z^4+16*_Z^2-1)*ln(-(1536*RootOf(256*_Z^4+16*_Z^2-1)^5*x^4+256*RootOf(256*_Z^4+16*_Z^2-1)^3*(x^4+1)^(1/2)*x^2+416*x^4*RootOf(256*_Z^4+16*_Z^2-1)^3-48*RootOf(256*_Z^4+16*_Z^2-1)^2*(x^4+1)^(3/4)*x-64*(x^4+1)^(1/4)*RootOf(256*_Z^4+16*_Z^2-1)^2*x^3+28*RootOf(256*_Z^4+16*_Z^2-1)*(x^4+1)^(1/2)*x^2+24*x^4*RootOf(256*_Z^4+16*_Z^2-1)-4*(x^4+1)^(3/4)*x-7*x^3*(x^4+1)^(1/4)+96*RootOf(256*_Z^4+16*_Z^2-1)^3+8*RootOf(256*_Z^4+16*_Z^2-1))/(64*RootOf(256*_Z^4+16*_Z^2-1)^3*x^2+4*RootOf(256*_Z^4+16*_Z^2-1)*x^2-1)/(64*RootOf(256*_Z^4+16*_Z^2-1)^3*x^2+4*RootOf(256*_Z^4+16*_Z^2-1)*x^2+1))+1/4*RootOf(_Z^2+16*RootOf(256*_Z^4+16*_Z^2-1)^2+1)*ln((1024*RootOf(_Z^2+16*RootOf(256*_Z^4+16*_Z^2-1)^2+1)*RootOf(256*_Z^4+16*_Z^2-1)^4*x^4-224*(x^4+1)^(1/2)*RootOf(256*_Z^4+16*_Z^2-1)^2*RootOf(_Z^2+16*RootOf(256*_Z^4+16*_Z^2-1)^2+1)*x^2-176*RootOf(_Z^2+16*RootOf(256*_Z^4+16*_Z^2-1)^2+1)*RootOf(256*_Z^4+16*_Z^2-1)^2*x^4-128*RootOf(256*_Z^4+16*_Z^2-1)^2*(x^4+1)^(3/4)*x-224*(x^4+1)^(1/4)*RootOf(256*_Z^4+16*_Z^2-1)^2*x^3+8*(x^4+1)^(1/2)*RootOf(_Z^2+16*RootOf(256*_Z^4+16*_Z^2-1)^2+1)*x^2+6*RootOf(_Z^2+16*RootOf(256*_Z^4+16*_Z^2-1)^2+1)*x^4+6*(x^4+1)^(3/4)*x+8*x^3*(x^4+1)^(1/4)-64*RootOf(256*_Z^4+16*_Z^2-1)^2*RootOf(_Z^2+16*RootOf(256*_Z^4+16*_Z^2-1)^2+1)+3*RootOf(_Z^2+16*RootOf(256*_Z^4+16*_Z^2-1)^2+1))/(16*RootOf(256*_Z^4+16*_Z^2-1)^2*x^4+1))-4*RootOf(256*_Z^4+16*_Z^2-1)^2*RootOf(_Z^2+16*RootOf(256*_Z^4+16*_Z^2-1)^2+1)*ln(-(384*RootOf(_Z^2+16*RootOf(256*_Z^4+16*_Z^2-1)^2+1)*RootOf(256*_Z^4+16*_Z^2-1)^4*x^4-64*(x^4+1)^(1/2)*RootOf(256*_Z^4+16*_Z^2-1)^2*RootOf(_Z^2+16*RootOf(256*_Z^4+16*_Z^2-1)^2+1)*x^2+104*RootOf(_Z^2+16*RootOf(256*_Z^4+16*_Z^2-1)^2+1)*RootOf(256*_Z^4+16*_Z^2-1)^2*x^4-64*RootOf(256*_Z^4+16*_Z^2-1)^2*(x^4+1)^(3/4)*x+112*(x^4+1)^(1/4)*RootOf(256*_Z^4+16*_Z^2-1)^2*x^3-7*(x^4+1)^(1/2)*RootOf(_Z^2+16*RootOf(256*_Z^4+16*_Z^2-1)^2+1)*x^2+6*RootOf(_Z^2+16*RootOf(256*_Z^4+16*_Z^2-1)^2+1)*x^4-7*(x^4+1)^(3/4)*x+11*x^3*(x^4+1)^(1/4)+24*RootOf(256*_Z^4+16*_Z^2-1)^2*RootOf(_Z^2+16*RootOf(256*_Z^4+16*_Z^2-1)^2+1)+2*RootOf(_Z^2+16*RootOf(256*_Z^4+16*_Z^2-1)^2+1))/(64*RootOf(256*_Z^4+16*_Z^2-1)^3*x^2+4*RootOf(256*_Z^4+16*_Z^2-1)*x^2-1)/(64*RootOf(256*_Z^4+16*_Z^2-1)^3*x^2+4*RootOf(256*_Z^4+16*_Z^2-1)*x^2+1))+16*RootOf(256*_Z^4+16*_Z^2-1)^3*ln(-(512*RootOf(256*_Z^4+16*_Z^2-1)^5*x^4+192*RootOf(256*_Z^4+16*_Z^2-1)^3*(x^4+1)^(1/2)*x^2-128*x^4*RootOf(256*_Z^4+16*_Z^2-1)^3+48*RootOf(256*_Z^4+16*_Z^2-1)^2*(x^4+1)^(3/4)*x-64*(x^4+1)^(1/4)*RootOf(256*_Z^4+16*_Z^2-1)^2*x^3-4*RootOf(256*_Z^4+16*_Z^2-1)*(x^4+1)^(1/2)*x^2+8*x^4*RootOf(256*_Z^4+16*_Z^2-1)-(x^4+1)^(3/4)*x+3*x^3*(x^4+1)^(1/4)-32*RootOf(256*_Z^4+16*_Z^2-1)^3+4*RootOf(256*_Z^4+16*_Z^2-1))/(16*RootOf(256*_Z^4+16*_Z^2-1)^2*x^4+1))+RootOf(256*_Z^4+16*_Z^2-1)*ln(-(512*RootOf(256*_Z^4+16*_Z^2-1)^5*x^4+192*RootOf(256*_Z^4+16*_Z^2-1)^3*(x^4+1)^(1/2)*x^2-128*x^4*RootOf(256*_Z^4+16*_Z^2-1)^3+48*RootOf(256*_Z^4+16*_Z^2-1)^2*(x^4+1)^(3/4)*x-64*(x^4+1)^(1/4)*RootOf(256*_Z^4+16*_Z^2-1)^2*x^3-4*RootOf(256*_Z^4+16*_Z^2-1)*(x^4+1)^(1/2)*x^2+8*x^4*RootOf(256*_Z^4+16*_Z^2-1)-(x^4+1)^(3/4)*x+3*x^3*(x^4+1)^(1/4)-32*RootOf(256*_Z^4+16*_Z^2-1)^3+4*RootOf(256*_Z^4+16*_Z^2-1))/(16*RootOf(256*_Z^4+16*_Z^2-1)^2*x^4+1))","C"
2405,0,0,173,0.013000," ","int((a*x^4+b*x^3)^(1/4)*(c*x^8-d)/x^8,x)","\[\int \frac{\left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}} \left(c \,x^{8}-d \right)}{x^{8}}\, dx\]"," ",0,"int((a*x^4+b*x^3)^(1/4)*(c*x^8-d)/x^8,x)","F"
2406,0,0,145,0.030000," ","int(x^4*(x^5+2)/(x^5+1)^(1/2)/(a*x^10-x^5-1),x)","\[\int \frac{x^{4} \left(x^{5}+2\right)}{\sqrt{x^{5}+1}\, \left(a \,x^{10}-x^{5}-1\right)}\, dx\]"," ",0,"int(x^4*(x^5+2)/(x^5+1)^(1/2)/(a*x^10-x^5-1),x)","F"
2407,0,0,145,0.046000," ","int(x^4*(x^5-2)/(x^5-1)^(1/2)/(a*x^10-x^5+1),x)","\[\int \frac{x^{4} \left(x^{5}-2\right)}{\sqrt{x^{5}-1}\, \left(a \,x^{10}-x^{5}+1\right)}\, dx\]"," ",0,"int(x^4*(x^5-2)/(x^5-1)^(1/2)/(a*x^10-x^5+1),x)","F"
2408,0,0,145,0.031000," ","int(x^4*(x^5+3)/(x^5+1)^(1/2)/(-1+a-(1+2*a)*x^5+a*x^10),x)","\[\int \frac{x^{4} \left(x^{5}+3\right)}{\sqrt{x^{5}+1}\, \left(-1+a -\left(1+2 a \right) x^{5}+a \,x^{10}\right)}\, dx\]"," ",0,"int(x^4*(x^5+3)/(x^5+1)^(1/2)/(-1+a-(1+2*a)*x^5+a*x^10),x)","F"
2409,1,149,12,1.818000," ","int(1/(x^2-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-4 a \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 c \,\textit{\_Z}^{6}+\left(6 c^{2}-2 b \right) \textit{\_Z}^{4}-a^{2} \textit{\_Z}^{3}+\left(-4 c^{3}+4 b c \right) \textit{\_Z}^{2}+a^{2} c \textit{\_Z} +c^{4}-2 b \,c^{2}+b^{2}\right)}{\sum}\frac{\left(-\textit{\_R}^{3}+\textit{\_R} c \right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{8 \textit{\_R}^{7}-24 \textit{\_R}^{5} c +24 \textit{\_R}^{3} c^{2}-8 \textit{\_R}^{3} b -3 \textit{\_R}^{2} a^{2}-8 \textit{\_R} \,c^{3}+8 \textit{\_R} b c +a^{2} c}\right)$&$149$\\ default&$\text{Expression too large to display}$&$7120$\\ \hline \end{longtable}"," ",0,"-4*a*sum((-_R^3+_R*c)/(8*_R^7-24*_R^5*c+24*_R^3*c^2-8*_R^3*b-3*_R^2*a^2-8*_R*c^3+8*_R*b*c+a^2*c)*ln((c+(a*x+b)^(1/2))^(1/2)-_R),_R=RootOf(_Z^8-4*c*_Z^6+(6*c^2-2*b)*_Z^4-a^2*_Z^3+(-4*c^3+4*b*c)*_Z^2+a^2*c*_Z+c^4-2*b*c^2+b^2))","B"
2410,1,149,12,1.658000," ","int(1/(x^2-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-4 a \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 c \,\textit{\_Z}^{6}+\left(6 c^{2}-2 b \right) \textit{\_Z}^{4}-a^{2} \textit{\_Z}^{3}+\left(-4 c^{3}+4 b c \right) \textit{\_Z}^{2}+a^{2} c \textit{\_Z} +c^{4}-2 b \,c^{2}+b^{2}\right)}{\sum}\frac{\left(-\textit{\_R}^{3}+\textit{\_R} c \right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{8 \textit{\_R}^{7}-24 \textit{\_R}^{5} c +24 \textit{\_R}^{3} c^{2}-8 \textit{\_R}^{3} b -3 \textit{\_R}^{2} a^{2}-8 \textit{\_R} \,c^{3}+8 \textit{\_R} b c +a^{2} c}\right)$&$149$\\ default&$\text{Expression too large to display}$&$7120$\\ \hline \end{longtable}"," ",0,"-4*a*sum((-_R^3+_R*c)/(8*_R^7-24*_R^5*c+24*_R^3*c^2-8*_R^3*b-3*_R^2*a^2-8*_R*c^3+8*_R*b*c+a^2*c)*ln((c+(a*x+b)^(1/2))^(1/2)-_R),_R=RootOf(_Z^8-4*c*_Z^6+(6*c^2-2*b)*_Z^4-a^2*_Z^3+(-4*c^3+4*b*c)*_Z^2+a^2*c*_Z+c^4-2*b*c^2+b^2))","B"
2411,0,0,151,0.034000," ","int(1/(a^2*x^2-b)^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(2/3),x)","\[\int \frac{1}{\sqrt{a^{2} x^{2}-b}\, \left(c +\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}}\right)^{\frac{2}{3}}}\, dx\]"," ",0,"int(1/(a^2*x^2-b)^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(2/3),x)","F"
2412,0,0,151,0.034000," ","int(1/(a^2*x^2-b)^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3),x)","\[\int \frac{1}{\sqrt{a^{2} x^{2}-b}\, \left(c +\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(a^2*x^2-b)^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3),x)","F"
2413,1,538,155,11.371000," ","int(1/(-3*x^2+1)^(1/3)/(x^2-3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(\frac{-192 \left(-3 x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-3\right) \RootOf \left(4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}-3\right)+48 \textit{\_Z}^{2}+1\right)^{2} x -8 \left(-3 x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-3\right)^{2} \RootOf \left(4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}-3\right)+48 \textit{\_Z}^{2}+1\right) x +384 \RootOf \left(4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}-3\right)+48 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}-3\right) x +16 \RootOf \left(4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}-3\right)+48 \textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{2}-3\right)^{2} x +12 \RootOf \left(4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}-3\right)+48 \textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{2}-3\right) x^{2}+24 \left(-3 x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}-3\right)+48 \textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{2}-3\right)+6 \left(-3 x^{2}+1\right)^{\frac{2}{3}}+12 \RootOf \left(4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}-3\right)+48 \textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{2}-3\right)+96 \RootOf \left(4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}-3\right)+48 \textit{\_Z}^{2}+1\right) x +4 \RootOf \left(\textit{\_Z}^{2}-3\right) x +3 x^{2}+3}{x^{2}-3}\right)}{12}-\frac{\ln \left(\frac{-48 \left(-3 x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}-3\right)+48 \textit{\_Z}^{2}+1\right) x -2 \left(-3 x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-3\right) x +6 \left(-3 x^{2}+1\right)^{\frac{2}{3}}-96 \RootOf \left(4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}-3\right)+48 \textit{\_Z}^{2}+1\right) x -4 \RootOf \left(\textit{\_Z}^{2}-3\right) x -3 x^{2}+6 \left(-3 x^{2}+1\right)^{\frac{1}{3}}-3}{x^{2}-3}\right) \RootOf \left(\textit{\_Z}^{2}-3\right)}{12}-\ln \left(\frac{-48 \left(-3 x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}-3\right)+48 \textit{\_Z}^{2}+1\right) x -2 \left(-3 x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{2}-3\right) x +6 \left(-3 x^{2}+1\right)^{\frac{2}{3}}-96 \RootOf \left(4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}-3\right)+48 \textit{\_Z}^{2}+1\right) x -4 \RootOf \left(\textit{\_Z}^{2}-3\right) x -3 x^{2}+6 \left(-3 x^{2}+1\right)^{\frac{1}{3}}-3}{x^{2}-3}\right) \RootOf \left(4 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}-3\right)+48 \textit{\_Z}^{2}+1\right)$&$538$\\ \hline \end{longtable}"," ",0,"-1/12*RootOf(_Z^2-3)*ln((-192*(-3*x^2+1)^(1/3)*RootOf(_Z^2-3)*RootOf(4*_Z*RootOf(_Z^2-3)+48*_Z^2+1)^2*x-8*(-3*x^2+1)^(1/3)*RootOf(_Z^2-3)^2*RootOf(4*_Z*RootOf(_Z^2-3)+48*_Z^2+1)*x+384*RootOf(4*_Z*RootOf(_Z^2-3)+48*_Z^2+1)^2*RootOf(_Z^2-3)*x+16*RootOf(4*_Z*RootOf(_Z^2-3)+48*_Z^2+1)*RootOf(_Z^2-3)^2*x+12*RootOf(4*_Z*RootOf(_Z^2-3)+48*_Z^2+1)*RootOf(_Z^2-3)*x^2+24*(-3*x^2+1)^(1/3)*RootOf(4*_Z*RootOf(_Z^2-3)+48*_Z^2+1)*RootOf(_Z^2-3)+6*(-3*x^2+1)^(2/3)+12*RootOf(4*_Z*RootOf(_Z^2-3)+48*_Z^2+1)*RootOf(_Z^2-3)+96*RootOf(4*_Z*RootOf(_Z^2-3)+48*_Z^2+1)*x+4*RootOf(_Z^2-3)*x+3*x^2+3)/(x^2-3))-1/12*ln((-48*(-3*x^2+1)^(1/3)*RootOf(4*_Z*RootOf(_Z^2-3)+48*_Z^2+1)*x-2*(-3*x^2+1)^(1/3)*RootOf(_Z^2-3)*x+6*(-3*x^2+1)^(2/3)-96*RootOf(4*_Z*RootOf(_Z^2-3)+48*_Z^2+1)*x-4*RootOf(_Z^2-3)*x-3*x^2+6*(-3*x^2+1)^(1/3)-3)/(x^2-3))*RootOf(_Z^2-3)-ln((-48*(-3*x^2+1)^(1/3)*RootOf(4*_Z*RootOf(_Z^2-3)+48*_Z^2+1)*x-2*(-3*x^2+1)^(1/3)*RootOf(_Z^2-3)*x+6*(-3*x^2+1)^(2/3)-96*RootOf(4*_Z*RootOf(_Z^2-3)+48*_Z^2+1)*x-4*RootOf(_Z^2-3)*x-3*x^2+6*(-3*x^2+1)^(1/3)-3)/(x^2-3))*RootOf(4*_Z*RootOf(_Z^2-3)+48*_Z^2+1)","C"
2414,0,0,152,0.135000," ","int((-a+x)/(x^2*(-a+x))^(1/3)/(a^2*d-2*a*d*x+(-1+d)*x^2),x)","\[\int \frac{-a +x}{\left(x^{2} \left(-a +x \right)\right)^{\frac{1}{3}} \left(a^{2} d -2 a d x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((-a+x)/(x^2*(-a+x))^(1/3)/(a^2*d-2*a*d*x+(-1+d)*x^2),x)","F"
2415,0,0,150,0.013000," ","int((2*x^8-a*x^4+b)/(a*x^4-b)^(1/4)/(3*a*x^4+b),x)","\[\int \frac{2 x^{8}-a \,x^{4}+b}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(3 a \,x^{4}+b \right)}\, dx\]"," ",0,"int((2*x^8-a*x^4+b)/(a*x^4-b)^(1/4)/(3*a*x^4+b),x)","F"
2416,0,0,180,180.000000," ","int((c*x^2+d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{c \,x^{2}+d}{\sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int((c*x^2+d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","F"
2417,0,0,175,0.013000," ","int((a*x^4+b*x^3)^(1/4)*(d*x^8-c)/x^4,x)","\[\int \frac{\left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}} \left(d \,x^{8}-c \right)}{x^{4}}\, dx\]"," ",0,"int((a*x^4+b*x^3)^(1/4)*(d*x^8-c)/x^4,x)","F"
2418,0,0,158,0.033000," ","int((a*x^2+b^2)^(5/2)/(b+(a*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{\left(a \,x^{2}+b^{2}\right)^{\frac{5}{2}}}{\sqrt{b +\sqrt{a \,x^{2}+b^{2}}}}\, dx\]"," ",0,"int((a*x^2+b^2)^(5/2)/(b+(a*x^2+b^2)^(1/2))^(1/2),x)","F"
2419,0,0,149,0.011000," ","int((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2),x)","\[\int \sqrt{x +\sqrt{x^{2}+1}}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2),x)","F"
2420,1,35837869,145,13.838000," ","int((_C3*x^2-_C4)*(3*_C3*x^2+3*_C4+x)/x/((_C3*x^2+_C0*x+_C4)/(_C3*x^2+_C1*x+_C4))^(1/2)/(_C3^2*x^4+2*_C3*_C4*x^2+_C4^2-x^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$35837869$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2421,0,0,148,0.059000," ","int((x^6+1)/(x^5+x)^(1/3)/(x^6-1),x)","\[\int \frac{x^{6}+1}{\left(x^{5}+x \right)^{\frac{1}{3}} \left(x^{6}-1\right)}\, dx\]"," ",0,"int((x^6+1)/(x^5+x)^(1/3)/(x^6-1),x)","F"
2422,1,15767,126,48.834000," ","int(1/x^2/(x^8-7*x^7+16*x^6-7*x^5-20*x^4+17*x^3+11*x^2-8*x-4)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$15767$\\ trager&$\text{Expression too large to display}$&$87802$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2423,1,131,158,0.198000," ","int((a^8*x^8+b^8)/(a^4*x^4+b^4)^(1/2)/(a^8*x^8-b^8),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(-\frac{\sqrt{2}\, x}{2 \sqrt{a^{4} x^{4}+b^{4}}}+\frac{\ln \left(-a b +\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{2 x}\right)}{8 a b}-\frac{\ln \left(a b +\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{2 x}\right)}{8 a b}+\frac{\arctan \left(\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{2 x a b}\right)}{4 a b}\right) \sqrt{2}}{2}$&$131$\\ default&$\frac{\sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, i\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}+b^{4}}}-\frac{b \left(-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 a^{2} b^{2} x^{2}+2 b^{4}\right) \sqrt{2}}{4 \sqrt{b^{4}}\, \sqrt{a^{4} x^{4}+b^{4}}}\right)}{4 \sqrt{b^{4}}}+\frac{a \sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, -i, \frac{\sqrt{-\frac{i a^{2}}{b^{2}}}}{\sqrt{\frac{i a^{2}}{b^{2}}}}\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, b \sqrt{a^{4} x^{4}+b^{4}}}\right)}{4 a}+\frac{b \left(-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 a^{2} b^{2} x^{2}+2 b^{4}\right) \sqrt{2}}{4 \sqrt{b^{4}}\, \sqrt{a^{4} x^{4}+b^{4}}}\right)}{4 \sqrt{b^{4}}}-\frac{a \sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, -i, \frac{\sqrt{-\frac{i a^{2}}{b^{2}}}}{\sqrt{\frac{i a^{2}}{b^{2}}}}\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, b \sqrt{a^{4} x^{4}+b^{4}}}\right)}{4 a}-b^{4} \left(\frac{x}{2 b^{4} \sqrt{\left(x^{4}+\frac{b^{4}}{a^{4}}\right) a^{4}}}+\frac{\sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, i\right)}{2 b^{4} \sqrt{\frac{i a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}+b^{4}}}\right)-\frac{\sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, i, \frac{\sqrt{-\frac{i a^{2}}{b^{2}}}}{\sqrt{\frac{i a^{2}}{b^{2}}}}\right)}{2 \sqrt{\frac{i a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}+b^{4}}}$&$595$\\ \hline \end{longtable}"," ",0,"1/2*(-1/2/(a^4*x^4+b^4)^(1/2)*2^(1/2)*x+1/8/a/b*ln(-a*b+1/2*(a^4*x^4+b^4)^(1/2)*2^(1/2)/x)-1/8/a/b*ln(a*b+1/2*(a^4*x^4+b^4)^(1/2)*2^(1/2)/x)+1/4/a/b*arctan(1/2*(a^4*x^4+b^4)^(1/2)*2^(1/2)/x/a/b))*2^(1/2)","A"
2424,1,403,46,0.156000," ","int((x+(1+x)^(1/2))^(1/2)/(x-(1+x)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{2 \left(\sqrt{5}+1\right) \sqrt{5}\, \left(\frac{\sqrt{\left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2+\sqrt{5}\right) \left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)+\sqrt{5}+1}}{2}+\frac{\left(2+\sqrt{5}\right) \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2+\sqrt{5}\right) \left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)+\sqrt{5}+1}\right)}{4}-\frac{\sqrt{\sqrt{5}+1}\, \arctanh \left(\frac{2 \sqrt{5}+2+\left(2+\sqrt{5}\right) \left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}{2 \sqrt{\sqrt{5}+1}\, \sqrt{\left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2+\sqrt{5}\right) \left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)+\sqrt{5}+1}}\right)}{2}\right)}{5}+\frac{2 \left(\sqrt{5}-1\right) \sqrt{5}\, \left(\frac{\sqrt{\left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2-\sqrt{5}\right) \left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)-\sqrt{5}+1}}{2}+\frac{\left(2-\sqrt{5}\right) \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2-\sqrt{5}\right) \left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)-\sqrt{5}+1}\right)}{4}+\frac{\left(-\sqrt{5}+1\right) \arctan \left(\frac{-2 \sqrt{5}+2+\left(2-\sqrt{5}\right) \left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}{2 \sqrt{\sqrt{5}-1}\, \sqrt{\left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2-\sqrt{5}\right) \left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)-\sqrt{5}+1}}\right)}{2 \sqrt{\sqrt{5}-1}}\right)}{5}$&$403$\\ default&$\frac{2 \left(\sqrt{5}+1\right) \sqrt{5}\, \left(\frac{\sqrt{\left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2+\sqrt{5}\right) \left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)+\sqrt{5}+1}}{2}+\frac{\left(2+\sqrt{5}\right) \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2+\sqrt{5}\right) \left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)+\sqrt{5}+1}\right)}{4}-\frac{\sqrt{\sqrt{5}+1}\, \arctanh \left(\frac{2 \sqrt{5}+2+\left(2+\sqrt{5}\right) \left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}{2 \sqrt{\sqrt{5}+1}\, \sqrt{\left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2+\sqrt{5}\right) \left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)+\sqrt{5}+1}}\right)}{2}\right)}{5}+\frac{2 \left(\sqrt{5}-1\right) \sqrt{5}\, \left(\frac{\sqrt{\left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2-\sqrt{5}\right) \left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)-\sqrt{5}+1}}{2}+\frac{\left(2-\sqrt{5}\right) \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2-\sqrt{5}\right) \left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)-\sqrt{5}+1}\right)}{4}+\frac{\left(-\sqrt{5}+1\right) \arctan \left(\frac{-2 \sqrt{5}+2+\left(2-\sqrt{5}\right) \left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}{2 \sqrt{\sqrt{5}-1}\, \sqrt{\left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2-\sqrt{5}\right) \left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)-\sqrt{5}+1}}\right)}{2 \sqrt{\sqrt{5}-1}}\right)}{5}$&$403$\\ \hline \end{longtable}"," ",0,"2/5*(5^(1/2)+1)*5^(1/2)*(1/2*(((1+x)^(1/2)-1/2*5^(1/2)-1/2)^2+(2+5^(1/2))*((1+x)^(1/2)-1/2*5^(1/2)-1/2)+5^(1/2)+1)^(1/2)+1/4*(2+5^(1/2))*ln(1/2+(1+x)^(1/2)+(((1+x)^(1/2)-1/2*5^(1/2)-1/2)^2+(2+5^(1/2))*((1+x)^(1/2)-1/2*5^(1/2)-1/2)+5^(1/2)+1)^(1/2))-1/2*(5^(1/2)+1)^(1/2)*arctanh(1/2*(2*5^(1/2)+2+(2+5^(1/2))*((1+x)^(1/2)-1/2*5^(1/2)-1/2))/(5^(1/2)+1)^(1/2)/(((1+x)^(1/2)-1/2*5^(1/2)-1/2)^2+(2+5^(1/2))*((1+x)^(1/2)-1/2*5^(1/2)-1/2)+5^(1/2)+1)^(1/2)))+2/5*(5^(1/2)-1)*5^(1/2)*(1/2*(((1+x)^(1/2)+1/2*5^(1/2)-1/2)^2+(2-5^(1/2))*((1+x)^(1/2)+1/2*5^(1/2)-1/2)-5^(1/2)+1)^(1/2)+1/4*(2-5^(1/2))*ln(1/2+(1+x)^(1/2)+(((1+x)^(1/2)+1/2*5^(1/2)-1/2)^2+(2-5^(1/2))*((1+x)^(1/2)+1/2*5^(1/2)-1/2)-5^(1/2)+1)^(1/2))+1/2*(-5^(1/2)+1)/(5^(1/2)-1)^(1/2)*arctan(1/2*(-2*5^(1/2)+2+(2-5^(1/2))*((1+x)^(1/2)+1/2*5^(1/2)-1/2))/(5^(1/2)-1)^(1/2)/(((1+x)^(1/2)+1/2*5^(1/2)-1/2)^2+(2-5^(1/2))*((1+x)^(1/2)+1/2*5^(1/2)-1/2)-5^(1/2)+1)^(1/2)))","B"
2425,1,403,46,0.149000," ","int((x+(1+x)^(1/2))^(1/2)/(x-(1+x)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{2 \left(\sqrt{5}+1\right) \sqrt{5}\, \left(\frac{\sqrt{\left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2+\sqrt{5}\right) \left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)+\sqrt{5}+1}}{2}+\frac{\left(2+\sqrt{5}\right) \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2+\sqrt{5}\right) \left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)+\sqrt{5}+1}\right)}{4}-\frac{\sqrt{\sqrt{5}+1}\, \arctanh \left(\frac{2 \sqrt{5}+2+\left(2+\sqrt{5}\right) \left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}{2 \sqrt{\sqrt{5}+1}\, \sqrt{\left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2+\sqrt{5}\right) \left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)+\sqrt{5}+1}}\right)}{2}\right)}{5}+\frac{2 \left(\sqrt{5}-1\right) \sqrt{5}\, \left(\frac{\sqrt{\left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2-\sqrt{5}\right) \left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)-\sqrt{5}+1}}{2}+\frac{\left(2-\sqrt{5}\right) \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2-\sqrt{5}\right) \left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)-\sqrt{5}+1}\right)}{4}+\frac{\left(-\sqrt{5}+1\right) \arctan \left(\frac{-2 \sqrt{5}+2+\left(2-\sqrt{5}\right) \left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}{2 \sqrt{\sqrt{5}-1}\, \sqrt{\left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2-\sqrt{5}\right) \left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)-\sqrt{5}+1}}\right)}{2 \sqrt{\sqrt{5}-1}}\right)}{5}$&$403$\\ default&$\frac{2 \left(\sqrt{5}+1\right) \sqrt{5}\, \left(\frac{\sqrt{\left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2+\sqrt{5}\right) \left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)+\sqrt{5}+1}}{2}+\frac{\left(2+\sqrt{5}\right) \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2+\sqrt{5}\right) \left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)+\sqrt{5}+1}\right)}{4}-\frac{\sqrt{\sqrt{5}+1}\, \arctanh \left(\frac{2 \sqrt{5}+2+\left(2+\sqrt{5}\right) \left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}{2 \sqrt{\sqrt{5}+1}\, \sqrt{\left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2+\sqrt{5}\right) \left(\sqrt{1+x}-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)+\sqrt{5}+1}}\right)}{2}\right)}{5}+\frac{2 \left(\sqrt{5}-1\right) \sqrt{5}\, \left(\frac{\sqrt{\left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2-\sqrt{5}\right) \left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)-\sqrt{5}+1}}{2}+\frac{\left(2-\sqrt{5}\right) \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{\left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2-\sqrt{5}\right) \left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)-\sqrt{5}+1}\right)}{4}+\frac{\left(-\sqrt{5}+1\right) \arctan \left(\frac{-2 \sqrt{5}+2+\left(2-\sqrt{5}\right) \left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)}{2 \sqrt{\sqrt{5}-1}\, \sqrt{\left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}+\left(2-\sqrt{5}\right) \left(\sqrt{1+x}+\frac{\sqrt{5}}{2}-\frac{1}{2}\right)-\sqrt{5}+1}}\right)}{2 \sqrt{\sqrt{5}-1}}\right)}{5}$&$403$\\ \hline \end{longtable}"," ",0,"2/5*(5^(1/2)+1)*5^(1/2)*(1/2*(((1+x)^(1/2)-1/2*5^(1/2)-1/2)^2+(2+5^(1/2))*((1+x)^(1/2)-1/2*5^(1/2)-1/2)+5^(1/2)+1)^(1/2)+1/4*(2+5^(1/2))*ln(1/2+(1+x)^(1/2)+(((1+x)^(1/2)-1/2*5^(1/2)-1/2)^2+(2+5^(1/2))*((1+x)^(1/2)-1/2*5^(1/2)-1/2)+5^(1/2)+1)^(1/2))-1/2*(5^(1/2)+1)^(1/2)*arctanh(1/2*(2*5^(1/2)+2+(2+5^(1/2))*((1+x)^(1/2)-1/2*5^(1/2)-1/2))/(5^(1/2)+1)^(1/2)/(((1+x)^(1/2)-1/2*5^(1/2)-1/2)^2+(2+5^(1/2))*((1+x)^(1/2)-1/2*5^(1/2)-1/2)+5^(1/2)+1)^(1/2)))+2/5*(5^(1/2)-1)*5^(1/2)*(1/2*(((1+x)^(1/2)+1/2*5^(1/2)-1/2)^2+(2-5^(1/2))*((1+x)^(1/2)+1/2*5^(1/2)-1/2)-5^(1/2)+1)^(1/2)+1/4*(2-5^(1/2))*ln(1/2+(1+x)^(1/2)+(((1+x)^(1/2)+1/2*5^(1/2)-1/2)^2+(2-5^(1/2))*((1+x)^(1/2)+1/2*5^(1/2)-1/2)-5^(1/2)+1)^(1/2))+1/2*(-5^(1/2)+1)/(5^(1/2)-1)^(1/2)*arctan(1/2*(-2*5^(1/2)+2+(2-5^(1/2))*((1+x)^(1/2)+1/2*5^(1/2)-1/2))/(5^(1/2)-1)^(1/2)/(((1+x)^(1/2)+1/2*5^(1/2)-1/2)^2+(2-5^(1/2))*((1+x)^(1/2)+1/2*5^(1/2)-1/2)-5^(1/2)+1)^(1/2)))","B"
2426,0,0,64,180.000000," ","int((c*x^2+d)*(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)/(c*x^2-d),x)","\[\int \frac{\left(c \,x^{2}+d \right) \sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}{c \,x^{2}-d}\, dx\]"," ",0,"int((c*x^2+d)*(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)/(c*x^2-d),x)","F"
2427,0,0,64,180.000000," ","int((c*x^2+d)*(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)/(c*x^2-d),x)","\[\int \frac{\left(c \,x^{2}+d \right) \sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}{c \,x^{2}-d}\, dx\]"," ",0,"int((c*x^2+d)*(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)/(c*x^2-d),x)","F"
2428,0,0,172,0.049000," ","int((-a/b^2+a^2*x^2/b^2)^(1/2)/x/(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{-\frac{a}{b^{2}}+\frac{a^{2} x^{2}}{b^{2}}}}{x \sqrt{a \,x^{2}+b x \sqrt{-\frac{a}{b^{2}}+\frac{a^{2} x^{2}}{b^{2}}}}}\, dx\]"," ",0,"int((-a/b^2+a^2*x^2/b^2)^(1/2)/x/(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2),x)","F"
2429,1,137,71,0.194000," ","int((x^2-1)/(x^2+1)/(1+(1+x)^(1/2))^(1/2)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}-\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}-\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+14 \textit{\_Z}^{8}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{4}+2\right)}{\sum}\frac{\left(\textit{\_R}^{4}-2 \textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+7 \textit{\_R}^{7}+3 \textit{\_R}^{5}-2 \textit{\_R}^{3}}\right)$&$137$\\ default&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}-\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}-\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+14 \textit{\_Z}^{8}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{4}+2\right)}{\sum}\frac{\left(\textit{\_R}^{4}-2 \textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+7 \textit{\_R}^{7}+3 \textit{\_R}^{5}-2 \textit{\_R}^{3}}\right)$&$137$\\ \hline \end{longtable}"," ",0,"8/5*(1+(1+(1+x)^(1/2))^(1/2))^(5/2)-16/3*(1+(1+(1+x)^(1/2))^(1/2))^(3/2)-sum((_R^4-2*_R^2)/(_R^15-7*_R^13+18*_R^11-20*_R^9+7*_R^7+3*_R^5-2*_R^3)*ln((1+(1+(1+x)^(1/2))^(1/2))^(1/2)-_R),_R=RootOf(_Z^16-8*_Z^14+24*_Z^12-32*_Z^10+14*_Z^8+8*_Z^6-8*_Z^4+2))","A"
2430,1,137,71,0.187000," ","int((x^2-1)/(x^2+1)/(1+(1+x)^(1/2))^(1/2)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}-\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}-\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+14 \textit{\_Z}^{8}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{4}+2\right)}{\sum}\frac{\left(\textit{\_R}^{4}-2 \textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+7 \textit{\_R}^{7}+3 \textit{\_R}^{5}-2 \textit{\_R}^{3}}\right)$&$137$\\ default&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}-\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}-\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+14 \textit{\_Z}^{8}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{4}+2\right)}{\sum}\frac{\left(\textit{\_R}^{4}-2 \textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+7 \textit{\_R}^{7}+3 \textit{\_R}^{5}-2 \textit{\_R}^{3}}\right)$&$137$\\ \hline \end{longtable}"," ",0,"8/5*(1+(1+(1+x)^(1/2))^(1/2))^(5/2)-16/3*(1+(1+(1+x)^(1/2))^(1/2))^(3/2)-sum((_R^4-2*_R^2)/(_R^15-7*_R^13+18*_R^11-20*_R^9+7*_R^7+3*_R^5-2*_R^3)*ln((1+(1+(1+x)^(1/2))^(1/2))^(1/2)-_R),_R=RootOf(_Z^16-8*_Z^14+24*_Z^12-32*_Z^10+14*_Z^8+8*_Z^6-8*_Z^4+2))","A"
2431,0,0,152,0.011000," ","int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2),x)","\[\int \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2),x)","F"
2432,1,2122,146,18.482000," ","int((2+3*x)/(3*x^2+4)^(1/3)/(9*x^2+52*x-12),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2122$\\ \hline \end{longtable}"," ",0,"RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*ln((788123448*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)^2*RootOf(_Z^3-196)^2*x^3+12185712*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)^3*x^3+14011083520*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)^2*RootOf(_Z^3-196)^2*x^2+237846000*(3*x^2+4)^(2/3)*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)^2*x+216634880*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)^3*x^2+26270781600*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)^2*RootOf(_Z^3-196)^2*x-792820000*(3*x^2+4)^(2/3)*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)^2-713538000*(3*x^2+4)^(1/3)*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)*x^2+406190400*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)^3*x-13674087*(3*x^2+4)^(1/3)*RootOf(_Z^3-196)^2*x^2+4756920000*(3*x^2+4)^(1/3)*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)*x+1793382948*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*x^3+91160580*(3*x^2+4)^(1/3)*RootOf(_Z^3-196)^2*x+27728712*RootOf(_Z^3-196)*x^3-7928200000*(3*x^2+4)^(1/3)*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)-35097406792*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*x^2+893373684*(3*x^2+4)^(2/3)*x-151934300*(3*x^2+4)^(1/3)*RootOf(_Z^3-196)^2-542664848*RootOf(_Z^3-196)*x^2+59779431600*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*x-2977912280*(3*x^2+4)^(2/3)+924290400*RootOf(_Z^3-196)*x-89306360416*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)-1380826304*RootOf(_Z^3-196))/(9*x-2)/(6+x)^2)-1/196*ln((788123448*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)^2*RootOf(_Z^3-196)^2*x^3-8164674*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)^3*x^3+14011083520*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)^2*RootOf(_Z^3-196)^2*x^2-237846000*(3*x^2+4)^(2/3)*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)^2*x-145149760*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)^3*x^2+26270781600*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)^2*RootOf(_Z^3-196)^2*x+792820000*(3*x^2+4)^(2/3)*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)^2+713538000*(3*x^2+4)^(1/3)*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)*x^2-272155800*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)^3*x-10033587*(3*x^2+4)^(1/3)*RootOf(_Z^3-196)^2*x^2-4756920000*(3*x^2+4)^(1/3)*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)*x-1005259500*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*x^3+66890580*(3*x^2+4)^(1/3)*RootOf(_Z^3-196)^2*x+10414125*RootOf(_Z^3-196)*x^3+7928200000*(3*x^2+4)^(1/3)*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)+49108490312*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*x^2+655527684*(3*x^2+4)^(2/3)*x-111484300*(3*x^2+4)^(1/3)*RootOf(_Z^3-196)^2-508746206*RootOf(_Z^3-196)*x^2-33508650000*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*x-2185092280*(3*x^2+4)^(2/3)+347137500*RootOf(_Z^3-196)*x+89306360416*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)-925181608*RootOf(_Z^3-196))/(9*x-2)/(6+x)^2)*RootOf(_Z^3-196)-ln((788123448*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)^2*RootOf(_Z^3-196)^2*x^3-8164674*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)^3*x^3+14011083520*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)^2*RootOf(_Z^3-196)^2*x^2-237846000*(3*x^2+4)^(2/3)*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)^2*x-145149760*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)^3*x^2+26270781600*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)^2*RootOf(_Z^3-196)^2*x+792820000*(3*x^2+4)^(2/3)*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)^2+713538000*(3*x^2+4)^(1/3)*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)*x^2-272155800*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)^3*x-10033587*(3*x^2+4)^(1/3)*RootOf(_Z^3-196)^2*x^2-4756920000*(3*x^2+4)^(1/3)*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)*x-1005259500*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*x^3+66890580*(3*x^2+4)^(1/3)*RootOf(_Z^3-196)^2*x+10414125*RootOf(_Z^3-196)*x^3+7928200000*(3*x^2+4)^(1/3)*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*RootOf(_Z^3-196)+49108490312*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*x^2+655527684*(3*x^2+4)^(2/3)*x-111484300*(3*x^2+4)^(1/3)*RootOf(_Z^3-196)^2-508746206*RootOf(_Z^3-196)*x^2-33508650000*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)*x-2185092280*(3*x^2+4)^(2/3)+347137500*RootOf(_Z^3-196)*x+89306360416*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)-925181608*RootOf(_Z^3-196))/(9*x-2)/(6+x)^2)*RootOf(RootOf(_Z^3-196)^2+196*_Z*RootOf(_Z^3-196)+38416*_Z^2)","C"
2433,1,143,185,0.296000," ","int((a*x^2+b*x+c)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(2 a x +b \right) \left(a \,x^{2}+b x +c \right)^{\frac{5}{2}}}{12 a}+\frac{5 \left(4 a c -b^{2}\right) \left(\frac{\left(2 a x +b \right) \left(a \,x^{2}+b x +c \right)^{\frac{3}{2}}}{8 a}+\frac{3 \left(4 a c -b^{2}\right) \left(\frac{\left(2 a x +b \right) \sqrt{a \,x^{2}+b x +c}}{4 a}+\frac{\left(4 a c -b^{2}\right) \ln \left(\frac{\frac{b}{2}+a x}{\sqrt{a}}+\sqrt{a \,x^{2}+b x +c}\right)}{8 a^{\frac{3}{2}}}\right)}{16 a}\right)}{24 a}$&$143$\\ risch&$\frac{\sqrt{a \,x^{2}+b x +c}\, \left(256 a^{5} x^{5}+640 a^{4} b \,x^{4}+832 a^{4} c \,x^{3}+432 a^{3} b^{2} x^{3}+1248 a^{3} b c \,x^{2}+8 a^{2} b^{3} x^{2}+1056 a^{3} c^{2} x +96 a^{2} b^{2} c x -10 a \,b^{4} x +528 a^{2} b \,c^{2}-160 a \,b^{3} c +15 b^{5}\right)}{1536 a^{3}}+\frac{5 \ln \left(\frac{\frac{b}{2}+a x}{\sqrt{a}}+\sqrt{a \,x^{2}+b x +c}\right) c^{3}}{16 \sqrt{a}}-\frac{15 \ln \left(\frac{\frac{b}{2}+a x}{\sqrt{a}}+\sqrt{a \,x^{2}+b x +c}\right) b^{2} c^{2}}{64 a^{\frac{3}{2}}}+\frac{15 \ln \left(\frac{\frac{b}{2}+a x}{\sqrt{a}}+\sqrt{a \,x^{2}+b x +c}\right) b^{4} c}{256 a^{\frac{5}{2}}}-\frac{5 \ln \left(\frac{\frac{b}{2}+a x}{\sqrt{a}}+\sqrt{a \,x^{2}+b x +c}\right) b^{6}}{1024 a^{\frac{7}{2}}}$&$261$\\ \hline \end{longtable}"," ",0,"1/12*(2*a*x+b)/a*(a*x^2+b*x+c)^(5/2)+5/24*(4*a*c-b^2)/a*(1/8*(2*a*x+b)/a*(a*x^2+b*x+c)^(3/2)+3/16*(4*a*c-b^2)/a*(1/4*(2*a*x+b)*(a*x^2+b*x+c)^(1/2)/a+1/8*(4*a*c-b^2)/a^(3/2)*ln((1/2*b+a*x)/a^(1/2)+(a*x^2+b*x+c)^(1/2))))","A"
2434,1,3552,137,14.080000," ","int((x^8-x^4+1)/x^2/(x^4-1)^(3/4)/(x^8-x^4-1),x)","\[\text{output too large to display}\]"," ",0,"-(x^4-1)^(1/4)/x+(-1/10*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*ln(-(32000*RootOf(6400*_Z^4-80*_Z^2-1)^4*x^12-1600*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^12+160*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*RootOf(6400*_Z^4-80*_Z^2-1)^2*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9-64000*RootOf(6400*_Z^4-80*_Z^2-1)^4*x^8+15*x^12-6*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9-800*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^6+3600*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^8+480*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*RootOf(6400*_Z^4-80*_Z^2-1)^2*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3-320*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*RootOf(6400*_Z^4-80*_Z^2-1)^2*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5+32000*RootOf(6400*_Z^4-80*_Z^2-1)^4*x^4+20*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6-35*x^8-8*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3+12*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5+800*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^2-2400*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^4+160*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*RootOf(6400*_Z^4-80*_Z^2-1)^2*(x^12-3*x^8+3*x^4-1)^(1/4)*x-20*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2+25*x^4-6*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*(x^12-3*x^8+3*x^4-1)^(1/4)*x+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)/(320*RootOf(6400*_Z^4-80*_Z^2-1)^3*x^2-12*RootOf(6400*_Z^4-80*_Z^2-1)*x^2+1)/(320*RootOf(6400*_Z^4-80*_Z^2-1)^3*x^2-12*RootOf(6400*_Z^4-80*_Z^2-1)*x^2-1)/(-1+x)^2/(1+x)^2/(x^2+1)^2)-2*RootOf(6400*_Z^4-80*_Z^2-1)*ln(-(3200*RootOf(6400*_Z^4-80*_Z^2-1)^4*x^12+80*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^12-320*RootOf(6400*_Z^4-80*_Z^2-1)^3*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9-6400*RootOf(6400*_Z^4-80*_Z^2-1)^4*x^8-8*RootOf(6400*_Z^4-80*_Z^2-1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9+80*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^6-200*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^8-960*RootOf(6400*_Z^4-80*_Z^2-1)^3*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3+640*RootOf(6400*_Z^4-80*_Z^2-1)^3*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5+3200*RootOf(6400*_Z^4-80*_Z^2-1)^4*x^4+(x^12-3*x^8+3*x^4-1)^(1/2)*x^6-4*RootOf(6400*_Z^4-80*_Z^2-1)*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3+16*RootOf(6400*_Z^4-80*_Z^2-1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5-80*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^2+160*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^4-320*RootOf(6400*_Z^4-80*_Z^2-1)^3*(x^12-3*x^8+3*x^4-1)^(1/4)*x-(x^12-3*x^8+3*x^4-1)^(1/2)*x^2-8*RootOf(6400*_Z^4-80*_Z^2-1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x-40*RootOf(6400*_Z^4-80*_Z^2-1)^2)/(80*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^4+1)/(-1+x)^2/(1+x)^2/(x^2+1)^2)-8*RootOf(6400*_Z^4-80*_Z^2-1)^2*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*ln((16000*RootOf(6400*_Z^4-80*_Z^2-1)^4*x^12+400*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^12-240*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*RootOf(6400*_Z^4-80*_Z^2-1)^2*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9-32000*RootOf(6400*_Z^4-80*_Z^2-1)^4*x^8-RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9-400*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^6-1000*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^8+320*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*RootOf(6400*_Z^4-80*_Z^2-1)^2*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3+480*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*RootOf(6400*_Z^4-80*_Z^2-1)^2*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5+16000*RootOf(6400*_Z^4-80*_Z^2-1)^4*x^4-5*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6+3*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3+2*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5+400*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^2+800*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^4-240*RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*RootOf(6400*_Z^4-80*_Z^2-1)^2*(x^12-3*x^8+3*x^4-1)^(1/4)*x+5*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2-RootOf(_Z^2+400*RootOf(6400*_Z^4-80*_Z^2-1)^2-5)*(x^12-3*x^8+3*x^4-1)^(1/4)*x-200*RootOf(6400*_Z^4-80*_Z^2-1)^2)/(80*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^4+1)/(-1+x)^2/(1+x)^2/(x^2+1)^2)+160*ln((6400*RootOf(6400*_Z^4-80*_Z^2-1)^4*x^12-320*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^12+1920*RootOf(6400*_Z^4-80*_Z^2-1)^3*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9-12800*RootOf(6400*_Z^4-80*_Z^2-1)^4*x^8+3*x^12-32*RootOf(6400*_Z^4-80*_Z^2-1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9+160*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^6+720*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^8-2560*RootOf(6400*_Z^4-80*_Z^2-1)^3*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3-3840*RootOf(6400*_Z^4-80*_Z^2-1)^3*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5+6400*RootOf(6400*_Z^4-80*_Z^2-1)^4*x^4-4*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6-7*x^8+56*RootOf(6400*_Z^4-80*_Z^2-1)*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3+64*RootOf(6400*_Z^4-80*_Z^2-1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5-160*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^2-480*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^4+1920*RootOf(6400*_Z^4-80*_Z^2-1)^3*(x^12-3*x^8+3*x^4-1)^(1/4)*x+4*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2+5*x^4-32*RootOf(6400*_Z^4-80*_Z^2-1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x+80*RootOf(6400*_Z^4-80*_Z^2-1)^2-1)/(320*RootOf(6400*_Z^4-80*_Z^2-1)^3*x^2-12*RootOf(6400*_Z^4-80*_Z^2-1)*x^2+1)/(320*RootOf(6400*_Z^4-80*_Z^2-1)^3*x^2-12*RootOf(6400*_Z^4-80*_Z^2-1)*x^2-1)/(-1+x)^2/(1+x)^2/(x^2+1)^2)*RootOf(6400*_Z^4-80*_Z^2-1)^3-2*ln((6400*RootOf(6400*_Z^4-80*_Z^2-1)^4*x^12-320*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^12+1920*RootOf(6400*_Z^4-80*_Z^2-1)^3*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9-12800*RootOf(6400*_Z^4-80*_Z^2-1)^4*x^8+3*x^12-32*RootOf(6400*_Z^4-80*_Z^2-1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^9+160*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^6+720*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^8-2560*RootOf(6400*_Z^4-80*_Z^2-1)^3*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3-3840*RootOf(6400*_Z^4-80*_Z^2-1)^3*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5+6400*RootOf(6400*_Z^4-80*_Z^2-1)^4*x^4-4*(x^12-3*x^8+3*x^4-1)^(1/2)*x^6-7*x^8+56*RootOf(6400*_Z^4-80*_Z^2-1)*(x^12-3*x^8+3*x^4-1)^(3/4)*x^3+64*RootOf(6400*_Z^4-80*_Z^2-1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x^5-160*(x^12-3*x^8+3*x^4-1)^(1/2)*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^2-480*RootOf(6400*_Z^4-80*_Z^2-1)^2*x^4+1920*RootOf(6400*_Z^4-80*_Z^2-1)^3*(x^12-3*x^8+3*x^4-1)^(1/4)*x+4*(x^12-3*x^8+3*x^4-1)^(1/2)*x^2+5*x^4-32*RootOf(6400*_Z^4-80*_Z^2-1)*(x^12-3*x^8+3*x^4-1)^(1/4)*x+80*RootOf(6400*_Z^4-80*_Z^2-1)^2-1)/(320*RootOf(6400*_Z^4-80*_Z^2-1)^3*x^2-12*RootOf(6400*_Z^4-80*_Z^2-1)*x^2+1)/(320*RootOf(6400*_Z^4-80*_Z^2-1)^3*x^2-12*RootOf(6400*_Z^4-80*_Z^2-1)*x^2-1)/(-1+x)^2/(1+x)^2/(x^2+1)^2)*RootOf(6400*_Z^4-80*_Z^2-1))/(x^4-1)^(3/4)*((x^4-1)^3)^(1/4)","C"
2435,0,0,65,180.000000," ","int((c*x^2-d)*(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)/(c*x^2+d),x)","\[\int \frac{\left(c \,x^{2}-d \right) \sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}{c \,x^{2}+d}\, dx\]"," ",0,"int((c*x^2-d)*(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)/(c*x^2+d),x)","F"
2436,0,0,65,180.000000," ","int((c*x^2-d)*(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)/(c*x^2+d),x)","\[\int \frac{\left(c \,x^{2}-d \right) \sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}{c \,x^{2}+d}\, dx\]"," ",0,"int((c*x^2-d)*(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)/(c*x^2+d),x)","F"
2437,0,0,149,0.014000," ","int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x+(x^2+1)^(1/2))^(1/2),x)","F"
2438,1,2399,153,14.908000," ","int(1/x/(3*x^2-6*x+4)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2399$\\ \hline \end{longtable}"," ",0,"1/3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*ln(-(12*RootOf(_Z^3-2)*x^3-120*RootOf(_Z^3-2)*x^2+240*RootOf(_Z^3-2)*x+30*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3-300*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^2+600*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x-60*(3*x^2-6*x+4)^(2/3)-400*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)+20*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-80*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2-32*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3-160*RootOf(_Z^3-2)+48*(3*x^2-6*x+4)^(2/3)*RootOf(_Z^3-2)^2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x-48*RootOf(_Z^3-2)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*(3*x^2-6*x+4)^(1/3)*x^2+192*(3*x^2-6*x+4)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x+8*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3-60*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^2-24*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x^2-192*(3*x^2-6*x+4)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)-96*(3*x^2-6*x+4)^(2/3)*RootOf(_Z^3-2)^2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)-15*RootOf(_Z^3-2)^2*(3*x^2-6*x+4)^(1/3)*x^2+60*(3*x^2-6*x+4)^(1/3)*RootOf(_Z^3-2)^2*x-60*(3*x^2-6*x+4)^(1/3)*RootOf(_Z^3-2)^2+30*(3*x^2-6*x+4)^(2/3)*x+120*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x+48*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x)/x^3)-1/6*ln(-(-RootOf(_Z^3-2)*x^3+24*RootOf(_Z^3-2)*x^2-48*RootOf(_Z^3-2)*x-10*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3+240*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^2-480*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x+36*(3*x^2-6*x+4)^(2/3)+320*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)+20*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-80*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2-8*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3+32*RootOf(_Z^3-2)-48*(3*x^2-6*x+4)^(2/3)*RootOf(_Z^3-2)^2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x+48*RootOf(_Z^3-2)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*(3*x^2-6*x+4)^(1/3)*x^2-192*(3*x^2-6*x+4)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x+2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3-60*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^2-6*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x^2+192*(3*x^2-6*x+4)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)+96*(3*x^2-6*x+4)^(2/3)*RootOf(_Z^3-2)^2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)+9*RootOf(_Z^3-2)^2*(3*x^2-6*x+4)^(1/3)*x^2-36*(3*x^2-6*x+4)^(1/3)*RootOf(_Z^3-2)^2*x+36*(3*x^2-6*x+4)^(1/3)*RootOf(_Z^3-2)^2-18*(3*x^2-6*x+4)^(2/3)*x+120*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x+12*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x)/x^3)*RootOf(_Z^3-2)-1/3*ln(-(-RootOf(_Z^3-2)*x^3+24*RootOf(_Z^3-2)*x^2-48*RootOf(_Z^3-2)*x-10*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3+240*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^2-480*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x+36*(3*x^2-6*x+4)^(2/3)+320*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)+20*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-80*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2-8*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3+32*RootOf(_Z^3-2)-48*(3*x^2-6*x+4)^(2/3)*RootOf(_Z^3-2)^2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x+48*RootOf(_Z^3-2)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*(3*x^2-6*x+4)^(1/3)*x^2-192*(3*x^2-6*x+4)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x+2*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3-60*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^2-6*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x^2+192*(3*x^2-6*x+4)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)+96*(3*x^2-6*x+4)^(2/3)*RootOf(_Z^3-2)^2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)+9*RootOf(_Z^3-2)^2*(3*x^2-6*x+4)^(1/3)*x^2-36*(3*x^2-6*x+4)^(1/3)*RootOf(_Z^3-2)^2*x+36*(3*x^2-6*x+4)^(1/3)*RootOf(_Z^3-2)^2-18*(3*x^2-6*x+4)^(2/3)*x+120*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x+12*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x)/x^3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)","C"
2439,0,0,158,0.010000," ","int(x^2*(a*x^4+b*x^3)^(1/4)/(a*x-b),x)","\[\int \frac{x^{2} \left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}}{a x -b}\, dx\]"," ",0,"int(x^2*(a*x^4+b*x^3)^(1/4)/(a*x-b),x)","F"
2440,0,0,150,0.073000," ","int((x^6-1)/(x^5+x)^(1/3)/(x^6+1),x)","\[\int \frac{x^{6}-1}{\left(x^{5}+x \right)^{\frac{1}{3}} \left(x^{6}+1\right)}\, dx\]"," ",0,"int((x^6-1)/(x^5+x)^(1/3)/(x^6+1),x)","F"
2441,0,0,56,0.041000," ","int((a*x^8-2*x^4+b)/(a*x^4-b)^(1/4)/(2*a*x^8-2*x^4+b),x)","\[\int \frac{a \,x^{8}-2 x^{4}+b}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(2 a \,x^{8}-2 x^{4}+b \right)}\, dx\]"," ",0,"int((a*x^8-2*x^4+b)/(a*x^4-b)^(1/4)/(2*a*x^8-2*x^4+b),x)","F"
2442,0,0,56,0.003000," ","int((a*x^8-2*x^4+b)/(a*x^4-b)^(1/4)/(2*a*x^8-2*x^4+b),x)","\[\int \frac{a \,x^{8}-2 x^{4}+b}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(2 a \,x^{8}-2 x^{4}+b \right)}\, dx\]"," ",0,"int((a*x^8-2*x^4+b)/(a*x^4-b)^(1/4)/(2*a*x^8-2*x^4+b),x)","F"
2443,0,0,54,0.048000," ","int((2*a*x^8+c*x^4-b)/(a*x^4-b)^(1/4)/(a*x^8-c*x^4+b),x)","\[\int \frac{2 a \,x^{8}+c \,x^{4}-b}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(a \,x^{8}-c \,x^{4}+b \right)}\, dx\]"," ",0,"int((2*a*x^8+c*x^4-b)/(a*x^4-b)^(1/4)/(a*x^8-c*x^4+b),x)","F"
2444,0,0,54,0.001000," ","int((2*a*x^8+c*x^4-b)/(a*x^4-b)^(1/4)/(a*x^8-c*x^4+b),x)","\[\int \frac{2 a \,x^{8}+c \,x^{4}-b}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(a \,x^{8}-c \,x^{4}+b \right)}\, dx\]"," ",0,"int((2*a*x^8+c*x^4-b)/(a*x^4-b)^(1/4)/(a*x^8-c*x^4+b),x)","F"
2445,0,0,178,0.013000," ","int((a*x^4-b*x^3)^(1/4)*(c*x^8-d)/x^4,x)","\[\int \frac{\left(a \,x^{4}-b \,x^{3}\right)^{\frac{1}{4}} \left(c \,x^{8}-d \right)}{x^{4}}\, dx\]"," ",0,"int((a*x^4-b*x^3)^(1/4)*(c*x^8-d)/x^4,x)","F"
2446,1,31,155,0.050000," ","int((b+(a*x^2+b^2)^(1/2))^(1/2)/x^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\left(b^{2}\right)^{\frac{1}{4}} \sqrt{2}\, \hypergeom \left(\left[-\frac{5}{2}, -\frac{1}{4}, \frac{1}{4}\right], \left[-\frac{3}{2}, \frac{1}{2}\right], -\frac{x^{2} a}{b^{2}}\right)}{5 x^{5}}$&$31$\\ \hline \end{longtable}"," ",0,"-1/5*(b^2)^(1/4)*2^(1/2)/x^5*hypergeom([-5/2,-1/4,1/4],[-3/2,1/2],-x^2*a/b^2)","C"
2447,0,0,155,0.046000," ","int((b+(a*x^2+b^2)^(1/2))^(1/2)/x^6/(a*x^2+b^2)^(1/2),x)","\[\int \frac{\sqrt{b +\sqrt{a \,x^{2}+b^{2}}}}{x^{6} \sqrt{a \,x^{2}+b^{2}}}\, dx\]"," ",0,"int((b+(a*x^2+b^2)^(1/2))^(1/2)/x^6/(a*x^2+b^2)^(1/2),x)","F"
2448,1,93,156,0.191000," ","int((d+(c+(a*x+b)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\frac{8 \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{9}{2}}}{9}-\frac{24 d \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{7}{2}}}{7}+\frac{8 \left(3 d^{2}-c \right) \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{5}{2}}}{5}-\frac{8 \left(d^{2}-c \right) d \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{3}{2}}}{3}}{a}$&$93$\\ default&$\frac{\frac{8 \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{9}{2}}}{9}-\frac{24 d \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{7}{2}}}{7}+\frac{8 \left(3 d^{2}-c \right) \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{5}{2}}}{5}-\frac{8 \left(d^{2}-c \right) d \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{3}{2}}}{3}}{a}$&$93$\\ \hline \end{longtable}"," ",0,"2/a*(4/9*(d+(c+(a*x+b)^(1/2))^(1/2))^(9/2)-12/7*d*(d+(c+(a*x+b)^(1/2))^(1/2))^(7/2)+4/5*(3*d^2-c)*(d+(c+(a*x+b)^(1/2))^(1/2))^(5/2)-4/3*(d^2-c)*d*(d+(c+(a*x+b)^(1/2))^(1/2))^(3/2))","A"
2449,0,0,151,0.078000," ","int(1/(a*x^2-b)/(x^3-x)^(1/3),x)","\[\int \frac{1}{\left(a \,x^{2}-b \right) \left(x^{3}-x \right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(a*x^2-b)/(x^3-x)^(1/3),x)","F"
2450,1,2528,129,47.787000," ","int(1/x^3/(x^3-1)/(x^3+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$2528$\\ trager&$\text{Expression too large to display}$&$4920$\\ \hline \end{longtable}"," ",0,"3/40*(9*x^3+3*x^2-x+5)/x^2/(x^2*(1+x))^(1/3)+1/2*RootOf(729*_Z^6-216*_Z^3+64)*ln((-1215*RootOf(729*_Z^6-216*_Z^3+64)^5*(x^3+x^2)^(1/3)*x+216*RootOf(729*_Z^6-216*_Z^3+64)^4*x^2+324*(x^3+x^2)^(2/3)*RootOf(729*_Z^6-216*_Z^3+64)^3+108*RootOf(729*_Z^6-216*_Z^3+64)^4*x-216*RootOf(729*_Z^6-216*_Z^3+64)^2*(x^3+x^2)^(1/3)*x+352*RootOf(729*_Z^6-216*_Z^3+64)*x^2-256*(x^3+x^2)^(2/3)+176*RootOf(729*_Z^6-216*_Z^3+64)*x)/(27*RootOf(729*_Z^6-216*_Z^3+64)^3*x-54*RootOf(729*_Z^6-216*_Z^3+64)^3+16*x+24)/x)+27/16*ln(-(3645*RootOf(729*_Z^6-216*_Z^3+64)^6*x^2-7290*RootOf(729*_Z^6-216*_Z^3+64)^6*x+6804*RootOf(729*_Z^6-216*_Z^3+64)^4*(x^3+x^2)^(1/3)*x-4104*RootOf(729*_Z^6-216*_Z^3+64)^3*x^2+3024*RootOf(729*_Z^6-216*_Z^3+64)^2*(x^3+x^2)^(2/3)+648*RootOf(729*_Z^6-216*_Z^3+64)^3*x-2016*RootOf(729*_Z^6-216*_Z^3+64)*(x^3+x^2)^(1/3)*x+768*x^2+256*x)/(27*RootOf(729*_Z^6-216*_Z^3+64)^3*x-54*RootOf(729*_Z^6-216*_Z^3+64)^3+16*x+24)/x)*RootOf(729*_Z^6-216*_Z^3+64)^4-1/2*ln(-(3645*RootOf(729*_Z^6-216*_Z^3+64)^6*x^2-7290*RootOf(729*_Z^6-216*_Z^3+64)^6*x+6804*RootOf(729*_Z^6-216*_Z^3+64)^4*(x^3+x^2)^(1/3)*x-4104*RootOf(729*_Z^6-216*_Z^3+64)^3*x^2+3024*RootOf(729*_Z^6-216*_Z^3+64)^2*(x^3+x^2)^(2/3)+648*RootOf(729*_Z^6-216*_Z^3+64)^3*x-2016*RootOf(729*_Z^6-216*_Z^3+64)*(x^3+x^2)^(1/3)*x+768*x^2+256*x)/(27*RootOf(729*_Z^6-216*_Z^3+64)^3*x-54*RootOf(729*_Z^6-216*_Z^3+64)^3+16*x+24)/x)*RootOf(729*_Z^6-216*_Z^3+64)-3/4*RootOf(729*_Z^6-216*_Z^3+64)^2*ln((-2187*RootOf(729*_Z^6-216*_Z^3+64)^8*x^2+4374*RootOf(729*_Z^6-216*_Z^3+64)^8*x-3888*RootOf(729*_Z^6-216*_Z^3+64)^5*x^2+3240*RootOf(729*_Z^6-216*_Z^3+64)^5*x+6048*(x^3+x^2)^(2/3)*RootOf(729*_Z^6-216*_Z^3+64)^3-1536*x^2*RootOf(729*_Z^6-216*_Z^3+64)^2+2688*RootOf(729*_Z^6-216*_Z^3+64)*(x^3+x^2)^(1/3)*x-2304*x*RootOf(729*_Z^6-216*_Z^3+64)^2-1792*(x^3+x^2)^(2/3))/(27*RootOf(729*_Z^6-216*_Z^3+64)^3*x-54*RootOf(729*_Z^6-216*_Z^3+64)^3-24*x-8)/x)-81/32*ln(-(2106*RootOf(729*_Z^6-216*_Z^3+64)^5*x^2-1296*RootOf(729*_Z^6-216*_Z^3+64)^4*(x^3+x^2)^(1/3)*x+1053*RootOf(729*_Z^6-216*_Z^3+64)^5*x+324*(x^3+x^2)^(2/3)*RootOf(729*_Z^6-216*_Z^3+64)^3-528*x^2*RootOf(729*_Z^6-216*_Z^3+64)^2+144*RootOf(729*_Z^6-216*_Z^3+64)*(x^3+x^2)^(1/3)*x-264*x*RootOf(729*_Z^6-216*_Z^3+64)^2+160*(x^3+x^2)^(2/3))/(27*RootOf(729*_Z^6-216*_Z^3+64)^3*x-54*RootOf(729*_Z^6-216*_Z^3+64)^3-24*x-8)/x)*RootOf(729*_Z^6-216*_Z^3+64)^5+3/4*ln(-(2106*RootOf(729*_Z^6-216*_Z^3+64)^5*x^2-1296*RootOf(729*_Z^6-216*_Z^3+64)^4*(x^3+x^2)^(1/3)*x+1053*RootOf(729*_Z^6-216*_Z^3+64)^5*x+324*(x^3+x^2)^(2/3)*RootOf(729*_Z^6-216*_Z^3+64)^3-528*x^2*RootOf(729*_Z^6-216*_Z^3+64)^2+144*RootOf(729*_Z^6-216*_Z^3+64)*(x^3+x^2)^(1/3)*x-264*x*RootOf(729*_Z^6-216*_Z^3+64)^2+160*(x^3+x^2)^(2/3))/(27*RootOf(729*_Z^6-216*_Z^3+64)^3*x-54*RootOf(729*_Z^6-216*_Z^3+64)^3-24*x-8)/x)*RootOf(729*_Z^6-216*_Z^3+64)^2+1/2*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*ln(-(3*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x^2+99*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x^2+360*(x^3+x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x-198*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x+42*(x^3+x^2)^(1/3)*RootOf(_Z^3-4)^2*x+720*(x^3+x^2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)*x+34*RootOf(_Z^3-4)*x^2+1122*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x^2+84*(x^3+x^2)^(2/3)+6*RootOf(_Z^3-4)*x+198*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x)/x/(-1+x))-1/6*ln((-30*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x^2-99*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x^2+360*(x^3+x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2+60*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x+198*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x+198*(x^3+x^2)^(1/3)*RootOf(_Z^3-4)^2*x+720*(x^3+x^2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)*x+300*RootOf(_Z^3-4)*x^2+990*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x^2+396*(x^3+x^2)^(2/3)+140*RootOf(_Z^3-4)*x+462*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x)/x/(-1+x))*RootOf(_Z^3-4)-1/2*ln((-30*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x^2-99*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x^2+360*(x^3+x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2+60*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x+198*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x+198*(x^3+x^2)^(1/3)*RootOf(_Z^3-4)^2*x+720*(x^3+x^2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)*x+300*RootOf(_Z^3-4)*x^2+990*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x^2+396*(x^3+x^2)^(2/3)+140*RootOf(_Z^3-4)*x+462*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x)/x/(-1+x))*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)","B"
2451,1,3857,129,79.578000," ","int(1/x^3/(x^3-1)/(x^3+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$3857$\\ trager&$\text{Expression too large to display}$&$4513$\\ \hline \end{longtable}"," ",0,"3/40*(9*x^3+3*x^2-x+5)/x^2/(x^2*(1+x))^(1/3)+1/2*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*ln((-3*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x^2+90*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x^2+360*(x^3+x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2+6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x-180*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x-240*(x^3+x^2)^(1/3)*RootOf(_Z^3-4)^2*x-126*(x^3+x^2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)*x+30*RootOf(_Z^3-4)*x^2-900*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x^2+396*(x^3+x^2)^(2/3)+14*RootOf(_Z^3-4)*x-420*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x)/x/(-1+x))+1/6*RootOf(_Z^3-4)*ln(-(30*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x^2-9*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x^2+360*(x^3+x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-60*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x+18*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x-240*(x^3+x^2)^(1/3)*RootOf(_Z^3-4)^2*x-594*(x^3+x^2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)*x+340*RootOf(_Z^3-4)*x^2-102*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x^2+84*(x^3+x^2)^(2/3)+60*RootOf(_Z^3-4)*x-18*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x)/x/(-1+x))-1/6*ln((-27*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)^2*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*(x^3+x^2)^(1/3)*x-156*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*x^2+108*(x^3+x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-78*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*x+60*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)^2*(x^3+x^2)^(1/3)*x-176*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)*x^2-240*(x^3+x^2)^(2/3)-88*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)*x)/(3*RootOf(_Z^3-4)^2*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2+12*x+4)/x)*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)-1/8*ln((-27*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)^2*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*(x^3+x^2)^(1/3)*x-156*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*x^2+108*(x^3+x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-78*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*x+60*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)^2*(x^3+x^2)^(1/3)*x-176*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)*x^2-240*(x^3+x^2)^(2/3)-88*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)*x)/(3*RootOf(_Z^3-4)^2*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2+12*x+4)/x)*RootOf(_Z^3-4)^2*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)+1/6*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)*ln(-(-9*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^4*x^2+18*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^4*x-126*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)^2*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*(x^3+x^2)^(1/3)*x+72*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*x^2+504*(x^3+x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-60*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*x-168*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)^2*(x^3+x^2)^(1/3)*x-128*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)*x^2+672*(x^3+x^2)^(2/3)-192*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)*x)/(3*RootOf(_Z^3-4)^2*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2+12*x+4)/x)-1/16*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)^2*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*ln(-(78*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)^2*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*x^2-144*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*(x^3+x^2)^(1/3)*x+39*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)^2*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*x+108*(x^3+x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2+16*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)^2*x^2-120*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)*(x^3+x^2)^(1/3)*x+8*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)^2*x+384*(x^3+x^2)^(2/3))/(3*RootOf(_Z^3-4)^2*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8*x-12)/x)-1/12*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)^2*ln((-9*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)^2*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^4*x^2+18*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)^2*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^4*x-96*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)^2*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*x^2+108*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)^2*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*x+1008*(x^3+x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-240*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)^2*x^2+672*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)*(x^3+x^2)^(1/3)*x-80*RootOf(_Z^3-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8)^2*x)/(3*RootOf(_Z^3-4)^2*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-8*x-12)/x)","B"
2452,0,0,130,0.020000," ","int(1/x^6/(a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{1}{x^{6} \left(a \,x^{3}-b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/x^6/(a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
2453,0,0,130,0.002000," ","int(1/x^6/(a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{1}{x^{6} \left(a \,x^{3}-b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/x^6/(a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
2454,1,335,57,3.144000," ","int((x^2-1)*(x^2+x+1)*(x^4+3*x^2+1)^(1/2)/(x^4+x^3+x^2+x+1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{\left(x^{2}+3 x +1\right) \sqrt{x^{4}+3 x^{2}+1}}{5 \left(x^{4}+x^{3}+x^{2}+x +1\right)}+\frac{3 \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{3}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{3}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticF \left(x \left(\frac{i \sqrt{5}}{2}-\frac{i}{2}\right), \frac{3}{2}+\frac{\sqrt{5}}{2}\right)}{5 \left(\frac{i \sqrt{5}}{2}-\frac{i}{2}\right) \sqrt{x^{4}+3 x^{2}+1}}-\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+\textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{\sum}\left(\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(-\frac{\arctanh \left(\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2}+3\right) \left(2 \underline{\hspace{1.25 ex}}\alpha^{3}+9 \underline{\hspace{1.25 ex}}\alpha^{2}+11 x^{2}+6 \underline{\hspace{1.25 ex}}\alpha  +12\right)}{22 \sqrt{-\underline{\hspace{1.25 ex}}\alpha^{3}+2 \underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha }\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{3}+2 \underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha }}-\frac{\sqrt{2}\, \left(-\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  -1\right) \sqrt{3 x^{2}+2-\sqrt{5}\, x^{2}}\, \sqrt{3 x^{2}+2+\sqrt{5}\, x^{2}}\, \EllipticPi \left(\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, x , -\frac{3 \underline{\hspace{1.25 ex}}\alpha^{3}}{2}-\frac{\underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{5}}{2}, \frac{\sqrt{-\frac{3}{2}-\frac{\sqrt{5}}{2}}}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}}\right)}{\sqrt{\sqrt{5}-3}\, \sqrt{x^{4}+3 x^{2}+1}}\right)\right)}{10}$&$335$\\ default&$\frac{3 \sqrt{1-\left(\frac{\sqrt{5}}{2}-\frac{3}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{3}{2}-\frac{\sqrt{5}}{2}\right) x^{2}}\, \EllipticF \left(x \left(\frac{i \sqrt{5}}{2}-\frac{i}{2}\right), \frac{3}{2}+\frac{\sqrt{5}}{2}\right)}{5 \left(\frac{i \sqrt{5}}{2}-\frac{i}{2}\right) \sqrt{x^{4}+3 x^{2}+1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+\textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{\sum}\left(-6 \underline{\hspace{1.25 ex}}\alpha^{3}-2 \underline{\hspace{1.25 ex}}\alpha^{2}-3 \underline{\hspace{1.25 ex}}\alpha  -4\right) \left(-\frac{\arctanh \left(\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2}+3\right) \left(2 \underline{\hspace{1.25 ex}}\alpha^{3}+9 \underline{\hspace{1.25 ex}}\alpha^{2}+11 x^{2}+6 \underline{\hspace{1.25 ex}}\alpha  +12\right)}{22 \sqrt{-\underline{\hspace{1.25 ex}}\alpha^{3}+2 \underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha }\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{3}+2 \underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha }}-\frac{\sqrt{2}\, \left(-\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  -1\right) \sqrt{3 x^{2}+2-\sqrt{5}\, x^{2}}\, \sqrt{3 x^{2}+2+\sqrt{5}\, x^{2}}\, \EllipticPi \left(\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, x , -\frac{3 \underline{\hspace{1.25 ex}}\alpha^{3}}{2}-\frac{\underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{5}}{2}, \frac{\sqrt{-\frac{3}{2}-\frac{\sqrt{5}}{2}}}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}}\right)}{\sqrt{\sqrt{5}-3}\, \sqrt{x^{4}+3 x^{2}+1}}\right)\right)}{10}+\frac{\left(-\frac{1}{5}-\frac{1}{5} x^{2}-\frac{3}{5} x \right) \sqrt{x^{4}+3 x^{2}+1}}{x^{4}+x^{3}+x^{2}+x +1}-\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+\textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} +1\right)}{\sum}\left(-6 \underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}-4 \underline{\hspace{1.25 ex}}\alpha  -3\right) \left(-\frac{\arctanh \left(\frac{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2}+3\right) \left(2 \underline{\hspace{1.25 ex}}\alpha^{3}+9 \underline{\hspace{1.25 ex}}\alpha^{2}+11 x^{2}+6 \underline{\hspace{1.25 ex}}\alpha  +12\right)}{22 \sqrt{-\underline{\hspace{1.25 ex}}\alpha^{3}+2 \underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha }\, \sqrt{x^{4}+3 x^{2}+1}}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{3}+2 \underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha }}-\frac{\sqrt{2}\, \left(-\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha  -1\right) \sqrt{3 x^{2}+2-\sqrt{5}\, x^{2}}\, \sqrt{3 x^{2}+2+\sqrt{5}\, x^{2}}\, \EllipticPi \left(\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}\, x , -\frac{3 \underline{\hspace{1.25 ex}}\alpha^{3}}{2}-\frac{\underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{5}}{2}, \frac{\sqrt{-\frac{3}{2}-\frac{\sqrt{5}}{2}}}{\sqrt{\frac{\sqrt{5}}{2}-\frac{3}{2}}}\right)}{\sqrt{\sqrt{5}-3}\, \sqrt{x^{4}+3 x^{2}+1}}\right)\right)}{10}$&$571$\\ trager&$-\frac{\left(x^{2}+3 x +1\right) \sqrt{x^{4}+3 x^{2}+1}}{5 \left(x^{4}+x^{3}+x^{2}+x +1\right)}-\frac{\RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right) \ln \left(-\frac{25 \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right)^{5} x -20 \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right)^{3} x^{2}-70 \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right)^{3} x -20 \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right)^{3}+28 \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right) x^{2}+49 \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right) x +16 \sqrt{x^{4}+3 x^{2}+1}+28 \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right)}{4 x^{2}+5 x \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right)^{2}-3 x +4}\right)}{5}+\frac{\ln \left(-\frac{25 \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right)^{5} x +20 \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right)^{3} x^{2}-70 \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right)^{3} x +20 \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right)^{3}-44 \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right) x^{2}+33 \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right) x +16 \sqrt{x^{4}+3 x^{2}+1}-44 \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right)}{5 x \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right)^{2}-4 x^{2}-7 x -4}\right) \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right)^{3}}{2}-\frac{9 \ln \left(-\frac{25 \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right)^{5} x +20 \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right)^{3} x^{2}-70 \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right)^{3} x +20 \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right)^{3}-44 \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right) x^{2}+33 \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right) x +16 \sqrt{x^{4}+3 x^{2}+1}-44 \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right)}{5 x \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right)^{2}-4 x^{2}-7 x -4}\right) \RootOf \left(5 \textit{\_Z}^{4}-10 \textit{\_Z}^{2}+1\right)}{10}$&$595$\\ elliptic&$-\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-2 \textit{\_Z}^{7}+3 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}+50 \textit{\_Z}^{4}-124 \textit{\_Z}^{3}+198 \textit{\_Z}^{2}-172 \textit{\_Z} +61\right)}{\sum}\frac{\left(\textit{\_R}^{6}-8 \textit{\_R}^{5}+17 \textit{\_R}^{4}+32 \textit{\_R}^{3}-191 \textit{\_R}^{2}+286 \textit{\_R} -142\right) \ln \left(\sqrt{x^{4}+3 x^{2}+1}-x^{2}-\textit{\_R} \right)}{4 \textit{\_R}^{7}-7 \textit{\_R}^{6}+9 \textit{\_R}^{5}-35 \textit{\_R}^{4}+100 \textit{\_R}^{3}-186 \textit{\_R}^{2}+198 \textit{\_R} -86}\right)}{2}+\frac{\frac{\left(\sqrt{x^{4}+3 x^{2}+1}-x^{2}\right)^{7}}{5}-\frac{18 \left(\sqrt{x^{4}+3 x^{2}+1}-x^{2}\right)^{6}}{5}+\frac{46 \left(\sqrt{x^{4}+3 x^{2}+1}-x^{2}\right)^{5}}{5}-4 \left(\sqrt{x^{4}+3 x^{2}+1}-x^{2}\right)^{4}-12 \left(\sqrt{x^{4}+3 x^{2}+1}-x^{2}\right)^{3}+\frac{66 \left(\sqrt{x^{4}+3 x^{2}+1}-x^{2}\right)^{2}}{5}+\frac{12 \sqrt{x^{4}+3 x^{2}+1}}{5}-\frac{12 x^{2}}{5}-\frac{29}{5}}{\left(\sqrt{x^{4}+3 x^{2}+1}-x^{2}\right)^{8}-2 \left(\sqrt{x^{4}+3 x^{2}+1}-x^{2}\right)^{7}+3 \left(\sqrt{x^{4}+3 x^{2}+1}-x^{2}\right)^{6}-14 \left(\sqrt{x^{4}+3 x^{2}+1}-x^{2}\right)^{5}+50 \left(\sqrt{x^{4}+3 x^{2}+1}-x^{2}\right)^{4}-124 \left(\sqrt{x^{4}+3 x^{2}+1}-x^{2}\right)^{3}+198 \left(\sqrt{x^{4}+3 x^{2}+1}-x^{2}\right)^{2}-172 \sqrt{x^{4}+3 x^{2}+1}+172 x^{2}+61}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-2 \textit{\_Z}^{7}+3 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}+50 \textit{\_Z}^{4}-124 \textit{\_Z}^{3}+198 \textit{\_Z}^{2}-172 \textit{\_Z} +61\right)}{\sum}\frac{\left(\textit{\_R}^{6}-34 \textit{\_R}^{5}+100 \textit{\_R}^{4}+80 \textit{\_R}^{3}-790 \textit{\_R}^{2}+1256 \textit{\_R} -634\right) \ln \left(\sqrt{x^{4}+3 x^{2}+1}-x^{2}-\textit{\_R} \right)}{4 \textit{\_R}^{7}-7 \textit{\_R}^{6}+9 \textit{\_R}^{5}-35 \textit{\_R}^{4}+100 \textit{\_R}^{3}-186 \textit{\_R}^{2}+198 \textit{\_R} -86}\right)}{10}+\frac{\left(\frac{-\frac{\left(x^{4}+3 x^{2}+1\right)^{\frac{3}{2}} \sqrt{2}}{10 x^{3}}+\frac{\sqrt{x^{4}+3 x^{2}+1}\, \sqrt{2}}{4 x}}{\frac{\left(x^{4}+3 x^{2}+1\right)^{2}}{4 x^{4}}-\frac{5 \left(x^{4}+3 x^{2}+1\right)}{4 x^{2}}+\frac{5}{4}}-\frac{\left(5+3 \sqrt{5}\right) \sqrt{5}\, \arctanh \left(\frac{\sqrt{x^{4}+3 x^{2}+1}\, \sqrt{2}}{x \sqrt{5+\sqrt{5}}}\right)}{25 \sqrt{5+\sqrt{5}}}-\frac{\left(3 \sqrt{5}-5\right) \sqrt{5}\, \arctanh \left(\frac{\sqrt{x^{4}+3 x^{2}+1}\, \sqrt{2}}{x \sqrt{5-\sqrt{5}}}\right)}{25 \sqrt{5-\sqrt{5}}}\right) \sqrt{2}}{2}$&$777$\\ \hline \end{longtable}"," ",0,"-1/5*(x^2+3*x+1)/(x^4+x^3+x^2+x+1)*(x^4+3*x^2+1)^(1/2)+3/5/(1/2*I*5^(1/2)-1/2*I)*(1-(1/2*5^(1/2)-3/2)*x^2)^(1/2)*(1-(-3/2-1/2*5^(1/2))*x^2)^(1/2)/(x^4+3*x^2+1)^(1/2)*EllipticF(x*(1/2*I*5^(1/2)-1/2*I),3/2+1/2*5^(1/2))-1/10*sum((_alpha^2-_alpha+1)*(-1/(-_alpha^3+2*_alpha^2-_alpha)^(1/2)*arctanh(1/22*(2*_alpha^2+3)*(2*_alpha^3+9*_alpha^2+11*x^2+6*_alpha+12)/(-_alpha^3+2*_alpha^2-_alpha)^(1/2)/(x^4+3*x^2+1)^(1/2))-2^(1/2)*(-_alpha^3-_alpha^2-_alpha-1)/(5^(1/2)-3)^(1/2)*(3*x^2+2-5^(1/2)*x^2)^(1/2)*(3*x^2+2+5^(1/2)*x^2)^(1/2)/(x^4+3*x^2+1)^(1/2)*EllipticPi((1/2*5^(1/2)-3/2)^(1/2)*x,-3/2*_alpha^3-1/2*_alpha^3*5^(1/2),(-3/2-1/2*5^(1/2))^(1/2)/(1/2*5^(1/2)-3/2)^(1/2))),_alpha=RootOf(_Z^4+_Z^3+_Z^2+_Z+1))","C"
2455,0,0,162,0.039000," ","int((a*x^4+b)/(a*x^4-b)/(a^2*x^8+c*x^4+b^2)^(1/4),x)","\[\int \frac{a \,x^{4}+b}{\left(a \,x^{4}-b \right) \left(a^{2} x^{8}+c \,x^{4}+b^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^4+b)/(a*x^4-b)/(a^2*x^8+c*x^4+b^2)^(1/4),x)","F"
2456,0,0,143,0.051000," ","int((-x^9+2*x^4)/(x^5-1)^(1/2)/(x^10-a*x^5+a),x)","\[\int \frac{-x^{9}+2 x^{4}}{\sqrt{x^{5}-1}\, \left(x^{10}-a \,x^{5}+a \right)}\, dx\]"," ",0,"int((-x^9+2*x^4)/(x^5-1)^(1/2)/(x^10-a*x^5+a),x)","F"
2457,0,0,141,0.051000," ","int((x^2+1)/(x^2-1)/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{x^{2}+1}{\left(x^{2}-1\right) \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^2+1)/(x^2-1)/(x+(x^2+1)^(1/2))^(1/2),x)","F"
2458,0,0,63,180.000000," ","int((c*x^2+d)/(c*x^2-d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{c \,x^{2}+d}{\left(c \,x^{2}-d \right) \sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int((c*x^2+d)/(c*x^2-d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","F"
2459,0,0,63,180.000000," ","int((c*x^2+d)/(c*x^2-d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{c \,x^{2}+d}{\left(c \,x^{2}-d \right) \sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int((c*x^2+d)/(c*x^2-d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","F"
2460,0,0,130,0.014000," ","int(1/x^6/(a*x^3+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{1}{x^{6} \left(a \,x^{3}+b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/x^6/(a*x^3+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
2461,0,0,130,0.003000," ","int(1/x^6/(a*x^3+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{1}{x^{6} \left(a \,x^{3}+b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/x^6/(a*x^3+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
2462,1,13530,188,0.916000," ","int((p*x^2-q)*(a*p*x^2+a*q+b*x)*(p^2*x^4+q^2)^(1/2)/x^3/(c*p*x^2+c*q+d*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$13530$\\ default&$\text{Expression too large to display}$&$13966$\\ elliptic&$\text{Expression too large to display}$&$30360$\\ \hline \end{longtable}"," ",0,"result too large to display","C"
2463,1,937,156,63.415000," ","int(x*(7*x^4+3)/(x^4+1)^(1/3)/(x^7+x^3-4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(\frac{-\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} x^{7}+2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{7}-\RootOf \left(\textit{\_Z}^{3}-2\right) x^{7}+2 x^{7} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)+6 \left(x^{4}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{2}-\RootOf \left(\textit{\_Z}^{3}-2\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{3}+2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}+6 x^{2} \left(x^{4}+1\right)^{\frac{2}{3}}-12 \left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right) x -\RootOf \left(\textit{\_Z}^{3}-2\right) x^{3}+2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{3}-4 \RootOf \left(\textit{\_Z}^{3}-2\right)+8 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)}{x^{7}+x^{3}-4}\right)}{2}-\frac{\ln \left(\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} x^{7}+4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{7}+6 \left(x^{4}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{2}+\RootOf \left(\textit{\_Z}^{3}-2\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{3}+4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}+6 \left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x -4 \RootOf \left(\textit{\_Z}^{3}-2\right)-16 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)}{x^{7}+x^{3}-4}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)}{2}-\ln \left(\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3} x^{7}+4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{7}+6 \left(x^{4}+1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{2}+\RootOf \left(\textit{\_Z}^{3}-2\right)^{3} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right) x^{3}+4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x^{3}+6 \left(x^{4}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2} x -4 \RootOf \left(\textit{\_Z}^{3}-2\right)-16 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)}{x^{7}+x^{3}-4}\right) \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+4 \textit{\_Z}^{2}\right)$&$937$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^3-2)*ln((-RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x^7+2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^7-RootOf(_Z^3-2)*x^7+2*x^7*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)+6*(x^4+1)^(2/3)*RootOf(_Z^3-2)^2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^2-RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3+2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3+6*x^2*(x^4+1)^(2/3)-12*(x^4+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x-RootOf(_Z^3-2)*x^3+2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3-4*RootOf(_Z^3-2)+8*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2))/(x^7+x^3-4))-1/2*ln((RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x^7+4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^7+6*(x^4+1)^(2/3)*RootOf(_Z^3-2)^2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^2+RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3+4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3+6*(x^4+1)^(1/3)*RootOf(_Z^3-2)^2*x-4*RootOf(_Z^3-2)-16*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2))/(x^7+x^3-4))*RootOf(_Z^3-2)-ln((RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x^7+4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^7+6*(x^4+1)^(2/3)*RootOf(_Z^3-2)^2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^2+RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3+4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3+6*(x^4+1)^(1/3)*RootOf(_Z^3-2)^2*x-4*RootOf(_Z^3-2)-16*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2))/(x^7+x^3-4))*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)","C"
2464,0,0,64,180.000000," ","int((c*x^2-d)/(c*x^2+d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{c \,x^{2}-d}{\left(c \,x^{2}+d \right) \sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int((c*x^2-d)/(c*x^2+d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","F"
2465,0,0,64,180.000000," ","int((c*x^2-d)/(c*x^2+d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{c \,x^{2}-d}{\left(c \,x^{2}+d \right) \sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int((c*x^2-d)/(c*x^2+d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","F"
2466,0,0,164,0.053000," ","int((a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{a^{2} x^{2}-b x}}{\sqrt{a \,x^{2}+x \sqrt{a^{2} x^{2}-b x}}}\, dx\]"," ",0,"int((a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(1/2),x)","F"
2467,0,0,167,0.240000," ","int((a-2*b+x)/((-a+x)*(-b+x))^(1/3)/(a^2+b*d-(2*a+d)*x+x^2),x)","\[\int \frac{a -2 b +x}{\left(\left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{3}} \left(a^{2}+b d -\left(2 a +d \right) x +x^{2}\right)}\, dx\]"," ",0,"int((a-2*b+x)/((-a+x)*(-b+x))^(1/3)/(a^2+b*d-(2*a+d)*x+x^2),x)","F"
2468,0,0,167,0.253000," ","int((-a*(a-2*b)-2*b*x+x^2)/((-a+x)*(-b+x))^(2/3)/(b+a^2*d-(2*a*d+1)*x+d*x^2),x)","\[\int \frac{-a \left(a -2 b \right)-2 b x +x^{2}}{\left(\left(-a +x \right) \left(-b +x \right)\right)^{\frac{2}{3}} \left(b +a^{2} d -\left(2 a d +1\right) x +d \,x^{2}\right)}\, dx\]"," ",0,"int((-a*(a-2*b)-2*b*x+x^2)/((-a+x)*(-b+x))^(2/3)/(b+a^2*d-(2*a*d+1)*x+d*x^2),x)","F"
2469,0,0,167,0.184000," ","int((-1+(2-k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(1-(b+2*k)*x+(k^2+b)*x^2),x)","\[\int \frac{-1+\left(2-k \right) x}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(1-\left(b +2 k \right) x +\left(k^{2}+b \right) x^{2}\right)}\, dx\]"," ",0,"int((-1+(2-k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(1-(b+2*k)*x+(k^2+b)*x^2),x)","F"
2470,0,0,169,0.027000," ","int((-3*k-2*(k^2+1)*x+k*(k^2+1)*x^2+4*k^2*x^3+k^3*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(-1+d-(2+d)*k*x-(k^2+d)*x^2+d*k*x^3),x)","\[\int \frac{-3 k -2 \left(k^{2}+1\right) x +k \left(k^{2}+1\right) x^{2}+4 k^{2} x^{3}+k^{3} x^{4}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{2}{3}} \left(-1+d -\left(2+d \right) k x -\left(k^{2}+d \right) x^{2}+d k \,x^{3}\right)}\, dx\]"," ",0,"int((-3*k-2*(k^2+1)*x+k*(k^2+1)*x^2+4*k^2*x^3+k^3*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(-1+d-(2+d)*k*x-(k^2+d)*x^2+d*k*x^3),x)","F"
2471,1,1608,125,13.671000," ","int((2*x^4-1)/(x^4+1)^(1/4)/(x^8+x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1608$\\ \hline \end{longtable}"," ",0,"-RootOf(6400*_Z^4-880*_Z^2-1)*ln(-(-64000*RootOf(6400*_Z^4-880*_Z^2-1)^5*x^4-12800*RootOf(6400*_Z^4-880*_Z^2-1)^3*(x^4+1)^(1/2)*x^2+23200*x^4*RootOf(6400*_Z^4-880*_Z^2-1)^3+320*(x^4+1)^(3/4)*RootOf(6400*_Z^4-880*_Z^2-1)^2*x-560*(x^4+1)^(1/4)*RootOf(6400*_Z^4-880*_Z^2-1)^2*x^3+1780*RootOf(6400*_Z^4-880*_Z^2-1)*(x^4+1)^(1/2)*x^2-1980*x^4*RootOf(6400*_Z^4-880*_Z^2-1)-47*(x^4+1)^(3/4)*x+76*x^3*(x^4+1)^(1/4)+4000*RootOf(6400*_Z^4-880*_Z^2-1)^3-550*RootOf(6400*_Z^4-880*_Z^2-1))/(80*RootOf(6400*_Z^4-880*_Z^2-1)^2*x^4-8*x^4+5))+1/20*RootOf(_Z^2+400*RootOf(6400*_Z^4-880*_Z^2-1)^2-55)*ln(5*(-3200*RootOf(_Z^2+400*RootOf(6400*_Z^4-880*_Z^2-1)^2-55)*RootOf(6400*_Z^4-880*_Z^2-1)^4*x^4+640*(x^4+1)^(1/2)*RootOf(6400*_Z^4-880*_Z^2-1)^2*RootOf(_Z^2+400*RootOf(6400*_Z^4-880*_Z^2-1)^2-55)*x^2-280*RootOf(_Z^2+400*RootOf(6400*_Z^4-880*_Z^2-1)^2-55)*RootOf(6400*_Z^4-880*_Z^2-1)^2*x^4+320*(x^4+1)^(3/4)*RootOf(6400*_Z^4-880*_Z^2-1)^2*x-560*(x^4+1)^(1/4)*RootOf(6400*_Z^4-880*_Z^2-1)^2*x^3+(x^4+1)^(1/2)*RootOf(_Z^2+400*RootOf(6400*_Z^4-880*_Z^2-1)^2-55)*x^2+3*(x^4+1)^(3/4)*x+x^3*(x^4+1)^(1/4)-200*RootOf(6400*_Z^4-880*_Z^2-1)^2*RootOf(_Z^2+400*RootOf(6400*_Z^4-880*_Z^2-1)^2-55))/(960*RootOf(6400*_Z^4-880*_Z^2-1)^3*x^2-116*RootOf(6400*_Z^4-880*_Z^2-1)*x^2+5)/(960*RootOf(6400*_Z^4-880*_Z^2-1)^3*x^2-116*RootOf(6400*_Z^4-880*_Z^2-1)*x^2-5))+4*RootOf(6400*_Z^4-880*_Z^2-1)^2*RootOf(_Z^2+400*RootOf(6400*_Z^4-880*_Z^2-1)^2-55)*ln((6400*RootOf(_Z^2+400*RootOf(6400*_Z^4-880*_Z^2-1)^2-55)*RootOf(6400*_Z^4-880*_Z^2-1)^4*x^4-1680*RootOf(_Z^2+400*RootOf(6400*_Z^4-880*_Z^2-1)^2-55)*RootOf(6400*_Z^4-880*_Z^2-1)^2*x^4-2400*(x^4+1)^(3/4)*RootOf(6400*_Z^4-880*_Z^2-1)^2*x-3200*(x^4+1)^(1/4)*RootOf(6400*_Z^4-880*_Z^2-1)^2*x^3+50*(x^4+1)^(1/2)*RootOf(_Z^2+400*RootOf(6400*_Z^4-880*_Z^2-1)^2-55)*x^2+54*RootOf(_Z^2+400*RootOf(6400*_Z^4-880*_Z^2-1)^2-55)*x^4+290*(x^4+1)^(3/4)*x+470*x^3*(x^4+1)^(1/4)-400*RootOf(6400*_Z^4-880*_Z^2-1)^2*RootOf(_Z^2+400*RootOf(6400*_Z^4-880*_Z^2-1)^2-55)+15*RootOf(_Z^2+400*RootOf(6400*_Z^4-880*_Z^2-1)^2-55))/(80*RootOf(6400*_Z^4-880*_Z^2-1)^2*x^4-8*x^4+5))+80*RootOf(6400*_Z^4-880*_Z^2-1)^3*ln(5*(-12800*RootOf(6400*_Z^4-880*_Z^2-1)^5*x^4+160*x^4*RootOf(6400*_Z^4-880*_Z^2-1)^3+240*(x^4+1)^(3/4)*RootOf(6400*_Z^4-880*_Z^2-1)^2*x+320*(x^4+1)^(1/4)*RootOf(6400*_Z^4-880*_Z^2-1)^2*x^3-100*RootOf(6400*_Z^4-880*_Z^2-1)*(x^4+1)^(1/2)*x^2+112*x^4*RootOf(6400*_Z^4-880*_Z^2-1)-4*(x^4+1)^(3/4)*x+3*x^3*(x^4+1)^(1/4)-800*RootOf(6400*_Z^4-880*_Z^2-1)^3+80*RootOf(6400*_Z^4-880*_Z^2-1))/(960*RootOf(6400*_Z^4-880*_Z^2-1)^3*x^2-116*RootOf(6400*_Z^4-880*_Z^2-1)*x^2+5)/(960*RootOf(6400*_Z^4-880*_Z^2-1)^3*x^2-116*RootOf(6400*_Z^4-880*_Z^2-1)*x^2-5))-11*RootOf(6400*_Z^4-880*_Z^2-1)*ln(5*(-12800*RootOf(6400*_Z^4-880*_Z^2-1)^5*x^4+160*x^4*RootOf(6400*_Z^4-880*_Z^2-1)^3+240*(x^4+1)^(3/4)*RootOf(6400*_Z^4-880*_Z^2-1)^2*x+320*(x^4+1)^(1/4)*RootOf(6400*_Z^4-880*_Z^2-1)^2*x^3-100*RootOf(6400*_Z^4-880*_Z^2-1)*(x^4+1)^(1/2)*x^2+112*x^4*RootOf(6400*_Z^4-880*_Z^2-1)-4*(x^4+1)^(3/4)*x+3*x^3*(x^4+1)^(1/4)-800*RootOf(6400*_Z^4-880*_Z^2-1)^3+80*RootOf(6400*_Z^4-880*_Z^2-1))/(960*RootOf(6400*_Z^4-880*_Z^2-1)^3*x^2-116*RootOf(6400*_Z^4-880*_Z^2-1)*x^2+5)/(960*RootOf(6400*_Z^4-880*_Z^2-1)^3*x^2-116*RootOf(6400*_Z^4-880*_Z^2-1)*x^2-5))","C"
2472,0,0,169,0.197000," ","int((-2*x+(1+k)*x^2)*(a-a*(1+k)*x+(a*k+1)*x^2)/(-1+x)/((1-x)*x*(-k*x+1))^(2/3)/(k*x-1)/(b-b*(1+k)*x+(b*k-1)*x^2),x)","\[\int \frac{\left(-2 x +\left(1+k \right) x^{2}\right) \left(a -a \left(1+k \right) x +\left(a k +1\right) x^{2}\right)}{\left(-1+x \right) \left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{2}{3}} \left(k x -1\right) \left(b -b \left(1+k \right) x +\left(b k -1\right) x^{2}\right)}\, dx\]"," ",0,"int((-2*x+(1+k)*x^2)*(a-a*(1+k)*x+(a*k+1)*x^2)/(-1+x)/((1-x)*x*(-k*x+1))^(2/3)/(k*x-1)/(b-b*(1+k)*x+(b*k-1)*x^2),x)","F"
2473,0,0,171,0.027000," ","int((-3*k+2*(k^2+1)*x+k*(k^2+1)*x^2-4*k^2*x^3+k^3*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(1-d-(2+d)*k*x+(k^2+d)*x^2+d*k*x^3),x)","\[\int \frac{-3 k +2 \left(k^{2}+1\right) x +k \left(k^{2}+1\right) x^{2}-4 k^{2} x^{3}+k^{3} x^{4}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{2}{3}} \left(1-d -\left(2+d \right) k x +\left(k^{2}+d \right) x^{2}+d k \,x^{3}\right)}\, dx\]"," ",0,"int((-3*k+2*(k^2+1)*x+k*(k^2+1)*x^2-4*k^2*x^3+k^3*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(1-d-(2+d)*k*x+(k^2+d)*x^2+d*k*x^3),x)","F"
2474,0,0,123,0.011000," ","int((x^3-x)^(1/3)*(a*x^6-b)/(c*x^6-d),x)","\[\int \frac{\left(x^{3}-x \right)^{\frac{1}{3}} \left(a \,x^{6}-b \right)}{c \,x^{6}-d}\, dx\]"," ",0,"int((x^3-x)^(1/3)*(a*x^6-b)/(c*x^6-d),x)","F"
2475,0,0,123,0.003000," ","int((x^3-x)^(1/3)*(a*x^6-b)/(c*x^6-d),x)","\[\int \frac{\left(x^{3}-x \right)^{\frac{1}{3}} \left(a \,x^{6}-b \right)}{c \,x^{6}-d}\, dx\]"," ",0,"int((x^3-x)^(1/3)*(a*x^6-b)/(c*x^6-d),x)","F"
2476,1,382,11,0.137000," ","int(1/(1-x*(a*x^2+b*x+c)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{4}+b \,\textit{\_Z}^{3}+c \,\textit{\_Z}^{2}-1\right)}{\sum}\frac{\ln \left(x -\textit{\_R} \right)}{4 \textit{\_R}^{3} a +3 \textit{\_R}^{2} b +2 \textit{\_R} c}\right)-\frac{\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8} a -2 \sqrt{a}\, \textit{\_Z}^{7} b +\textit{\_Z}^{6} b^{2}+2 \sqrt{a}\, \textit{\_Z}^{5} b c +\left(-2 a \,c^{2}-2 b^{2} c -16 a^{2}\right) \textit{\_Z}^{4}+\left(32 a^{\frac{3}{2}} b +2 \sqrt{a}\, c^{2} b \right) \textit{\_Z}^{3}+\left(b^{2} c^{2}-24 a \,b^{2}\right) \textit{\_Z}^{2}+\left(-2 \sqrt{a}\, c^{3} b +8 \sqrt{a}\, b^{3}\right) \textit{\_Z} +a \,c^{4}-b^{4}\right)}{\sum}\frac{\left(a \left(a \,\textit{\_R}^{6}-\left(-a c -b^{2}\right) \textit{\_R}^{4}-c \left(a c +b^{2}\right) \textit{\_R}^{2}-a \,c^{3}\right)+2 b \left(-\textit{\_R}^{5} a^{\frac{3}{2}}+c^{2} \textit{\_R} \,a^{\frac{3}{2}}\right)\right) \ln \left(\sqrt{a \,x^{2}+b x +c}-\sqrt{a}\, x -\textit{\_R} \right)}{4 \textit{\_R}^{7} a +3 \textit{\_R}^{5} b^{2}-4 \textit{\_R}^{3} a \,c^{2}-4 \textit{\_R}^{3} b^{2} c -32 \textit{\_R}^{3} a^{2}+\textit{\_R} \,b^{2} c^{2}-24 a \,b^{2} \textit{\_R} +b \left(-7 \textit{\_R}^{6} \sqrt{a}+5 c \,\textit{\_R}^{4} \sqrt{a}+48 \textit{\_R}^{2} a^{\frac{3}{2}}+3 c^{2} \textit{\_R}^{2} \sqrt{a}-\sqrt{a}\, c^{3}+4 b^{2} \sqrt{a}\right)}}{a}$&$382$\\ \hline \end{longtable}"," ",0,"-sum(1/(4*_R^3*a+3*_R^2*b+2*_R*c)*ln(x-_R),_R=RootOf(_Z^4*a+_Z^3*b+_Z^2*c-1))-1/a*sum((a*(a*_R^6-(-a*c-b^2)*_R^4-c*(a*c+b^2)*_R^2-a*c^3)+2*b*(-_R^5*a^(3/2)+c^2*_R*a^(3/2)))/(4*_R^7*a+3*_R^5*b^2-4*_R^3*a*c^2-4*_R^3*b^2*c-32*_R^3*a^2+_R*b^2*c^2-24*a*b^2*_R+b*(-7*_R^6*a^(1/2)+5*c*_R^4*a^(1/2)+48*_R^2*a^(3/2)+3*c^2*_R^2*a^(1/2)-a^(1/2)*c^3+4*b^2*a^(1/2)))*ln((a*x^2+b*x+c)^(1/2)-a^(1/2)*x-_R),_R=RootOf(_Z^8*a-2*a^(1/2)*_Z^7*b+_Z^6*b^2+2*a^(1/2)*_Z^5*b*c+(-2*a*c^2-2*b^2*c-16*a^2)*_Z^4+(32*a^(3/2)*b+2*a^(1/2)*c^2*b)*_Z^3+(b^2*c^2-24*a*b^2)*_Z^2+(-2*a^(1/2)*c^3*b+8*a^(1/2)*b^3)*_Z+a*c^4-b^4))","B"
2477,0,0,131,0.058000," ","int((a*x^2-b)/(2*a*x^2-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{a \,x^{2}-b}{\left(2 a \,x^{2}-b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a*x^2-b)/(2*a*x^2-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
2478,0,0,131,0.003000," ","int((a*x^2-b)/(2*a*x^2-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{a \,x^{2}-b}{\left(2 a \,x^{2}-b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a*x^2-b)/(2*a*x^2-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
2479,0,0,131,0.056000," ","int((a*x^2+b)/(2*a*x^2+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{a \,x^{2}+b}{\left(2 a \,x^{2}+b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a*x^2+b)/(2*a*x^2+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
2480,0,0,131,0.003000," ","int((a*x^2+b)/(2*a*x^2+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{a \,x^{2}+b}{\left(2 a \,x^{2}+b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a*x^2+b)/(2*a*x^2+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
2481,0,0,174,0.016000," ","int(x*(4*a*b-3*(a+b)*x+2*x^2)/(x^2*(-a+x)*(-b+x))^(1/3)/(-a*b+(a+b)*x-x^2+d*x^4),x)","\[\int \frac{x \left(4 a b -3 \left(a +b \right) x +2 x^{2}\right)}{\left(x^{2} \left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{3}} \left(-a b +\left(a +b \right) x -x^{2}+d \,x^{4}\right)}\, dx\]"," ",0,"int(x*(4*a*b-3*(a+b)*x+2*x^2)/(x^2*(-a+x)*(-b+x))^(1/3)/(-a*b+(a+b)*x-x^2+d*x^4),x)","F"
2482,0,0,43,0.014000," ","int((a*x^4+b)^(1/4)*(3*a*x^4+2*b)/x^6/(a*x^8+b),x)","\[\int \frac{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(3 a \,x^{4}+2 b \right)}{x^{6} \left(a \,x^{8}+b \right)}\, dx\]"," ",0,"int((a*x^4+b)^(1/4)*(3*a*x^4+2*b)/x^6/(a*x^8+b),x)","F"
2483,0,0,43,0.003000," ","int((a*x^4+b)^(1/4)*(3*a*x^4+2*b)/x^6/(a*x^8+b),x)","\[\int \frac{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(3 a \,x^{4}+2 b \right)}{x^{6} \left(a \,x^{8}+b \right)}\, dx\]"," ",0,"int((a*x^4+b)^(1/4)*(3*a*x^4+2*b)/x^6/(a*x^8+b),x)","F"
2484,1,105,11,0.122000," ","int((x+(1+x)^(1/2))^(1/2)/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)}{\sum}\frac{\left(\textit{\_R}^{6}-2 \textit{\_R}^{5}+2 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+5 \textit{\_R}^{4}+10 \textit{\_R}^{3}-18 \textit{\_R}^{2}+10 \textit{\_R} -1}\right)}{2}$&$105$\\ default&$\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)}{\sum}\frac{\left(\textit{\_R}^{6}-2 \textit{\_R}^{5}+2 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+5 \textit{\_R}^{4}+10 \textit{\_R}^{3}-18 \textit{\_R}^{2}+10 \textit{\_R} -1}\right)}{2}$&$105$\\ \hline \end{longtable}"," ",0,"1/2*sum((_R^6-2*_R^5+2*_R+1)/(_R^7-3*_R^5+5*_R^4+10*_R^3-18*_R^2+10*_R-1)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^8-4*_Z^6+8*_Z^5+20*_Z^4-48*_Z^3+40*_Z^2-8*_Z+1))","B"
2485,1,105,11,0.120000," ","int((x+(1+x)^(1/2))^(1/2)/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)}{\sum}\frac{\left(\textit{\_R}^{6}-2 \textit{\_R}^{5}+2 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+5 \textit{\_R}^{4}+10 \textit{\_R}^{3}-18 \textit{\_R}^{2}+10 \textit{\_R} -1}\right)}{2}$&$105$\\ default&$\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)}{\sum}\frac{\left(\textit{\_R}^{6}-2 \textit{\_R}^{5}+2 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+5 \textit{\_R}^{4}+10 \textit{\_R}^{3}-18 \textit{\_R}^{2}+10 \textit{\_R} -1}\right)}{2}$&$105$\\ \hline \end{longtable}"," ",0,"1/2*sum((_R^6-2*_R^5+2*_R+1)/(_R^7-3*_R^5+5*_R^4+10*_R^3-18*_R^2+10*_R-1)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^8-4*_Z^6+8*_Z^5+20*_Z^4-48*_Z^3+40*_Z^2-8*_Z+1))","B"
2486,1,107,11,0.093000," ","int((x+(1+x)^(1/2))^(1/2)/(x^2-(1+x)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-8 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+3 \textit{\_Z}^{2}+6 \textit{\_Z} -1\right)}{\sum}\frac{\left(\textit{\_R}^{6}-2 \textit{\_R}^{5}+2 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{7}-12 \textit{\_R}^{5}+40 \textit{\_R}^{4}-16 \textit{\_R}^{3}-3 \textit{\_R}^{2}+3 \textit{\_R} +3}\right)$&$107$\\ default&$2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-8 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+3 \textit{\_Z}^{2}+6 \textit{\_Z} -1\right)}{\sum}\frac{\left(\textit{\_R}^{6}-2 \textit{\_R}^{5}+2 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{7}-12 \textit{\_R}^{5}+40 \textit{\_R}^{4}-16 \textit{\_R}^{3}-3 \textit{\_R}^{2}+3 \textit{\_R} +3}\right)$&$107$\\ \hline \end{longtable}"," ",0,"2*sum((_R^6-2*_R^5+2*_R+1)/(4*_R^7-12*_R^5+40*_R^4-16*_R^3-3*_R^2+3*_R+3)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^8-4*_Z^6+16*_Z^5-8*_Z^4-2*_Z^3+3*_Z^2+6*_Z-1))","B"
2487,1,107,11,0.088000," ","int((x+(1+x)^(1/2))^(1/2)/(x^2-(1+x)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-8 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+3 \textit{\_Z}^{2}+6 \textit{\_Z} -1\right)}{\sum}\frac{\left(\textit{\_R}^{6}-2 \textit{\_R}^{5}+2 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{7}-12 \textit{\_R}^{5}+40 \textit{\_R}^{4}-16 \textit{\_R}^{3}-3 \textit{\_R}^{2}+3 \textit{\_R} +3}\right)$&$107$\\ default&$2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}-8 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+3 \textit{\_Z}^{2}+6 \textit{\_Z} -1\right)}{\sum}\frac{\left(\textit{\_R}^{6}-2 \textit{\_R}^{5}+2 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{4 \textit{\_R}^{7}-12 \textit{\_R}^{5}+40 \textit{\_R}^{4}-16 \textit{\_R}^{3}-3 \textit{\_R}^{2}+3 \textit{\_R} +3}\right)$&$107$\\ \hline \end{longtable}"," ",0,"2*sum((_R^6-2*_R^5+2*_R+1)/(4*_R^7-12*_R^5+40*_R^4-16*_R^3-3*_R^2+3*_R+3)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^8-4*_Z^6+16*_Z^5-8*_Z^4-2*_Z^3+3*_Z^2+6*_Z-1))","B"
2488,0,0,159,0.154000," ","int(x^2/(x^2*(-a+x))^(2/3)/(-a^2+2*a*x+(-1+d)*x^2),x)","\[\int \frac{x^{2}}{\left(x^{2} \left(-a +x \right)\right)^{\frac{2}{3}} \left(-a^{2}+2 a x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int(x^2/(x^2*(-a+x))^(2/3)/(-a^2+2*a*x+(-1+d)*x^2),x)","F"
2489,0,0,171,0.018000," ","int((-2+(1+k)*x)*(1-(1+k)*x+(a+k)*x^2)/x/((1-x)*x*(-k*x+1))^(2/3)/(1-(1+k)*x+(-b+k)*x^2),x)","\[\int \frac{\left(-2+\left(1+k \right) x \right) \left(1-\left(1+k \right) x +\left(a +k \right) x^{2}\right)}{x \left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{2}{3}} \left(1-\left(1+k \right) x +\left(-b +k \right) x^{2}\right)}\, dx\]"," ",0,"int((-2+(1+k)*x)*(1-(1+k)*x+(a+k)*x^2)/x/((1-x)*x*(-k*x+1))^(2/3)/(1-(1+k)*x+(-b+k)*x^2),x)","F"
2490,0,0,174,0.022000," ","int((-2*a^2*b*x+a*(3*a+2*b)*x^2-4*a*x^3+x^4)/(x^2*(-a+x)*(-b+x))^(2/3)/(-a^2+2*a*x-(b*d+1)*x^2+d*x^3),x)","\[\int \frac{-2 a^{2} b x +a \left(3 a +2 b \right) x^{2}-4 a \,x^{3}+x^{4}}{\left(x^{2} \left(-a +x \right) \left(-b +x \right)\right)^{\frac{2}{3}} \left(-a^{2}+2 a x -\left(b d +1\right) x^{2}+d \,x^{3}\right)}\, dx\]"," ",0,"int((-2*a^2*b*x+a*(3*a+2*b)*x^2-4*a*x^3+x^4)/(x^2*(-a+x)*(-b+x))^(2/3)/(-a^2+2*a*x-(b*d+1)*x^2+d*x^3),x)","F"
2491,1,1368,172,2.853000," ","int(1/(81*x^4-135*x^3+54*x^2+12*x-8)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1368$\\ \hline \end{longtable}"," ",0,"1/4*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)*ln(-(648*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x^3-3645*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x^3-864*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x^2+4860*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x^2+288*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x+540*(81*x^4-135*x^3+54*x^2+12*x-8)^(2/3)*RootOf(_Z^3-9)^2*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)-1620*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x-2160*(81*x^4-135*x^3+54*x^2+12*x-8)^(1/3)*RootOf(_Z^3-9)^2*x-2592*(81*x^4-135*x^3+54*x^2+12*x-8)^(1/3)*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)*x+3456*RootOf(_Z^3-9)*x^3-19440*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^3+1440*(81*x^4-135*x^3+54*x^2+12*x-8)^(1/3)*RootOf(_Z^3-9)^2+1728*(81*x^4-135*x^3+54*x^2+12*x-8)^(1/3)*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)-864*RootOf(_Z^3-9)*x^2+4860*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^2-3456*RootOf(_Z^3-9)*x+1008*(81*x^4-135*x^3+54*x^2+12*x-8)^(2/3)+19440*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)*x+1664*RootOf(_Z^3-9)-9360*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2))/(-2+3*x)^3)+1/9*RootOf(_Z^3-9)*ln(-(810*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x^3-729*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x^3-1080*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x^2+972*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x^2+360*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x-270*(81*x^4-135*x^3+54*x^2+12*x-8)^(2/3)*RootOf(_Z^3-9)^2*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)-324*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x+1080*(81*x^4-135*x^3+54*x^2+12*x-8)^(1/3)*RootOf(_Z^3-9)^2*x+1134*(81*x^4-135*x^3+54*x^2+12*x-8)^(1/3)*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)*x-1080*RootOf(_Z^3-9)*x^3+972*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^3-720*(81*x^4-135*x^3+54*x^2+12*x-8)^(1/3)*RootOf(_Z^3-9)^2-756*(81*x^4-135*x^3+54*x^2+12*x-8)^(1/3)*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)-3240*RootOf(_Z^3-9)*x^2+2916*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^2+5760*RootOf(_Z^3-9)*x-576*(81*x^4-135*x^3+54*x^2+12*x-8)^(2/3)-5184*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2)*x-2080*RootOf(_Z^3-9)+1872*RootOf(16*RootOf(_Z^3-9)^2+36*_Z*RootOf(_Z^3-9)+81*_Z^2))/(-2+3*x)^3)","C"
2492,1,2719,155,32.327000," ","int((x^2+1)/(x^2-x-1)/(x^6-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2719$\\ \hline \end{longtable}"," ",0,"-1/6*ln(-(7*RootOf(_Z^3-2)*x^6+3*RootOf(_Z^3-2)*x^5+18*x^2*(x^6-1)^(2/3)-5*RootOf(_Z^3-2)*x^3+3*RootOf(_Z^3-2)*x-50*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3+30*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x+18*x*(x^6-1)^(2/3)-18*(x^6-1)^(2/3)-70*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)+100*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3+48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x^2-7*RootOf(_Z^3-2)+10*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3+30*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^5+70*x^6*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)+9*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)-60*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^5-6*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x^5-60*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x-6*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x+9*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x^4+18*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x^3-48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2-9*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x^2-18*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x+48*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)+48*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^4+48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x+96*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^3-48*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^2-96*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x)/(x^2-x-1)^3)*RootOf(_Z^3-2)-1/3*ln(-(7*RootOf(_Z^3-2)*x^6+3*RootOf(_Z^3-2)*x^5+18*x^2*(x^6-1)^(2/3)-5*RootOf(_Z^3-2)*x^3+3*RootOf(_Z^3-2)*x-50*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3+30*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x+18*x*(x^6-1)^(2/3)-18*(x^6-1)^(2/3)-70*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)+100*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3+48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x^2-7*RootOf(_Z^3-2)+10*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3+30*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^5+70*x^6*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)+9*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)-60*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^5-6*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x^5-60*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x-6*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x+9*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x^4+18*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x^3-48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2-9*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x^2-18*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x+48*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)+48*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^4+48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x+96*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^3-48*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^2-96*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x)/(x^2-x-1)^3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)+1/3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*ln((28*RootOf(_Z^3-2)*x^6+36*RootOf(_Z^3-2)*x^5+30*x^2*(x^6-1)^(2/3)-60*RootOf(_Z^3-2)*x^3+36*RootOf(_Z^3-2)*x-150*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3+90*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x+30*x*(x^6-1)^(2/3)-30*(x^6-1)^(2/3)-70*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)-100*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3+48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x^2-28*RootOf(_Z^3-2)-40*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3+90*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^5+70*x^6*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)+15*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)+60*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^5+24*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x^5+60*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x+24*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x+15*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x^4+30*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x^3-48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2-15*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x^2-30*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x+48*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)+48*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^4+48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x+96*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^3-48*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^2-96*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x)/(x^2-x-1)^3)","C"
2493,1,2702,155,31.433000," ","int((x^2+1)/(x^2-x-1)/(x^6-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2702$\\ \hline \end{longtable}"," ",0,"-1/6*ln(-(35*RootOf(_Z^3-2)*x^6+45*RootOf(_Z^3-2)*x^5-30*x^2*(x^6-1)^(2/3)-75*RootOf(_Z^3-2)*x^3+45*RootOf(_Z^3-2)*x-30*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3+18*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x-30*x*(x^6-1)^(2/3)+30*(x^6-1)^(2/3)-14*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)-20*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x^2-35*RootOf(_Z^3-2)-50*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3+18*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^5+14*x^6*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)-9*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)+12*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^5+30*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x^5+12*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x+30*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x-9*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x^4-18*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x^3+48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2+9*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x^2+18*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x+30*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)+30*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^4-48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x+60*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^3-30*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^2-60*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x)/(x^2-x-1)^3)*RootOf(_Z^3-2)-1/3*ln(-(35*RootOf(_Z^3-2)*x^6+45*RootOf(_Z^3-2)*x^5-30*x^2*(x^6-1)^(2/3)-75*RootOf(_Z^3-2)*x^3+45*RootOf(_Z^3-2)*x-30*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3+18*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x-30*x*(x^6-1)^(2/3)+30*(x^6-1)^(2/3)-14*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)-20*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3-48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x^2-35*RootOf(_Z^3-2)-50*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3+18*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^5+14*x^6*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)-9*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)+12*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^5+30*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x^5+12*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x+30*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x-9*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x^4-18*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x^3+48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2+9*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x^2+18*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x+30*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)+30*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^4-48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x+60*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^3-30*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^2-60*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x)/(x^2-x-1)^3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)+1/6*RootOf(_Z^3-2)*ln(-(-35*RootOf(_Z^3-2)*x^6-15*RootOf(_Z^3-2)*x^5+18*x^2*(x^6-1)^(2/3)+25*RootOf(_Z^3-2)*x^3-15*RootOf(_Z^3-2)*x+40*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3-24*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x+18*x*(x^6-1)^(2/3)-18*(x^6-1)^(2/3)+56*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)-80*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^3+48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x^2+35*RootOf(_Z^3-2)-50*RootOf(_Z^3-2)^3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^3-24*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^5-56*x^6*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)+15*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)+48*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^5+30*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x^5+48*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x+30*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x+15*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x^4+30*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x^3-48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2-15*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x^2-30*RootOf(_Z^3-2)^2*(x^6-1)^(1/3)*x-18*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)-18*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^4+48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x-36*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^3+18*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^2+36*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x)/(x^2-x-1)^3)","C"
2494,1,676,186,26.466000," ","int((4*x^6+3*x^5-2*x^4+2)*(x^7+x^6-x^5+2*x^3-x)^(1/3)/(x^6+x^5-x^4+x^2-1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{x \left(x^{7}+x^{6}-x^{5}+2 x^{3}-x \right)^{\frac{1}{3}}}{x^{6}+x^{5}-x^{4}+x^{2}-1}+\frac{\ln \left(-\frac{-726439828539024 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{6}-726439828539024 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{5}-948727463035299 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}+726439828539024 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}-948727463035299 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{5}-222287634496275 x^{6}+948727463035299 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}-222287634496275 x^{5}+222287634496275 x^{4}+1131297147498108 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{7}+x^{6}-x^{5}+2 x^{3}-x \right)^{\frac{2}{3}}-142851734429343 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{7}+x^{6}-x^{5}+2 x^{3}-x \right)^{\frac{1}{3}} x -1695026266591056 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+47617244809781 \left(x^{7}+x^{6}-x^{5}+2 x^{3}-x \right)^{\frac{2}{3}}+329481804356255 x \left(x^{7}+x^{6}-x^{5}+2 x^{3}-x \right)^{\frac{1}{3}}+726439828539024 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-518671147157975 x^{2}+948727463035299 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+222287634496275}{x^{6}+x^{5}-x^{4}+x^{2}-1}\right)}{3}+\RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(\frac{-59576925050199 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{6}-59576925050199 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{5}+262005584529741 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{6}+59576925050199 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{4}+262005584529741 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{5}-148191756330850 x^{6}-262005584529741 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{4}-148191756330850 x^{5}+148191756330850 x^{4}+1131297147498108 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{7}+x^{6}-x^{5}+2 x^{3}-x \right)^{\frac{2}{3}}-988445413068765 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \left(x^{7}+x^{6}-x^{5}+2 x^{3}-x \right)^{\frac{1}{3}} x +139012825117131 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{2}+329481804356255 \left(x^{7}+x^{6}-x^{5}+2 x^{3}-x \right)^{\frac{2}{3}}+47617244809781 x \left(x^{7}+x^{6}-x^{5}+2 x^{3}-x \right)^{\frac{1}{3}}+59576925050199 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-518671147157975 x^{2}-262005584529741 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+148191756330850}{x^{6}+x^{5}-x^{4}+x^{2}-1}\right)$&$676$\\ risch&$\text{Expression too large to display}$&$3644$\\ \hline \end{longtable}"," ",0,"-x*(x^7+x^6-x^5+2*x^3-x)^(1/3)/(x^6+x^5-x^4+x^2-1)+1/3*ln(-(-726439828539024*RootOf(9*_Z^2+3*_Z+1)^2*x^6-726439828539024*RootOf(9*_Z^2+3*_Z+1)^2*x^5-948727463035299*RootOf(9*_Z^2+3*_Z+1)*x^6+726439828539024*RootOf(9*_Z^2+3*_Z+1)^2*x^4-948727463035299*RootOf(9*_Z^2+3*_Z+1)*x^5-222287634496275*x^6+948727463035299*RootOf(9*_Z^2+3*_Z+1)*x^4-222287634496275*x^5+222287634496275*x^4+1131297147498108*RootOf(9*_Z^2+3*_Z+1)*(x^7+x^6-x^5+2*x^3-x)^(2/3)-142851734429343*RootOf(9*_Z^2+3*_Z+1)*(x^7+x^6-x^5+2*x^3-x)^(1/3)*x-1695026266591056*RootOf(9*_Z^2+3*_Z+1)*x^2+47617244809781*(x^7+x^6-x^5+2*x^3-x)^(2/3)+329481804356255*x*(x^7+x^6-x^5+2*x^3-x)^(1/3)+726439828539024*RootOf(9*_Z^2+3*_Z+1)^2-518671147157975*x^2+948727463035299*RootOf(9*_Z^2+3*_Z+1)+222287634496275)/(x^6+x^5-x^4+x^2-1))+RootOf(9*_Z^2+3*_Z+1)*ln((-59576925050199*RootOf(9*_Z^2+3*_Z+1)^2*x^6-59576925050199*RootOf(9*_Z^2+3*_Z+1)^2*x^5+262005584529741*RootOf(9*_Z^2+3*_Z+1)*x^6+59576925050199*RootOf(9*_Z^2+3*_Z+1)^2*x^4+262005584529741*RootOf(9*_Z^2+3*_Z+1)*x^5-148191756330850*x^6-262005584529741*RootOf(9*_Z^2+3*_Z+1)*x^4-148191756330850*x^5+148191756330850*x^4+1131297147498108*RootOf(9*_Z^2+3*_Z+1)*(x^7+x^6-x^5+2*x^3-x)^(2/3)-988445413068765*RootOf(9*_Z^2+3*_Z+1)*(x^7+x^6-x^5+2*x^3-x)^(1/3)*x+139012825117131*RootOf(9*_Z^2+3*_Z+1)*x^2+329481804356255*(x^7+x^6-x^5+2*x^3-x)^(2/3)+47617244809781*x*(x^7+x^6-x^5+2*x^3-x)^(1/3)+59576925050199*RootOf(9*_Z^2+3*_Z+1)^2-518671147157975*x^2-262005584529741*RootOf(9*_Z^2+3*_Z+1)+148191756330850)/(x^6+x^5-x^4+x^2-1))","C"
2495,0,0,167,0.144000," ","int((-1+(-1+2*k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(b-(1+2*b)*x+(b+k)*x^2),x)","\[\int \frac{-1+\left(-1+2 k \right) x}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(b -\left(1+2 b \right) x +\left(b +k \right) x^{2}\right)}\, dx\]"," ",0,"int((-1+(-1+2*k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(b-(1+2*b)*x+(b+k)*x^2),x)","F"
2496,1,984,175,0.707000," ","int((a^2*x^3+b^2)^(1/2)*(a^2*x^6+c*x^3+2*b^2)/x^7/(a^2*x^6-b^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\sqrt{a^{2} x^{3}+b^{2}}\, \left(a^{2} x^{3}+2 x^{3} c +2 b^{2}\right)}{6 b^{2} x^{6}}+\frac{a^{2} \left(\frac{i \left(6 a^{2} b +6 a \,b^{2}+2 a c +2 b c \right) \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}-b \right)}{\sum}\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i a \left(2 x +\frac{-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{a \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i a \left(2 x +\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(i \left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  \sqrt{3}\, a -i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}}+2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-\left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  a -\left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  +i \sqrt{3}\, b^{2}-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  -3 b^{2}}{2 b \left(a +b \right)}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{2 \left(a +b \right) \sqrt{a^{2} x^{3}+b^{2}}}\right)}{3 a^{2} b}-\frac{2 \left(a^{2}-12 b^{2}-2 c \right) \arctanh \left(\frac{\sqrt{a^{2} x^{3}+b^{2}}}{\sqrt{b^{2}}}\right)}{3 \sqrt{b^{2}}}-\frac{i \left(-6 a^{2} b +6 a \,b^{2}+2 a c -2 b c \right) \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}+b \right)}{\sum}\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i a \left(2 x +\frac{-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{a \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i a \left(2 x +\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(i \left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  \sqrt{3}\, a -i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}}+2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-\left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  a -\left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  +i \sqrt{3}\, b^{2}-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  -3 b^{2}}{2 b \left(a -b \right)}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{2 \left(a -b \right) \sqrt{a^{2} x^{3}+b^{2}}}\right)}{3 a^{2} b}\right)}{4 b^{2}}$&$984$\\ default&$-\frac{c \left(-\frac{\sqrt{a^{2} x^{3}+b^{2}}}{3 x^{3}}-\frac{a^{2} \arctanh \left(\frac{\sqrt{a^{2} x^{3}+b^{2}}}{\sqrt{b^{2}}}\right)}{3 \sqrt{b^{2}}}\right)}{b^{2}}+\frac{a^{2} \left(3 a b +c \right) \left(\frac{2 \sqrt{a^{2} x^{3}+b^{2}}}{3 a}+\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}-b \right)}{\sum}\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i a \left(2 x +\frac{-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{a \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i a \left(2 x +\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(i \left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  \sqrt{3}\, a -i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}}+2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-\left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  a -\left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  +i \sqrt{3}\, b^{2}-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  -3 b^{2}}{2 b \left(a +b \right)}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{2 \sqrt{a^{2} x^{3}+b^{2}}}\right)}{3 a^{2}}\right)}{2 b^{3}}+\frac{a^{2} \left(3 a b -c \right) \left(\frac{2 \sqrt{a^{2} x^{3}+b^{2}}}{3 a}+\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{3}+b \right)}{\sum}\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i a \left(2 x +\frac{-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{a \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i a \left(2 x +\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(i \left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  \sqrt{3}\, a -i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}}+2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-\left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  a -\left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  +i \sqrt{3}\, b^{2}-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  -3 b^{2}}{2 b \left(a -b \right)}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{2 \sqrt{a^{2} x^{3}+b^{2}}}\right)}{3 a^{2}}\right)}{2 b^{3}}-\frac{3 a^{2} \left(\frac{2 \sqrt{a^{2} x^{3}+b^{2}}}{3}-\frac{2 b^{2} \arctanh \left(\frac{\sqrt{a^{2} x^{3}+b^{2}}}{\sqrt{b^{2}}}\right)}{3 \sqrt{b^{2}}}\right)}{b^{2}}+\frac{\sqrt{a^{2} x^{3}+b^{2}}}{3 x^{6}}+\frac{a^{2} \sqrt{a^{2} x^{3}+b^{2}}}{6 b^{2} x^{3}}-\frac{a^{4} \arctanh \left(\frac{\sqrt{a^{2} x^{3}+b^{2}}}{\sqrt{b^{2}}}\right)}{6 b^{2} \sqrt{b^{2}}}$&$1088$\\ elliptic&$\text{Expression too large to display}$&$3271$\\ \hline \end{longtable}"," ",0,"1/6*(a^2*x^3+b^2)^(1/2)*(a^2*x^3+2*c*x^3+2*b^2)/b^2/x^6+1/4/b^2*a^2*(1/3*I*(6*a^2*b+6*a*b^2+2*a*c+2*b*c)/a^2/b*2^(1/2)*sum(1/(a+b)*(-a*b^2)^(1/3)*(1/2*I*a*(2*x+1/a*(-I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3)))/(-a*b^2)^(1/3))^(1/2)*(a*(x-1/a*(-a*b^2)^(1/3))/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3)))^(1/2)*(-1/2*I*a*(2*x+1/a*(I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3)))/(-a*b^2)^(1/3))^(1/2)/(a^2*x^3+b^2)^(1/2)*(I*(-a*b^2)^(1/3)*_alpha*3^(1/2)*a-I*3^(1/2)*(-a*b^2)^(2/3)+2*_alpha^2*a^2-(-a*b^2)^(1/3)*_alpha*a-(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2/a*(-a*b^2)^(1/3)-1/2*I*3^(1/2)/a*(-a*b^2)^(1/3))*3^(1/2)*a/(-a*b^2)^(1/3))^(1/2),-1/2*(2*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha^2*a-I*(-a*b^2)^(2/3)*3^(1/2)*_alpha+I*3^(1/2)*b^2-3*(-a*b^2)^(2/3)*_alpha-3*b^2)/b/(a+b),(I*3^(1/2)/a*(-a*b^2)^(1/3)/(-3/2/a*(-a*b^2)^(1/3)+1/2*I*3^(1/2)/a*(-a*b^2)^(1/3)))^(1/2)),_alpha=RootOf(_Z^3*a-b))-2/3*(a^2-12*b^2-2*c)*arctanh((a^2*x^3+b^2)^(1/2)/(b^2)^(1/2))/(b^2)^(1/2)-1/3*I*(-6*a^2*b+6*a*b^2+2*a*c-2*b*c)/a^2/b*2^(1/2)*sum(1/(a-b)*(-a*b^2)^(1/3)*(1/2*I*a*(2*x+1/a*(-I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3)))/(-a*b^2)^(1/3))^(1/2)*(a*(x-1/a*(-a*b^2)^(1/3))/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3)))^(1/2)*(-1/2*I*a*(2*x+1/a*(I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3)))/(-a*b^2)^(1/3))^(1/2)/(a^2*x^3+b^2)^(1/2)*(I*(-a*b^2)^(1/3)*_alpha*3^(1/2)*a-I*3^(1/2)*(-a*b^2)^(2/3)+2*_alpha^2*a^2-(-a*b^2)^(1/3)*_alpha*a-(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2/a*(-a*b^2)^(1/3)-1/2*I*3^(1/2)/a*(-a*b^2)^(1/3))*3^(1/2)*a/(-a*b^2)^(1/3))^(1/2),1/2*(2*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha^2*a-I*(-a*b^2)^(2/3)*3^(1/2)*_alpha+I*3^(1/2)*b^2-3*(-a*b^2)^(2/3)*_alpha-3*b^2)/b/(a-b),(I*3^(1/2)/a*(-a*b^2)^(1/3)/(-3/2/a*(-a*b^2)^(1/3)+1/2*I*3^(1/2)/a*(-a*b^2)^(1/3)))^(1/2)),_alpha=RootOf(_Z^3*a+b)))","C"
2497,0,0,161,0.038000," ","int(x^7*(-4*a+3*x)/(x^2*(-a+x))^(2/3)/(d*x^8-a^2+2*a*x-x^2),x)","\[\int \frac{x^{7} \left(-4 a +3 x \right)}{\left(x^{2} \left(-a +x \right)\right)^{\frac{2}{3}} \left(d \,x^{8}-a^{2}+2 a x -x^{2}\right)}\, dx\]"," ",0,"int(x^7*(-4*a+3*x)/(x^2*(-a+x))^(2/3)/(d*x^8-a^2+2*a*x-x^2),x)","F"
2498,0,0,174,0.158000," ","int((-1+2*x+(k^2-2*k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(b-(2*b*k+1)*x+(b*k^2+1)*x^2),x)","\[\int \frac{-1+2 x +\left(k^{2}-2 k \right) x^{2}}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{2}{3}} \left(b -\left(2 b k +1\right) x +\left(b \,k^{2}+1\right) x^{2}\right)}\, dx\]"," ",0,"int((-1+2*x+(k^2-2*k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(b-(2*b*k+1)*x+(b*k^2+1)*x^2),x)","F"
2499,1,14413,134,61.448000," ","int(1/(x^3-x^2)^(1/3)/(x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$14413$\\ risch&$\text{Expression too large to display}$&$16404$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2500,1,20141,134,151.210000," ","int(1/(x^3-x^2)^(1/3)/(x^4-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$20141$\\ trager&$\text{Expression too large to display}$&$27937$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2501,1,1702,160,25.615000," ","int((x^4-x^2)^(1/3)/x/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1702$\\ \hline \end{longtable}"," ",0,"-1/4*ln(-(5842000*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^4*x^4+11606848*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^3*x^4-24828500*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^4*x^2-49329104*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^3*x^2-2555875*x^4*RootOf(_Z^3+2)^2-5077996*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^4+33610788*(x^4-x^2)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2+5842000*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^4+11606848*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^3+1339950*(x^4-x^2)^(1/3)*RootOf(_Z^3+2)*x^2-33610788*(x^4-x^2)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^2+28479750*x^2*RootOf(_Z^3+2)^2+56583384*x^2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)+2679900*(x^4-x^2)^(2/3)-1339950*(x^4-x^2)^(1/3)*RootOf(_Z^3+2)+33610788*(x^4-x^2)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)-2555875*RootOf(_Z^3+2)^2-5077996*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2))/(x^2+1)^2)*RootOf(_Z^3+2)-1/2*ln(-(5842000*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^4*x^4+11606848*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^3*x^4-24828500*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^4*x^2-49329104*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^3*x^2-2555875*x^4*RootOf(_Z^3+2)^2-5077996*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^4+33610788*(x^4-x^2)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2+5842000*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^4+11606848*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^3+1339950*(x^4-x^2)^(1/3)*RootOf(_Z^3+2)*x^2-33610788*(x^4-x^2)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^2+28479750*x^2*RootOf(_Z^3+2)^2+56583384*x^2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)+2679900*(x^4-x^2)^(2/3)-1339950*(x^4-x^2)^(1/3)*RootOf(_Z^3+2)+33610788*(x^4-x^2)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)-2555875*RootOf(_Z^3+2)^2-5077996*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2))/(x^2+1)^2)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)+1/2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*ln((38576*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^4*x^4-11606848*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^3*x^4-163948*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^4*x^2+49329104*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^3*x^2-21699*x^4*RootOf(_Z^3+2)^2+6528852*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^4+33610788*(x^4-x^2)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2+38576*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^4-11606848*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^3-18145344*(x^4-x^2)^(1/3)*RootOf(_Z^3+2)*x^2-33610788*(x^4-x^2)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^2-24110*x^2*RootOf(_Z^3+2)^2+7254280*x^2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)-36290688*(x^4-x^2)^(2/3)+18145344*(x^4-x^2)^(1/3)*RootOf(_Z^3+2)+33610788*(x^4-x^2)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)-21699*RootOf(_Z^3+2)^2+6528852*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2))/(x^2+1)^2)","C"
2502,0,0,164,0.014000," ","int((a*x^6+b)/x^3/(a*x^3-b)/(a*x^4+b*x)^(1/4),x)","\[\int \frac{a \,x^{6}+b}{x^{3} \left(a \,x^{3}-b \right) \left(a \,x^{4}+b x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^6+b)/x^3/(a*x^3-b)/(a*x^4+b*x)^(1/4),x)","F"
2503,1,1580,47,1.220000," ","int((a*x+(a*x-b)^(1/2))^(1/2)/x^2/(a*x-b)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$2 a \left(-\frac{-\frac{\left(\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}\right)^{\frac{3}{2}}}{\sqrt{-b}\, \left(\sqrt{a x -b}-\sqrt{-b}\right)}+\frac{\left(1+2 \sqrt{-b}\right) \left(\sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}+\frac{\left(1+2 \sqrt{-b}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}\right)}{2}-\left(-b \right)^{\frac{1}{4}} \ln \left(\frac{2 \sqrt{-b}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+2 \left(-b \right)^{\frac{1}{4}} \sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}}{\sqrt{a x -b}-\sqrt{-b}}\right)\right)}{2 \sqrt{-b}}+\frac{\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}}{2}+\frac{\left(4 \sqrt{-b}-\left(1+2 \sqrt{-b}\right)^{2}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}\right)}{4}}{\sqrt{-b}}}{4 b}+\frac{\sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}+\frac{\left(1+2 \sqrt{-b}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}\right)}{2}-\left(-b \right)^{\frac{1}{4}} \ln \left(\frac{2 \sqrt{-b}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+2 \left(-b \right)^{\frac{1}{4}} \sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}}{\sqrt{a x -b}-\sqrt{-b}}\right)}{4 b \sqrt{-b}}-\frac{\frac{\left(\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}\right)^{\frac{3}{2}}}{\sqrt{-b}\, \left(\sqrt{a x -b}+\sqrt{-b}\right)}-\frac{\left(1-2 \sqrt{-b}\right) \left(\sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}+\frac{\left(1-2 \sqrt{-b}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}\right)}{2}+\frac{\sqrt{-b}\, \ln \left(\frac{-2 \sqrt{-b}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)+2 \sqrt{-\sqrt{-b}}\, \sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}}{\sqrt{a x -b}+\sqrt{-b}}\right)}{\sqrt{-\sqrt{-b}}}\right)}{2 \sqrt{-b}}-\frac{2 \left(\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}}{4}+\frac{\left(-4 \sqrt{-b}-\left(1-2 \sqrt{-b}\right)^{2}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}\right)}{8}\right)}{\sqrt{-b}}}{4 b}-\frac{\sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}+\frac{\left(1-2 \sqrt{-b}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}\right)}{2}+\frac{\sqrt{-b}\, \ln \left(\frac{-2 \sqrt{-b}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)+2 \sqrt{-\sqrt{-b}}\, \sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}}{\sqrt{a x -b}+\sqrt{-b}}\right)}{\sqrt{-\sqrt{-b}}}}{4 b \sqrt{-b}}\right)$&$1580$\\ default&$2 a \left(-\frac{-\frac{\left(\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}\right)^{\frac{3}{2}}}{\sqrt{-b}\, \left(\sqrt{a x -b}-\sqrt{-b}\right)}+\frac{\left(1+2 \sqrt{-b}\right) \left(\sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}+\frac{\left(1+2 \sqrt{-b}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}\right)}{2}-\left(-b \right)^{\frac{1}{4}} \ln \left(\frac{2 \sqrt{-b}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+2 \left(-b \right)^{\frac{1}{4}} \sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}}{\sqrt{a x -b}-\sqrt{-b}}\right)\right)}{2 \sqrt{-b}}+\frac{\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}}{2}+\frac{\left(4 \sqrt{-b}-\left(1+2 \sqrt{-b}\right)^{2}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}\right)}{4}}{\sqrt{-b}}}{4 b}+\frac{\sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}+\frac{\left(1+2 \sqrt{-b}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}\right)}{2}-\left(-b \right)^{\frac{1}{4}} \ln \left(\frac{2 \sqrt{-b}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+2 \left(-b \right)^{\frac{1}{4}} \sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}}{\sqrt{a x -b}-\sqrt{-b}}\right)}{4 b \sqrt{-b}}-\frac{\frac{\left(\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}\right)^{\frac{3}{2}}}{\sqrt{-b}\, \left(\sqrt{a x -b}+\sqrt{-b}\right)}-\frac{\left(1-2 \sqrt{-b}\right) \left(\sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}+\frac{\left(1-2 \sqrt{-b}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}\right)}{2}+\frac{\sqrt{-b}\, \ln \left(\frac{-2 \sqrt{-b}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)+2 \sqrt{-\sqrt{-b}}\, \sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}}{\sqrt{a x -b}+\sqrt{-b}}\right)}{\sqrt{-\sqrt{-b}}}\right)}{2 \sqrt{-b}}-\frac{2 \left(\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}}{4}+\frac{\left(-4 \sqrt{-b}-\left(1-2 \sqrt{-b}\right)^{2}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}\right)}{8}\right)}{\sqrt{-b}}}{4 b}-\frac{\sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}+\frac{\left(1-2 \sqrt{-b}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}\right)}{2}+\frac{\sqrt{-b}\, \ln \left(\frac{-2 \sqrt{-b}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)+2 \sqrt{-\sqrt{-b}}\, \sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}}{\sqrt{a x -b}+\sqrt{-b}}\right)}{\sqrt{-\sqrt{-b}}}}{4 b \sqrt{-b}}\right)$&$1580$\\ \hline \end{longtable}"," ",0,"2*a*(-1/4/b*(-1/(-b)^(1/2)/((a*x-b)^(1/2)-(-b)^(1/2))*(((a*x-b)^(1/2)-(-b)^(1/2))^2+(1+2*(-b)^(1/2))*((a*x-b)^(1/2)-(-b)^(1/2))+(-b)^(1/2))^(3/2)+1/2*(1+2*(-b)^(1/2))/(-b)^(1/2)*((((a*x-b)^(1/2)-(-b)^(1/2))^2+(1+2*(-b)^(1/2))*((a*x-b)^(1/2)-(-b)^(1/2))+(-b)^(1/2))^(1/2)+1/2*(1+2*(-b)^(1/2))*ln(1/2+(a*x-b)^(1/2)+(((a*x-b)^(1/2)-(-b)^(1/2))^2+(1+2*(-b)^(1/2))*((a*x-b)^(1/2)-(-b)^(1/2))+(-b)^(1/2))^(1/2))-(-b)^(1/4)*ln((2*(-b)^(1/2)+(1+2*(-b)^(1/2))*((a*x-b)^(1/2)-(-b)^(1/2))+2*(-b)^(1/4)*(((a*x-b)^(1/2)-(-b)^(1/2))^2+(1+2*(-b)^(1/2))*((a*x-b)^(1/2)-(-b)^(1/2))+(-b)^(1/2))^(1/2))/((a*x-b)^(1/2)-(-b)^(1/2))))+2/(-b)^(1/2)*(1/4*(2*(a*x-b)^(1/2)+1)*(((a*x-b)^(1/2)-(-b)^(1/2))^2+(1+2*(-b)^(1/2))*((a*x-b)^(1/2)-(-b)^(1/2))+(-b)^(1/2))^(1/2)+1/8*(4*(-b)^(1/2)-(1+2*(-b)^(1/2))^2)*ln(1/2+(a*x-b)^(1/2)+(((a*x-b)^(1/2)-(-b)^(1/2))^2+(1+2*(-b)^(1/2))*((a*x-b)^(1/2)-(-b)^(1/2))+(-b)^(1/2))^(1/2))))+1/4/b/(-b)^(1/2)*((((a*x-b)^(1/2)-(-b)^(1/2))^2+(1+2*(-b)^(1/2))*((a*x-b)^(1/2)-(-b)^(1/2))+(-b)^(1/2))^(1/2)+1/2*(1+2*(-b)^(1/2))*ln(1/2+(a*x-b)^(1/2)+(((a*x-b)^(1/2)-(-b)^(1/2))^2+(1+2*(-b)^(1/2))*((a*x-b)^(1/2)-(-b)^(1/2))+(-b)^(1/2))^(1/2))-(-b)^(1/4)*ln((2*(-b)^(1/2)+(1+2*(-b)^(1/2))*((a*x-b)^(1/2)-(-b)^(1/2))+2*(-b)^(1/4)*(((a*x-b)^(1/2)-(-b)^(1/2))^2+(1+2*(-b)^(1/2))*((a*x-b)^(1/2)-(-b)^(1/2))+(-b)^(1/2))^(1/2))/((a*x-b)^(1/2)-(-b)^(1/2))))-1/4/b*(1/(-b)^(1/2)/((a*x-b)^(1/2)+(-b)^(1/2))*(((a*x-b)^(1/2)+(-b)^(1/2))^2+(1-2*(-b)^(1/2))*((a*x-b)^(1/2)+(-b)^(1/2))-(-b)^(1/2))^(3/2)-1/2*(1-2*(-b)^(1/2))/(-b)^(1/2)*((((a*x-b)^(1/2)+(-b)^(1/2))^2+(1-2*(-b)^(1/2))*((a*x-b)^(1/2)+(-b)^(1/2))-(-b)^(1/2))^(1/2)+1/2*(1-2*(-b)^(1/2))*ln(1/2+(a*x-b)^(1/2)+(((a*x-b)^(1/2)+(-b)^(1/2))^2+(1-2*(-b)^(1/2))*((a*x-b)^(1/2)+(-b)^(1/2))-(-b)^(1/2))^(1/2))+(-b)^(1/2)/(-(-b)^(1/2))^(1/2)*ln((-2*(-b)^(1/2)+(1-2*(-b)^(1/2))*((a*x-b)^(1/2)+(-b)^(1/2))+2*(-(-b)^(1/2))^(1/2)*(((a*x-b)^(1/2)+(-b)^(1/2))^2+(1-2*(-b)^(1/2))*((a*x-b)^(1/2)+(-b)^(1/2))-(-b)^(1/2))^(1/2))/((a*x-b)^(1/2)+(-b)^(1/2))))-2/(-b)^(1/2)*(1/4*(2*(a*x-b)^(1/2)+1)*(((a*x-b)^(1/2)+(-b)^(1/2))^2+(1-2*(-b)^(1/2))*((a*x-b)^(1/2)+(-b)^(1/2))-(-b)^(1/2))^(1/2)+1/8*(-4*(-b)^(1/2)-(1-2*(-b)^(1/2))^2)*ln(1/2+(a*x-b)^(1/2)+(((a*x-b)^(1/2)+(-b)^(1/2))^2+(1-2*(-b)^(1/2))*((a*x-b)^(1/2)+(-b)^(1/2))-(-b)^(1/2))^(1/2))))-1/4/b/(-b)^(1/2)*((((a*x-b)^(1/2)+(-b)^(1/2))^2+(1-2*(-b)^(1/2))*((a*x-b)^(1/2)+(-b)^(1/2))-(-b)^(1/2))^(1/2)+1/2*(1-2*(-b)^(1/2))*ln(1/2+(a*x-b)^(1/2)+(((a*x-b)^(1/2)+(-b)^(1/2))^2+(1-2*(-b)^(1/2))*((a*x-b)^(1/2)+(-b)^(1/2))-(-b)^(1/2))^(1/2))+(-b)^(1/2)/(-(-b)^(1/2))^(1/2)*ln((-2*(-b)^(1/2)+(1-2*(-b)^(1/2))*((a*x-b)^(1/2)+(-b)^(1/2))+2*(-(-b)^(1/2))^(1/2)*(((a*x-b)^(1/2)+(-b)^(1/2))^2+(1-2*(-b)^(1/2))*((a*x-b)^(1/2)+(-b)^(1/2))-(-b)^(1/2))^(1/2))/((a*x-b)^(1/2)+(-b)^(1/2)))))","B"
2504,1,910,151,12.244000," ","int((3+x)/(x^2-1)^(1/3)/(2*x^2-x+5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{3}-12\right) \ln \left(-\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-12\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-12\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-12\right)^{3} x^{2}+1818 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-12\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-12\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-12\right)^{2} x^{2}-9 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-12\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-12\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-12\right)^{3} x -5454 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-12\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-12\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-12\right)^{2} x -1215 \left(x^{2}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-12\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-12\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-12\right)^{2}-405 \left(x^{2}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-12\right)^{2} x -3006 \left(x^{2}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-12\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-12\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-12\right) x +405 \left(x^{2}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-12\right)^{2}+3006 \left(x^{2}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-12\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-12\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-12\right)+2 \RootOf \left(\textit{\_Z}^{3}-12\right) x^{2}+1212 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-12\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-12\right)+36 \textit{\_Z}^{2}\right) x^{2}-13 \RootOf \left(\textit{\_Z}^{3}-12\right) x -7878 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-12\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-12\right)+36 \textit{\_Z}^{2}\right) x +576 \left(x^{2}-1\right)^{\frac{2}{3}}-7 \RootOf \left(\textit{\_Z}^{3}-12\right)-4242 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-12\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-12\right)+36 \textit{\_Z}^{2}\right)}{2 x^{2}-x +5}\right)}{6}+\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-12\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-12\right)+36 \textit{\_Z}^{2}\right) \ln \left(\frac{303 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-12\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-12\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-12\right)^{3} x^{2}+18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-12\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-12\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-12\right)^{2} x^{2}-909 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-12\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-12\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-12\right)^{3} x -54 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-12\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-12\right)+36 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-12\right)^{2} x -1215 \left(x^{2}-1\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-12\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-12\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-12\right)^{2}-405 \left(x^{2}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-12\right)^{2} x +576 \left(x^{2}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-12\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-12\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-12\right) x +405 \left(x^{2}-1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-12\right)^{2}-576 \left(x^{2}-1\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-12\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-12\right)+36 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-12\right)+404 \RootOf \left(\textit{\_Z}^{3}-12\right) x^{2}+24 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-12\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-12\right)+36 \textit{\_Z}^{2}\right) x^{2}-505 \RootOf \left(\textit{\_Z}^{3}-12\right) x -30 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-12\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-12\right)+36 \textit{\_Z}^{2}\right) x -3006 \left(x^{2}-1\right)^{\frac{2}{3}}+707 \RootOf \left(\textit{\_Z}^{3}-12\right)+42 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-12\right)^{2}+6 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-12\right)+36 \textit{\_Z}^{2}\right)}{2 x^{2}-x +5}\right)$&$910$\\ \hline \end{longtable}"," ",0,"1/6*RootOf(_Z^3-12)*ln(-(3*RootOf(RootOf(_Z^3-12)^2+6*_Z*RootOf(_Z^3-12)+36*_Z^2)*RootOf(_Z^3-12)^3*x^2+1818*RootOf(RootOf(_Z^3-12)^2+6*_Z*RootOf(_Z^3-12)+36*_Z^2)^2*RootOf(_Z^3-12)^2*x^2-9*RootOf(RootOf(_Z^3-12)^2+6*_Z*RootOf(_Z^3-12)+36*_Z^2)*RootOf(_Z^3-12)^3*x-5454*RootOf(RootOf(_Z^3-12)^2+6*_Z*RootOf(_Z^3-12)+36*_Z^2)^2*RootOf(_Z^3-12)^2*x-1215*(x^2-1)^(2/3)*RootOf(RootOf(_Z^3-12)^2+6*_Z*RootOf(_Z^3-12)+36*_Z^2)*RootOf(_Z^3-12)^2-405*(x^2-1)^(1/3)*RootOf(_Z^3-12)^2*x-3006*(x^2-1)^(1/3)*RootOf(RootOf(_Z^3-12)^2+6*_Z*RootOf(_Z^3-12)+36*_Z^2)*RootOf(_Z^3-12)*x+405*(x^2-1)^(1/3)*RootOf(_Z^3-12)^2+3006*(x^2-1)^(1/3)*RootOf(RootOf(_Z^3-12)^2+6*_Z*RootOf(_Z^3-12)+36*_Z^2)*RootOf(_Z^3-12)+2*RootOf(_Z^3-12)*x^2+1212*RootOf(RootOf(_Z^3-12)^2+6*_Z*RootOf(_Z^3-12)+36*_Z^2)*x^2-13*RootOf(_Z^3-12)*x-7878*RootOf(RootOf(_Z^3-12)^2+6*_Z*RootOf(_Z^3-12)+36*_Z^2)*x+576*(x^2-1)^(2/3)-7*RootOf(_Z^3-12)-4242*RootOf(RootOf(_Z^3-12)^2+6*_Z*RootOf(_Z^3-12)+36*_Z^2))/(2*x^2-x+5))+RootOf(RootOf(_Z^3-12)^2+6*_Z*RootOf(_Z^3-12)+36*_Z^2)*ln((303*RootOf(RootOf(_Z^3-12)^2+6*_Z*RootOf(_Z^3-12)+36*_Z^2)*RootOf(_Z^3-12)^3*x^2+18*RootOf(RootOf(_Z^3-12)^2+6*_Z*RootOf(_Z^3-12)+36*_Z^2)^2*RootOf(_Z^3-12)^2*x^2-909*RootOf(RootOf(_Z^3-12)^2+6*_Z*RootOf(_Z^3-12)+36*_Z^2)*RootOf(_Z^3-12)^3*x-54*RootOf(RootOf(_Z^3-12)^2+6*_Z*RootOf(_Z^3-12)+36*_Z^2)^2*RootOf(_Z^3-12)^2*x-1215*(x^2-1)^(2/3)*RootOf(RootOf(_Z^3-12)^2+6*_Z*RootOf(_Z^3-12)+36*_Z^2)*RootOf(_Z^3-12)^2-405*(x^2-1)^(1/3)*RootOf(_Z^3-12)^2*x+576*(x^2-1)^(1/3)*RootOf(RootOf(_Z^3-12)^2+6*_Z*RootOf(_Z^3-12)+36*_Z^2)*RootOf(_Z^3-12)*x+405*(x^2-1)^(1/3)*RootOf(_Z^3-12)^2-576*(x^2-1)^(1/3)*RootOf(RootOf(_Z^3-12)^2+6*_Z*RootOf(_Z^3-12)+36*_Z^2)*RootOf(_Z^3-12)+404*RootOf(_Z^3-12)*x^2+24*RootOf(RootOf(_Z^3-12)^2+6*_Z*RootOf(_Z^3-12)+36*_Z^2)*x^2-505*RootOf(_Z^3-12)*x-30*RootOf(RootOf(_Z^3-12)^2+6*_Z*RootOf(_Z^3-12)+36*_Z^2)*x-3006*(x^2-1)^(2/3)+707*RootOf(_Z^3-12)+42*RootOf(RootOf(_Z^3-12)^2+6*_Z*RootOf(_Z^3-12)+36*_Z^2))/(2*x^2-x+5))","C"
2505,0,0,173,0.016000," ","int((-2+(1+k)*x)*(1-(1+k)*x+(a+k)*x^2)/x^2/((1-x)*x*(-k*x+1))^(1/3)/(1-(1+k)*x+(-b+k)*x^2),x)","\[\int \frac{\left(-2+\left(1+k \right) x \right) \left(1-\left(1+k \right) x +\left(a +k \right) x^{2}\right)}{x^{2} \left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(1-\left(1+k \right) x +\left(-b +k \right) x^{2}\right)}\, dx\]"," ",0,"int((-2+(1+k)*x)*(1-(1+k)*x+(a+k)*x^2)/x^2/((1-x)*x*(-k*x+1))^(1/3)/(1-(1+k)*x+(-b+k)*x^2),x)","F"
2506,0,0,169,0.044000," ","int((x^3-2)*(x^4+x^3+x)^(1/3)/(x^3+1)/(x^3-x^2+1),x)","\[\int \frac{\left(x^{3}-2\right) \left(x^{4}+x^{3}+x \right)^{\frac{1}{3}}}{\left(x^{3}+1\right) \left(x^{3}-x^{2}+1\right)}\, dx\]"," ",0,"int((x^3-2)*(x^4+x^3+x)^(1/3)/(x^3+1)/(x^3-x^2+1),x)","F"
2507,0,0,59,0.148000," ","int((a*x^4+b*x^3)^(1/4)/(a*x+2*x^2-2*b),x)","\[\int \frac{\left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}}{a x +2 x^{2}-2 b}\, dx\]"," ",0,"int((a*x^4+b*x^3)^(1/4)/(a*x+2*x^2-2*b),x)","F"
2508,0,0,59,0.005000," ","int((a*x^4+b*x^3)^(1/4)/(a*x+2*x^2-2*b),x)","\[\int \frac{\left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}}{a x +2 x^{2}-2 b}\, dx\]"," ",0,"int((a*x^4+b*x^3)^(1/4)/(a*x+2*x^2-2*b),x)","F"
2509,0,0,164,0.013000," ","int((x^3+1)^(2/3)*(2*x^6-1)/x^6/(2*x^3-1),x)","\[\int \frac{\left(x^{3}+1\right)^{\frac{2}{3}} \left(2 x^{6}-1\right)}{x^{6} \left(2 x^{3}-1\right)}\, dx\]"," ",0,"int((x^3+1)^(2/3)*(2*x^6-1)/x^6/(2*x^3-1),x)","F"
2510,0,0,177,0.039000," ","int((a*x^4-b)/(a*x^4+b)/(a^2*x^8+c*x^4+b^2)^(1/4),x)","\[\int \frac{a \,x^{4}-b}{\left(a \,x^{4}+b \right) \left(a^{2} x^{8}+c \,x^{4}+b^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^4-b)/(a*x^4+b)/(a^2*x^8+c*x^4+b^2)^(1/4),x)","F"
2511,1,109,11,0.148000," ","int((x+(1+x)^(1/2))^(1/2)/(1+x)^(1/2)/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)}{\sum}\frac{\left(2 \textit{\_R}^{5}-5 \textit{\_R}^{4}+5 \textit{\_R}^{2}-1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+5 \textit{\_R}^{4}+10 \textit{\_R}^{3}-18 \textit{\_R}^{2}+10 \textit{\_R} -1}\right)}{2}$&$109$\\ default&$-\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)}{\sum}\frac{\left(2 \textit{\_R}^{5}-5 \textit{\_R}^{4}+5 \textit{\_R}^{2}-1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+5 \textit{\_R}^{4}+10 \textit{\_R}^{3}-18 \textit{\_R}^{2}+10 \textit{\_R} -1}\right)}{2}$&$109$\\ \hline \end{longtable}"," ",0,"-1/2*sum((2*_R^5-5*_R^4+5*_R^2-1)/(_R^7-3*_R^5+5*_R^4+10*_R^3-18*_R^2+10*_R-1)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^8-4*_Z^6+8*_Z^5+20*_Z^4-48*_Z^3+40*_Z^2-8*_Z+1))","B"
2512,1,109,11,0.146000," ","int((x+(1+x)^(1/2))^(1/2)/(1+x)^(1/2)/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)}{\sum}\frac{\left(2 \textit{\_R}^{5}-5 \textit{\_R}^{4}+5 \textit{\_R}^{2}-1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+5 \textit{\_R}^{4}+10 \textit{\_R}^{3}-18 \textit{\_R}^{2}+10 \textit{\_R} -1}\right)}{2}$&$109$\\ default&$-\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)}{\sum}\frac{\left(2 \textit{\_R}^{5}-5 \textit{\_R}^{4}+5 \textit{\_R}^{2}-1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+5 \textit{\_R}^{4}+10 \textit{\_R}^{3}-18 \textit{\_R}^{2}+10 \textit{\_R} -1}\right)}{2}$&$109$\\ \hline \end{longtable}"," ",0,"-1/2*sum((2*_R^5-5*_R^4+5*_R^2-1)/(_R^7-3*_R^5+5*_R^4+10*_R^3-18*_R^2+10*_R-1)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^8-4*_Z^6+8*_Z^5+20*_Z^4-48*_Z^3+40*_Z^2-8*_Z+1))","B"
2513,1,2403,175,38.335000," ","int((2+x)^2*(9*x^3-30*x^2+66*x-19)^(1/3)/(-3+2*x)^2/(x^3-6*x^2+6*x-5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2403$\\ risch&$\text{Expression too large to display}$&$3445$\\ \hline \end{longtable}"," ",0,"(9*x^3-30*x^2+66*x-19)^(1/3)/(-3+2*x)-1/3*ln((4042340134560*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)^2*RootOf(_Z^3-2)^3*x^3-332299625211918*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)^4*x^3-5597086340160*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)^2*RootOf(_Z^3-2)^3*x^2+460107173370348*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)^4*x^2+33582518040960*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)^2*RootOf(_Z^3-2)^3*x-672529373074512*(9*x^3-30*x^2+66*x-19)^(2/3)*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)^2*x-2760643040222088*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)^4*x+1008794059611768*(9*x^3-30*x^2+66*x-19)^(2/3)*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)^2+3753601553520*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)*x^3-308563937696781*RootOf(_Z^3-2)^2*x^3+3710761539141168*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*(9*x^3-30*x^2+66*x-19)^(1/3)*x^2-14999599107360*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)*x^2+149450971794336*RootOf(_Z^3-2)*(9*x^3-30*x^2+66*x-19)^(1/3)*x^2+1233038536042758*RootOf(_Z^3-2)^2*x^2-11132284617423504*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*(9*x^3-30*x^2+66*x-19)^(1/3)*x+26282614428000*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)*x+28351223523420*(9*x^3-30*x^2+66*x-19)^(2/3)*x-448352915383008*RootOf(_Z^3-2)*(9*x^3-30*x^2+66*x-19)^(1/3)*x-2160556171249650*RootOf(_Z^3-2)^2*x+8349213463067628*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*(9*x^3-30*x^2+66*x-19)^(1/3)-10619163369360*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)-42526835285130*(9*x^3-30*x^2+66*x-19)^(2/3)+336264686537256*RootOf(_Z^3-2)*(9*x^3-30*x^2+66*x-19)^(1/3)+872945840834483*RootOf(_Z^3-2)^2)/(x^2-x+1)/(-5+x))*RootOf(_Z^3-2)-6*ln((4042340134560*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)^2*RootOf(_Z^3-2)^3*x^3-332299625211918*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)^4*x^3-5597086340160*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)^2*RootOf(_Z^3-2)^3*x^2+460107173370348*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)^4*x^2+33582518040960*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)^2*RootOf(_Z^3-2)^3*x-672529373074512*(9*x^3-30*x^2+66*x-19)^(2/3)*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)^2*x-2760643040222088*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)^4*x+1008794059611768*(9*x^3-30*x^2+66*x-19)^(2/3)*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)^2+3753601553520*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)*x^3-308563937696781*RootOf(_Z^3-2)^2*x^3+3710761539141168*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*(9*x^3-30*x^2+66*x-19)^(1/3)*x^2-14999599107360*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)*x^2+149450971794336*RootOf(_Z^3-2)*(9*x^3-30*x^2+66*x-19)^(1/3)*x^2+1233038536042758*RootOf(_Z^3-2)^2*x^2-11132284617423504*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*(9*x^3-30*x^2+66*x-19)^(1/3)*x+26282614428000*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)*x+28351223523420*(9*x^3-30*x^2+66*x-19)^(2/3)*x-448352915383008*RootOf(_Z^3-2)*(9*x^3-30*x^2+66*x-19)^(1/3)*x-2160556171249650*RootOf(_Z^3-2)^2*x+8349213463067628*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*(9*x^3-30*x^2+66*x-19)^(1/3)-10619163369360*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)-42526835285130*(9*x^3-30*x^2+66*x-19)^(2/3)+336264686537256*RootOf(_Z^3-2)*(9*x^3-30*x^2+66*x-19)^(1/3)+872945840834483*RootOf(_Z^3-2)^2)/(x^2-x+1)/(-5+x))*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)+1/3*RootOf(_Z^3-2)*ln((2990696626907262*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)^2*RootOf(_Z^3-2)^3*x^3-112287225960*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)^4*x^3-4140964560333132*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)^2*RootOf(_Z^3-2)^3*x^2+155474620560*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)^4*x^2+24845787361998792*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)^2*RootOf(_Z^3-2)^3*x+336264686537256*(9*x^3-30*x^2+66*x-19)^(2/3)*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)^2*x-932847723360*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)^4*x-504397029805884*(9*x^3-30*x^2+66*x-19)^(2/3)*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)^2-2444775814059111*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)*x^3+91790351380*RootOf(_Z^3-2)^2*x^3+510322023421560*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*(9*x^3-30*x^2+66*x-19)^(1/3)*x^2+10637239651014474*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)*x^2-74725485897168*RootOf(_Z^3-2)*(9*x^3-30*x^2+66*x-19)^(1/3)*x^2-399380572920*RootOf(_Z^3-2)^2*x^2-1530966070264680*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*(9*x^3-30*x^2+66*x-19)^(1/3)*x-16684362501024762*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)*x+51538354710294*(9*x^3-30*x^2+66*x-19)^(2/3)*x+224176457691504*RootOf(_Z^3-2)*(9*x^3-30*x^2+66*x-19)^(1/3)*x+626422875960*RootOf(_Z^3-2)^2*x+1148224552698510*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*(9*x^3-30*x^2+66*x-19)^(1/3)+7856512567510347*RootOf(RootOf(_Z^3-2)^2+18*_Z*RootOf(_Z^3-2)+324*_Z^2)*RootOf(_Z^3-2)-77307532065441*(9*x^3-30*x^2+66*x-19)^(2/3)-168132343268628*RootOf(_Z^3-2)*(9*x^3-30*x^2+66*x-19)^(1/3)-294976760260*RootOf(_Z^3-2)^2)/(x^2-x+1)/(-5+x))","C"
2514,1,2738,164,27.830000," ","int((x^3+1)/(x^3-1)/(x^4+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2738$\\ \hline \end{longtable}"," ",0,"1/4*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*ln((37494*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x^3-8004*RootOf(_Z^3-4)^3*x^3*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)-93735*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x^2+20010*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x^2+37494*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x-8004*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x-158472*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*(x^4+x^2)^(2/3)-316944*(x^4+x^2)^(1/3)*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)*x-124980*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*x^3+91368*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^2*x+26680*RootOf(_Z^3-4)*x^3-449928*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*x^2+96048*RootOf(_Z^3-4)*x^2-124980*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*x+26680*RootOf(_Z^3-4)*x+182736*(x^4+x^2)^(2/3))/(-1+x)^2/x)-1/6*ln((37494*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+33000*RootOf(_Z^3-4)^3*x^3*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)-93735*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x^2-82500*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x^2+37494*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x+33000*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x+158472*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*(x^4+x^2)^(2/3)+316944*(x^4+x^2)^(1/3)*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)*x+224964*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*x^3+302664*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^2*x+198000*RootOf(_Z^3-4)*x^3+199968*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*x^2+176000*RootOf(_Z^3-4)*x^2+224964*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*x+198000*RootOf(_Z^3-4)*x+605328*(x^4+x^2)^(2/3))/(-1+x)^2/x)*RootOf(_Z^3-4)-1/4*ln((37494*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x^3+33000*RootOf(_Z^3-4)^3*x^3*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)-93735*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x^2-82500*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x^2+37494*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x+33000*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x+158472*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*(x^4+x^2)^(2/3)+316944*(x^4+x^2)^(1/3)*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)*x+224964*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*x^3+302664*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^2*x+198000*RootOf(_Z^3-4)*x^3+199968*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*x^2+176000*RootOf(_Z^3-4)*x^2+224964*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*x+198000*RootOf(_Z^3-4)*x+605328*(x^4+x^2)^(2/3))/(-1+x)^2/x)*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)+2/3*ln((3150*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^4*x^3-7875*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^4*x^2+3150*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^4*x+5352*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*x^3-29232*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*(x^4+x^2)^(2/3)+29232*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*(x^4+x^2)^(1/3)*x-53280*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*x^2+5352*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*x-71808*x^3+102336*(x^4+x^2)^(2/3)-102336*x*(x^4+x^2)^(1/3)-47872*x^2-71808*x)/x/(x^2+x+1))+1/4*ln((3150*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^4*x^3-7875*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^4*x^2+3150*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^4*x+5352*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*x^3-29232*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*(x^4+x^2)^(2/3)+29232*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*(x^4+x^2)^(1/3)*x-53280*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*x^2+5352*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*x-71808*x^3+102336*(x^4+x^2)^(2/3)-102336*x*(x^4+x^2)^(1/3)-47872*x^2-71808*x)/x/(x^2+x+1))*RootOf(_Z^3-4)^2*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)-1/4*RootOf(_Z^3-4)^2*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*ln((3150*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^4*x^3-7875*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^4*x^2+3150*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^4*x+11448*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*x^3+29232*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*(x^4+x^2)^(2/3)-29232*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*(x^4+x^2)^(1/3)*x+11280*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*x^2+11448*RootOf(4*RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2*x-63680*x^3+180288*(x^4+x^2)^(2/3)-180288*x*(x^4+x^2)^(1/3)+38208*x^2-63680*x)/x/(x^2+x+1))","C"
2515,0,0,178,0.017000," ","int(x*(4*a*b-3*(a+b)*x+2*x^2)/(x^2*(-a+x)*(-b+x))^(1/3)/(-a*b*d+(a+b)*d*x-d*x^2+x^4),x)","\[\int \frac{x \left(4 a b -3 \left(a +b \right) x +2 x^{2}\right)}{\left(x^{2} \left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{3}} \left(-a b d +\left(a +b \right) d x -d \,x^{2}+x^{4}\right)}\, dx\]"," ",0,"int(x*(4*a*b-3*(a+b)*x+2*x^2)/(x^2*(-a+x)*(-b+x))^(1/3)/(-a*b*d+(a+b)*d*x-d*x^2+x^4),x)","F"
2516,1,96,142,0.182000," ","int((a*x^4+b)^(1/2)/(a*x^4-b),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(\frac{\arctan \left(\frac{\sqrt{a \,x^{4}+b}\, \sqrt{2}}{2 x \left(a b \right)^{\frac{1}{4}}}\right)}{2 \left(a b \right)^{\frac{1}{4}}}-\frac{\ln \left(\frac{\frac{\sqrt{a \,x^{4}+b}\, \sqrt{2}}{2 x}+\left(a b \right)^{\frac{1}{4}}}{\frac{\sqrt{a \,x^{4}+b}\, \sqrt{2}}{2 x}-\left(a b \right)^{\frac{1}{4}}}\right)}{4 \left(a b \right)^{\frac{1}{4}}}\right) \sqrt{2}}{2}$&$96$\\ elliptic&$\frac{\left(\frac{\arctan \left(\frac{\sqrt{a \,x^{4}+b}\, \sqrt{2}}{2 x \left(a b \right)^{\frac{1}{4}}}\right)}{2 \left(a b \right)^{\frac{1}{4}}}-\frac{\ln \left(\frac{\frac{\sqrt{a \,x^{4}+b}\, \sqrt{2}}{2 x}+\left(a b \right)^{\frac{1}{4}}}{\frac{\sqrt{a \,x^{4}+b}\, \sqrt{2}}{2 x}-\left(a b \right)^{\frac{1}{4}}}\right)}{4 \left(a b \right)^{\frac{1}{4}}}\right) \sqrt{2}}{2}$&$96$\\ \hline \end{longtable}"," ",0,"1/2*(1/2/(a*b)^(1/4)*arctan(1/2*(a*x^4+b)^(1/2)*2^(1/2)/x/(a*b)^(1/4))-1/4/(a*b)^(1/4)*ln((1/2*(a*x^4+b)^(1/2)*2^(1/2)/x+(a*b)^(1/4))/(1/2*(a*x^4+b)^(1/2)*2^(1/2)/x-(a*b)^(1/4))))*2^(1/2)","A"
2517,1,1804,158,39.620000," ","int((x^2+1)/(x^2+x-1)/(x^6-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1804$\\ \hline \end{longtable}"," ",0,"1/6*RootOf(_Z^3+2)*ln(-(72*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x-30*x^2*(x^6-1)^(2/3)+7*RootOf(_Z^3+2)*x^6-9*RootOf(_Z^3+2)*x-9*RootOf(_Z^3+2)*x^5+30*x*(x^6-1)^(2/3)+30*(x^6-1)^(2/3)-7*RootOf(_Z^3+2)+15*RootOf(_Z^3+2)*x^3+56*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)-48*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x+6*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x+48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x^2-48*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^5+6*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^5+80*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^3-10*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^3-56*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^6-120*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^3+72*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^5+24*RootOf(_Z^3+2)^2*(x^6-1)^(1/3)*x^4-48*RootOf(_Z^3+2)^2*(x^6-1)^(1/3)*x^3-48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2-24*RootOf(_Z^3+2)^2*(x^6-1)^(1/3)*x^2+48*RootOf(_Z^3+2)^2*(x^6-1)^(1/3)*x+18*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)+18*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^4-48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x-36*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^3-18*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^2+36*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x+24*RootOf(_Z^3+2)^2*(x^6-1)^(1/3))/(x^2+x-1)^3)+1/3*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*ln(-(-3*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x+9*x^2*(x^6-1)^(2/3)-14*RootOf(_Z^3+2)*x^6+6*RootOf(_Z^3+2)*x+6*RootOf(_Z^3+2)*x^5-9*x*(x^6-1)^(2/3)-9*(x^6-1)^(2/3)+14*RootOf(_Z^3+2)-10*RootOf(_Z^3+2)*x^3-7*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)-6*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x+12*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x-24*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x^2-6*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^5+12*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^5+10*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^3-20*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^3+7*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^6+5*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^3-3*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^5-12*RootOf(_Z^3+2)^2*(x^6-1)^(1/3)*x^4+24*RootOf(_Z^3+2)^2*(x^6-1)^(1/3)*x^3+24*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2+12*RootOf(_Z^3+2)^2*(x^6-1)^(1/3)*x^2-24*RootOf(_Z^3+2)^2*(x^6-1)^(1/3)*x-15*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)-15*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^4+24*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x+30*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^3+15*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^2-30*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x-12*RootOf(_Z^3+2)^2*(x^6-1)^(1/3))/(x^2+x-1)^3)","C"
2518,1,2695,158,38.991000," ","int((x^2+1)/(x^2+x-1)/(x^6-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2695$\\ \hline \end{longtable}"," ",0,"-1/6*ln(-(18*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x-30*x^2*(x^6-1)^(2/3)-35*RootOf(_Z^3+2)*x^6+45*RootOf(_Z^3+2)*x+45*RootOf(_Z^3+2)*x^5+30*x*(x^6-1)^(2/3)+30*(x^6-1)^(2/3)+35*RootOf(_Z^3+2)-75*RootOf(_Z^3+2)*x^3+14*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)-12*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x-30*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x+48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x^2-12*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^5-30*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^5+20*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^3+50*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^3-14*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^6-30*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^3+18*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^5-9*RootOf(_Z^3+2)^2*(x^6-1)^(1/3)*x^4+18*RootOf(_Z^3+2)^2*(x^6-1)^(1/3)*x^3-48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2+9*RootOf(_Z^3+2)^2*(x^6-1)^(1/3)*x^2-18*RootOf(_Z^3+2)^2*(x^6-1)^(1/3)*x+30*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)+30*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^4-48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x-60*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^3-30*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^2+60*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x-9*RootOf(_Z^3+2)^2*(x^6-1)^(1/3))/(x^2+x-1)^3)*RootOf(_Z^3+2)-1/3*ln(-(18*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x-30*x^2*(x^6-1)^(2/3)-35*RootOf(_Z^3+2)*x^6+45*RootOf(_Z^3+2)*x+45*RootOf(_Z^3+2)*x^5+30*x*(x^6-1)^(2/3)+30*(x^6-1)^(2/3)+35*RootOf(_Z^3+2)-75*RootOf(_Z^3+2)*x^3+14*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)-12*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x-30*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x+48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x^2-12*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^5-30*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^5+20*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^3+50*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^3-14*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^6-30*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^3+18*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^5-9*RootOf(_Z^3+2)^2*(x^6-1)^(1/3)*x^4+18*RootOf(_Z^3+2)^2*(x^6-1)^(1/3)*x^3-48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2+9*RootOf(_Z^3+2)^2*(x^6-1)^(1/3)*x^2-18*RootOf(_Z^3+2)^2*(x^6-1)^(1/3)*x+30*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)+30*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^4-48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x-60*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^3-30*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^2+60*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x-9*RootOf(_Z^3+2)^2*(x^6-1)^(1/3))/(x^2+x-1)^3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)+1/6*RootOf(_Z^3+2)*ln((24*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x-18*x^2*(x^6-1)^(2/3)-35*RootOf(_Z^3+2)*x^6+15*RootOf(_Z^3+2)*x+15*RootOf(_Z^3+2)*x^5+18*x*(x^6-1)^(2/3)+18*(x^6-1)^(2/3)+35*RootOf(_Z^3+2)-25*RootOf(_Z^3+2)*x^3+56*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)+48*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x+30*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x+48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x^2+48*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^5+30*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^5-80*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^3-50*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^3-56*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^6-40*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^3+24*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^5-15*RootOf(_Z^3+2)^2*(x^6-1)^(1/3)*x^4+30*RootOf(_Z^3+2)^2*(x^6-1)^(1/3)*x^3-48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2+15*RootOf(_Z^3+2)^2*(x^6-1)^(1/3)*x^2-30*RootOf(_Z^3+2)^2*(x^6-1)^(1/3)*x+18*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)+18*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^4-48*(x^6-1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x-36*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^3-18*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x^2+36*(x^6-1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x-15*RootOf(_Z^3+2)^2*(x^6-1)^(1/3))/(x^2+x-1)^3)","C"
2519,1,84511,23,173.959000," ","int(x^3*(x^3-x^2)^(1/3)/(x^6+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$84511$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2520,0,0,56,0.043000," ","int((2*a*x^8-2*c*x^4+b)/(a*x^4-b)^(1/4)/(2*a*x^8-c*x^4-2*b),x)","\[\int \frac{2 a \,x^{8}-2 c \,x^{4}+b}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(2 a \,x^{8}-c \,x^{4}-2 b \right)}\, dx\]"," ",0,"int((2*a*x^8-2*c*x^4+b)/(a*x^4-b)^(1/4)/(2*a*x^8-c*x^4-2*b),x)","F"
2521,0,0,56,0.003000," ","int((2*a*x^8-2*c*x^4+b)/(a*x^4-b)^(1/4)/(2*a*x^8-c*x^4-2*b),x)","\[\int \frac{2 a \,x^{8}-2 c \,x^{4}+b}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(2 a \,x^{8}-c \,x^{4}-2 b \right)}\, dx\]"," ",0,"int((2*a*x^8-2*c*x^4+b)/(a*x^4-b)^(1/4)/(2*a*x^8-c*x^4-2*b),x)","F"
2522,1,2405,139,28.153000," ","int(1/x^3/(x^3+1)/(x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2405$\\ risch&$\text{Expression too large to display}$&$4131$\\ \hline \end{longtable}"," ",0,"3/40*(9*x^2+6*x+5)*(x^3-x^2)^(2/3)/x^4+644972544*RootOf(139314069504*_Z^6-373248*_Z^3+1)^5*ln(-(-1289945088*RootOf(139314069504*_Z^6-373248*_Z^3+1)^5*x^2-26873856*RootOf(139314069504*_Z^6-373248*_Z^3+1)^4*(x^3-x^2)^(1/3)*x+644972544*RootOf(139314069504*_Z^6-373248*_Z^3+1)^5*x+373248*RootOf(139314069504*_Z^6-373248*_Z^3+1)^3*(x^3-x^2)^(2/3)+6912*RootOf(139314069504*_Z^6-373248*_Z^3+1)^2*x^2-3456*RootOf(139314069504*_Z^6-373248*_Z^3+1)^2*x-(x^3-x^2)^(2/3))/(373248*RootOf(139314069504*_Z^6-373248*_Z^3+1)^3*x-746496*RootOf(139314069504*_Z^6-373248*_Z^3+1)^3+x+1)/x)-644972544*RootOf(139314069504*_Z^6-373248*_Z^3+1)^5*ln((-644972544*RootOf(139314069504*_Z^6-373248*_Z^3+1)^5*x^2-26873856*RootOf(139314069504*_Z^6-373248*_Z^3+1)^4*(x^3-x^2)^(1/3)*x+1289945088*RootOf(139314069504*_Z^6-373248*_Z^3+1)^5*x+373248*RootOf(139314069504*_Z^6-373248*_Z^3+1)^3*(x^3-x^2)^(2/3)+3456*RootOf(139314069504*_Z^6-373248*_Z^3+1)^2*x^2-1728*RootOf(139314069504*_Z^6-373248*_Z^3+1)^2*x-(x^3-x^2)^(2/3))/(373248*RootOf(139314069504*_Z^6-373248*_Z^3+1)^3*x-746496*RootOf(139314069504*_Z^6-373248*_Z^3+1)^3+x+1)/x)+1728*RootOf(139314069504*_Z^6-373248*_Z^3+1)^2*ln((-644972544*RootOf(139314069504*_Z^6-373248*_Z^3+1)^5*x^2-26873856*RootOf(139314069504*_Z^6-373248*_Z^3+1)^4*(x^3-x^2)^(1/3)*x+1289945088*RootOf(139314069504*_Z^6-373248*_Z^3+1)^5*x+373248*RootOf(139314069504*_Z^6-373248*_Z^3+1)^3*(x^3-x^2)^(2/3)+3456*RootOf(139314069504*_Z^6-373248*_Z^3+1)^2*x^2-1728*RootOf(139314069504*_Z^6-373248*_Z^3+1)^2*x-(x^3-x^2)^(2/3))/(373248*RootOf(139314069504*_Z^6-373248*_Z^3+1)^3*x-746496*RootOf(139314069504*_Z^6-373248*_Z^3+1)^3+x+1)/x)+24*RootOf(139314069504*_Z^6-373248*_Z^3+1)*ln((80621568*RootOf(139314069504*_Z^6-373248*_Z^3+1)^4*(x^3-x^2)^(1/3)*x-1492992*RootOf(139314069504*_Z^6-373248*_Z^3+1)^3*x^2+15552*(x^3-x^2)^(2/3)*RootOf(139314069504*_Z^6-373248*_Z^3+1)^2+746496*RootOf(139314069504*_Z^6-373248*_Z^3+1)^3*x-216*RootOf(139314069504*_Z^6-373248*_Z^3+1)*(x^3-x^2)^(1/3)*x+2*x^2-x)/(373248*RootOf(139314069504*_Z^6-373248*_Z^3+1)^3*x-746496*RootOf(139314069504*_Z^6-373248*_Z^3+1)^3-2*x+1)/x)+8957952*RootOf(139314069504*_Z^6-373248*_Z^3+1)^4*ln((-644972544*RootOf(139314069504*_Z^6-373248*_Z^3+1)^5*x^2+1289945088*RootOf(139314069504*_Z^6-373248*_Z^3+1)^5*x+373248*(x^3-x^2)^(1/3)*RootOf(139314069504*_Z^6-373248*_Z^3+1)^3*x-1728*RootOf(139314069504*_Z^6-373248*_Z^3+1)^2*x^2+72*RootOf(139314069504*_Z^6-373248*_Z^3+1)*(x^3-x^2)^(2/3)-1728*RootOf(139314069504*_Z^6-373248*_Z^3+1)^2*x-x*(x^3-x^2)^(1/3))/(373248*RootOf(139314069504*_Z^6-373248*_Z^3+1)^3*x-746496*RootOf(139314069504*_Z^6-373248*_Z^3+1)^3-2*x+1)/x)-24*RootOf(139314069504*_Z^6-373248*_Z^3+1)*ln((-644972544*RootOf(139314069504*_Z^6-373248*_Z^3+1)^5*x^2+1289945088*RootOf(139314069504*_Z^6-373248*_Z^3+1)^5*x+373248*(x^3-x^2)^(1/3)*RootOf(139314069504*_Z^6-373248*_Z^3+1)^3*x-1728*RootOf(139314069504*_Z^6-373248*_Z^3+1)^2*x^2+72*RootOf(139314069504*_Z^6-373248*_Z^3+1)*(x^3-x^2)^(2/3)-1728*RootOf(139314069504*_Z^6-373248*_Z^3+1)^2*x-x*(x^3-x^2)^(1/3))/(373248*RootOf(139314069504*_Z^6-373248*_Z^3+1)^3*x-746496*RootOf(139314069504*_Z^6-373248*_Z^3+1)^3-2*x+1)/x)+24*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)*ln(-(-72*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)*RootOf(_Z^3-4)^3*x^2-31104*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)^2*RootOf(_Z^3-4)^2*x^2+1728*(x^3-x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)*RootOf(_Z^3-4)^2+144*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)*RootOf(_Z^3-4)^3*x+62208*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)^2*RootOf(_Z^3-4)^2*x+15*RootOf(_Z^3-4)^2*(x^3-x^2)^(1/3)*x+3456*(x^3-x^2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)*RootOf(_Z^3-4)*x+11*RootOf(_Z^3-4)*x^2+4752*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)*x^2+30*(x^3-x^2)^(2/3)-RootOf(_Z^3-4)*x-432*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)*x)/x/(1+x))-1/6*ln((144*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)*RootOf(_Z^3-4)^3*x^2+31104*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)^2*RootOf(_Z^3-4)^2*x^2+1728*(x^3-x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)*RootOf(_Z^3-4)^2-288*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)*RootOf(_Z^3-4)^3*x-62208*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)^2*RootOf(_Z^3-4)^2*x+9*RootOf(_Z^3-4)^2*(x^3-x^2)^(1/3)*x+3456*(x^3-x^2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)*RootOf(_Z^3-4)*x+26*RootOf(_Z^3-4)*x^2+5616*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)*x^2+18*(x^3-x^2)^(2/3)-10*RootOf(_Z^3-4)*x-2160*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)*x)/x/(1+x))*RootOf(_Z^3-4)-24*ln((144*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)*RootOf(_Z^3-4)^3*x^2+31104*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)^2*RootOf(_Z^3-4)^2*x^2+1728*(x^3-x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)*RootOf(_Z^3-4)^2-288*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)*RootOf(_Z^3-4)^3*x-62208*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)^2*RootOf(_Z^3-4)^2*x+9*RootOf(_Z^3-4)^2*(x^3-x^2)^(1/3)*x+3456*(x^3-x^2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)*RootOf(_Z^3-4)*x+26*RootOf(_Z^3-4)*x^2+5616*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)*x^2+18*(x^3-x^2)^(2/3)-10*RootOf(_Z^3-4)*x-2160*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)*x)/x/(1+x))*RootOf(RootOf(_Z^3-4)^2+144*_Z*RootOf(_Z^3-4)+20736*_Z^2)","B"
2523,1,14154,51,206.976000," ","int((x^2-1)*(x^4+x^3)^(1/4)/(x^4+x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$14154$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2524,1,14158,51,211.978000," ","int((x^2-1)*(x^4+x^3)^(1/4)/(x^4+x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$14158$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2525,0,0,61,0.038000," ","int((a*x^2-b)*(a*x^4-b*x^2)^(1/4)/(x^4-a*x^2+b),x)","\[\int \frac{\left(a \,x^{2}-b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}{x^{4}-a \,x^{2}+b}\, dx\]"," ",0,"int((a*x^2-b)*(a*x^4-b*x^2)^(1/4)/(x^4-a*x^2+b),x)","F"
2526,0,0,61,0.003000," ","int((a*x^2-b)*(a*x^4-b*x^2)^(1/4)/(x^4-a*x^2+b),x)","\[\int \frac{\left(a \,x^{2}-b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}{x^{4}-a \,x^{2}+b}\, dx\]"," ",0,"int((a*x^2-b)*(a*x^4-b*x^2)^(1/4)/(x^4-a*x^2+b),x)","F"
2527,0,0,166,0.070000," ","int((a*x^2-b^2)^2/(a*x^2+b^2)^2/(b+(a*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{\left(a \,x^{2}-b^{2}\right)^{2}}{\left(a \,x^{2}+b^{2}\right)^{2} \sqrt{b +\sqrt{a \,x^{2}+b^{2}}}}\, dx\]"," ",0,"int((a*x^2-b^2)^2/(a*x^2+b^2)^2/(b+(a*x^2+b^2)^(1/2))^(1/2),x)","F"
2528,0,0,180,0.219000," ","int((-2+(1+k)*x)*(a-a*(1+k)*x+(a*k+1)*x^2)/(-1+x)/((1-x)*x*(-k*x+1))^(1/3)/(k*x-1)/(b-b*(1+k)*x+(b*k-1)*x^2),x)","\[\int \frac{\left(-2+\left(1+k \right) x \right) \left(a -a \left(1+k \right) x +\left(a k +1\right) x^{2}\right)}{\left(-1+x \right) \left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(k x -1\right) \left(b -b \left(1+k \right) x +\left(b k -1\right) x^{2}\right)}\, dx\]"," ",0,"int((-2+(1+k)*x)*(a-a*(1+k)*x+(a*k+1)*x^2)/(-1+x)/((1-x)*x*(-k*x+1))^(1/3)/(k*x-1)/(b-b*(1+k)*x+(b*k-1)*x^2),x)","F"
2529,0,0,184,0.011000," ","int((x^3+b)^3/(x^3+a)^(1/3),x)","\[\int \frac{\left(x^{3}+b \right)^{3}}{\left(x^{3}+a \right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((x^3+b)^3/(x^3+a)^(1/3),x)","F"
2530,0,0,80,180.000000," ","int((x^3-x^2+1)/(x^3-x^2-1)/(x^3+x^2)^(1/3),x)","\[\int \frac{x^{3}-x^{2}+1}{\left(x^{3}-x^{2}-1\right) \left(x^{3}+x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((x^3-x^2+1)/(x^3-x^2-1)/(x^3+x^2)^(1/3),x)","F"
2531,1,253926,80,396.220000," ","int((x^3-x^2+1)/(x^3-x^2-1)/(x^3+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$253926$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2532,0,0,178,0.026000," ","int((-3+(-2*k^2+1)*x+3*k^2*x^2+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(-1+d-(2+d)*x-(d*k^2+1)*x^2+d*k^2*x^3),x)","\[\int \frac{-3+\left(-2 k^{2}+1\right) x +3 k^{2} x^{2}+k^{2} x^{3}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{1}{3}} \left(-1+d -\left(2+d \right) x -\left(d \,k^{2}+1\right) x^{2}+d \,k^{2} x^{3}\right)}\, dx\]"," ",0,"int((-3+(-2*k^2+1)*x+3*k^2*x^2+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(-1+d-(2+d)*x-(d*k^2+1)*x^2+d*k^2*x^3),x)","F"
2533,1,108,142,0.189000," ","int(x^2/(a*x^4-b)/(a*x^4+b)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(-\frac{\left(a b \right)^{\frac{1}{4}} \ln \left(\frac{\frac{\sqrt{a \,x^{4}+b}\, \sqrt{2}}{2 x}+\left(a b \right)^{\frac{1}{4}}}{\frac{\sqrt{a \,x^{4}+b}\, \sqrt{2}}{2 x}-\left(a b \right)^{\frac{1}{4}}}\right)}{8 a b}-\frac{\left(a b \right)^{\frac{1}{4}} \arctan \left(\frac{\sqrt{a \,x^{4}+b}\, \sqrt{2}}{2 x \left(a b \right)^{\frac{1}{4}}}\right)}{4 a b}\right) \sqrt{2}}{2}$&$108$\\ elliptic&$\frac{\left(-\frac{\left(a b \right)^{\frac{1}{4}} \ln \left(\frac{\frac{\sqrt{a \,x^{4}+b}\, \sqrt{2}}{2 x}+\left(a b \right)^{\frac{1}{4}}}{\frac{\sqrt{a \,x^{4}+b}\, \sqrt{2}}{2 x}-\left(a b \right)^{\frac{1}{4}}}\right)}{8 a b}-\frac{\left(a b \right)^{\frac{1}{4}} \arctan \left(\frac{\sqrt{a \,x^{4}+b}\, \sqrt{2}}{2 x \left(a b \right)^{\frac{1}{4}}}\right)}{4 a b}\right) \sqrt{2}}{2}$&$108$\\ \hline \end{longtable}"," ",0,"1/2*(-1/8*(a*b)^(1/4)/a/b*ln((1/2*(a*x^4+b)^(1/2)*2^(1/2)/x+(a*b)^(1/4))/(1/2*(a*x^4+b)^(1/2)*2^(1/2)/x-(a*b)^(1/4)))-1/4*(a*b)^(1/4)/a/b*arctan(1/2*(a*x^4+b)^(1/2)*2^(1/2)/x/(a*b)^(1/4)))*2^(1/2)","A"
2534,0,0,170,0.048000," ","int((-1+x)*(k*x-1)*(-2+(1+k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(b-2*(b*k+b)*x+(b*k^2+4*b*k+b)*x^2-2*b*k*(1+k)*x^3+(b*k^2-1)*x^4),x)","\[\int \frac{\left(-1+x \right) \left(k x -1\right) \left(-2+\left(1+k \right) x \right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(b -2 \left(b k +b \right) x +\left(b \,k^{2}+4 b k +b \right) x^{2}-2 b k \left(1+k \right) x^{3}+\left(b \,k^{2}-1\right) x^{4}\right)}\, dx\]"," ",0,"int((-1+x)*(k*x-1)*(-2+(1+k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(b-2*(b*k+b)*x+(b*k^2+4*b*k+b)*x^2-2*b*k*(1+k)*x^3+(b*k^2-1)*x^4),x)","F"
2535,1,198,84,0.559000," ","int((f*x^2-g)*(c+(a*x+b)^(1/2))^(1/2)/(d*x^2+e),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{-\frac{4 f \left(-\frac{\left(c +\sqrt{a x +b}\right)^{\frac{5}{2}}}{5}+\frac{c \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}\right)}{d}+\frac{a^{2} \left(\munderset{\textit{\_R} =\RootOf \left(d \,\textit{\_Z}^{8}-4 c d \,\textit{\_Z}^{6}+\left(6 c^{2} d -2 b d \right) \textit{\_Z}^{4}+\left(-4 c^{3} d +4 b c d \right) \textit{\_Z}^{2}+c^{4} d -2 b \,c^{2} d +a^{2} e +b^{2} d \right)}{\sum}\frac{\left(\left(-d g -e f \right) \textit{\_R}^{4}+c \left(d g +e f \right) \textit{\_R}^{2}\right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5} c +3 \textit{\_R}^{3} c^{2}-\textit{\_R}^{3} b -\textit{\_R} \,c^{3}+\textit{\_R} b c}\right)}{2 d^{2}}}{a}$&$198$\\ default&$\frac{-\frac{4 f \left(-\frac{\left(c +\sqrt{a x +b}\right)^{\frac{5}{2}}}{5}+\frac{c \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}\right)}{d}+\frac{a^{2} \left(\munderset{\textit{\_R} =\RootOf \left(d \,\textit{\_Z}^{8}-4 c d \,\textit{\_Z}^{6}+\left(6 c^{2} d -2 b d \right) \textit{\_Z}^{4}+\left(-4 c^{3} d +4 b c d \right) \textit{\_Z}^{2}+c^{4} d -2 b \,c^{2} d +a^{2} e +b^{2} d \right)}{\sum}\frac{\left(\left(-d g -e f \right) \textit{\_R}^{4}+c \left(d g +e f \right) \textit{\_R}^{2}\right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5} c +3 \textit{\_R}^{3} c^{2}-\textit{\_R}^{3} b -\textit{\_R} \,c^{3}+\textit{\_R} b c}\right)}{2 d^{2}}}{a}$&$198$\\ \hline \end{longtable}"," ",0,"2/a*(-2*f/d*(-1/5*(c+(a*x+b)^(1/2))^(5/2)+1/3*c*(c+(a*x+b)^(1/2))^(3/2))+1/4*a^2/d^2*sum(((-d*g-e*f)*_R^4+c*(d*g+e*f)*_R^2)/(_R^7-3*_R^5*c+3*_R^3*c^2-_R^3*b-_R*c^3+_R*b*c)*ln((c+(a*x+b)^(1/2))^(1/2)-_R),_R=RootOf(d*_Z^8-4*c*d*_Z^6+(6*c^2*d-2*b*d)*_Z^4+(-4*c^3*d+4*b*c*d)*_Z^2+c^4*d-2*b*c^2*d+a^2*e+b^2*d)))","B"
2536,0,0,39,0.388000," ","int((a^2*x^2+b^2)^(1/2)/(d+c*x^2+(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)),x)","\[\int \frac{\sqrt{a^{2} x^{2}+b^{2}}}{d +c \,x^{2}+\sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int((a^2*x^2+b^2)^(1/2)/(d+c*x^2+(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)),x)","F"
2537,0,0,39,0.003000," ","int((a^2*x^2+b^2)^(1/2)/(d+c*x^2+(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)),x)","\[\int \frac{\sqrt{a^{2} x^{2}+b^{2}}}{d +c \,x^{2}+\sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int((a^2*x^2+b^2)^(1/2)/(d+c*x^2+(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)),x)","F"
2538,1,71,163,0.669000," ","int((1-(1-(1-1/x)^(1/2))^(1/2))^(1/2)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{8 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{\frac{9}{2}}}{9}-\frac{24 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{\frac{7}{2}}}{7}+\frac{16 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{\frac{5}{2}}}{5}$&$71$\\ default&$\frac{8 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{\frac{9}{2}}}{9}-\frac{24 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{\frac{7}{2}}}{7}+\frac{16 \left(1-\sqrt{1-\sqrt{1-\frac{1}{x}}}\right)^{\frac{5}{2}}}{5}$&$71$\\ \hline \end{longtable}"," ",0,"8/9*(1-(1-(1-1/x)^(1/2))^(1/2))^(9/2)-24/7*(1-(1-(1-1/x)^(1/2))^(1/2))^(7/2)+16/5*(1-(1-(1-1/x)^(1/2))^(1/2))^(5/2)","A"
2539,1,1110,161,24.309000," ","int((x^4+x^2)^(1/3)/x/(x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1110$\\ \hline \end{longtable}"," ",0,"1/4*RootOf(_Z^3-2)*ln((2247248*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^4*x^4+2103504*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^3*x^4-9550804*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^4*x^2-8939892*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^3*x^2-3511325*RootOf(_Z^3-2)^2*x^4-3286725*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^4+2247248*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^4+2103504*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^3+34713150*(x^4+x^2)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2-30056942*RootOf(_Z^3-2)^2*x^2-28134366*RootOf(_Z^3-2)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^2+10021887*RootOf(_Z^3-2)*(x^4+x^2)^(1/3)*x^2-14669376*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*(x^4+x^2)^(1/3)*x^2-3511325*RootOf(_Z^3-2)^2-3286725*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)+10021887*(x^4+x^2)^(1/3)*RootOf(_Z^3-2)-14669376*(x^4+x^2)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)+14669376*(x^4+x^2)^(2/3))/(-1+x)^2/(1+x)^2)+1/2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*ln((2247248*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^4*x^4+2390992*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^3*x^4-9550804*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^4*x^2-10161716*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^3*x^2+5758573*RootOf(_Z^3-2)^2*x^4+6126917*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^4+2247248*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^4+2390992*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^3-34713150*(x^4+x^2)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2+20506138*RootOf(_Z^3-2)^2*x^2+21817802*RootOf(_Z^3-2)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^2-7334688*RootOf(_Z^3-2)*(x^4+x^2)^(1/3)*x^2+20043774*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*(x^4+x^2)^(1/3)*x^2+5758573*RootOf(_Z^3-2)^2+6126917*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)-7334688*(x^4+x^2)^(1/3)*RootOf(_Z^3-2)+20043774*(x^4+x^2)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)-20043774*(x^4+x^2)^(2/3))/(-1+x)^2/(1+x)^2)","C"
2540,0,0,177,180.000000," ","int(1/(d*x+c)/(a^2*x^2+b)^(1/2)/(a*x-(a^2*x^2+b)^(1/2))^(1/2),x)","\[\int \frac{1}{\left(d x +c \right) \sqrt{a^{2} x^{2}+b}\, \sqrt{a x -\sqrt{a^{2} x^{2}+b}}}\, dx\]"," ",0,"int(1/(d*x+c)/(a^2*x^2+b)^(1/2)/(a*x-(a^2*x^2+b)^(1/2))^(1/2),x)","F"
2541,1,215,147,0.257000," ","int((1+x)^(1/2)*(1+(1+x)^(1/2))^(1/2)/x^2/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{1}{2 \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-1\right)}-\frac{\ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-1\right)}{2}-\frac{1}{2 \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}+1\right)}+\frac{\ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}+1\right)}{2}+\frac{\frac{\left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{2}-\frac{3 \sqrt{1+\sqrt{1+\sqrt{1+x}}}}{2}}{\left(1+\sqrt{1+\sqrt{1+x}}\right)^{2}-2 \sqrt{1+\sqrt{1+x}}-3}-\frac{\left(8+\sqrt{2}\right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{1+\sqrt{1+\sqrt{1+x}}}}{\sqrt{1+\sqrt{2}}}\right)}{8 \sqrt{1+\sqrt{2}}}+\frac{\left(-8+\sqrt{2}\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{1+\sqrt{1+\sqrt{1+x}}}}{\sqrt{\sqrt{2}-1}}\right)}{8 \sqrt{\sqrt{2}-1}}$&$215$\\ default&$-\frac{1}{2 \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-1\right)}-\frac{\ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-1\right)}{2}-\frac{1}{2 \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}+1\right)}+\frac{\ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}+1\right)}{2}+\frac{\frac{\left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{2}-\frac{3 \sqrt{1+\sqrt{1+\sqrt{1+x}}}}{2}}{\left(1+\sqrt{1+\sqrt{1+x}}\right)^{2}-2 \sqrt{1+\sqrt{1+x}}-3}-\frac{\left(8+\sqrt{2}\right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{1+\sqrt{1+\sqrt{1+x}}}}{\sqrt{1+\sqrt{2}}}\right)}{8 \sqrt{1+\sqrt{2}}}+\frac{\left(-8+\sqrt{2}\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{1+\sqrt{1+\sqrt{1+x}}}}{\sqrt{\sqrt{2}-1}}\right)}{8 \sqrt{\sqrt{2}-1}}$&$215$\\ \hline \end{longtable}"," ",0,"-1/2/((1+(1+(1+x)^(1/2))^(1/2))^(1/2)-1)-1/2*ln((1+(1+(1+x)^(1/2))^(1/2))^(1/2)-1)-1/2/((1+(1+(1+x)^(1/2))^(1/2))^(1/2)+1)+1/2*ln((1+(1+(1+x)^(1/2))^(1/2))^(1/2)+1)+2*(1/4*(1+(1+(1+x)^(1/2))^(1/2))^(3/2)-3/4*(1+(1+(1+x)^(1/2))^(1/2))^(1/2))/((1+(1+(1+x)^(1/2))^(1/2))^2-2*(1+(1+x)^(1/2))^(1/2)-3)-1/8*(8+2^(1/2))*2^(1/2)/(1+2^(1/2))^(1/2)*arctanh((1+(1+(1+x)^(1/2))^(1/2))^(1/2)/(1+2^(1/2))^(1/2))+1/8*(-8+2^(1/2))*2^(1/2)/(2^(1/2)-1)^(1/2)*arctan((1+(1+(1+x)^(1/2))^(1/2))^(1/2)/(2^(1/2)-1)^(1/2))","A"
2542,0,0,174,0.156000," ","int((-1+(2-k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(b-(2*b*k+1)*x+(b*k^2+1)*x^2),x)","\[\int \frac{-1+\left(2-k \right) x}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(b -\left(2 b k +1\right) x +\left(b \,k^{2}+1\right) x^{2}\right)}\, dx\]"," ",0,"int((-1+(2-k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(b-(2*b*k+1)*x+(b*k^2+1)*x^2),x)","F"
2543,1,1916,144,13.094000," ","int(1/x^6/(x^3-1)/(x^3+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$1916$\\ trager&$\text{Expression too large to display}$&$2268$\\ \hline \end{longtable}"," ",0,"3/52360*(4491*x^6+1497*x^5-499*x^4+6095*x^3+300*x^2-220*x+3080)/x^5/(x^2*(1+x))^(1/3)-81/32*ln(-(2106*RootOf(729*_Z^6-216*_Z^3+64)^5*x^2-1296*RootOf(729*_Z^6-216*_Z^3+64)^4*(x^3+x^2)^(1/3)*x+1053*RootOf(729*_Z^6-216*_Z^3+64)^5*x+324*(x^3+x^2)^(2/3)*RootOf(729*_Z^6-216*_Z^3+64)^3-528*RootOf(729*_Z^6-216*_Z^3+64)^2*x^2+144*RootOf(729*_Z^6-216*_Z^3+64)*(x^3+x^2)^(1/3)*x-264*x*RootOf(729*_Z^6-216*_Z^3+64)^2+160*(x^3+x^2)^(2/3))/(27*RootOf(729*_Z^6-216*_Z^3+64)^3*x-54*RootOf(729*_Z^6-216*_Z^3+64)^3-24*x-8)/x)*RootOf(729*_Z^6-216*_Z^3+64)^5+3/4*ln(-(2106*RootOf(729*_Z^6-216*_Z^3+64)^5*x^2-1296*RootOf(729*_Z^6-216*_Z^3+64)^4*(x^3+x^2)^(1/3)*x+1053*RootOf(729*_Z^6-216*_Z^3+64)^5*x+324*(x^3+x^2)^(2/3)*RootOf(729*_Z^6-216*_Z^3+64)^3-528*RootOf(729*_Z^6-216*_Z^3+64)^2*x^2+144*RootOf(729*_Z^6-216*_Z^3+64)*(x^3+x^2)^(1/3)*x-264*x*RootOf(729*_Z^6-216*_Z^3+64)^2+160*(x^3+x^2)^(2/3))/(27*RootOf(729*_Z^6-216*_Z^3+64)^3*x-54*RootOf(729*_Z^6-216*_Z^3+64)^3-24*x-8)/x)*RootOf(729*_Z^6-216*_Z^3+64)^2-27/16*RootOf(729*_Z^6-216*_Z^3+64)^4*ln((-729*RootOf(729*_Z^6-216*_Z^3+64)^5*(x^3+x^2)^(1/3)*x-1404*RootOf(729*_Z^6-216*_Z^3+64)^4*x^2+324*(x^3+x^2)^(2/3)*RootOf(729*_Z^6-216*_Z^3+64)^3-702*RootOf(729*_Z^6-216*_Z^3+64)^4*x+576*RootOf(729*_Z^6-216*_Z^3+64)^2*(x^3+x^2)^(1/3)*x+64*x^2*RootOf(729*_Z^6-216*_Z^3+64)-256*(x^3+x^2)^(2/3)+32*RootOf(729*_Z^6-216*_Z^3+64)*x)/(27*RootOf(729*_Z^6-216*_Z^3+64)^3*x-54*RootOf(729*_Z^6-216*_Z^3+64)^3+16*x+24)/x)+1/2*RootOf(729*_Z^6-216*_Z^3+64)*ln(-(-729*RootOf(729*_Z^6-216*_Z^3+64)^6*x^2+1458*RootOf(729*_Z^6-216*_Z^3+64)^6*x-6804*RootOf(729*_Z^6-216*_Z^3+64)^4*(x^3+x^2)^(1/3)*x+1728*RootOf(729*_Z^6-216*_Z^3+64)^3*x^2+3024*(x^3+x^2)^(2/3)*RootOf(729*_Z^6-216*_Z^3+64)^2-1944*RootOf(729*_Z^6-216*_Z^3+64)^3*x-960*x^2-320*x)/(27*RootOf(729*_Z^6-216*_Z^3+64)^3*x-54*RootOf(729*_Z^6-216*_Z^3+64)^3+16*x+24)/x)-3/4*RootOf(729*_Z^6-216*_Z^3+64)^2*ln((-2187*RootOf(729*_Z^6-216*_Z^3+64)^8*x^2+4374*RootOf(729*_Z^6-216*_Z^3+64)^8*x-3888*RootOf(729*_Z^6-216*_Z^3+64)^5*x^2+3240*RootOf(729*_Z^6-216*_Z^3+64)^5*x+6048*(x^3+x^2)^(2/3)*RootOf(729*_Z^6-216*_Z^3+64)^3-1536*RootOf(729*_Z^6-216*_Z^3+64)^2*x^2+2688*RootOf(729*_Z^6-216*_Z^3+64)*(x^3+x^2)^(1/3)*x-2304*x*RootOf(729*_Z^6-216*_Z^3+64)^2-1792*(x^3+x^2)^(2/3))/(27*RootOf(729*_Z^6-216*_Z^3+64)^3*x-54*RootOf(729*_Z^6-216*_Z^3+64)^3-24*x-8)/x)+1/6*RootOf(_Z^3-4)*ln(-(30*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x^2-9*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x^2-60*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x+360*(x^3+x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2+18*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x-240*(x^3+x^2)^(1/3)*RootOf(_Z^3-4)^2*x-594*(x^3+x^2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)*x+340*RootOf(_Z^3-4)*x^2-102*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x^2+60*RootOf(_Z^3-4)*x+84*(x^3+x^2)^(2/3)-18*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x)/x/(-1+x))+1/2*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*ln(-(3*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x^2-90*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x^2-6*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x-360*(x^3+x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2+180*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x+240*(x^3+x^2)^(1/3)*RootOf(_Z^3-4)^2*x+126*(x^3+x^2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)*x-30*RootOf(_Z^3-4)*x^2+900*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x^2-14*RootOf(_Z^3-4)*x-396*(x^3+x^2)^(2/3)+420*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x)/x/(-1+x))","B"
2544,1,2069,144,33.906000," ","int(1/x^6/(x^3-1)/(x^3+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$2069$\\ trager&$\text{Expression too large to display}$&$4312$\\ \hline \end{longtable}"," ",0,"3/52360*(4491*x^6+1497*x^5-499*x^4+6095*x^3+300*x^2-220*x+3080)/x^5/(x^2*(1+x))^(1/3)+1/2*RootOf(729*_Z^6-216*_Z^3+64)*ln(-(-729*RootOf(729*_Z^6-216*_Z^3+64)^6*x^2+1458*RootOf(729*_Z^6-216*_Z^3+64)^6*x-6804*RootOf(729*_Z^6-216*_Z^3+64)^4*(x^3+x^2)^(1/3)*x+1728*RootOf(729*_Z^6-216*_Z^3+64)^3*x^2+3024*(x^3+x^2)^(2/3)*RootOf(729*_Z^6-216*_Z^3+64)^2-1944*RootOf(729*_Z^6-216*_Z^3+64)^3*x-960*x^2-320*x)/(27*RootOf(729*_Z^6-216*_Z^3+64)^3*x-54*RootOf(729*_Z^6-216*_Z^3+64)^3+16*x+24)/x)-3/4*RootOf(729*_Z^6-216*_Z^3+64)^2*ln(-(-162*RootOf(729*_Z^6-216*_Z^3+64)^5*x^2+243*RootOf(729*_Z^6-216*_Z^3+64)^4*(x^3+x^2)^(1/3)*x-81*RootOf(729*_Z^6-216*_Z^3+64)^5*x+162*(x^3+x^2)^(2/3)*RootOf(729*_Z^6-216*_Z^3+64)^3+312*RootOf(729*_Z^6-216*_Z^3+64)^2*x^2+120*RootOf(729*_Z^6-216*_Z^3+64)*(x^3+x^2)^(1/3)*x+156*x*RootOf(729*_Z^6-216*_Z^3+64)^2+80*(x^3+x^2)^(2/3))/(27*RootOf(729*_Z^6-216*_Z^3+64)^3*x-54*RootOf(729*_Z^6-216*_Z^3+64)^3-24*x-8)/x)-27/16*RootOf(729*_Z^6-216*_Z^3+64)^4*ln((-729*RootOf(729*_Z^6-216*_Z^3+64)^5*(x^3+x^2)^(1/3)*x-1404*RootOf(729*_Z^6-216*_Z^3+64)^4*x^2+324*(x^3+x^2)^(2/3)*RootOf(729*_Z^6-216*_Z^3+64)^3-702*RootOf(729*_Z^6-216*_Z^3+64)^4*x+576*RootOf(729*_Z^6-216*_Z^3+64)^2*(x^3+x^2)^(1/3)*x+64*x^2*RootOf(729*_Z^6-216*_Z^3+64)-256*(x^3+x^2)^(2/3)+32*RootOf(729*_Z^6-216*_Z^3+64)*x)/(27*RootOf(729*_Z^6-216*_Z^3+64)^3*x-54*RootOf(729*_Z^6-216*_Z^3+64)^3+16*x+24)/x)+81/32*RootOf(729*_Z^6-216*_Z^3+64)^5*ln((10935*RootOf(729*_Z^6-216*_Z^3+64)^8*x^2-21870*RootOf(729*_Z^6-216*_Z^3+64)^8*x+5832*RootOf(729*_Z^6-216*_Z^3+64)^5*x^2+9072*RootOf(729*_Z^6-216*_Z^3+64)^4*(x^3+x^2)^(1/3)*x+11016*RootOf(729*_Z^6-216*_Z^3+64)^5*x+6048*(x^3+x^2)^(2/3)*RootOf(729*_Z^6-216*_Z^3+64)^3-384*RootOf(729*_Z^6-216*_Z^3+64)^2*x^2-2688*RootOf(729*_Z^6-216*_Z^3+64)*(x^3+x^2)^(1/3)*x-576*x*RootOf(729*_Z^6-216*_Z^3+64)^2-1792*(x^3+x^2)^(2/3))/(27*RootOf(729*_Z^6-216*_Z^3+64)^3*x-54*RootOf(729*_Z^6-216*_Z^3+64)^3-24*x-8)/x)+1/6*RootOf(_Z^3-4)*ln((33*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x^2+9*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x^2-66*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x+360*(x^3+x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-18*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x+42*(x^3+x^2)^(1/3)*RootOf(_Z^3-4)^2*x-594*(x^3+x^2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)*x-330*RootOf(_Z^3-4)*x^2-90*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x^2-154*RootOf(_Z^3-4)*x+396*(x^3+x^2)^(2/3)-42*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x)/x/(-1+x))-1/6*ln((33*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x^2+90*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x^2-66*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x-360*(x^3+x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-180*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x-198*(x^3+x^2)^(1/3)*RootOf(_Z^3-4)^2*x+126*(x^3+x^2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)*x+374*RootOf(_Z^3-4)*x^2+1020*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x^2+66*RootOf(_Z^3-4)*x-84*(x^3+x^2)^(2/3)+180*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x)/x/(-1+x))*RootOf(_Z^3-4)-1/2*ln((33*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x^2+90*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x^2-66*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^3*x-360*(x^3+x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)^2-180*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)^2*RootOf(_Z^3-4)^2*x-198*(x^3+x^2)^(1/3)*RootOf(_Z^3-4)^2*x+126*(x^3+x^2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*RootOf(_Z^3-4)*x+374*RootOf(_Z^3-4)*x^2+1020*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x^2+66*RootOf(_Z^3-4)*x-84*(x^3+x^2)^(2/3)+180*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)*x)/x/(-1+x))*RootOf(RootOf(_Z^3-4)^2+3*_Z*RootOf(_Z^3-4)+9*_Z^2)","B"
2545,0,0,180,0.026000," ","int((3+(-2*k^2+1)*x-3*k^2*x^2+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(1-d-(2+d)*x+(d*k^2+1)*x^2+d*k^2*x^3),x)","\[\int \frac{3+\left(-2 k^{2}+1\right) x -3 k^{2} x^{2}+k^{2} x^{3}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{1}{3}} \left(1-d -\left(2+d \right) x +\left(d \,k^{2}+1\right) x^{2}+d \,k^{2} x^{3}\right)}\, dx\]"," ",0,"int((3+(-2*k^2+1)*x-3*k^2*x^2+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(1-d-(2+d)*x+(d*k^2+1)*x^2+d*k^2*x^3),x)","F"
2546,0,0,165,0.013000," ","int((x^3+1)^(2/3)*(x^6-4*x^3+8)/x^6/(x^3+2),x)","\[\int \frac{\left(x^{3}+1\right)^{\frac{2}{3}} \left(x^{6}-4 x^{3}+8\right)}{x^{6} \left(x^{3}+2\right)}\, dx\]"," ",0,"int((x^3+1)^(2/3)*(x^6-4*x^3+8)/x^6/(x^3+2),x)","F"
2547,0,0,165,0.012000," ","int((x^3-1)^(2/3)*(x^6+2*x^3+8)/x^6/(x^3-2),x)","\[\int \frac{\left(x^{3}-1\right)^{\frac{2}{3}} \left(x^{6}+2 x^{3}+8\right)}{x^{6} \left(x^{3}-2\right)}\, dx\]"," ",0,"int((x^3-1)^(2/3)*(x^6+2*x^3+8)/x^6/(x^3-2),x)","F"
2548,0,0,206,0.027000," ","int((p*x^3-2*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)*(c*x^4+b*x^2*(p*x^3+q)+a*(p*x^3+q)^2)/x^9,x)","\[\int \frac{\left(p \,x^{3}-2 q \right) \sqrt{p^{2} x^{6}-2 p q \,x^{4}+2 p q \,x^{3}+q^{2}}\, \left(c \,x^{4}+b \,x^{2} \left(p \,x^{3}+q \right)+a \left(p \,x^{3}+q \right)^{2}\right)}{x^{9}}\, dx\]"," ",0,"int((p*x^3-2*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)*(c*x^4+b*x^2*(p*x^3+q)+a*(p*x^3+q)^2)/x^9,x)","F"
2549,0,0,193,0.008000," ","int((a*x^2-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{a \,x^{2}-b}{\left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a*x^2-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
2550,0,0,193,0.010000," ","int((a*x^2+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{a \,x^{2}+b}{\left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a*x^2+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
2551,0,0,203,0.023000," ","int((-a^2*b+4*a*b*x-(2*a+3*b)*x^2+2*x^3)/(x*(-a+x)^2*(-b+x)^3)^(1/4)/(b+(a^2*d-1)*x-2*a*d*x^2+d*x^3),x)","\[\int \frac{-a^{2} b +4 a b x -\left(2 a +3 b \right) x^{2}+2 x^{3}}{\left(x \left(-a +x \right)^{2} \left(-b +x \right)^{3}\right)^{\frac{1}{4}} \left(b +\left(a^{2} d -1\right) x -2 a d \,x^{2}+d \,x^{3}\right)}\, dx\]"," ",0,"int((-a^2*b+4*a*b*x-(2*a+3*b)*x^2+2*x^3)/(x*(-a+x)^2*(-b+x)^3)^(1/4)/(b+(a^2*d-1)*x-2*a*d*x^2+d*x^3),x)","F"
2552,0,0,78,0.013000," ","int((a*x^2+b)*(a*x^4+b*x^3)^(1/4)/x^2/(a*x^2-b),x)","\[\int \frac{\left(a \,x^{2}+b \right) \left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}}{x^{2} \left(a \,x^{2}-b \right)}\, dx\]"," ",0,"int((a*x^2+b)*(a*x^4+b*x^3)^(1/4)/x^2/(a*x^2-b),x)","F"
2553,0,0,203,0.025000," ","int((a*b^3-(6*a-b)*b^2*x+9*a*b*x^2-(4*a+3*b)*x^3+2*x^4)/(x*(-a+x)^2*(-b+x)^3)^(1/4)/(-a^2+(-b^3*d+2*a)*x+(3*b^2*d-1)*x^2-3*b*d*x^3+d*x^4),x)","\[\int \frac{a \,b^{3}-\left(6 a -b \right) b^{2} x +9 a b \,x^{2}-\left(4 a +3 b \right) x^{3}+2 x^{4}}{\left(x \left(-a +x \right)^{2} \left(-b +x \right)^{3}\right)^{\frac{1}{4}} \left(-a^{2}+\left(-b^{3} d +2 a \right) x +\left(3 b^{2} d -1\right) x^{2}-3 b d \,x^{3}+d \,x^{4}\right)}\, dx\]"," ",0,"int((a*b^3-(6*a-b)*b^2*x+9*a*b*x^2-(4*a+3*b)*x^3+2*x^4)/(x*(-a+x)^2*(-b+x)^3)^(1/4)/(-a^2+(-b^3*d+2*a)*x+(3*b^2*d-1)*x^2-3*b*d*x^3+d*x^4),x)","F"
2554,0,0,50,0.016000," ","int((a*x^4-b)^(1/4)*(a*x^8+c*x^4+b)/x^6/(2*a*x^8+b),x)","\[\int \frac{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(a \,x^{8}+c \,x^{4}+b \right)}{x^{6} \left(2 a \,x^{8}+b \right)}\, dx\]"," ",0,"int((a*x^4-b)^(1/4)*(a*x^8+c*x^4+b)/x^6/(2*a*x^8+b),x)","F"
2555,0,0,50,0.003000," ","int((a*x^4-b)^(1/4)*(a*x^8+c*x^4+b)/x^6/(2*a*x^8+b),x)","\[\int \frac{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(a \,x^{8}+c \,x^{4}+b \right)}{x^{6} \left(2 a \,x^{8}+b \right)}\, dx\]"," ",0,"int((a*x^4-b)^(1/4)*(a*x^8+c*x^4+b)/x^6/(2*a*x^8+b),x)","F"
2556,0,0,179,180.000000," ","int(1/(c*x+d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{1}{\left(c x +d \right) \sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int(1/(c*x+d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","F"
2557,0,0,205,0.028000," ","int((2*p*x^3-q)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)*(b*q*x+c*x^2+b*p*x^4+a*(p*x^3+q)^2)/x^5,x)","\[\int \frac{\left(2 p \,x^{3}-q \right) \sqrt{p^{2} x^{6}+2 p q \,x^{3}-2 p q \,x^{2}+q^{2}}\, \left(b q x +c \,x^{2}+b p \,x^{4}+a \left(p \,x^{3}+q \right)^{2}\right)}{x^{5}}\, dx\]"," ",0,"int((2*p*x^3-q)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)*(b*q*x+c*x^2+b*p*x^4+a*(p*x^3+q)^2)/x^5,x)","F"
2558,0,0,178,0.234000," ","int((-a*(a-2*b)-2*b*x+x^2)/((-a+x)*(-b+x))^(2/3)/(a^2+b*d-(2*a+d)*x+x^2),x)","\[\int \frac{-a \left(a -2 b \right)-2 b x +x^{2}}{\left(\left(-a +x \right) \left(-b +x \right)\right)^{\frac{2}{3}} \left(a^{2}+b d -\left(2 a +d \right) x +x^{2}\right)}\, dx\]"," ",0,"int((-a*(a-2*b)-2*b*x+x^2)/((-a+x)*(-b+x))^(2/3)/(a^2+b*d-(2*a+d)*x+x^2),x)","F"
2559,0,0,176,0.248000," ","int((a-2*b+x)/((-a+x)*(-b+x))^(1/3)/(b+a^2*d+(-2*a*d-1)*x+d*x^2),x)","\[\int \frac{a -2 b +x}{\left(\left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{3}} \left(b +a^{2} d +\left(-2 a d -1\right) x +d \,x^{2}\right)}\, dx\]"," ",0,"int((a-2*b+x)/((-a+x)*(-b+x))^(1/3)/(b+a^2*d+(-2*a*d-1)*x+d*x^2),x)","F"
2560,0,0,176,0.261000," ","int((a-2*b+x)/((-a+x)*(-b+x))^(1/3)/(b+a^2*d-(2*a*d+1)*x+d*x^2),x)","\[\int \frac{a -2 b +x}{\left(\left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{3}} \left(b +a^{2} d -\left(2 a d +1\right) x +d \,x^{2}\right)}\, dx\]"," ",0,"int((a-2*b+x)/((-a+x)*(-b+x))^(1/3)/(b+a^2*d-(2*a*d+1)*x+d*x^2),x)","F"
2561,0,0,183,0.168000," ","int((-1+2*k*x+(1-2*k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(b-(1+2*b)*x+(b+k)*x^2),x)","\[\int \frac{-1+2 k x +\left(1-2 k \right) x^{2}}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{2}{3}} \left(b -\left(1+2 b \right) x +\left(b +k \right) x^{2}\right)}\, dx\]"," ",0,"int((-1+2*k*x+(1-2*k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(b-(1+2*b)*x+(b+k)*x^2),x)","F"
2562,1,1587,177,3.679000," ","int((-1+x)/(1+x)/(x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1587$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^2-2*_Z+4)*ln((5*RootOf(_Z^2-2*_Z+4)^2*x^2+48*RootOf(_Z^2-2*_Z+4)*(x^3-x^2)^(2/3)+48*RootOf(_Z^2-2*_Z+4)*(x^3-x^2)^(1/3)*x-10*RootOf(_Z^2-2*_Z+4)^2*x+38*RootOf(_Z^2-2*_Z+4)*x^2-36*(x^3-x^2)^(2/3)-36*x*(x^3-x^2)^(1/3)-6*RootOf(_Z^2-2*_Z+4)*x-16*x^2+4*x)/x)-1/2*ln((5*RootOf(_Z^2-2*_Z+4)^2*x^2-10*RootOf(_Z^2-2*_Z+4)^2*x-48*RootOf(_Z^2-2*_Z+4)*(x^3-x^2)^(2/3)-48*RootOf(_Z^2-2*_Z+4)*(x^3-x^2)^(1/3)*x-58*RootOf(_Z^2-2*_Z+4)*x^2+46*RootOf(_Z^2-2*_Z+4)*x+60*(x^3-x^2)^(2/3)+60*x*(x^3-x^2)^(1/3)+80*x^2-48*x)/x)*RootOf(_Z^2-2*_Z+4)+ln((5*RootOf(_Z^2-2*_Z+4)^2*x^2-10*RootOf(_Z^2-2*_Z+4)^2*x-48*RootOf(_Z^2-2*_Z+4)*(x^3-x^2)^(2/3)-48*RootOf(_Z^2-2*_Z+4)*(x^3-x^2)^(1/3)*x-58*RootOf(_Z^2-2*_Z+4)*x^2+46*RootOf(_Z^2-2*_Z+4)*x+60*(x^3-x^2)^(2/3)+60*x*(x^3-x^2)^(1/3)+80*x^2-48*x)/x)-ln((4*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^2+3*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^2-8*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x-6*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x+48*(x^3-x^2)^(2/3)*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2+72*RootOf(_Z^3-4)^2*(x^3-x^2)^(1/3)*x+96*(x^3-x^2)^(1/3)*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)*x+208*RootOf(_Z^3-4)*x^2+156*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*x^2-80*RootOf(_Z^3-4)*x-60*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*x+144*(x^3-x^2)^(2/3))/x/(1+x))*RootOf(_Z^3-4)-1/2*ln((4*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^2+3*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^2-8*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x-6*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x+48*(x^3-x^2)^(2/3)*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2+72*RootOf(_Z^3-4)^2*(x^3-x^2)^(1/3)*x+96*(x^3-x^2)^(1/3)*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)*x+208*RootOf(_Z^3-4)*x^2+156*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*x^2-80*RootOf(_Z^3-4)*x-60*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*x+144*(x^3-x^2)^(2/3))/x/(1+x))*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)+1/2*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*ln((2*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^2+3*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^2-4*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x-6*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x-48*(x^3-x^2)^(2/3)*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2-120*RootOf(_Z^3-4)^2*(x^3-x^2)^(1/3)*x-96*(x^3-x^2)^(1/3)*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)*x-88*RootOf(_Z^3-4)*x^2-132*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*x^2+8*RootOf(_Z^3-4)*x+12*RootOf(4*RootOf(_Z^3-4)^2+2*_Z*RootOf(_Z^3-4)+_Z^2)*x-240*(x^3-x^2)^(2/3))/x/(1+x))","C"
2563,0,0,177,0.030000," ","int((x^6+x^3+x-1)^(2/3)*(3*x^6-2*x+3)/(x^6+x-1)/(x^6-x^3+x-1),x)","\[\int \frac{\left(x^{6}+x^{3}+x -1\right)^{\frac{2}{3}} \left(3 x^{6}-2 x +3\right)}{\left(x^{6}+x -1\right) \left(x^{6}-x^{3}+x -1\right)}\, dx\]"," ",0,"int((x^6+x^3+x-1)^(2/3)*(3*x^6-2*x+3)/(x^6+x-1)/(x^6-x^3+x-1),x)","F"
2564,0,0,145,0.052000," ","int((2*x^8-2*x^4-1)/(x^4-1)^(1/4)/(x^8-x^4-1),x)","\[\int \frac{2 x^{8}-2 x^{4}-1}{\left(x^{4}-1\right)^{\frac{1}{4}} \left(x^{8}-x^{4}-1\right)}\, dx\]"," ",0,"int((2*x^8-2*x^4-1)/(x^4-1)^(1/4)/(x^8-x^4-1),x)","F"
2565,0,0,145,0.030000," ","int((2*x^8+2*x^4-1)/(x^4+1)^(1/4)/(x^8+x^4-1),x)","\[\int \frac{2 x^{8}+2 x^{4}-1}{\left(x^{4}+1\right)^{\frac{1}{4}} \left(x^{8}+x^{4}-1\right)}\, dx\]"," ",0,"int((2*x^8+2*x^4-1)/(x^4+1)^(1/4)/(x^8+x^4-1),x)","F"
2566,0,0,184,0.156000," ","int((-a*b+(2*a-b)*x)/(x*(-a+x)*(-b+x))^(1/3)/(-a^2+(-b*d+2*a)*x+(-1+d)*x^2),x)","\[\int \frac{-a b +\left(2 a -b \right) x}{\left(x \left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{3}} \left(-a^{2}+\left(-b d +2 a \right) x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((-a*b+(2*a-b)*x)/(x*(-a+x)*(-b+x))^(1/3)/(-a^2+(-b*d+2*a)*x+(-1+d)*x^2),x)","F"
2567,0,0,45,0.015000," ","int((a*x^4-4*b)*(a*x^4-b)^(1/4)/x^6/(a*x^8-8*b),x)","\[\int \frac{\left(a \,x^{4}-4 b \right) \left(a \,x^{4}-b \right)^{\frac{1}{4}}}{x^{6} \left(a \,x^{8}-8 b \right)}\, dx\]"," ",0,"int((a*x^4-4*b)*(a*x^4-b)^(1/4)/x^6/(a*x^8-8*b),x)","F"
2568,0,0,45,0.003000," ","int((a*x^4-4*b)*(a*x^4-b)^(1/4)/x^6/(a*x^8-8*b),x)","\[\int \frac{\left(a \,x^{4}-4 b \right) \left(a \,x^{4}-b \right)^{\frac{1}{4}}}{x^{6} \left(a \,x^{8}-8 b \right)}\, dx\]"," ",0,"int((a*x^4-4*b)*(a*x^4-b)^(1/4)/x^6/(a*x^8-8*b),x)","F"
2569,1,1000,178,3.596000," ","int(x/(1+x)/(x^3-x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{2}+48 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}-30 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}-x^{2}\right)^{\frac{1}{3}} x +2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x -16 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-36 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+96 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}+18 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x -64 x^{2}+16 x}{x}\right)+\frac{\RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x^{2}+24 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}-x^{2}\right)^{\frac{2}{3}}-9 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) \left(x^{3}-x^{2}\right)^{\frac{1}{3}} x -4 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right)^{2} x -19 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x^{2}-30 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}+48 x \left(x^{3}-x^{2}\right)^{\frac{1}{3}}+10 \RootOf \left(\textit{\_Z}^{2}-2 \textit{\_Z} +4\right) x -10 x^{2}+6 x}{x}\right)}{2}+\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+\textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\textit{\_Z}^{2}\right) \ln \left(\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+\textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{2}-2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+\textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{2}-2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+\textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x +4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+\textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x +24 \left(x^{3}-x^{2}\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+\textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}-48 \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} \left(x^{3}-x^{2}\right)^{\frac{1}{3}} x -30 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+\textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) \left(x^{3}-x^{2}\right)^{\frac{1}{3}} x +26 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{2}-52 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+\textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\textit{\_Z}^{2}\right) x^{2}-10 \RootOf \left(\textit{\_Z}^{3}-4\right) x +20 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+\textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\textit{\_Z}^{2}\right) x +36 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}}{x \left(1+x \right)}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{3}-4\right) \ln \left(\frac{2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+\textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x^{2}-\RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+\textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x^{2}-4 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+\textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{3} x +2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+\textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} x -24 \left(x^{3}-x^{2}\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+\textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+48 \RootOf \left(\textit{\_Z}^{3}-4\right)^{2} \left(x^{3}-x^{2}\right)^{\frac{1}{3}} x +18 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+\textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-4\right) \left(x^{3}-x^{2}\right)^{\frac{1}{3}} x -44 \RootOf \left(\textit{\_Z}^{3}-4\right) x^{2}+22 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+\textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\textit{\_Z}^{2}\right) x^{2}+4 \RootOf \left(\textit{\_Z}^{3}-4\right) x -2 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-4\right)^{2}+\textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-4\right)+\textit{\_Z}^{2}\right) x -60 \left(x^{3}-x^{2}\right)^{\frac{2}{3}}}{x \left(1+x \right)}\right)}{2}$&$1000$\\ \hline \end{longtable}"," ",0,"-ln((-RootOf(_Z^2-2*_Z+4)^2*x^2+48*RootOf(_Z^2-2*_Z+4)*(x^3-x^2)^(2/3)-30*RootOf(_Z^2-2*_Z+4)*(x^3-x^2)^(1/3)*x+2*RootOf(_Z^2-2*_Z+4)^2*x-16*RootOf(_Z^2-2*_Z+4)*x^2-36*(x^3-x^2)^(2/3)+96*x*(x^3-x^2)^(1/3)+18*RootOf(_Z^2-2*_Z+4)*x-64*x^2+16*x)/x)+1/2*RootOf(_Z^2-2*_Z+4)*ln(-(2*RootOf(_Z^2-2*_Z+4)^2*x^2+24*RootOf(_Z^2-2*_Z+4)*(x^3-x^2)^(2/3)-9*RootOf(_Z^2-2*_Z+4)*(x^3-x^2)^(1/3)*x-4*RootOf(_Z^2-2*_Z+4)^2*x-19*RootOf(_Z^2-2*_Z+4)*x^2-30*(x^3-x^2)^(2/3)+48*x*(x^3-x^2)^(1/3)+10*RootOf(_Z^2-2*_Z+4)*x-10*x^2+6*x)/x)+1/2*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*ln((RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^2-2*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^2-2*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x+4*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x+24*(x^3-x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2-48*RootOf(_Z^3-4)^2*(x^3-x^2)^(1/3)*x-30*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)*(x^3-x^2)^(1/3)*x+26*RootOf(_Z^3-4)*x^2-52*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x^2-10*RootOf(_Z^3-4)*x+20*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x+36*(x^3-x^2)^(2/3))/x/(1+x))+1/2*RootOf(_Z^3-4)*ln((2*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x^2-RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x^2-4*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x+2*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x-24*(x^3-x^2)^(2/3)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2+48*RootOf(_Z^3-4)^2*(x^3-x^2)^(1/3)*x+18*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)*(x^3-x^2)^(1/3)*x-44*RootOf(_Z^3-4)*x^2+22*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x^2+4*RootOf(_Z^3-4)*x-2*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x-60*(x^3-x^2)^(2/3))/x/(1+x))","C"
2570,1,1679,179,5.727000," ","int((x^3-x^2)^(1/3)/(x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1679$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^3-2)*ln((-6*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^4*x^2-4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^3*x^2+12*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^4*x+8*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^3*x+48*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*(x^3-x^2)^(2/3)-39*RootOf(_Z^3-2)^2*x^2-26*RootOf(_Z^3-2)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^2+30*(x^3-x^2)^(1/3)*RootOf(_Z^3-2)*x-36*(x^3-x^2)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x+15*RootOf(_Z^3-2)^2*x+10*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x+18*(x^3-x^2)^(2/3))/x/(1+x))+RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*ln(-(6*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^4*x^2+8*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^3*x^2-12*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^4*x-16*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^3*x+48*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*(x^3-x^2)^(2/3)-33*RootOf(_Z^3-2)^2*x^2-44*RootOf(_Z^3-2)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^2+18*(x^3-x^2)^(1/3)*RootOf(_Z^3-2)*x-60*(x^3-x^2)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x+3*RootOf(_Z^3-2)^2*x+4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x+30*(x^3-x^2)^(2/3))/x/(1+x))-RootOf(_Z^3-2)^2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*ln((5*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^4*x^2-10*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^4*x+24*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*(x^3-x^2)^(2/3)+24*(x^3-x^2)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x+29*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x^2-23*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x+15*(x^3-x^2)^(2/3)+15*x*(x^3-x^2)^(1/3)+20*x^2-12*x)/x)+RootOf(_Z^3-2)^2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*ln(-(-5*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^4*x^2+10*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^4*x+24*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*(x^3-x^2)^(2/3)+24*(x^3-x^2)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x+19*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x^2-3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x+9*(x^3-x^2)^(2/3)+9*x*(x^3-x^2)^(1/3)+4*x^2-x)/x)+ln(-(-5*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^4*x^2+10*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^4*x+24*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*(x^3-x^2)^(2/3)+24*(x^3-x^2)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x+19*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x^2-3*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x+9*(x^3-x^2)^(2/3)+9*x*(x^3-x^2)^(1/3)+4*x^2-x)/x)","C"
2571,0,0,179,180.000000," ","int(x^2*(a^2*x^4+b)^(1/2)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x)","\[\int x^{2} \sqrt{a^{2} x^{4}+b}\, \sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}\, dx\]"," ",0,"int(x^2*(a^2*x^4+b)^(1/2)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x)","F"
2572,0,0,184,0.078000," ","int((a^2*x^2-b*x)^(3/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x)","\[\int \frac{\left(a^{2} x^{2}-b x \right)^{\frac{3}{2}}}{\left(a \,x^{2}+x \sqrt{a^{2} x^{2}-b x}\right)^{\frac{3}{2}}}\, dx\]"," ",0,"int((a^2*x^2-b*x)^(3/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x)","F"
2573,0,0,187,0.025000," ","int((-3*k+(k^2-2)*x+3*k*x^2+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(-1+d-(2+d)*k*x-(k^2+d)*x^2+d*k*x^3),x)","\[\int \frac{-3 k +\left(k^{2}-2\right) x +3 k \,x^{2}+k^{2} x^{3}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{1}{3}} \left(-1+d -\left(2+d \right) k x -\left(k^{2}+d \right) x^{2}+d k \,x^{3}\right)}\, dx\]"," ",0,"int((-3*k+(k^2-2)*x+3*k*x^2+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(-1+d-(2+d)*k*x-(k^2+d)*x^2+d*k*x^3),x)","F"
2574,0,0,178,0.015000," ","int((b*x+a)/x/(c*x-d)/(x^4-x^3)^(1/4),x)","\[\int \frac{b x +a}{x \left(c x -d \right) \left(x^{4}-x^{3}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((b*x+a)/x/(c*x-d)/(x^4-x^3)^(1/4),x)","F"
2575,0,0,181,0.052000," ","int((-4+3*x)*((b*x^4+a*x-a)/(d*x^4+c*x-c))^(1/4)/(-1+x)/x,x)","\[\int \frac{\left(-4+3 x \right) \left(\frac{b \,x^{4}+a x -a}{d \,x^{4}+c x -c}\right)^{\frac{1}{4}}}{\left(-1+x \right) x}\, dx\]"," ",0,"int((-4+3*x)*((b*x^4+a*x-a)/(d*x^4+c*x-c))^(1/4)/(-1+x)/x,x)","F"
2576,0,0,167,0.023000," ","int((x^3+1)^(2/3)*(2*x^6-2*x^3+1)/x^6/(2*x^6-x^3-1),x)","\[\int \frac{\left(x^{3}+1\right)^{\frac{2}{3}} \left(2 x^{6}-2 x^{3}+1\right)}{x^{6} \left(2 x^{6}-x^{3}-1\right)}\, dx\]"," ",0,"int((x^3+1)^(2/3)*(2*x^6-2*x^3+1)/x^6/(2*x^6-x^3-1),x)","F"
2577,1,116,173,3.094000," ","int(2/(3+x)/(8*x^2-8*x+2)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{3 \left(-1+2 x \right) 2^{\frac{1}{3}}}{7 \left(\left(-1+2 x \right)^{2}\right)^{\frac{2}{3}}}+\frac{\left(\frac{7^{\frac{2}{3}} \ln \left(\left(-1+2 x \right)^{\frac{1}{3}}+7^{\frac{1}{3}}\right)}{49}-\frac{7^{\frac{2}{3}} \ln \left(\left(-1+2 x \right)^{\frac{2}{3}}-7^{\frac{1}{3}} \left(-1+2 x \right)^{\frac{1}{3}}+7^{\frac{2}{3}}\right)}{98}-\frac{\sqrt{3}\, 7^{\frac{2}{3}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \,7^{\frac{2}{3}} \left(-1+2 x \right)^{\frac{1}{3}}}{7}-1\right)}{3}\right)}{49}\right) 2^{\frac{1}{3}} \left(-1+2 x \right)^{\frac{4}{3}}}{\left(\left(-1+2 x \right)^{2}\right)^{\frac{2}{3}}}$&$116$\\ trager&$-\frac{3 \left(8 x^{2}-8 x +2\right)^{\frac{1}{3}}}{7 \left(-1+2 x \right)}+\frac{3 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-98\right)^{2}+21 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-98\right)+441 \textit{\_Z}^{2}\right) \ln \left(\frac{-12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-98\right)^{2}+21 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-98\right)+441 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-98\right)^{4} x^{2}-420 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-98\right)^{2}+21 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-98\right)+441 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-98\right)^{3} x^{2}+6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-98\right)^{2}+21 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-98\right)+441 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-98\right)^{4} x +210 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-98\right)^{2}+21 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-98\right)+441 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-98\right)^{3} x +105 \left(8 x^{2}-8 x +2\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-98\right)^{2}+21 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-98\right)+441 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-98\right)^{2}-64 \RootOf \left(\textit{\_Z}^{3}-98\right)^{2} x^{2}-2240 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-98\right)^{2}+21 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-98\right)+441 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-98\right) x^{2}-588 \left(8 x^{2}-8 x +2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-98\right) x -9408 \left(8 x^{2}-8 x +2\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-98\right)^{2}+21 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-98\right)+441 \textit{\_Z}^{2}\right) x +260 \RootOf \left(\textit{\_Z}^{3}-98\right)^{2} x +9100 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-98\right)^{2}+21 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-98\right)+441 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-98\right) x -1568 \left(8 x^{2}-8 x +2\right)^{\frac{2}{3}}+294 \left(8 x^{2}-8 x +2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-98\right)+4704 \left(8 x^{2}-8 x +2\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-98\right)^{2}+21 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-98\right)+441 \textit{\_Z}^{2}\right)-114 \RootOf \left(\textit{\_Z}^{3}-98\right)^{2}-3990 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-98\right)^{2}+21 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-98\right)+441 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-98\right)}{\left(3+x \right) \left(-1+2 x \right)}\right)}{7}+\frac{\RootOf \left(\textit{\_Z}^{3}-98\right) \ln \left(-\frac{12 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-98\right)^{2}+21 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-98\right)+441 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-98\right)^{4} x^{2}-168 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-98\right)^{2}+21 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-98\right)+441 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-98\right)^{3} x^{2}-6 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-98\right)^{2}+21 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-98\right)+441 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-98\right)^{4} x +84 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-98\right)^{2}+21 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-98\right)+441 \textit{\_Z}^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-98\right)^{3} x +105 \left(8 x^{2}-8 x +2\right)^{\frac{2}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-98\right)^{2}+21 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-98\right)+441 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-98\right)^{2}-8 \RootOf \left(\textit{\_Z}^{3}-98\right)^{2} x^{2}+112 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-98\right)^{2}+21 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-98\right)+441 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-98\right) x^{2}+448 \left(8 x^{2}-8 x +2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-98\right) x +12348 \left(8 x^{2}-8 x +2\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-98\right)^{2}+21 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-98\right)+441 \textit{\_Z}^{2}\right) x +232 \RootOf \left(\textit{\_Z}^{3}-98\right)^{2} x -3248 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-98\right)^{2}+21 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-98\right)+441 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-98\right) x +2058 \left(8 x^{2}-8 x +2\right)^{\frac{2}{3}}-224 \left(8 x^{2}-8 x +2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-98\right)-6174 \left(8 x^{2}-8 x +2\right)^{\frac{1}{3}} \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-98\right)^{2}+21 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-98\right)+441 \textit{\_Z}^{2}\right)-114 \RootOf \left(\textit{\_Z}^{3}-98\right)^{2}+1596 \RootOf \left(\RootOf \left(\textit{\_Z}^{3}-98\right)^{2}+21 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-98\right)+441 \textit{\_Z}^{2}\right) \RootOf \left(\textit{\_Z}^{3}-98\right)}{\left(3+x \right) \left(-1+2 x \right)}\right)}{49}$&$1008$\\ \hline \end{longtable}"," ",0,"-3/7*(-1+2*x)*2^(1/3)/((-1+2*x)^2)^(2/3)+(1/49*7^(2/3)*ln((-1+2*x)^(1/3)+7^(1/3))-1/98*7^(2/3)*ln((-1+2*x)^(2/3)-7^(1/3)*(-1+2*x)^(1/3)+7^(2/3))-1/49*3^(1/2)*7^(2/3)*arctan(1/3*3^(1/2)*(2/7*7^(2/3)*(-1+2*x)^(1/3)-1)))*2^(1/3)/((-1+2*x)^2)^(2/3)*(-1+2*x)^(4/3)","A"
2578,0,0,186,0.019000," ","int((1-(-3+2*k)*x-(4+k)*x^2+3*k*x^3)/((1-x)*x*(-k*x+1))^(1/3)/(-1+(5+b)*x-(b*k+10)*x^2+10*x^3-5*x^4+x^5),x)","\[\int \frac{1-\left(-3+2 k \right) x -\left(4+k \right) x^{2}+3 k \,x^{3}}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(-1+\left(5+b \right) x -\left(b k +10\right) x^{2}+10 x^{3}-5 x^{4}+x^{5}\right)}\, dx\]"," ",0,"int((1-(-3+2*k)*x-(4+k)*x^2+3*k*x^3)/((1-x)*x*(-k*x+1))^(1/3)/(-1+(5+b)*x-(b*k+10)*x^2+10*x^3-5*x^4+x^5),x)","F"
2579,0,0,179,0.010000," ","int(1/x/((1+x)*(2*q*x+x^2+q))^(1/3),x)","\[\int \frac{1}{x \left(\left(1+x \right) \left(2 q x +x^{2}+q \right)\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/x/((1+x)*(2*q*x+x^2+q))^(1/3),x)","F"
2580,0,0,185,0.183000," ","int((-1+2*x+(k^2-2*k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(1-(b+2*k)*x+(k^2+b)*x^2),x)","\[\int \frac{-1+2 x +\left(k^{2}-2 k \right) x^{2}}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{2}{3}} \left(1-\left(b +2 k \right) x +\left(k^{2}+b \right) x^{2}\right)}\, dx\]"," ",0,"int((-1+2*x+(k^2-2*k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(1-(b+2*k)*x+(k^2+b)*x^2),x)","F"
2581,0,0,189,0.025000," ","int((3*k+(k^2-2)*x-3*k*x^2+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(1-d-(2+d)*k*x+(k^2+d)*x^2+d*k*x^3),x)","\[\int \frac{3 k +\left(k^{2}-2\right) x -3 k \,x^{2}+k^{2} x^{3}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{1}{3}} \left(1-d -\left(2+d \right) k x +\left(k^{2}+d \right) x^{2}+d k \,x^{3}\right)}\, dx\]"," ",0,"int((3*k+(k^2-2)*x-3*k*x^2+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(1-d-(2+d)*k*x+(k^2+d)*x^2+d*k*x^3),x)","F"
2582,0,0,179,0.029000," ","int((3+2*(k^2+1)*x-(k^2+1)*x^2-4*k^2*x^3-k^2*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(1-d-(1+2*d)*x-(k^2+d)*x^2+k^2*x^3),x)","\[\int \frac{3+2 \left(k^{2}+1\right) x -\left(k^{2}+1\right) x^{2}-4 k^{2} x^{3}-k^{2} x^{4}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{2}{3}} \left(1-d -\left(1+2 d \right) x -\left(k^{2}+d \right) x^{2}+k^{2} x^{3}\right)}\, dx\]"," ",0,"int((3+2*(k^2+1)*x-(k^2+1)*x^2-4*k^2*x^3-k^2*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(1-d-(1+2*d)*x-(k^2+d)*x^2+k^2*x^3),x)","F"
2583,1,2833,187,17.914000," ","int((((-1+x)/(1+2*x))^(1/4)-3*((-1+x)/(1+2*x))^(3/4))/(-1+x)/(1+x)^2/(-1+2*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2833$\\ \hline \end{longtable}"," ",0,"1/6*(1+2*x)/(1+x)*(-(1-x)/(1+2*x))^(1/4)-1/2*(1+2*x)/(1+x)*(-(1-x)/(1+2*x))^(3/4)-1/72*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)*ln((6082560*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)*(-(1-x)/(1+2*x))^(1/2)*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2*x+3041280*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)*(-(1-x)/(1+2*x))^(1/2)*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+852480*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)*x+7855988*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)*(-(1-x)/(1+2*x))^(1/2)*x-978388992*(-(1-x)/(1+2*x))^(1/4)*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2*x+5925856678*(-(1-x)/(1+2*x))^(3/4)*x+170496*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)+3927994*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)*(-(1-x)/(1+2*x))^(1/2)-489194496*(-(1-x)/(1+2*x))^(1/4)*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+2962928339*(-(1-x)/(1+2*x))^(3/4)-43791825*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)*x-2592476040*(-(1-x)/(1+2*x))^(1/4)*x-8758365*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)-1296238020*(-(1-x)/(1+2*x))^(1/4))/(1+x))+2/3*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)*ln((291962880*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^3*(-(1-x)/(1+2*x))^(1/2)*x+145981440*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^3*(-(1-x)/(1+2*x))^(1/2)+40919040*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^3*x+978388992*(-(1-x)/(1+2*x))^(1/4)*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2*x+1170163776*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)*(-(1-x)/(1+2*x))^(1/2)*x+5925856678*(-(1-x)/(1+2*x))^(3/4)*x+8183808*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^3+489194496*(-(1-x)/(1+2*x))^(1/4)*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+585081888*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)*(-(1-x)/(1+2*x))^(1/2)+2962928339*(-(1-x)/(1+2*x))^(3/4)+2318857200*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)*x+2592476040*(-(1-x)/(1+2*x))^(1/4)*x+463771440*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)+1296238020*(-(1-x)/(1+2*x))^(1/4))/(1+x))+5/9*ln((16*(-(1-x)/(1+2*x))^(3/4)*x+8*(-(1-x)/(1+2*x))^(3/4)+16*(-(1-x)/(1+2*x))^(1/2)*x+8*(-(1-x)/(1+2*x))^(1/2)+8*(-(1-x)/(1+2*x))^(1/4)*x+4*(-(1-x)/(1+2*x))^(1/4)+6*x-3)/(-1+2*x))+98304/2962928339*ln((16*(-(1-x)/(1+2*x))^(3/4)*x+8*(-(1-x)/(1+2*x))^(3/4)+16*(-(1-x)/(1+2*x))^(1/2)*x+8*(-(1-x)/(1+2*x))^(1/2)+8*(-(1-x)/(1+2*x))^(1/4)*x+4*(-(1-x)/(1+2*x))^(1/4)+6*x-3)/(-1+2*x))*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^3*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)+260480/2962928339*ln((16*(-(1-x)/(1+2*x))^(3/4)*x+8*(-(1-x)/(1+2*x))^(3/4)+16*(-(1-x)/(1+2*x))^(1/2)*x+8*(-(1-x)/(1+2*x))^(1/2)+8*(-(1-x)/(1+2*x))^(1/4)*x+4*(-(1-x)/(1+2*x))^(1/4)+6*x-3)/(-1+2*x))*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)-196608/2962928339*ln((7077888*(-(1-x)/(1+2*x))^(1/2)*x*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^3+3538944*(-(1-x)/(1+2*x))^(1/2)*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^3*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)+7077888*(-(1-x)/(1+2*x))^(1/4)*x*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^3+3538944*(-(1-x)/(1+2*x))^(1/4)*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^3*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)-1769472*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^3*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)*x+18754560*(-(1-x)/(1+2*x))^(1/2)*x*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)+4423680*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^3*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)+9377280*(-(1-x)/(1+2*x))^(1/2)*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)+18754560*(-(1-x)/(1+2*x))^(1/4)*x*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)+47406853424*(-(1-x)/(1+2*x))^(3/4)*x+9377280*(-(1-x)/(1+2*x))^(1/4)*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)-4688640*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)*x+23703426712*(-(1-x)/(1+2*x))^(3/4)+23703426712*(-(1-x)/(1+2*x))^(1/2)*x+11721600*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)+11851713356*(-(1-x)/(1+2*x))^(1/2)+5925856678*x-14814641695)/(-1+2*x))*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^3*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)-520960/2962928339*ln((7077888*(-(1-x)/(1+2*x))^(1/2)*x*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^3+3538944*(-(1-x)/(1+2*x))^(1/2)*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^3*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)+7077888*(-(1-x)/(1+2*x))^(1/4)*x*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^3+3538944*(-(1-x)/(1+2*x))^(1/4)*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^3*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)-1769472*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^3*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)*x+18754560*(-(1-x)/(1+2*x))^(1/2)*x*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)+4423680*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^3*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)+9377280*(-(1-x)/(1+2*x))^(1/2)*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)+18754560*(-(1-x)/(1+2*x))^(1/4)*x*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)+47406853424*(-(1-x)/(1+2*x))^(3/4)*x+9377280*(-(1-x)/(1+2*x))^(1/4)*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)-4688640*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)*x+23703426712*(-(1-x)/(1+2*x))^(3/4)+23703426712*(-(1-x)/(1+2*x))^(1/2)*x+11721600*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)+11851713356*(-(1-x)/(1+2*x))^(1/2)+5925856678*x-14814641695)/(-1+2*x))*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)*RootOf(_Z^2+2304*RootOf(42467328*_Z^4+225054720*_Z^2-2817592561)^2+12210)","C"
2584,1,722,11,0.817000," ","int((p*x^2-q)*(p^2*x^4+q^2)^(1/2)/(b*x^3+a*(p*x^2+q)^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{b \sqrt{p^{2}}\, \left(\munderset{\textit{\_R} =\RootOf \left(p^{4} \textit{\_Z}^{12} a^{2}-12 \sqrt{p^{2}}\, \textit{\_Z}^{11} a^{2} p^{3} q +54 p^{4} \textit{\_Z}^{10} a^{2} q^{2}-\left(100 \sqrt{p^{2}}\, a^{2} p^{3} q^{3}-8 \sqrt{p^{2}}\, b^{2}\right) \textit{\_Z}^{9}+15 p^{4} \textit{\_Z}^{8} a^{2} q^{4}-\left(-168 \sqrt{p^{2}}\, a^{2} p^{3} q^{5}+24 \sqrt{p^{2}}\, b^{2} q^{2}\right) \textit{\_Z}^{7}-76 p^{4} \textit{\_Z}^{6} a^{2} q^{6}-\left(168 \sqrt{p^{2}}\, a^{2} p^{3} q^{7}-24 \sqrt{p^{2}}\, b^{2} q^{4}\right) \textit{\_Z}^{5}+15 p^{4} \textit{\_Z}^{4} a^{2} q^{8}-\left(-100 \sqrt{p^{2}}\, a^{2} p^{3} q^{9}+8 \sqrt{p^{2}}\, b^{2} q^{6}\right) \textit{\_Z}^{3}+54 p^{4} \textit{\_Z}^{2} a^{2} q^{10}+12 \sqrt{p^{2}}\, \textit{\_Z} \,a^{2} p^{3} q^{11}+a^{2} p^{4} q^{12}\right)}{\sum}\frac{\left(p \left(-\textit{\_R}^{9}+2 q^{4} \textit{\_R}^{5}-q^{8} \textit{\_R} \right)+2 q \left(-\textit{\_R}^{8} \sqrt{p^{2}}-q^{2} \textit{\_R}^{6} \sqrt{p^{2}}+q^{4} \textit{\_R}^{4} \sqrt{p^{2}}+q^{6} \textit{\_R}^{2} \sqrt{p^{2}}\right)\right) \ln \left(\sqrt{p^{2} x^{4}+q^{2}}-x^{2} \sqrt{p^{2}}-\textit{\_R} \right)}{a^{2} p^{4} \left(-\textit{\_R}^{11}-45 q^{2} \textit{\_R}^{9}-10 q^{4} \textit{\_R}^{7}+38 q^{6} \textit{\_R}^{5}-5 q^{8} \textit{\_R}^{3}-9 q^{10} \textit{\_R} \right)+11 \sqrt{p^{2}}\, \textit{\_R}^{10} a^{2} p^{3} q +75 \sqrt{p^{2}}\, \textit{\_R}^{8} a^{2} p^{3} q^{3}-98 \sqrt{p^{2}}\, \textit{\_R}^{6} a^{2} p^{3} q^{5}+70 \sqrt{p^{2}}\, \textit{\_R}^{4} a^{2} p^{3} q^{7}-25 \sqrt{p^{2}}\, \textit{\_R}^{2} a^{2} p^{3} q^{9}-\sqrt{p^{2}}\, a^{2} p^{3} q^{11}-6 \sqrt{p^{2}}\, \textit{\_R}^{8} b^{2}+14 \sqrt{p^{2}}\, \textit{\_R}^{6} b^{2} q^{2}-10 \sqrt{p^{2}}\, \textit{\_R}^{4} b^{2} q^{4}+2 \sqrt{p^{2}}\, \textit{\_R}^{2} b^{2} q^{6}}\right)}{6}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(8 a^{2} \textit{\_Z}^{6}+24 a^{2} p q \,\textit{\_Z}^{4}+24 a^{2} p^{2} q^{2} \textit{\_Z}^{2}+8 a^{2} p^{3} q^{3}-b^{2}\right)}{\sum}\frac{\left(\textit{\_R}^{4}+\textit{\_R}^{2} p q \right) \ln \left(\frac{\sqrt{p^{2} x^{4}+q^{2}}\, \sqrt{2}}{2 x}-\textit{\_R} \right)}{\textit{\_R}^{5}+2 p q \,\textit{\_R}^{3}+p^{2} q^{2} \textit{\_R}}\right) \sqrt{2}}{12 a}$&$722$\\ elliptic&$\frac{b \sqrt{p^{2}}\, \left(\munderset{\textit{\_R} =\RootOf \left(p^{4} \textit{\_Z}^{12} a^{2}-12 \sqrt{p^{2}}\, \textit{\_Z}^{11} a^{2} p^{3} q +54 p^{4} \textit{\_Z}^{10} a^{2} q^{2}-\left(100 \sqrt{p^{2}}\, a^{2} p^{3} q^{3}-8 \sqrt{p^{2}}\, b^{2}\right) \textit{\_Z}^{9}+15 p^{4} \textit{\_Z}^{8} a^{2} q^{4}-\left(-168 \sqrt{p^{2}}\, a^{2} p^{3} q^{5}+24 \sqrt{p^{2}}\, b^{2} q^{2}\right) \textit{\_Z}^{7}-76 p^{4} \textit{\_Z}^{6} a^{2} q^{6}-\left(168 \sqrt{p^{2}}\, a^{2} p^{3} q^{7}-24 \sqrt{p^{2}}\, b^{2} q^{4}\right) \textit{\_Z}^{5}+15 p^{4} \textit{\_Z}^{4} a^{2} q^{8}-\left(-100 \sqrt{p^{2}}\, a^{2} p^{3} q^{9}+8 \sqrt{p^{2}}\, b^{2} q^{6}\right) \textit{\_Z}^{3}+54 p^{4} \textit{\_Z}^{2} a^{2} q^{10}+12 \sqrt{p^{2}}\, \textit{\_Z} \,a^{2} p^{3} q^{11}+a^{2} p^{4} q^{12}\right)}{\sum}\frac{\left(p \left(-\textit{\_R}^{9}+2 q^{4} \textit{\_R}^{5}-q^{8} \textit{\_R} \right)+2 q \left(-\textit{\_R}^{8} \sqrt{p^{2}}-q^{2} \textit{\_R}^{6} \sqrt{p^{2}}+q^{4} \textit{\_R}^{4} \sqrt{p^{2}}+q^{6} \textit{\_R}^{2} \sqrt{p^{2}}\right)\right) \ln \left(\sqrt{p^{2} x^{4}+q^{2}}-x^{2} \sqrt{p^{2}}-\textit{\_R} \right)}{a^{2} p^{4} \left(-\textit{\_R}^{11}-45 q^{2} \textit{\_R}^{9}-10 q^{4} \textit{\_R}^{7}+38 q^{6} \textit{\_R}^{5}-5 q^{8} \textit{\_R}^{3}-9 q^{10} \textit{\_R} \right)+11 \sqrt{p^{2}}\, \textit{\_R}^{10} a^{2} p^{3} q +75 \sqrt{p^{2}}\, \textit{\_R}^{8} a^{2} p^{3} q^{3}-98 \sqrt{p^{2}}\, \textit{\_R}^{6} a^{2} p^{3} q^{5}+70 \sqrt{p^{2}}\, \textit{\_R}^{4} a^{2} p^{3} q^{7}-25 \sqrt{p^{2}}\, \textit{\_R}^{2} a^{2} p^{3} q^{9}-\sqrt{p^{2}}\, a^{2} p^{3} q^{11}-6 \sqrt{p^{2}}\, \textit{\_R}^{8} b^{2}+14 \sqrt{p^{2}}\, \textit{\_R}^{6} b^{2} q^{2}-10 \sqrt{p^{2}}\, \textit{\_R}^{4} b^{2} q^{4}+2 \sqrt{p^{2}}\, \textit{\_R}^{2} b^{2} q^{6}}\right)}{6}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(8 a^{2} \textit{\_Z}^{6}+24 a^{2} p q \,\textit{\_Z}^{4}+24 a^{2} p^{2} q^{2} \textit{\_Z}^{2}+8 a^{2} p^{3} q^{3}-b^{2}\right)}{\sum}\frac{\left(\textit{\_R}^{4}+\textit{\_R}^{2} p q \right) \ln \left(\frac{\sqrt{p^{2} x^{4}+q^{2}}\, \sqrt{2}}{2 x}-\textit{\_R} \right)}{\textit{\_R}^{5}+2 p q \,\textit{\_R}^{3}+p^{2} q^{2} \textit{\_R}}\right) \sqrt{2}}{12 a}$&$722$\\ \hline \end{longtable}"," ",0,"1/6*b*(p^2)^(1/2)*sum((p*(-_R^9+2*_R^5*q^4-_R*q^8)+2*q*(-_R^8*(p^2)^(1/2)-q^2*_R^6*(p^2)^(1/2)+q^4*_R^4*(p^2)^(1/2)+q^6*_R^2*(p^2)^(1/2)))/(a^2*p^4*(-_R^11-45*_R^9*q^2-10*_R^7*q^4+38*_R^5*q^6-5*_R^3*q^8-9*_R*q^10)+11*(p^2)^(1/2)*_R^10*a^2*p^3*q+75*(p^2)^(1/2)*_R^8*a^2*p^3*q^3-98*(p^2)^(1/2)*_R^6*a^2*p^3*q^5+70*(p^2)^(1/2)*_R^4*a^2*p^3*q^7-25*(p^2)^(1/2)*_R^2*a^2*p^3*q^9-(p^2)^(1/2)*a^2*p^3*q^11-6*(p^2)^(1/2)*_R^8*b^2+14*(p^2)^(1/2)*_R^6*b^2*q^2-10*(p^2)^(1/2)*_R^4*b^2*q^4+2*(p^2)^(1/2)*_R^2*b^2*q^6)*ln((p^2*x^4+q^2)^(1/2)-x^2*(p^2)^(1/2)-_R),_R=RootOf(p^4*_Z^12*a^2-12*(p^2)^(1/2)*_Z^11*a^2*p^3*q+54*p^4*_Z^10*a^2*q^2-(100*(p^2)^(1/2)*a^2*p^3*q^3-8*(p^2)^(1/2)*b^2)*_Z^9+15*p^4*_Z^8*a^2*q^4-(-168*(p^2)^(1/2)*a^2*p^3*q^5+24*(p^2)^(1/2)*b^2*q^2)*_Z^7-76*p^4*_Z^6*a^2*q^6-(168*(p^2)^(1/2)*a^2*p^3*q^7-24*(p^2)^(1/2)*b^2*q^4)*_Z^5+15*p^4*_Z^4*a^2*q^8-(-100*(p^2)^(1/2)*a^2*p^3*q^9+8*(p^2)^(1/2)*b^2*q^6)*_Z^3+54*p^4*_Z^2*a^2*q^10+12*(p^2)^(1/2)*_Z*a^2*p^3*q^11+a^2*p^4*q^12))+1/12/a*sum((_R^4+_R^2*p*q)/(_R^5+2*_R^3*p*q+_R*p^2*q^2)*ln(1/2*(p^2*x^4+q^2)^(1/2)*2^(1/2)/x-_R),_R=RootOf(8*_Z^6*a^2+24*_Z^4*a^2*p*q+24*_Z^2*a^2*p^2*q^2+8*a^2*p^3*q^3-b^2))*2^(1/2)","B"
2585,1,722,11,0.254000," ","int((p*x^2-q)*(p^2*x^4+q^2)^(1/2)/(b*x^3+a*(p*x^2+q)^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{b \sqrt{p^{2}}\, \left(\munderset{\textit{\_R} =\RootOf \left(p^{4} \textit{\_Z}^{12} a^{2}-12 \sqrt{p^{2}}\, \textit{\_Z}^{11} a^{2} p^{3} q +54 p^{4} \textit{\_Z}^{10} a^{2} q^{2}-\left(100 \sqrt{p^{2}}\, a^{2} p^{3} q^{3}-8 \sqrt{p^{2}}\, b^{2}\right) \textit{\_Z}^{9}+15 p^{4} \textit{\_Z}^{8} a^{2} q^{4}-\left(-168 \sqrt{p^{2}}\, a^{2} p^{3} q^{5}+24 \sqrt{p^{2}}\, b^{2} q^{2}\right) \textit{\_Z}^{7}-76 p^{4} \textit{\_Z}^{6} a^{2} q^{6}-\left(168 \sqrt{p^{2}}\, a^{2} p^{3} q^{7}-24 \sqrt{p^{2}}\, b^{2} q^{4}\right) \textit{\_Z}^{5}+15 p^{4} \textit{\_Z}^{4} a^{2} q^{8}-\left(-100 \sqrt{p^{2}}\, a^{2} p^{3} q^{9}+8 \sqrt{p^{2}}\, b^{2} q^{6}\right) \textit{\_Z}^{3}+54 p^{4} \textit{\_Z}^{2} a^{2} q^{10}+12 \sqrt{p^{2}}\, \textit{\_Z} \,a^{2} p^{3} q^{11}+a^{2} p^{4} q^{12}\right)}{\sum}\frac{\left(p \left(-\textit{\_R}^{9}+2 q^{4} \textit{\_R}^{5}-q^{8} \textit{\_R} \right)+2 q \left(-\textit{\_R}^{8} \sqrt{p^{2}}-q^{2} \textit{\_R}^{6} \sqrt{p^{2}}+q^{4} \textit{\_R}^{4} \sqrt{p^{2}}+q^{6} \textit{\_R}^{2} \sqrt{p^{2}}\right)\right) \ln \left(\sqrt{p^{2} x^{4}+q^{2}}-x^{2} \sqrt{p^{2}}-\textit{\_R} \right)}{a^{2} p^{4} \left(-\textit{\_R}^{11}-45 q^{2} \textit{\_R}^{9}-10 q^{4} \textit{\_R}^{7}+38 q^{6} \textit{\_R}^{5}-5 q^{8} \textit{\_R}^{3}-9 q^{10} \textit{\_R} \right)+11 \sqrt{p^{2}}\, \textit{\_R}^{10} a^{2} p^{3} q +75 \sqrt{p^{2}}\, \textit{\_R}^{8} a^{2} p^{3} q^{3}-98 \sqrt{p^{2}}\, \textit{\_R}^{6} a^{2} p^{3} q^{5}+70 \sqrt{p^{2}}\, \textit{\_R}^{4} a^{2} p^{3} q^{7}-25 \sqrt{p^{2}}\, \textit{\_R}^{2} a^{2} p^{3} q^{9}-\sqrt{p^{2}}\, a^{2} p^{3} q^{11}-6 \sqrt{p^{2}}\, \textit{\_R}^{8} b^{2}+14 \sqrt{p^{2}}\, \textit{\_R}^{6} b^{2} q^{2}-10 \sqrt{p^{2}}\, \textit{\_R}^{4} b^{2} q^{4}+2 \sqrt{p^{2}}\, \textit{\_R}^{2} b^{2} q^{6}}\right)}{6}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(8 a^{2} \textit{\_Z}^{6}+24 a^{2} p q \,\textit{\_Z}^{4}+24 a^{2} p^{2} q^{2} \textit{\_Z}^{2}+8 a^{2} p^{3} q^{3}-b^{2}\right)}{\sum}\frac{\left(\textit{\_R}^{4}+\textit{\_R}^{2} p q \right) \ln \left(\frac{\sqrt{p^{2} x^{4}+q^{2}}\, \sqrt{2}}{2 x}-\textit{\_R} \right)}{\textit{\_R}^{5}+2 p q \,\textit{\_R}^{3}+p^{2} q^{2} \textit{\_R}}\right) \sqrt{2}}{12 a}$&$722$\\ elliptic&$\frac{b \sqrt{p^{2}}\, \left(\munderset{\textit{\_R} =\RootOf \left(p^{4} \textit{\_Z}^{12} a^{2}-12 \sqrt{p^{2}}\, \textit{\_Z}^{11} a^{2} p^{3} q +54 p^{4} \textit{\_Z}^{10} a^{2} q^{2}-\left(100 \sqrt{p^{2}}\, a^{2} p^{3} q^{3}-8 \sqrt{p^{2}}\, b^{2}\right) \textit{\_Z}^{9}+15 p^{4} \textit{\_Z}^{8} a^{2} q^{4}-\left(-168 \sqrt{p^{2}}\, a^{2} p^{3} q^{5}+24 \sqrt{p^{2}}\, b^{2} q^{2}\right) \textit{\_Z}^{7}-76 p^{4} \textit{\_Z}^{6} a^{2} q^{6}-\left(168 \sqrt{p^{2}}\, a^{2} p^{3} q^{7}-24 \sqrt{p^{2}}\, b^{2} q^{4}\right) \textit{\_Z}^{5}+15 p^{4} \textit{\_Z}^{4} a^{2} q^{8}-\left(-100 \sqrt{p^{2}}\, a^{2} p^{3} q^{9}+8 \sqrt{p^{2}}\, b^{2} q^{6}\right) \textit{\_Z}^{3}+54 p^{4} \textit{\_Z}^{2} a^{2} q^{10}+12 \sqrt{p^{2}}\, \textit{\_Z} \,a^{2} p^{3} q^{11}+a^{2} p^{4} q^{12}\right)}{\sum}\frac{\left(p \left(-\textit{\_R}^{9}+2 q^{4} \textit{\_R}^{5}-q^{8} \textit{\_R} \right)+2 q \left(-\textit{\_R}^{8} \sqrt{p^{2}}-q^{2} \textit{\_R}^{6} \sqrt{p^{2}}+q^{4} \textit{\_R}^{4} \sqrt{p^{2}}+q^{6} \textit{\_R}^{2} \sqrt{p^{2}}\right)\right) \ln \left(\sqrt{p^{2} x^{4}+q^{2}}-x^{2} \sqrt{p^{2}}-\textit{\_R} \right)}{a^{2} p^{4} \left(-\textit{\_R}^{11}-45 q^{2} \textit{\_R}^{9}-10 q^{4} \textit{\_R}^{7}+38 q^{6} \textit{\_R}^{5}-5 q^{8} \textit{\_R}^{3}-9 q^{10} \textit{\_R} \right)+11 \sqrt{p^{2}}\, \textit{\_R}^{10} a^{2} p^{3} q +75 \sqrt{p^{2}}\, \textit{\_R}^{8} a^{2} p^{3} q^{3}-98 \sqrt{p^{2}}\, \textit{\_R}^{6} a^{2} p^{3} q^{5}+70 \sqrt{p^{2}}\, \textit{\_R}^{4} a^{2} p^{3} q^{7}-25 \sqrt{p^{2}}\, \textit{\_R}^{2} a^{2} p^{3} q^{9}-\sqrt{p^{2}}\, a^{2} p^{3} q^{11}-6 \sqrt{p^{2}}\, \textit{\_R}^{8} b^{2}+14 \sqrt{p^{2}}\, \textit{\_R}^{6} b^{2} q^{2}-10 \sqrt{p^{2}}\, \textit{\_R}^{4} b^{2} q^{4}+2 \sqrt{p^{2}}\, \textit{\_R}^{2} b^{2} q^{6}}\right)}{6}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(8 a^{2} \textit{\_Z}^{6}+24 a^{2} p q \,\textit{\_Z}^{4}+24 a^{2} p^{2} q^{2} \textit{\_Z}^{2}+8 a^{2} p^{3} q^{3}-b^{2}\right)}{\sum}\frac{\left(\textit{\_R}^{4}+\textit{\_R}^{2} p q \right) \ln \left(\frac{\sqrt{p^{2} x^{4}+q^{2}}\, \sqrt{2}}{2 x}-\textit{\_R} \right)}{\textit{\_R}^{5}+2 p q \,\textit{\_R}^{3}+p^{2} q^{2} \textit{\_R}}\right) \sqrt{2}}{12 a}$&$722$\\ \hline \end{longtable}"," ",0,"1/6*b*(p^2)^(1/2)*sum((p*(-_R^9+2*_R^5*q^4-_R*q^8)+2*q*(-_R^8*(p^2)^(1/2)-q^2*_R^6*(p^2)^(1/2)+q^4*_R^4*(p^2)^(1/2)+q^6*_R^2*(p^2)^(1/2)))/(a^2*p^4*(-_R^11-45*_R^9*q^2-10*_R^7*q^4+38*_R^5*q^6-5*_R^3*q^8-9*_R*q^10)+11*(p^2)^(1/2)*_R^10*a^2*p^3*q+75*(p^2)^(1/2)*_R^8*a^2*p^3*q^3-98*(p^2)^(1/2)*_R^6*a^2*p^3*q^5+70*(p^2)^(1/2)*_R^4*a^2*p^3*q^7-25*(p^2)^(1/2)*_R^2*a^2*p^3*q^9-(p^2)^(1/2)*a^2*p^3*q^11-6*(p^2)^(1/2)*_R^8*b^2+14*(p^2)^(1/2)*_R^6*b^2*q^2-10*(p^2)^(1/2)*_R^4*b^2*q^4+2*(p^2)^(1/2)*_R^2*b^2*q^6)*ln((p^2*x^4+q^2)^(1/2)-x^2*(p^2)^(1/2)-_R),_R=RootOf(p^4*_Z^12*a^2-12*(p^2)^(1/2)*_Z^11*a^2*p^3*q+54*p^4*_Z^10*a^2*q^2-(100*(p^2)^(1/2)*a^2*p^3*q^3-8*(p^2)^(1/2)*b^2)*_Z^9+15*p^4*_Z^8*a^2*q^4-(-168*(p^2)^(1/2)*a^2*p^3*q^5+24*(p^2)^(1/2)*b^2*q^2)*_Z^7-76*p^4*_Z^6*a^2*q^6-(168*(p^2)^(1/2)*a^2*p^3*q^7-24*(p^2)^(1/2)*b^2*q^4)*_Z^5+15*p^4*_Z^4*a^2*q^8-(-100*(p^2)^(1/2)*a^2*p^3*q^9+8*(p^2)^(1/2)*b^2*q^6)*_Z^3+54*p^4*_Z^2*a^2*q^10+12*(p^2)^(1/2)*_Z*a^2*p^3*q^11+a^2*p^4*q^12))+1/12/a*sum((_R^4+_R^2*p*q)/(_R^5+2*_R^3*p*q+_R*p^2*q^2)*ln(1/2*(p^2*x^4+q^2)^(1/2)*2^(1/2)/x-_R),_R=RootOf(8*_Z^6*a^2+24*_Z^4*a^2*p*q+24*_Z^2*a^2*p^2*q^2+8*a^2*p^3*q^3-b^2))*2^(1/2)","B"
2586,0,0,179,0.094000," ","int((x^2-1)^2/(x^2+1)^2/(x^4+1)^(1/2)/(x^2+(x^4+1)^(1/2))^(1/2),x)","\[\int \frac{\left(x^{2}-1\right)^{2}}{\left(x^{2}+1\right)^{2} \sqrt{x^{4}+1}\, \sqrt{x^{2}+\sqrt{x^{4}+1}}}\, dx\]"," ",0,"int((x^2-1)^2/(x^2+1)^2/(x^4+1)^(1/2)/(x^2+(x^4+1)^(1/2))^(1/2),x)","F"
2587,0,0,180,0.031000," ","int((-3+2*(k^2+1)*x+(k^2+1)*x^2-4*k^2*x^3+k^2*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(-1+d+(-1-2*d)*x+(k^2+d)*x^2+k^2*x^3),x)","\[\int \frac{-3+2 \left(k^{2}+1\right) x +\left(k^{2}+1\right) x^{2}-4 k^{2} x^{3}+k^{2} x^{4}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{2}{3}} \left(-1+d +\left(-1-2 d \right) x +\left(k^{2}+d \right) x^{2}+k^{2} x^{3}\right)}\, dx\]"," ",0,"int((-3+2*(k^2+1)*x+(k^2+1)*x^2-4*k^2*x^3+k^2*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(-1+d+(-1-2*d)*x+(k^2+d)*x^2+k^2*x^3),x)","F"
2588,0,0,178,0.064000," ","int(x^3*(-2+(1+k)*x)/((1-x)*x*(-k*x+1))^(2/3)/(1-(2+2*k)*x+(k^2+4*k+1)*x^2-(2*k^2+2*k)*x^3+(k^2-b)*x^4),x)","\[\int \frac{x^{3} \left(-2+\left(1+k \right) x \right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{2}{3}} \left(1-\left(2+2 k \right) x +\left(k^{2}+4 k +1\right) x^{2}-\left(2 k^{2}+2 k \right) x^{3}+\left(k^{2}-b \right) x^{4}\right)}\, dx\]"," ",0,"int(x^3*(-2+(1+k)*x)/((1-x)*x*(-k*x+1))^(2/3)/(1-(2+2*k)*x+(k^2+4*k+1)*x^2-(2*k^2+2*k)*x^3+(k^2-b)*x^4),x)","F"
2589,0,0,180,0.089000," ","int((x^2+1)^2/(x^2-1)^2/(x^4+1)^(1/2)/(x^2+(x^4+1)^(1/2))^(1/2),x)","\[\int \frac{\left(x^{2}+1\right)^{2}}{\left(x^{2}-1\right)^{2} \sqrt{x^{4}+1}\, \sqrt{x^{2}+\sqrt{x^{4}+1}}}\, dx\]"," ",0,"int((x^2+1)^2/(x^2-1)^2/(x^4+1)^(1/2)/(x^2+(x^4+1)^(1/2))^(1/2),x)","F"
2590,0,0,180,0.087000," ","int((x^2-1)^2*(x^2+(x^4+1)^(1/2))^(1/2)/(x^2+1)^2/(x^4+1)^(1/2),x)","\[\int \frac{\left(x^{2}-1\right)^{2} \sqrt{x^{2}+\sqrt{x^{4}+1}}}{\left(x^{2}+1\right)^{2} \sqrt{x^{4}+1}}\, dx\]"," ",0,"int((x^2-1)^2*(x^2+(x^4+1)^(1/2))^(1/2)/(x^2+1)^2/(x^4+1)^(1/2),x)","F"
2591,1,157,97,0.247000," ","int((x^2-1)/(x^2+1)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{7}{2}}}{7}-\frac{24 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}+\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}-\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+14 \textit{\_Z}^{8}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{4}+2\right)}{\sum}\frac{\left(\textit{\_R}^{6}-3 \textit{\_R}^{4}+2 \textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+7 \textit{\_R}^{7}+3 \textit{\_R}^{5}-2 \textit{\_R}^{3}}\right)$&$157$\\ default&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{7}{2}}}{7}-\frac{24 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}+\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}-\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+14 \textit{\_Z}^{8}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{4}+2\right)}{\sum}\frac{\left(\textit{\_R}^{6}-3 \textit{\_R}^{4}+2 \textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+7 \textit{\_R}^{7}+3 \textit{\_R}^{5}-2 \textit{\_R}^{3}}\right)$&$157$\\ \hline \end{longtable}"," ",0,"8/7*(1+(1+(1+x)^(1/2))^(1/2))^(7/2)-24/5*(1+(1+(1+x)^(1/2))^(1/2))^(5/2)+16/3*(1+(1+(1+x)^(1/2))^(1/2))^(3/2)-sum((_R^6-3*_R^4+2*_R^2)/(_R^15-7*_R^13+18*_R^11-20*_R^9+7*_R^7+3*_R^5-2*_R^3)*ln((1+(1+(1+x)^(1/2))^(1/2))^(1/2)-_R),_R=RootOf(_Z^16-8*_Z^14+24*_Z^12-32*_Z^10+14*_Z^8+8*_Z^6-8*_Z^4+2))","A"
2592,1,157,97,0.244000," ","int((x^2-1)/(x^2+1)/(1+(1+(1+x)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{7}{2}}}{7}-\frac{24 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}+\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}-\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+14 \textit{\_Z}^{8}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{4}+2\right)}{\sum}\frac{\left(\textit{\_R}^{6}-3 \textit{\_R}^{4}+2 \textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+7 \textit{\_R}^{7}+3 \textit{\_R}^{5}-2 \textit{\_R}^{3}}\right)$&$157$\\ default&$\frac{8 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{7}{2}}}{7}-\frac{24 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{5}{2}}}{5}+\frac{16 \left(1+\sqrt{1+\sqrt{1+x}}\right)^{\frac{3}{2}}}{3}-\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{16}-8 \textit{\_Z}^{14}+24 \textit{\_Z}^{12}-32 \textit{\_Z}^{10}+14 \textit{\_Z}^{8}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{4}+2\right)}{\sum}\frac{\left(\textit{\_R}^{6}-3 \textit{\_R}^{4}+2 \textit{\_R}^{2}\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{1+x}}}-\textit{\_R} \right)}{\textit{\_R}^{15}-7 \textit{\_R}^{13}+18 \textit{\_R}^{11}-20 \textit{\_R}^{9}+7 \textit{\_R}^{7}+3 \textit{\_R}^{5}-2 \textit{\_R}^{3}}\right)$&$157$\\ \hline \end{longtable}"," ",0,"8/7*(1+(1+(1+x)^(1/2))^(1/2))^(7/2)-24/5*(1+(1+(1+x)^(1/2))^(1/2))^(5/2)+16/3*(1+(1+(1+x)^(1/2))^(1/2))^(3/2)-sum((_R^6-3*_R^4+2*_R^2)/(_R^15-7*_R^13+18*_R^11-20*_R^9+7*_R^7+3*_R^5-2*_R^3)*ln((1+(1+(1+x)^(1/2))^(1/2))^(1/2)-_R),_R=RootOf(_Z^16-8*_Z^14+24*_Z^12-32*_Z^10+14*_Z^8+8*_Z^6-8*_Z^4+2))","A"
2593,0,0,185,0.161000," ","int((-2+x)*(x^3-x^2+x)^(1/3)/(-1+x)/(x^2+x-1),x)","\[\int \frac{\left(-2+x \right) \left(x^{3}-x^{2}+x \right)^{\frac{1}{3}}}{\left(-1+x \right) \left(x^{2}+x -1\right)}\, dx\]"," ",0,"int((-2+x)*(x^3-x^2+x)^(1/3)/(-1+x)/(x^2+x-1),x)","F"
2594,1,1603,177,12.540000," ","int((x^2+1)*(x^3+x^2)^(1/3)/(x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1603$\\ risch&$\text{Expression too large to display}$&$2565$\\ \hline \end{longtable}"," ",0,"(1/6+1/2*x)*(x^3+x^2)^(1/3)+RootOf(_Z^3-2)*ln(-(-RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^3*x^2+10*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^4*x^2+2*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^3*x-20*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^4*x+120*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*(x^3+x^2)^(2/3)-17*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)*x^2+170*RootOf(_Z^3-2)^2*x^2-198*(x^3+x^2)^(1/3)*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*x-240*(x^3+x^2)^(1/3)*RootOf(_Z^3-2)*x-3*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)*x+30*RootOf(_Z^3-2)^2*x+42*(x^3+x^2)^(2/3))/x/(-1+x))-ln((10*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^3*x^2-RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^4*x^2-20*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^3*x+2*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^4*x+120*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*(x^3+x^2)^(2/3)-150*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)*x^2+15*RootOf(_Z^3-2)^2*x^2-42*(x^3+x^2)^(1/3)*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*x-240*(x^3+x^2)^(1/3)*RootOf(_Z^3-2)*x-70*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)*x+7*RootOf(_Z^3-2)^2*x+198*(x^3+x^2)^(2/3))/x/(-1+x))*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)-ln((10*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^3*x^2-RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^4*x^2-20*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^3*x+2*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^4*x+120*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*(x^3+x^2)^(2/3)-150*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)*x^2+15*RootOf(_Z^3-2)^2*x^2-42*(x^3+x^2)^(1/3)*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*x-240*(x^3+x^2)^(1/3)*RootOf(_Z^3-2)*x-70*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)*x+7*RootOf(_Z^3-2)^2*x+198*(x^3+x^2)^(2/3))/x/(-1+x))*RootOf(_Z^3-2)-17/9*ln((-RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^4*x^2+2*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^4*x+96*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*(x^3+x^2)^(2/3)-126*(x^3+x^2)^(1/3)*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*x+28*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*x^2-18*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*x+252*(x^3+x^2)^(2/3)-60*x*(x^3+x^2)^(1/3)-196*x^2-140*x)/x)-17/18*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*ln(-(-4*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^4*x^2+8*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^4*x+48*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*(x^3+x^2)^(2/3)+15*(x^3+x^2)^(1/3)*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*x-71*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*x^2-10*RootOf(RootOf(_Z^3-2)^2+_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*x-30*(x^3+x^2)^(2/3)+126*x*(x^3+x^2)^(1/3)-112*x^2-42*x)/x)","C"
2595,0,0,197,0.041000," ","int((a*x-b)/x/(a^3*x^3-b^3)^(1/3),x)","\[\int \frac{a x -b}{x \left(a^{3} x^{3}-b^{3}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a*x-b)/x/(a^3*x^3-b^3)^(1/3),x)","F"
2596,0,0,185,0.042000," ","int((x^3-2)*(x^4+2*x^3+x)^(1/3)/(x^3+1)/(x^3+x^2+1),x)","\[\int \frac{\left(x^{3}-2\right) \left(x^{4}+2 x^{3}+x \right)^{\frac{1}{3}}}{\left(x^{3}+1\right) \left(x^{3}+x^{2}+1\right)}\, dx\]"," ",0,"int((x^3-2)*(x^4+2*x^3+x)^(1/3)/(x^3+1)/(x^3+x^2+1),x)","F"
2597,1,466,169,6.375000," ","int(x^4/(x^4-1)^(1/4)/(2*x^8-2*x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{7} \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{8}+1\right)^{7} x^{4}+2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{8}+1\right)^{5} x^{2}-\RootOf \left(\textit{\_Z}^{8}+1\right)^{3} x^{4}-2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{2} x^{3}+2 \left(x^{4}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{8}+1\right)^{3}}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}-x^{4}+1}\right)}{8}+\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{5} \ln \left(-\frac{2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{8}+1\right)^{7} x^{2}-2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{6} x^{3}+\RootOf \left(\textit{\_Z}^{8}+1\right)^{5} x^{4}-\RootOf \left(\textit{\_Z}^{8}+1\right) x^{4}+2 \left(x^{4}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{8}+1\right)}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}+x^{4}-1}\right)}{8}+\frac{\RootOf \left(\textit{\_Z}^{8}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{8}+1\right)^{9} x^{4}+2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{6} x^{3}+\RootOf \left(\textit{\_Z}^{8}+1\right)^{5} x^{4}-2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{8}+1\right)^{3} x^{2}-\RootOf \left(\textit{\_Z}^{8}+1\right)^{5}+2 \left(x^{4}-1\right)^{\frac{3}{4}} x}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}+x^{4}-1}\right)}{8}+\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{3} \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{8}+1\right)^{11} x^{4}-\RootOf \left(\textit{\_Z}^{8}+1\right)^{7} x^{4}+\RootOf \left(\textit{\_Z}^{8}+1\right)^{7}+2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{2} x^{3}+2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{8}+1\right) x^{2}+2 \left(x^{4}-1\right)^{\frac{3}{4}} x}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}-x^{4}+1}\right)}{8}$&$466$\\ \hline \end{longtable}"," ",0,"-1/8*RootOf(_Z^8+1)^7*ln(-(-RootOf(_Z^8+1)^7*x^4+2*(x^4-1)^(1/2)*RootOf(_Z^8+1)^5*x^2-RootOf(_Z^8+1)^3*x^4-2*(x^4-1)^(1/4)*RootOf(_Z^8+1)^2*x^3+2*(x^4-1)^(3/4)*x+RootOf(_Z^8+1)^3)/(RootOf(_Z^8+1)^4*x^4-x^4+1))+1/8*RootOf(_Z^8+1)^5*ln(-(2*(x^4-1)^(1/2)*RootOf(_Z^8+1)^7*x^2-2*(x^4-1)^(1/4)*RootOf(_Z^8+1)^6*x^3+RootOf(_Z^8+1)^5*x^4-RootOf(_Z^8+1)*x^4+2*(x^4-1)^(3/4)*x+RootOf(_Z^8+1))/(RootOf(_Z^8+1)^4*x^4+x^4-1))+1/8*RootOf(_Z^8+1)*ln(-(-RootOf(_Z^8+1)^9*x^4+2*(x^4-1)^(1/4)*RootOf(_Z^8+1)^6*x^3+RootOf(_Z^8+1)^5*x^4-2*(x^4-1)^(1/2)*RootOf(_Z^8+1)^3*x^2-RootOf(_Z^8+1)^5+2*(x^4-1)^(3/4)*x)/(RootOf(_Z^8+1)^4*x^4+x^4-1))+1/8*RootOf(_Z^8+1)^3*ln(-(-RootOf(_Z^8+1)^11*x^4-RootOf(_Z^8+1)^7*x^4+RootOf(_Z^8+1)^7+2*(x^4-1)^(1/4)*RootOf(_Z^8+1)^2*x^3+2*(x^4-1)^(1/2)*RootOf(_Z^8+1)*x^2+2*(x^4-1)^(3/4)*x)/(RootOf(_Z^8+1)^4*x^4-x^4+1))","C"
2598,1,614,169,6.040000," ","int((x^4-1)^(3/4)/(2*x^8-2*x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{3} \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{8}+1\right)^{7} x^{4}+2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{8}+1\right)^{5} x^{2}-\RootOf \left(\textit{\_Z}^{8}+1\right)^{3} x^{4}-2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{2} x^{3}+2 \left(x^{4}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{8}+1\right)^{3}}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}-x^{4}+1}\right)}{8}-\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{7} \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{8}+1\right)^{11} x^{4}-2 \RootOf \left(\textit{\_Z}^{8}+1\right)^{7} x^{4}+2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{6} x^{3}-2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{8}+1\right)^{5} x^{2}+2 \left(x^{4}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x +\RootOf \left(\textit{\_Z}^{8}+1\right)^{7}-\RootOf \left(\textit{\_Z}^{8}+1\right)^{3} x^{4}-2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{2} x^{3}+2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{8}+1\right) x^{2}-2 \left(x^{4}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{8}+1\right)^{3}}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}-x^{4}+1}\right)}{8}-\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{5} \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{8}+1\right)^{9} x^{4}+2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{6} x^{3}+\RootOf \left(\textit{\_Z}^{8}+1\right)^{5} x^{4}-2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{8}+1\right)^{3} x^{2}-\RootOf \left(\textit{\_Z}^{8}+1\right)^{5}+2 \left(x^{4}-1\right)^{\frac{3}{4}} x}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}+x^{4}-1}\right)}{8}-\frac{\RootOf \left(\textit{\_Z}^{8}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{8}+1\right)^{9} x^{4}-2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{8}+1\right)^{7} x^{2}-2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{6} x^{3}+2 \left(x^{4}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x +2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{8}+1\right)^{3} x^{2}+2 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{8}+1\right)^{5}+\RootOf \left(\textit{\_Z}^{8}+1\right) x^{4}+2 \left(x^{4}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{8}+1\right)}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}+x^{4}-1}\right)}{8}$&$614$\\ \hline \end{longtable}"," ",0,"1/8*RootOf(_Z^8+1)^3*ln(-(-RootOf(_Z^8+1)^7*x^4+2*(x^4-1)^(1/2)*RootOf(_Z^8+1)^5*x^2-RootOf(_Z^8+1)^3*x^4-2*(x^4-1)^(1/4)*RootOf(_Z^8+1)^2*x^3+2*(x^4-1)^(3/4)*x+RootOf(_Z^8+1)^3)/(RootOf(_Z^8+1)^4*x^4-x^4+1))-1/8*RootOf(_Z^8+1)^7*ln((-RootOf(_Z^8+1)^11*x^4-2*RootOf(_Z^8+1)^7*x^4+2*(x^4-1)^(1/4)*RootOf(_Z^8+1)^6*x^3-2*(x^4-1)^(1/2)*RootOf(_Z^8+1)^5*x^2+2*(x^4-1)^(3/4)*RootOf(_Z^8+1)^4*x+RootOf(_Z^8+1)^7-RootOf(_Z^8+1)^3*x^4-2*(x^4-1)^(1/4)*RootOf(_Z^8+1)^2*x^3+2*(x^4-1)^(1/2)*RootOf(_Z^8+1)*x^2-2*(x^4-1)^(3/4)*x+RootOf(_Z^8+1)^3)/(RootOf(_Z^8+1)^4*x^4-x^4+1))-1/8*RootOf(_Z^8+1)^5*ln(-(-RootOf(_Z^8+1)^9*x^4+2*(x^4-1)^(1/4)*RootOf(_Z^8+1)^6*x^3+RootOf(_Z^8+1)^5*x^4-2*(x^4-1)^(1/2)*RootOf(_Z^8+1)^3*x^2-RootOf(_Z^8+1)^5+2*(x^4-1)^(3/4)*x)/(RootOf(_Z^8+1)^4*x^4+x^4-1))-1/8*RootOf(_Z^8+1)*ln(-(-RootOf(_Z^8+1)^9*x^4-2*(x^4-1)^(1/2)*RootOf(_Z^8+1)^7*x^2-2*(x^4-1)^(1/4)*RootOf(_Z^8+1)^6*x^3+2*(x^4-1)^(3/4)*RootOf(_Z^8+1)^4*x+2*(x^4-1)^(1/2)*RootOf(_Z^8+1)^3*x^2+2*(x^4-1)^(1/4)*RootOf(_Z^8+1)^2*x^3-RootOf(_Z^8+1)^5+RootOf(_Z^8+1)*x^4+2*(x^4-1)^(3/4)*x-RootOf(_Z^8+1))/(RootOf(_Z^8+1)^4*x^4+x^4-1))","C"
2599,1,600,169,6.769000," ","int(x^4/(x^4+1)^(1/4)/(2*x^8+2*x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{5} \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{9} x^{4}+2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{8}+1\right)^{7} x^{2}-2 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{6} x^{3}+2 \left(x^{4}+1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x -2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{8}+1\right)^{3} x^{2}+2 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{8}+1\right)^{5}-\RootOf \left(\textit{\_Z}^{8}+1\right) x^{4}+2 \left(x^{4}+1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{8}+1\right)}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}+x^{4}+1}\right)}{8}-\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{7} \ln \left(\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{11} x^{4}-2 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{6} x^{3}+2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{8}+1\right)^{5} x^{2}+2 \left(x^{4}+1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x +\RootOf \left(\textit{\_Z}^{8}+1\right)^{7}-\RootOf \left(\textit{\_Z}^{8}+1\right)^{3} x^{4}+2 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{2} x^{3}+2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{8}+1\right) x^{2}-2 \left(x^{4}+1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{8}+1\right)^{3}}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}-x^{4}-1}\right)}{8}-\frac{\RootOf \left(\textit{\_Z}^{8}+1\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{8}+1\right)^{9} x^{4}+2 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{6} x^{3}+\RootOf \left(\textit{\_Z}^{8}+1\right)^{5} x^{4}-2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{8}+1\right)^{3} x^{2}+\RootOf \left(\textit{\_Z}^{8}+1\right)^{5}+2 \left(x^{4}+1\right)^{\frac{3}{4}} x}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}+x^{4}+1}\right)}{8}-\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{3} \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{8}+1\right)^{11} x^{4}-\RootOf \left(\textit{\_Z}^{8}+1\right)^{7} x^{4}-\RootOf \left(\textit{\_Z}^{8}+1\right)^{7}+2 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{2} x^{3}+2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{8}+1\right) x^{2}+2 \left(x^{4}+1\right)^{\frac{3}{4}} x}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}-x^{4}-1}\right)}{8}$&$600$\\ \hline \end{longtable}"," ",0,"-1/8*RootOf(_Z^8+1)^5*ln(-(RootOf(_Z^8+1)^9*x^4+2*(x^4+1)^(1/2)*RootOf(_Z^8+1)^7*x^2-2*(x^4+1)^(1/4)*RootOf(_Z^8+1)^6*x^3+2*(x^4+1)^(3/4)*RootOf(_Z^8+1)^4*x-2*(x^4+1)^(1/2)*RootOf(_Z^8+1)^3*x^2+2*(x^4+1)^(1/4)*RootOf(_Z^8+1)^2*x^3-RootOf(_Z^8+1)^5-RootOf(_Z^8+1)*x^4+2*(x^4+1)^(3/4)*x-RootOf(_Z^8+1))/(RootOf(_Z^8+1)^4*x^4+x^4+1))-1/8*RootOf(_Z^8+1)^7*ln((RootOf(_Z^8+1)^11*x^4-2*(x^4+1)^(1/4)*RootOf(_Z^8+1)^6*x^3+2*(x^4+1)^(1/2)*RootOf(_Z^8+1)^5*x^2+2*(x^4+1)^(3/4)*RootOf(_Z^8+1)^4*x+RootOf(_Z^8+1)^7-RootOf(_Z^8+1)^3*x^4+2*(x^4+1)^(1/4)*RootOf(_Z^8+1)^2*x^3+2*(x^4+1)^(1/2)*RootOf(_Z^8+1)*x^2-2*(x^4+1)^(3/4)*x-RootOf(_Z^8+1)^3)/(RootOf(_Z^8+1)^4*x^4-x^4-1))-1/8*RootOf(_Z^8+1)*ln(-(-RootOf(_Z^8+1)^9*x^4+2*(x^4+1)^(1/4)*RootOf(_Z^8+1)^6*x^3+RootOf(_Z^8+1)^5*x^4-2*(x^4+1)^(1/2)*RootOf(_Z^8+1)^3*x^2+RootOf(_Z^8+1)^5+2*(x^4+1)^(3/4)*x)/(RootOf(_Z^8+1)^4*x^4+x^4+1))-1/8*RootOf(_Z^8+1)^3*ln(-(-RootOf(_Z^8+1)^11*x^4-RootOf(_Z^8+1)^7*x^4-RootOf(_Z^8+1)^7+2*(x^4+1)^(1/4)*RootOf(_Z^8+1)^2*x^3+2*(x^4+1)^(1/2)*RootOf(_Z^8+1)*x^2+2*(x^4+1)^(3/4)*x)/(RootOf(_Z^8+1)^4*x^4-x^4-1))","C"
2600,1,535,169,6.141000," ","int((x^4+1)^(3/4)/(2*x^8+2*x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{5} \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{9} x^{4}+2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{8}+1\right)^{7} x^{2}+2 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{6} x^{3}-2 \RootOf \left(\textit{\_Z}^{8}+1\right)^{5} x^{4}+2 \left(x^{4}+1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x +2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{8}+1\right)^{3} x^{2}-2 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{8}+1\right)^{5}+\RootOf \left(\textit{\_Z}^{8}+1\right) x^{4}+2 \left(x^{4}+1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{8}+1\right)}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}+x^{4}+1}\right)}{8}-\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{7} \ln \left(\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{11} x^{4}+\RootOf \left(\textit{\_Z}^{8}+1\right)^{7} x^{4}+\RootOf \left(\textit{\_Z}^{8}+1\right)^{7}-2 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{2} x^{3}-2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{8}+1\right) x^{2}-2 \left(x^{4}+1\right)^{\frac{3}{4}} x}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}-x^{4}-1}\right)}{8}-\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{3} \ln \left(\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{7} x^{4}-2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{8}+1\right)^{5} x^{2}+\RootOf \left(\textit{\_Z}^{8}+1\right)^{3} x^{4}+2 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{2} x^{3}-2 \left(x^{4}+1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{8}+1\right)^{3}}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}-x^{4}-1}\right)}{8}+\frac{\RootOf \left(\textit{\_Z}^{8}+1\right) \ln \left(\frac{2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{8}+1\right)^{7} x^{2}+2 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{6} x^{3}+\RootOf \left(\textit{\_Z}^{8}+1\right)^{5} x^{4}-\RootOf \left(\textit{\_Z}^{8}+1\right) x^{4}-2 \left(x^{4}+1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{8}+1\right)}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}+x^{4}+1}\right)}{8}$&$535$\\ \hline \end{longtable}"," ",0,"-1/8*RootOf(_Z^8+1)^5*ln(-(RootOf(_Z^8+1)^9*x^4+2*(x^4+1)^(1/2)*RootOf(_Z^8+1)^7*x^2+2*(x^4+1)^(1/4)*RootOf(_Z^8+1)^6*x^3-2*RootOf(_Z^8+1)^5*x^4+2*(x^4+1)^(3/4)*RootOf(_Z^8+1)^4*x+2*(x^4+1)^(1/2)*RootOf(_Z^8+1)^3*x^2-2*(x^4+1)^(1/4)*RootOf(_Z^8+1)^2*x^3-RootOf(_Z^8+1)^5+RootOf(_Z^8+1)*x^4+2*(x^4+1)^(3/4)*x+RootOf(_Z^8+1))/(RootOf(_Z^8+1)^4*x^4+x^4+1))-1/8*RootOf(_Z^8+1)^7*ln((RootOf(_Z^8+1)^11*x^4+RootOf(_Z^8+1)^7*x^4+RootOf(_Z^8+1)^7-2*(x^4+1)^(1/4)*RootOf(_Z^8+1)^2*x^3-2*(x^4+1)^(1/2)*RootOf(_Z^8+1)*x^2-2*(x^4+1)^(3/4)*x)/(RootOf(_Z^8+1)^4*x^4-x^4-1))-1/8*RootOf(_Z^8+1)^3*ln((RootOf(_Z^8+1)^7*x^4-2*(x^4+1)^(1/2)*RootOf(_Z^8+1)^5*x^2+RootOf(_Z^8+1)^3*x^4+2*(x^4+1)^(1/4)*RootOf(_Z^8+1)^2*x^3-2*(x^4+1)^(3/4)*x+RootOf(_Z^8+1)^3)/(RootOf(_Z^8+1)^4*x^4-x^4-1))+1/8*RootOf(_Z^8+1)*ln((2*(x^4+1)^(1/2)*RootOf(_Z^8+1)^7*x^2+2*(x^4+1)^(1/4)*RootOf(_Z^8+1)^6*x^3+RootOf(_Z^8+1)^5*x^4-RootOf(_Z^8+1)*x^4-2*(x^4+1)^(3/4)*x-RootOf(_Z^8+1))/(RootOf(_Z^8+1)^4*x^4+x^4+1))","C"
2601,0,0,189,0.062000," ","int(x^2*(a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x)","\[\int \frac{x^{2} \sqrt{a^{2} x^{2}-b x}}{\left(a \,x^{2}+x \sqrt{a^{2} x^{2}-b x}\right)^{\frac{3}{2}}}\, dx\]"," ",0,"int(x^2*(a^2*x^2-b*x)^(1/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x)","F"
2602,0,0,167,0.053000," ","int((x^2+(x^4+1)^(1/2))^(1/2)/(1+x)/(x^4+1)^(1/2),x)","\[\int \frac{\sqrt{x^{2}+\sqrt{x^{4}+1}}}{\left(1+x \right) \sqrt{x^{4}+1}}\, dx\]"," ",0,"int((x^2+(x^4+1)^(1/2))^(1/2)/(1+x)/(x^4+1)^(1/2),x)","F"
2603,0,0,11,0.070000," ","int((a*x^2-b)/(2*a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{a \,x^{2}-b}{\left(2 a \,x^{3}-b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a*x^2-b)/(2*a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
2604,0,0,11,0.004000," ","int((a*x^2-b)/(2*a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{a \,x^{2}-b}{\left(2 a \,x^{3}-b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a*x^2-b)/(2*a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
2605,0,0,192,0.020000," ","int((2*a*b*x-3*a*x^2+x^3)/(x^2*(-a+x)*(-b+x))^(1/3)/(-a^2+2*a*x-(b*d+1)*x^2+d*x^3),x)","\[\int \frac{2 a b x -3 a \,x^{2}+x^{3}}{\left(x^{2} \left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{3}} \left(-a^{2}+2 a x -\left(b d +1\right) x^{2}+d \,x^{3}\right)}\, dx\]"," ",0,"int((2*a*b*x-3*a*x^2+x^3)/(x^2*(-a+x)*(-b+x))^(1/3)/(-a^2+2*a*x-(b*d+1)*x^2+d*x^3),x)","F"
2606,0,0,188,0.021000," ","int(((k^2-2)*x+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(1-d+(d*k^2-2)*x^2+x^4),x)","\[\int \frac{\left(k^{2}-2\right) x +k^{2} x^{3}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{1}{3}} \left(1-d +\left(d \,k^{2}-2\right) x^{2}+x^{4}\right)}\, dx\]"," ",0,"int(((k^2-2)*x+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(1-d+(d*k^2-2)*x^2+x^4),x)","F"
2607,1,2021,168,23.737000," ","int((1+2*x)*(x^4+x^3)^(1/4)/(x^2+x-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2021$\\ risch&$\text{Expression too large to display}$&$3988$\\ \hline \end{longtable}"," ",0,"2*(x^4+x^3)^(1/4)-1/2*RootOf(_Z^2+1)*ln((2*(x^4+x^3)^(1/2)*RootOf(_Z^2+1)*x-2*RootOf(_Z^2+1)*x^3-RootOf(_Z^2+1)*x^2+2*(x^4+x^3)^(3/4)-2*x^2*(x^4+x^3)^(1/4))/x^2)-RootOf(_Z^2+4*RootOf(16*_Z^4-4*_Z^2-1)^2-1)*ln(-(152*RootOf(_Z^2+4*RootOf(16*_Z^4-4*_Z^2-1)^2-1)*RootOf(16*_Z^4-4*_Z^2-1)^4*x^3-152*RootOf(_Z^2+4*RootOf(16*_Z^4-4*_Z^2-1)^2-1)*RootOf(16*_Z^4-4*_Z^2-1)^4*x^2-296*RootOf(_Z^2+4*RootOf(16*_Z^4-4*_Z^2-1)^2-1)*RootOf(16*_Z^4-4*_Z^2-1)^2*(x^4+x^3)^(1/2)*x+290*RootOf(_Z^2+4*RootOf(16*_Z^4-4*_Z^2-1)^2-1)*RootOf(16*_Z^4-4*_Z^2-1)^2*x^3+128*RootOf(_Z^2+4*RootOf(16*_Z^4-4*_Z^2-1)^2-1)*RootOf(16*_Z^4-4*_Z^2-1)^2*x^2-180*RootOf(16*_Z^4-4*_Z^2-1)^2*(x^4+x^3)^(3/4)+296*RootOf(16*_Z^4-4*_Z^2-1)^2*(x^4+x^3)^(1/4)*x^2-45*RootOf(_Z^2+4*RootOf(16*_Z^4-4*_Z^2-1)^2-1)*(x^4+x^3)^(1/2)*x+42*RootOf(_Z^2+4*RootOf(16*_Z^4-4*_Z^2-1)^2-1)*x^3+24*RootOf(_Z^2+4*RootOf(16*_Z^4-4*_Z^2-1)^2-1)*x^2-29*(x^4+x^3)^(3/4)+45*x^2*(x^4+x^3)^(1/4))/(4*x*RootOf(16*_Z^4-4*_Z^2-1)^2-4*RootOf(16*_Z^4-4*_Z^2-1)^2+x)/x^2)+2*RootOf(16*_Z^4-4*_Z^2-1)*ln((304*x^3*RootOf(16*_Z^4-4*_Z^2-1)^5-304*RootOf(16*_Z^4-4*_Z^2-1)^5*x^2+592*RootOf(16*_Z^4-4*_Z^2-1)^3*(x^4+x^3)^(1/2)*x-732*RootOf(16*_Z^4-4*_Z^2-1)^3*x^3-104*RootOf(16*_Z^4-4*_Z^2-1)^3*x^2-180*RootOf(16*_Z^4-4*_Z^2-1)^2*(x^4+x^3)^(3/4)+296*RootOf(16*_Z^4-4*_Z^2-1)^2*(x^4+x^3)^(1/4)*x^2-238*RootOf(16*_Z^4-4*_Z^2-1)*(x^4+x^3)^(1/2)*x+248*RootOf(16*_Z^4-4*_Z^2-1)*x^3+93*RootOf(16*_Z^4-4*_Z^2-1)*x^2+74*(x^4+x^3)^(3/4)-119*x^2*(x^4+x^3)^(1/4))/(4*x*RootOf(16*_Z^4-4*_Z^2-1)^2-4*RootOf(16*_Z^4-4*_Z^2-1)^2-2*x+1)/x^2)+1/2*ln((2*(x^4+x^3)^(3/4)-2*(x^4+x^3)^(1/2)*x+2*x^2*(x^4+x^3)^(1/4)-2*x^3-x^2)/x^2)-8*RootOf(16*_Z^4-4*_Z^2-1)^3*ln((192*x^3*RootOf(16*_Z^4-4*_Z^2-1)^5-192*RootOf(16*_Z^4-4*_Z^2-1)^5*x^2+360*RootOf(16*_Z^4-4*_Z^2-1)^3*(x^4+x^3)^(1/2)*x+364*RootOf(16*_Z^4-4*_Z^2-1)^3*x^3+164*RootOf(16*_Z^4-4*_Z^2-1)^3*x^2+180*RootOf(16*_Z^4-4*_Z^2-1)^2*(x^4+x^3)^(3/4)+296*RootOf(16*_Z^4-4*_Z^2-1)^2*(x^4+x^3)^(1/4)*x^2+58*RootOf(16*_Z^4-4*_Z^2-1)*(x^4+x^3)^(1/2)*x+49*RootOf(16*_Z^4-4*_Z^2-1)*x^3+28*RootOf(16*_Z^4-4*_Z^2-1)*x^2+29*(x^4+x^3)^(3/4)+45*x^2*(x^4+x^3)^(1/4))/(4*x*RootOf(16*_Z^4-4*_Z^2-1)^2-4*RootOf(16*_Z^4-4*_Z^2-1)^2+x)/x^2)+2*RootOf(16*_Z^4-4*_Z^2-1)*ln((192*x^3*RootOf(16*_Z^4-4*_Z^2-1)^5-192*RootOf(16*_Z^4-4*_Z^2-1)^5*x^2+360*RootOf(16*_Z^4-4*_Z^2-1)^3*(x^4+x^3)^(1/2)*x+364*RootOf(16*_Z^4-4*_Z^2-1)^3*x^3+164*RootOf(16*_Z^4-4*_Z^2-1)^3*x^2+180*RootOf(16*_Z^4-4*_Z^2-1)^2*(x^4+x^3)^(3/4)+296*RootOf(16*_Z^4-4*_Z^2-1)^2*(x^4+x^3)^(1/4)*x^2+58*RootOf(16*_Z^4-4*_Z^2-1)*(x^4+x^3)^(1/2)*x+49*RootOf(16*_Z^4-4*_Z^2-1)*x^3+28*RootOf(16*_Z^4-4*_Z^2-1)*x^2+29*(x^4+x^3)^(3/4)+45*x^2*(x^4+x^3)^(1/4))/(4*x*RootOf(16*_Z^4-4*_Z^2-1)^2-4*RootOf(16*_Z^4-4*_Z^2-1)^2+x)/x^2)+4*RootOf(16*_Z^4-4*_Z^2-1)^2*RootOf(_Z^2+4*RootOf(16*_Z^4-4*_Z^2-1)^2-1)*ln((192*RootOf(_Z^2+4*RootOf(16*_Z^4-4*_Z^2-1)^2-1)*RootOf(16*_Z^4-4*_Z^2-1)^4*x^3-192*RootOf(_Z^2+4*RootOf(16*_Z^4-4*_Z^2-1)^2-1)*RootOf(16*_Z^4-4*_Z^2-1)^4*x^2-360*RootOf(_Z^2+4*RootOf(16*_Z^4-4*_Z^2-1)^2-1)*RootOf(16*_Z^4-4*_Z^2-1)^2*(x^4+x^3)^(1/2)*x-460*RootOf(_Z^2+4*RootOf(16*_Z^4-4*_Z^2-1)^2-1)*RootOf(16*_Z^4-4*_Z^2-1)^2*x^3-68*RootOf(_Z^2+4*RootOf(16*_Z^4-4*_Z^2-1)^2-1)*RootOf(16*_Z^4-4*_Z^2-1)^2*x^2-360*RootOf(16*_Z^4-4*_Z^2-1)^2*(x^4+x^3)^(3/4)-592*RootOf(16*_Z^4-4*_Z^2-1)^2*(x^4+x^3)^(1/4)*x^2+148*RootOf(_Z^2+4*RootOf(16*_Z^4-4*_Z^2-1)^2-1)*(x^4+x^3)^(1/2)*x+152*RootOf(_Z^2+4*RootOf(16*_Z^4-4*_Z^2-1)^2-1)*x^3+57*RootOf(_Z^2+4*RootOf(16*_Z^4-4*_Z^2-1)^2-1)*x^2+148*(x^4+x^3)^(3/4)+238*x^2*(x^4+x^3)^(1/4))/(4*x*RootOf(16*_Z^4-4*_Z^2-1)^2-4*RootOf(16*_Z^4-4*_Z^2-1)^2-2*x+1)/x^2)","C"
2608,0,0,188,0.028000," ","int(((2*k^2-1)*x-2*k^4*x^3+k^4*x^5)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(-1+d+(-2*d*k^2+1)*x^2+d*k^4*x^4),x)","\[\int \frac{\left(2 k^{2}-1\right) x -2 k^{4} x^{3}+k^{4} x^{5}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{2}{3}} \left(-1+d +\left(-2 d \,k^{2}+1\right) x^{2}+d \,k^{4} x^{4}\right)}\, dx\]"," ",0,"int(((2*k^2-1)*x-2*k^4*x^3+k^4*x^5)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(-1+d+(-2*d*k^2+1)*x^2+d*k^4*x^4),x)","F"
2609,0,0,185,0.069000," ","int((-a+x)*(-b+x)*(-2*a*b+(a+b)*x)/(x*(-a+x)*(-b+x))^(1/3)/(a^2*b^2*d-2*a*b*(a+b)*d*x+(a^2+4*a*b+b^2)*d*x^2-2*(a+b)*d*x^3+(-1+d)*x^4),x)","\[\int \frac{\left(-a +x \right) \left(-b +x \right) \left(-2 a b +\left(a +b \right) x \right)}{\left(x \left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{3}} \left(a^{2} b^{2} d -2 a b \left(a +b \right) d x +\left(a^{2}+4 a b +b^{2}\right) d \,x^{2}-2 \left(a +b \right) d \,x^{3}+\left(-1+d \right) x^{4}\right)}\, dx\]"," ",0,"int((-a+x)*(-b+x)*(-2*a*b+(a+b)*x)/(x*(-a+x)*(-b+x))^(1/3)/(a^2*b^2*d-2*a*b*(a+b)*d*x+(a^2+4*a*b+b^2)*d*x^2-2*(a+b)*d*x^3+(-1+d)*x^4),x)","F"
2610,1,703,173,0.391000," ","int((a^2*x^3+b^2)^(1/2)*(a^2*x^6+c*x^3+2*b^2)/x/(a^2*x^6+b^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 \sqrt{a^{2} x^{3}+b^{2}}}{3}-\frac{4 b^{2} \arctanh \left(\frac{\sqrt{a^{2} x^{3}+b^{2}}}{\sqrt{b^{2}}}\right)}{3 \sqrt{b^{2}}}-\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{2} \textit{\_Z}^{6}+b^{2}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{3} a^{2} b^{2}+\underline{\hspace{1.25 ex}}\alpha^{3} a^{2} c +a^{2} b^{2}+b^{2} c \right) \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i a \left(2 x +\frac{-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{a \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i a \left(2 x +\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(2 a^{2} \left(a^{2} \underline{\hspace{1.25 ex}}\alpha^{5}-b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}\right)+i a^{3} \left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{4} \sqrt{3}-i a^{2} \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}}-a^{3} \left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{4}-a^{2} \underline{\hspace{1.25 ex}}\alpha^{3} \left(-a \,b^{2}\right)^{\frac{2}{3}}-i \left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  \sqrt{3}\, b^{2} a +i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, b^{2}+\left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  \,b^{2} a +\left(-a \,b^{2}\right)^{\frac{2}{3}} b^{2}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5} a^{3}-i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{4} a^{2}+i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} a^{2} b^{2}-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{4} a^{2}-2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a \,b^{2}+i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  \,b^{2}-3 \underline{\hspace{1.25 ex}}\alpha^{3} a^{2} b^{2}-i \sqrt{3}\, b^{4}+3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  \,b^{2}+3 b^{4}}{2 b^{2} \left(a^{2}+b^{2}\right)}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha^{3} \left(a^{2}+b^{2}\right) \sqrt{a^{2} x^{3}+b^{2}}}\right)}{6 a^{3} b^{2}}$&$703$\\ elliptic&$\text{Expression too large to display}$&$12449$\\ \hline \end{longtable}"," ",0,"2/3*(a^2*x^3+b^2)^(1/2)-4/3*b^2*arctanh((a^2*x^3+b^2)^(1/2)/(b^2)^(1/2))/(b^2)^(1/2)-1/6*I/a^3/b^2*2^(1/2)*sum((-_alpha^3*a^2*b^2+_alpha^3*a^2*c+a^2*b^2+b^2*c)/_alpha^3/(a^2+b^2)*(-a*b^2)^(1/3)*(1/2*I*a*(2*x+1/a*(-I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3)))/(-a*b^2)^(1/3))^(1/2)*(a*(x-1/a*(-a*b^2)^(1/3))/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3)))^(1/2)*(-1/2*I*a*(2*x+1/a*(I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3)))/(-a*b^2)^(1/3))^(1/2)/(a^2*x^3+b^2)^(1/2)*(2*a^2*(_alpha^5*a^2-_alpha^2*b^2)+I*a^3*(-a*b^2)^(1/3)*_alpha^4*3^(1/2)-I*a^2*_alpha^3*3^(1/2)*(-a*b^2)^(2/3)-a^3*(-a*b^2)^(1/3)*_alpha^4-a^2*_alpha^3*(-a*b^2)^(2/3)-I*(-a*b^2)^(1/3)*_alpha*3^(1/2)*b^2*a+I*(-a*b^2)^(2/3)*3^(1/2)*b^2+(-a*b^2)^(1/3)*_alpha*b^2*a+(-a*b^2)^(2/3)*b^2)*EllipticPi(1/3*3^(1/2)*(I*(x+1/2/a*(-a*b^2)^(1/3)-1/2*I*3^(1/2)/a*(-a*b^2)^(1/3))*3^(1/2)*a/(-a*b^2)^(1/3))^(1/2),1/2*(2*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha^5*a^3-I*(-a*b^2)^(2/3)*3^(1/2)*_alpha^4*a^2+I*3^(1/2)*_alpha^3*a^2*b^2-3*(-a*b^2)^(2/3)*_alpha^4*a^2-2*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha^2*a*b^2+I*(-a*b^2)^(2/3)*3^(1/2)*_alpha*b^2-3*_alpha^3*a^2*b^2-I*3^(1/2)*b^4+3*(-a*b^2)^(2/3)*_alpha*b^2+3*b^4)/b^2/(a^2+b^2),(I*3^(1/2)/a*(-a*b^2)^(1/3)/(-3/2/a*(-a*b^2)^(1/3)+1/2*I*3^(1/2)/a*(-a*b^2)^(1/3)))^(1/2)),_alpha=RootOf(_Z^6*a^2+b^2))","C"
2611,1,686,175,0.575000," ","int((x^4+x)^(1/2)*(a*x^6+b)/(c*x^6-d),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{a \left(\frac{x \sqrt{x^{4}+x}}{3}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{c}+\frac{\left(a d +b c \right) \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(c \,\textit{\_Z}^{6}-d \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{3}-1\right) \left(1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{5}-\underline{\hspace{1.25 ex}}\alpha^{4}+\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  -1\right) \left(-1-i \sqrt{3}\right) \sqrt{\frac{x \left(3+i \sqrt{3}\right)}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \sqrt{3}+2 x -1}{\left(1+x \right) \left(1-i \sqrt{3}\right)}}\, \sqrt{-\frac{-1+2 x -i \sqrt{3}}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\frac{\underline{\hspace{1.25 ex}}\alpha^{5} c \EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5} c +3 \underline{\hspace{1.25 ex}}\alpha^{5} c +i \sqrt{3}\, d +3 d}{6 d}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{d}\right)}{\underline{\hspace{1.25 ex}}\alpha^{4} \left(c -d \right) \left(3+i \sqrt{3}\right) \sqrt{x \left(1+x \right) \left(i \sqrt{3}+2 x -1\right) \left(-1+2 x -i \sqrt{3}\right)}}\right)}{3 c}$&$686$\\ elliptic&$\frac{a x \sqrt{x^{4}+x}}{3 c}-\frac{a \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{c \left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}-\frac{\sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(c \,\textit{\_Z}^{6}-d \right)}{\sum}\frac{\left(a d +b c \right) \left(\underline{\hspace{1.25 ex}}\alpha^{3}+1\right) \left(1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{5}-\underline{\hspace{1.25 ex}}\alpha^{4}+\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  -1\right) \left(-1-i \sqrt{3}\right) \sqrt{\frac{x \left(3+i \sqrt{3}\right)}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \sqrt{3}+2 x -1}{\left(1+x \right) \left(1-i \sqrt{3}\right)}}\, \sqrt{-\frac{-1+2 x -i \sqrt{3}}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\frac{\underline{\hspace{1.25 ex}}\alpha^{5} c \EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5} c +3 \underline{\hspace{1.25 ex}}\alpha^{5} c +i \sqrt{3}\, d +3 d}{6 d}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{d}\right)}{\underline{\hspace{1.25 ex}}\alpha^{4} \left(c -d \right) \left(3+i \sqrt{3}\right) \sqrt{x \left(1+x \right) \left(i \sqrt{3}+2 x -1\right) \left(-1+2 x -i \sqrt{3}\right)}}\right)}{3 c}$&$686$\\ risch&$\frac{a \,x^{2} \left(x^{3}+1\right)}{3 c \sqrt{x \left(x^{3}+1\right)}}+\frac{-\frac{2 a \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{2 \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(c \,\textit{\_Z}^{6}-d \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{3} a d -\underline{\hspace{1.25 ex}}\alpha^{3} b c -a d -b c \right) \left(1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{5}-\underline{\hspace{1.25 ex}}\alpha^{4}+\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  -1\right) \left(-1-i \sqrt{3}\right) \sqrt{\frac{x \left(3+i \sqrt{3}\right)}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \sqrt{3}+2 x -1}{\left(1+x \right) \left(1-i \sqrt{3}\right)}}\, \sqrt{-\frac{-1+2 x -i \sqrt{3}}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\frac{\underline{\hspace{1.25 ex}}\alpha^{5} c \EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5} c +3 \underline{\hspace{1.25 ex}}\alpha^{5} c +i \sqrt{3}\, d +3 d}{6 d}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{d}\right)}{\underline{\hspace{1.25 ex}}\alpha^{4} \left(c -d \right) \left(3+i \sqrt{3}\right) \sqrt{x \left(1+x \right) \left(i \sqrt{3}+2 x -1\right) \left(-1+2 x -i \sqrt{3}\right)}}\right)}{3}}{2 c}$&$706$\\ \hline \end{longtable}"," ",0,"1/c*a*(1/3*x*(x^4+x)^(1/2)-(-1/2-1/2*I*3^(1/2))*((3/2+1/2*I*3^(1/2))*x/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2)*(1+x)^2*(-(x-1/2+1/2*I*3^(1/2))/(1/2-1/2*I*3^(1/2))/(1+x))^(1/2)*(-(x-1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2)/(3/2+1/2*I*3^(1/2))/(x*(1+x)*(x-1/2+1/2*I*3^(1/2))*(x-1/2-1/2*I*3^(1/2)))^(1/2)*(-EllipticF(((3/2+1/2*I*3^(1/2))*x/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2),((-3/2+1/2*I*3^(1/2))*(-1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+EllipticPi(((3/2+1/2*I*3^(1/2))*x/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2),(1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)),((-3/2+1/2*I*3^(1/2))*(-1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))))+1/3*(a*d+b*c)/c*4^(1/2)*sum((-_alpha^3-1)/_alpha^4*(1+x)^2*(_alpha^5-_alpha^4+_alpha^3-_alpha^2+_alpha-1)/(c-d)*(-1-I*3^(1/2))*(x/(1+x)*(3+I*3^(1/2))/(1+I*3^(1/2)))^(1/2)*(-1/(1+x)*(I*3^(1/2)+2*x-1)/(1-I*3^(1/2)))^(1/2)*(-1/(1+x)*(-1+2*x-I*3^(1/2))/(1+I*3^(1/2)))^(1/2)/(3+I*3^(1/2))/(x*(1+x)*(I*3^(1/2)+2*x-1)*(-1+2*x-I*3^(1/2)))^(1/2)*(EllipticF(((3/2+1/2*I*3^(1/2))*x/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2),((-3/2+1/2*I*3^(1/2))*(-1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+_alpha^5*c/d*EllipticPi(((3/2+1/2*I*3^(1/2))*x/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2),1/6*(I*3^(1/2)*_alpha^5*c+3*_alpha^5*c+I*3^(1/2)*d+3*d)/d,((-3/2+1/2*I*3^(1/2))*(-1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))),_alpha=RootOf(_Z^6*c-d))","C"
2612,0,0,188,0.045000," ","int(x*(k*x-1)*(1-2*k*x+(-1+2*k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(-1+4*x+(-6+b)*x^2+(-2*b*k+4)*x^3+(b*k^2-1)*x^4),x)","\[\int \frac{x \left(k x -1\right) \left(1-2 k x +\left(-1+2 k \right) x^{2}\right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{2}{3}} \left(-1+4 x +\left(-6+b \right) x^{2}+\left(-2 b k +4\right) x^{3}+\left(b \,k^{2}-1\right) x^{4}\right)}\, dx\]"," ",0,"int(x*(k*x-1)*(1-2*k*x+(-1+2*k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(-1+4*x+(-6+b)*x^2+(-2*b*k+4)*x^3+(b*k^2-1)*x^4),x)","F"
2613,0,0,170,0.047000," ","int((a*p*x^4+4*b*p*x^3-3*a*q)/(p*x^4+q)^(1/3)/(a^3*d*x^3+3*a^2*b*d*x^2+c*p*x^4+3*a*b^2*d*x+b^3*d+c*q),x)","\[\int \frac{p a \,x^{4}+4 b p \,x^{3}-3 a q}{\left(p \,x^{4}+q \right)^{\frac{1}{3}} \left(a^{3} d \,x^{3}+3 a^{2} b d \,x^{2}+c p \,x^{4}+3 a \,b^{2} d x +b^{3} d +c q \right)}\, dx\]"," ",0,"int((a*p*x^4+4*b*p*x^3-3*a*q)/(p*x^4+q)^(1/3)/(a^3*d*x^3+3*a^2*b*d*x^2+c*p*x^4+3*a*b^2*d*x+b^3*d+c*q),x)","F"
2614,1,189,14,0.149000," ","int(x^2/(x^2-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{2 \left(-\frac{\left(c +\sqrt{a x +b}\right)^{2}}{2}+c \left(c +\sqrt{a x +b}\right)-2 a^{2} \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 c \,\textit{\_Z}^{6}+\left(6 c^{2}-2 b \right) \textit{\_Z}^{4}-a^{2} \textit{\_Z}^{3}+\left(-4 c^{3}+4 b c \right) \textit{\_Z}^{2}+a^{2} c \textit{\_Z} +c^{4}-2 b \,c^{2}+b^{2}\right)}{\sum}\frac{\left(\textit{\_R}^{6}-2 \textit{\_R}^{4} c +\textit{\_R}^{2} c^{2}\right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{8 \textit{\_R}^{7}-24 \textit{\_R}^{5} c +24 \textit{\_R}^{3} c^{2}-8 \textit{\_R}^{3} b -3 \textit{\_R}^{2} a^{2}-8 \textit{\_R} \,c^{3}+8 \textit{\_R} b c +a^{2} c}\right)\right)}{a}$&$189$\\ default&$-\frac{2 \left(-\frac{\left(c +\sqrt{a x +b}\right)^{2}}{2}+c \left(c +\sqrt{a x +b}\right)-2 a^{2} \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 c \,\textit{\_Z}^{6}+\left(6 c^{2}-2 b \right) \textit{\_Z}^{4}-a^{2} \textit{\_Z}^{3}+\left(-4 c^{3}+4 b c \right) \textit{\_Z}^{2}+a^{2} c \textit{\_Z} +c^{4}-2 b \,c^{2}+b^{2}\right)}{\sum}\frac{\left(\textit{\_R}^{6}-2 \textit{\_R}^{4} c +\textit{\_R}^{2} c^{2}\right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{8 \textit{\_R}^{7}-24 \textit{\_R}^{5} c +24 \textit{\_R}^{3} c^{2}-8 \textit{\_R}^{3} b -3 \textit{\_R}^{2} a^{2}-8 \textit{\_R} \,c^{3}+8 \textit{\_R} b c +a^{2} c}\right)\right)}{a}$&$189$\\ \hline \end{longtable}"," ",0,"-2/a*(-1/2*(c+(a*x+b)^(1/2))^2+c*(c+(a*x+b)^(1/2))-2*a^2*sum((_R^6-2*_R^4*c+_R^2*c^2)/(8*_R^7-24*_R^5*c+24*_R^3*c^2-8*_R^3*b-3*_R^2*a^2-8*_R*c^3+8*_R*b*c+a^2*c)*ln((c+(a*x+b)^(1/2))^(1/2)-_R),_R=RootOf(_Z^8-4*c*_Z^6+(6*c^2-2*b)*_Z^4-a^2*_Z^3+(-4*c^3+4*b*c)*_Z^2+a^2*c*_Z+c^4-2*b*c^2+b^2)))","B"
2615,1,189,14,0.143000," ","int(x^2/(x^2-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{2 \left(-\frac{\left(c +\sqrt{a x +b}\right)^{2}}{2}+c \left(c +\sqrt{a x +b}\right)-2 a^{2} \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 c \,\textit{\_Z}^{6}+\left(6 c^{2}-2 b \right) \textit{\_Z}^{4}-a^{2} \textit{\_Z}^{3}+\left(-4 c^{3}+4 b c \right) \textit{\_Z}^{2}+a^{2} c \textit{\_Z} +c^{4}-2 b \,c^{2}+b^{2}\right)}{\sum}\frac{\left(\textit{\_R}^{6}-2 \textit{\_R}^{4} c +\textit{\_R}^{2} c^{2}\right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{8 \textit{\_R}^{7}-24 \textit{\_R}^{5} c +24 \textit{\_R}^{3} c^{2}-8 \textit{\_R}^{3} b -3 \textit{\_R}^{2} a^{2}-8 \textit{\_R} \,c^{3}+8 \textit{\_R} b c +a^{2} c}\right)\right)}{a}$&$189$\\ default&$-\frac{2 \left(-\frac{\left(c +\sqrt{a x +b}\right)^{2}}{2}+c \left(c +\sqrt{a x +b}\right)-2 a^{2} \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 c \,\textit{\_Z}^{6}+\left(6 c^{2}-2 b \right) \textit{\_Z}^{4}-a^{2} \textit{\_Z}^{3}+\left(-4 c^{3}+4 b c \right) \textit{\_Z}^{2}+a^{2} c \textit{\_Z} +c^{4}-2 b \,c^{2}+b^{2}\right)}{\sum}\frac{\left(\textit{\_R}^{6}-2 \textit{\_R}^{4} c +\textit{\_R}^{2} c^{2}\right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{8 \textit{\_R}^{7}-24 \textit{\_R}^{5} c +24 \textit{\_R}^{3} c^{2}-8 \textit{\_R}^{3} b -3 \textit{\_R}^{2} a^{2}-8 \textit{\_R} \,c^{3}+8 \textit{\_R} b c +a^{2} c}\right)\right)}{a}$&$189$\\ \hline \end{longtable}"," ",0,"-2/a*(-1/2*(c+(a*x+b)^(1/2))^2+c*(c+(a*x+b)^(1/2))-2*a^2*sum((_R^6-2*_R^4*c+_R^2*c^2)/(8*_R^7-24*_R^5*c+24*_R^3*c^2-8*_R^3*b-3*_R^2*a^2-8*_R*c^3+8*_R*b*c+a^2*c)*ln((c+(a*x+b)^(1/2))^(1/2)-_R),_R=RootOf(_Z^8-4*c*_Z^6+(6*c^2-2*b)*_Z^4-a^2*_Z^3+(-4*c^3+4*b*c)*_Z^2+a^2*c*_Z+c^4-2*b*c^2+b^2)))","B"
2616,0,0,189,0.026000," ","int((3+(2*k^2-1)*x-3*k^2*x^2-k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(1-d-(1+2*d)*x-(k^2+d)*x^2+k^2*x^3),x)","\[\int \frac{3+\left(2 k^{2}-1\right) x -3 k^{2} x^{2}-k^{2} x^{3}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{1}{3}} \left(1-d -\left(1+2 d \right) x -\left(k^{2}+d \right) x^{2}+k^{2} x^{3}\right)}\, dx\]"," ",0,"int((3+(2*k^2-1)*x-3*k^2*x^2-k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(1-d-(1+2*d)*x-(k^2+d)*x^2+k^2*x^3),x)","F"
2617,0,0,189,0.026000," ","int((3+(-2*k^2+1)*x-3*k^2*x^2+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(-1+d-(1+2*d)*x+(k^2+d)*x^2+k^2*x^3),x)","\[\int \frac{3+\left(-2 k^{2}+1\right) x -3 k^{2} x^{2}+k^{2} x^{3}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{1}{3}} \left(-1+d -\left(1+2 d \right) x +\left(k^{2}+d \right) x^{2}+k^{2} x^{3}\right)}\, dx\]"," ",0,"int((3+(-2*k^2+1)*x-3*k^2*x^2+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(-1+d-(1+2*d)*x+(k^2+d)*x^2+k^2*x^3),x)","F"
2618,1,281,197,0.175000," ","int((a^4*x^4-b^4)^(1/2)*(a^4*x^4+b^4)/(a^8*x^8+b^8-c*x^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(\frac{\ln \left(\frac{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}-\frac{\left(2 a^{4} b^{4}-c \right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{2 x}+\frac{\sqrt{2 a^{4} b^{4}-c}}{2}}{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}+\frac{\left(2 a^{4} b^{4}-c \right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{2 x}+\frac{\sqrt{2 a^{4} b^{4}-c}}{2}}\right)}{4 \left(2 a^{4} b^{4}-c \right)^{\frac{1}{4}}}+\frac{\arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{\left(2 a^{4} b^{4}-c \right)^{\frac{1}{4}} x}+1\right)}{2 \left(2 a^{4} b^{4}-c \right)^{\frac{1}{4}}}+\frac{\arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{\left(2 a^{4} b^{4}-c \right)^{\frac{1}{4}} x}-1\right)}{2 \left(2 a^{4} b^{4}-c \right)^{\frac{1}{4}}}\right) \sqrt{2}}{2}$&$281$\\ elliptic&$\frac{\left(\frac{\ln \left(\frac{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}-\frac{\left(2 a^{4} b^{4}-c \right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{2 x}+\frac{\sqrt{2 a^{4} b^{4}-c}}{2}}{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}+\frac{\left(2 a^{4} b^{4}-c \right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{2 x}+\frac{\sqrt{2 a^{4} b^{4}-c}}{2}}\right)}{4 \left(2 a^{4} b^{4}-c \right)^{\frac{1}{4}}}+\frac{\arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{\left(2 a^{4} b^{4}-c \right)^{\frac{1}{4}} x}+1\right)}{2 \left(2 a^{4} b^{4}-c \right)^{\frac{1}{4}}}+\frac{\arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{\left(2 a^{4} b^{4}-c \right)^{\frac{1}{4}} x}-1\right)}{2 \left(2 a^{4} b^{4}-c \right)^{\frac{1}{4}}}\right) \sqrt{2}}{2}$&$281$\\ \hline \end{longtable}"," ",0,"1/2*(1/4/(2*a^4*b^4-c)^(1/4)*ln((1/2*(a^4*x^4-b^4)/x^2-1/2*(2*a^4*b^4-c)^(1/4)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x+1/2*(2*a^4*b^4-c)^(1/2))/(1/2*(a^4*x^4-b^4)/x^2+1/2*(2*a^4*b^4-c)^(1/4)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x+1/2*(2*a^4*b^4-c)^(1/2)))+1/2/(2*a^4*b^4-c)^(1/4)*arctan(1/(2*a^4*b^4-c)^(1/4)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x+1)+1/2/(2*a^4*b^4-c)^(1/4)*arctan(1/(2*a^4*b^4-c)^(1/4)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x-1))*2^(1/2)","A"
2619,1,281,197,0.182000," ","int((a^8*x^8-b^8)/(a^4*x^4-b^4)^(1/2)/(a^8*x^8+b^8-c*x^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\ln \left(\frac{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}-\frac{\left(2 a^{4} b^{4}-c \right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{2 x}+\frac{\sqrt{2 a^{4} b^{4}-c}}{2}}{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}+\frac{\left(2 a^{4} b^{4}-c \right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{2 x}+\frac{\sqrt{2 a^{4} b^{4}-c}}{2}}\right)}{4 \left(2 a^{4} b^{4}-c \right)^{\frac{1}{4}}}+\frac{\arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{\left(2 a^{4} b^{4}-c \right)^{\frac{1}{4}} x}+1\right)}{2 \left(2 a^{4} b^{4}-c \right)^{\frac{1}{4}}}+\frac{\arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{\left(2 a^{4} b^{4}-c \right)^{\frac{1}{4}} x}-1\right)}{2 \left(2 a^{4} b^{4}-c \right)^{\frac{1}{4}}}\right) \sqrt{2}}{2}$&$281$\\ default&$\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{\sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{8} \textit{\_Z}^{8}+b^{8}-c \,\textit{\_Z}^{4}\right)}{\sum}\frac{\left(-2 b^{8}+\underline{\hspace{1.25 ex}}\alpha^{4} c \right) \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{6} a^{8}+a^{4} b^{4} x^{2}-\underline{\hspace{1.25 ex}}\alpha^{2} c \right)}{b^{4} \sqrt{a^{4} \underline{\hspace{1.25 ex}}\alpha^{4}-b^{4}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{\sqrt{a^{4} \underline{\hspace{1.25 ex}}\alpha^{4}-b^{4}}}+\frac{2 \underline{\hspace{1.25 ex}}\alpha^{3} \left(\underline{\hspace{1.25 ex}}\alpha^{4} a^{8}-c \right) \sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{4} a^{8}-c \right)}{a^{2} b^{6}}, \frac{\sqrt{\frac{a^{2}}{b^{2}}}}{\sqrt{-\frac{a^{2}}{b^{2}}}}\right)}{\sqrt{-\frac{a^{2}}{b^{2}}}\, b^{8} \sqrt{a^{4} x^{4}-b^{4}}}\right)}{\underline{\hspace{1.25 ex}}\alpha^{3} \left(2 \underline{\hspace{1.25 ex}}\alpha^{4} a^{8}-c \right)}\right)}{8}$&$331$\\ \hline \end{longtable}"," ",0,"1/2*(1/4/(2*a^4*b^4-c)^(1/4)*ln((1/2*(a^4*x^4-b^4)/x^2-1/2*(2*a^4*b^4-c)^(1/4)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x+1/2*(2*a^4*b^4-c)^(1/2))/(1/2*(a^4*x^4-b^4)/x^2+1/2*(2*a^4*b^4-c)^(1/4)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x+1/2*(2*a^4*b^4-c)^(1/2)))+1/2/(2*a^4*b^4-c)^(1/4)*arctan(1/(2*a^4*b^4-c)^(1/4)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x+1)+1/2/(2*a^4*b^4-c)^(1/4)*arctan(1/(2*a^4*b^4-c)^(1/4)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x-1))*2^(1/2)","A"
2620,1,1056,33,1.055000," ","int((a*x+(a*x-b)^(1/2))^(1/2)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$2 a \left(\frac{\sqrt{-b}\, \left(\frac{\left(\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}\right)^{\frac{3}{2}}}{\sqrt{-b}\, \left(\sqrt{a x -b}+\sqrt{-b}\right)}-\frac{\left(1-2 \sqrt{-b}\right) \left(\sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}+\frac{\left(1-2 \sqrt{-b}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}\right)}{2}+\frac{\sqrt{-b}\, \ln \left(\frac{-2 \sqrt{-b}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)+2 \sqrt{-\sqrt{-b}}\, \sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}}{\sqrt{a x -b}+\sqrt{-b}}\right)}{\sqrt{-\sqrt{-b}}}\right)}{2 \sqrt{-b}}-\frac{2 \left(\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}}{4}+\frac{\left(-4 \sqrt{-b}-\left(1-2 \sqrt{-b}\right)^{2}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}\right)}{8}\right)}{\sqrt{-b}}\right)}{4 b}-\frac{\sqrt{-b}\, \left(-\frac{\left(\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}\right)^{\frac{3}{2}}}{\sqrt{-b}\, \left(\sqrt{a x -b}-\sqrt{-b}\right)}+\frac{\left(1+2 \sqrt{-b}\right) \left(\sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}+\frac{\left(1+2 \sqrt{-b}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}\right)}{2}-\left(-b \right)^{\frac{1}{4}} \ln \left(\frac{2 \sqrt{-b}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+2 \left(-b \right)^{\frac{1}{4}} \sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}}{\sqrt{a x -b}-\sqrt{-b}}\right)\right)}{2 \sqrt{-b}}+\frac{\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}}{2}+\frac{\left(4 \sqrt{-b}-\left(1+2 \sqrt{-b}\right)^{2}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}\right)}{4}}{\sqrt{-b}}\right)}{4 b}\right)$&$1056$\\ default&$2 a \left(\frac{\sqrt{-b}\, \left(\frac{\left(\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}\right)^{\frac{3}{2}}}{\sqrt{-b}\, \left(\sqrt{a x -b}+\sqrt{-b}\right)}-\frac{\left(1-2 \sqrt{-b}\right) \left(\sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}+\frac{\left(1-2 \sqrt{-b}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}\right)}{2}+\frac{\sqrt{-b}\, \ln \left(\frac{-2 \sqrt{-b}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)+2 \sqrt{-\sqrt{-b}}\, \sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}}{\sqrt{a x -b}+\sqrt{-b}}\right)}{\sqrt{-\sqrt{-b}}}\right)}{2 \sqrt{-b}}-\frac{2 \left(\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}}{4}+\frac{\left(-4 \sqrt{-b}-\left(1-2 \sqrt{-b}\right)^{2}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}\right)}{8}\right)}{\sqrt{-b}}\right)}{4 b}-\frac{\sqrt{-b}\, \left(-\frac{\left(\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}\right)^{\frac{3}{2}}}{\sqrt{-b}\, \left(\sqrt{a x -b}-\sqrt{-b}\right)}+\frac{\left(1+2 \sqrt{-b}\right) \left(\sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}+\frac{\left(1+2 \sqrt{-b}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}\right)}{2}-\left(-b \right)^{\frac{1}{4}} \ln \left(\frac{2 \sqrt{-b}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+2 \left(-b \right)^{\frac{1}{4}} \sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}}{\sqrt{a x -b}-\sqrt{-b}}\right)\right)}{2 \sqrt{-b}}+\frac{\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}}{2}+\frac{\left(4 \sqrt{-b}-\left(1+2 \sqrt{-b}\right)^{2}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}\right)}{4}}{\sqrt{-b}}\right)}{4 b}\right)$&$1056$\\ \hline \end{longtable}"," ",0,"2*a*(1/4*(-b)^(1/2)/b*(1/(-b)^(1/2)/((a*x-b)^(1/2)+(-b)^(1/2))*(((a*x-b)^(1/2)+(-b)^(1/2))^2+(1-2*(-b)^(1/2))*((a*x-b)^(1/2)+(-b)^(1/2))-(-b)^(1/2))^(3/2)-1/2*(1-2*(-b)^(1/2))/(-b)^(1/2)*((((a*x-b)^(1/2)+(-b)^(1/2))^2+(1-2*(-b)^(1/2))*((a*x-b)^(1/2)+(-b)^(1/2))-(-b)^(1/2))^(1/2)+1/2*(1-2*(-b)^(1/2))*ln(1/2+(a*x-b)^(1/2)+(((a*x-b)^(1/2)+(-b)^(1/2))^2+(1-2*(-b)^(1/2))*((a*x-b)^(1/2)+(-b)^(1/2))-(-b)^(1/2))^(1/2))+(-b)^(1/2)/(-(-b)^(1/2))^(1/2)*ln((-2*(-b)^(1/2)+(1-2*(-b)^(1/2))*((a*x-b)^(1/2)+(-b)^(1/2))+2*(-(-b)^(1/2))^(1/2)*(((a*x-b)^(1/2)+(-b)^(1/2))^2+(1-2*(-b)^(1/2))*((a*x-b)^(1/2)+(-b)^(1/2))-(-b)^(1/2))^(1/2))/((a*x-b)^(1/2)+(-b)^(1/2))))-2/(-b)^(1/2)*(1/4*(2*(a*x-b)^(1/2)+1)*(((a*x-b)^(1/2)+(-b)^(1/2))^2+(1-2*(-b)^(1/2))*((a*x-b)^(1/2)+(-b)^(1/2))-(-b)^(1/2))^(1/2)+1/8*(-4*(-b)^(1/2)-(1-2*(-b)^(1/2))^2)*ln(1/2+(a*x-b)^(1/2)+(((a*x-b)^(1/2)+(-b)^(1/2))^2+(1-2*(-b)^(1/2))*((a*x-b)^(1/2)+(-b)^(1/2))-(-b)^(1/2))^(1/2))))-1/4*(-b)^(1/2)/b*(-1/(-b)^(1/2)/((a*x-b)^(1/2)-(-b)^(1/2))*(((a*x-b)^(1/2)-(-b)^(1/2))^2+(1+2*(-b)^(1/2))*((a*x-b)^(1/2)-(-b)^(1/2))+(-b)^(1/2))^(3/2)+1/2*(1+2*(-b)^(1/2))/(-b)^(1/2)*((((a*x-b)^(1/2)-(-b)^(1/2))^2+(1+2*(-b)^(1/2))*((a*x-b)^(1/2)-(-b)^(1/2))+(-b)^(1/2))^(1/2)+1/2*(1+2*(-b)^(1/2))*ln(1/2+(a*x-b)^(1/2)+(((a*x-b)^(1/2)-(-b)^(1/2))^2+(1+2*(-b)^(1/2))*((a*x-b)^(1/2)-(-b)^(1/2))+(-b)^(1/2))^(1/2))-(-b)^(1/4)*ln((2*(-b)^(1/2)+(1+2*(-b)^(1/2))*((a*x-b)^(1/2)-(-b)^(1/2))+2*(-b)^(1/4)*(((a*x-b)^(1/2)-(-b)^(1/2))^2+(1+2*(-b)^(1/2))*((a*x-b)^(1/2)-(-b)^(1/2))+(-b)^(1/2))^(1/2))/((a*x-b)^(1/2)-(-b)^(1/2))))+2/(-b)^(1/2)*(1/4*(2*(a*x-b)^(1/2)+1)*(((a*x-b)^(1/2)-(-b)^(1/2))^2+(1+2*(-b)^(1/2))*((a*x-b)^(1/2)-(-b)^(1/2))+(-b)^(1/2))^(1/2)+1/8*(4*(-b)^(1/2)-(1+2*(-b)^(1/2))^2)*ln(1/2+(a*x-b)^(1/2)+(((a*x-b)^(1/2)-(-b)^(1/2))^2+(1+2*(-b)^(1/2))*((a*x-b)^(1/2)-(-b)^(1/2))+(-b)^(1/2))^(1/2)))))","B"
2621,0,0,192,0.171000," ","int((-1+2*k*x+(1-2*k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(1-(2+b)*x+(b*k+1)*x^2),x)","\[\int \frac{-1+2 k x +\left(1-2 k \right) x^{2}}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{2}{3}} \left(1-\left(2+b \right) x +\left(b k +1\right) x^{2}\right)}\, dx\]"," ",0,"int((-1+2*k*x+(1-2*k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(1-(2+b)*x+(b*k+1)*x^2),x)","F"
2622,1,1845,188,11.036000," ","int(x^3*(x^2+3)/(x^2+1)/(-x^3+x^2+1)^(1/3)/(x^3+x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1845$\\ \hline \end{longtable}"," ",0,"ln((-RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*RootOf(_Z^3+4)^4*x^3-6*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^2*(-x^3+x^2+1)^(1/3)*x^2-4*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^2*x^3+2*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^2+12*(-x^3+x^2+1)^(2/3)*x+12*(-x^3+x^2+1)^(1/3)*x^2+2*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)-4*x^3+4*x^2+4)/(x^2+1))+1/2*RootOf(_Z^3+4)*ln((RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^3*x^3-2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+3*RootOf(_Z^3+4)^2*(-x^3+x^2+1)^(1/3)*x^2+6*(-x^3+x^2+1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)*x^2+RootOf(_Z^3+4)*x^3-2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^3+6*(-x^3+x^2+1)^(2/3)*x-RootOf(_Z^3+4)*x^2+2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^2-RootOf(_Z^3+4)+2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2))/(x^3+x^2+1))-1/2*ln(-(RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^3*x^3-4*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+4*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*(-x^3+x^2+1)^(2/3)*x-RootOf(_Z^3+4)^2*(-x^3+x^2+1)^(1/3)*x^2-10*(-x^3+x^2+1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)*x^2-3*RootOf(_Z^3+4)*x^3+12*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^3-10*(-x^3+x^2+1)^(2/3)*x+RootOf(_Z^3+4)*x^2-4*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^2+RootOf(_Z^3+4)-4*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2))/(x^3+x^2+1))*RootOf(_Z^3+4)-ln(-(RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^3*x^3-4*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+4*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*(-x^3+x^2+1)^(2/3)*x-RootOf(_Z^3+4)^2*(-x^3+x^2+1)^(1/3)*x^2-10*(-x^3+x^2+1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)*x^2-3*RootOf(_Z^3+4)*x^3+12*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^3-10*(-x^3+x^2+1)^(2/3)*x+RootOf(_Z^3+4)*x^2-4*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^2+RootOf(_Z^3+4)-4*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2))/(x^3+x^2+1))*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)-ln(-(-RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*RootOf(_Z^3+4)^4*x^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*(-x^3+x^2+1)^(2/3)*x+6*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^2*(-x^3+x^2+1)^(1/3)*x^2+2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^2*x^3-2*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^2-12*(-x^3+x^2+1)^(2/3)*x-2*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)+8*x^3-4*x^2-4)/(x^2+1))+1/2*ln(-(-RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)^2*RootOf(_Z^3+4)^4*x^3+6*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*(-x^3+x^2+1)^(2/3)*x+6*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^2*(-x^3+x^2+1)^(1/3)*x^2+2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*RootOf(_Z^3+4)^2*x^3-2*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)*x^2-12*(-x^3+x^2+1)^(2/3)*x-2*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)+8*x^3-4*x^2-4)/(x^2+1))*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+2*_Z*RootOf(_Z^3+4)+4*_Z^2)","C"
2623,1,851,182,5.302000," ","int((x^2+1)*(x^4-x^3)^(1/4)/(2*x^2+x-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\left(-\frac{5}{16}+\frac{x}{4}\right) \left(x^{4}-x^{3}\right)^{\frac{1}{4}}-\frac{2 \RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(\frac{3 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{3}+4 \left(x^{4}-x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}-\RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{2}+4 \sqrt{x^{4}-x^{3}}\, \RootOf \left(\textit{\_Z}^{4}-2\right) x +4 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(1+x \right)}\right)}{3}-\frac{2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(\frac{-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}-4 \left(x^{4}-x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}+4 \sqrt{x^{4}-x^{3}}\, \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x +4 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(1+x \right)}\right)}{3}+\frac{57 \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(\frac{2 \sqrt{x^{4}-x^{3}}\, \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x -2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{3}+\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{2}+4 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}-4 x^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}}{x^{2}}\right)}{128}-\frac{5 \ln \left(\frac{4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \sqrt{x^{4}-x^{3}}\, x +2 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}+4 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}+4 x^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}}{x^{2} \left(-1+2 x \right)}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}}{48}+\frac{5 \ln \left(\frac{4 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \sqrt{x^{4}-x^{3}}\, x +2 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}+4 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}+4 x^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}}{x^{2} \left(-1+2 x \right)}\right) \RootOf \left(\textit{\_Z}^{4}-2\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)}{48}-\frac{5 \RootOf \left(\textit{\_Z}^{4}-2\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \left(x^{4}-x^{3}\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{2}+2 \sqrt{x^{4}-x^{3}}\, \RootOf \left(\textit{\_Z}^{4}-2\right) \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x +2 \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \sqrt{x^{4}-x^{3}}\, x +\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right) x^{2}-\RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{2}+4 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}}{x^{2} \left(-1+2 x \right)}\right)}{24}-\frac{57 \ln \left(\frac{2 \left(x^{4}-x^{3}\right)^{\frac{3}{4}}-2 \sqrt{x^{4}-x^{3}}\, x +2 x^{2} \left(x^{4}-x^{3}\right)^{\frac{1}{4}}-2 x^{3}+x^{2}}{x^{2}}\right)}{64}$&$851$\\ \hline \end{longtable}"," ",0,"(-5/16+1/4*x)*(x^4-x^3)^(1/4)-2/3*RootOf(_Z^4-2)*ln((3*RootOf(_Z^4-2)^3*x^3+4*(x^4-x^3)^(1/4)*RootOf(_Z^4-2)^2*x^2-RootOf(_Z^4-2)^3*x^2+4*(x^4-x^3)^(1/2)*RootOf(_Z^4-2)*x+4*(x^4-x^3)^(3/4))/x^2/(1+x))-2/3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln((-3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*x^3+RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^2*x^2-4*(x^4-x^3)^(1/4)*RootOf(_Z^4-2)^2*x^2+4*(x^4-x^3)^(1/2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x+4*(x^4-x^3)^(3/4))/x^2/(1+x))+57/128*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln((2*(x^4-x^3)^(1/2)*RootOf(_Z^4-2)^3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x-2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^3*x^3+RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)^3*x^2+4*(x^4-x^3)^(3/4)-4*x^2*(x^4-x^3)^(1/4))/x^2)-5/48*ln((4*RootOf(_Z^4-2)^2*(x^4-x^3)^(1/2)*x+2*RootOf(_Z^4-2)^2*x^3-RootOf(_Z^4-2)^2*x^2+4*(x^4-x^3)^(3/4)+4*x^2*(x^4-x^3)^(1/4))/x^2/(-1+2*x))*RootOf(_Z^4-2)^2+5/48*ln((4*RootOf(_Z^4-2)^2*(x^4-x^3)^(1/2)*x+2*RootOf(_Z^4-2)^2*x^3-RootOf(_Z^4-2)^2*x^2+4*(x^4-x^3)^(3/4)+4*x^2*(x^4-x^3)^(1/4))/x^2/(-1+2*x))*RootOf(_Z^4-2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)-5/24*RootOf(_Z^4-2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln((2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*(x^4-x^3)^(1/4)*RootOf(_Z^4-2)^3*x^2+2*(x^4-x^3)^(1/2)*RootOf(_Z^4-2)*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x+2*RootOf(_Z^4-2)^2*(x^4-x^3)^(1/2)*x+RootOf(_Z^2+RootOf(_Z^4-2)^2)*RootOf(_Z^4-2)*x^2-RootOf(_Z^4-2)^2*x^2+4*(x^4-x^3)^(3/4))/x^2/(-1+2*x))-57/64*ln((2*(x^4-x^3)^(3/4)-2*(x^4-x^3)^(1/2)*x+2*x^2*(x^4-x^3)^(1/4)-2*x^3+x^2)/x^2)","C"
2624,0,0,153,0.015000," ","int((a*x^4+b*x^2)^(1/4)*(x^8+a*x^4+b)/(a*x^4+b),x)","\[\int \frac{\left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}} \left(x^{8}+a \,x^{4}+b \right)}{a \,x^{4}+b}\, dx\]"," ",0,"int((a*x^4+b*x^2)^(1/4)*(x^8+a*x^4+b)/(a*x^4+b),x)","F"
2625,0,0,153,0.004000," ","int((a*x^4+b*x^2)^(1/4)*(x^8+a*x^4+b)/(a*x^4+b),x)","\[\int \frac{\left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}} \left(x^{8}+a \,x^{4}+b \right)}{a \,x^{4}+b}\, dx\]"," ",0,"int((a*x^4+b*x^2)^(1/4)*(x^8+a*x^4+b)/(a*x^4+b),x)","F"
2626,1,874,168,20.135000," ","int(1/(x^2-1)^(1/3)/(x^2+3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{6}+108\right) \ln \left(\frac{9072 x^{3} \left(x^{2}-1\right)^{\frac{2}{3}}-3888 x \left(x^{2}-1\right)^{\frac{2}{3}}-486 \RootOf \left(\textit{\_Z}^{6}+108\right)-27 \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+72 x^{3} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+189 \RootOf \left(\textit{\_Z}^{6}+108\right)^{4} x^{2}-225 \RootOf \left(\textit{\_Z}^{6}+108\right)^{4} x^{4}-72 x^{5} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}-1296 x^{5} \RootOf \left(\textit{\_Z}^{6}+108\right)-\RootOf \left(\textit{\_Z}^{6}+108\right)^{4} x^{6}+1296 \RootOf \left(\textit{\_Z}^{6}+108\right) x^{3}-4050 \RootOf \left(\textit{\_Z}^{6}+108\right) x^{4}+3402 \RootOf \left(\textit{\_Z}^{6}+108\right) x^{2}-18 \RootOf \left(\textit{\_Z}^{6}+108\right) x^{6}+1296 \left(x^{2}-1\right)^{\frac{2}{3}} x^{4}+3888 \left(x^{2}-1\right)^{\frac{2}{3}} x^{2}+6 \RootOf \left(\textit{\_Z}^{6}+108\right)^{5} \left(x^{2}-1\right)^{\frac{1}{3}} x^{5}+108 \RootOf \left(\textit{\_Z}^{6}+108\right)^{5} \left(x^{2}-1\right)^{\frac{1}{3}} x^{4}+144 \RootOf \left(\textit{\_Z}^{6}+108\right)^{5} \left(x^{2}-1\right)^{\frac{1}{3}} x^{3}+36 \RootOf \left(\textit{\_Z}^{6}+108\right)^{2} \left(x^{2}-1\right)^{\frac{1}{3}} x^{5}+648 \RootOf \left(\textit{\_Z}^{6}+108\right)^{2} \left(x^{2}-1\right)^{\frac{1}{3}} x^{4}+864 \RootOf \left(\textit{\_Z}^{6}+108\right)^{2} \left(x^{2}-1\right)^{\frac{1}{3}} x^{3}-648 \RootOf \left(\textit{\_Z}^{6}+108\right)^{2} \left(x^{2}-1\right)^{\frac{1}{3}} x^{2}-324 \RootOf \left(\textit{\_Z}^{6}+108\right)^{2} \left(x^{2}-1\right)^{\frac{1}{3}} x -108 \RootOf \left(\textit{\_Z}^{6}+108\right)^{5} \left(x^{2}-1\right)^{\frac{1}{3}} x^{2}-54 \RootOf \left(\textit{\_Z}^{6}+108\right)^{5} \left(x^{2}-1\right)^{\frac{1}{3}} x}{\left(x^{2}+3\right)^{3}}\right)}{36}+\frac{\ln \left(\frac{\RootOf \left(\textit{\_Z}^{6}+108\right)^{4} x^{6}+72 x^{5} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+225 \RootOf \left(\textit{\_Z}^{6}+108\right)^{4} x^{4}-36 \RootOf \left(\textit{\_Z}^{6}+108\right)^{2} \left(x^{2}-1\right)^{\frac{1}{3}} x^{5}-72 x^{3} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}-648 \RootOf \left(\textit{\_Z}^{6}+108\right)^{2} \left(x^{2}-1\right)^{\frac{1}{3}} x^{4}-189 \RootOf \left(\textit{\_Z}^{6}+108\right)^{4} x^{2}-864 \RootOf \left(\textit{\_Z}^{6}+108\right)^{2} \left(x^{2}-1\right)^{\frac{1}{3}} x^{3}+648 \left(x^{2}-1\right)^{\frac{2}{3}} x^{4}+648 \RootOf \left(\textit{\_Z}^{6}+108\right)^{2} \left(x^{2}-1\right)^{\frac{1}{3}} x^{2}+4536 x^{3} \left(x^{2}-1\right)^{\frac{2}{3}}+27 \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+324 \RootOf \left(\textit{\_Z}^{6}+108\right)^{2} \left(x^{2}-1\right)^{\frac{1}{3}} x +1944 \left(x^{2}-1\right)^{\frac{2}{3}} x^{2}-1944 x \left(x^{2}-1\right)^{\frac{2}{3}}}{\left(x^{2}+3\right)^{3}}\right) \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}}{432}-\frac{\ln \left(\frac{\RootOf \left(\textit{\_Z}^{6}+108\right)^{4} x^{6}+72 x^{5} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+225 \RootOf \left(\textit{\_Z}^{6}+108\right)^{4} x^{4}-36 \RootOf \left(\textit{\_Z}^{6}+108\right)^{2} \left(x^{2}-1\right)^{\frac{1}{3}} x^{5}-72 x^{3} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}-648 \RootOf \left(\textit{\_Z}^{6}+108\right)^{2} \left(x^{2}-1\right)^{\frac{1}{3}} x^{4}-189 \RootOf \left(\textit{\_Z}^{6}+108\right)^{4} x^{2}-864 \RootOf \left(\textit{\_Z}^{6}+108\right)^{2} \left(x^{2}-1\right)^{\frac{1}{3}} x^{3}+648 \left(x^{2}-1\right)^{\frac{2}{3}} x^{4}+648 \RootOf \left(\textit{\_Z}^{6}+108\right)^{2} \left(x^{2}-1\right)^{\frac{1}{3}} x^{2}+4536 x^{3} \left(x^{2}-1\right)^{\frac{2}{3}}+27 \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+324 \RootOf \left(\textit{\_Z}^{6}+108\right)^{2} \left(x^{2}-1\right)^{\frac{1}{3}} x +1944 \left(x^{2}-1\right)^{\frac{2}{3}} x^{2}-1944 x \left(x^{2}-1\right)^{\frac{2}{3}}}{\left(x^{2}+3\right)^{3}}\right) \RootOf \left(\textit{\_Z}^{6}+108\right)}{72}$&$874$\\ \hline \end{longtable}"," ",0,"-1/36*RootOf(_Z^6+108)*ln((9072*x^3*(x^2-1)^(2/3)-3888*x*(x^2-1)^(2/3)+72*x^3*RootOf(_Z^6+108)^4+189*RootOf(_Z^6+108)^4*x^2-225*RootOf(_Z^6+108)^4*x^4-72*x^5*RootOf(_Z^6+108)^4-1296*x^5*RootOf(_Z^6+108)-RootOf(_Z^6+108)^4*x^6+1296*RootOf(_Z^6+108)*x^3-4050*RootOf(_Z^6+108)*x^4+3402*RootOf(_Z^6+108)*x^2-27*RootOf(_Z^6+108)^4-486*RootOf(_Z^6+108)-18*RootOf(_Z^6+108)*x^6+1296*(x^2-1)^(2/3)*x^4+3888*(x^2-1)^(2/3)*x^2+6*RootOf(_Z^6+108)^5*(x^2-1)^(1/3)*x^5+108*RootOf(_Z^6+108)^5*(x^2-1)^(1/3)*x^4+144*RootOf(_Z^6+108)^5*(x^2-1)^(1/3)*x^3+36*RootOf(_Z^6+108)^2*(x^2-1)^(1/3)*x^5+648*RootOf(_Z^6+108)^2*(x^2-1)^(1/3)*x^4+864*RootOf(_Z^6+108)^2*(x^2-1)^(1/3)*x^3-648*RootOf(_Z^6+108)^2*(x^2-1)^(1/3)*x^2-324*RootOf(_Z^6+108)^2*(x^2-1)^(1/3)*x-108*RootOf(_Z^6+108)^5*(x^2-1)^(1/3)*x^2-54*RootOf(_Z^6+108)^5*(x^2-1)^(1/3)*x)/(x^2+3)^3)+1/432*ln((RootOf(_Z^6+108)^4*x^6+72*x^5*RootOf(_Z^6+108)^4+225*RootOf(_Z^6+108)^4*x^4-36*RootOf(_Z^6+108)^2*(x^2-1)^(1/3)*x^5-72*x^3*RootOf(_Z^6+108)^4-648*RootOf(_Z^6+108)^2*(x^2-1)^(1/3)*x^4-189*RootOf(_Z^6+108)^4*x^2-864*RootOf(_Z^6+108)^2*(x^2-1)^(1/3)*x^3+648*(x^2-1)^(2/3)*x^4+648*RootOf(_Z^6+108)^2*(x^2-1)^(1/3)*x^2+4536*x^3*(x^2-1)^(2/3)+27*RootOf(_Z^6+108)^4+324*RootOf(_Z^6+108)^2*(x^2-1)^(1/3)*x+1944*(x^2-1)^(2/3)*x^2-1944*x*(x^2-1)^(2/3))/(x^2+3)^3)*RootOf(_Z^6+108)^4-1/72*ln((RootOf(_Z^6+108)^4*x^6+72*x^5*RootOf(_Z^6+108)^4+225*RootOf(_Z^6+108)^4*x^4-36*RootOf(_Z^6+108)^2*(x^2-1)^(1/3)*x^5-72*x^3*RootOf(_Z^6+108)^4-648*RootOf(_Z^6+108)^2*(x^2-1)^(1/3)*x^4-189*RootOf(_Z^6+108)^4*x^2-864*RootOf(_Z^6+108)^2*(x^2-1)^(1/3)*x^3+648*(x^2-1)^(2/3)*x^4+648*RootOf(_Z^6+108)^2*(x^2-1)^(1/3)*x^2+4536*x^3*(x^2-1)^(2/3)+27*RootOf(_Z^6+108)^4+324*RootOf(_Z^6+108)^2*(x^2-1)^(1/3)*x+1944*(x^2-1)^(2/3)*x^2-1944*x*(x^2-1)^(2/3))/(x^2+3)^3)*RootOf(_Z^6+108)","C"
2627,1,1175,169,10.684000," ","int((1+x)/(x^2+3*x+1)/(-x^3+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1175$\\ \hline \end{longtable}"," ",0,"-1/10*ln(-(15*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2)*RootOf(_Z^3-20)^3*x+25*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2)*RootOf(_Z^3-20)^2+100*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2)^2*RootOf(_Z^3-20)^2*x-11*(-x^3+1)^(1/3)*RootOf(_Z^3-20)^2*x-50*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2)*RootOf(_Z^3-20)*x+11*(-x^3+1)^(1/3)*RootOf(_Z^3-20)^2+50*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2)*RootOf(_Z^3-20)+39*RootOf(_Z^3-20)*x^2+260*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2)*x^2+27*RootOf(_Z^3-20)*x+110*(-x^3+1)^(2/3)+180*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2)*x+39*RootOf(_Z^3-20)+260*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2))/(x^2+3*x+1))*RootOf(_Z^3-20)-ln(-(15*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2)*RootOf(_Z^3-20)^3*x+25*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2)*RootOf(_Z^3-20)^2+100*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2)^2*RootOf(_Z^3-20)^2*x-11*(-x^3+1)^(1/3)*RootOf(_Z^3-20)^2*x-50*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2)*RootOf(_Z^3-20)*x+11*(-x^3+1)^(1/3)*RootOf(_Z^3-20)^2+50*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2)*RootOf(_Z^3-20)+39*RootOf(_Z^3-20)*x^2+260*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2)*x^2+27*RootOf(_Z^3-20)*x+110*(-x^3+1)^(2/3)+180*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2)*x+39*RootOf(_Z^3-20)+260*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2))/(x^2+3*x+1))*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2)+RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2)*ln((5*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2)*RootOf(_Z^3-20)^3*x+25*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2)*RootOf(_Z^3-20)^2-100*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2)^2*RootOf(_Z^3-20)^2*x+6*(-x^3+1)^(1/3)*RootOf(_Z^3-20)^2*x-50*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2)*RootOf(_Z^3-20)*x-6*(-x^3+1)^(1/3)*RootOf(_Z^3-20)^2+50*(-x^3+1)^(1/3)*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2)*RootOf(_Z^3-20)-13*RootOf(_Z^3-20)*x^2+260*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2)*x^2+RootOf(_Z^3-20)*x-60*(-x^3+1)^(2/3)-20*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2)*x-13*RootOf(_Z^3-20)+260*RootOf(RootOf(_Z^3-20)^2+10*_Z*RootOf(_Z^3-20)+100*_Z^2))/(x^2+3*x+1))","C"
2628,0,0,187,0.027000," ","int((3*k+2*(k^2+1)*x-k*(k^2+1)*x^2-4*k^2*x^3-k^3*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(1-d-(1+2*d)*k*x-(d*k^2+1)*x^2+k*x^3),x)","\[\int \frac{3 k +2 \left(k^{2}+1\right) x -k \left(k^{2}+1\right) x^{2}-4 k^{2} x^{3}-k^{3} x^{4}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{2}{3}} \left(1-d -\left(1+2 d \right) k x -\left(d \,k^{2}+1\right) x^{2}+k \,x^{3}\right)}\, dx\]"," ",0,"int((3*k+2*(k^2+1)*x-k*(k^2+1)*x^2-4*k^2*x^3-k^3*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(1-d-(1+2*d)*k*x-(d*k^2+1)*x^2+k*x^3),x)","F"
2629,1,681,179,0.587000," ","int((x^4-x)^(1/2)*(a*x^6+b)/(c*x^6-d),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{a \left(\frac{x \sqrt{x^{4}-x}}{3}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{c}-\frac{\left(a d +b c \right) \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(c \,\textit{\_Z}^{6}-d \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{3}+1\right) \left(-1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{5}+\underline{\hspace{1.25 ex}}\alpha^{4}+\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(1-i \sqrt{3}\right) \sqrt{\frac{x \left(-3+i \sqrt{3}\right)}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{\left(-1+x \right) \left(-1-i \sqrt{3}\right)}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\frac{\underline{\hspace{1.25 ex}}\alpha^{5} c \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5} c -3 \underline{\hspace{1.25 ex}}\alpha^{5} c -i \sqrt{3}\, d +3 d}{6 d}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{d}\right)}{\underline{\hspace{1.25 ex}}\alpha^{4} \left(c -d \right) \left(-3+i \sqrt{3}\right) \sqrt{x \left(-1+x \right) \left(i \sqrt{3}+2 x +1\right) \left(1+2 x -i \sqrt{3}\right)}}\right)}{3 c}$&$681$\\ elliptic&$\frac{a x \sqrt{x^{4}-x}}{3 c}-\frac{a \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{c \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{\sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(c \,\textit{\_Z}^{6}-d \right)}{\sum}\frac{\left(a d +b c \right) \left(\underline{\hspace{1.25 ex}}\alpha^{3}-1\right) \left(-1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{5}+\underline{\hspace{1.25 ex}}\alpha^{4}+\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(1-i \sqrt{3}\right) \sqrt{\frac{x \left(-3+i \sqrt{3}\right)}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{\left(-1+x \right) \left(-1-i \sqrt{3}\right)}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\frac{\underline{\hspace{1.25 ex}}\alpha^{5} c \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5} c -3 \underline{\hspace{1.25 ex}}\alpha^{5} c -i \sqrt{3}\, d +3 d}{6 d}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{d}\right)}{\underline{\hspace{1.25 ex}}\alpha^{4} \left(c -d \right) \left(-3+i \sqrt{3}\right) \sqrt{x \left(-1+x \right) \left(i \sqrt{3}+2 x +1\right) \left(1+2 x -i \sqrt{3}\right)}}\right)}{3 c}$&$681$\\ risch&$\frac{a \,x^{2} \left(x^{3}-1\right)}{3 c \sqrt{x \left(x^{3}-1\right)}}-\frac{\frac{2 a \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{2 \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(c \,\textit{\_Z}^{6}-d \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{3} a d -\underline{\hspace{1.25 ex}}\alpha^{3} b c +a d +b c \right) \left(-1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{5}+\underline{\hspace{1.25 ex}}\alpha^{4}+\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(1-i \sqrt{3}\right) \sqrt{\frac{x \left(-3+i \sqrt{3}\right)}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{\left(-1+x \right) \left(-1-i \sqrt{3}\right)}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\frac{\underline{\hspace{1.25 ex}}\alpha^{5} c \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5} c -3 \underline{\hspace{1.25 ex}}\alpha^{5} c -i \sqrt{3}\, d +3 d}{6 d}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{d}\right)}{\underline{\hspace{1.25 ex}}\alpha^{4} \left(c -d \right) \left(-3+i \sqrt{3}\right) \sqrt{x \left(-1+x \right) \left(i \sqrt{3}+2 x +1\right) \left(1+2 x -i \sqrt{3}\right)}}\right)}{3}}{2 c}$&$697$\\ \hline \end{longtable}"," ",0,"1/c*a*(1/3*x*(x^4-x)^(1/2)-(1/2-1/2*I*3^(1/2))*((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2)*(-1+x)^2*((x+1/2+1/2*I*3^(1/2))/(-1/2-1/2*I*3^(1/2))/(-1+x))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2)/(-3/2+1/2*I*3^(1/2))/(x*(-1+x)*(x+1/2+1/2*I*3^(1/2))*(x+1/2-1/2*I*3^(1/2)))^(1/2)*(EllipticF(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-EllipticPi(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),(-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)),((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))))-1/3*(a*d+b*c)/c*4^(1/2)*sum((-_alpha^3+1)/_alpha^4*(-1+x)^2*(_alpha^5+_alpha^4+_alpha^3+_alpha^2+_alpha+1)/(c-d)*(1-I*3^(1/2))*(x/(-1+x)*(-3+I*3^(1/2))/(-1+I*3^(1/2)))^(1/2)*(1/(-1+x)*(I*3^(1/2)+2*x+1)/(-1-I*3^(1/2)))^(1/2)*(1/(-1+x)*(1+2*x-I*3^(1/2))/(-1+I*3^(1/2)))^(1/2)/(-3+I*3^(1/2))/(x*(-1+x)*(I*3^(1/2)+2*x+1)*(1+2*x-I*3^(1/2)))^(1/2)*(EllipticF(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-_alpha^5*c/d*EllipticPi(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),1/6*(I*3^(1/2)*_alpha^5*c-3*_alpha^5*c-I*3^(1/2)*d+3*d)/d,((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))),_alpha=RootOf(_Z^6*c-d))","C"
2630,0,0,198,0.165000," ","int((a^2*b-2*a^2*x+(2*a-b)*x^2)/(x*(-a+x)*(-b+x))^(2/3)/(a^2*d+(-2*a*d+b)*x+(-1+d)*x^2),x)","\[\int \frac{a^{2} b -2 a^{2} x +\left(2 a -b \right) x^{2}}{\left(x \left(-a +x \right) \left(-b +x \right)\right)^{\frac{2}{3}} \left(a^{2} d +\left(-2 a d +b \right) x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((a^2*b-2*a^2*x+(2*a-b)*x^2)/(x*(-a+x)*(-b+x))^(2/3)/(a^2*d+(-2*a*d+b)*x+(-1+d)*x^2),x)","F"
2631,0,0,202,0.021000," ","int((2*a*b^2*x-b*(2*a+b)*x^2+x^4)/(x*(-a+x)*(-b+x)^2)^(2/3)/(-a*b^2+b*(2*a+b)*x-(a+2*b+d)*x^2+x^3),x)","\[\int \frac{2 a \,b^{2} x -b \left(2 a +b \right) x^{2}+x^{4}}{\left(x \left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{2}{3}} \left(-a \,b^{2}+b \left(2 a +b \right) x -\left(a +2 b +d \right) x^{2}+x^{3}\right)}\, dx\]"," ",0,"int((2*a*b^2*x-b*(2*a+b)*x^2+x^4)/(x*(-a+x)*(-b+x)^2)^(2/3)/(-a*b^2+b*(2*a+b)*x-(a+2*b+d)*x^2+x^3),x)","F"
2632,0,0,188,0.024000," ","int((-3*k+2*(k^2+1)*x+k*(k^2+1)*x^2-4*k^2*x^3+k^3*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(-1+d-(1+2*d)*k*x+(d*k^2+1)*x^2+k*x^3),x)","\[\int \frac{-3 k +2 \left(k^{2}+1\right) x +k \left(k^{2}+1\right) x^{2}-4 k^{2} x^{3}+k^{3} x^{4}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{2}{3}} \left(-1+d -\left(1+2 d \right) k x +\left(d \,k^{2}+1\right) x^{2}+k \,x^{3}\right)}\, dx\]"," ",0,"int((-3*k+2*(k^2+1)*x+k*(k^2+1)*x^2-4*k^2*x^3+k^3*x^4)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(-1+d-(1+2*d)*k*x+(d*k^2+1)*x^2+k*x^3),x)","F"
2633,1,544,58,7.298000," ","int((1-((-1+3*x)*(3+4*x))^(3/2))/(1+((-1+3*x)*(3+4*x))^(3/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-x -\frac{4 \RootOf \left(\textit{\_Z}^{2}-217\right) \ln \left(\frac{24 \RootOf \left(\textit{\_Z}^{2}-217\right) x +217 \sqrt{12 x^{2}+5 x -3}+5 \RootOf \left(\textit{\_Z}^{2}-217\right)}{\RootOf \left(\textit{\_Z}^{2}-217\right) x -5 x +8}\right)}{651}+\frac{4 \RootOf \left(\textit{\_Z}^{2}+4659291081 \RootOf \left(1842993 \textit{\_Z}^{4}+1953 \textit{\_Z}^{2}+1\right)^{2}+4937401\right) \ln \left(-\frac{88776 x \RootOf \left(\textit{\_Z}^{2}+4659291081 \RootOf \left(1842993 \textit{\_Z}^{4}+1953 \textit{\_Z}^{2}+1\right)^{2}+4937401\right) \RootOf \left(1842993 \textit{\_Z}^{4}+1953 \textit{\_Z}^{2}+1\right)^{2}+5119425 \RootOf \left(1842993 \textit{\_Z}^{4}+1953 \textit{\_Z}^{2}+1\right)^{2} \sqrt{12 x^{2}+5 x -3}+18495 \RootOf \left(\textit{\_Z}^{2}+4659291081 \RootOf \left(1842993 \textit{\_Z}^{4}+1953 \textit{\_Z}^{2}+1\right)^{2}+4937401\right) \RootOf \left(1842993 \textit{\_Z}^{4}+1953 \textit{\_Z}^{2}+1\right)^{2}+24 \RootOf \left(\textit{\_Z}^{2}+4659291081 \RootOf \left(1842993 \textit{\_Z}^{4}+1953 \textit{\_Z}^{2}+1\right)^{2}+4937401\right) x -45506 \sqrt{12 x^{2}+5 x -3}+5 \RootOf \left(\textit{\_Z}^{2}+4659291081 \RootOf \left(1842993 \textit{\_Z}^{4}+1953 \textit{\_Z}^{2}+1\right)^{2}+4937401\right)}{3474 x \RootOf \left(\textit{\_Z}^{2}+4659291081 \RootOf \left(1842993 \textit{\_Z}^{4}+1953 \textit{\_Z}^{2}+1\right)^{2}+4937401\right) \RootOf \left(1842993 \textit{\_Z}^{4}+1953 \textit{\_Z}^{2}+1\right)^{2}+1023885 \RootOf \left(1842993 \textit{\_Z}^{4}+1953 \textit{\_Z}^{2}+1\right)^{2} x +3 \RootOf \left(\textit{\_Z}^{2}+4659291081 \RootOf \left(1842993 \textit{\_Z}^{4}+1953 \textit{\_Z}^{2}+1\right)^{2}+4937401\right) x -970 x +1694}\right)}{68259}+4 \RootOf \left(1842993 \textit{\_Z}^{4}+1953 \textit{\_Z}^{2}+1\right) \ln \left(\frac{2019920328 \RootOf \left(1842993 \textit{\_Z}^{4}+1953 \textit{\_Z}^{2}+1\right)^{3} x +1706475 \RootOf \left(1842993 \textit{\_Z}^{4}+1953 \textit{\_Z}^{2}+1\right)^{2} \sqrt{12 x^{2}+5 x -3}+420816735 \RootOf \left(1842993 \textit{\_Z}^{4}+1953 \textit{\_Z}^{2}+1\right)^{3}+1594416 \RootOf \left(1842993 \textit{\_Z}^{4}+1953 \textit{\_Z}^{2}+1\right) x +16977 \sqrt{12 x^{2}+5 x -3}+332170 \RootOf \left(1842993 \textit{\_Z}^{4}+1953 \textit{\_Z}^{2}+1\right)}{237131766 \RootOf \left(1842993 \textit{\_Z}^{4}+1953 \textit{\_Z}^{2}+1\right)^{3} x +1023885 \RootOf \left(1842993 \textit{\_Z}^{4}+1953 \textit{\_Z}^{2}+1\right)^{2} x +46509 \RootOf \left(1842993 \textit{\_Z}^{4}+1953 \textit{\_Z}^{2}+1\right) x +2055 x -1694}\right)$&$544$\\ default&$\text{Expression too large to display}$&$2076$\\ \hline \end{longtable}"," ",0,"-x-4/651*RootOf(_Z^2-217)*ln((24*RootOf(_Z^2-217)*x+217*(12*x^2+5*x-3)^(1/2)+5*RootOf(_Z^2-217))/(RootOf(_Z^2-217)*x-5*x+8))+4/68259*RootOf(_Z^2+4659291081*RootOf(1842993*_Z^4+1953*_Z^2+1)^2+4937401)*ln(-(88776*x*RootOf(_Z^2+4659291081*RootOf(1842993*_Z^4+1953*_Z^2+1)^2+4937401)*RootOf(1842993*_Z^4+1953*_Z^2+1)^2+5119425*RootOf(1842993*_Z^4+1953*_Z^2+1)^2*(12*x^2+5*x-3)^(1/2)+18495*RootOf(_Z^2+4659291081*RootOf(1842993*_Z^4+1953*_Z^2+1)^2+4937401)*RootOf(1842993*_Z^4+1953*_Z^2+1)^2+24*RootOf(_Z^2+4659291081*RootOf(1842993*_Z^4+1953*_Z^2+1)^2+4937401)*x-45506*(12*x^2+5*x-3)^(1/2)+5*RootOf(_Z^2+4659291081*RootOf(1842993*_Z^4+1953*_Z^2+1)^2+4937401))/(3474*x*RootOf(_Z^2+4659291081*RootOf(1842993*_Z^4+1953*_Z^2+1)^2+4937401)*RootOf(1842993*_Z^4+1953*_Z^2+1)^2+1023885*RootOf(1842993*_Z^4+1953*_Z^2+1)^2*x+3*RootOf(_Z^2+4659291081*RootOf(1842993*_Z^4+1953*_Z^2+1)^2+4937401)*x-970*x+1694))+4*RootOf(1842993*_Z^4+1953*_Z^2+1)*ln((2019920328*RootOf(1842993*_Z^4+1953*_Z^2+1)^3*x+1706475*RootOf(1842993*_Z^4+1953*_Z^2+1)^2*(12*x^2+5*x-3)^(1/2)+420816735*RootOf(1842993*_Z^4+1953*_Z^2+1)^3+1594416*RootOf(1842993*_Z^4+1953*_Z^2+1)*x+16977*(12*x^2+5*x-3)^(1/2)+332170*RootOf(1842993*_Z^4+1953*_Z^2+1))/(237131766*RootOf(1842993*_Z^4+1953*_Z^2+1)^3*x+1023885*RootOf(1842993*_Z^4+1953*_Z^2+1)^2*x+46509*RootOf(1842993*_Z^4+1953*_Z^2+1)*x+2055*x-1694))","B"
2634,0,0,202,0.074000," ","int(1/(a^2*x^2-b*x)^(3/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x)","\[\int \frac{1}{\left(a^{2} x^{2}-b x \right)^{\frac{3}{2}} \left(a \,x^{2}+x \sqrt{a^{2} x^{2}-b x}\right)^{\frac{3}{2}}}\, dx\]"," ",0,"int(1/(a^2*x^2-b*x)^(3/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x)","F"
2635,0,0,189,0.010000," ","int(1/x/((-1+x)*(-2*q*x+x^2+q))^(1/3),x)","\[\int \frac{1}{x \left(\left(-1+x \right) \left(-2 q x +x^{2}+q \right)\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/x/((-1+x)*(-2*q*x+x^2+q))^(1/3),x)","F"
2636,0,0,193,0.161000," ","int((a*b+(-2*a+b)*x)/(x*(-a+x)*(-b+x))^(1/3)/(a^2*d+(-2*a*d+b)*x+(-1+d)*x^2),x)","\[\int \frac{a b +\left(-2 a +b \right) x}{\left(x \left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{3}} \left(a^{2} d +\left(-2 a d +b \right) x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((a*b+(-2*a+b)*x)/(x*(-a+x)*(-b+x))^(1/3)/(a^2*d+(-2*a*d+b)*x+(-1+d)*x^2),x)","F"
2637,0,0,169,0.050000," ","int((x^4+1)/(x^4-x^2-1)/(x^4-x^2)^(1/4),x)","\[\int \frac{x^{4}+1}{\left(x^{4}-x^{2}-1\right) \left(x^{4}-x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((x^4+1)/(x^4-x^2-1)/(x^4-x^2)^(1/4),x)","F"
2638,0,0,203,0.055000," ","int(x^3*(-a/b^2+a^2*x^2/b^2)^(1/2)/(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2),x)","\[\int \frac{x^{3} \sqrt{-\frac{a}{b^{2}}+\frac{a^{2} x^{2}}{b^{2}}}}{\sqrt{a \,x^{2}+b x \sqrt{-\frac{a}{b^{2}}+\frac{a^{2} x^{2}}{b^{2}}}}}\, dx\]"," ",0,"int(x^3*(-a/b^2+a^2*x^2/b^2)^(1/2)/(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/2),x)","F"
2639,0,0,184,0.012000," ","int((x^3-x)^(1/3)*(x^4-2)/x^4/(x^2+1),x)","\[\int \frac{\left(x^{3}-x \right)^{\frac{1}{3}} \left(x^{4}-2\right)}{x^{4} \left(x^{2}+1\right)}\, dx\]"," ",0,"int((x^3-x)^(1/3)*(x^4-2)/x^4/(x^2+1),x)","F"
2640,0,0,176,0.046000," ","int(2*(a*p*x^5-2*b*p*x^3+3*a*q*x)/(p*x^4+q)^(1/3)/(b^3*d+c*q+3*a*b^2*d*x^2+(3*a^2*b*d+c*p)*x^4+a^3*d*x^6),x)","\[\int \frac{2 a p \,x^{5}-4 b p \,x^{3}+6 a q x}{\left(p \,x^{4}+q \right)^{\frac{1}{3}} \left(b^{3} d +c q +3 a \,b^{2} d \,x^{2}+\left(3 a^{2} b d +c p \right) x^{4}+a^{3} d \,x^{6}\right)}\, dx\]"," ",0,"int(2*(a*p*x^5-2*b*p*x^3+3*a*q*x)/(p*x^4+q)^(1/3)/(b^3*d+c*q+3*a*b^2*d*x^2+(3*a^2*b*d+c*p)*x^4+a^3*d*x^6),x)","F"
2641,0,0,223,0.027000," ","int((b^2-2*b*x+x^2)*(-a^2*b+4*a*b*x-(2*a+3*b)*x^2+2*x^3)/(x*(-a+x)^2*(-b+x)^3)^(3/4)/(b*d+(a^2-d)*x-2*a*x^2+x^3),x)","\[\int \frac{\left(b^{2}-2 b x +x^{2}\right) \left(-a^{2} b +4 a b x -\left(2 a +3 b \right) x^{2}+2 x^{3}\right)}{\left(x \left(-a +x \right)^{2} \left(-b +x \right)^{3}\right)^{\frac{3}{4}} \left(b d +\left(a^{2}-d \right) x -2 a \,x^{2}+x^{3}\right)}\, dx\]"," ",0,"int((b^2-2*b*x+x^2)*(-a^2*b+4*a*b*x-(2*a+3*b)*x^2+2*x^3)/(x*(-a+x)^2*(-b+x)^3)^(3/4)/(b*d+(a^2-d)*x-2*a*x^2+x^3),x)","F"
2642,0,0,199,0.023000," ","int((-2+(1+k)*x)*(1-2*(1+k)*x+(k^2+4*k+1)*x^2-2*(k^2+k)*x^3+(k^2+a)*x^4)/x^3/((1-x)*x*(-k*x+1))^(2/3)/(1-(1+k)*x+(-b+k)*x^2),x)","\[\int \frac{\left(-2+\left(1+k \right) x \right) \left(1-2 \left(1+k \right) x +\left(k^{2}+4 k +1\right) x^{2}-2 \left(k^{2}+k \right) x^{3}+\left(k^{2}+a \right) x^{4}\right)}{x^{3} \left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{2}{3}} \left(1-\left(1+k \right) x +\left(-b +k \right) x^{2}\right)}\, dx\]"," ",0,"int((-2+(1+k)*x)*(1-2*(1+k)*x+(k^2+4*k+1)*x^2-2*(k^2+k)*x^3+(k^2+a)*x^4)/x^3/((1-x)*x*(-k*x+1))^(2/3)/(1-(1+k)*x+(-b+k)*x^2),x)","F"
2643,1,67417,23,65.688000," ","int((x^3+1)*(x^3-x^2)^(1/3)/(x^6+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$67417$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2644,0,0,18,180.000000," ","int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d)/(a^2*x^4+b)^(1/2),x)","\[\int \frac{\sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}{\left(c \,x^{2}+d \right) \sqrt{a^{2} x^{4}+b}}\, dx\]"," ",0,"int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d)/(a^2*x^4+b)^(1/2),x)","F"
2645,0,0,18,180.000000," ","int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d)/(a^2*x^4+b)^(1/2),x)","\[\int \frac{\sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}{\left(c \,x^{2}+d \right) \sqrt{a^{2} x^{4}+b}}\, dx\]"," ",0,"int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d)/(a^2*x^4+b)^(1/2),x)","F"
2646,0,0,85,180.000000," ","int((a*x+(a^2*x^2+b)^(1/2))^(1/2)*(c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2)/(a^2*x^2+b)^(3/2),x)","\[\int \frac{\sqrt{a x +\sqrt{a^{2} x^{2}+b}}\, \sqrt{c +\sqrt{a x +\sqrt{a^{2} x^{2}+b}}}}{\left(a^{2} x^{2}+b \right)^{\frac{3}{2}}}\, dx\]"," ",0,"int((a*x+(a^2*x^2+b)^(1/2))^(1/2)*(c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2)/(a^2*x^2+b)^(3/2),x)","F"
2647,0,0,85,180.000000," ","int((a*x+(a^2*x^2+b)^(1/2))^(1/2)*(c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2)/(a^2*x^2+b)^(3/2),x)","\[\int \frac{\sqrt{a x +\sqrt{a^{2} x^{2}+b}}\, \sqrt{c +\sqrt{a x +\sqrt{a^{2} x^{2}+b}}}}{\left(a^{2} x^{2}+b \right)^{\frac{3}{2}}}\, dx\]"," ",0,"int((a*x+(a^2*x^2+b)^(1/2))^(1/2)*(c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2)/(a^2*x^2+b)^(3/2),x)","F"
2648,1,171,204,0.205000," ","int((a*k*x+k*x^2+1)/(k*x^2-1)/((-x^2+1)*(-k^2*x^2+1))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\frac{a \ln \left(\frac{-\frac{2 \left(k^{2}-2 k +1\right)}{k}+\left(-k^{2}+2 k -1\right) \left(x^{2}-\frac{1}{k}\right)+2 \sqrt{-\frac{k^{2}-2 k +1}{k}}\, \sqrt{k^{2} \left(x^{2}-\frac{1}{k}\right)^{2}+\left(-k^{2}+2 k -1\right) \left(x^{2}-\frac{1}{k}\right)-\frac{k^{2}-2 k +1}{k}}}{x^{2}-\frac{1}{k}}\right)}{2 \sqrt{-\frac{k^{2}-2 k +1}{k}}}+\frac{\arctan \left(\frac{\sqrt{\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)}}{x \left(-1+k \right)}\right)}{-1+k}$&$171$\\ default&$\frac{\sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticF \left(x , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}+\frac{a \arctanh \left(-\frac{k \,x^{2}}{\sqrt{-\frac{1}{k}+2-k}\, \sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}+\frac{k}{2 \sqrt{-\frac{1}{k}+2-k}\, \sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}+\frac{k^{2} x^{2}}{2 \sqrt{-\frac{1}{k}+2-k}\, \sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}+\frac{1}{2 \sqrt{-\frac{1}{k}+2-k}\, \sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}\, k}+\frac{x^{2}}{2 \sqrt{-\frac{1}{k}+2-k}\, \sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}-\frac{1}{\sqrt{-\frac{1}{k}+2-k}\, \sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}\right)}{2 \sqrt{-\frac{1}{k}+2-k}}-\frac{2 \sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticPi \left(x , k , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}$&$364$\\ \hline \end{longtable}"," ",0,"-1/2*a/(-(k^2-2*k+1)/k)^(1/2)*ln((-2*(k^2-2*k+1)/k+(-k^2+2*k-1)*(x^2-1/k)+2*(-(k^2-2*k+1)/k)^(1/2)*(k^2*(x^2-1/k)^2+(-k^2+2*k-1)*(x^2-1/k)-(k^2-2*k+1)/k)^(1/2))/(x^2-1/k))+1/(-1+k)*arctan(((-x^2+1)*(-k^2*x^2+1))^(1/2)/x/(-1+k))","A"
2649,0,0,196,0.023000," ","int((3*k+(-k^2+2)*x-3*k*x^2-k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(1-d-(1+2*d)*k*x+(-d*k^2-1)*x^2+k*x^3),x)","\[\int \frac{3 k +\left(-k^{2}+2\right) x -3 k \,x^{2}-k^{2} x^{3}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{1}{3}} \left(1-d -\left(1+2 d \right) k x +\left(-d \,k^{2}-1\right) x^{2}+k \,x^{3}\right)}\, dx\]"," ",0,"int((3*k+(-k^2+2)*x-3*k*x^2-k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(1-d-(1+2*d)*k*x+(-d*k^2-1)*x^2+k*x^3),x)","F"
2650,0,0,196,0.024000," ","int((3*k+(k^2-2)*x-3*k*x^2+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(-1+d-(1+2*d)*k*x+(d*k^2+1)*x^2+k*x^3),x)","\[\int \frac{3 k +\left(k^{2}-2\right) x -3 k \,x^{2}+k^{2} x^{3}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{1}{3}} \left(-1+d -\left(1+2 d \right) k x +\left(d \,k^{2}+1\right) x^{2}+k \,x^{3}\right)}\, dx\]"," ",0,"int((3*k+(k^2-2)*x-3*k*x^2+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(-1+d-(1+2*d)*k*x+(d*k^2+1)*x^2+k*x^3),x)","F"
2651,0,0,74,0.065000," ","int((a*x^4-b*x^3)^(1/4)/(c*x^2+d),x)","\[\int \frac{\left(a \,x^{4}-b \,x^{3}\right)^{\frac{1}{4}}}{c \,x^{2}+d}\, dx\]"," ",0,"int((a*x^4-b*x^3)^(1/4)/(c*x^2+d),x)","F"
2652,0,0,74,0.004000," ","int((a*x^4-b*x^3)^(1/4)/(c*x^2+d),x)","\[\int \frac{\left(a \,x^{4}-b \,x^{3}\right)^{\frac{1}{4}}}{c \,x^{2}+d}\, dx\]"," ",0,"int((a*x^4-b*x^3)^(1/4)/(c*x^2+d),x)","F"
2653,0,0,192,180.000000," ","int((c*x^4+d)/x/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{c \,x^{4}+d}{x \sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int((c*x^4+d)/x/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","F"
2654,0,0,188,0.034000," ","int((x^2+1)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{x^{2}+1}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^2+1)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x+(x^2+1)^(1/2))^(1/2),x)","F"
2655,0,0,188,0.028000," ","int((x^2+1)^(1/2)*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2),x)","\[\int \sqrt{x^{2}+1}\, \sqrt{x +\sqrt{x^{2}+1}}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^2+1)^(1/2)*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2),x)","F"
2656,0,0,193,0.078000," ","int((x^4-x^3)^(1/4)/x/(a*x-b),x)","\[\int \frac{\left(x^{4}-x^{3}\right)^{\frac{1}{4}}}{x \left(a x -b \right)}\, dx\]"," ",0,"int((x^4-x^3)^(1/4)/x/(a*x-b),x)","F"
2657,0,0,191,0.058000," ","int(x^3*(-2*a*b+(a+b)*x)/(x*(-a+x)*(-b+x))^(2/3)/(-a^2*b^2+2*a*b*(a+b)*x-(a^2+4*a*b+b^2)*x^2+2*(a+b)*x^3+(-1+d)*x^4),x)","\[\int \frac{x^{3} \left(-2 a b +\left(a +b \right) x \right)}{\left(x \left(-a +x \right) \left(-b +x \right)\right)^{\frac{2}{3}} \left(-a^{2} b^{2}+2 a b \left(a +b \right) x -\left(a^{2}+4 a b +b^{2}\right) x^{2}+2 \left(a +b \right) x^{3}+\left(-1+d \right) x^{4}\right)}\, dx\]"," ",0,"int(x^3*(-2*a*b+(a+b)*x)/(x*(-a+x)*(-b+x))^(2/3)/(-a^2*b^2+2*a*b*(a+b)*x-(a^2+4*a*b+b^2)*x^2+2*(a+b)*x^3+(-1+d)*x^4),x)","F"
2658,0,0,157,0.068000," ","int((2*x^6+1)/(x^3+x)^(1/3)/(x^6-1),x)","\[\int \frac{2 x^{6}+1}{\left(x^{3}+x \right)^{\frac{1}{3}} \left(x^{6}-1\right)}\, dx\]"," ",0,"int((2*x^6+1)/(x^3+x)^(1/3)/(x^6-1),x)","F"
2659,0,0,157,0.003000," ","int((2*x^6+1)/(x^3+x)^(1/3)/(x^6-1),x)","\[\int \frac{2 x^{6}+1}{\left(x^{3}+x \right)^{\frac{1}{3}} \left(x^{6}-1\right)}\, dx\]"," ",0,"int((2*x^6+1)/(x^3+x)^(1/3)/(x^6-1),x)","F"
2660,0,0,174,0.015000," ","int((a*x^3-4*b)*(a*x^3+b)^(1/3)/x^5/(a*x^3-2*b),x)","\[\int \frac{\left(a \,x^{3}-4 b \right) \left(a \,x^{3}+b \right)^{\frac{1}{3}}}{x^{5} \left(a \,x^{3}-2 b \right)}\, dx\]"," ",0,"int((a*x^3-4*b)*(a*x^3+b)^(1/3)/x^5/(a*x^3-2*b),x)","F"
2661,0,0,194,0.021000," ","int((-2*a^2*b*x+a*(3*a+2*b)*x^2-4*a*x^3+x^4)/(x^2*(-a+x)*(-b+x))^(2/3)/(-a^2*d+2*a*d*x-(b+d)*x^2+x^3),x)","\[\int \frac{-2 a^{2} b x +a \left(3 a +2 b \right) x^{2}-4 a \,x^{3}+x^{4}}{\left(x^{2} \left(-a +x \right) \left(-b +x \right)\right)^{\frac{2}{3}} \left(-a^{2} d +2 a d x -\left(b +d \right) x^{2}+x^{3}\right)}\, dx\]"," ",0,"int((-2*a^2*b*x+a*(3*a+2*b)*x^2-4*a*x^3+x^4)/(x^2*(-a+x)*(-b+x))^(2/3)/(-a^2*d+2*a*d*x-(b+d)*x^2+x^3),x)","F"
2662,0,0,202,0.019000," ","int((-2+(1+k)*x)*(1-2*(1+k)*x+(k^2+4*k+1)*x^2-2*(k^2+k)*x^3+(k^2+a)*x^4)/x^4/((1-x)*x*(-k*x+1))^(1/3)/(1-(1+k)*x+(-b+k)*x^2),x)","\[\int \frac{\left(-2+\left(1+k \right) x \right) \left(1-2 \left(1+k \right) x +\left(k^{2}+4 k +1\right) x^{2}-2 \left(k^{2}+k \right) x^{3}+\left(k^{2}+a \right) x^{4}\right)}{x^{4} \left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(1-\left(1+k \right) x +\left(-b +k \right) x^{2}\right)}\, dx\]"," ",0,"int((-2+(1+k)*x)*(1-2*(1+k)*x+(k^2+4*k+1)*x^2-2*(k^2+k)*x^3+(k^2+a)*x^4)/x^4/((1-x)*x*(-k*x+1))^(1/3)/(1-(1+k)*x+(-b+k)*x^2),x)","F"
2663,1,675,171,0.562000," ","int(x^6*(x^4+x)^(1/2)/(a*x^6+b),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{x \sqrt{x^{4}+x}}{3 a}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{a \left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}+\frac{b \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{6}+b \right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{3}+1\right) \left(1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{5}-\underline{\hspace{1.25 ex}}\alpha^{4}+\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  -1\right) \left(-1-i \sqrt{3}\right) \sqrt{\frac{x \left(3+i \sqrt{3}\right)}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \sqrt{3}+2 x -1}{\left(1+x \right) \left(1-i \sqrt{3}\right)}}\, \sqrt{-\frac{-1+2 x -i \sqrt{3}}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\frac{\underline{\hspace{1.25 ex}}\alpha^{5} a \EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, -\frac{i \underline{\hspace{1.25 ex}}\alpha^{5} \sqrt{3}\, a +3 \underline{\hspace{1.25 ex}}\alpha^{5} a -i \sqrt{3}\, b -3 b}{6 b}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{b}\right)}{\underline{\hspace{1.25 ex}}\alpha^{4} \left(a +b \right) \left(3+i \sqrt{3}\right) \sqrt{x \left(1+x \right) \left(i \sqrt{3}+2 x -1\right) \left(-1+2 x -i \sqrt{3}\right)}}\right)}{3 a}$&$675$\\ default&$\frac{\frac{x \sqrt{x^{4}+x}}{3}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}}{a}-\frac{b \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{6}+b \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{3}-1\right) \left(1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{5}-\underline{\hspace{1.25 ex}}\alpha^{4}+\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  -1\right) \left(-1-i \sqrt{3}\right) \sqrt{\frac{x \left(3+i \sqrt{3}\right)}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \sqrt{3}+2 x -1}{\left(1+x \right) \left(1-i \sqrt{3}\right)}}\, \sqrt{-\frac{-1+2 x -i \sqrt{3}}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\frac{\underline{\hspace{1.25 ex}}\alpha^{5} a \EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, -\frac{i \underline{\hspace{1.25 ex}}\alpha^{5} \sqrt{3}\, a +3 \underline{\hspace{1.25 ex}}\alpha^{5} a -i \sqrt{3}\, b -3 b}{6 b}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{b}\right)}{\underline{\hspace{1.25 ex}}\alpha^{4} \left(a +b \right) \left(3+i \sqrt{3}\right) \sqrt{x \left(1+x \right) \left(i \sqrt{3}+2 x -1\right) \left(-1+2 x -i \sqrt{3}\right)}}\right)}{3 a}$&$676$\\ risch&$\frac{x^{2} \left(x^{3}+1\right)}{3 a \sqrt{x \left(x^{3}+1\right)}}+\frac{-\frac{2 \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(1+x \right)^{2} \sqrt{-\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \sqrt{-\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(1+x \right) \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}-\frac{2 b \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{6}+b \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{3}-1\right) \left(1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{5}-\underline{\hspace{1.25 ex}}\alpha^{4}+\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  -1\right) \left(-1-i \sqrt{3}\right) \sqrt{\frac{x \left(3+i \sqrt{3}\right)}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \sqrt{-\frac{i \sqrt{3}+2 x -1}{\left(1+x \right) \left(1-i \sqrt{3}\right)}}\, \sqrt{-\frac{-1+2 x -i \sqrt{3}}{\left(1+x \right) \left(1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\frac{\underline{\hspace{1.25 ex}}\alpha^{5} a \EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(1+x \right)}}, -\frac{i \underline{\hspace{1.25 ex}}\alpha^{5} \sqrt{3}\, a +3 \underline{\hspace{1.25 ex}}\alpha^{5} a -i \sqrt{3}\, b -3 b}{6 b}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{b}\right)}{\underline{\hspace{1.25 ex}}\alpha^{4} \left(a +b \right) \left(3+i \sqrt{3}\right) \sqrt{x \left(1+x \right) \left(i \sqrt{3}+2 x -1\right) \left(-1+2 x -i \sqrt{3}\right)}}\right)}{3}}{2 a}$&$686$\\ \hline \end{longtable}"," ",0,"1/3*x*(x^4+x)^(1/2)/a-1/a*(-1/2-1/2*I*3^(1/2))*((3/2+1/2*I*3^(1/2))*x/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2)*(1+x)^2*(-(x-1/2+1/2*I*3^(1/2))/(1/2-1/2*I*3^(1/2))/(1+x))^(1/2)*(-(x-1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2)/(3/2+1/2*I*3^(1/2))/(x*(1+x)*(x-1/2+1/2*I*3^(1/2))*(x-1/2-1/2*I*3^(1/2)))^(1/2)*(-EllipticF(((3/2+1/2*I*3^(1/2))*x/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2),((-3/2+1/2*I*3^(1/2))*(-1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+EllipticPi(((3/2+1/2*I*3^(1/2))*x/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2),(1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)),((-3/2+1/2*I*3^(1/2))*(-1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)))+1/3*b/a*4^(1/2)*sum((_alpha^3+1)/_alpha^4*(1+x)^2*(_alpha^5-_alpha^4+_alpha^3-_alpha^2+_alpha-1)/(a+b)*(-1-I*3^(1/2))*(x/(1+x)*(3+I*3^(1/2))/(1+I*3^(1/2)))^(1/2)*(-1/(1+x)*(I*3^(1/2)+2*x-1)/(1-I*3^(1/2)))^(1/2)*(-1/(1+x)*(-1+2*x-I*3^(1/2))/(1+I*3^(1/2)))^(1/2)/(3+I*3^(1/2))/(x*(1+x)*(I*3^(1/2)+2*x-1)*(-1+2*x-I*3^(1/2)))^(1/2)*(EllipticF(((3/2+1/2*I*3^(1/2))*x/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2),((-3/2+1/2*I*3^(1/2))*(-1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))-_alpha^5*a/b*EllipticPi(((3/2+1/2*I*3^(1/2))*x/(1/2+1/2*I*3^(1/2))/(1+x))^(1/2),-1/6*(I*_alpha^5*3^(1/2)*a+3*_alpha^5*a-I*3^(1/2)*b-3*b)/b,((-3/2+1/2*I*3^(1/2))*(-1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))),_alpha=RootOf(_Z^6*a+b))","C"
2664,0,0,160,0.013000," ","int((a*x^4+b*x^2)^(1/4)*(x^8-a*x^4-b)/(a*x^4-b),x)","\[\int \frac{\left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}} \left(x^{8}-a \,x^{4}-b \right)}{a \,x^{4}-b}\, dx\]"," ",0,"int((a*x^4+b*x^2)^(1/4)*(x^8-a*x^4-b)/(a*x^4-b),x)","F"
2665,0,0,160,0.003000," ","int((a*x^4+b*x^2)^(1/4)*(x^8-a*x^4-b)/(a*x^4-b),x)","\[\int \frac{\left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}} \left(x^{8}-a \,x^{4}-b \right)}{a \,x^{4}-b}\, dx\]"," ",0,"int((a*x^4+b*x^2)^(1/4)*(x^8-a*x^4-b)/(a*x^4-b),x)","F"
2666,0,0,190,180.000000," ","int((5*x^7+2*x^4-2)*(x^8+x^5-x^3+x)^(1/3)/(2*x^7+2*x^4+x^2+2)^2,x)","\[\int \frac{\left(5 x^{7}+2 x^{4}-2\right) \left(x^{8}+x^{5}-x^{3}+x \right)^{\frac{1}{3}}}{\left(2 x^{7}+2 x^{4}+x^{2}+2\right)^{2}}\, dx\]"," ",0,"int((5*x^7+2*x^4-2)*(x^8+x^5-x^3+x)^(1/3)/(2*x^7+2*x^4+x^2+2)^2,x)","F"
2667,1,487,177,0.280000," ","int((a^5*x^5-b^5)/(a^2*x^3+b^2*x)^(1/2)/(a^5*x^5+b^5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{i b \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticF \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}+b^{2} x}}-\frac{2 i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{4} \textit{\_Z}^{4}-a^{3} b \,\textit{\_Z}^{3}+a^{2} b^{2} \textit{\_Z}^{2}-a \,b^{3} \textit{\_Z} +b^{4}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{3} a^{3}+2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b -3 \underline{\hspace{1.25 ex}}\alpha  a \,b^{2}+4 b^{3}\right) \underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-i \underline{\hspace{1.25 ex}}\alpha  a b -\underline{\hspace{1.25 ex}}\alpha  a b +i b^{2}\right) \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, -\frac{\underline{\hspace{1.25 ex}}\alpha  \left(i \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-i \underline{\hspace{1.25 ex}}\alpha  a b +\underline{\hspace{1.25 ex}}\alpha  a b -b^{2}\right) a}{b^{3}}, \frac{\sqrt{2}}{2}\right)}{\left(4 \underline{\hspace{1.25 ex}}\alpha^{3} a^{3}-3 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b +2 \underline{\hspace{1.25 ex}}\alpha  a \,b^{2}-b^{3}\right) \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}\right)}{5 b^{2}}-\frac{2 i b^{2} \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, -\frac{i b}{a \left(-\frac{i b}{a}+\frac{b}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{5 a^{2} \sqrt{a^{2} x^{3}+b^{2} x}\, \left(-\frac{i b}{a}+\frac{b}{a}\right)}$&$487$\\ elliptic&$\text{Expression too large to display}$&$2185$\\ \hline \end{longtable}"," ",0,"I*b/a*(-I*(x+I*b/a)/b*a)^(1/2)*2^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(a^2*x^3+b^2*x)^(1/2)*EllipticF((-I*(x+I*b/a)/b*a)^(1/2),1/2*2^(1/2))-2/5*I/b^2*2^(1/2)*sum((-_alpha^3*a^3+2*_alpha^2*a^2*b-3*_alpha*a*b^2+4*b^3)/(4*_alpha^3*a^3-3*_alpha^2*a^2*b+2*_alpha*a*b^2-b^3)*_alpha*(-I*_alpha*a*b+_alpha^2*a^2+I*b^2-_alpha*a*b)*(-I*(x+I*b/a)/b*a)^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(x*(a^2*x^2+b^2))^(1/2)*EllipticPi((-I*(x+I*b/a)/b*a)^(1/2),-_alpha*(I*_alpha^2*a^2-I*_alpha*a*b+_alpha*a*b-b^2)*a/b^3,1/2*2^(1/2)),_alpha=RootOf(_Z^4*a^4-_Z^3*a^3*b+_Z^2*a^2*b^2-_Z*a*b^3+b^4))-2/5*I*b^2/a^2*(-I*(x+I*b/a)/b*a)^(1/2)*2^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(a^2*x^3+b^2*x)^(1/2)/(-I*b/a+b/a)*EllipticPi((-I*(x+I*b/a)/b*a)^(1/2),-I*b/a/(-I*b/a+b/a),1/2*2^(1/2))","C"
2668,1,482,177,0.279000," ","int((a^5*x^5+b^5)/(a^2*x^3+b^2*x)^(1/2)/(a^5*x^5-b^5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{i b \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticF \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}+b^{2} x}}+\frac{2 i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{4} \textit{\_Z}^{4}+a^{3} b \,\textit{\_Z}^{3}+a^{2} b^{2} \textit{\_Z}^{2}+a \,b^{3} \textit{\_Z} +b^{4}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{3} a^{3}-2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b -3 \underline{\hspace{1.25 ex}}\alpha  a \,b^{2}-4 b^{3}\right) \underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-i \underline{\hspace{1.25 ex}}\alpha  a b +\underline{\hspace{1.25 ex}}\alpha  a b -i b^{2}\right) \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, -\frac{\underline{\hspace{1.25 ex}}\alpha  \left(i \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+i \underline{\hspace{1.25 ex}}\alpha  a b +\underline{\hspace{1.25 ex}}\alpha  a b +b^{2}\right) a}{b^{3}}, \frac{\sqrt{2}}{2}\right)}{\left(4 \underline{\hspace{1.25 ex}}\alpha^{3} a^{3}+3 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b +2 \underline{\hspace{1.25 ex}}\alpha  a \,b^{2}+b^{3}\right) \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}\right)}{5 b^{2}}+\frac{2 i b^{2} \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, -\frac{i b}{a \left(-\frac{i b}{a}-\frac{b}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{5 a^{2} \sqrt{a^{2} x^{3}+b^{2} x}\, \left(-\frac{i b}{a}-\frac{b}{a}\right)}$&$482$\\ elliptic&$\text{Expression too large to display}$&$2129$\\ \hline \end{longtable}"," ",0,"I*b/a*(-I*(x+I*b/a)/b*a)^(1/2)*2^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(a^2*x^3+b^2*x)^(1/2)*EllipticF((-I*(x+I*b/a)/b*a)^(1/2),1/2*2^(1/2))+2/5*I/b^2*2^(1/2)*sum((-_alpha^3*a^3-2*_alpha^2*a^2*b-3*_alpha*a*b^2-4*b^3)/(4*_alpha^3*a^3+3*_alpha^2*a^2*b+2*_alpha*a*b^2+b^3)*_alpha*(-I*_alpha*a*b+_alpha^2*a^2-I*b^2+_alpha*a*b)*(-I*(x+I*b/a)/b*a)^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(x*(a^2*x^2+b^2))^(1/2)*EllipticPi((-I*(x+I*b/a)/b*a)^(1/2),-_alpha*(I*_alpha^2*a^2+I*_alpha*a*b+_alpha*a*b+b^2)*a/b^3,1/2*2^(1/2)),_alpha=RootOf(_Z^4*a^4+_Z^3*a^3*b+_Z^2*a^2*b^2+_Z*a*b^3+b^4))+2/5*I*b^2/a^2*(-I*(x+I*b/a)/b*a)^(1/2)*2^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(a^2*x^3+b^2*x)^(1/2)/(-I*b/a-b/a)*EllipticPi((-I*(x+I*b/a)/b*a)^(1/2),-I*b/a/(-I*b/a-b/a),1/2*2^(1/2))","C"
2669,0,0,188,0.011000," ","int((2*x^8-a*x^4-2*b)/x^4/(a*x^4-b)^(1/4)/(2*a*x^4-b),x)","\[\int \frac{2 x^{8}-a \,x^{4}-2 b}{x^{4} \left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(2 a \,x^{4}-b \right)}\, dx\]"," ",0,"int((2*x^8-a*x^4-2*b)/x^4/(a*x^4-b)^(1/4)/(2*a*x^4-b),x)","F"
2670,1,231,181,1.142000," ","int((x^16-1)/(x^4-1)^(1/2)/(x^16+x^8+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(-\frac{\ln \left(\frac{x^{4}-1}{x^{2}}+\frac{\sqrt{x^{4}-1}\, \sqrt{2}}{x}+1\right)}{8}+\frac{\arctan \left(1+\frac{\sqrt{x^{4}-1}\, \sqrt{2}}{x}\right)}{4}+\frac{\ln \left(\frac{x^{4}-1}{x^{2}}-\frac{\sqrt{x^{4}-1}\, \sqrt{2}}{x}+1\right)}{8}+\frac{\arctan \left(-1+\frac{\sqrt{x^{4}-1}\, \sqrt{2}}{x}\right)}{4}+\frac{3^{\frac{3}{4}} \arctan \left(\frac{3^{\frac{3}{4}} \sqrt{x^{4}-1}\, \sqrt{2}}{3 x}+1\right)}{12}+\frac{3^{\frac{3}{4}} \arctan \left(\frac{3^{\frac{3}{4}} \sqrt{x^{4}-1}\, \sqrt{2}}{3 x}-1\right)}{12}+\frac{3^{\frac{3}{4}} \ln \left(\frac{\frac{x^{4}-1}{2 x^{2}}-\frac{3^{\frac{1}{4}} \sqrt{x^{4}-1}\, \sqrt{2}}{2 x}+\frac{\sqrt{3}}{2}}{\frac{x^{4}-1}{2 x^{2}}+\frac{3^{\frac{1}{4}} \sqrt{x^{4}-1}\, \sqrt{2}}{2 x}+\frac{\sqrt{3}}{2}}\right)}{24}\right) \sqrt{2}}{2}$&$231$\\ default&$-\frac{i \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticF \left(i x , i\right)}{\sqrt{x^{4}-1}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}-\textit{\_Z}^{2}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}-1\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}-2}\, \sqrt{x^{4}-1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{2}-2}}+\frac{2 i \left(-\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticPi \left(i x , \underline{\hspace{1.25 ex}}\alpha^{2}-1, i\right)}{\sqrt{x^{4}-1}}\right)\right)}{16}+\frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{\arctanh \left(\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x^{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\sqrt{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}-1}}\right)}{2 \sqrt{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}+\frac{i \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticPi \left(i x , \frac{1}{2}+\frac{i \sqrt{3}}{2}, i\right)}{\sqrt{x^{4}-1}}\right)}{8}+\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-\frac{\arctanh \left(\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x^{2}+\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\sqrt{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}-1}}\right)}{2 \sqrt{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}+\frac{i \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticPi \left(i x , \frac{1}{2}-\frac{i \sqrt{3}}{2}, i\right)}{\sqrt{x^{4}-1}}\right)}{8}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{6}-\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}-1}\, \sqrt{x^{4}-1}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4}-1}}+\frac{2 i \left(-\underline{\hspace{1.25 ex}}\alpha^{7}+\underline{\hspace{1.25 ex}}\alpha^{3}\right) \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticPi \left(i x , \underline{\hspace{1.25 ex}}\alpha^{6}-\underline{\hspace{1.25 ex}}\alpha^{2}, i\right)}{\sqrt{x^{4}-1}}\right)\right)}{16}+\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{\arctanh \left(\frac{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x^{2}+\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\sqrt{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}-1}}\right)}{2 \sqrt{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}+\frac{i \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticPi \left(i x , \frac{1}{2}-\frac{i \sqrt{3}}{2}, i\right)}{\sqrt{x^{4}-1}}\right)}{8}+\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(\frac{\arctanh \left(\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x^{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}{\sqrt{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}-1}}\right)}{2 \sqrt{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}+\frac{i \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticPi \left(i x , \frac{1}{2}+\frac{i \sqrt{3}}{2}, i\right)}{\sqrt{x^{4}-1}}\right)}{8}$&$685$\\ \hline \end{longtable}"," ",0,"1/2*(-1/8*ln((x^4-1)/x^2+(x^4-1)^(1/2)*2^(1/2)/x+1)+1/4*arctan(1+(x^4-1)^(1/2)*2^(1/2)/x)+1/8*ln((x^4-1)/x^2-(x^4-1)^(1/2)*2^(1/2)/x+1)+1/4*arctan(-1+(x^4-1)^(1/2)*2^(1/2)/x)+1/12*3^(3/4)*arctan(1/3*3^(3/4)*(x^4-1)^(1/2)*2^(1/2)/x+1)+1/12*3^(3/4)*arctan(1/3*3^(3/4)*(x^4-1)^(1/2)*2^(1/2)/x-1)+1/24*3^(3/4)*ln((1/2*(x^4-1)/x^2-1/2*3^(1/4)*(x^4-1)^(1/2)*2^(1/2)/x+1/2*3^(1/2))/(1/2*(x^4-1)/x^2+1/2*3^(1/4)*(x^4-1)^(1/2)*2^(1/2)/x+1/2*3^(1/2))))*2^(1/2)","A"
2671,0,0,201,0.019000," ","int((2*a*b*x-3*a*x^2+x^3)/(x^2*(-a+x)*(-b+x))^(1/3)/(-a^2*d+2*a*d*x-(b+d)*x^2+x^3),x)","\[\int \frac{2 a b x -3 a \,x^{2}+x^{3}}{\left(x^{2} \left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{3}} \left(-a^{2} d +2 a d x -\left(b +d \right) x^{2}+x^{3}\right)}\, dx\]"," ",0,"int((2*a*b*x-3*a*x^2+x^3)/(x^2*(-a+x)*(-b+x))^(1/3)/(-a^2*d+2*a*d*x-(b+d)*x^2+x^3),x)","F"
2672,0,0,80,0.010000," ","int((c*x^2+d)*(a*x^4+b*x^3)^(1/4)/x^2/(c*x^2-d),x)","\[\int \frac{\left(c \,x^{2}+d \right) \left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}}{x^{2} \left(c \,x^{2}-d \right)}\, dx\]"," ",0,"int((c*x^2+d)*(a*x^4+b*x^3)^(1/4)/x^2/(c*x^2-d),x)","F"
2673,0,0,80,0.004000," ","int((c*x^2+d)*(a*x^4+b*x^3)^(1/4)/x^2/(c*x^2-d),x)","\[\int \frac{\left(c \,x^{2}+d \right) \left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}}{x^{2} \left(c \,x^{2}-d \right)}\, dx\]"," ",0,"int((c*x^2+d)*(a*x^4+b*x^3)^(1/4)/x^2/(c*x^2-d),x)","F"
2674,0,0,11,0.103000," ","int((x^4-1)/(x^4+1)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x)","\[\int \frac{x^{4}-1}{\left(x^{4}+1\right) \sqrt{a \,x^{4}+b \,x^{3}+c \,x^{2}+b x +a}}\, dx\]"," ",0,"int((x^4-1)/(x^4+1)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x)","F"
2675,0,0,197,0.019000," ","int(((k^2-2)*x+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(-1+d+(k^2-2*d)*x^2+d*x^4),x)","\[\int \frac{\left(k^{2}-2\right) x +k^{2} x^{3}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{1}{3}} \left(-1+d +\left(k^{2}-2 d \right) x^{2}+d \,x^{4}\right)}\, dx\]"," ",0,"int(((k^2-2)*x+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(-1+d+(k^2-2*d)*x^2+d*x^4),x)","F"
2676,0,0,197,0.026000," ","int(((2*k^2-1)*x-2*k^4*x^3+k^4*x^5)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(1-d+(-2*k^2+d)*x^2+k^4*x^4),x)","\[\int \frac{\left(2 k^{2}-1\right) x -2 k^{4} x^{3}+k^{4} x^{5}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{2}{3}} \left(1-d +\left(-2 k^{2}+d \right) x^{2}+k^{4} x^{4}\right)}\, dx\]"," ",0,"int(((2*k^2-1)*x-2*k^4*x^3+k^4*x^5)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(1-d+(-2*k^2+d)*x^2+k^4*x^4),x)","F"
2677,1,679,173,31.685000," ","int((x^6-2)*(x^6-x^4+1)/(x^6+1)^(1/4)/(x^12+x^8+2*x^6+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{8}+16\right)^{5} \ln \left(\frac{\RootOf \left(\textit{\_Z}^{8}+16\right)^{8} x^{4}-4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{6} \sqrt{x^{6}+1}\, x^{2}+4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{4} x^{6}-8 \RootOf \left(\textit{\_Z}^{8}+16\right)^{5} \left(x^{6}+1\right)^{\frac{1}{4}} x^{3}-4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{4} x^{4}+16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{3} \left(x^{6}+1\right)^{\frac{3}{4}} x +16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{2} \sqrt{x^{6}+1}\, x^{2}-16 x^{6}+4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{4}-16}{\RootOf \left(\textit{\_Z}^{8}+16\right)^{4} x^{4}-4 x^{6}-4}\right)}{16}-\frac{\RootOf \left(\textit{\_Z}^{8}+16\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{8}+16\right)^{8} x^{4}+4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{6} \sqrt{x^{6}+1}\, x^{2}+4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{4} x^{6}+8 \RootOf \left(\textit{\_Z}^{8}+16\right)^{5} \left(x^{6}+1\right)^{\frac{1}{4}} x^{3}+4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{4} x^{4}+16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{3} \left(x^{6}+1\right)^{\frac{3}{4}} x +16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{2} \sqrt{x^{6}+1}\, x^{2}+16 x^{6}+4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{4}+16}{\RootOf \left(\textit{\_Z}^{8}+16\right)^{4} x^{4}-4 x^{6}-4}\right)}{4}-\frac{\RootOf \left(\textit{\_Z}^{8}+16\right)^{3} \ln \left(\frac{\RootOf \left(\textit{\_Z}^{8}+16\right)^{10} x^{4}-4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{6} x^{6}-4 x^{4} \RootOf \left(\textit{\_Z}^{8}+16\right)^{6}+16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{4} \sqrt{x^{6}+1}\, x^{2}+16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{2} x^{6}-32 \RootOf \left(\textit{\_Z}^{8}+16\right)^{3} \left(x^{6}+1\right)^{\frac{3}{4}} x -4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{6}+64 \RootOf \left(\textit{\_Z}^{8}+16\right) \left(x^{6}+1\right)^{\frac{1}{4}} x^{3}-64 x^{2} \sqrt{x^{6}+1}+16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{2}}{\RootOf \left(\textit{\_Z}^{8}+16\right)^{4} x^{4}+4 x^{6}+4}\right)}{8}-\frac{\RootOf \left(\textit{\_Z}^{8}+16\right)^{7} \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{8}+16\right)^{10} x^{4}-4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{6} x^{6}+4 x^{4} \RootOf \left(\textit{\_Z}^{8}+16\right)^{6}-16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{4} \sqrt{x^{6}+1}\, x^{2}-16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{2} x^{6}+32 \RootOf \left(\textit{\_Z}^{8}+16\right)^{3} \left(x^{6}+1\right)^{\frac{3}{4}} x -4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{6}+64 \RootOf \left(\textit{\_Z}^{8}+16\right) \left(x^{6}+1\right)^{\frac{1}{4}} x^{3}-64 x^{2} \sqrt{x^{6}+1}-16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{2}}{\RootOf \left(\textit{\_Z}^{8}+16\right)^{4} x^{4}+4 x^{6}+4}\right)}{32}$&$679$\\ \hline \end{longtable}"," ",0,"-1/16*RootOf(_Z^8+16)^5*ln((RootOf(_Z^8+16)^8*x^4-4*RootOf(_Z^8+16)^6*(x^6+1)^(1/2)*x^2+4*RootOf(_Z^8+16)^4*x^6-8*RootOf(_Z^8+16)^5*(x^6+1)^(1/4)*x^3-4*RootOf(_Z^8+16)^4*x^4+16*RootOf(_Z^8+16)^3*(x^6+1)^(3/4)*x+16*RootOf(_Z^8+16)^2*(x^6+1)^(1/2)*x^2-16*x^6+4*RootOf(_Z^8+16)^4-16)/(RootOf(_Z^8+16)^4*x^4-4*x^6-4))-1/4*RootOf(_Z^8+16)*ln((RootOf(_Z^8+16)^8*x^4+4*RootOf(_Z^8+16)^6*(x^6+1)^(1/2)*x^2+4*RootOf(_Z^8+16)^4*x^6+8*RootOf(_Z^8+16)^5*(x^6+1)^(1/4)*x^3+4*RootOf(_Z^8+16)^4*x^4+16*RootOf(_Z^8+16)^3*(x^6+1)^(3/4)*x+16*RootOf(_Z^8+16)^2*(x^6+1)^(1/2)*x^2+16*x^6+4*RootOf(_Z^8+16)^4+16)/(RootOf(_Z^8+16)^4*x^4-4*x^6-4))-1/8*RootOf(_Z^8+16)^3*ln((RootOf(_Z^8+16)^10*x^4-4*RootOf(_Z^8+16)^6*x^6-4*x^4*RootOf(_Z^8+16)^6+16*RootOf(_Z^8+16)^4*(x^6+1)^(1/2)*x^2+16*RootOf(_Z^8+16)^2*x^6-32*RootOf(_Z^8+16)^3*(x^6+1)^(3/4)*x-4*RootOf(_Z^8+16)^6+64*RootOf(_Z^8+16)*(x^6+1)^(1/4)*x^3-64*x^2*(x^6+1)^(1/2)+16*RootOf(_Z^8+16)^2)/(RootOf(_Z^8+16)^4*x^4+4*x^6+4))-1/32*RootOf(_Z^8+16)^7*ln(-(RootOf(_Z^8+16)^10*x^4-4*RootOf(_Z^8+16)^6*x^6+4*x^4*RootOf(_Z^8+16)^6-16*RootOf(_Z^8+16)^4*(x^6+1)^(1/2)*x^2-16*RootOf(_Z^8+16)^2*x^6+32*RootOf(_Z^8+16)^3*(x^6+1)^(3/4)*x-4*RootOf(_Z^8+16)^6+64*RootOf(_Z^8+16)*(x^6+1)^(1/4)*x^3-64*x^2*(x^6+1)^(1/2)-16*RootOf(_Z^8+16)^2)/(RootOf(_Z^8+16)^4*x^4+4*x^6+4))","C"
2678,0,0,230,0.028000," ","int((2*p*x^3-q)*(a*p*x^3+a*q+b*x)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)/x^3/(c*p*x^3+c*q+d*x),x)","\[\int \frac{\left(2 p \,x^{3}-q \right) \left(a p \,x^{3}+a q +b x \right) \sqrt{p^{2} x^{6}+2 p q \,x^{3}-2 p q \,x^{2}+q^{2}}}{x^{3} \left(c p \,x^{3}+c q +d x \right)}\, dx\]"," ",0,"int((2*p*x^3-q)*(a*p*x^3+a*q+b*x)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)/x^3/(c*p*x^3+c*q+d*x),x)","F"
2679,0,0,189,0.039000," ","int((x^2-1)/(x^2+1)/(x^2+(x^4+1)^(1/2))^(1/2),x)","\[\int \frac{x^{2}-1}{\left(x^{2}+1\right) \sqrt{x^{2}+\sqrt{x^{4}+1}}}\, dx\]"," ",0,"int((x^2-1)/(x^2+1)/(x^2+(x^4+1)^(1/2))^(1/2),x)","F"
2680,0,0,189,0.035000," ","int((x^2-1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^2+1),x)","\[\int \frac{\left(x^{2}-1\right) \sqrt{x^{2}+\sqrt{x^{4}+1}}}{x^{2}+1}\, dx\]"," ",0,"int((x^2-1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^2+1),x)","F"
2681,0,0,195,0.029000," ","int((x^2+1)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2),x)","\[\int \sqrt{x^{2}+1}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^2+1)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2),x)","F"
2682,0,0,191,0.176000," ","int(x*(-a+x)/(x^2*(-a+x))^(2/3)/(a^2*d-2*a*d*x+(-1+d)*x^2),x)","\[\int \frac{x \left(-a +x \right)}{\left(x^{2} \left(-a +x \right)\right)^{\frac{2}{3}} \left(a^{2} d -2 a d x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int(x*(-a+x)/(x^2*(-a+x))^(2/3)/(a^2*d-2*a*d*x+(-1+d)*x^2),x)","F"
2683,0,0,191,0.176000," ","int(x/(x^2*(-a+x))^(1/3)/(a^2*d-2*a*d*x+(-1+d)*x^2),x)","\[\int \frac{x}{\left(x^{2} \left(-a +x \right)\right)^{\frac{1}{3}} \left(a^{2} d -2 a d x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int(x/(x^2*(-a+x))^(1/3)/(a^2*d-2*a*d*x+(-1+d)*x^2),x)","F"
2684,0,0,191,0.177000," ","int((-a*x+x^2)/(x^2*(-a+x))^(2/3)/(a^2*d-2*a*d*x+(-1+d)*x^2),x)","\[\int \frac{-a x +x^{2}}{\left(x^{2} \left(-a +x \right)\right)^{\frac{2}{3}} \left(a^{2} d -2 a d x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((-a*x+x^2)/(x^2*(-a+x))^(2/3)/(a^2*d-2*a*d*x+(-1+d)*x^2),x)","F"
2685,1,1639,187,21.081000," ","int((-1+x)/(1+x)/(x^3-1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1639$\\ \hline \end{longtable}"," ",0,"-1/2*ln(-(5*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x+3*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x+4*(x^3-1)^(2/3)*RootOf(_Z^3-4)^2*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)+13*(x^3-1)^(1/3)*RootOf(_Z^3-4)^2*x+4*(x^3-1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)*x-13*(x^3-1)^(1/3)*RootOf(_Z^3-4)^2-4*(x^3-1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)+35*RootOf(_Z^3-4)*x^2+21*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x^2+30*RootOf(_Z^3-4)*x+18*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x+52*(x^3-1)^(2/3)+35*RootOf(_Z^3-4)+21*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2))/(1+x)^2)*RootOf(_Z^3-4)-1/2*ln(-(5*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x+3*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x+4*(x^3-1)^(2/3)*RootOf(_Z^3-4)^2*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)+13*(x^3-1)^(1/3)*RootOf(_Z^3-4)^2*x+4*(x^3-1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)*x-13*(x^3-1)^(1/3)*RootOf(_Z^3-4)^2-4*(x^3-1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)+35*RootOf(_Z^3-4)*x^2+21*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x^2+30*RootOf(_Z^3-4)*x+18*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x+52*(x^3-1)^(2/3)+35*RootOf(_Z^3-4)+21*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2))/(1+x)^2)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)+1/2*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*ln((2*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^3*x-3*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*RootOf(_Z^3-4)^2*x+4*(x^3-1)^(2/3)*RootOf(_Z^3-4)^2*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)-9*(x^3-1)^(1/3)*RootOf(_Z^3-4)^2*x+4*(x^3-1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)*x+9*(x^3-1)^(1/3)*RootOf(_Z^3-4)^2-4*(x^3-1)^(1/3)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)-14*RootOf(_Z^3-4)*x^2+21*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x^2-4*RootOf(_Z^3-4)*x+6*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x-36*(x^3-1)^(2/3)-14*RootOf(_Z^3-4)+21*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2))/(1+x)^2)-1/3*ln(-RootOf(_Z^3-4)^4*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*x^3-6*(x^3-1)^(2/3)*RootOf(_Z^3-4)^2*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x+2*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2*x^3-4*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2-24*x^2*(x^3-1)^(1/3)+8*x^3-8)+1/3*ln(RootOf(_Z^3-4)^4*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*x^3+12*(x^3-1)^(2/3)*RootOf(_Z^3-4)^2*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x-12*(x^3-1)^(1/3)*RootOf(_Z^3-4)^2*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x^2+4*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2*x^3-4*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2+48*x*(x^3-1)^(2/3)-32*x^3+16)+1/12*ln(RootOf(_Z^3-4)^4*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)^2*x^3+12*(x^3-1)^(2/3)*RootOf(_Z^3-4)^2*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x-12*(x^3-1)^(1/3)*RootOf(_Z^3-4)^2*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*x^2+4*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2*x^3-4*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2+48*x*(x^3-1)^(2/3)-32*x^3+16)*RootOf(RootOf(_Z^3-4)^2+_Z*RootOf(_Z^3-4)+_Z^2)*RootOf(_Z^3-4)^2","C"
2686,1,1278,195,6.893000," ","int((x^2+1)*(x^3-x^2)^(1/3)/(x^2-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1278$\\ risch&$\text{Expression too large to display}$&$2369$\\ \hline \end{longtable}"," ",0,"(-1/6+1/2*x)*(x^3-x^2)^(1/3)+1/3*RootOf(9*_Z^2-51*_Z+289)*ln(-(-45*RootOf(9*_Z^2-51*_Z+289)^2*x^2+1224*RootOf(9*_Z^2-51*_Z+289)*(x^3-x^2)^(2/3)+1224*(x^3-x^2)^(1/3)*RootOf(9*_Z^2-51*_Z+289)*x+90*RootOf(9*_Z^2-51*_Z+289)^2*x+1479*RootOf(9*_Z^2-51*_Z+289)*x^2-4335*(x^3-x^2)^(2/3)-4335*x*(x^3-x^2)^(1/3)-1173*RootOf(9*_Z^2-51*_Z+289)*x-5780*x^2+3468*x)/x)+17/9*ln((45*RootOf(9*_Z^2-51*_Z+289)^2*x^2+1224*RootOf(9*_Z^2-51*_Z+289)*(x^3-x^2)^(2/3)+1224*(x^3-x^2)^(1/3)*RootOf(9*_Z^2-51*_Z+289)*x-90*RootOf(9*_Z^2-51*_Z+289)^2*x+969*RootOf(9*_Z^2-51*_Z+289)*x^2-2601*(x^3-x^2)^(2/3)-2601*x*(x^3-x^2)^(1/3)-153*RootOf(9*_Z^2-51*_Z+289)*x-1156*x^2+289*x)/x)-1/3*ln((45*RootOf(9*_Z^2-51*_Z+289)^2*x^2+1224*RootOf(9*_Z^2-51*_Z+289)*(x^3-x^2)^(2/3)+1224*(x^3-x^2)^(1/3)*RootOf(9*_Z^2-51*_Z+289)*x-90*RootOf(9*_Z^2-51*_Z+289)^2*x+969*RootOf(9*_Z^2-51*_Z+289)*x^2-2601*(x^3-x^2)^(2/3)-2601*x*(x^3-x^2)^(1/3)-153*RootOf(9*_Z^2-51*_Z+289)*x-1156*x^2+289*x)/x)*RootOf(9*_Z^2-51*_Z+289)+RootOf(_Z^3-2)*ln(-(9*RootOf(9*RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^4*x^2+RootOf(9*RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^3*x^2-18*RootOf(9*RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^4*x-2*RootOf(9*RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^3*x-72*(x^3-x^2)^(2/3)*RootOf(9*RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2+351*RootOf(_Z^3-2)^2*x^2+39*RootOf(9*RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)*x^2-135*RootOf(_Z^3-2)^2*x-270*(x^3-x^2)^(1/3)*RootOf(_Z^3-2)*x-15*RootOf(9*RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)*x+54*(x^3-x^2)^(1/3)*RootOf(9*RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+_Z^2)*x-162*(x^3-x^2)^(2/3))/x/(1+x))+1/3*RootOf(9*RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+_Z^2)*ln(-(9*RootOf(9*RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^4*x^2+2*RootOf(9*RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^3*x^2-18*RootOf(9*RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^4*x-4*RootOf(9*RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^3*x+72*(x^3-x^2)^(2/3)*RootOf(9*RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2-297*RootOf(_Z^3-2)^2*x^2-66*RootOf(9*RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)*x^2+27*RootOf(_Z^3-2)^2*x+162*(x^3-x^2)^(1/3)*RootOf(_Z^3-2)*x+6*RootOf(9*RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)*x-90*(x^3-x^2)^(1/3)*RootOf(9*RootOf(_Z^3-2)^2+3*_Z*RootOf(_Z^3-2)+_Z^2)*x+270*(x^3-x^2)^(2/3))/x/(1+x))","C"
2687,0,0,60,0.042000," ","int((a*x^4+b)/(x^4-a*x^2-b)/(a*x^4-b*x^2)^(1/4),x)","\[\int \frac{a \,x^{4}+b}{\left(x^{4}-a \,x^{2}-b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^4+b)/(x^4-a*x^2-b)/(a*x^4-b*x^2)^(1/4),x)","F"
2688,0,0,60,0.004000," ","int((a*x^4+b)/(x^4-a*x^2-b)/(a*x^4-b*x^2)^(1/4),x)","\[\int \frac{a \,x^{4}+b}{\left(x^{4}-a \,x^{2}-b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^4+b)/(x^4-a*x^2-b)/(a*x^4-b*x^2)^(1/4),x)","F"
2689,0,0,205,0.020000," ","int(((-2*k^2+1)*x+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(1-d+(-2*k^2+d)*x^2+k^4*x^4),x)","\[\int \frac{\left(-2 k^{2}+1\right) x +k^{2} x^{3}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{1}{3}} \left(1-d +\left(-2 k^{2}+d \right) x^{2}+k^{4} x^{4}\right)}\, dx\]"," ",0,"int(((-2*k^2+1)*x+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(1-d+(-2*k^2+d)*x^2+k^4*x^4),x)","F"
2690,0,0,205,0.026000," ","int(((-k^2+2)*x-2*x^3+k^2*x^5)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(-1+d+(k^2-2*d)*x^2+d*x^4),x)","\[\int \frac{\left(-k^{2}+2\right) x -2 x^{3}+k^{2} x^{5}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{2}{3}} \left(-1+d +\left(k^{2}-2 d \right) x^{2}+d \,x^{4}\right)}\, dx\]"," ",0,"int(((-k^2+2)*x-2*x^3+k^2*x^5)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(-1+d+(k^2-2*d)*x^2+d*x^4),x)","F"
2691,1,31,196,0.044000," ","int(1/x^4/(b+(a*x^2+b^2)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{2}\, \hypergeom \left(\left[-\frac{3}{2}, \frac{1}{4}, \frac{3}{4}\right], \left[-\frac{1}{2}, \frac{3}{2}\right], -\frac{x^{2} a}{b^{2}}\right)}{6 \left(b^{2}\right)^{\frac{1}{4}} x^{3}}$&$31$\\ \hline \end{longtable}"," ",0,"-1/6/(b^2)^(1/4)*2^(1/2)/x^3*hypergeom([-3/2,1/4,3/4],[-1/2,3/2],-x^2*a/b^2)","C"
2692,0,0,208,0.121000," ","int((-a*(a-5*b)-(3*a+5*b)*x+4*x^2)/((-a+x)*(-b+x))^(1/3)/(-a^5+b*d-(-5*a^4+d)*x-10*a^3*x^2+10*a^2*x^3-5*a*x^4+x^5),x)","\[\int \frac{-a \left(a -5 b \right)-\left(3 a +5 b \right) x +4 x^{2}}{\left(\left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{3}} \left(-a^{5}+b d -\left(-5 a^{4}+d \right) x -10 a^{3} x^{2}+10 a^{2} x^{3}-5 a \,x^{4}+x^{5}\right)}\, dx\]"," ",0,"int((-a*(a-5*b)-(3*a+5*b)*x+4*x^2)/((-a+x)*(-b+x))^(1/3)/(-a^5+b*d-(-5*a^4+d)*x-10*a^3*x^2+10*a^2*x^3-5*a*x^4+x^5),x)","F"
2693,1,668,177,0.560000," ","int(x^6*(x^4-x)^(1/2)/(a*x^6+b),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{x \sqrt{x^{4}-x}}{3 a}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{a \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}-\frac{b \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{6} a +b \right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{3}-1\right) \left(-1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{5}+\underline{\hspace{1.25 ex}}\alpha^{4}+\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(1-i \sqrt{3}\right) \sqrt{\frac{x \left(-3+i \sqrt{3}\right)}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{\left(-1+x \right) \left(-1-i \sqrt{3}\right)}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\frac{\underline{\hspace{1.25 ex}}\alpha^{5} a \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, -\frac{i \underline{\hspace{1.25 ex}}\alpha^{5} \sqrt{3}\, a -3 \underline{\hspace{1.25 ex}}\alpha^{5} a +i \sqrt{3}\, b -3 b}{6 b}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{b}\right)}{\underline{\hspace{1.25 ex}}\alpha^{4} \left(a +b \right) \left(-3+i \sqrt{3}\right) \sqrt{x \left(-1+x \right) \left(i \sqrt{3}+2 x +1\right) \left(1+2 x -i \sqrt{3}\right)}}\right)}{3 a}$&$668$\\ default&$\frac{\frac{x \sqrt{x^{4}-x}}{3}-\frac{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}}{a}+\frac{b \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{6} a +b \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{3}+1\right) \left(-1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{5}+\underline{\hspace{1.25 ex}}\alpha^{4}+\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(1-i \sqrt{3}\right) \sqrt{\frac{x \left(-3+i \sqrt{3}\right)}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{\left(-1+x \right) \left(-1-i \sqrt{3}\right)}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\frac{\underline{\hspace{1.25 ex}}\alpha^{5} a \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, -\frac{i \underline{\hspace{1.25 ex}}\alpha^{5} \sqrt{3}\, a -3 \underline{\hspace{1.25 ex}}\alpha^{5} a +i \sqrt{3}\, b -3 b}{6 b}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{b}\right)}{\underline{\hspace{1.25 ex}}\alpha^{4} \left(a +b \right) \left(-3+i \sqrt{3}\right) \sqrt{x \left(-1+x \right) \left(i \sqrt{3}+2 x +1\right) \left(1+2 x -i \sqrt{3}\right)}}\right)}{3 a}$&$669$\\ risch&$\frac{x^{2} \left(x^{3}-1\right)}{3 a \sqrt{x \left(x^{3}-1\right)}}-\frac{\frac{2 \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(-1+x \right)^{2} \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \frac{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x \left(-1+x \right) \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}}-\frac{2 b \sqrt{4}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{6} a +b \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{3}+1\right) \left(-1+x \right)^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{5}+\underline{\hspace{1.25 ex}}\alpha^{4}+\underline{\hspace{1.25 ex}}\alpha^{3}+\underline{\hspace{1.25 ex}}\alpha^{2}+\underline{\hspace{1.25 ex}}\alpha  +1\right) \left(1-i \sqrt{3}\right) \sqrt{\frac{x \left(-3+i \sqrt{3}\right)}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \sqrt{\frac{i \sqrt{3}+2 x +1}{\left(-1+x \right) \left(-1-i \sqrt{3}\right)}}\, \sqrt{\frac{1+2 x -i \sqrt{3}}{\left(-1+x \right) \left(-1+i \sqrt{3}\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\frac{\underline{\hspace{1.25 ex}}\alpha^{5} a \EllipticPi \left(\sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-1+x \right)}}, -\frac{i \underline{\hspace{1.25 ex}}\alpha^{5} \sqrt{3}\, a -3 \underline{\hspace{1.25 ex}}\alpha^{5} a +i \sqrt{3}\, b -3 b}{6 b}, \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)}{b}\right)}{\underline{\hspace{1.25 ex}}\alpha^{4} \left(a +b \right) \left(-3+i \sqrt{3}\right) \sqrt{x \left(-1+x \right) \left(i \sqrt{3}+2 x +1\right) \left(1+2 x -i \sqrt{3}\right)}}\right)}{3}}{2 a}$&$677$\\ \hline \end{longtable}"," ",0,"1/3*x*(x^4-x)^(1/2)/a-1/a*(1/2-1/2*I*3^(1/2))*((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2)*(-1+x)^2*((x+1/2+1/2*I*3^(1/2))/(-1/2-1/2*I*3^(1/2))/(-1+x))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2)/(-3/2+1/2*I*3^(1/2))/(x*(-1+x)*(x+1/2+1/2*I*3^(1/2))*(x+1/2-1/2*I*3^(1/2)))^(1/2)*(EllipticF(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-EllipticPi(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),(-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)),((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)))-1/3*b/a*4^(1/2)*sum((_alpha^3-1)/_alpha^4*(-1+x)^2*(_alpha^5+_alpha^4+_alpha^3+_alpha^2+_alpha+1)/(a+b)*(1-I*3^(1/2))*(x/(-1+x)*(-3+I*3^(1/2))/(-1+I*3^(1/2)))^(1/2)*(1/(-1+x)*(I*3^(1/2)+2*x+1)/(-1-I*3^(1/2)))^(1/2)*(1/(-1+x)*(1+2*x-I*3^(1/2))/(-1+I*3^(1/2)))^(1/2)/(-3+I*3^(1/2))/(x*(-1+x)*(I*3^(1/2)+2*x+1)*(1+2*x-I*3^(1/2)))^(1/2)*(EllipticF(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))+_alpha^5*a/b*EllipticPi(((-3/2+1/2*I*3^(1/2))*x/(-1/2+1/2*I*3^(1/2))/(-1+x))^(1/2),-1/6*(I*_alpha^5*3^(1/2)*a-3*_alpha^5*a+I*3^(1/2)*b-3*b)/b,((3/2+1/2*I*3^(1/2))*(1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))),_alpha=RootOf(_Z^6*a+b))","C"
2694,1,678,184,0.319000," ","int((a^6*x^6+b^6)/(a^2*x^3-b^2*x)^(1/2)/(a^6*x^6-b^6),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\frac{2 x}{3 \sqrt{\left(x^{2}-\frac{b^{2}}{a^{2}}\right) a^{2} x}}+\frac{2 b \sqrt{1+\frac{a x}{b}}\, \sqrt{2-\frac{2 a x}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{3 a \sqrt{a^{2} x^{3}-b^{2} x}}-\frac{a \sqrt{2}\, \sqrt{\frac{a x +b}{b}}\, \sqrt{-\frac{a x -b}{b}}\, \sqrt{-\frac{a x}{b}}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}-\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{\frac{a x +b}{b}}, -\frac{\underline{\hspace{1.25 ex}}\alpha  a -2 b}{3 b}, \frac{\sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha^{2}}{2 \underline{\hspace{1.25 ex}}\alpha  a -b}\right)}{9 \sqrt{x \left(a^{2} x^{2}-b^{2}\right)}}+\frac{4 \sqrt{2}\, \sqrt{\frac{a x +b}{b}}\, \sqrt{-\frac{a x -b}{b}}\, \sqrt{-\frac{a x}{b}}\, b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}-\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{\frac{a x +b}{b}}, -\frac{\underline{\hspace{1.25 ex}}\alpha  a -2 b}{3 b}, \frac{\sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha }{2 \underline{\hspace{1.25 ex}}\alpha  a -b}\right)}{9 \sqrt{x \left(a^{2} x^{2}-b^{2}\right)}}-\frac{4 \sqrt{2}\, \sqrt{\frac{a x +b}{b}}\, \sqrt{-\frac{a x -b}{b}}\, \sqrt{-\frac{a x}{b}}\, b^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}-\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{\frac{a x +b}{b}}, -\frac{\underline{\hspace{1.25 ex}}\alpha  a -2 b}{3 b}, \frac{\sqrt{2}}{2}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  a -b}\right)}{9 a \sqrt{x \left(a^{2} x^{2}-b^{2}\right)}}+\frac{\sqrt{2}\, \sqrt{\frac{a x +b}{b}}\, \sqrt{-\frac{a x -b}{b}}\, \sqrt{-\frac{a x}{b}}\, a \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}+\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \EllipticPi \left(\sqrt{\frac{a x +b}{b}}, -\frac{\underline{\hspace{1.25 ex}}\alpha  a}{b}, \frac{\sqrt{2}}{2}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  a +b}\right)}{3 \sqrt{x \left(a^{2} x^{2}-b^{2}\right)}}+\frac{2 \sqrt{2}\, \sqrt{\frac{a x +b}{b}}\, \sqrt{-\frac{a x -b}{b}}\, \sqrt{-\frac{a x}{b}}\, b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}+\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \EllipticPi \left(\sqrt{\frac{a x +b}{b}}, -\frac{\underline{\hspace{1.25 ex}}\alpha  a}{b}, \frac{\sqrt{2}}{2}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  a +b}\right)}{3 \sqrt{x \left(a^{2} x^{2}-b^{2}\right)}}$&$678$\\ default&$\frac{b \sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{2 \left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}-b^{2} x}}-\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}-\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha  a +2 b \right) \left(\underline{\hspace{1.25 ex}}\alpha  a -2 b \right) \sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{\left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, -\frac{\underline{\hspace{1.25 ex}}\alpha  a -2 b}{3 b}, \frac{\sqrt{2}}{2}\right)}{\left(2 \underline{\hspace{1.25 ex}}\alpha  a -b \right) \sqrt{x \left(a^{2} x^{2}-b^{2}\right)}}\right)}{9 a}-\frac{b \left(-\frac{a^{2} x^{2}-a b x}{b^{2} a \sqrt{\left(x +\frac{b}{a}\right) \left(a^{2} x^{2}-a b x \right)}}+\frac{\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{2 \left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{2 a \sqrt{a^{2} x^{3}-b^{2} x}}+\frac{\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{2 \left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \left(-\frac{2 b \EllipticE \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a}+\frac{b \EllipticF \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a}\right)}{2 b \sqrt{a^{2} x^{3}-b^{2} x}}\right)}{3}+\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}+\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha  a -2 b \right) \underline{\hspace{1.25 ex}}\alpha  \sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{\left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, -\frac{\underline{\hspace{1.25 ex}}\alpha  a}{b}, \frac{\sqrt{2}}{2}\right)}{\left(2 \underline{\hspace{1.25 ex}}\alpha  a +b \right) \sqrt{x \left(a^{2} x^{2}-b^{2}\right)}}\right)}{3}+\frac{b \left(-\frac{a^{2} x^{2}+a b x}{b^{2} a \sqrt{\left(x -\frac{b}{a}\right) \left(a^{2} x^{2}+a b x \right)}}-\frac{\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{2 \left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{2 a \sqrt{a^{2} x^{3}-b^{2} x}}+\frac{\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{2 \left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \left(-\frac{2 b \EllipticE \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a}+\frac{b \EllipticF \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a}\right)}{2 b \sqrt{a^{2} x^{3}-b^{2} x}}\right)}{3}$&$828$\\ \hline \end{longtable}"," ",0,"-2/3*x/((x^2-b^2/a^2)*a^2*x)^(1/2)+2/3*b/a*(1+a*x/b)^(1/2)*(2-2*a*x/b)^(1/2)*(-a*x/b)^(1/2)/(a^2*x^3-b^2*x)^(1/2)*EllipticF(((x+b/a)/b*a)^(1/2),1/2*2^(1/2))-1/9*a*2^(1/2)*((a*x+b)/b)^(1/2)*(-(a*x-b)/b)^(1/2)*(-a*x/b)^(1/2)/(x*(a^2*x^2-b^2))^(1/2)*sum(1/(2*_alpha*a-b)*EllipticPi(((a*x+b)/b)^(1/2),-1/3*(_alpha*a-2*b)/b,1/2*2^(1/2))*_alpha^2,_alpha=RootOf(_Z^2*a^2-_Z*a*b+b^2))+4/9*2^(1/2)*((a*x+b)/b)^(1/2)*(-(a*x-b)/b)^(1/2)*(-a*x/b)^(1/2)/(x*(a^2*x^2-b^2))^(1/2)*b*sum(1/(2*_alpha*a-b)*EllipticPi(((a*x+b)/b)^(1/2),-1/3*(_alpha*a-2*b)/b,1/2*2^(1/2))*_alpha,_alpha=RootOf(_Z^2*a^2-_Z*a*b+b^2))-4/9/a*2^(1/2)*((a*x+b)/b)^(1/2)*(-(a*x-b)/b)^(1/2)*(-a*x/b)^(1/2)/(x*(a^2*x^2-b^2))^(1/2)*b^2*sum(1/(2*_alpha*a-b)*EllipticPi(((a*x+b)/b)^(1/2),-1/3*(_alpha*a-2*b)/b,1/2*2^(1/2)),_alpha=RootOf(_Z^2*a^2-_Z*a*b+b^2))+1/3*2^(1/2)*((a*x+b)/b)^(1/2)*(-(a*x-b)/b)^(1/2)*(-a*x/b)^(1/2)/(x*(a^2*x^2-b^2))^(1/2)*a*sum(1/(2*_alpha*a+b)*_alpha^2*EllipticPi(((a*x+b)/b)^(1/2),-_alpha/b*a,1/2*2^(1/2)),_alpha=RootOf(_Z^2*a^2+_Z*a*b+b^2))+2/3*2^(1/2)*((a*x+b)/b)^(1/2)*(-(a*x-b)/b)^(1/2)*(-a*x/b)^(1/2)/(x*(a^2*x^2-b^2))^(1/2)*b*sum(1/(2*_alpha*a+b)*_alpha*EllipticPi(((a*x+b)/b)^(1/2),-_alpha/b*a,1/2*2^(1/2)),_alpha=RootOf(_Z^2*a^2+_Z*a*b+b^2))","C"
2695,0,0,207,0.172000," ","int((a^2*b-2*a^2*x+(2*a-b)*x^2)/(x*(-a+x)*(-b+x))^(2/3)/(a^2+(b*d-2*a)*x+(1-d)*x^2),x)","\[\int \frac{a^{2} b -2 a^{2} x +\left(2 a -b \right) x^{2}}{\left(x \left(-a +x \right) \left(-b +x \right)\right)^{\frac{2}{3}} \left(a^{2}+\left(b d -2 a \right) x +\left(1-d \right) x^{2}\right)}\, dx\]"," ",0,"int((a^2*b-2*a^2*x+(2*a-b)*x^2)/(x*(-a+x)*(-b+x))^(2/3)/(a^2+(b*d-2*a)*x+(1-d)*x^2),x)","F"
2696,1,681,189,0.300000," ","int((a^6*x^6+b^6)/(a^2*x^3+b^2*x)^(1/2)/(a^6*x^6-b^6),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{i b \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticF \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}+b^{2} x}}+\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}-\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha  a +2 b \right) \left(i \underline{\hspace{1.25 ex}}\alpha  a -i b +b \right) \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, -\frac{\underline{\hspace{1.25 ex}}\alpha  a -i b -b}{b}, \frac{\sqrt{2}}{2}\right)}{\left(2 \underline{\hspace{1.25 ex}}\alpha  a -b \right) \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}\right)}{3 a}-\frac{i b^{2} \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, -\frac{i b}{a \left(-\frac{i b}{a}+\frac{b}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{3 a^{2} \sqrt{a^{2} x^{3}+b^{2} x}\, \left(-\frac{i b}{a}+\frac{b}{a}\right)}+\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}+\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha  a -2 b \right) \left(i \underline{\hspace{1.25 ex}}\alpha  a +i b +b \right) \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, \frac{\underline{\hspace{1.25 ex}}\alpha  a -i b +b}{b}, \frac{\sqrt{2}}{2}\right)}{\left(2 \underline{\hspace{1.25 ex}}\alpha  a +b \right) \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}\right)}{3 a}+\frac{i b^{2} \sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}\, \sqrt{2}\, \sqrt{\frac{i \left(x -\frac{i b}{a}\right) a}{b}}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, -\frac{i b}{a \left(-\frac{i b}{a}-\frac{b}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{3 a^{2} \sqrt{a^{2} x^{3}+b^{2} x}\, \left(-\frac{i b}{a}-\frac{b}{a}\right)}$&$681$\\ elliptic&$\frac{i b \sqrt{-\frac{i x a}{b}+1}\, \sqrt{2}\, \sqrt{\frac{i x a}{b}+1}\, \sqrt{\frac{i x a}{b}}\, \EllipticF \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}+b^{2} x}}-\frac{a \sqrt{2}\, \sqrt{-\frac{i \left(a x +i b \right)}{b}}\, \sqrt{-\frac{i \left(-a x +i b \right)}{b}}\, \sqrt{\frac{i x a}{b}}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}-\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-\frac{i \left(a x +i b \right)}{b}}, \frac{-\underline{\hspace{1.25 ex}}\alpha  a +i b +b}{b}, \frac{\sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha^{2}}{2 \underline{\hspace{1.25 ex}}\alpha  a -b}\right)}{3 \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}+\frac{\sqrt{2}\, \sqrt{-\frac{i \left(a x +i b \right)}{b}}\, \sqrt{-\frac{i \left(-a x +i b \right)}{b}}\, \sqrt{\frac{i x a}{b}}\, b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}-\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-\frac{i \left(a x +i b \right)}{b}}, \frac{-\underline{\hspace{1.25 ex}}\alpha  a +i b +b}{b}, \frac{\sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha }{2 \underline{\hspace{1.25 ex}}\alpha  a -b}\right)}{\sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}-\frac{2 \sqrt{2}\, \sqrt{-\frac{i \left(a x +i b \right)}{b}}\, \sqrt{-\frac{i \left(-a x +i b \right)}{b}}\, \sqrt{\frac{i x a}{b}}\, b^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}-\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-\frac{i \left(a x +i b \right)}{b}}, \frac{-\underline{\hspace{1.25 ex}}\alpha  a +i b +b}{b}, \frac{\sqrt{2}}{2}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  a -b}\right)}{3 a \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}+\frac{i \sqrt{2}\, \sqrt{-\frac{i \left(a x +i b \right)}{b}}\, \sqrt{-\frac{i \left(-a x +i b \right)}{b}}\, \sqrt{\frac{i x a}{b}}\, b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}-\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-\frac{i \left(a x +i b \right)}{b}}, \frac{-\underline{\hspace{1.25 ex}}\alpha  a +i b +b}{b}, \frac{\sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha }{2 \underline{\hspace{1.25 ex}}\alpha  a -b}\right)}{3 \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}-\frac{2 i \sqrt{2}\, \sqrt{-\frac{i \left(a x +i b \right)}{b}}\, \sqrt{-\frac{i \left(-a x +i b \right)}{b}}\, \sqrt{\frac{i x a}{b}}\, b^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}-\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-\frac{i \left(a x +i b \right)}{b}}, \frac{-\underline{\hspace{1.25 ex}}\alpha  a +i b +b}{b}, \frac{\sqrt{2}}{2}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  a -b}\right)}{3 a \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}-\frac{i b^{2} \sqrt{-\frac{i x a}{b}+1}\, \sqrt{2}\, \sqrt{\frac{i x a}{b}+1}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, -\frac{i b}{a \left(-\frac{i b}{a}+b \right)}, \frac{\sqrt{2}}{2}\right)}{3 a \sqrt{a^{2} x^{3}+b^{2} x}\, \left(-\frac{i b}{a}+b \right)}-\frac{a \sqrt{2}\, \sqrt{-\frac{i \left(a x +i b \right)}{b}}\, \sqrt{-\frac{i \left(-a x +i b \right)}{b}}\, \sqrt{\frac{i x a}{b}}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}+\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-\frac{i \left(a x +i b \right)}{b}}, -\frac{-\underline{\hspace{1.25 ex}}\alpha  a +i b -b}{b}, \frac{\sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha^{2}}{2 \underline{\hspace{1.25 ex}}\alpha  a +b}\right)}{3 \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}-\frac{\sqrt{2}\, \sqrt{-\frac{i \left(a x +i b \right)}{b}}\, \sqrt{-\frac{i \left(-a x +i b \right)}{b}}\, \sqrt{\frac{i x a}{b}}\, b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}+\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-\frac{i \left(a x +i b \right)}{b}}, -\frac{-\underline{\hspace{1.25 ex}}\alpha  a +i b -b}{b}, \frac{\sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha }{2 \underline{\hspace{1.25 ex}}\alpha  a +b}\right)}{\sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}-\frac{2 \sqrt{2}\, \sqrt{-\frac{i \left(a x +i b \right)}{b}}\, \sqrt{-\frac{i \left(-a x +i b \right)}{b}}\, \sqrt{\frac{i x a}{b}}\, b^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}+\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-\frac{i \left(a x +i b \right)}{b}}, -\frac{-\underline{\hspace{1.25 ex}}\alpha  a +i b -b}{b}, \frac{\sqrt{2}}{2}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  a +b}\right)}{3 a \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}+\frac{i \sqrt{2}\, \sqrt{-\frac{i \left(a x +i b \right)}{b}}\, \sqrt{-\frac{i \left(-a x +i b \right)}{b}}\, \sqrt{\frac{i x a}{b}}\, b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}+\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-\frac{i \left(a x +i b \right)}{b}}, -\frac{-\underline{\hspace{1.25 ex}}\alpha  a +i b -b}{b}, \frac{\sqrt{2}}{2}\right) \underline{\hspace{1.25 ex}}\alpha }{2 \underline{\hspace{1.25 ex}}\alpha  a +b}\right)}{3 \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}+\frac{2 i \sqrt{2}\, \sqrt{-\frac{i \left(a x +i b \right)}{b}}\, \sqrt{-\frac{i \left(-a x +i b \right)}{b}}\, \sqrt{\frac{i x a}{b}}\, b^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}+\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{-\frac{i \left(a x +i b \right)}{b}}, -\frac{-\underline{\hspace{1.25 ex}}\alpha  a +i b -b}{b}, \frac{\sqrt{2}}{2}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  a +b}\right)}{3 a \sqrt{x \left(a^{2} x^{2}+b^{2}\right)}}+\frac{i b^{2} \sqrt{-\frac{i x a}{b}+1}\, \sqrt{2}\, \sqrt{\frac{i x a}{b}+1}\, \sqrt{\frac{i x a}{b}}\, \EllipticPi \left(\sqrt{-\frac{i \left(x +\frac{i b}{a}\right) a}{b}}, -\frac{i b}{a \left(-\frac{i b}{a}-b \right)}, \frac{\sqrt{2}}{2}\right)}{3 a \sqrt{a^{2} x^{3}+b^{2} x}\, \left(-\frac{i b}{a}-b \right)}$&$1660$\\ \hline \end{longtable}"," ",0,"I*b/a*(-I*(x+I*b/a)/b*a)^(1/2)*2^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(a^2*x^3+b^2*x)^(1/2)*EllipticF((-I*(x+I*b/a)/b*a)^(1/2),1/2*2^(1/2))+1/3*I/a*2^(1/2)*sum((-_alpha*a+2*b)/(2*_alpha*a-b)*(I*_alpha*a-I*b+b)*(-I*(x+I*b/a)/b*a)^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(x*(a^2*x^2+b^2))^(1/2)*EllipticPi((-I*(x+I*b/a)/b*a)^(1/2),-(_alpha*a-b-I*b)/b,1/2*2^(1/2)),_alpha=RootOf(_Z^2*a^2-_Z*a*b+b^2))-1/3*I*b^2/a^2*(-I*(x+I*b/a)/b*a)^(1/2)*2^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(a^2*x^3+b^2*x)^(1/2)/(-I*b/a+b/a)*EllipticPi((-I*(x+I*b/a)/b*a)^(1/2),-I*b/a/(-I*b/a+b/a),1/2*2^(1/2))+1/3*I/a*2^(1/2)*sum((-_alpha*a-2*b)/(2*_alpha*a+b)*(I*_alpha*a+I*b+b)*(-I*(x+I*b/a)/b*a)^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(x*(a^2*x^2+b^2))^(1/2)*EllipticPi((-I*(x+I*b/a)/b*a)^(1/2),(_alpha*a+b-I*b)/b,1/2*2^(1/2)),_alpha=RootOf(_Z^2*a^2+_Z*a*b+b^2))+1/3*I*b^2/a^2*(-I*(x+I*b/a)/b*a)^(1/2)*2^(1/2)*(I*(x-I*b/a)/b*a)^(1/2)*(I*x/b*a)^(1/2)/(a^2*x^3+b^2*x)^(1/2)/(-I*b/a-b/a)*EllipticPi((-I*(x+I*b/a)/b*a)^(1/2),-I*b/a/(-I*b/a-b/a),1/2*2^(1/2))","C"
2697,0,0,205,0.057000," ","int((5*x^7+2)*(x^8-x^3-x)^(1/3)/(x^7-1)/(x^7+x^2-1),x)","\[\int \frac{\left(5 x^{7}+2\right) \left(x^{8}-x^{3}-x \right)^{\frac{1}{3}}}{\left(x^{7}-1\right) \left(x^{7}+x^{2}-1\right)}\, dx\]"," ",0,"int((5*x^7+2)*(x^8-x^3-x)^(1/3)/(x^7-1)/(x^7+x^2-1),x)","F"
2698,1,468,185,7.395000," ","int(x^6*(x^3-4)/(x^3-1)^(3/4)/(x^8+x^6-2*x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{8}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{11} x^{4}+\RootOf \left(\textit{\_Z}^{8}+1\right)^{7} x^{3}-\RootOf \left(\textit{\_Z}^{8}+1\right)^{7}+2 \left(x^{3}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{2} x^{3}-2 \sqrt{x^{3}-1}\, \RootOf \left(\textit{\_Z}^{8}+1\right) x^{2}+2 \left(x^{3}-1\right)^{\frac{3}{4}} x}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}-x^{3}+1}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{3} \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{8}+1\right)^{9} x^{4}+2 \left(x^{3}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{6} x^{3}+\RootOf \left(\textit{\_Z}^{8}+1\right)^{5} x^{3}-2 \sqrt{x^{3}-1}\, \RootOf \left(\textit{\_Z}^{8}+1\right)^{3} x^{2}-\RootOf \left(\textit{\_Z}^{8}+1\right)^{5}+2 \left(x^{3}-1\right)^{\frac{3}{4}} x}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}+x^{3}-1}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{7} \ln \left(-\frac{-2 \sqrt{x^{3}-1}\, \RootOf \left(\textit{\_Z}^{8}+1\right)^{7} x^{2}-2 \left(x^{3}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{6} x^{3}-\RootOf \left(\textit{\_Z}^{8}+1\right)^{5} x^{4}+2 \left(x^{3}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{8}+1\right) x^{3}-\RootOf \left(\textit{\_Z}^{8}+1\right)}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}+x^{3}-1}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{5} \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{8}+1\right)^{7} x^{4}+2 \sqrt{x^{3}-1}\, \RootOf \left(\textit{\_Z}^{8}+1\right)^{5} x^{2}-2 \left(x^{3}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{2} x^{3}-\RootOf \left(\textit{\_Z}^{8}+1\right)^{3} x^{3}+2 \left(x^{3}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{8}+1\right)^{3}}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}-x^{3}+1}\right)}{2}$&$468$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^8+1)*ln(-(RootOf(_Z^8+1)^11*x^4+RootOf(_Z^8+1)^7*x^3-RootOf(_Z^8+1)^7+2*(x^3-1)^(1/4)*RootOf(_Z^8+1)^2*x^3-2*(x^3-1)^(1/2)*RootOf(_Z^8+1)*x^2+2*(x^3-1)^(3/4)*x)/(RootOf(_Z^8+1)^4*x^4-x^3+1))+1/2*RootOf(_Z^8+1)^3*ln(-(-RootOf(_Z^8+1)^9*x^4+2*(x^3-1)^(1/4)*RootOf(_Z^8+1)^6*x^3+RootOf(_Z^8+1)^5*x^3-2*(x^3-1)^(1/2)*RootOf(_Z^8+1)^3*x^2-RootOf(_Z^8+1)^5+2*(x^3-1)^(3/4)*x)/(RootOf(_Z^8+1)^4*x^4+x^3-1))+1/2*RootOf(_Z^8+1)^7*ln(-(-2*(x^3-1)^(1/2)*RootOf(_Z^8+1)^7*x^2-2*(x^3-1)^(1/4)*RootOf(_Z^8+1)^6*x^3-RootOf(_Z^8+1)^5*x^4+2*(x^3-1)^(3/4)*x+RootOf(_Z^8+1)*x^3-RootOf(_Z^8+1))/(RootOf(_Z^8+1)^4*x^4+x^3-1))-1/2*RootOf(_Z^8+1)^5*ln(-(-RootOf(_Z^8+1)^7*x^4+2*(x^3-1)^(1/2)*RootOf(_Z^8+1)^5*x^2-2*(x^3-1)^(1/4)*RootOf(_Z^8+1)^2*x^3-RootOf(_Z^8+1)^3*x^3+2*(x^3-1)^(3/4)*x+RootOf(_Z^8+1)^3)/(RootOf(_Z^8+1)^4*x^4-x^3+1))","C"
2699,1,462,185,12.576000," ","int(x^6*(x^5+4)/(x^5-1)^(3/4)/(x^10+x^8-2*x^5+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{3} \ln \left(\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{9} x^{4}+2 \left(x^{5}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{6} x^{3}-\RootOf \left(\textit{\_Z}^{8}+1\right)^{5} x^{5}+2 \sqrt{x^{5}-1}\, \RootOf \left(\textit{\_Z}^{8}+1\right)^{3} x^{2}+\RootOf \left(\textit{\_Z}^{8}+1\right)^{5}+2 \left(x^{5}-1\right)^{\frac{3}{4}} x}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}+x^{5}-1}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{8}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{11} x^{4}+\RootOf \left(\textit{\_Z}^{8}+1\right)^{7} x^{5}-\RootOf \left(\textit{\_Z}^{8}+1\right)^{7}+2 \left(x^{5}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{2} x^{3}-2 \sqrt{x^{5}-1}\, \RootOf \left(\textit{\_Z}^{8}+1\right) x^{2}+2 \left(x^{5}-1\right)^{\frac{3}{4}} x}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}-x^{5}+1}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{5} \ln \left(\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{7} x^{4}-2 \sqrt{x^{5}-1}\, \RootOf \left(\textit{\_Z}^{8}+1\right)^{5} x^{2}+\RootOf \left(\textit{\_Z}^{8}+1\right)^{3} x^{5}-2 \left(x^{5}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{2} x^{3}+2 \left(x^{5}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{8}+1\right)^{3}}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}-x^{5}+1}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{8}+1\right)^{7} \ln \left(\frac{-2 \sqrt{x^{5}-1}\, \RootOf \left(\textit{\_Z}^{8}+1\right)^{7} x^{2}-2 \left(x^{5}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+1\right)^{6} x^{3}-\RootOf \left(\textit{\_Z}^{8}+1\right)^{5} x^{4}+\RootOf \left(\textit{\_Z}^{8}+1\right) x^{5}+2 \left(x^{5}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{8}+1\right)}{\RootOf \left(\textit{\_Z}^{8}+1\right)^{4} x^{4}+x^{5}-1}\right)}{2}$&$462$\\ \hline \end{longtable}"," ",0,"1/2*RootOf(_Z^8+1)^3*ln((RootOf(_Z^8+1)^9*x^4+2*(x^5-1)^(1/4)*RootOf(_Z^8+1)^6*x^3-RootOf(_Z^8+1)^5*x^5+2*(x^5-1)^(1/2)*RootOf(_Z^8+1)^3*x^2+RootOf(_Z^8+1)^5+2*(x^5-1)^(3/4)*x)/(RootOf(_Z^8+1)^4*x^4+x^5-1))-1/2*RootOf(_Z^8+1)*ln((RootOf(_Z^8+1)^11*x^4+RootOf(_Z^8+1)^7*x^5-RootOf(_Z^8+1)^7+2*(x^5-1)^(1/4)*RootOf(_Z^8+1)^2*x^3-2*(x^5-1)^(1/2)*RootOf(_Z^8+1)*x^2+2*(x^5-1)^(3/4)*x)/(RootOf(_Z^8+1)^4*x^4-x^5+1))-1/2*RootOf(_Z^8+1)^5*ln((RootOf(_Z^8+1)^7*x^4-2*(x^5-1)^(1/2)*RootOf(_Z^8+1)^5*x^2+RootOf(_Z^8+1)^3*x^5-2*(x^5-1)^(1/4)*RootOf(_Z^8+1)^2*x^3+2*(x^5-1)^(3/4)*x-RootOf(_Z^8+1)^3)/(RootOf(_Z^8+1)^4*x^4-x^5+1))-1/2*RootOf(_Z^8+1)^7*ln((-2*(x^5-1)^(1/2)*RootOf(_Z^8+1)^7*x^2-2*(x^5-1)^(1/4)*RootOf(_Z^8+1)^6*x^3-RootOf(_Z^8+1)^5*x^4+RootOf(_Z^8+1)*x^5+2*(x^5-1)^(3/4)*x-RootOf(_Z^8+1))/(RootOf(_Z^8+1)^4*x^4+x^5-1))","C"
2700,1,226,84,0.470000," ","int((a*x+b)^(1/2)*(f*x^2-g)/(d*x^2+e)/(c+(a*x+b)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\frac{4 f \left(\frac{\left(c +\sqrt{a x +b}\right)^{\frac{5}{2}}}{5}-\frac{2 c \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}+c^{2} \sqrt{c +\sqrt{a x +b}}\right)}{d}-\frac{a^{2} \left(\munderset{\textit{\_R} =\RootOf \left(d \,\textit{\_Z}^{8}-4 c d \,\textit{\_Z}^{6}+\left(6 c^{2} d -2 b d \right) \textit{\_Z}^{4}+\left(-4 c^{3} d +4 b c d \right) \textit{\_Z}^{2}+c^{4} d -2 b \,c^{2} d +a^{2} e +b^{2} d \right)}{\sum}\frac{\left(\textit{\_R}^{4} \left(d g +e f \right)+2 c \left(-d g -e f \right) \textit{\_R}^{2}+c^{2} d g +c^{2} e f \right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5} c +3 \textit{\_R}^{3} c^{2}-\textit{\_R}^{3} b -\textit{\_R} \,c^{3}+\textit{\_R} b c}\right)}{2 d^{2}}}{a}$&$226$\\ default&$\frac{\frac{4 f \left(\frac{\left(c +\sqrt{a x +b}\right)^{\frac{5}{2}}}{5}-\frac{2 c \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}+c^{2} \sqrt{c +\sqrt{a x +b}}\right)}{d}-\frac{a^{2} \left(\munderset{\textit{\_R} =\RootOf \left(d \,\textit{\_Z}^{8}-4 c d \,\textit{\_Z}^{6}+\left(6 c^{2} d -2 b d \right) \textit{\_Z}^{4}+\left(-4 c^{3} d +4 b c d \right) \textit{\_Z}^{2}+c^{4} d -2 b \,c^{2} d +a^{2} e +b^{2} d \right)}{\sum}\frac{\left(\textit{\_R}^{4} \left(d g +e f \right)+2 c \left(-d g -e f \right) \textit{\_R}^{2}+c^{2} d g +c^{2} e f \right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5} c +3 \textit{\_R}^{3} c^{2}-\textit{\_R}^{3} b -\textit{\_R} \,c^{3}+\textit{\_R} b c}\right)}{2 d^{2}}}{a}$&$226$\\ \hline \end{longtable}"," ",0,"2/a*(2*f/d*(1/5*(c+(a*x+b)^(1/2))^(5/2)-2/3*c*(c+(a*x+b)^(1/2))^(3/2)+c^2*(c+(a*x+b)^(1/2))^(1/2))-1/4*a^2/d^2*sum((_R^4*(d*g+e*f)+2*c*(-d*g-e*f)*_R^2+c^2*d*g+c^2*e*f)/(_R^7-3*_R^5*c+3*_R^3*c^2-_R^3*b-_R*c^3+_R*b*c)*ln((c+(a*x+b)^(1/2))^(1/2)-_R),_R=RootOf(d*_Z^8-4*c*d*_Z^6+(6*c^2*d-2*b*d)*_Z^4+(-4*c^3*d+4*b*c*d)*_Z^2+c^4*d-2*b*c^2*d+a^2*e+b^2*d)))","B"
2701,0,0,191,0.049000," ","int((x^4+1)^(1/2)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^2+1),x)","\[\int \frac{\sqrt{x^{4}+1}\, \sqrt{x^{2}+\sqrt{x^{4}+1}}}{x^{2}+1}\, dx\]"," ",0,"int((x^4+1)^(1/2)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^2+1),x)","F"
2702,1,128,60,0.087000," ","int(x/(x^2-(1+x)^(1/2)*(1+(1+x)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+\textit{\_Z} -1\right)}{\sum}\frac{\left(8 \textit{\_R}^{4}+6 \textit{\_R}^{3}-12 \textit{\_R}^{2}-5 \textit{\_R} +1\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{5 \textit{\_R}^{4}+4 \textit{\_R}^{3}-6 \textit{\_R}^{2}-2 \textit{\_R} +1}\right)}{11}+\frac{6 \ln \left(\sqrt{1+x}-\sqrt{1+\sqrt{1+x}}\right)}{11}-\frac{4 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}-1\right) \sqrt{5}}{5}\right)}{55}$&$128$\\ default&$\frac{4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+\textit{\_Z} -1\right)}{\sum}\frac{\left(8 \textit{\_R}^{4}+6 \textit{\_R}^{3}-12 \textit{\_R}^{2}-5 \textit{\_R} +1\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{5 \textit{\_R}^{4}+4 \textit{\_R}^{3}-6 \textit{\_R}^{2}-2 \textit{\_R} +1}\right)}{11}+\frac{6 \ln \left(\sqrt{1+x}-\sqrt{1+\sqrt{1+x}}\right)}{11}-\frac{4 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}-1\right) \sqrt{5}}{5}\right)}{55}$&$128$\\ \hline \end{longtable}"," ",0,"4/11*sum((8*_R^4+6*_R^3-12*_R^2-5*_R+1)/(5*_R^4+4*_R^3-6*_R^2-2*_R+1)*ln((1+(1+x)^(1/2))^(1/2)-_R),_R=RootOf(_Z^5+_Z^4-2*_Z^3-_Z^2+_Z-1))+6/11*ln((1+x)^(1/2)-(1+(1+x)^(1/2))^(1/2))-4/55*5^(1/2)*arctanh(1/5*(2*(1+(1+x)^(1/2))^(1/2)-1)*5^(1/2))","B"
2703,1,128,60,0.082000," ","int(x/(x^2-(1+x)^(1/2)*(1+(1+x)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+\textit{\_Z} -1\right)}{\sum}\frac{\left(8 \textit{\_R}^{4}+6 \textit{\_R}^{3}-12 \textit{\_R}^{2}-5 \textit{\_R} +1\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{5 \textit{\_R}^{4}+4 \textit{\_R}^{3}-6 \textit{\_R}^{2}-2 \textit{\_R} +1}\right)}{11}+\frac{6 \ln \left(\sqrt{1+x}-\sqrt{1+\sqrt{1+x}}\right)}{11}-\frac{4 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}-1\right) \sqrt{5}}{5}\right)}{55}$&$128$\\ default&$\frac{4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+\textit{\_Z} -1\right)}{\sum}\frac{\left(8 \textit{\_R}^{4}+6 \textit{\_R}^{3}-12 \textit{\_R}^{2}-5 \textit{\_R} +1\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{5 \textit{\_R}^{4}+4 \textit{\_R}^{3}-6 \textit{\_R}^{2}-2 \textit{\_R} +1}\right)}{11}+\frac{6 \ln \left(\sqrt{1+x}-\sqrt{1+\sqrt{1+x}}\right)}{11}-\frac{4 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}-1\right) \sqrt{5}}{5}\right)}{55}$&$128$\\ \hline \end{longtable}"," ",0,"4/11*sum((8*_R^4+6*_R^3-12*_R^2-5*_R+1)/(5*_R^4+4*_R^3-6*_R^2-2*_R+1)*ln((1+(1+x)^(1/2))^(1/2)-_R),_R=RootOf(_Z^5+_Z^4-2*_Z^3-_Z^2+_Z-1))+6/11*ln((1+x)^(1/2)-(1+(1+x)^(1/2))^(1/2))-4/55*5^(1/2)*arctanh(1/5*(2*(1+(1+x)^(1/2))^(1/2)-1)*5^(1/2))","B"
2704,1,188,90,0.543000," ","int((a*x+b)^(1/2)*(1+(a*x+b)^(1/2))^(1/2)/x^2/(1+(1+(a*x+b)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$2 a \left(\frac{\frac{\left(1+\sqrt{1+\sqrt{a x +b}}\right)^{\frac{5}{2}}}{2}-\frac{3 \left(1+\sqrt{1+\sqrt{a x +b}}\right)^{\frac{3}{2}}}{2}+\sqrt{1+\sqrt{1+\sqrt{a x +b}}}}{-\left(1+\sqrt{1+\sqrt{a x +b}}\right)^{4}+4 \left(1+\sqrt{1+\sqrt{a x +b}}\right)^{3}-4 \left(1+\sqrt{1+\sqrt{a x +b}}\right)^{2}+b}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+4 \textit{\_Z}^{4}-b \right)}{\sum}\frac{\left(-5 \textit{\_R}^{4}+9 \textit{\_R}^{2}-2\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{a x +b}}}-\textit{\_R} \right)}{-\textit{\_R}^{7}+3 \textit{\_R}^{5}-2 \textit{\_R}^{3}}\right)}{16}\right)$&$188$\\ default&$2 a \left(\frac{\frac{\left(1+\sqrt{1+\sqrt{a x +b}}\right)^{\frac{5}{2}}}{2}-\frac{3 \left(1+\sqrt{1+\sqrt{a x +b}}\right)^{\frac{3}{2}}}{2}+\sqrt{1+\sqrt{1+\sqrt{a x +b}}}}{-\left(1+\sqrt{1+\sqrt{a x +b}}\right)^{4}+4 \left(1+\sqrt{1+\sqrt{a x +b}}\right)^{3}-4 \left(1+\sqrt{1+\sqrt{a x +b}}\right)^{2}+b}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+4 \textit{\_Z}^{4}-b \right)}{\sum}\frac{\left(-5 \textit{\_R}^{4}+9 \textit{\_R}^{2}-2\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{a x +b}}}-\textit{\_R} \right)}{-\textit{\_R}^{7}+3 \textit{\_R}^{5}-2 \textit{\_R}^{3}}\right)}{16}\right)$&$188$\\ \hline \end{longtable}"," ",0,"2*a*(4*(1/8*(1+(1+(a*x+b)^(1/2))^(1/2))^(5/2)-3/8*(1+(1+(a*x+b)^(1/2))^(1/2))^(3/2)+1/4*(1+(1+(a*x+b)^(1/2))^(1/2))^(1/2))/(-(1+(1+(a*x+b)^(1/2))^(1/2))^4+4*(1+(1+(a*x+b)^(1/2))^(1/2))^3-4*(1+(1+(a*x+b)^(1/2))^(1/2))^2+b)+1/16*sum((-5*_R^4+9*_R^2-2)/(-_R^7+3*_R^5-2*_R^3)*ln((1+(1+(a*x+b)^(1/2))^(1/2))^(1/2)-_R),_R=RootOf(_Z^8-4*_Z^6+4*_Z^4-b)))","B"
2705,1,188,90,0.448000," ","int((a*x+b)^(1/2)*(1+(a*x+b)^(1/2))^(1/2)/x^2/(1+(1+(a*x+b)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$2 a \left(\frac{\frac{\left(1+\sqrt{1+\sqrt{a x +b}}\right)^{\frac{5}{2}}}{2}-\frac{3 \left(1+\sqrt{1+\sqrt{a x +b}}\right)^{\frac{3}{2}}}{2}+\sqrt{1+\sqrt{1+\sqrt{a x +b}}}}{-\left(1+\sqrt{1+\sqrt{a x +b}}\right)^{4}+4 \left(1+\sqrt{1+\sqrt{a x +b}}\right)^{3}-4 \left(1+\sqrt{1+\sqrt{a x +b}}\right)^{2}+b}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+4 \textit{\_Z}^{4}-b \right)}{\sum}\frac{\left(-5 \textit{\_R}^{4}+9 \textit{\_R}^{2}-2\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{a x +b}}}-\textit{\_R} \right)}{-\textit{\_R}^{7}+3 \textit{\_R}^{5}-2 \textit{\_R}^{3}}\right)}{16}\right)$&$188$\\ default&$2 a \left(\frac{\frac{\left(1+\sqrt{1+\sqrt{a x +b}}\right)^{\frac{5}{2}}}{2}-\frac{3 \left(1+\sqrt{1+\sqrt{a x +b}}\right)^{\frac{3}{2}}}{2}+\sqrt{1+\sqrt{1+\sqrt{a x +b}}}}{-\left(1+\sqrt{1+\sqrt{a x +b}}\right)^{4}+4 \left(1+\sqrt{1+\sqrt{a x +b}}\right)^{3}-4 \left(1+\sqrt{1+\sqrt{a x +b}}\right)^{2}+b}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+4 \textit{\_Z}^{4}-b \right)}{\sum}\frac{\left(-5 \textit{\_R}^{4}+9 \textit{\_R}^{2}-2\right) \ln \left(\sqrt{1+\sqrt{1+\sqrt{a x +b}}}-\textit{\_R} \right)}{-\textit{\_R}^{7}+3 \textit{\_R}^{5}-2 \textit{\_R}^{3}}\right)}{16}\right)$&$188$\\ \hline \end{longtable}"," ",0,"2*a*(4*(1/8*(1+(1+(a*x+b)^(1/2))^(1/2))^(5/2)-3/8*(1+(1+(a*x+b)^(1/2))^(1/2))^(3/2)+1/4*(1+(1+(a*x+b)^(1/2))^(1/2))^(1/2))/(-(1+(1+(a*x+b)^(1/2))^(1/2))^4+4*(1+(1+(a*x+b)^(1/2))^(1/2))^3-4*(1+(1+(a*x+b)^(1/2))^(1/2))^2+b)+1/16*sum((-5*_R^4+9*_R^2-2)/(-_R^7+3*_R^5-2*_R^3)*ln((1+(1+(a*x+b)^(1/2))^(1/2))^(1/2)-_R),_R=RootOf(_Z^8-4*_Z^6+4*_Z^4-b)))","B"
2706,0,0,92,0.011000," ","int(x^4*(a*x^4+b*x^2)^(1/4)/(x^4+a*x^2+b),x)","\[\int \frac{x^{4} \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}{x^{4}+a \,x^{2}+b}\, dx\]"," ",0,"int(x^4*(a*x^4+b*x^2)^(1/4)/(x^4+a*x^2+b),x)","F"
2707,0,0,92,0.003000," ","int(x^4*(a*x^4+b*x^2)^(1/4)/(x^4+a*x^2+b),x)","\[\int \frac{x^{4} \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}{x^{4}+a \,x^{2}+b}\, dx\]"," ",0,"int(x^4*(a*x^4+b*x^2)^(1/4)/(x^4+a*x^2+b),x)","F"
2708,0,0,187,0.052000," ","int((a*x+b)*(a*p*x^4+4*b*p*x^3-3*a*q)/(p*x^4+q)^(2/3)/(a^3*c*x^3+3*a^2*b*c*x^2+d*p*x^4+3*a*b^2*c*x+b^3*c+d*q),x)","\[\int \frac{\left(a x +b \right) \left(p a \,x^{4}+4 b p \,x^{3}-3 a q \right)}{\left(p \,x^{4}+q \right)^{\frac{2}{3}} \left(a^{3} c \,x^{3}+3 a^{2} b c \,x^{2}+d p \,x^{4}+3 a \,b^{2} c x +b^{3} c +d q \right)}\, dx\]"," ",0,"int((a*x+b)*(a*p*x^4+4*b*p*x^3-3*a*q)/(p*x^4+q)^(2/3)/(a^3*c*x^3+3*a^2*b*c*x^2+d*p*x^4+3*a*b^2*c*x+b^3*c+d*q),x)","F"
2709,1,746,199,0.419000," ","int((a^2*x^3+b^2)^(1/2)*(a^2*x^6+c*x^3+2*b^2)/x^7/(a^2*x^6+b^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{\sqrt{a^{2} x^{3}+b^{2}}\, \left(a^{2} x^{3}+2 x^{3} c +2 b^{2}\right)}{6 b^{2} x^{6}}-\frac{a^{2} \left(-\frac{2 \left(a^{2}+4 b^{2}-2 c \right) \arctanh \left(\frac{\sqrt{a^{2} x^{3}+b^{2}}}{\sqrt{b^{2}}}\right)}{3 \sqrt{b^{2}}}-\frac{2 i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{6} a^{2}+b^{2}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{3} a^{2} b^{2}+\underline{\hspace{1.25 ex}}\alpha^{3} a^{2} c +a^{2} b^{2}+b^{2} c \right) \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i a \left(2 x +\frac{-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{a \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i a \left(2 x +\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(2 a^{2} \left(a^{2} \underline{\hspace{1.25 ex}}\alpha^{5}-b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}\right)+i a^{3} \left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{4} \sqrt{3}-i a^{2} \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}}-a^{3} \left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{4}-a^{2} \underline{\hspace{1.25 ex}}\alpha^{3} \left(-a \,b^{2}\right)^{\frac{2}{3}}-i \left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  \sqrt{3}\, b^{2} a +i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, b^{2}+\left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  \,b^{2} a +\left(-a \,b^{2}\right)^{\frac{2}{3}} b^{2}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5} a^{3}-i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{4} a^{2}+i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} a^{2} b^{2}-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{4} a^{2}-2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a \,b^{2}+i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  \,b^{2}-3 \underline{\hspace{1.25 ex}}\alpha^{3} a^{2} b^{2}-i \sqrt{3}\, b^{4}+3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  \,b^{2}+3 b^{4}}{2 b^{2} \left(a^{2}+b^{2}\right)}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha^{3} \left(a^{2}+b^{2}\right) \sqrt{a^{2} x^{3}+b^{2}}}\right)}{3 a^{3} b^{2}}\right)}{4 b^{2}}$&$746$\\ default&$\frac{c \left(-\frac{\sqrt{a^{2} x^{3}+b^{2}}}{3 x^{3}}-\frac{a^{2} \arctanh \left(\frac{\sqrt{a^{2} x^{3}+b^{2}}}{\sqrt{b^{2}}}\right)}{3 \sqrt{b^{2}}}\right)}{b^{2}}-\frac{a^{2} \left(\frac{2 \sqrt{a^{2} x^{3}+b^{2}}}{3}-\frac{2 b^{2} \arctanh \left(\frac{\sqrt{a^{2} x^{3}+b^{2}}}{\sqrt{b^{2}}}\right)}{3 \sqrt{b^{2}}}\right)}{b^{2}}-\frac{\sqrt{a^{2} x^{3}+b^{2}}}{3 x^{6}}-\frac{a^{2} \sqrt{a^{2} x^{3}+b^{2}}}{6 b^{2} x^{3}}+\frac{a^{4} \arctanh \left(\frac{\sqrt{a^{2} x^{3}+b^{2}}}{\sqrt{b^{2}}}\right)}{6 b^{2} \sqrt{b^{2}}}+\frac{a^{2} \left(\frac{2 \sqrt{a^{2} x^{3}+b^{2}}}{3}+\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{6} a^{2}+b^{2}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{3} a^{2} b^{2}+\underline{\hspace{1.25 ex}}\alpha^{3} a^{2} c +a^{2} b^{2}+b^{2} c \right) \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i a \left(2 x +\frac{-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{a \left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i a \left(2 x +\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}+\left(-a \,b^{2}\right)^{\frac{1}{3}}}{a}\right)}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(2 a^{2} \left(a^{2} \underline{\hspace{1.25 ex}}\alpha^{5}-b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}\right)+i a^{3} \left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{4} \sqrt{3}-i a^{2} \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{2}{3}}-a^{3} \left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{4}-a^{2} \underline{\hspace{1.25 ex}}\alpha^{3} \left(-a \,b^{2}\right)^{\frac{2}{3}}-i \left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  \sqrt{3}\, b^{2} a +i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, b^{2}+\left(-a \,b^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  \,b^{2} a +\left(-a \,b^{2}\right)^{\frac{2}{3}} b^{2}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}\right) \sqrt{3}\, a}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5} a^{3}-i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{4} a^{2}+i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} a^{2} b^{2}-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{4} a^{2}-2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a \,b^{2}+i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  \,b^{2}-3 \underline{\hspace{1.25 ex}}\alpha^{3} a^{2} b^{2}-i \sqrt{3}\, b^{4}+3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  \,b^{2}+3 b^{4}}{2 b^{2} \left(a^{2}+b^{2}\right)}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{a \left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 a}\right)}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha^{3} \left(a^{2}+b^{2}\right) \sqrt{a^{2} x^{3}+b^{2}}}\right)}{6 a^{3} b^{2}}\right)}{b^{2}}$&$864$\\ elliptic&$\text{Expression too large to display}$&$12546$\\ \hline \end{longtable}"," ",0,"-1/6*(a^2*x^3+b^2)^(1/2)*(a^2*x^3+2*c*x^3+2*b^2)/b^2/x^6-1/4/b^2*a^2*(-2/3*(a^2+4*b^2-2*c)*arctanh((a^2*x^3+b^2)^(1/2)/(b^2)^(1/2))/(b^2)^(1/2)-2/3*I/a^3/b^2*2^(1/2)*sum((-_alpha^3*a^2*b^2+_alpha^3*a^2*c+a^2*b^2+b^2*c)/_alpha^3/(a^2+b^2)*(-a*b^2)^(1/3)*(1/2*I*a*(2*x+1/a*(-I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3)))/(-a*b^2)^(1/3))^(1/2)*(a*(x-1/a*(-a*b^2)^(1/3))/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3)))^(1/2)*(-1/2*I*a*(2*x+1/a*(I*3^(1/2)*(-a*b^2)^(1/3)+(-a*b^2)^(1/3)))/(-a*b^2)^(1/3))^(1/2)/(a^2*x^3+b^2)^(1/2)*(2*a^2*(_alpha^5*a^2-_alpha^2*b^2)+I*a^3*(-a*b^2)^(1/3)*_alpha^4*3^(1/2)-I*a^2*_alpha^3*3^(1/2)*(-a*b^2)^(2/3)-a^3*(-a*b^2)^(1/3)*_alpha^4-a^2*_alpha^3*(-a*b^2)^(2/3)-I*(-a*b^2)^(1/3)*_alpha*3^(1/2)*b^2*a+I*(-a*b^2)^(2/3)*3^(1/2)*b^2+(-a*b^2)^(1/3)*_alpha*b^2*a+(-a*b^2)^(2/3)*b^2)*EllipticPi(1/3*3^(1/2)*(I*(x+1/2/a*(-a*b^2)^(1/3)-1/2*I*3^(1/2)/a*(-a*b^2)^(1/3))*3^(1/2)*a/(-a*b^2)^(1/3))^(1/2),1/2*(2*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha^5*a^3-I*(-a*b^2)^(2/3)*3^(1/2)*_alpha^4*a^2+I*3^(1/2)*_alpha^3*a^2*b^2-3*(-a*b^2)^(2/3)*_alpha^4*a^2-2*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha^2*a*b^2+I*(-a*b^2)^(2/3)*3^(1/2)*_alpha*b^2-3*_alpha^3*a^2*b^2-I*3^(1/2)*b^4+3*(-a*b^2)^(2/3)*_alpha*b^2+3*b^4)/b^2/(a^2+b^2),(I*3^(1/2)/a*(-a*b^2)^(1/3)/(-3/2/a*(-a*b^2)^(1/3)+1/2*I*3^(1/2)/a*(-a*b^2)^(1/3)))^(1/2)),_alpha=RootOf(_Z^6*a^2+b^2)))","C"
2710,1,42,14,0.738000," ","int((x^4-2)*(x^4+2)^(1/2)/(x^4+x^2+2)/(x^4+2*x^2+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(2 \arctan \left(\frac{\sqrt{x^{4}+2}\, \sqrt{2}}{2 x}\right)-\sqrt{2}\, \arctan \left(\frac{\sqrt{x^{4}+2}}{x}\right)\right) \sqrt{2}}{2}$&$42$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x^{4}-2 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{2}+4 \sqrt{x^{4}+2}\, x +2 \RootOf \left(\textit{\_Z}^{2}+2\right)}{x^{4}+2 x^{2}+2}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}-2 \sqrt{x^{4}+2}\, x +2 \RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{4}+x^{2}+2}\right)}{2}$&$125$\\ default&$\frac{\sqrt{2}\, \sqrt{4-2 i \sqrt{2}\, x^{2}}\, \sqrt{4+2 i \sqrt{2}\, x^{2}}\, \EllipticF \left(\frac{x \sqrt{2}\, \sqrt{i \sqrt{2}}}{2}, i\right)}{4 \sqrt{i \sqrt{2}}\, \sqrt{x^{4}+2}}+\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+2 \textit{\_Z}^{2}+2\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{2 \arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}-2\right)}{\sqrt{-2 \underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{x^{4}+2}}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{2}}}-\frac{2^{\frac{3}{4}} \left(-\underline{\hspace{1.25 ex}}\alpha^{3}-2 \underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{2-i \sqrt{2}\, x^{2}}\, \sqrt{2+i \sqrt{2}\, x^{2}}\, \EllipticPi \left(\frac{x \sqrt{2}\, \sqrt{i \sqrt{2}}}{2}, \frac{i \sqrt{2}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{2}+i \sqrt{2}, \frac{\sqrt{-\frac{i \sqrt{2}}{2}}\, \sqrt{2}}{\sqrt{i \sqrt{2}}}\right)}{\sqrt{i}\, \sqrt{x^{4}+2}}\right)\right)}{8}-\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+\textit{\_Z}^{2}+2\right)}{\sum}\underline{\hspace{1.25 ex}}\alpha  \left(-\frac{4 \arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}-1\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{x^{4}+2}}\right)}{\sqrt{-\underline{\hspace{1.25 ex}}\alpha^{2}}}-\frac{2 \,2^{\frac{1}{4}} \left(-\underline{\hspace{1.25 ex}}\alpha^{3}-\underline{\hspace{1.25 ex}}\alpha  \right) \sqrt{2-i \sqrt{2}\, x^{2}}\, \sqrt{2+i \sqrt{2}\, x^{2}}\, \EllipticPi \left(\frac{x \sqrt{2}\, \sqrt{i \sqrt{2}}}{2}, \frac{i \sqrt{2}\, \underline{\hspace{1.25 ex}}\alpha^{2}}{2}+\frac{i \sqrt{2}}{2}, \frac{\sqrt{-\frac{i \sqrt{2}}{2}}\, \sqrt{2}}{\sqrt{i \sqrt{2}}}\right)}{\sqrt{i}\, \sqrt{x^{4}+2}}\right)\right)}{16}$&$370$\\ \hline \end{longtable}"," ",0,"1/2*(2*arctan(1/2*(x^4+2)^(1/2)*2^(1/2)/x)-2^(1/2)*arctan((x^4+2)^(1/2)/x))*2^(1/2)","B"
2711,0,0,196,0.037000," ","int(x^2*(x^8-2)*(x^8-2*x^4+2)^(1/4)/(x^8+2)/(2*x^8-x^4+4),x)","\[\int \frac{x^{2} \left(x^{8}-2\right) \left(x^{8}-2 x^{4}+2\right)^{\frac{1}{4}}}{\left(x^{8}+2\right) \left(2 x^{8}-x^{4}+4\right)}\, dx\]"," ",0,"int(x^2*(x^8-2)*(x^8-2*x^4+2)^(1/4)/(x^8+2)/(2*x^8-x^4+4),x)","F"
2712,1,143,44,0.129000," ","int((x^2-1)/(x^2+1)/(x+(1+x)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$2 \sqrt{x +\sqrt{1+x}}-\ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)-\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)}{\sum}\frac{\left(4 \textit{\_R}^{4}-4 \textit{\_R}^{3}+5 \textit{\_R}^{2}-4 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+5 \textit{\_R}^{4}+10 \textit{\_R}^{3}-18 \textit{\_R}^{2}+10 \textit{\_R} -1}\right)$&$143$\\ default&$2 \sqrt{x +\sqrt{1+x}}-\ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)-\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)}{\sum}\frac{\left(4 \textit{\_R}^{4}-4 \textit{\_R}^{3}+5 \textit{\_R}^{2}-4 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+5 \textit{\_R}^{4}+10 \textit{\_R}^{3}-18 \textit{\_R}^{2}+10 \textit{\_R} -1}\right)$&$143$\\ \hline \end{longtable}"," ",0,"2*(x+(1+x)^(1/2))^(1/2)-ln(1/2+(1+x)^(1/2)+(x+(1+x)^(1/2))^(1/2))-sum((4*_R^4-4*_R^3+5*_R^2-4*_R+1)/(_R^7-3*_R^5+5*_R^4+10*_R^3-18*_R^2+10*_R-1)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^8-4*_Z^6+8*_Z^5+20*_Z^4-48*_Z^3+40*_Z^2-8*_Z+1))","B"
2713,1,143,44,0.132000," ","int((x^2-1)/(x^2+1)/(x+(1+x)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$2 \sqrt{x +\sqrt{1+x}}-\ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)-\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)}{\sum}\frac{\left(4 \textit{\_R}^{4}-4 \textit{\_R}^{3}+5 \textit{\_R}^{2}-4 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+5 \textit{\_R}^{4}+10 \textit{\_R}^{3}-18 \textit{\_R}^{2}+10 \textit{\_R} -1}\right)$&$143$\\ default&$2 \sqrt{x +\sqrt{1+x}}-\ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)-\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)}{\sum}\frac{\left(4 \textit{\_R}^{4}-4 \textit{\_R}^{3}+5 \textit{\_R}^{2}-4 \textit{\_R} +1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+5 \textit{\_R}^{4}+10 \textit{\_R}^{3}-18 \textit{\_R}^{2}+10 \textit{\_R} -1}\right)$&$143$\\ \hline \end{longtable}"," ",0,"2*(x+(1+x)^(1/2))^(1/2)-ln(1/2+(1+x)^(1/2)+(x+(1+x)^(1/2))^(1/2))-sum((4*_R^4-4*_R^3+5*_R^2-4*_R+1)/(_R^7-3*_R^5+5*_R^4+10*_R^3-18*_R^2+10*_R-1)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^8-4*_Z^6+8*_Z^5+20*_Z^4-48*_Z^3+40*_Z^2-8*_Z+1))","B"
2714,0,0,186,0.038000," ","int(1/(a^2*x^2-b)^(1/2)/(a*x^2+x*(a^2*x^2-b)^(1/2))^(1/3),x)","\[\int \frac{1}{\sqrt{a^{2} x^{2}-b}\, \left(a \,x^{2}+x \sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(a^2*x^2-b)^(1/2)/(a*x^2+x*(a^2*x^2-b)^(1/2))^(1/3),x)","F"
2715,1,1551,208,0.716000," ","int((a*x-b)^(1/2)/(1+(a*x+(a*x-b)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{-\sqrt{\left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)^{2}-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)+1}+\frac{3 \ln \left(\sqrt{a x -b}+\frac{1}{2}+\sqrt{\left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)^{2}-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)+1}\right)}{2}-\sqrt{\left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)^{2}+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)+1}+\frac{3 \ln \left(\sqrt{a x -b}+\frac{1}{2}+\sqrt{\left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)^{2}+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)+1}\right)}{2}-2 \sqrt{a x -b}-\frac{\ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{4}+\ln \left(a x +\sqrt{a x -b}-1\right)+\frac{2 b \arctanh \left(\frac{2+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)}{2 \sqrt{\left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)^{2}+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)+1}}\right)}{\sqrt{5-4 b}}-\frac{2 b \arctanh \left(\frac{2-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)}{2 \sqrt{\left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)^{2}-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)+1}}\right)}{\sqrt{5-4 b}}-\frac{\sqrt{5-4 b}\, \ln \left(\sqrt{a x -b}+\frac{1}{2}+\sqrt{\left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)^{2}+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)+1}\right)}{2}-\frac{6 \arctan \left(\frac{2 \sqrt{a x -b}+1}{\sqrt{-5+4 b}}\right)}{\sqrt{-5+4 b}}+\arctanh \left(\frac{2-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)}{2 \sqrt{\left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)^{2}-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)+1}}\right)+\arctanh \left(\frac{2+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)}{2 \sqrt{\left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)^{2}+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)+1}}\right)-\frac{2 b \sqrt{\left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)^{2}+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)+1}}{\sqrt{5-4 b}}+\frac{2 b \sqrt{\left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)^{2}-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)+1}}{\sqrt{5-4 b}}+\frac{4 \arctan \left(\frac{2 \sqrt{a x -b}+1}{\sqrt{-5+4 b}}\right) b}{\sqrt{-5+4 b}}+\frac{\sqrt{5-4 b}\, \ln \left(\sqrt{a x -b}+\frac{1}{2}+\sqrt{\left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)^{2}-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)+1}\right)}{2}+\ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right) b -\frac{3 \sqrt{\left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)^{2}-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)+1}}{\sqrt{5-4 b}}-b \ln \left(\sqrt{a x -b}+\frac{1}{2}+\sqrt{\left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)^{2}-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)+1}\right)+\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{2}+\frac{3 \sqrt{\left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)^{2}+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)+1}}{\sqrt{5-4 b}}-b \ln \left(\sqrt{a x -b}+\frac{1}{2}+\sqrt{\left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)^{2}+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)+1}\right)+\frac{3 \arctanh \left(\frac{2-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)}{2 \sqrt{\left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)^{2}-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)+1}}\right)}{\sqrt{5-4 b}}-\frac{3 \arctanh \left(\frac{2+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)}{2 \sqrt{\left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)^{2}+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)+1}}\right)}{\sqrt{5-4 b}}}{a}$&$1551$\\ default&$\frac{-\sqrt{\left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)^{2}-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)+1}+\frac{3 \ln \left(\sqrt{a x -b}+\frac{1}{2}+\sqrt{\left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)^{2}-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)+1}\right)}{2}-\sqrt{\left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)^{2}+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)+1}+\frac{3 \ln \left(\sqrt{a x -b}+\frac{1}{2}+\sqrt{\left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)^{2}+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)+1}\right)}{2}-2 \sqrt{a x -b}-\frac{\ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{4}+\ln \left(a x +\sqrt{a x -b}-1\right)+\frac{2 b \arctanh \left(\frac{2+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)}{2 \sqrt{\left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)^{2}+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)+1}}\right)}{\sqrt{5-4 b}}-\frac{2 b \arctanh \left(\frac{2-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)}{2 \sqrt{\left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)^{2}-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)+1}}\right)}{\sqrt{5-4 b}}-\frac{\sqrt{5-4 b}\, \ln \left(\sqrt{a x -b}+\frac{1}{2}+\sqrt{\left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)^{2}+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)+1}\right)}{2}-\frac{6 \arctan \left(\frac{2 \sqrt{a x -b}+1}{\sqrt{-5+4 b}}\right)}{\sqrt{-5+4 b}}+\arctanh \left(\frac{2-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)}{2 \sqrt{\left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)^{2}-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)+1}}\right)+\arctanh \left(\frac{2+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)}{2 \sqrt{\left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)^{2}+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)+1}}\right)-\frac{2 b \sqrt{\left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)^{2}+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)+1}}{\sqrt{5-4 b}}+\frac{2 b \sqrt{\left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)^{2}-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)+1}}{\sqrt{5-4 b}}+\frac{4 \arctan \left(\frac{2 \sqrt{a x -b}+1}{\sqrt{-5+4 b}}\right) b}{\sqrt{-5+4 b}}+\frac{\sqrt{5-4 b}\, \ln \left(\sqrt{a x -b}+\frac{1}{2}+\sqrt{\left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)^{2}-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)+1}\right)}{2}+\ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right) b -\frac{3 \sqrt{\left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)^{2}-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)+1}}{\sqrt{5-4 b}}-b \ln \left(\sqrt{a x -b}+\frac{1}{2}+\sqrt{\left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)^{2}-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)+1}\right)+\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{2}+\frac{3 \sqrt{\left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)^{2}+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)+1}}{\sqrt{5-4 b}}-b \ln \left(\sqrt{a x -b}+\frac{1}{2}+\sqrt{\left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)^{2}+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)+1}\right)+\frac{3 \arctanh \left(\frac{2-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)}{2 \sqrt{\left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)^{2}-\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}+\frac{\sqrt{5-4 b}}{2}\right)+1}}\right)}{\sqrt{5-4 b}}-\frac{3 \arctanh \left(\frac{2+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)}{2 \sqrt{\left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)^{2}+\sqrt{5-4 b}\, \left(\sqrt{a x -b}+\frac{1}{2}-\frac{\sqrt{5-4 b}}{2}\right)+1}}\right)}{\sqrt{5-4 b}}}{a}$&$1551$\\ \hline \end{longtable}"," ",0,"2/a*(-1/2*(((a*x-b)^(1/2)+1/2+1/2*(5-4*b)^(1/2))^2-(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2+1/2*(5-4*b)^(1/2))+1)^(1/2)+3/4*ln((a*x-b)^(1/2)+1/2+(((a*x-b)^(1/2)+1/2+1/2*(5-4*b)^(1/2))^2-(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2+1/2*(5-4*b)^(1/2))+1)^(1/2))+1/2*arctanh(1/2*(2-(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2+1/2*(5-4*b)^(1/2)))/(((a*x-b)^(1/2)+1/2+1/2*(5-4*b)^(1/2))^2-(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2+1/2*(5-4*b)^(1/2))+1)^(1/2))-1/2*(((a*x-b)^(1/2)+1/2-1/2*(5-4*b)^(1/2))^2+(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2-1/2*(5-4*b)^(1/2))+1)^(1/2)+3/4*ln((a*x-b)^(1/2)+1/2+(((a*x-b)^(1/2)+1/2-1/2*(5-4*b)^(1/2))^2+(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2-1/2*(5-4*b)^(1/2))+1)^(1/2))+1/2*arctanh(1/2*(2+(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2-1/2*(5-4*b)^(1/2)))/(((a*x-b)^(1/2)+1/2-1/2*(5-4*b)^(1/2))^2+(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2-1/2*(5-4*b)^(1/2))+1)^(1/2))-(a*x-b)^(1/2)-1/8*ln(1/2+(a*x-b)^(1/2)+(a*x+(a*x-b)^(1/2))^(1/2))+1/2*ln(a*x+(a*x-b)^(1/2)-1)-1/4*(5-4*b)^(1/2)*ln((a*x-b)^(1/2)+1/2+(((a*x-b)^(1/2)+1/2-1/2*(5-4*b)^(1/2))^2+(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2-1/2*(5-4*b)^(1/2))+1)^(1/2))-3/(-5+4*b)^(1/2)*arctan((2*(a*x-b)^(1/2)+1)/(-5+4*b)^(1/2))-1/(5-4*b)^(1/2)*b*(((a*x-b)^(1/2)+1/2-1/2*(5-4*b)^(1/2))^2+(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2-1/2*(5-4*b)^(1/2))+1)^(1/2)+1/(5-4*b)^(1/2)*b*arctanh(1/2*(2+(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2-1/2*(5-4*b)^(1/2)))/(((a*x-b)^(1/2)+1/2-1/2*(5-4*b)^(1/2))^2+(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2-1/2*(5-4*b)^(1/2))+1)^(1/2))+1/(5-4*b)^(1/2)*b*(((a*x-b)^(1/2)+1/2+1/2*(5-4*b)^(1/2))^2-(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2+1/2*(5-4*b)^(1/2))+1)^(1/2)-1/(5-4*b)^(1/2)*b*arctanh(1/2*(2-(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2+1/2*(5-4*b)^(1/2)))/(((a*x-b)^(1/2)+1/2+1/2*(5-4*b)^(1/2))^2-(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2+1/2*(5-4*b)^(1/2))+1)^(1/2))+2/(-5+4*b)^(1/2)*arctan((2*(a*x-b)^(1/2)+1)/(-5+4*b)^(1/2))*b+1/4*(5-4*b)^(1/2)*ln((a*x-b)^(1/2)+1/2+(((a*x-b)^(1/2)+1/2+1/2*(5-4*b)^(1/2))^2-(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2+1/2*(5-4*b)^(1/2))+1)^(1/2))+1/2*ln(1/2+(a*x-b)^(1/2)+(a*x+(a*x-b)^(1/2))^(1/2))*b-3/2/(5-4*b)^(1/2)*(((a*x-b)^(1/2)+1/2+1/2*(5-4*b)^(1/2))^2-(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2+1/2*(5-4*b)^(1/2))+1)^(1/2)+3/2/(5-4*b)^(1/2)*arctanh(1/2*(2-(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2+1/2*(5-4*b)^(1/2)))/(((a*x-b)^(1/2)+1/2+1/2*(5-4*b)^(1/2))^2-(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2+1/2*(5-4*b)^(1/2))+1)^(1/2))-1/2*b*ln((a*x-b)^(1/2)+1/2+(((a*x-b)^(1/2)+1/2+1/2*(5-4*b)^(1/2))^2-(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2+1/2*(5-4*b)^(1/2))+1)^(1/2))+1/4*(2*(a*x-b)^(1/2)+1)*(a*x+(a*x-b)^(1/2))^(1/2)+3/2/(5-4*b)^(1/2)*(((a*x-b)^(1/2)+1/2-1/2*(5-4*b)^(1/2))^2+(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2-1/2*(5-4*b)^(1/2))+1)^(1/2)-3/2/(5-4*b)^(1/2)*arctanh(1/2*(2+(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2-1/2*(5-4*b)^(1/2)))/(((a*x-b)^(1/2)+1/2-1/2*(5-4*b)^(1/2))^2+(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2-1/2*(5-4*b)^(1/2))+1)^(1/2))-1/2*b*ln((a*x-b)^(1/2)+1/2+(((a*x-b)^(1/2)+1/2-1/2*(5-4*b)^(1/2))^2+(5-4*b)^(1/2)*((a*x-b)^(1/2)+1/2-1/2*(5-4*b)^(1/2))+1)^(1/2)))","B"
2716,1,60,219,1.046000," ","int(x*(1+2^(1/2)+2^(1/2)*x+x^2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(\sqrt{2}\, x +4 x^{2}+4 \sqrt{2}+1\right) \sqrt{1+\sqrt{2}+\sqrt{2}\, x +x^{2}}}{12}+\left(-\frac{1}{2}-\frac{\sqrt{2}}{8}\right) \arcsinh \left(\frac{x +\frac{\sqrt{2}}{2}}{\sqrt{\frac{1}{2}+\sqrt{2}}}\right)$&$60$\\ default&$\frac{\left(1+\sqrt{2}+\sqrt{2}\, x +x^{2}\right)^{\frac{3}{2}}}{3}-\frac{\sqrt{2}\, \left(\frac{\left(\sqrt{2}+2 x \right) \sqrt{1+\sqrt{2}+\sqrt{2}\, x +x^{2}}}{4}+\frac{\left(2+4 \sqrt{2}\right) \arcsinh \left(\frac{x +\frac{\sqrt{2}}{2}}{\sqrt{\frac{1}{2}+\sqrt{2}}}\right)}{8}\right)}{2}$&$74$\\ trager&$\left(\frac{\sqrt{2}\, x}{12}+\frac{x^{2}}{3}+\frac{\sqrt{2}}{3}+\frac{1}{12}\right) \sqrt{1+\sqrt{2}+\sqrt{2}\, x +x^{2}}+\frac{\left(3 \sqrt{2}-2\right) \left(1+\sqrt{2}\right) \ln \left(-2 x -\sqrt{2}+2 \sqrt{1+\sqrt{2}+\sqrt{2}\, x +x^{2}}\right)}{8}$&$77$\\ \hline \end{longtable}"," ",0,"1/12*(2^(1/2)*x+4*x^2+4*2^(1/2)+1)*(1+2^(1/2)+2^(1/2)*x+x^2)^(1/2)+(-1/2-1/8*2^(1/2))*arcsinh(1/(1/2+2^(1/2))^(1/2)*(x+1/2*2^(1/2)))","A"
2717,0,0,195,0.185000," ","int((-a*x+x^2)/(x^2*(-a+x))^(2/3)/(a^2-2*a*x+(1-d)*x^2),x)","\[\int \frac{-a x +x^{2}}{\left(x^{2} \left(-a +x \right)\right)^{\frac{2}{3}} \left(a^{2}-2 a x +\left(1-d \right) x^{2}\right)}\, dx\]"," ",0,"int((-a*x+x^2)/(x^2*(-a+x))^(2/3)/(a^2-2*a*x+(1-d)*x^2),x)","F"
2718,0,0,195,0.184000," ","int(x/(x^2*(-a+x))^(1/3)/(-a^2+2*a*x+(-1+d)*x^2),x)","\[\int \frac{x}{\left(x^{2} \left(-a +x \right)\right)^{\frac{1}{3}} \left(-a^{2}+2 a x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int(x/(x^2*(-a+x))^(1/3)/(-a^2+2*a*x+(-1+d)*x^2),x)","F"
2719,0,0,203,0.022000," ","int((-a*b*x^2+x^4)/(x^2*(-a+x)*(-b+x))^(2/3)/(a^2*b^2-2*a*b*(a+b)*x+(a^2+4*a*b+b^2-d)*x^2-2*(a+b)*x^3+x^4),x)","\[\int \frac{-a b \,x^{2}+x^{4}}{\left(x^{2} \left(-a +x \right) \left(-b +x \right)\right)^{\frac{2}{3}} \left(a^{2} b^{2}-2 a b \left(a +b \right) x +\left(a^{2}+4 a b +b^{2}-d \right) x^{2}-2 \left(a +b \right) x^{3}+x^{4}\right)}\, dx\]"," ",0,"int((-a*b*x^2+x^4)/(x^2*(-a+x)*(-b+x))^(2/3)/(a^2*b^2-2*a*b*(a+b)*x+(a^2+4*a*b+b^2-d)*x^2-2*(a+b)*x^3+x^4),x)","F"
2720,0,0,195,0.006000," ","int(((a*x^10+4*a*x^8+x^8+6*a*x^6+4*x^6+4*a*x^4+6*x^4+a*x^2+4*x^2+1)/x^2)^(1/4)/x,x)","\[\int \frac{\left(\frac{a \,x^{10}+4 a \,x^{8}+x^{8}+6 a \,x^{6}+4 x^{6}+4 a \,x^{4}+6 x^{4}+a \,x^{2}+4 x^{2}+1}{x^{2}}\right)^{\frac{1}{4}}}{x}\, dx\]"," ",0,"int(((a*x^10+4*a*x^8+x^8+6*a*x^6+4*x^6+4*a*x^4+6*x^4+a*x^2+4*x^2+1)/x^2)^(1/4)/x,x)","F"
2721,1,110,192,2.558000," ","int((8*x^2-8*x+2)^(1/3)/(3+x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 \,2^{\frac{1}{3}} \left(\left(-1+2 x \right)^{2}\right)^{\frac{1}{3}}}{2}+\frac{\left(7^{\frac{2}{3}} \ln \left(\left(-1+2 x \right)^{\frac{1}{3}}+7^{\frac{1}{3}}\right)-\frac{7^{\frac{2}{3}} \ln \left(\left(-1+2 x \right)^{\frac{2}{3}}-7^{\frac{1}{3}} \left(-1+2 x \right)^{\frac{1}{3}}+7^{\frac{2}{3}}\right)}{2}-\sqrt{3}\, 7^{\frac{2}{3}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \,7^{\frac{2}{3}} \left(-1+2 x \right)^{\frac{1}{3}}}{7}-1\right)}{3}\right)\right) 2^{\frac{1}{3}} \left(\left(-1+2 x \right)^{2}\right)^{\frac{1}{3}}}{\left(-1+2 x \right)^{\frac{2}{3}}}$&$110$\\ trager&$\text{Expression too large to display}$&$1484$\\ \hline \end{longtable}"," ",0,"3/2*2^(1/3)*((-1+2*x)^2)^(1/3)+(7^(2/3)*ln((-1+2*x)^(1/3)+7^(1/3))-1/2*7^(2/3)*ln((-1+2*x)^(2/3)-7^(1/3)*(-1+2*x)^(1/3)+7^(2/3))-3^(1/2)*7^(2/3)*arctan(1/3*3^(1/2)*(2/7*7^(2/3)*(-1+2*x)^(1/3)-1)))*2^(1/3)*((-1+2*x)^2)^(1/3)/(-1+2*x)^(2/3)","A"
2722,0,0,189,0.049000," ","int((a*x+b)*(b*p*x^2-a*q)/(p*x^3+q)^(2/3)/(b^3*c+d*q+3*a*b^2*c*x+3*a^2*b*c*x^2+(a^3*c+d*p)*x^3),x)","\[\int \frac{\left(a x +b \right) \left(b p \,x^{2}-a q \right)}{\left(p \,x^{3}+q \right)^{\frac{2}{3}} \left(b^{3} c +d q +3 a \,b^{2} c x +3 a^{2} b c \,x^{2}+\left(a^{3} c +d p \right) x^{3}\right)}\, dx\]"," ",0,"int((a*x+b)*(b*p*x^2-a*q)/(p*x^3+q)^(2/3)/(b^3*c+d*q+3*a*b^2*c*x+3*a^2*b*c*x^2+(a^3*c+d*p)*x^3),x)","F"
2723,0,0,210,0.123000," ","int((-b+x)*(-a*(a-2*b)-2*b*x+x^2)/((-a+x)*(-b+x))^(2/3)/(a^4-b^2*d-2*(2*a^3-b*d)*x+(6*a^2-d)*x^2-4*a*x^3+x^4),x)","\[\int \frac{\left(-b +x \right) \left(-a \left(a -2 b \right)-2 b x +x^{2}\right)}{\left(\left(-a +x \right) \left(-b +x \right)\right)^{\frac{2}{3}} \left(a^{4}-b^{2} d -2 \left(2 a^{3}-b d \right) x +\left(6 a^{2}-d \right) x^{2}-4 a \,x^{3}+x^{4}\right)}\, dx\]"," ",0,"int((-b+x)*(-a*(a-2*b)-2*b*x+x^2)/((-a+x)*(-b+x))^(2/3)/(a^4-b^2*d-2*(2*a^3-b*d)*x+(6*a^2-d)*x^2-4*a*x^3+x^4),x)","F"
2724,0,0,182,0.016000," ","int((x^5+1)^(1/2)*(x^5+2)/x^6/(a*x^10-x^5-1),x)","\[\int \frac{\sqrt{x^{5}+1}\, \left(x^{5}+2\right)}{x^{6} \left(a \,x^{10}-x^{5}-1\right)}\, dx\]"," ",0,"int((x^5+1)^(1/2)*(x^5+2)/x^6/(a*x^10-x^5-1),x)","F"
2725,0,0,182,0.017000," ","int((x^5-2)*(x^5-1)^(1/2)/x^6/(a*x^10-x^5+1),x)","\[\int \frac{\left(x^{5}-2\right) \sqrt{x^{5}-1}}{x^{6} \left(a \,x^{10}-x^{5}+1\right)}\, dx\]"," ",0,"int((x^5-2)*(x^5-1)^(1/2)/x^6/(a*x^10-x^5+1),x)","F"
2726,1,126,64,0.599000," ","int(1/(x^2-(1+x)^(1/2)*(1+(1+x)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{2 \ln \left(\sqrt{1+x}-\sqrt{1+\sqrt{1+x}}\right)}{11}-\frac{28 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}-1\right) \sqrt{5}}{5}\right)}{55}+\frac{4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+\textit{\_Z} -1\right)}{\sum}\frac{\left(\textit{\_R}^{4}-2 \textit{\_R}^{3}-7 \textit{\_R}^{2}-2 \textit{\_R} +7\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{5 \textit{\_R}^{4}+4 \textit{\_R}^{3}-6 \textit{\_R}^{2}-2 \textit{\_R} +1}\right)}{11}$&$126$\\ default&$\text{Expression too large to display}$&$2204$\\ \hline \end{longtable}"," ",0,"-2/11*ln((1+x)^(1/2)-(1+(1+x)^(1/2))^(1/2))-28/55*5^(1/2)*arctanh(1/5*(2*(1+(1+x)^(1/2))^(1/2)-1)*5^(1/2))+4/11*sum((_R^4-2*_R^3-7*_R^2-2*_R+7)/(5*_R^4+4*_R^3-6*_R^2-2*_R+1)*ln((1+(1+x)^(1/2))^(1/2)-_R),_R=RootOf(_Z^5+_Z^4-2*_Z^3-_Z^2+_Z-1))","A"
2727,1,126,64,0.496000," ","int(1/(x^2-(1+x)^(1/2)*(1+(1+x)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{2 \ln \left(\sqrt{1+x}-\sqrt{1+\sqrt{1+x}}\right)}{11}-\frac{28 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}-1\right) \sqrt{5}}{5}\right)}{55}+\frac{4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+\textit{\_Z} -1\right)}{\sum}\frac{\left(\textit{\_R}^{4}-2 \textit{\_R}^{3}-7 \textit{\_R}^{2}-2 \textit{\_R} +7\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{5 \textit{\_R}^{4}+4 \textit{\_R}^{3}-6 \textit{\_R}^{2}-2 \textit{\_R} +1}\right)}{11}$&$126$\\ default&$\text{Expression too large to display}$&$2204$\\ \hline \end{longtable}"," ",0,"-2/11*ln((1+x)^(1/2)-(1+(1+x)^(1/2))^(1/2))-28/55*5^(1/2)*arctanh(1/5*(2*(1+(1+x)^(1/2))^(1/2)-1)*5^(1/2))+4/11*sum((_R^4-2*_R^3-7*_R^2-2*_R+7)/(5*_R^4+4*_R^3-6*_R^2-2*_R+1)*ln((1+(1+x)^(1/2))^(1/2)-_R),_R=RootOf(_Z^5+_Z^4-2*_Z^3-_Z^2+_Z-1))","A"
2728,1,186113818,181,162.933000," ","int(x*(_C3*x^2-_C4)/((_C3*x^2+_C0*x+_C4)/(_C3*x^2+_C1*x+_C4))^(1/2)/(3*_C3*x^2+3*_C4+x)/(_C3^2*x^4+2*_C3*_C4*x^2+_C4^2-x^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$186113818$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2729,0,0,71,0.078000," ","int(1/(a*x^4-b)^2/(a*x^4-b*x^2)^(1/4),x)","\[\int \frac{1}{\left(a \,x^{4}-b \right)^{2} \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(a*x^4-b)^2/(a*x^4-b*x^2)^(1/4),x)","F"
2730,0,0,71,0.005000," ","int(1/(a*x^4-b)^2/(a*x^4-b*x^2)^(1/4),x)","\[\int \frac{1}{\left(a \,x^{4}-b \right)^{2} \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(a*x^4-b)^2/(a*x^4-b*x^2)^(1/4),x)","F"
2731,0,0,239,0.036000," ","int((p*x^3-2*q)*(a*p*x^3+b*x^2+a*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)/x^5/(c*p*x^3+d*x^2+c*q),x)","\[\int \frac{\left(p \,x^{3}-2 q \right) \left(a p \,x^{3}+b \,x^{2}+a q \right) \sqrt{p^{2} x^{6}-2 p q \,x^{4}+2 p q \,x^{3}+q^{2}}}{x^{5} \left(c p \,x^{3}+d \,x^{2}+c q \right)}\, dx\]"," ",0,"int((p*x^3-2*q)*(a*p*x^3+b*x^2+a*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)/x^5/(c*p*x^3+d*x^2+c*q),x)","F"
2732,0,0,212,0.043000," ","int(-(-1+x)*x*(-1+2*x+(k^2-2*k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(1-4*k*x+(6*k^2-b)*x^2+(-4*k^3+2*b)*x^3+(k^4-b)*x^4),x)","\[\int -\frac{\left(-1+x \right) x \left(-1+2 x +\left(k^{2}-2 k \right) x^{2}\right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{2}{3}} \left(1-4 k x +\left(6 k^{2}-b \right) x^{2}+\left(-4 k^{3}+2 b \right) x^{3}+\left(k^{4}-b \right) x^{4}\right)}\, dx\]"," ",0,"int(-(-1+x)*x*(-1+2*x+(k^2-2*k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(1-4*k*x+(6*k^2-b)*x^2+(-4*k^3+2*b)*x^3+(k^4-b)*x^4),x)","F"
2733,0,0,244,0.030000," ","int((p*x^3-2*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)*(b*x^8+a*(p*x^3+q)^4)/x^13,x)","\[\int \frac{\left(p \,x^{3}-2 q \right) \sqrt{p^{2} x^{6}-2 p q \,x^{4}+2 p q \,x^{3}+q^{2}}\, \left(b \,x^{8}+a \left(p \,x^{3}+q \right)^{4}\right)}{x^{13}}\, dx\]"," ",0,"int((p*x^3-2*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)*(b*x^8+a*(p*x^3+q)^4)/x^13,x)","F"
2734,1,145,65,0.083000," ","int(x^2/(x^2-(1+x)^(1/2)*(1+(1+x)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\left(1+\sqrt{1+x}\right)^{2}-2 \sqrt{1+x}-2+\frac{4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+\textit{\_Z} -1\right)}{\sum}\frac{\left(-2 \textit{\_R}^{4}+4 \textit{\_R}^{3}+3 \textit{\_R}^{2}-7 \textit{\_R} -3\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{5 \textit{\_R}^{4}+4 \textit{\_R}^{3}-6 \textit{\_R}^{2}-2 \textit{\_R} +1}\right)}{11}+\frac{4 \ln \left(\sqrt{1+x}-\sqrt{1+\sqrt{1+x}}\right)}{11}-\frac{32 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}-1\right) \sqrt{5}}{5}\right)}{55}$&$145$\\ default&$\left(1+\sqrt{1+x}\right)^{2}-2 \sqrt{1+x}-2+\frac{4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+\textit{\_Z} -1\right)}{\sum}\frac{\left(-2 \textit{\_R}^{4}+4 \textit{\_R}^{3}+3 \textit{\_R}^{2}-7 \textit{\_R} -3\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{5 \textit{\_R}^{4}+4 \textit{\_R}^{3}-6 \textit{\_R}^{2}-2 \textit{\_R} +1}\right)}{11}+\frac{4 \ln \left(\sqrt{1+x}-\sqrt{1+\sqrt{1+x}}\right)}{11}-\frac{32 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}-1\right) \sqrt{5}}{5}\right)}{55}$&$145$\\ \hline \end{longtable}"," ",0,"(1+(1+x)^(1/2))^2-2*(1+x)^(1/2)-2+4/11*sum((-2*_R^4+4*_R^3+3*_R^2-7*_R-3)/(5*_R^4+4*_R^3-6*_R^2-2*_R+1)*ln((1+(1+x)^(1/2))^(1/2)-_R),_R=RootOf(_Z^5+_Z^4-2*_Z^3-_Z^2+_Z-1))+4/11*ln((1+x)^(1/2)-(1+(1+x)^(1/2))^(1/2))-32/55*5^(1/2)*arctanh(1/5*(2*(1+(1+x)^(1/2))^(1/2)-1)*5^(1/2))","B"
2735,1,145,65,0.084000," ","int(x^2/(x^2-(1+x)^(1/2)*(1+(1+x)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\left(1+\sqrt{1+x}\right)^{2}-2 \sqrt{1+x}-2+\frac{4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+\textit{\_Z} -1\right)}{\sum}\frac{\left(-2 \textit{\_R}^{4}+4 \textit{\_R}^{3}+3 \textit{\_R}^{2}-7 \textit{\_R} -3\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{5 \textit{\_R}^{4}+4 \textit{\_R}^{3}-6 \textit{\_R}^{2}-2 \textit{\_R} +1}\right)}{11}+\frac{4 \ln \left(\sqrt{1+x}-\sqrt{1+\sqrt{1+x}}\right)}{11}-\frac{32 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}-1\right) \sqrt{5}}{5}\right)}{55}$&$145$\\ default&$\left(1+\sqrt{1+x}\right)^{2}-2 \sqrt{1+x}-2+\frac{4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+\textit{\_Z} -1\right)}{\sum}\frac{\left(-2 \textit{\_R}^{4}+4 \textit{\_R}^{3}+3 \textit{\_R}^{2}-7 \textit{\_R} -3\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{5 \textit{\_R}^{4}+4 \textit{\_R}^{3}-6 \textit{\_R}^{2}-2 \textit{\_R} +1}\right)}{11}+\frac{4 \ln \left(\sqrt{1+x}-\sqrt{1+\sqrt{1+x}}\right)}{11}-\frac{32 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}-1\right) \sqrt{5}}{5}\right)}{55}$&$145$\\ \hline \end{longtable}"," ",0,"(1+(1+x)^(1/2))^2-2*(1+x)^(1/2)-2+4/11*sum((-2*_R^4+4*_R^3+3*_R^2-7*_R-3)/(5*_R^4+4*_R^3-6*_R^2-2*_R+1)*ln((1+(1+x)^(1/2))^(1/2)-_R),_R=RootOf(_Z^5+_Z^4-2*_Z^3-_Z^2+_Z-1))+4/11*ln((1+x)^(1/2)-(1+(1+x)^(1/2))^(1/2))-32/55*5^(1/2)*arctanh(1/5*(2*(1+(1+x)^(1/2))^(1/2)-1)*5^(1/2))","B"
2736,1,10683,186,15.045000," ","int(1/x/(x^4-4*x^3+6*x^2-4*x+1)^(1/5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$10683$\\ \hline \end{longtable}"," ",0,"result too large to display","C"
2737,1,8780,190,74.654000," ","int((x^2-x+1)/(x^2-1)/(x^4+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$8780$\\ \hline \end{longtable}"," ",0,"result too large to display","C"
2738,0,0,190,0.065000," ","int((x^2+x+1)/(x^2-1)/(x^4+x^2)^(1/3),x)","\[\int \frac{x^{2}+x +1}{\left(x^{2}-1\right) \left(x^{4}+x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((x^2+x+1)/(x^2-1)/(x^4+x^2)^(1/3),x)","F"
2739,1,650,69,3.665000," ","int((x^2-1)*(x^4+x^3-x^2-x+1)^(1/2)/x^2/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{4}+x^{3}-x^{2}-x +1}}{x}-\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+\textit{\_Z}^{2}+6\right) \ln \left(\frac{51 \RootOf \left(\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+\textit{\_Z}^{2}+6\right) \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{4} x^{2}-51 \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{4} \RootOf \left(\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+\textit{\_Z}^{2}+6\right)+250 \RootOf \left(\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+\textit{\_Z}^{2}+6\right) \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2} x^{2}-136 \RootOf \left(\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+\textit{\_Z}^{2}+6\right) \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2} x +448 \sqrt{x^{4}+x^{3}-x^{2}-x +1}\, \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}-250 \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+\textit{\_Z}^{2}+6\right)-89 \RootOf \left(\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+\textit{\_Z}^{2}+6\right) x^{2}-712 \RootOf \left(\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+\textit{\_Z}^{2}+6\right) x +816 \sqrt{x^{4}+x^{3}-x^{2}-x +1}+89 \RootOf \left(\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+\textit{\_Z}^{2}+6\right)}{\left(x \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}-\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+x -5\right)^{2}}\right)}{2}-\frac{\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right) \ln \left(-\frac{-51 \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{5} x^{2}+51 \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{5}-362 x^{2} \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{3}-136 x \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{3}+448 \sqrt{x^{4}+x^{3}-x^{2}-x +1}\, \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+362 \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{3}-247 x^{2} \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)-104 x \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)+1872 \sqrt{x^{4}+x^{3}-x^{2}-x +1}+247 \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)}{\left(x \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}-\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+5 x -1\right)^{2}}\right)}{2}-\frac{\ln \left(-\frac{2-x -2 x^{2}+2 \sqrt{x^{4}+x^{3}-x^{2}-x +1}}{x}\right)}{2}$&$650$\\ risch&$\text{Expression too large to display}$&$186639$\\ elliptic&$\text{Expression too large to display}$&$286046$\\ default&$\text{Expression too large to display}$&$339777$\\ \hline \end{longtable}"," ",0,"(x^4+x^3-x^2-x+1)^(1/2)/x-1/2*RootOf(RootOf(_Z^4+6*_Z^2+13)^2+_Z^2+6)*ln((51*RootOf(RootOf(_Z^4+6*_Z^2+13)^2+_Z^2+6)*RootOf(_Z^4+6*_Z^2+13)^4*x^2-51*RootOf(_Z^4+6*_Z^2+13)^4*RootOf(RootOf(_Z^4+6*_Z^2+13)^2+_Z^2+6)+250*RootOf(RootOf(_Z^4+6*_Z^2+13)^2+_Z^2+6)*RootOf(_Z^4+6*_Z^2+13)^2*x^2-136*RootOf(RootOf(_Z^4+6*_Z^2+13)^2+_Z^2+6)*RootOf(_Z^4+6*_Z^2+13)^2*x+448*(x^4+x^3-x^2-x+1)^(1/2)*RootOf(_Z^4+6*_Z^2+13)^2-250*RootOf(_Z^4+6*_Z^2+13)^2*RootOf(RootOf(_Z^4+6*_Z^2+13)^2+_Z^2+6)-89*RootOf(RootOf(_Z^4+6*_Z^2+13)^2+_Z^2+6)*x^2-712*RootOf(RootOf(_Z^4+6*_Z^2+13)^2+_Z^2+6)*x+816*(x^4+x^3-x^2-x+1)^(1/2)+89*RootOf(RootOf(_Z^4+6*_Z^2+13)^2+_Z^2+6))/(x*RootOf(_Z^4+6*_Z^2+13)^2-RootOf(_Z^4+6*_Z^2+13)^2+x-5)^2)-1/2*RootOf(_Z^4+6*_Z^2+13)*ln(-(-51*RootOf(_Z^4+6*_Z^2+13)^5*x^2+51*RootOf(_Z^4+6*_Z^2+13)^5-362*x^2*RootOf(_Z^4+6*_Z^2+13)^3-136*x*RootOf(_Z^4+6*_Z^2+13)^3+448*(x^4+x^3-x^2-x+1)^(1/2)*RootOf(_Z^4+6*_Z^2+13)^2+362*RootOf(_Z^4+6*_Z^2+13)^3-247*x^2*RootOf(_Z^4+6*_Z^2+13)-104*x*RootOf(_Z^4+6*_Z^2+13)+1872*(x^4+x^3-x^2-x+1)^(1/2)+247*RootOf(_Z^4+6*_Z^2+13))/(x*RootOf(_Z^4+6*_Z^2+13)^2-RootOf(_Z^4+6*_Z^2+13)^2+5*x-1)^2)-1/2*ln(-(2-x-2*x^2+2*(x^4+x^3-x^2-x+1)^(1/2))/x)","B"
2740,1,648,69,2.566000," ","int((x^2-1)*(x^4+x^3-x^2-x+1)^(1/2)/x^2/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\sqrt{x^{4}+x^{3}-x^{2}-x +1}}{x}-\frac{\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right) \ln \left(-\frac{-51 \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{5} x^{2}+51 \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{5}-362 x^{2} \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{3}-136 x \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{3}+448 \sqrt{x^{4}+x^{3}-x^{2}-x +1}\, \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+362 \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{3}-247 x^{2} \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)-104 x \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)+1872 \sqrt{x^{4}+x^{3}-x^{2}-x +1}+247 \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)}{\left(x \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}-\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+5 x -1\right)^{2}}\right)}{2}-\frac{\RootOf \left(\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+\textit{\_Z}^{2}+6\right) \ln \left(\frac{51 \RootOf \left(\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+\textit{\_Z}^{2}+6\right) \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{4} x^{2}-51 \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{4} \RootOf \left(\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+\textit{\_Z}^{2}+6\right)+250 \RootOf \left(\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+\textit{\_Z}^{2}+6\right) \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2} x^{2}-136 \RootOf \left(\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+\textit{\_Z}^{2}+6\right) \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2} x +448 \sqrt{x^{4}+x^{3}-x^{2}-x +1}\, \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}-250 \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2} \RootOf \left(\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+\textit{\_Z}^{2}+6\right)-89 \RootOf \left(\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+\textit{\_Z}^{2}+6\right) x^{2}-712 \RootOf \left(\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+\textit{\_Z}^{2}+6\right) x +816 \sqrt{x^{4}+x^{3}-x^{2}-x +1}+89 \RootOf \left(\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+\textit{\_Z}^{2}+6\right)}{\left(x \RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}-\RootOf \left(\textit{\_Z}^{4}+6 \textit{\_Z}^{2}+13\right)^{2}+x -5\right)^{2}}\right)}{2}+\frac{\ln \left(-\frac{2 x^{2}+2 \sqrt{x^{4}+x^{3}-x^{2}-x +1}+x -2}{x}\right)}{2}$&$648$\\ risch&$\text{Expression too large to display}$&$186639$\\ elliptic&$\text{Expression too large to display}$&$286046$\\ default&$\text{Expression too large to display}$&$339777$\\ \hline \end{longtable}"," ",0,"(x^4+x^3-x^2-x+1)^(1/2)/x-1/2*RootOf(_Z^4+6*_Z^2+13)*ln(-(-51*RootOf(_Z^4+6*_Z^2+13)^5*x^2+51*RootOf(_Z^4+6*_Z^2+13)^5-362*x^2*RootOf(_Z^4+6*_Z^2+13)^3-136*x*RootOf(_Z^4+6*_Z^2+13)^3+448*(x^4+x^3-x^2-x+1)^(1/2)*RootOf(_Z^4+6*_Z^2+13)^2+362*RootOf(_Z^4+6*_Z^2+13)^3-247*x^2*RootOf(_Z^4+6*_Z^2+13)-104*x*RootOf(_Z^4+6*_Z^2+13)+1872*(x^4+x^3-x^2-x+1)^(1/2)+247*RootOf(_Z^4+6*_Z^2+13))/(x*RootOf(_Z^4+6*_Z^2+13)^2-RootOf(_Z^4+6*_Z^2+13)^2+5*x-1)^2)-1/2*RootOf(RootOf(_Z^4+6*_Z^2+13)^2+_Z^2+6)*ln((51*RootOf(RootOf(_Z^4+6*_Z^2+13)^2+_Z^2+6)*RootOf(_Z^4+6*_Z^2+13)^4*x^2-51*RootOf(_Z^4+6*_Z^2+13)^4*RootOf(RootOf(_Z^4+6*_Z^2+13)^2+_Z^2+6)+250*RootOf(RootOf(_Z^4+6*_Z^2+13)^2+_Z^2+6)*RootOf(_Z^4+6*_Z^2+13)^2*x^2-136*RootOf(RootOf(_Z^4+6*_Z^2+13)^2+_Z^2+6)*RootOf(_Z^4+6*_Z^2+13)^2*x+448*(x^4+x^3-x^2-x+1)^(1/2)*RootOf(_Z^4+6*_Z^2+13)^2-250*RootOf(_Z^4+6*_Z^2+13)^2*RootOf(RootOf(_Z^4+6*_Z^2+13)^2+_Z^2+6)-89*RootOf(RootOf(_Z^4+6*_Z^2+13)^2+_Z^2+6)*x^2-712*RootOf(RootOf(_Z^4+6*_Z^2+13)^2+_Z^2+6)*x+816*(x^4+x^3-x^2-x+1)^(1/2)+89*RootOf(RootOf(_Z^4+6*_Z^2+13)^2+_Z^2+6))/(x*RootOf(_Z^4+6*_Z^2+13)^2-RootOf(_Z^4+6*_Z^2+13)^2+x-5)^2)+1/2*ln(-(2*x^2+2*(x^4+x^3-x^2-x+1)^(1/2)+x-2)/x)","B"
2741,1,1854,189,42.027000," ","int((x^3-1)^(2/3)*(x^3+4)/x^6/(x^6-x^3-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$1854$\\ trager&$\text{Expression too large to display}$&$1899$\\ \hline \end{longtable}"," ",0,"-1/20*(13*x^6-21*x^3+8)/x^5/(x^3-1)^(1/3)-1/3*ln((-12*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^3*x^3+9*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+24*(x^3-1)^(2/3)*RootOf(_Z^3+4)^2*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*x+8*(x^3-1)^(1/3)*RootOf(_Z^3+4)^2*x^2-48*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)*(x^3-1)^(1/3)*x^2-16*RootOf(_Z^3+4)*x^3+12*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*x^3+16*x*(x^3-1)^(2/3)+16*RootOf(_Z^3+4)-12*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2))/(x^2-x+1)/(1+x))*RootOf(_Z^3+4)-1/2*ln((-12*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^3*x^3+9*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+24*(x^3-1)^(2/3)*RootOf(_Z^3+4)^2*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*x+8*(x^3-1)^(1/3)*RootOf(_Z^3+4)^2*x^2-48*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)*(x^3-1)^(1/3)*x^2-16*RootOf(_Z^3+4)*x^3+12*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*x^3+16*x*(x^3-1)^(2/3)+16*RootOf(_Z^3+4)-12*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2))/(x^2-x+1)/(1+x))*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)+1/2*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*ln(-(-18*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^3*x^3-9*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)^2*RootOf(_Z^3+4)^2*x^3+24*(x^3-1)^(2/3)*RootOf(_Z^3+4)^2*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*x-40*(x^3-1)^(1/3)*RootOf(_Z^3+4)^2*x^2-48*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)*(x^3-1)^(1/3)*x^2+72*RootOf(_Z^3+4)*x^3+36*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*x^3-80*x*(x^3-1)^(2/3)-24*RootOf(_Z^3+4)-12*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2))/(x^2-x+1)/(1+x))+1/16*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)*ln(-(-6*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^4*x^3+9*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)^2*RootOf(_Z^3+4)^3*x^3+48*RootOf(_Z^3+4)^2*x^3-72*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)*x^3-96*RootOf(_Z^3+4)*(x^3-1)^(1/3)*x^2+192*x*(x^3-1)^(2/3)-32*RootOf(_Z^3+4)^2+48*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4))/(x^3-2))-1/24*ln(-(3*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^4*x^3-9*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)^2*RootOf(_Z^3+4)^3*x^3+60*(x^3-1)^(2/3)*RootOf(_Z^3+4)^2*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*x+16*RootOf(_Z^3+4)^2*x^3-48*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)*x^3+16*RootOf(_Z^3+4)*(x^3-1)^(1/3)*x^2+120*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*(x^3-1)^(1/3)*x^2-32*x*(x^3-1)^(2/3)-16*RootOf(_Z^3+4)^2+48*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4))/(x^3-2))*RootOf(_Z^3+4)^2-1/16*ln(-(3*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)^4*x^3-9*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)^2*RootOf(_Z^3+4)^3*x^3+60*(x^3-1)^(2/3)*RootOf(_Z^3+4)^2*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*x+16*RootOf(_Z^3+4)^2*x^3-48*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)*x^3+16*RootOf(_Z^3+4)*(x^3-1)^(1/3)*x^2+120*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*(x^3-1)^(1/3)*x^2-32*x*(x^3-1)^(2/3)-16*RootOf(_Z^3+4)^2+48*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4))/(x^3-2))*RootOf(4*RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+9*_Z^2)*RootOf(_Z^3+4)","C"
2742,0,0,198,180.000000," ","int((c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3)/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/4),x)","\[\int \frac{\left(c +\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}}\right)^{\frac{1}{3}}}{\sqrt{a^{2} x^{2}-b}\, \left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3)/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/4),x)","F"
2743,1,2150,177,26.690000," ","int((x^2+x)*(x^4+x^3)^(1/4)/(x^2+x-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2150$\\ risch&$\text{Expression too large to display}$&$4380$\\ \hline \end{longtable}"," ",0,"(1/8+1/2*x)*(x^4+x^3)^(1/4)-1/40*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*ln((1075*RootOf(25*_Z^4+320*_Z^2-4096)^4*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x^3-1075*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*RootOf(25*_Z^4+320*_Z^2-4096)^4*x^2-104960*(x^4+x^3)^(1/2)*RootOf(25*_Z^4+320*_Z^2-4096)^2*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x-104640*RootOf(25*_Z^4+320*_Z^2-4096)^2*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x^3-1152000*(x^4+x^3)^(3/4)*RootOf(25*_Z^4+320*_Z^2-4096)^2-1894400*RootOf(25*_Z^4+320*_Z^2-4096)^2*(x^4+x^3)^(1/4)*x^2-46720*RootOf(25*_Z^4+320*_Z^2-4096)^2*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x^2+843776*(x^4+x^3)^(1/2)*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x+745472*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x^3+9502720*(x^4+x^3)^(3/4)+14745600*x^2*(x^4+x^3)^(1/4)+425984*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x^2)/(5*x*RootOf(25*_Z^4+320*_Z^2-4096)^2-5*RootOf(25*_Z^4+320*_Z^2-4096)^2-64*x)/x^2)-1/8*RootOf(25*_Z^4+320*_Z^2-4096)*ln((1075*x^3*RootOf(25*_Z^4+320*_Z^2-4096)^5-1075*x^2*RootOf(25*_Z^4+320*_Z^2-4096)^5+104960*RootOf(25*_Z^4+320*_Z^2-4096)^3*(x^4+x^3)^(1/2)*x+132160*x^3*RootOf(25*_Z^4+320*_Z^2-4096)^3+19200*x^2*RootOf(25*_Z^4+320*_Z^2-4096)^3+230400*(x^4+x^3)^(3/4)*RootOf(25*_Z^4+320*_Z^2-4096)^2+378880*RootOf(25*_Z^4+320*_Z^2-4096)^2*(x^4+x^3)^(1/4)*x^2+2187264*RootOf(25*_Z^4+320*_Z^2-4096)*(x^4+x^3)^(1/2)*x+2260992*RootOf(25*_Z^4+320*_Z^2-4096)*x^3+847872*x^2*RootOf(25*_Z^4+320*_Z^2-4096)+4849664*(x^4+x^3)^(3/4)+7798784*x^2*(x^4+x^3)^(1/4))/(5*x*RootOf(25*_Z^4+320*_Z^2-4096)^2-5*RootOf(25*_Z^4+320*_Z^2-4096)^2+128*x-64)/x^2)+29/2048*RootOf(25*_Z^4+320*_Z^2-4096)*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*ln((2*(x^4+x^3)^(1/2)*RootOf(25*_Z^4+320*_Z^2-4096)*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x-2*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*RootOf(25*_Z^4+320*_Z^2-4096)*x^3-RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*RootOf(25*_Z^4+320*_Z^2-4096)*x^2+128*(x^4+x^3)^(3/4)-128*x^2*(x^4+x^3)^(1/4))/x^2)+29/32*ln((2*(x^4+x^3)^(3/4)+2*(x^4+x^3)^(1/2)*x+2*x^2*(x^4+x^3)^(1/4)+2*x^3+x^2)/x^2)+1/512*RootOf(25*_Z^4+320*_Z^2-4096)^2*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*ln((325*RootOf(25*_Z^4+320*_Z^2-4096)^4*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x^3-325*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*RootOf(25*_Z^4+320*_Z^2-4096)^4*x^2-32960*(x^4+x^3)^(1/2)*RootOf(25*_Z^4+320*_Z^2-4096)^2*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x+40160*RootOf(25*_Z^4+320*_Z^2-4096)^2*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x^3+576000*(x^4+x^3)^(3/4)*RootOf(25*_Z^4+320*_Z^2-4096)^2-947200*RootOf(25*_Z^4+320*_Z^2-4096)^2*(x^4+x^3)^(1/4)*x^2+5600*RootOf(25*_Z^4+320*_Z^2-4096)^2*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x^2-671744*(x^4+x^3)^(1/2)*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x+704512*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x^3+12124160*(x^4+x^3)^(3/4)-19496960*x^2*(x^4+x^3)^(1/4)+264192*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x^2)/(5*x*RootOf(25*_Z^4+320*_Z^2-4096)^2-5*RootOf(25*_Z^4+320*_Z^2-4096)^2+128*x-64)/x^2)+5/512*ln(-(325*x^3*RootOf(25*_Z^4+320*_Z^2-4096)^5-325*x^2*RootOf(25*_Z^4+320*_Z^2-4096)^5+32960*RootOf(25*_Z^4+320*_Z^2-4096)^3*(x^4+x^3)^(1/2)*x-31840*x^3*RootOf(25*_Z^4+320*_Z^2-4096)^3-13920*x^2*RootOf(25*_Z^4+320*_Z^2-4096)^3+115200*(x^4+x^3)^(3/4)*RootOf(25*_Z^4+320*_Z^2-4096)^2-189440*RootOf(25*_Z^4+320*_Z^2-4096)^2*(x^4+x^3)^(1/4)*x^2-249856*RootOf(25*_Z^4+320*_Z^2-4096)*(x^4+x^3)^(1/2)*x+243712*RootOf(25*_Z^4+320*_Z^2-4096)*x^3+139264*x^2*RootOf(25*_Z^4+320*_Z^2-4096)-950272*(x^4+x^3)^(3/4)+1474560*x^2*(x^4+x^3)^(1/4))/(5*x*RootOf(25*_Z^4+320*_Z^2-4096)^2-5*RootOf(25*_Z^4+320*_Z^2-4096)^2-64*x)/x^2)*RootOf(25*_Z^4+320*_Z^2-4096)^3+1/8*ln(-(325*x^3*RootOf(25*_Z^4+320*_Z^2-4096)^5-325*x^2*RootOf(25*_Z^4+320*_Z^2-4096)^5+32960*RootOf(25*_Z^4+320*_Z^2-4096)^3*(x^4+x^3)^(1/2)*x-31840*x^3*RootOf(25*_Z^4+320*_Z^2-4096)^3-13920*x^2*RootOf(25*_Z^4+320*_Z^2-4096)^3+115200*(x^4+x^3)^(3/4)*RootOf(25*_Z^4+320*_Z^2-4096)^2-189440*RootOf(25*_Z^4+320*_Z^2-4096)^2*(x^4+x^3)^(1/4)*x^2-249856*RootOf(25*_Z^4+320*_Z^2-4096)*(x^4+x^3)^(1/2)*x+243712*RootOf(25*_Z^4+320*_Z^2-4096)*x^3+139264*x^2*RootOf(25*_Z^4+320*_Z^2-4096)-950272*(x^4+x^3)^(3/4)+1474560*x^2*(x^4+x^3)^(1/4))/(5*x*RootOf(25*_Z^4+320*_Z^2-4096)^2-5*RootOf(25*_Z^4+320*_Z^2-4096)^2-64*x)/x^2)*RootOf(25*_Z^4+320*_Z^2-4096)","C"
2744,0,0,243,0.007000," ","int((x^4+b)^2/(x^20+a*x^16+4*b*x^16+4*a*b*x^12+6*b^2*x^12+6*a*b^2*x^8+4*b^3*x^8+4*a*b^3*x^4+b^4*x^4+a*b^4)^(1/4),x)","\[\int \frac{\left(x^{4}+b \right)^{2}}{\left(x^{20}+a \,x^{16}+4 b \,x^{16}+4 a b \,x^{12}+6 b^{2} x^{12}+6 a \,b^{2} x^{8}+4 b^{3} x^{8}+4 a \,b^{3} x^{4}+b^{4} x^{4}+a \,b^{4}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((x^4+b)^2/(x^20+a*x^16+4*b*x^16+4*a*b*x^12+6*b^2*x^12+6*a*b^2*x^8+4*b^3*x^8+4*a*b^3*x^4+b^4*x^4+a*b^4)^(1/4),x)","F"
2745,0,0,245,0.028000," ","int((2*p*x^3-q)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)*(b*x^4+a*(p*x^3+q)^4)/x^7,x)","\[\int \frac{\left(2 p \,x^{3}-q \right) \sqrt{p^{2} x^{6}+2 p q \,x^{3}-2 p q \,x^{2}+q^{2}}\, \left(b \,x^{4}+a \left(p \,x^{3}+q \right)^{4}\right)}{x^{7}}\, dx\]"," ",0,"int((2*p*x^3-q)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)*(b*x^4+a*(p*x^3+q)^4)/x^7,x)","F"
2746,0,0,77,0.039000," ","int((1-(x-(x^2+1)^(1/2))^(1/2))/(x^4-2*x^2*(x^2+1)^(1/2)),x)","\[\int \frac{1-\sqrt{x -\sqrt{x^{2}+1}}}{x^{4}-2 x^{2} \sqrt{x^{2}+1}}\, dx\]"," ",0,"int((1-(x-(x^2+1)^(1/2))^(1/2))/(x^4-2*x^2*(x^2+1)^(1/2)),x)","F"
2747,0,0,199,0.040000," ","int(1/(a^2*x^2-b)^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/6),x)","\[\int \frac{1}{\sqrt{a^{2} x^{2}-b}\, \left(c +\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}}\right)^{\frac{1}{6}}}\, dx\]"," ",0,"int(1/(a^2*x^2-b)^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/6),x)","F"
2748,0,0,212,0.022000," ","int(((-2*k^2+1)*x+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(-1+d+(-2*d*k^2+1)*x^2+d*k^4*x^4),x)","\[\int \frac{\left(-2 k^{2}+1\right) x +k^{2} x^{3}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{1}{3}} \left(-1+d +\left(-2 d \,k^{2}+1\right) x^{2}+d \,k^{4} x^{4}\right)}\, dx\]"," ",0,"int(((-2*k^2+1)*x+k^2*x^3)/((-x^2+1)*(-k^2*x^2+1))^(1/3)/(-1+d+(-2*d*k^2+1)*x^2+d*k^4*x^4),x)","F"
2749,0,0,212,0.027000," ","int(((-k^2+2)*x-2*x^3+k^2*x^5)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(1-d+(d*k^2-2)*x^2+x^4),x)","\[\int \frac{\left(-k^{2}+2\right) x -2 x^{3}+k^{2} x^{5}}{\left(\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)\right)^{\frac{2}{3}} \left(1-d +\left(d \,k^{2}-2\right) x^{2}+x^{4}\right)}\, dx\]"," ",0,"int(((-k^2+2)*x-2*x^3+k^2*x^5)/((-x^2+1)*(-k^2*x^2+1))^(2/3)/(1-d+(d*k^2-2)*x^2+x^4),x)","F"
2750,0,0,187,0.010000," ","int((x^4-1)*(x^4-x^2)^(1/4)/(x^4-x^2-1),x)","\[\int \frac{\left(x^{4}-1\right) \left(x^{4}-x^{2}\right)^{\frac{1}{4}}}{x^{4}-x^{2}-1}\, dx\]"," ",0,"int((x^4-1)*(x^4-x^2)^(1/4)/(x^4-x^2-1),x)","F"
2751,0,0,207,0.018000," ","int((1+(3-2*k)*x-(4+k)*x^2+3*k*x^3)/((1-x)*x*(-k*x+1))^(1/3)/(-b+(1+5*b)*x-(10*b+k)*x^2+10*b*x^3-5*b*x^4+b*x^5),x)","\[\int \frac{1+\left(3-2 k \right) x -\left(4+k \right) x^{2}+3 k \,x^{3}}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(-b +\left(1+5 b \right) x -\left(10 b +k \right) x^{2}+10 b \,x^{3}-5 b \,x^{4}+b \,x^{5}\right)}\, dx\]"," ",0,"int((1+(3-2*k)*x-(4+k)*x^2+3*k*x^3)/((1-x)*x*(-k*x+1))^(1/3)/(-b+(1+5*b)*x-(10*b+k)*x^2+10*b*x^3-5*b*x^4+b*x^5),x)","F"
2752,1,9712,145,141.390000," ","int(x^3/(x^3-x^2)^(1/3)/(x^6-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$9712$\\ risch&$\text{Expression too large to display}$&$15043$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2753,0,0,23,0.045000," ","int((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1),x)","\[\int \frac{\sqrt{x +\sqrt{x^{2}+1}}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{-x^{2}+1}\, dx\]"," ",0,"int((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1),x)","F"
2754,0,0,23,0.003000," ","int((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1),x)","\[\int \frac{\sqrt{x +\sqrt{x^{2}+1}}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{-x^{2}+1}\, dx\]"," ",0,"int((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1),x)","F"
2755,0,0,201,180.000000," ","int(1/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/4)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3),x)","\[\int \frac{1}{\sqrt{a^{2} x^{2}-b}\, \left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}} \left(c +\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/4)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3),x)","F"
2756,0,0,226,0.188000," ","int((-b+x)*(a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^2)^(2/3)/(b-(a*d+1)*x+d*x^2),x)","\[\int \frac{\left(-b +x \right) \left(a b -2 b x +x^{2}\right)}{\left(x \left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{2}{3}} \left(b -\left(a d +1\right) x +d \,x^{2}\right)}\, dx\]"," ",0,"int((-b+x)*(a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^2)^(2/3)/(b-(a*d+1)*x+d*x^2),x)","F"
2757,0,0,222,0.135000," ","int((a-5*b+4*x)*(-a^3+3*a^2*x-3*a*x^2+x^3)/((-a+x)*(-b+x))^(2/3)/(-a^5+b*d-(-5*a^4+d)*x-10*a^3*x^2+10*a^2*x^3-5*a*x^4+x^5),x)","\[\int \frac{\left(a -5 b +4 x \right) \left(-a^{3}+3 a^{2} x -3 a \,x^{2}+x^{3}\right)}{\left(\left(-a +x \right) \left(-b +x \right)\right)^{\frac{2}{3}} \left(-a^{5}+b d -\left(-5 a^{4}+d \right) x -10 a^{3} x^{2}+10 a^{2} x^{3}-5 a \,x^{4}+x^{5}\right)}\, dx\]"," ",0,"int((a-5*b+4*x)*(-a^3+3*a^2*x-3*a*x^2+x^3)/((-a+x)*(-b+x))^(2/3)/(-a^5+b*d-(-5*a^4+d)*x-10*a^3*x^2+10*a^2*x^3-5*a*x^4+x^5),x)","F"
2758,1,180,95,0.183000," ","int((1-x^3*(5+4*x)^(1/3)-x^3*(5+4*x)^(2/3))/(1-x*(5+4*x)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{3 \left(5+4 x \right)^{\frac{19}{6}}}{608}+\frac{3 \left(5+4 x \right)^{\frac{17}{6}}}{544}-\frac{15 \left(5+4 x \right)^{\frac{13}{6}}}{208}-\frac{15 \left(5+4 x \right)^{\frac{11}{6}}}{176}+\frac{3 \left(5+4 x \right)^{\frac{5}{3}}}{80}+\frac{3 \left(5+4 x \right)^{\frac{4}{3}}}{64}+\frac{75 \left(5+4 x \right)^{\frac{7}{6}}}{224}+\frac{15 \left(5+4 x \right)^{\frac{5}{6}}}{32}-\frac{15 \left(5+4 x \right)^{\frac{2}{3}}}{32}-\frac{15 \left(5+4 x \right)^{\frac{1}{3}}}{16}+\frac{3 \left(5+4 x \right)^{\frac{1}{6}}}{2}-3 \ln \left(1+\left(5+4 x \right)^{\frac{1}{6}}\right)+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}-4\right)}{\sum}\frac{\left(2 \textit{\_R}^{5}-\textit{\_R}^{4}+2 \textit{\_R}^{3}-8 \textit{\_R}^{2}+3 \textit{\_R} -4\right) \ln \left(\left(5+4 x \right)^{\frac{1}{6}}-\textit{\_R} \right)}{2 \textit{\_R}^{5}-\textit{\_R}^{2}}\right)}{2}$&$180$\\ default&$\frac{3 \left(5+4 x \right)^{\frac{19}{6}}}{608}+\frac{3 \left(5+4 x \right)^{\frac{17}{6}}}{544}-\frac{15 \left(5+4 x \right)^{\frac{13}{6}}}{208}-\frac{15 \left(5+4 x \right)^{\frac{11}{6}}}{176}+\frac{3 \left(5+4 x \right)^{\frac{5}{3}}}{80}+\frac{3 \left(5+4 x \right)^{\frac{4}{3}}}{64}+\frac{75 \left(5+4 x \right)^{\frac{7}{6}}}{224}+\frac{15 \left(5+4 x \right)^{\frac{5}{6}}}{32}-\frac{15 \left(5+4 x \right)^{\frac{2}{3}}}{32}-\frac{15 \left(5+4 x \right)^{\frac{1}{3}}}{16}+\frac{3 \left(5+4 x \right)^{\frac{1}{6}}}{2}-3 \ln \left(1+\left(5+4 x \right)^{\frac{1}{6}}\right)+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}-4\right)}{\sum}\frac{\left(2 \textit{\_R}^{5}-\textit{\_R}^{4}+2 \textit{\_R}^{3}-8 \textit{\_R}^{2}+3 \textit{\_R} -4\right) \ln \left(\left(5+4 x \right)^{\frac{1}{6}}-\textit{\_R} \right)}{2 \textit{\_R}^{5}-\textit{\_R}^{2}}\right)}{2}$&$180$\\ \hline \end{longtable}"," ",0,"3/608*(5+4*x)^(19/6)+3/544*(5+4*x)^(17/6)-15/208*(5+4*x)^(13/6)-15/176*(5+4*x)^(11/6)+3/80*(5+4*x)^(5/3)+3/64*(5+4*x)^(4/3)+75/224*(5+4*x)^(7/6)+15/32*(5+4*x)^(5/6)-15/32*(5+4*x)^(2/3)-15/16*(5+4*x)^(1/3)+3/2*(5+4*x)^(1/6)-3*ln(1+(5+4*x)^(1/6))+1/2*sum((2*_R^5-_R^4+2*_R^3-8*_R^2+3*_R-4)/(2*_R^5-_R^2)*ln((5+4*x)^(1/6)-_R),_R=RootOf(_Z^6-_Z^3-4))","A"
2759,0,0,192,0.165000," ","int(x^3*(_C3*x^3-2*_C4)*((_C3*x^3+_C0*x^2+_C4)/(_C3*x^3+_C1*x^2+_C4))^(1/2)/(2*_C3*x^3+x^2+2*_C4)/(_C3^2*x^6+2*_C3*_C4*x^3-x^4+_C4^2),x)","\[\int \frac{x^{3} \left(\textit{\_C3} \,x^{3}-2 \textit{\_C4} \right) \sqrt{\frac{\textit{\_C3} \,x^{3}+\textit{\_C0} \,x^{2}+\textit{\_C4}}{\textit{\_C3} \,x^{3}+\textit{\_C1} \,x^{2}+\textit{\_C4}}}}{\left(2 \textit{\_C3} \,x^{3}+x^{2}+2 \textit{\_C4} \right) \left(\textit{\_C3}^{2} x^{6}+2 \textit{\_C3} \textit{\_C4} \,x^{3}-x^{4}+\textit{\_C4}^{2}\right)}\, dx\]"," ",0,"int(x^3*(_C3*x^3-2*_C4)*((_C3*x^3+_C0*x^2+_C4)/(_C3*x^3+_C1*x^2+_C4))^(1/2)/(2*_C3*x^3+x^2+2*_C4)/(_C3^2*x^6+2*_C3*_C4*x^3-x^4+_C4^2),x)","F"
2760,0,0,192,0.142000," ","int(x^5*(2*_C3*x^5-3*_C4)*((_C3*x^5+_C0*x^3+_C4)/(_C3*x^5+_C1*x^3+_C4))^(1/2)/(2*_C3*x^5+x^3+2*_C4)/(_C3^2*x^10+2*_C3*_C4*x^5-x^6+_C4^2),x)","\[\int \frac{x^{5} \left(2 \textit{\_C3} \,x^{5}-3 \textit{\_C4} \right) \sqrt{\frac{\textit{\_C3} \,x^{5}+\textit{\_C0} \,x^{3}+\textit{\_C4}}{\textit{\_C3} \,x^{5}+\textit{\_C1} \,x^{3}+\textit{\_C4}}}}{\left(2 \textit{\_C3} \,x^{5}+x^{3}+2 \textit{\_C4} \right) \left(\textit{\_C3}^{2} x^{10}+2 \textit{\_C3} \textit{\_C4} \,x^{5}-x^{6}+\textit{\_C4}^{2}\right)}\, dx\]"," ",0,"int(x^5*(2*_C3*x^5-3*_C4)*((_C3*x^5+_C0*x^3+_C4)/(_C3*x^5+_C1*x^3+_C4))^(1/2)/(2*_C3*x^5+x^3+2*_C4)/(_C3^2*x^10+2*_C3*_C4*x^5-x^6+_C4^2),x)","F"
2761,1,67,11,2.247000," ","int((x^2-1)^2*(x^3+x)/(x^4+1)^(1/2)/(x^8-2*x^6+4*x^4-2*x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+1\right)}{\sum}\textit{\_R} \ln \left(\left(-x^{2}+\sqrt{x^{4}+1}\right)^{2}+\left(\textit{\_R}^{3}-\textit{\_R}^{2}+\textit{\_R} +1\right) \left(-x^{2}+\sqrt{x^{4}+1}\right)-\textit{\_R}^{3}+\textit{\_R}^{2}-\textit{\_R} \right)\right)}{4}$&$67$\\ elliptic&$\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+1\right)}{\sum}\textit{\_R} \ln \left(\left(-x^{2}+\sqrt{x^{4}+1}\right)^{2}+\left(\textit{\_R}^{3}-\textit{\_R}^{2}+\textit{\_R} +1\right) \left(-x^{2}+\sqrt{x^{4}+1}\right)-\textit{\_R}^{3}+\textit{\_R}^{2}-\textit{\_R} \right)\right)}{4}$&$67$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{\sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}-\RootOf \left(\textit{\_Z}^{4}+1\right) x^{4}-\sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}+x^{2} \sqrt{x^{4}+1}+\RootOf \left(\textit{\_Z}^{4}+1\right) x^{2}-\sqrt{x^{4}+1}-\RootOf \left(\textit{\_Z}^{4}+1\right)}{\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}+x^{4}-x^{2}+1}\right)}{4}-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}+1\right)^{5} x^{2}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{4}+\sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}+\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}-\sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{2}-x^{2} \sqrt{x^{4}+1}-\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}+\sqrt{x^{4}+1}}{\RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{2}-x^{4}+x^{2}-1}\right)}{4}$&$275$\\ \hline \end{longtable}"," ",0,"1/4*sum(_R*ln((-x^2+(x^4+1)^(1/2))^2+(_R^3-_R^2+_R+1)*(-x^2+(x^4+1)^(1/2))-_R^3+_R^2-_R),_R=RootOf(_Z^4+1))","B"
2762,1,1909,189,22.595000," ","int((2*x^2+x-1)*(x^4-x^3)^(1/4)/(x^2-x-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1909$\\ risch&$\text{Expression too large to display}$&$3971$\\ \hline \end{longtable}"," ",0,"(11/4+x)*(x^4-x^3)^(1/4)-49/16*ln((2*(x^4-x^3)^(3/4)-2*(x^4-x^3)^(1/2)*x+2*x^2*(x^4-x^3)^(1/4)-2*x^3+x^2)/x^2)+49/16*RootOf(_Z^2+1)*ln((2*(x^4-x^3)^(1/2)*RootOf(_Z^2+1)*x-2*RootOf(_Z^2+1)*x^3+2*(x^4-x^3)^(3/4)-2*x^2*(x^4-x^3)^(1/4)+RootOf(_Z^2+1)*x^2)/x^2)+1/4*RootOf(_Z^4-176*_Z^2-256)*ln(-(RootOf(_Z^4-176*_Z^2-256)^5*x^3-2*RootOf(_Z^4-176*_Z^2-256)^5*x^2+1040*RootOf(_Z^4-176*_Z^2-256)^3*(x^4-x^3)^(1/2)*x+584*RootOf(_Z^4-176*_Z^2-256)^3*x^3-288*RootOf(_Z^4-176*_Z^2-256)^3*x^2-14400*(x^4-x^3)^(3/4)*RootOf(_Z^4-176*_Z^2-256)^2-9280*RootOf(_Z^4-176*_Z^2-256)^2*(x^4-x^3)^(1/4)*x^2-30720*RootOf(_Z^4-176*_Z^2-256)*(x^4-x^3)^(1/2)*x+36864*RootOf(_Z^4-176*_Z^2-256)*x^3-10368*RootOf(_Z^4-176*_Z^2-256)*x^2-51200*(x^4-x^3)^(3/4)+35840*x^2*(x^4-x^3)^(1/4))/(x*RootOf(_Z^4-176*_Z^2-256)^2-2*RootOf(_Z^4-176*_Z^2-256)^2+32*x+16)/x^2)-1/4*RootOf(RootOf(_Z^4-176*_Z^2-256)^2+_Z^2-176)*ln((RootOf(RootOf(_Z^4-176*_Z^2-256)^2+_Z^2-176)*RootOf(_Z^4-176*_Z^2-256)^4*x^3-2*RootOf(RootOf(_Z^4-176*_Z^2-256)^2+_Z^2-176)*RootOf(_Z^4-176*_Z^2-256)^4*x^2-1040*(x^4-x^3)^(1/2)*RootOf(_Z^4-176*_Z^2-256)^2*RootOf(RootOf(_Z^4-176*_Z^2-256)^2+_Z^2-176)*x-936*RootOf(RootOf(_Z^4-176*_Z^2-256)^2+_Z^2-176)*RootOf(_Z^4-176*_Z^2-256)^2*x^3+992*RootOf(RootOf(_Z^4-176*_Z^2-256)^2+_Z^2-176)*RootOf(_Z^4-176*_Z^2-256)^2*x^2-14400*(x^4-x^3)^(3/4)*RootOf(_Z^4-176*_Z^2-256)^2-9280*RootOf(_Z^4-176*_Z^2-256)^2*(x^4-x^3)^(1/4)*x^2+152320*(x^4-x^3)^(1/2)*RootOf(RootOf(_Z^4-176*_Z^2-256)^2+_Z^2-176)*x+170624*RootOf(RootOf(_Z^4-176*_Z^2-256)^2+_Z^2-176)*x^3-123008*RootOf(RootOf(_Z^4-176*_Z^2-256)^2+_Z^2-176)*x^2+2585600*(x^4-x^3)^(3/4)+1597440*x^2*(x^4-x^3)^(1/4))/(x*RootOf(_Z^4-176*_Z^2-256)^2-2*RootOf(_Z^4-176*_Z^2-256)^2-208*x+336)/x^2)-1/64*ln((31*RootOf(_Z^4-176*_Z^2-256)^5*x^3-62*RootOf(_Z^4-176*_Z^2-256)^5*x^2+19040*RootOf(_Z^4-176*_Z^2-256)^3*(x^4-x^3)^(1/2)*x-26816*RootOf(_Z^4-176*_Z^2-256)^3*x^3+26352*RootOf(_Z^4-176*_Z^2-256)^3*x^2-28800*(x^4-x^3)^(3/4)*RootOf(_Z^4-176*_Z^2-256)^2+18560*RootOf(_Z^4-176*_Z^2-256)^2*(x^4-x^3)^(1/4)*x^2-3384320*RootOf(_Z^4-176*_Z^2-256)*(x^4-x^3)^(1/2)*x+3775744*RootOf(_Z^4-176*_Z^2-256)*x^3-2722048*RootOf(_Z^4-176*_Z^2-256)*x^2+5171200*(x^4-x^3)^(3/4)-3194880*x^2*(x^4-x^3)^(1/4))/(x*RootOf(_Z^4-176*_Z^2-256)^2-2*RootOf(_Z^4-176*_Z^2-256)^2-208*x+336)/x^2)*RootOf(_Z^4-176*_Z^2-256)^3+11/4*ln((31*RootOf(_Z^4-176*_Z^2-256)^5*x^3-62*RootOf(_Z^4-176*_Z^2-256)^5*x^2+19040*RootOf(_Z^4-176*_Z^2-256)^3*(x^4-x^3)^(1/2)*x-26816*RootOf(_Z^4-176*_Z^2-256)^3*x^3+26352*RootOf(_Z^4-176*_Z^2-256)^3*x^2-28800*(x^4-x^3)^(3/4)*RootOf(_Z^4-176*_Z^2-256)^2+18560*RootOf(_Z^4-176*_Z^2-256)^2*(x^4-x^3)^(1/4)*x^2-3384320*RootOf(_Z^4-176*_Z^2-256)*(x^4-x^3)^(1/2)*x+3775744*RootOf(_Z^4-176*_Z^2-256)*x^3-2722048*RootOf(_Z^4-176*_Z^2-256)*x^2+5171200*(x^4-x^3)^(3/4)-3194880*x^2*(x^4-x^3)^(1/4))/(x*RootOf(_Z^4-176*_Z^2-256)^2-2*RootOf(_Z^4-176*_Z^2-256)^2-208*x+336)/x^2)*RootOf(_Z^4-176*_Z^2-256)-1/64*RootOf(_Z^4-176*_Z^2-256)^2*RootOf(RootOf(_Z^4-176*_Z^2-256)^2+_Z^2-176)*ln(-(31*RootOf(RootOf(_Z^4-176*_Z^2-256)^2+_Z^2-176)*RootOf(_Z^4-176*_Z^2-256)^4*x^3-62*RootOf(RootOf(_Z^4-176*_Z^2-256)^2+_Z^2-176)*RootOf(_Z^4-176*_Z^2-256)^4*x^2-19040*(x^4-x^3)^(1/2)*RootOf(_Z^4-176*_Z^2-256)^2*RootOf(RootOf(_Z^4-176*_Z^2-256)^2+_Z^2-176)*x+15904*RootOf(RootOf(_Z^4-176*_Z^2-256)^2+_Z^2-176)*RootOf(_Z^4-176*_Z^2-256)^2*x^3-4528*RootOf(RootOf(_Z^4-176*_Z^2-256)^2+_Z^2-176)*RootOf(_Z^4-176*_Z^2-256)^2*x^2-28800*(x^4-x^3)^(3/4)*RootOf(_Z^4-176*_Z^2-256)^2+18560*RootOf(_Z^4-176*_Z^2-256)^2*(x^4-x^3)^(1/4)*x^2-33280*(x^4-x^3)^(1/2)*RootOf(RootOf(_Z^4-176*_Z^2-256)^2+_Z^2-176)*x+16384*RootOf(RootOf(_Z^4-176*_Z^2-256)^2+_Z^2-176)*x^3-4608*RootOf(RootOf(_Z^4-176*_Z^2-256)^2+_Z^2-176)*x^2-102400*(x^4-x^3)^(3/4)-71680*x^2*(x^4-x^3)^(1/4))/(x*RootOf(_Z^4-176*_Z^2-256)^2-2*RootOf(_Z^4-176*_Z^2-256)^2+32*x+16)/x^2)","C"
2763,1,684,189,31.653000," ","int((x^6+2)*(x^6+x^4-1)/(x^6-1)^(1/4)/(x^12+x^8-2*x^6+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{8}+16\right)^{3} \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{8}+16\right)^{10} x^{4}+4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{6} x^{6}-4 x^{4} \RootOf \left(\textit{\_Z}^{8}+16\right)^{6}+16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{4} \sqrt{x^{6}-1}\, x^{2}+16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{2} x^{6}+32 \RootOf \left(\textit{\_Z}^{8}+16\right)^{3} \left(x^{6}-1\right)^{\frac{3}{4}} x -4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{6}+64 \RootOf \left(\textit{\_Z}^{8}+16\right) \left(x^{6}-1\right)^{\frac{1}{4}} x^{3}+64 x^{2} \sqrt{x^{6}-1}-16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{2}}{\RootOf \left(\textit{\_Z}^{8}+16\right)^{4} x^{4}+4 x^{6}-4}\right)}{8}-\frac{\RootOf \left(\textit{\_Z}^{8}+16\right)^{5} \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{8}+16\right)^{8} x^{4}-4 \sqrt{x^{6}-1}\, \RootOf \left(\textit{\_Z}^{8}+16\right)^{6} x^{2}-4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{4} x^{6}+8 \left(x^{6}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+16\right)^{5} x^{3}-4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{4} x^{4}+16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{3} \left(x^{6}-1\right)^{\frac{3}{4}} x -16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{2} \sqrt{x^{6}-1}\, x^{2}-16 x^{6}+4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{4}+16}{\RootOf \left(\textit{\_Z}^{8}+16\right)^{4} x^{4}-4 x^{6}+4}\right)}{16}+\frac{\RootOf \left(\textit{\_Z}^{8}+16\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{8}+16\right)^{8} x^{4}+4 \sqrt{x^{6}-1}\, \RootOf \left(\textit{\_Z}^{8}+16\right)^{6} x^{2}-4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{4} x^{6}-8 \left(x^{6}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+16\right)^{5} x^{3}+4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{4} x^{4}+16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{3} \left(x^{6}-1\right)^{\frac{3}{4}} x -16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{2} \sqrt{x^{6}-1}\, x^{2}+16 x^{6}+4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{4}-16}{\RootOf \left(\textit{\_Z}^{8}+16\right)^{4} x^{4}-4 x^{6}+4}\right)}{4}-\frac{\RootOf \left(\textit{\_Z}^{8}+16\right)^{7} \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{8}+16\right)^{10} x^{4}+4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{6} x^{6}+4 x^{4} \RootOf \left(\textit{\_Z}^{8}+16\right)^{6}-16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{4} \sqrt{x^{6}-1}\, x^{2}-16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{2} x^{6}+32 \RootOf \left(\textit{\_Z}^{8}+16\right)^{3} \left(x^{6}-1\right)^{\frac{3}{4}} x -4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{6}-64 \RootOf \left(\textit{\_Z}^{8}+16\right) \left(x^{6}-1\right)^{\frac{1}{4}} x^{3}+64 x^{2} \sqrt{x^{6}-1}+16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{2}}{\RootOf \left(\textit{\_Z}^{8}+16\right)^{4} x^{4}+4 x^{6}-4}\right)}{32}$&$684$\\ \hline \end{longtable}"," ",0,"-1/8*RootOf(_Z^8+16)^3*ln(-(-RootOf(_Z^8+16)^10*x^4+4*RootOf(_Z^8+16)^6*x^6-4*x^4*RootOf(_Z^8+16)^6+16*RootOf(_Z^8+16)^4*(x^6-1)^(1/2)*x^2+16*RootOf(_Z^8+16)^2*x^6+32*RootOf(_Z^8+16)^3*(x^6-1)^(3/4)*x-4*RootOf(_Z^8+16)^6+64*RootOf(_Z^8+16)*(x^6-1)^(1/4)*x^3+64*x^2*(x^6-1)^(1/2)-16*RootOf(_Z^8+16)^2)/(RootOf(_Z^8+16)^4*x^4+4*x^6-4))-1/16*RootOf(_Z^8+16)^5*ln((-RootOf(_Z^8+16)^8*x^4-4*(x^6-1)^(1/2)*RootOf(_Z^8+16)^6*x^2-4*RootOf(_Z^8+16)^4*x^6+8*(x^6-1)^(1/4)*RootOf(_Z^8+16)^5*x^3-4*RootOf(_Z^8+16)^4*x^4+16*RootOf(_Z^8+16)^3*(x^6-1)^(3/4)*x-16*RootOf(_Z^8+16)^2*(x^6-1)^(1/2)*x^2-16*x^6+4*RootOf(_Z^8+16)^4+16)/(RootOf(_Z^8+16)^4*x^4-4*x^6+4))+1/4*RootOf(_Z^8+16)*ln((-RootOf(_Z^8+16)^8*x^4+4*(x^6-1)^(1/2)*RootOf(_Z^8+16)^6*x^2-4*RootOf(_Z^8+16)^4*x^6-8*(x^6-1)^(1/4)*RootOf(_Z^8+16)^5*x^3+4*RootOf(_Z^8+16)^4*x^4+16*RootOf(_Z^8+16)^3*(x^6-1)^(3/4)*x-16*RootOf(_Z^8+16)^2*(x^6-1)^(1/2)*x^2+16*x^6+4*RootOf(_Z^8+16)^4-16)/(RootOf(_Z^8+16)^4*x^4-4*x^6+4))-1/32*RootOf(_Z^8+16)^7*ln(-(-RootOf(_Z^8+16)^10*x^4+4*RootOf(_Z^8+16)^6*x^6+4*x^4*RootOf(_Z^8+16)^6-16*RootOf(_Z^8+16)^4*(x^6-1)^(1/2)*x^2-16*RootOf(_Z^8+16)^2*x^6+32*RootOf(_Z^8+16)^3*(x^6-1)^(3/4)*x-4*RootOf(_Z^8+16)^6-64*RootOf(_Z^8+16)*(x^6-1)^(1/4)*x^3+64*x^2*(x^6-1)^(1/2)+16*RootOf(_Z^8+16)^2)/(RootOf(_Z^8+16)^4*x^4+4*x^6-4))","C"
2764,0,0,221,180.000000," ","int(1/(c*x+d)^2/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{1}{\left(c x +d \right)^{2} \sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int(1/(c*x+d)^2/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","F"
2765,0,0,204,0.108000," ","int((x^2+1)^2/(x^2-1)^2/(x^2+(x^4+1)^(1/2))^(1/2),x)","\[\int \frac{\left(x^{2}+1\right)^{2}}{\left(x^{2}-1\right)^{2} \sqrt{x^{2}+\sqrt{x^{4}+1}}}\, dx\]"," ",0,"int((x^2+1)^2/(x^2-1)^2/(x^2+(x^4+1)^(1/2))^(1/2),x)","F"
2766,0,0,230,0.266000," ","int((a*(a*b+a*c-2*b*c)-2*(a^2-b*c)*x+(2*a-b-c)*x^2)/((-a+x)*(-b+x)*(-c+x))^(2/3)/(a^2-b*c*d+(b*d+c*d-2*a)*x+(1-d)*x^2),x)","\[\int \frac{a \left(a b +a c -2 b c \right)-2 \left(a^{2}-b c \right) x +\left(2 a -b -c \right) x^{2}}{\left(\left(-a +x \right) \left(-b +x \right) \left(-c +x \right)\right)^{\frac{2}{3}} \left(a^{2}-b c d +\left(b d +c d -2 a \right) x +\left(1-d \right) x^{2}\right)}\, dx\]"," ",0,"int((a*(a*b+a*c-2*b*c)-2*(a^2-b*c)*x+(2*a-b-c)*x^2)/((-a+x)*(-b+x)*(-c+x))^(2/3)/(a^2-b*c*d+(b*d+c*d-2*a)*x+(1-d)*x^2),x)","F"
2767,1,82800,228,0.375000," ","int((x^4+1)/(x^4-1)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$82800$\\ \hline \end{longtable}"," ",0,"result too large to display","C"
2768,0,0,205,0.086000," ","int((x^2-1)^2/(x^2+1)^2/(x^2+(x^4+1)^(1/2))^(1/2),x)","\[\int \frac{\left(x^{2}-1\right)^{2}}{\left(x^{2}+1\right)^{2} \sqrt{x^{2}+\sqrt{x^{4}+1}}}\, dx\]"," ",0,"int((x^2-1)^2/(x^2+1)^2/(x^2+(x^4+1)^(1/2))^(1/2),x)","F"
2769,0,0,233,0.022000," ","int((2*a*b^2-b*(2*a+b)*x+x^3)/(x*(-a+x)*(-b+x)^2)^(1/3)/(-a*b^2+b*(2*a+b)*x-(a+2*b+d)*x^2+x^3),x)","\[\int \frac{2 a \,b^{2}-b \left(2 a +b \right) x +x^{3}}{\left(x \left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{3}} \left(-a \,b^{2}+b \left(2 a +b \right) x -\left(a +2 b +d \right) x^{2}+x^{3}\right)}\, dx\]"," ",0,"int((2*a*b^2-b*(2*a+b)*x+x^3)/(x*(-a+x)*(-b+x)^2)^(1/3)/(-a*b^2+b*(2*a+b)*x-(a+2*b+d)*x^2+x^3),x)","F"
2770,0,0,203,0.046000," ","int((c*x-d)/x/(a*x^3-b)^(1/3),x)","\[\int \frac{c x -d}{x \left(a \,x^{3}-b \right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((c*x-d)/x/(a*x^3-b)^(1/3),x)","F"
2771,1,267,225,0.244000," ","int((a^4*x^4-b^4+c^2*x^2)/(a^4*x^4-b^4)^(1/2)/(a^4*x^4+b^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{\sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}+\frac{\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4} a^{4}+b^{4}\right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2} c^{2}-2 b^{4}\right) \left(-\frac{\sqrt{2}\, \arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}\right) a^{4}}{\sqrt{-2 b^{4}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{\sqrt{-b^{4}}}+\frac{4 \underline{\hspace{1.25 ex}}\alpha^{3} a^{4} \sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}}{b^{2}}, \frac{\sqrt{\frac{a^{2}}{b^{2}}}}{\sqrt{-\frac{a^{2}}{b^{2}}}}\right)}{\sqrt{-\frac{a^{2}}{b^{2}}}\, b^{4} \sqrt{a^{4} x^{4}-b^{4}}}\right)}{\underline{\hspace{1.25 ex}}\alpha^{3}}}{16 a^{4}}$&$267$\\ elliptic&$\frac{\left(\frac{c^{2} \left(a^{4} b^{4}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}+\frac{\left(a^{4} b^{4}\right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}}{x}+\sqrt{a^{4} b^{4}}}{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}-\frac{\left(a^{4} b^{4}\right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}}{x}+\sqrt{a^{4} b^{4}}}\right)}{16 a^{4} b^{4}}+\frac{c^{2} \left(a^{4} b^{4}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}}{\left(a^{4} b^{4}\right)^{\frac{1}{4}} x}+1\right)}{8 a^{4} b^{4}}+\frac{c^{2} \left(a^{4} b^{4}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}}{\left(a^{4} b^{4}\right)^{\frac{1}{4}} x}-1\right)}{8 a^{4} b^{4}}+\frac{\sqrt{2}\, \ln \left(\frac{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}-\frac{\left(a^{4} b^{4}\right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}}{x}+\sqrt{a^{4} b^{4}}}{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}+\frac{\left(a^{4} b^{4}\right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}}{x}+\sqrt{a^{4} b^{4}}}\right)}{8 \left(a^{4} b^{4}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}}{\left(a^{4} b^{4}\right)^{\frac{1}{4}} x}+1\right)}{4 \left(a^{4} b^{4}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}}{\left(a^{4} b^{4}\right)^{\frac{1}{4}} x}-1\right)}{4 \left(a^{4} b^{4}\right)^{\frac{1}{4}}}\right) \sqrt{2}}{2}$&$476$\\ \hline \end{longtable}"," ",0,"1/(-a^2/b^2)^(1/2)*(a^2*x^2/b^2+1)^(1/2)*(1-a^2*x^2/b^2)^(1/2)/(a^4*x^4-b^4)^(1/2)*EllipticF(x*(-a^2/b^2)^(1/2),I)+1/16/a^4*sum((_alpha^2*c^2-2*b^4)/_alpha^3*(-2^(1/2)/(-b^4)^(1/2)*arctanh(_alpha^2*(_alpha^2+x^2)*a^4/(-2*b^4)^(1/2)/(a^4*x^4-b^4)^(1/2))+4/(-a^2/b^2)^(1/2)*_alpha^3*a^4/b^4*(a^2*x^2/b^2+1)^(1/2)*(1-a^2*x^2/b^2)^(1/2)/(a^4*x^4-b^4)^(1/2)*EllipticPi(x*(-a^2/b^2)^(1/2),_alpha^2*a^2/b^2,(a^2/b^2)^(1/2)/(-a^2/b^2)^(1/2))),_alpha=RootOf(_Z^4*a^4+b^4))","C"
2772,1,81718,227,0.304000," ","int(x^2/(-x^4+1)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$81718$\\ \hline \end{longtable}"," ",0,"result too large to display","C"
2773,0,0,225,0.046000," ","int(x*(-b+x)*(-a^2*b+2*a^2*x+(-2*a+b)*x^2)/(x*(-a+x)*(-b+x))^(2/3)/(-a^4+4*a^3*x+(b^2*d-6*a^2)*x^2+2*(-b*d+2*a)*x^3+(-1+d)*x^4),x)","\[\int \frac{x \left(-b +x \right) \left(-a^{2} b +2 a^{2} x +\left(-2 a +b \right) x^{2}\right)}{\left(x \left(-a +x \right) \left(-b +x \right)\right)^{\frac{2}{3}} \left(-a^{4}+4 a^{3} x +\left(b^{2} d -6 a^{2}\right) x^{2}+2 \left(-b d +2 a \right) x^{3}+\left(-1+d \right) x^{4}\right)}\, dx\]"," ",0,"int(x*(-b+x)*(-a^2*b+2*a^2*x+(-2*a+b)*x^2)/(x*(-a+x)*(-b+x))^(2/3)/(-a^4+4*a^3*x+(b^2*d-6*a^2)*x^2+2*(-b*d+2*a)*x^3+(-1+d)*x^4),x)","F"
2774,0,0,195,0.020000," ","int((x^3-1)^(2/3)*(x^6-8*x^3+8)/x^6/(x^3-4)/(x^3-2),x)","\[\int \frac{\left(x^{3}-1\right)^{\frac{2}{3}} \left(x^{6}-8 x^{3}+8\right)}{x^{6} \left(x^{3}-4\right) \left(x^{3}-2\right)}\, dx\]"," ",0,"int((x^3-1)^(2/3)*(x^6-8*x^3+8)/x^6/(x^3-4)/(x^3-2),x)","F"
2775,0,0,207,0.043000," ","int((c+(a*x+(a^2*x^2-b)^(1/2))^(3/4))^(4/3)/(a^2*x^2-b)^(1/2),x)","\[\int \frac{\left(c +\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{3}{4}}\right)^{\frac{4}{3}}}{\sqrt{a^{2} x^{2}-b}}\, dx\]"," ",0,"int((c+(a*x+(a^2*x^2-b)^(1/2))^(3/4))^(4/3)/(a^2*x^2-b)^(1/2),x)","F"
2776,0,0,210,0.069000," ","int(1/(a*x-b)/(a^3*x^3+b^3)^(1/3),x)","\[\int \frac{1}{\left(a x -b \right) \left(a^{3} x^{3}+b^{3}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(a*x-b)/(a^3*x^3+b^3)^(1/3),x)","F"
2777,0,0,220,0.042000," ","int((a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/3)/(-a/b^2+a^2*x^2/b^2)^(1/2),x)","\[\int \frac{\left(a \,x^{2}+b x \sqrt{-\frac{a}{b^{2}}+\frac{a^{2} x^{2}}{b^{2}}}\right)^{\frac{1}{3}}}{\sqrt{-\frac{a}{b^{2}}+\frac{a^{2} x^{2}}{b^{2}}}}\, dx\]"," ",0,"int((a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/3)/(-a/b^2+a^2*x^2/b^2)^(1/2),x)","F"
2778,0,0,56,0.063000," ","int((x^2+1)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1),x)","\[\int \frac{\sqrt{x^{2}+1}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{-x^{2}+1}\, dx\]"," ",0,"int((x^2+1)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1),x)","F"
2779,0,0,56,0.003000," ","int((x^2+1)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1),x)","\[\int \frac{\sqrt{x^{2}+1}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{-x^{2}+1}\, dx\]"," ",0,"int((x^2+1)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1),x)","F"
2780,0,0,235,0.044000," ","int((-b+x)/((-a+x)*(-b+x)^2)^(2/3)/(b-a*d+(-1+d)*x),x)","\[\int \frac{-b +x}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{2}{3}} \left(b -a d +\left(-1+d \right) x \right)}\, dx\]"," ",0,"int((-b+x)/((-a+x)*(-b+x)^2)^(2/3)/(b-a*d+(-1+d)*x),x)","F"
2781,1,4832,11,0.315000," ","int((b*p*x^3-a*q*x)/(p*x^4+q)^(1/2)/(b^2*c+d*q+2*a*b*c*x^2+(a^2*c+d*p)*x^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$4832$\\ elliptic&$\text{Expression too large to display}$&$4832$\\ \hline \end{longtable}"," ",0,"-1/4/(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)/(-a^2*c-d*p)/(c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2-2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2)*ln((2*c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2-2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2-2*p*(a*b*c-(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p)*(x^2+(-a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(-a^2*c-d*p))+2*(c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2-2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2)*(p*(x^2+(-a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(-a^2*c-d*p))^2-2*p*(a*b*c-(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p)*(x^2+(-a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(-a^2*c-d*p))+c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2-2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2))/(x^2+(-a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(-a^2*c-d*p)))*a^3*c*q-1/4/(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)/(-a^2*c-d*p)/(c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2-2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2)*ln((2*c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2-2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2-2*p*(a*b*c-(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p)*(x^2+(-a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(-a^2*c-d*p))+2*(c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2-2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2)*(p*(x^2+(-a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(-a^2*c-d*p))^2-2*p*(a*b*c-(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p)*(x^2+(-a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(-a^2*c-d*p))+c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2-2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2))/(x^2+(-a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(-a^2*c-d*p)))*a*b^2*c*p-1/4/(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)/(-a^2*c-d*p)/(c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2-2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2)*ln((2*c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2-2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2-2*p*(a*b*c-(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p)*(x^2+(-a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(-a^2*c-d*p))+2*(c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2-2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2)*(p*(x^2+(-a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(-a^2*c-d*p))^2-2*p*(a*b*c-(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p)*(x^2+(-a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(-a^2*c-d*p))+c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2-2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2))/(x^2+(-a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(-a^2*c-d*p)))*a*d*p*q+1/4/(-a^2*c-d*p)/(c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2-2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2)*ln((2*c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2-2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2-2*p*(a*b*c-(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p)*(x^2+(-a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(-a^2*c-d*p))+2*(c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2-2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2)*(p*(x^2+(-a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(-a^2*c-d*p))^2-2*p*(a*b*c-(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p)*(x^2+(-a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(-a^2*c-d*p))+c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2-2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2))/(x^2+(-a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(-a^2*c-d*p)))*b*p-1/4/(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)/(a^2*c+d*p)/(c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2+2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2)*ln((2*c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2+2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2-2*p*(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p)*(x^2+(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p))+2*(c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2+2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2)*(p*(x^2+(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p))^2-2*p*(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p)*(x^2+(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p))+c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2+2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2))/(x^2+(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p)))*a^3*c*q-1/4/(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)/(a^2*c+d*p)/(c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2+2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2)*ln((2*c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2+2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2-2*p*(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p)*(x^2+(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p))+2*(c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2+2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2)*(p*(x^2+(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p))^2-2*p*(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p)*(x^2+(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p))+c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2+2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2))/(x^2+(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p)))*a*b^2*c*p-1/4/(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)/(a^2*c+d*p)/(c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2+2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2)*ln((2*c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2+2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2-2*p*(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p)*(x^2+(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p))+2*(c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2+2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2)*(p*(x^2+(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p))^2-2*p*(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p)*(x^2+(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p))+c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2+2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2))/(x^2+(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p)))*a*d*p*q-1/4/(a^2*c+d*p)/(c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2+2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2)*ln((2*c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2+2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2-2*p*(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p)*(x^2+(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p))+2*(c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2+2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2)*(p*(x^2+(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p))^2-2*p*(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p)*(x^2+(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p))+c*(a^4*c*q+a^2*b^2*c*p+a^2*d*p*q-b^2*d*p^2+2*(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2)*a*b*p)/(a^2*c+d*p)^2)^(1/2))/(x^2+(a*b*c+(-d*(a^2*c*q+b^2*c*p+d*p*q))^(1/2))/(a^2*c+d*p)))*b*p","B"
2782,1,7274,199,2.998000," ","int((a*x+b)^2*(a*p*x^3+3*b*p*x^2-2*a*q)/(p*x^3+q)^(1/2)/(b^4*c+d*q^2+4*a*b^3*c*x+6*a^2*b^2*c*x^2+(4*a^3*b*c+2*d*p*q)*x^3+a^4*c*x^4+d*p^2*x^6),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$7274$\\ elliptic&$\text{Expression too large to display}$&$7274$\\ \hline \end{longtable}"," ",0,"result too large to display","C"
2783,0,0,59,0.046000," ","int((x^2+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{\left(x^{2}+1\right) \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right)^{2} \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^2+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x)","F"
2784,0,0,59,0.005000," ","int((x^2+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{\left(x^{2}+1\right) \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right)^{2} \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^2+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x)","F"
2785,1,312,224,0.174000," ","int((k^4*x^4-1)/((1-x)*x*(-k^2*x+1))^(1/2)/(a*k^4*x^4+b*x^2+a),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\frac{2 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{a \,k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,k^{4} \textit{\_Z}^{4}+b \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2} b +2 a \right) \left(a \,k^{6} \underline{\hspace{1.25 ex}}\alpha^{3}+a \,k^{4} \underline{\hspace{1.25 ex}}\alpha^{2}+k^{2} \underline{\hspace{1.25 ex}}\alpha  a +k^{2} \underline{\hspace{1.25 ex}}\alpha  b +a +b \right) \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{a \,k^{6} \underline{\hspace{1.25 ex}}\alpha^{3}+a \,k^{4} \underline{\hspace{1.25 ex}}\alpha^{2}+k^{2} \underline{\hspace{1.25 ex}}\alpha  a +k^{2} \underline{\hspace{1.25 ex}}\alpha  b +a +b}{a \,k^{4}+a +b}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(2 a \,k^{4} \underline{\hspace{1.25 ex}}\alpha^{2}+b \right) \left(a \,k^{4}+a +b \right) \sqrt{x \left(k^{2} x^{2}-k^{2} x -x +1\right)}}}{a}$&$312$\\ default&$-\frac{2 \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{a \,k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}-\frac{\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,k^{4} \textit{\_Z}^{4}+b \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{2} b -2 a \right) \left(a \,k^{6} \underline{\hspace{1.25 ex}}\alpha^{3}+a \,k^{4} \underline{\hspace{1.25 ex}}\alpha^{2}+k^{2} \underline{\hspace{1.25 ex}}\alpha  a +k^{2} \underline{\hspace{1.25 ex}}\alpha  b +a +b \right) \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{a \,k^{6} \underline{\hspace{1.25 ex}}\alpha^{3}+a \,k^{4} \underline{\hspace{1.25 ex}}\alpha^{2}+k^{2} \underline{\hspace{1.25 ex}}\alpha  a +k^{2} \underline{\hspace{1.25 ex}}\alpha  b +a +b}{a \,k^{4}+a +b}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(2 a \,k^{4} \underline{\hspace{1.25 ex}}\alpha^{2}+b \right) \left(a \,k^{4}+a +b \right) \sqrt{x \left(k^{2} x^{2}-k^{2} x -x +1\right)}}}{a}$&$314$\\ \hline \end{longtable}"," ",0,"-2/a/k^2*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticF((-(x-1/k^2)*k^2)^(1/2),(1/k^2/(1/k^2-1))^(1/2))+1/a*sum((_alpha^2*b+2*a)/_alpha/(2*_alpha^2*a*k^4+b)*(_alpha^3*a*k^6+_alpha^2*a*k^4+_alpha*a*k^2+_alpha*b*k^2+a+b)/(a*k^4+a+b)*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(x*(k^2*x^2-k^2*x-x+1))^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),(_alpha^3*a*k^6+_alpha^2*a*k^4+_alpha*a*k^2+_alpha*b*k^2+a+b)/(a*k^4+a+b),(1/k^2/(1/k^2-1))^(1/2)),_alpha=RootOf(_Z^4*a*k^4+_Z^2*b+a))","C"
2786,0,0,214,0.041000," ","int(x^5*(-4*a+3*x)/(x^2*(-a+x))^(1/3)/(d*x^8-a^2+2*a*x-x^2),x)","\[\int \frac{x^{5} \left(-4 a +3 x \right)}{\left(x^{2} \left(-a +x \right)\right)^{\frac{1}{3}} \left(d \,x^{8}-a^{2}+2 a x -x^{2}\right)}\, dx\]"," ",0,"int(x^5*(-4*a+3*x)/(x^2*(-a+x))^(1/3)/(d*x^8-a^2+2*a*x-x^2),x)","F"
2787,1,18,223,0.193000," ","int(1/8*(1-x)^(1/2)/(1+x)^(7/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{\left(x +4\right) \left(1-x \right)^{\frac{3}{2}}}{120 \left(1+x \right)^{\frac{5}{2}}}$&$18$\\ default&$-\frac{\sqrt{1-x}}{20 \left(1+x \right)^{\frac{5}{2}}}+\frac{\sqrt{1-x}}{120 \left(1+x \right)^{\frac{3}{2}}}+\frac{\sqrt{1-x}}{120 \sqrt{1+x}}$&$44$\\ risch&$-\frac{\sqrt{\left(1+x \right) \left(1-x \right)}\, \left(x^{3}+2 x^{2}-7 x +4\right)}{120 \sqrt{1-x}\, \left(1+x \right)^{\frac{5}{2}} \sqrt{-\left(-1+x \right) \left(1+x \right)}}$&$49$\\ \hline \end{longtable}"," ",0,"-1/120*(x+4)*(1-x)^(3/2)/(1+x)^(5/2)","A"
2788,0,0,237,0.025000," ","int((2*a*b^2-b*(2*a+b)*x+x^3)/(x*(-a+x)*(-b+x)^2)^(1/3)/(-a*b^2*d+b*(2*a+b)*d*x-(a*d+2*b*d+1)*x^2+d*x^3),x)","\[\int \frac{2 a \,b^{2}-b \left(2 a +b \right) x +x^{3}}{\left(x \left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{3}} \left(-a \,b^{2} d +b \left(2 a +b \right) d x -\left(a d +2 b d +1\right) x^{2}+d \,x^{3}\right)}\, dx\]"," ",0,"int((2*a*b^2-b*(2*a+b)*x+x^3)/(x*(-a+x)*(-b+x)^2)^(1/3)/(-a*b^2*d+b*(2*a+b)*d*x-(a*d+2*b*d+1)*x^2+d*x^3),x)","F"
2789,1,2230,191,25.563000," ","int((x^2-x)*(x^4-x^3)^(1/4)/(x^2-x-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2230$\\ risch&$\text{Expression too large to display}$&$4529$\\ \hline \end{longtable}"," ",0,"(-1/8+1/2*x)*(x^4-x^3)^(1/4)+29/32*ln((2*(x^4-x^3)^(3/4)+2*(x^4-x^3)^(1/2)*x+2*x^2*(x^4-x^3)^(1/4)+2*x^3-x^2)/x^2)+1/40*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*ln((425*RootOf(25*_Z^4+320*_Z^2-4096)^4*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x^3-850*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*RootOf(25*_Z^4+320*_Z^2-4096)^4*x^2-39040*(x^4-x^3)^(1/2)*RootOf(25*_Z^4+320*_Z^2-4096)^2*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x+51840*RootOf(25*_Z^4+320*_Z^2-4096)^2*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x^3-43840*RootOf(25*_Z^4+320*_Z^2-4096)^2*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x^2+1152000*(x^4-x^3)^(3/4)*RootOf(25*_Z^4+320*_Z^2-4096)^2-742400*RootOf(25*_Z^4+320*_Z^2-4096)^2*(x^4-x^3)^(1/4)*x^2-843776*(x^4-x^3)^(1/2)*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x+851968*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x^3-532480*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x^2+24248320*(x^4-x^3)^(3/4)-14745600*x^2*(x^4-x^3)^(1/4))/(5*x*RootOf(25*_Z^4+320*_Z^2-4096)^2-10*RootOf(25*_Z^4+320*_Z^2-4096)^2+128*x-192)/x^2)+1/8*RootOf(25*_Z^4+320*_Z^2-4096)*ln((425*x^3*RootOf(25*_Z^4+320*_Z^2-4096)^5-850*x^2*RootOf(25*_Z^4+320*_Z^2-4096)^5+39040*RootOf(25*_Z^4+320*_Z^2-4096)^3*(x^4-x^3)^(1/2)*x-40960*x^3*RootOf(25*_Z^4+320*_Z^2-4096)^3+22080*x^2*RootOf(25*_Z^4+320*_Z^2-4096)^3-230400*(x^4-x^3)^(3/4)*RootOf(25*_Z^4+320*_Z^2-4096)^2+148480*RootOf(25*_Z^4+320*_Z^2-4096)^2*(x^4-x^3)^(1/4)*x^2-344064*RootOf(25*_Z^4+320*_Z^2-4096)*(x^4-x^3)^(1/2)*x+258048*RootOf(25*_Z^4+320*_Z^2-4096)*x^3-110592*x^2*RootOf(25*_Z^4+320*_Z^2-4096)+1900544*(x^4-x^3)^(3/4)-1048576*x^2*(x^4-x^3)^(1/4))/(5*x*RootOf(25*_Z^4+320*_Z^2-4096)^2-10*RootOf(25*_Z^4+320*_Z^2-4096)^2-64*x+64)/x^2)-1/512*RootOf(25*_Z^4+320*_Z^2-4096)^2*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*ln(-(325*RootOf(25*_Z^4+320*_Z^2-4096)^4*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x^3-650*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*RootOf(25*_Z^4+320*_Z^2-4096)^4*x^2-32960*(x^4-x^3)^(1/2)*RootOf(25*_Z^4+320*_Z^2-4096)^2*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x-31840*RootOf(25*_Z^4+320*_Z^2-4096)^2*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x^3+17920*RootOf(25*_Z^4+320*_Z^2-4096)^2*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x^2+576000*(x^4-x^3)^(3/4)*RootOf(25*_Z^4+320*_Z^2-4096)^2+371200*RootOf(25*_Z^4+320*_Z^2-4096)^2*(x^4-x^3)^(1/4)*x^2+249856*(x^4-x^3)^(1/2)*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x+243712*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x^3-104448*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x^2-4751360*(x^4-x^3)^(3/4)-2621440*x^2*(x^4-x^3)^(1/4))/(5*x*RootOf(25*_Z^4+320*_Z^2-4096)^2-10*RootOf(25*_Z^4+320*_Z^2-4096)^2-64*x+64)/x^2)+5/512*ln(-(325*x^3*RootOf(25*_Z^4+320*_Z^2-4096)^5-650*x^2*RootOf(25*_Z^4+320*_Z^2-4096)^5+32960*RootOf(25*_Z^4+320*_Z^2-4096)^3*(x^4-x^3)^(1/2)*x+40160*x^3*RootOf(25*_Z^4+320*_Z^2-4096)^3-34560*x^2*RootOf(25*_Z^4+320*_Z^2-4096)^3-115200*(x^4-x^3)^(3/4)*RootOf(25*_Z^4+320*_Z^2-4096)^2-74240*RootOf(25*_Z^4+320*_Z^2-4096)^2*(x^4-x^3)^(1/4)*x^2+671744*RootOf(25*_Z^4+320*_Z^2-4096)*(x^4-x^3)^(1/2)*x+704512*RootOf(25*_Z^4+320*_Z^2-4096)*x^3-440320*x^2*RootOf(25*_Z^4+320*_Z^2-4096)-2424832*(x^4-x^3)^(3/4)-1474560*x^2*(x^4-x^3)^(1/4))/(5*x*RootOf(25*_Z^4+320*_Z^2-4096)^2-10*RootOf(25*_Z^4+320*_Z^2-4096)^2+128*x-192)/x^2)*RootOf(25*_Z^4+320*_Z^2-4096)^3+1/8*ln(-(325*x^3*RootOf(25*_Z^4+320*_Z^2-4096)^5-650*x^2*RootOf(25*_Z^4+320*_Z^2-4096)^5+32960*RootOf(25*_Z^4+320*_Z^2-4096)^3*(x^4-x^3)^(1/2)*x+40160*x^3*RootOf(25*_Z^4+320*_Z^2-4096)^3-34560*x^2*RootOf(25*_Z^4+320*_Z^2-4096)^3-115200*(x^4-x^3)^(3/4)*RootOf(25*_Z^4+320*_Z^2-4096)^2-74240*RootOf(25*_Z^4+320*_Z^2-4096)^2*(x^4-x^3)^(1/4)*x^2+671744*RootOf(25*_Z^4+320*_Z^2-4096)*(x^4-x^3)^(1/2)*x+704512*RootOf(25*_Z^4+320*_Z^2-4096)*x^3-440320*x^2*RootOf(25*_Z^4+320*_Z^2-4096)-2424832*(x^4-x^3)^(3/4)-1474560*x^2*(x^4-x^3)^(1/4))/(5*x*RootOf(25*_Z^4+320*_Z^2-4096)^2-10*RootOf(25*_Z^4+320*_Z^2-4096)^2+128*x-192)/x^2)*RootOf(25*_Z^4+320*_Z^2-4096)-29/2048*RootOf(25*_Z^4+320*_Z^2-4096)*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*ln(-(2*(x^4-x^3)^(1/2)*RootOf(25*_Z^4+320*_Z^2-4096)*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*x-2*RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*RootOf(25*_Z^4+320*_Z^2-4096)*x^3+RootOf(_Z^2+25*RootOf(25*_Z^4+320*_Z^2-4096)^2+320)*RootOf(25*_Z^4+320*_Z^2-4096)*x^2-128*(x^4-x^3)^(3/4)+128*x^2*(x^4-x^3)^(1/4))/x^2)","C"
2790,1,190,92,0.511000," ","int((a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)/x/(d+(c+(a*x+b)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{8 \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{5}{2}}}{5}-\frac{16 d \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{3}{2}}}{3}+8 d^{2} \sqrt{d +\sqrt{c +\sqrt{a x +b}}}+b \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 d \,\textit{\_Z}^{6}+\left(6 d^{2}-2 c \right) \textit{\_Z}^{4}+\left(-4 d^{3}+4 c d \right) \textit{\_Z}^{2}+d^{4}-2 c \,d^{2}+c^{2}-b \right)}{\sum}\frac{\left(-\textit{\_R}^{4}+2 \textit{\_R}^{2} d -d^{2}\right) \ln \left(\sqrt{d +\sqrt{c +\sqrt{a x +b}}}-\textit{\_R} \right)}{-\textit{\_R}^{7}+3 \textit{\_R}^{5} d -3 \textit{\_R}^{3} d^{2}+\textit{\_R}^{3} c +\textit{\_R} \,d^{3}-\textit{\_R} c d}\right)$&$190$\\ default&$\frac{8 \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{5}{2}}}{5}-\frac{16 d \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{3}{2}}}{3}+8 d^{2} \sqrt{d +\sqrt{c +\sqrt{a x +b}}}+b \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 d \,\textit{\_Z}^{6}+\left(6 d^{2}-2 c \right) \textit{\_Z}^{4}+\left(-4 d^{3}+4 c d \right) \textit{\_Z}^{2}+d^{4}-2 c \,d^{2}+c^{2}-b \right)}{\sum}\frac{\left(-\textit{\_R}^{4}+2 \textit{\_R}^{2} d -d^{2}\right) \ln \left(\sqrt{d +\sqrt{c +\sqrt{a x +b}}}-\textit{\_R} \right)}{-\textit{\_R}^{7}+3 \textit{\_R}^{5} d -3 \textit{\_R}^{3} d^{2}+\textit{\_R}^{3} c +\textit{\_R} \,d^{3}-\textit{\_R} c d}\right)$&$190$\\ \hline \end{longtable}"," ",0,"8/5*(d+(c+(a*x+b)^(1/2))^(1/2))^(5/2)-16/3*d*(d+(c+(a*x+b)^(1/2))^(1/2))^(3/2)+8*d^2*(d+(c+(a*x+b)^(1/2))^(1/2))^(1/2)+b*sum((-_R^4+2*_R^2*d-d^2)/(-_R^7+3*_R^5*d-3*_R^3*d^2+_R^3*c+_R*d^3-_R*c*d)*ln((d+(c+(a*x+b)^(1/2))^(1/2))^(1/2)-_R),_R=RootOf(_Z^8-4*d*_Z^6+(6*d^2-2*c)*_Z^4+(-4*d^3+4*c*d)*_Z^2+d^4-2*c*d^2+c^2-b))","B"
2791,1,190,92,0.526000," ","int((a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)/x/(d+(c+(a*x+b)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{8 \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{5}{2}}}{5}-\frac{16 d \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{3}{2}}}{3}+8 d^{2} \sqrt{d +\sqrt{c +\sqrt{a x +b}}}+b \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 d \,\textit{\_Z}^{6}+\left(6 d^{2}-2 c \right) \textit{\_Z}^{4}+\left(-4 d^{3}+4 c d \right) \textit{\_Z}^{2}+d^{4}-2 c \,d^{2}+c^{2}-b \right)}{\sum}\frac{\left(-\textit{\_R}^{4}+2 \textit{\_R}^{2} d -d^{2}\right) \ln \left(\sqrt{d +\sqrt{c +\sqrt{a x +b}}}-\textit{\_R} \right)}{-\textit{\_R}^{7}+3 \textit{\_R}^{5} d -3 \textit{\_R}^{3} d^{2}+\textit{\_R}^{3} c +\textit{\_R} \,d^{3}-\textit{\_R} c d}\right)$&$190$\\ default&$\frac{8 \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{5}{2}}}{5}-\frac{16 d \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{3}{2}}}{3}+8 d^{2} \sqrt{d +\sqrt{c +\sqrt{a x +b}}}+b \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 d \,\textit{\_Z}^{6}+\left(6 d^{2}-2 c \right) \textit{\_Z}^{4}+\left(-4 d^{3}+4 c d \right) \textit{\_Z}^{2}+d^{4}-2 c \,d^{2}+c^{2}-b \right)}{\sum}\frac{\left(-\textit{\_R}^{4}+2 \textit{\_R}^{2} d -d^{2}\right) \ln \left(\sqrt{d +\sqrt{c +\sqrt{a x +b}}}-\textit{\_R} \right)}{-\textit{\_R}^{7}+3 \textit{\_R}^{5} d -3 \textit{\_R}^{3} d^{2}+\textit{\_R}^{3} c +\textit{\_R} \,d^{3}-\textit{\_R} c d}\right)$&$190$\\ \hline \end{longtable}"," ",0,"8/5*(d+(c+(a*x+b)^(1/2))^(1/2))^(5/2)-16/3*d*(d+(c+(a*x+b)^(1/2))^(1/2))^(3/2)+8*d^2*(d+(c+(a*x+b)^(1/2))^(1/2))^(1/2)+b*sum((-_R^4+2*_R^2*d-d^2)/(-_R^7+3*_R^5*d-3*_R^3*d^2+_R^3*c+_R*d^3-_R*c*d)*ln((d+(c+(a*x+b)^(1/2))^(1/2))^(1/2)-_R),_R=RootOf(_Z^8-4*d*_Z^6+(6*d^2-2*c)*_Z^4+(-4*d^3+4*c*d)*_Z^2+d^4-2*c*d^2+c^2-b))","B"
2792,0,0,225,0.022000," ","int(1/(1+(a*x+(a^2*x^2-b)^(1/2))^(1/2))^(1/2),x)","\[\int \frac{1}{\sqrt{1+\sqrt{a x +\sqrt{a^{2} x^{2}-b}}}}\, dx\]"," ",0,"int(1/(1+(a*x+(a^2*x^2-b)^(1/2))^(1/2))^(1/2),x)","F"
2793,0,0,218,0.076000," ","int((-1+x)*(k*x-1)*(-2*x+(1+k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(b-2*b*(1+k)*x+(b*k^2+4*b*k+b)*x^2-2*b*k*(1+k)*x^3+(b*k^2-1)*x^4),x)","\[\int \frac{\left(-1+x \right) \left(k x -1\right) \left(-2 x +\left(1+k \right) x^{2}\right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{2}{3}} \left(b -2 b \left(1+k \right) x +\left(b \,k^{2}+4 b k +b \right) x^{2}-2 b k \left(1+k \right) x^{3}+\left(b \,k^{2}-1\right) x^{4}\right)}\, dx\]"," ",0,"int((-1+x)*(k*x-1)*(-2*x+(1+k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(b-2*b*(1+k)*x+(b*k^2+4*b*k+b)*x^2-2*b*k*(1+k)*x^3+(b*k^2-1)*x^4),x)","F"
2794,0,0,212,0.023000," ","int((-1+2*(-2+k)*x+3*k*x^2)*(x^3-3*x^2+3*x-1)/((1-x)*x*(-k*x+1))^(2/3)/(-b+(1+5*b)*x-(10*b+k)*x^2+10*b*x^3-5*b*x^4+b*x^5),x)","\[\int \frac{\left(-1+2 \left(-2+k \right) x +3 k \,x^{2}\right) \left(x^{3}-3 x^{2}+3 x -1\right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{2}{3}} \left(-b +\left(1+5 b \right) x -\left(10 b +k \right) x^{2}+10 b \,x^{3}-5 b \,x^{4}+b \,x^{5}\right)}\, dx\]"," ",0,"int((-1+2*(-2+k)*x+3*k*x^2)*(x^3-3*x^2+3*x-1)/((1-x)*x*(-k*x+1))^(2/3)/(-b+(1+5*b)*x-(10*b+k)*x^2+10*b*x^3-5*b*x^4+b*x^5),x)","F"
2795,0,0,51,0.017000," ","int((a*x^4+2*b)^(1/4)*(a*x^8-4*b)/x^6/(a*x^8+c*x^4-4*b),x)","\[\int \frac{\left(a \,x^{4}+2 b \right)^{\frac{1}{4}} \left(a \,x^{8}-4 b \right)}{x^{6} \left(a \,x^{8}+c \,x^{4}-4 b \right)}\, dx\]"," ",0,"int((a*x^4+2*b)^(1/4)*(a*x^8-4*b)/x^6/(a*x^8+c*x^4-4*b),x)","F"
2796,0,0,51,0.006000," ","int((a*x^4+2*b)^(1/4)*(a*x^8-4*b)/x^6/(a*x^8+c*x^4-4*b),x)","\[\int \frac{\left(a \,x^{4}+2 b \right)^{\frac{1}{4}} \left(a \,x^{8}-4 b \right)}{x^{6} \left(a \,x^{8}+c \,x^{4}-4 b \right)}\, dx\]"," ",0,"int((a*x^4+2*b)^(1/4)*(a*x^8-4*b)/x^6/(a*x^8+c*x^4-4*b),x)","F"
2797,1,435,235,0.266000," ","int((a^12*x^12-b^12)/(a^4*x^4-b^4)^(1/2)/(a^12*x^12+b^12),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(-\frac{\ln \left(a^{2} b^{2}+\frac{a b \sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{x}+\frac{a^{4} x^{4}-b^{4}}{x^{2}}\right)}{6 a b}+\frac{\arctan \left(\frac{2 a b +\frac{2 \sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{x}}{2 a b}\right)}{3 a b}+\frac{\sqrt{2}\, \ln \left(\frac{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}-\frac{\left(a^{4} b^{4}\right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}}{x}+\sqrt{a^{4} b^{4}}}{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}+\frac{\left(a^{4} b^{4}\right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}}{x}+\sqrt{a^{4} b^{4}}}\right)}{24 \left(a^{4} b^{4}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}}{\left(a^{4} b^{4}\right)^{\frac{1}{4}} x}+1\right)}{12 \left(a^{4} b^{4}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}}{\left(a^{4} b^{4}\right)^{\frac{1}{4}} x}-1\right)}{12 \left(a^{4} b^{4}\right)^{\frac{1}{4}}}+\frac{\ln \left(a^{2} b^{2}-\frac{a b \sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{x}+\frac{a^{4} x^{4}-b^{4}}{x^{2}}\right)}{6 a b}+\frac{\arctan \left(\frac{-2 a b +\frac{2 \sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{x}}{2 a b}\right)}{3 a b}\right) \sqrt{2}}{2}$&$435$\\ default&$\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{\sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}-\frac{b^{4} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{8} \textit{\_Z}^{8}-a^{4} b^{4} \textit{\_Z}^{4}+b^{8}\right)}{\sum}\frac{\left(-a^{4} \underline{\hspace{1.25 ex}}\alpha^{4}+2 b^{4}\right) \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{6} a^{4}-\underline{\hspace{1.25 ex}}\alpha^{2} b^{4}+b^{4} x^{2}\right) a^{4}}{b^{4} \sqrt{a^{4} \underline{\hspace{1.25 ex}}\alpha^{4}-b^{4}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{\sqrt{a^{4} \underline{\hspace{1.25 ex}}\alpha^{4}-b^{4}}}+\frac{2 a^{4} \underline{\hspace{1.25 ex}}\alpha^{3} \left(a^{4} \underline{\hspace{1.25 ex}}\alpha^{4}-b^{4}\right) \sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(a^{4} \underline{\hspace{1.25 ex}}\alpha^{4}-b^{4}\right) a^{2}}{b^{6}}, \frac{\sqrt{\frac{a^{2}}{b^{2}}}}{\sqrt{-\frac{a^{2}}{b^{2}}}}\right)}{\sqrt{-\frac{a^{2}}{b^{2}}}\, b^{8} \sqrt{a^{4} x^{4}-b^{4}}}\right)}{\underline{\hspace{1.25 ex}}\alpha^{3} \left(2 a^{4} \underline{\hspace{1.25 ex}}\alpha^{4}-b^{4}\right)}\right)}{12 a^{4}}-\frac{b^{4} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4} a^{4}+b^{4}\right)}{\sum}\frac{-\frac{\sqrt{2}\, \arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}\right) a^{4}}{\sqrt{-2 b^{4}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{\sqrt{-b^{4}}}+\frac{4 \underline{\hspace{1.25 ex}}\alpha^{3} a^{4} \sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}}{b^{2}}, \frac{\sqrt{\frac{a^{2}}{b^{2}}}}{\sqrt{-\frac{a^{2}}{b^{2}}}}\right)}{\sqrt{-\frac{a^{2}}{b^{2}}}\, b^{4} \sqrt{a^{4} x^{4}-b^{4}}}}{\underline{\hspace{1.25 ex}}\alpha^{3}}\right)}{24 a^{4}}$&$541$\\ \hline \end{longtable}"," ",0,"1/2*(-1/6/a/b*ln(a^2*b^2+a*b*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x+(a^4*x^4-b^4)/x^2)+1/3/a/b*arctan(1/2*(2*a*b+2*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x)/a/b)+1/24/(a^4*b^4)^(1/4)*2^(1/2)*ln((1/2*(a^4*x^4-b^4)/x^2-(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x+(a^4*b^4)^(1/2))/(1/2*(a^4*x^4-b^4)/x^2+(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x+(a^4*b^4)^(1/2)))+1/12/(a^4*b^4)^(1/4)*2^(1/2)*arctan(1/(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x+1)+1/12/(a^4*b^4)^(1/4)*2^(1/2)*arctan(1/(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x-1)+1/6/a/b*ln(a^2*b^2-a*b*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x+(a^4*x^4-b^4)/x^2)+1/3/a/b*arctan(1/2*(-2*a*b+2*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x)/a/b))*2^(1/2)","A"
2798,1,1540,11,0.274000," ","int(1/(1-(1+x)*(a*x^2+b*x+c)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{4}+\left(2 a +b \right) \textit{\_Z}^{3}+\left(a +2 b +c \right) \textit{\_Z}^{2}+\left(b +2 c \right) \textit{\_Z} +c -1\right)}{\sum}\frac{\ln \left(x -\textit{\_R} \right)}{4 \textit{\_R}^{3} a +6 \textit{\_R}^{2} a +3 \textit{\_R}^{2} b +2 \textit{\_R} a +4 \textit{\_R} b +2 \textit{\_R} c +b +2 c}\right)+\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8} a -\left(4 a^{\frac{3}{2}}+2 \sqrt{a}\, b \right) \textit{\_Z}^{7}-\left(-4 a^{2}-10 a b -b^{2}\right) \textit{\_Z}^{6}-\left(12 a^{\frac{3}{2}} b +4 a^{\frac{3}{2}} c +8 b^{2} \sqrt{a}-2 \sqrt{a}\, b c \right) \textit{\_Z}^{5}-\left(-8 a^{2} c -13 a \,b^{2}-2 a b c +2 a \,c^{2}-2 b^{3}+2 b^{2} c +16 a^{2}\right) \textit{\_Z}^{4}-\left(16 a^{\frac{3}{2}} c b -4 a^{\frac{3}{2}} c^{2}-32 a^{\frac{3}{2}} b +6 \sqrt{a}\, b^{3}-4 \sqrt{a}\, c \,b^{2}-2 \sqrt{a}\, c^{2} b \right) \textit{\_Z}^{3}-\left(-4 a^{2} c^{2}-10 a \,b^{2} c +10 a b \,c^{2}-b^{4}+2 b^{3} c -b^{2} c^{2}+24 a \,b^{2}\right) \textit{\_Z}^{2}-\left(4 a^{\frac{3}{2}} c^{2} b -4 a^{\frac{3}{2}} c^{3}+2 \sqrt{a}\, c \,b^{3}-4 \sqrt{a}\, c^{2} b^{2}+2 \sqrt{a}\, c^{3} b -8 \sqrt{a}\, b^{3}\right) \textit{\_Z} +a \,b^{2} c^{2}-2 a b \,c^{3}+a \,c^{4}-b^{4}\right)}{\sum}\frac{\left(b \left(5 a \,\textit{\_R}^{4}+\left(6 a c +b^{2}\right) \textit{\_R}^{2}+a \,c^{2}\right)-2 \textit{\_R}^{5} a^{\frac{3}{2}}+4 \textit{\_R}^{3} \left(-a^{\frac{3}{2}} c -b^{2} \sqrt{a}\right)+2 c \textit{\_R} \left(-a^{\frac{3}{2}} c -b^{2} \sqrt{a}\right)\right) \ln \left(\sqrt{a \,x^{2}+b x +c}-\sqrt{a}\, x -\textit{\_R} \right)}{-3 \textit{\_R}^{5} b^{2}-4 \sqrt{a}\, b^{3}-12 a^{2} \textit{\_R}^{5}-2 a^{\frac{3}{2}} c^{3}+2 a^{\frac{3}{2}} c^{2} b +\sqrt{a}\, c \,b^{3}-4 \textit{\_R}^{7} a +32 \textit{\_R}^{3} a^{2}+\sqrt{a}\, c^{3} b +4 \textit{\_R}^{3} a \,c^{2}-4 \textit{\_R}^{3} b^{3}-\textit{\_R} \,b^{4}+14 a^{\frac{3}{2}} \textit{\_R}^{6}-\textit{\_R} \,b^{2} c^{2}+24 a \,b^{2} \textit{\_R} -2 \sqrt{a}\, c^{2} b^{2}-6 a^{\frac{3}{2}} \textit{\_R}^{2} c^{2}+20 \sqrt{a}\, \textit{\_R}^{4} b^{2}+9 \sqrt{a}\, \textit{\_R}^{2} b^{3}-16 a^{2} \textit{\_R}^{3} c +30 a^{\frac{3}{2}} \textit{\_R}^{4} b +10 a^{\frac{3}{2}} \textit{\_R}^{4} c +2 \textit{\_R} \,b^{3} c -30 \textit{\_R}^{5} a b -26 \textit{\_R}^{3} a \,b^{2}-4 a^{2} \textit{\_R} \,c^{2}-48 a^{\frac{3}{2}} \textit{\_R}^{2} b +7 \sqrt{a}\, \textit{\_R}^{6} b -10 \textit{\_R} a \,b^{2} c +10 \textit{\_R} a b \,c^{2}+24 a^{\frac{3}{2}} \textit{\_R}^{2} b c -5 \sqrt{a}\, \textit{\_R}^{4} b c -3 \sqrt{a}\, \textit{\_R}^{2} b \,c^{2}-6 \sqrt{a}\, \textit{\_R}^{2} b^{2} c -4 \textit{\_R}^{3} a b c +4 \textit{\_R}^{3} b^{2} c}\right)-\frac{\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8} a -\left(4 a^{\frac{3}{2}}+2 \sqrt{a}\, b \right) \textit{\_Z}^{7}-\left(-4 a^{2}-10 a b -b^{2}\right) \textit{\_Z}^{6}-\left(12 a^{\frac{3}{2}} b +4 a^{\frac{3}{2}} c +8 b^{2} \sqrt{a}-2 \sqrt{a}\, b c \right) \textit{\_Z}^{5}-\left(-8 a^{2} c -13 a \,b^{2}-2 a b c +2 a \,c^{2}-2 b^{3}+2 b^{2} c +16 a^{2}\right) \textit{\_Z}^{4}-\left(16 a^{\frac{3}{2}} c b -4 a^{\frac{3}{2}} c^{2}-32 a^{\frac{3}{2}} b +6 \sqrt{a}\, b^{3}-4 \sqrt{a}\, c \,b^{2}-2 \sqrt{a}\, c^{2} b \right) \textit{\_Z}^{3}-\left(-4 a^{2} c^{2}-10 a \,b^{2} c +10 a b \,c^{2}-b^{4}+2 b^{3} c -b^{2} c^{2}+24 a \,b^{2}\right) \textit{\_Z}^{2}-\left(4 a^{\frac{3}{2}} c^{2} b -4 a^{\frac{3}{2}} c^{3}+2 \sqrt{a}\, c \,b^{3}-4 \sqrt{a}\, c^{2} b^{2}+2 \sqrt{a}\, c^{3} b -8 \sqrt{a}\, b^{3}\right) \textit{\_Z} +a \,b^{2} c^{2}-2 a b \,c^{3}+a \,c^{4}-b^{4}\right)}{\sum}\frac{\left(a \left(-a \,\textit{\_R}^{6}+\left(-a c -b^{2}\right) \textit{\_R}^{4}+c \left(a c +b^{2}\right) \textit{\_R}^{2}+a \,c^{3}\right)+2 b \left(\textit{\_R}^{5} a^{\frac{3}{2}}-c^{2} \textit{\_R} \,a^{\frac{3}{2}}\right)\right) \ln \left(\sqrt{a \,x^{2}+b x +c}-\sqrt{a}\, x -\textit{\_R} \right)}{-3 \textit{\_R}^{5} b^{2}-4 \sqrt{a}\, b^{3}-12 a^{2} \textit{\_R}^{5}-2 a^{\frac{3}{2}} c^{3}+2 a^{\frac{3}{2}} c^{2} b +\sqrt{a}\, c \,b^{3}-4 \textit{\_R}^{7} a +32 \textit{\_R}^{3} a^{2}+\sqrt{a}\, c^{3} b +4 \textit{\_R}^{3} a \,c^{2}-4 \textit{\_R}^{3} b^{3}-\textit{\_R} \,b^{4}+14 a^{\frac{3}{2}} \textit{\_R}^{6}-\textit{\_R} \,b^{2} c^{2}+24 a \,b^{2} \textit{\_R} -2 \sqrt{a}\, c^{2} b^{2}-6 a^{\frac{3}{2}} \textit{\_R}^{2} c^{2}+20 \sqrt{a}\, \textit{\_R}^{4} b^{2}+9 \sqrt{a}\, \textit{\_R}^{2} b^{3}-16 a^{2} \textit{\_R}^{3} c +30 a^{\frac{3}{2}} \textit{\_R}^{4} b +10 a^{\frac{3}{2}} \textit{\_R}^{4} c +2 \textit{\_R} \,b^{3} c -30 \textit{\_R}^{5} a b -26 \textit{\_R}^{3} a \,b^{2}-4 a^{2} \textit{\_R} \,c^{2}-48 a^{\frac{3}{2}} \textit{\_R}^{2} b +7 \sqrt{a}\, \textit{\_R}^{6} b -10 \textit{\_R} a \,b^{2} c +10 \textit{\_R} a b \,c^{2}+24 a^{\frac{3}{2}} \textit{\_R}^{2} b c -5 \sqrt{a}\, \textit{\_R}^{4} b c -3 \sqrt{a}\, \textit{\_R}^{2} b \,c^{2}-6 \sqrt{a}\, \textit{\_R}^{2} b^{2} c -4 \textit{\_R}^{3} a b c +4 \textit{\_R}^{3} b^{2} c}}{a}$&$1540$\\ \hline \end{longtable}"," ",0,"-sum(1/(4*_R^3*a+6*_R^2*a+3*_R^2*b+2*_R*a+4*_R*b+2*_R*c+b+2*c)*ln(x-_R),_R=RootOf(a*_Z^4+(2*a+b)*_Z^3+(a+2*b+c)*_Z^2+(b+2*c)*_Z+c-1))+sum((b*(5*a*_R^4+(6*a*c+b^2)*_R^2+a*c^2)-2*_R^5*a^(3/2)+4*_R^3*(-a^(3/2)*c-b^2*a^(1/2))+2*c*_R*(-a^(3/2)*c-b^2*a^(1/2)))/(-3*_R^5*b^2-4*a^(1/2)*b^3-12*a^2*_R^5-2*a^(3/2)*c^3+2*a^(3/2)*c^2*b+a^(1/2)*c*b^3-4*_R^7*a+32*_R^3*a^2+a^(1/2)*c^3*b+4*_R^3*a*c^2-4*_R^3*b^3-_R*b^4+14*a^(3/2)*_R^6-_R*b^2*c^2+24*a*b^2*_R-2*a^(1/2)*c^2*b^2-6*a^(3/2)*_R^2*c^2+20*a^(1/2)*_R^4*b^2+9*a^(1/2)*_R^2*b^3-16*a^2*_R^3*c+30*a^(3/2)*_R^4*b+10*a^(3/2)*_R^4*c+2*_R*b^3*c-30*_R^5*a*b-26*_R^3*a*b^2-4*a^2*_R*c^2-48*a^(3/2)*_R^2*b+7*a^(1/2)*_R^6*b-10*_R*a*b^2*c+10*_R*a*b*c^2+24*a^(3/2)*_R^2*b*c-5*a^(1/2)*_R^4*b*c-3*a^(1/2)*_R^2*b*c^2-6*a^(1/2)*_R^2*b^2*c-4*_R^3*a*b*c+4*_R^3*b^2*c)*ln((a*x^2+b*x+c)^(1/2)-a^(1/2)*x-_R),_R=RootOf(_Z^8*a-(4*a^(3/2)+2*a^(1/2)*b)*_Z^7-(-4*a^2-10*a*b-b^2)*_Z^6-(12*a^(3/2)*b+4*a^(3/2)*c+8*b^2*a^(1/2)-2*a^(1/2)*b*c)*_Z^5-(-8*a^2*c-13*a*b^2-2*a*b*c+2*a*c^2-2*b^3+2*b^2*c+16*a^2)*_Z^4-(16*a^(3/2)*c*b-4*a^(3/2)*c^2-32*a^(3/2)*b+6*a^(1/2)*b^3-4*a^(1/2)*c*b^2-2*a^(1/2)*c^2*b)*_Z^3-(-4*a^2*c^2-10*a*b^2*c+10*a*b*c^2-b^4+2*b^3*c-b^2*c^2+24*a*b^2)*_Z^2-(4*a^(3/2)*c^2*b-4*a^(3/2)*c^3+2*a^(1/2)*c*b^3-4*a^(1/2)*c^2*b^2+2*a^(1/2)*c^3*b-8*a^(1/2)*b^3)*_Z+a*b^2*c^2-2*a*b*c^3+a*c^4-b^4))-1/a*sum((a*(-a*_R^6+(-a*c-b^2)*_R^4+c*(a*c+b^2)*_R^2+a*c^3)+2*b*(_R^5*a^(3/2)-c^2*_R*a^(3/2)))/(-3*_R^5*b^2-4*a^(1/2)*b^3-12*a^2*_R^5-2*a^(3/2)*c^3+2*a^(3/2)*c^2*b+a^(1/2)*c*b^3-4*_R^7*a+32*_R^3*a^2+a^(1/2)*c^3*b+4*_R^3*a*c^2-4*_R^3*b^3-_R*b^4+14*a^(3/2)*_R^6-_R*b^2*c^2+24*a*b^2*_R-2*a^(1/2)*c^2*b^2-6*a^(3/2)*_R^2*c^2+20*a^(1/2)*_R^4*b^2+9*a^(1/2)*_R^2*b^3-16*a^2*_R^3*c+30*a^(3/2)*_R^4*b+10*a^(3/2)*_R^4*c+2*_R*b^3*c-30*_R^5*a*b-26*_R^3*a*b^2-4*a^2*_R*c^2-48*a^(3/2)*_R^2*b+7*a^(1/2)*_R^6*b-10*_R*a*b^2*c+10*_R*a*b*c^2+24*a^(3/2)*_R^2*b*c-5*a^(1/2)*_R^4*b*c-3*a^(1/2)*_R^2*b*c^2-6*a^(1/2)*_R^2*b^2*c-4*_R^3*a*b*c+4*_R^3*b^2*c)*ln((a*x^2+b*x+c)^(1/2)-a^(1/2)*x-_R),_R=RootOf(_Z^8*a-(4*a^(3/2)+2*a^(1/2)*b)*_Z^7-(-4*a^2-10*a*b-b^2)*_Z^6-(12*a^(3/2)*b+4*a^(3/2)*c+8*b^2*a^(1/2)-2*a^(1/2)*b*c)*_Z^5-(-8*a^2*c-13*a*b^2-2*a*b*c+2*a*c^2-2*b^3+2*b^2*c+16*a^2)*_Z^4-(16*a^(3/2)*c*b-4*a^(3/2)*c^2-32*a^(3/2)*b+6*a^(1/2)*b^3-4*a^(1/2)*c*b^2-2*a^(1/2)*c^2*b)*_Z^3-(-4*a^2*c^2-10*a*b^2*c+10*a*b*c^2-b^4+2*b^3*c-b^2*c^2+24*a*b^2)*_Z^2-(4*a^(3/2)*c^2*b-4*a^(3/2)*c^3+2*a^(1/2)*c*b^3-4*a^(1/2)*c^2*b^2+2*a^(1/2)*c^3*b-8*a^(1/2)*b^3)*_Z+a*b^2*c^2-2*a*b*c^3+a*c^4-b^4))","B"
2799,0,0,76,180.000000," ","int((-x^4+1)*(-x^9+x^8+4*x^7-4*x^6-6*x^5+6*x^4+4*x^3-4*x^2-x+1)^(1/4)/(x^4+1),x)","\[\int \frac{\left(-x^{4}+1\right) \left(-x^{9}+x^{8}+4 x^{7}-4 x^{6}-6 x^{5}+6 x^{4}+4 x^{3}-4 x^{2}-x +1\right)^{\frac{1}{4}}}{x^{4}+1}\, dx\]"," ",0,"int((-x^4+1)*(-x^9+x^8+4*x^7-4*x^6-6*x^5+6*x^4+4*x^3-4*x^2-x+1)^(1/4)/(x^4+1),x)","F"
2800,0,0,228,0.121000," ","int((-a*(a-5*b)-(3*a+5*b)*x+4*x^2)/((-a+x)*(-b+x))^(1/3)/(b-a^5*d-(-5*a^4*d+1)*x-10*a^3*d*x^2+10*a^2*d*x^3-5*a*d*x^4+d*x^5),x)","\[\int \frac{-a \left(a -5 b \right)-\left(3 a +5 b \right) x +4 x^{2}}{\left(\left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{3}} \left(b -a^{5} d -\left(-5 a^{4} d +1\right) x -10 a^{3} d \,x^{2}+10 a^{2} d \,x^{3}-5 a d \,x^{4}+d \,x^{5}\right)}\, dx\]"," ",0,"int((-a*(a-5*b)-(3*a+5*b)*x+4*x^2)/((-a+x)*(-b+x))^(1/3)/(b-a^5*d-(-5*a^4*d+1)*x-10*a^3*d*x^2+10*a^2*d*x^3-5*a*d*x^4+d*x^5),x)","F"
2801,1,2032,118,142.885000," ","int((x^8+1)/(x^4-x^2)^(1/4)/(x^8-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$2032$\\ trager&$\text{Expression too large to display}$&$2041$\\ \hline \end{longtable}"," ",0,"-x/(x^2*(x^2-1))^(1/4)-1/2*ln((2*(x^4-x^2)^(3/4)-2*(x^4-x^2)^(1/2)*x+2*x^2*(x^4-x^2)^(1/4)-2*x^3+x)/x)+1/2*RootOf(_Z^2+1)*ln(-(2*(x^4-x^2)^(1/2)*RootOf(_Z^2+1)*x-2*RootOf(_Z^2+1)*x^3-2*(x^4-x^2)^(3/4)+2*x^2*(x^4-x^2)^(1/4)+RootOf(_Z^2+1)*x)/x)-1/8*RootOf(_Z^2+1)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*ln((-367*(x^4-x^2)^(1/2)*RootOf(_Z^2+1)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^3*x+8*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x^3+3038*RootOf(_Z^2+1)*(x^4-x^2)^(1/4)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^2*x^2-1519*(x^4-x^2)^(1/2)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^3*x-418*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x^3-734*(x^4-x^2)^(1/4)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^2*x^2-32*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x-7544*RootOf(_Z^2+1)*(x^4-x^2)^(3/4)+4932*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*x^3+1152*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x-4608*(x^4-x^2)^(3/4)-1918*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*x)/x/(RootOf(_Z^2+1)*x^2+4*x^2-4*RootOf(_Z^2+1)+1))-1/8*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*ln((-1519*(x^4-x^2)^(1/2)*RootOf(_Z^2+1)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^3*x+274*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x^3-3038*RootOf(_Z^2+1)*(x^4-x^2)^(1/4)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^2*x^2+367*(x^4-x^2)^(1/2)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^3*x-4924*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x^3+734*(x^4-x^2)^(1/4)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^2*x^2-1096*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x-7544*RootOf(_Z^2+1)*(x^4-x^2)^(3/4)-144*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*x^3+1886*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x-4608*(x^4-x^2)^(3/4)+56*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*x)/x/(RootOf(_Z^2+1)*x^2+4*x^2-4*RootOf(_Z^2+1)+1))-1/8*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*ln((1519*(x^4-x^2)^(1/2)*RootOf(_Z^2+1)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^3*x+274*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x^3+3038*RootOf(_Z^2+1)*(x^4-x^2)^(1/4)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^2*x^2+367*(x^4-x^2)^(1/2)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^3*x+4924*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x^3+734*(x^4-x^2)^(1/4)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^2*x^2-1096*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x+7544*RootOf(_Z^2+1)*(x^4-x^2)^(3/4)-144*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*x^3-1886*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x-4608*(x^4-x^2)^(3/4)+56*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*x)/x/(RootOf(_Z^2+1)*x^2-4*x^2-4*RootOf(_Z^2+1)-1))-1/8*RootOf(_Z^2+1)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*ln(-(367*(x^4-x^2)^(1/2)*RootOf(_Z^2+1)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^3*x+8*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x^3+3038*RootOf(_Z^2+1)*(x^4-x^2)^(1/4)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^2*x^2-1519*(x^4-x^2)^(1/2)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^3*x+418*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x^3+734*(x^4-x^2)^(1/4)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^2*x^2-32*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x-7544*RootOf(_Z^2+1)*(x^4-x^2)^(3/4)+4932*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*x^3-1152*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x+4608*(x^4-x^2)^(3/4)-1918*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*x)/x/(RootOf(_Z^2+1)*x^2-4*x^2-4*RootOf(_Z^2+1)-1))+1/16*RootOf(_Z^2+1)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*ln(((x^4-x^2)^(1/2)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^3*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^3*RootOf(_Z^2+1)*x-4*(x^4-x^2)^(1/4)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^2*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^2*x^2-12*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x^3+4*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x+32*(x^4-x^2)^(3/4))/x/(x^2+1))+1/16*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*ln((-(x^4-x^2)^(1/2)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^3*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^3*x+4*(x^4-x^2)^(1/4)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^2*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^2*x^2-12*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*x^3+32*(x^4-x^2)^(3/4)+4*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*x)/x/(x^2+1))","B"
2802,1,2036,118,135.701000," ","int((x^8+1)/(x^4-x^2)^(1/4)/(x^8-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$2036$\\ trager&$\text{Expression too large to display}$&$2042$\\ \hline \end{longtable}"," ",0,"-x/(x^2*(x^2-1))^(1/4)+1/2*RootOf(_Z^2+1)*ln((-2*(x^4-x^2)^(1/2)*RootOf(_Z^2+1)*x+2*RootOf(_Z^2+1)*x^3+2*(x^4-x^2)^(3/4)-2*x^2*(x^4-x^2)^(1/4)-RootOf(_Z^2+1)*x)/x)+1/2*ln((2*(x^4-x^2)^(3/4)+2*(x^4-x^2)^(1/2)*x+2*x^2*(x^4-x^2)^(1/4)+2*x^3-x)/x)+1/8*RootOf(_Z^2+1)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*ln(-(-367*(x^4-x^2)^(1/2)*RootOf(_Z^2+1)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^3*x-1519*(x^4-x^2)^(1/2)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^3*x-3038*RootOf(_Z^2+1)*(x^4-x^2)^(1/4)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^2*x^2+8*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x^3+734*(x^4-x^2)^(1/4)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^2*x^2-418*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x^3+7544*RootOf(_Z^2+1)*(x^4-x^2)^(3/4)-32*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x+4932*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*x^3+4608*(x^4-x^2)^(3/4)+1152*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x-1918*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*x)/x/(RootOf(_Z^2+1)*x^2+4*x^2-4*RootOf(_Z^2+1)+1))-1/8*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*ln(-(1519*(x^4-x^2)^(1/2)*RootOf(_Z^2+1)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^3*x-367*(x^4-x^2)^(1/2)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^3*x+3038*RootOf(_Z^2+1)*(x^4-x^2)^(1/4)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^2*x^2-274*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x^3-734*(x^4-x^2)^(1/4)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^2*x^2+4924*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x^3+7544*RootOf(_Z^2+1)*(x^4-x^2)^(3/4)+1096*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x+144*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*x^3+4608*(x^4-x^2)^(3/4)-1886*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x-56*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*x)/x/(RootOf(_Z^2+1)*x^2+4*x^2-4*RootOf(_Z^2+1)+1))-1/8*RootOf(_Z^2+1)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*ln((-367*(x^4-x^2)^(1/2)*RootOf(_Z^2+1)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^3*x+1519*(x^4-x^2)^(1/2)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^3*x-3038*RootOf(_Z^2+1)*(x^4-x^2)^(1/4)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^2*x^2-8*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x^3-734*(x^4-x^2)^(1/4)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^2*x^2-418*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x^3+7544*RootOf(_Z^2+1)*(x^4-x^2)^(3/4)+32*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x-4932*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*x^3-4608*(x^4-x^2)^(3/4)+1152*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x+1918*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*x)/x/(RootOf(_Z^2+1)*x^2-4*x^2-4*RootOf(_Z^2+1)-1))+1/8*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*ln((-1519*(x^4-x^2)^(1/2)*RootOf(_Z^2+1)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^3*x-367*(x^4-x^2)^(1/2)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^3*x+3038*RootOf(_Z^2+1)*(x^4-x^2)^(1/4)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^2*x^2-274*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x^3+734*(x^4-x^2)^(1/4)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^2*x^2-4924*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x^3+7544*RootOf(_Z^2+1)*(x^4-x^2)^(3/4)+1096*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)^2*x+144*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*x^3-4608*(x^4-x^2)^(3/4)+1886*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x-56*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*x)/x/(RootOf(_Z^2+1)*x^2-4*x^2-4*RootOf(_Z^2+1)-1))+1/16*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*ln((-(x^4-x^2)^(1/2)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^3*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^3*x+4*(x^4-x^2)^(1/4)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^2*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^2*x^2-12*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*x^3+32*(x^4-x^2)^(3/4)+4*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*x)/x/(x^2+1))-1/16*RootOf(_Z^2+1)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*ln((-(x^4-x^2)^(1/2)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^3*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^3*RootOf(_Z^2+1)*x-4*(x^4-x^2)^(1/4)*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)^2*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)^2*x^2+12*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x^3-4*RootOf(_Z^4-8*RootOf(_Z^2+1)-8)*RootOf(_Z^4+8*RootOf(_Z^2+1)-8)*RootOf(_Z^2+1)*x+32*(x^4-x^2)^(3/4))/x/(x^2+1))","B"
2803,0,0,237,0.164000," ","int((a*b-(a+b)*x+x^2)/((-a+x)*(-b+x)^2)^(2/3)/(a^2-b^2*d-2*(-b*d+a)*x+(1-d)*x^2),x)","\[\int \frac{a b -\left(a +b \right) x +x^{2}}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{2}{3}} \left(a^{2}-b^{2} d -2 \left(-b d +a \right) x +\left(1-d \right) x^{2}\right)}\, dx\]"," ",0,"int((a*b-(a+b)*x+x^2)/((-a+x)*(-b+x)^2)^(2/3)/(a^2-b^2*d-2*(-b*d+a)*x+(1-d)*x^2),x)","F"
2804,0,0,201,0.064000," ","int((x^2+(x^4+1)^(1/2))^(1/2)/(x^4-1)/(x^4+1)^(1/2),x)","\[\int \frac{\sqrt{x^{2}+\sqrt{x^{4}+1}}}{\left(x^{4}-1\right) \sqrt{x^{4}+1}}\, dx\]"," ",0,"int((x^2+(x^4+1)^(1/2))^(1/2)/(x^4-1)/(x^4+1)^(1/2),x)","F"
2805,1,12539,220,172.652000," ","int((x^6-1)/(x^4-x^2)^(1/3)/(x^6+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$12539$\\ \hline \end{longtable}"," ",0,"result too large to display","C"
2806,0,0,208,0.032000," ","int((x^2+(x^4+1)^(1/2))^(1/2)/(1+x),x)","\[\int \frac{\sqrt{x^{2}+\sqrt{x^{4}+1}}}{1+x}\, dx\]"," ",0,"int((x^2+(x^4+1)^(1/2))^(1/2)/(1+x),x)","F"
2807,0,0,208,0.071000," ","int((a*x^2+b)/(-a*x^2+b)/(a*x^5+b*x^3)^(1/4),x)","\[\int \frac{a \,x^{2}+b}{\left(-a \,x^{2}+b \right) \left(a \,x^{5}+b \,x^{3}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x^2+b)/(-a*x^2+b)/(a*x^5+b*x^3)^(1/4),x)","F"
2808,1,693,205,14.726000," ","int((x^3+4)*(x^4+x^3+1)/(x^3+1)^(1/4)/(x^8+x^6+2*x^3+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{8}+16\right)^{7} \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{8}+16\right)^{11} x^{4}+4 x^{4} \RootOf \left(\textit{\_Z}^{8}+16\right)^{7}+16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{6} \left(x^{3}+1\right)^{\frac{1}{4}} x^{3}-4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{7} x^{3}+16 \sqrt{x^{3}+1}\, \RootOf \left(\textit{\_Z}^{8}+16\right)^{5} x^{2}-4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{7}-16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{3} x^{3}+64 \sqrt{x^{3}+1}\, \RootOf \left(\textit{\_Z}^{8}+16\right) x^{2}+128 \left(x^{3}+1\right)^{\frac{3}{4}} x -16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{3}}{\RootOf \left(\textit{\_Z}^{8}+16\right)^{4} x^{4}+4 x^{3}+4}\right)}{16}-\frac{\RootOf \left(\textit{\_Z}^{8}+16\right) \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{8}+16\right)^{9} x^{4}+4 \sqrt{x^{3}+1}\, \RootOf \left(\textit{\_Z}^{8}+16\right)^{7} x^{2}-4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{5} x^{4}-4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{5} x^{3}+16 \sqrt{x^{3}+1}\, \RootOf \left(\textit{\_Z}^{8}+16\right)^{3} x^{2}-32 \left(x^{3}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+16\right)^{2} x^{3}-4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{5}+64 \left(x^{3}+1\right)^{\frac{3}{4}} x -16 x^{3} \RootOf \left(\textit{\_Z}^{8}+16\right)-16 \RootOf \left(\textit{\_Z}^{8}+16\right)}{\RootOf \left(\textit{\_Z}^{8}+16\right)^{4} x^{4}-4 x^{3}-4}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{8}+16\right)^{3} \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{8}+16\right)^{11} x^{4}-4 x^{4} \RootOf \left(\textit{\_Z}^{8}+16\right)^{7}-16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{6} \left(x^{3}+1\right)^{\frac{1}{4}} x^{3}-4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{7} x^{3}-16 \sqrt{x^{3}+1}\, \RootOf \left(\textit{\_Z}^{8}+16\right)^{5} x^{2}-4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{7}+16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{3} x^{3}+64 \sqrt{x^{3}+1}\, \RootOf \left(\textit{\_Z}^{8}+16\right) x^{2}+128 \left(x^{3}+1\right)^{\frac{3}{4}} x +16 \RootOf \left(\textit{\_Z}^{8}+16\right)^{3}}{\RootOf \left(\textit{\_Z}^{8}+16\right)^{4} x^{4}+4 x^{3}+4}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{8}+16\right)^{5} \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{8}+16\right)^{9} x^{4}+4 \sqrt{x^{3}+1}\, \RootOf \left(\textit{\_Z}^{8}+16\right)^{7} x^{2}-4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{5} x^{4}+4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{5} x^{3}-16 \sqrt{x^{3}+1}\, \RootOf \left(\textit{\_Z}^{8}+16\right)^{3} x^{2}+32 \left(x^{3}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{8}+16\right)^{2} x^{3}+4 \RootOf \left(\textit{\_Z}^{8}+16\right)^{5}+64 \left(x^{3}+1\right)^{\frac{3}{4}} x -16 x^{3} \RootOf \left(\textit{\_Z}^{8}+16\right)-16 \RootOf \left(\textit{\_Z}^{8}+16\right)}{\RootOf \left(\textit{\_Z}^{8}+16\right)^{4} x^{4}-4 x^{3}-4}\right)}{8}$&$693$\\ \hline \end{longtable}"," ",0,"-1/16*RootOf(_Z^8+16)^7*ln(-(RootOf(_Z^8+16)^11*x^4+4*x^4*RootOf(_Z^8+16)^7+16*RootOf(_Z^8+16)^6*(x^3+1)^(1/4)*x^3-4*RootOf(_Z^8+16)^7*x^3+16*(x^3+1)^(1/2)*RootOf(_Z^8+16)^5*x^2-4*RootOf(_Z^8+16)^7-16*RootOf(_Z^8+16)^3*x^3+64*(x^3+1)^(1/2)*RootOf(_Z^8+16)*x^2+128*(x^3+1)^(3/4)*x-16*RootOf(_Z^8+16)^3)/(RootOf(_Z^8+16)^4*x^4+4*x^3+4))-1/2*RootOf(_Z^8+16)*ln(-(-RootOf(_Z^8+16)^9*x^4+4*(x^3+1)^(1/2)*RootOf(_Z^8+16)^7*x^2-4*RootOf(_Z^8+16)^5*x^4-4*RootOf(_Z^8+16)^5*x^3+16*(x^3+1)^(1/2)*RootOf(_Z^8+16)^3*x^2-32*(x^3+1)^(1/4)*RootOf(_Z^8+16)^2*x^3-4*RootOf(_Z^8+16)^5+64*(x^3+1)^(3/4)*x-16*x^3*RootOf(_Z^8+16)-16*RootOf(_Z^8+16))/(RootOf(_Z^8+16)^4*x^4-4*x^3-4))+1/4*RootOf(_Z^8+16)^3*ln(-(RootOf(_Z^8+16)^11*x^4-4*x^4*RootOf(_Z^8+16)^7-16*RootOf(_Z^8+16)^6*(x^3+1)^(1/4)*x^3-4*RootOf(_Z^8+16)^7*x^3-16*(x^3+1)^(1/2)*RootOf(_Z^8+16)^5*x^2-4*RootOf(_Z^8+16)^7+16*RootOf(_Z^8+16)^3*x^3+64*(x^3+1)^(1/2)*RootOf(_Z^8+16)*x^2+128*(x^3+1)^(3/4)*x+16*RootOf(_Z^8+16)^3)/(RootOf(_Z^8+16)^4*x^4+4*x^3+4))+1/8*RootOf(_Z^8+16)^5*ln(-(RootOf(_Z^8+16)^9*x^4+4*(x^3+1)^(1/2)*RootOf(_Z^8+16)^7*x^2-4*RootOf(_Z^8+16)^5*x^4+4*RootOf(_Z^8+16)^5*x^3-16*(x^3+1)^(1/2)*RootOf(_Z^8+16)^3*x^2+32*(x^3+1)^(1/4)*RootOf(_Z^8+16)^2*x^3+4*RootOf(_Z^8+16)^5+64*(x^3+1)^(3/4)*x-16*x^3*RootOf(_Z^8+16)-16*RootOf(_Z^8+16))/(RootOf(_Z^8+16)^4*x^4-4*x^3-4))","C"
2809,1,169,82,0.160000," ","int(x^2*(1+x)^(1/2)/(x^2-(1+x)^(1/2)*(1+(1+x)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{2 \left(1+\sqrt{1+x}\right)^{3}}{3}-2 \left(1+\sqrt{1+x}\right)^{2}+2 \sqrt{1+x}+2+4 \sqrt{1+\sqrt{1+x}}+\frac{10 \ln \left(\sqrt{1+x}-\sqrt{1+\sqrt{1+x}}\right)}{11}-\frac{36 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}-1\right) \sqrt{5}}{5}\right)}{55}+\frac{4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+\textit{\_Z} -1\right)}{\sum}\frac{\left(-5 \textit{\_R}^{4}-\textit{\_R}^{3}+2 \textit{\_R}^{2}-\textit{\_R} +9\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{5 \textit{\_R}^{4}+4 \textit{\_R}^{3}-6 \textit{\_R}^{2}-2 \textit{\_R} +1}\right)}{11}$&$169$\\ default&$\frac{2 \left(1+\sqrt{1+x}\right)^{3}}{3}-2 \left(1+\sqrt{1+x}\right)^{2}+2 \sqrt{1+x}+2+4 \sqrt{1+\sqrt{1+x}}+\frac{10 \ln \left(\sqrt{1+x}-\sqrt{1+\sqrt{1+x}}\right)}{11}-\frac{36 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}-1\right) \sqrt{5}}{5}\right)}{55}+\frac{4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+\textit{\_Z} -1\right)}{\sum}\frac{\left(-5 \textit{\_R}^{4}-\textit{\_R}^{3}+2 \textit{\_R}^{2}-\textit{\_R} +9\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{5 \textit{\_R}^{4}+4 \textit{\_R}^{3}-6 \textit{\_R}^{2}-2 \textit{\_R} +1}\right)}{11}$&$169$\\ \hline \end{longtable}"," ",0,"2/3*(1+(1+x)^(1/2))^3-2*(1+(1+x)^(1/2))^2+2*(1+x)^(1/2)+2+4*(1+(1+x)^(1/2))^(1/2)+10/11*ln((1+x)^(1/2)-(1+(1+x)^(1/2))^(1/2))-36/55*5^(1/2)*arctanh(1/5*(2*(1+(1+x)^(1/2))^(1/2)-1)*5^(1/2))+4/11*sum((-5*_R^4-_R^3+2*_R^2-_R+9)/(5*_R^4+4*_R^3-6*_R^2-2*_R+1)*ln((1+(1+x)^(1/2))^(1/2)-_R),_R=RootOf(_Z^5+_Z^4-2*_Z^3-_Z^2+_Z-1))","B"
2810,1,169,82,0.151000," ","int(x^2*(1+x)^(1/2)/(x^2-(1+x)^(1/2)*(1+(1+x)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{2 \left(1+\sqrt{1+x}\right)^{3}}{3}-2 \left(1+\sqrt{1+x}\right)^{2}+2 \sqrt{1+x}+2+4 \sqrt{1+\sqrt{1+x}}+\frac{10 \ln \left(\sqrt{1+x}-\sqrt{1+\sqrt{1+x}}\right)}{11}-\frac{36 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}-1\right) \sqrt{5}}{5}\right)}{55}+\frac{4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+\textit{\_Z} -1\right)}{\sum}\frac{\left(-5 \textit{\_R}^{4}-\textit{\_R}^{3}+2 \textit{\_R}^{2}-\textit{\_R} +9\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{5 \textit{\_R}^{4}+4 \textit{\_R}^{3}-6 \textit{\_R}^{2}-2 \textit{\_R} +1}\right)}{11}$&$169$\\ default&$\frac{2 \left(1+\sqrt{1+x}\right)^{3}}{3}-2 \left(1+\sqrt{1+x}\right)^{2}+2 \sqrt{1+x}+2+4 \sqrt{1+\sqrt{1+x}}+\frac{10 \ln \left(\sqrt{1+x}-\sqrt{1+\sqrt{1+x}}\right)}{11}-\frac{36 \sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{1+\sqrt{1+x}}-1\right) \sqrt{5}}{5}\right)}{55}+\frac{4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+\textit{\_Z} -1\right)}{\sum}\frac{\left(-5 \textit{\_R}^{4}-\textit{\_R}^{3}+2 \textit{\_R}^{2}-\textit{\_R} +9\right) \ln \left(\sqrt{1+\sqrt{1+x}}-\textit{\_R} \right)}{5 \textit{\_R}^{4}+4 \textit{\_R}^{3}-6 \textit{\_R}^{2}-2 \textit{\_R} +1}\right)}{11}$&$169$\\ \hline \end{longtable}"," ",0,"2/3*(1+(1+x)^(1/2))^3-2*(1+(1+x)^(1/2))^2+2*(1+x)^(1/2)+2+4*(1+(1+x)^(1/2))^(1/2)+10/11*ln((1+x)^(1/2)-(1+(1+x)^(1/2))^(1/2))-36/55*5^(1/2)*arctanh(1/5*(2*(1+(1+x)^(1/2))^(1/2)-1)*5^(1/2))+4/11*sum((-5*_R^4-_R^3+2*_R^2-_R+9)/(5*_R^4+4*_R^3-6*_R^2-2*_R+1)*ln((1+(1+x)^(1/2))^(1/2)-_R),_R=RootOf(_Z^5+_Z^4-2*_Z^3-_Z^2+_Z-1))","B"
2811,0,0,236,0.015000," ","int((x^4-a*x-b)*(a*x^4+b*x^3)^(1/4)/(a*x-b),x)","\[\int \frac{\left(x^{4}-a x -b \right) \left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}}{a x -b}\, dx\]"," ",0,"int((x^4-a*x-b)*(a*x^4+b*x^3)^(1/4)/(a*x-b),x)","F"
2812,0,0,242,0.022000," ","int((-4*a+b+3*x)*(-b^3+3*b^2*x-3*b*x^2+x^3)/((-a+x)*(-b+x)^2)^(2/3)/(a+b^4*d-(4*b^3*d+1)*x+6*b^2*d*x^2-4*b*d*x^3+d*x^4),x)","\[\int \frac{\left(-4 a +b +3 x \right) \left(-b^{3}+3 b^{2} x -3 b \,x^{2}+x^{3}\right)}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{2}{3}} \left(a +b^{4} d -\left(4 b^{3} d +1\right) x +6 b^{2} d \,x^{2}-4 b d \,x^{3}+d \,x^{4}\right)}\, dx\]"," ",0,"int((-4*a+b+3*x)*(-b^3+3*b^2*x-3*b*x^2+x^3)/((-a+x)*(-b+x)^2)^(2/3)/(a+b^4*d-(4*b^3*d+1)*x+6*b^2*d*x^2-4*b*d*x^3+d*x^4),x)","F"
2813,0,0,222,0.045000," ","int(x^2*(-2+(1+k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(1-(2+2*k)*x+(k^2+4*k+1)*x^2-(2*k^2+2*k)*x^3+(k^2-b)*x^4),x)","\[\int \frac{x^{2} \left(-2+\left(1+k \right) x \right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(1-\left(2+2 k \right) x +\left(k^{2}+4 k +1\right) x^{2}-\left(2 k^{2}+2 k \right) x^{3}+\left(k^{2}-b \right) x^{4}\right)}\, dx\]"," ",0,"int(x^2*(-2+(1+k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(1-(2+2*k)*x+(k^2+4*k+1)*x^2-(2*k^2+2*k)*x^3+(k^2-b)*x^4),x)","F"
2814,0,0,248,0.050000," ","int(1/(c+(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)),x)","\[\int \frac{1}{c +\sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int(1/(c+(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)),x)","F"
2815,1,1563,208,2.986000," ","int((-7+x)*(3*x^3-5*x^2+x+1)^(1/3)/(-5+x)/(-1+x)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1563$\\ \hline \end{longtable}"," ",0,"-3/32*(13*x-1)/(-1+x)^2*(3*x^3-5*x^2+x+1)^(1/3)+6*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)*ln(-(32256*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)^2*RootOf(_Z^3+4)^3*x^2+192*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)*RootOf(_Z^3+4)^4*x^2-32256*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)^2*RootOf(_Z^3+4)^3*x-192*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)*RootOf(_Z^3+4)^4*x+576*(3*x^3-5*x^2+x+1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)*RootOf(_Z^3+4)^2-4200*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)*RootOf(_Z^3+4)*x^2-25*RootOf(_Z^3+4)^2*x^2+2304*(3*x^3-5*x^2+x+1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)*x-42*(3*x^3-5*x^2+x+1)^(1/3)*RootOf(_Z^3+4)*x+6384*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)*RootOf(_Z^3+4)*x+38*RootOf(_Z^3+4)^2*x+42*(3*x^3-5*x^2+x+1)^(2/3)-2304*(3*x^3-5*x^2+x+1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)+42*(3*x^3-5*x^2+x+1)^(1/3)*RootOf(_Z^3+4)-2184*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)*RootOf(_Z^3+4)-13*RootOf(_Z^3+4)^2)/(-5+x)/(-1+x))-1/8*ln((-64512*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)^2*RootOf(_Z^3+4)^3*x^2-960*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)*RootOf(_Z^3+4)^4*x^2+64512*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)^2*RootOf(_Z^3+4)^3*x+960*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)*RootOf(_Z^3+4)^4*x+1152*(3*x^3-5*x^2+x+1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)*RootOf(_Z^3+4)^2-3024*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)*RootOf(_Z^3+4)*x^2-45*RootOf(_Z^3+4)^2*x^2+4608*(3*x^3-5*x^2+x+1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)*x+180*(3*x^3-5*x^2+x+1)^(1/3)*RootOf(_Z^3+4)*x+7392*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)*RootOf(_Z^3+4)*x+110*RootOf(_Z^3+4)^2*x-180*(3*x^3-5*x^2+x+1)^(2/3)-4608*(3*x^3-5*x^2+x+1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)-180*(3*x^3-5*x^2+x+1)^(1/3)*RootOf(_Z^3+4)-4368*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)*RootOf(_Z^3+4)-65*RootOf(_Z^3+4)^2)/(-5+x)/(-1+x))*RootOf(_Z^3+4)-6*ln((-64512*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)^2*RootOf(_Z^3+4)^3*x^2-960*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)*RootOf(_Z^3+4)^4*x^2+64512*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)^2*RootOf(_Z^3+4)^3*x+960*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)*RootOf(_Z^3+4)^4*x+1152*(3*x^3-5*x^2+x+1)^(2/3)*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)*RootOf(_Z^3+4)^2-3024*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)*RootOf(_Z^3+4)*x^2-45*RootOf(_Z^3+4)^2*x^2+4608*(3*x^3-5*x^2+x+1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)*x+180*(3*x^3-5*x^2+x+1)^(1/3)*RootOf(_Z^3+4)*x+7392*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)*RootOf(_Z^3+4)*x+110*RootOf(_Z^3+4)^2*x-180*(3*x^3-5*x^2+x+1)^(2/3)-4608*(3*x^3-5*x^2+x+1)^(1/3)*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)-180*(3*x^3-5*x^2+x+1)^(1/3)*RootOf(_Z^3+4)-4368*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)*RootOf(_Z^3+4)-65*RootOf(_Z^3+4)^2)/(-5+x)/(-1+x))*RootOf(RootOf(_Z^3+4)^2+48*_Z*RootOf(_Z^3+4)+2304*_Z^2)","C"
2816,0,0,226,0.093000," ","int((a^2*x^2+b^2)/(a^2*x^2-b^2)^3/(a*x^3-b*x^2)^(1/3),x)","\[\int \frac{a^{2} x^{2}+b^{2}}{\left(a^{2} x^{2}-b^{2}\right)^{3} \left(a \,x^{3}-b \,x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a^2*x^2+b^2)/(a^2*x^2-b^2)^3/(a*x^3-b*x^2)^(1/3),x)","F"
2817,0,0,236,180.000000," ","int((c*x+d)/(c*x-d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{c x +d}{\left(c x -d \right) \sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int((c*x+d)/(c*x-d)/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","F"
2818,0,0,62,0.175000," ","int((a*x^4-b*x^3)^(1/4)/(-2*c*x+x^2-d),x)","\[\int \frac{\left(a \,x^{4}-b \,x^{3}\right)^{\frac{1}{4}}}{-2 c x +x^{2}-d}\, dx\]"," ",0,"int((a*x^4-b*x^3)^(1/4)/(-2*c*x+x^2-d),x)","F"
2819,0,0,62,0.005000," ","int((a*x^4-b*x^3)^(1/4)/(-2*c*x+x^2-d),x)","\[\int \frac{\left(a \,x^{4}-b \,x^{3}\right)^{\frac{1}{4}}}{-2 c x +x^{2}-d}\, dx\]"," ",0,"int((a*x^4-b*x^3)^(1/4)/(-2*c*x+x^2-d),x)","F"
2820,0,0,227,0.036000," ","int(x*(k*x-1)*(-1+(-1+2*k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(-1+4*x+(-6+b)*x^2+(-2*b*k+4)*x^3+(b*k^2-1)*x^4),x)","\[\int \frac{x \left(k x -1\right) \left(-1+\left(-1+2 k \right) x \right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(-1+4 x +\left(-6+b \right) x^{2}+\left(-2 b k +4\right) x^{3}+\left(b \,k^{2}-1\right) x^{4}\right)}\, dx\]"," ",0,"int(x*(k*x-1)*(-1+(-1+2*k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(-1+4*x+(-6+b)*x^2+(-2*b*k+4)*x^3+(b*k^2-1)*x^4),x)","F"
2821,0,0,229,0.020000," ","int((1+(-2+3*k)*x-(4*k^2+k)*x^2+3*k^2*x^3)/((1-x)*x*(-k*x+1))^(1/3)/(-b+(5*b*k+1)*x-(10*b*k^2+1)*x^2+10*b*k^3*x^3-5*b*k^4*x^4+b*k^5*x^5),x)","\[\int \frac{1+\left(-2+3 k \right) x -\left(4 k^{2}+k \right) x^{2}+3 k^{2} x^{3}}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(-b +\left(5 b k +1\right) x -\left(10 b \,k^{2}+1\right) x^{2}+10 b \,k^{3} x^{3}-5 b \,k^{4} x^{4}+b \,k^{5} x^{5}\right)}\, dx\]"," ",0,"int((1+(-2+3*k)*x-(4*k^2+k)*x^2+3*k^2*x^3)/((1-x)*x*(-k*x+1))^(1/3)/(-b+(5*b*k+1)*x-(10*b*k^2+1)*x^2+10*b*k^3*x^3-5*b*k^4*x^4+b*k^5*x^5),x)","F"
2822,0,0,268,180.000000," ","int((c*x+d)^2/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{\left(c x +d \right)^{2}}{\sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int((c*x+d)^2/(a*x+(a^2*x^2+b^2)^(1/2))^(1/2),x)","F"
2823,0,0,15,180.000000," ","int((1-(-3*x^10+x^9-9*x^7+3*x^6-9*x^4+3*x^3-3*x+1)^(1/3))/(x^2+(-3*x^10+x^9-9*x^7+3*x^6-9*x^4+3*x^3-3*x+1)^(1/3)),x)","\[\int \frac{1-\left(-3 x^{10}+x^{9}-9 x^{7}+3 x^{6}-9 x^{4}+3 x^{3}-3 x +1\right)^{\frac{1}{3}}}{x^{2}+\left(-3 x^{10}+x^{9}-9 x^{7}+3 x^{6}-9 x^{4}+3 x^{3}-3 x +1\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((1-(-3*x^10+x^9-9*x^7+3*x^6-9*x^4+3*x^3-3*x+1)^(1/3))/(x^2+(-3*x^10+x^9-9*x^7+3*x^6-9*x^4+3*x^3-3*x+1)^(1/3)),x)","F"
2824,0,0,223,0.039000," ","int((-k*x+1)/(1+(-2+k)*x)/((1-x)*x*(-k*x+1))^(2/3),x)","\[\int \frac{-k x +1}{\left(1+\left(-2+k \right) x \right) \left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{2}{3}}}\, dx\]"," ",0,"int((-k*x+1)/(1+(-2+k)*x)/((1-x)*x*(-k*x+1))^(2/3),x)","F"
2825,1,290058,91,254.254000," ","int((x^3+x^2+1)/(x^3+x^2-1)/(x^3+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$290058$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2826,1,147111,91,143.059000," ","int((x^3+x^2+1)/(x^3+x^2-1)/(x^3+x^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$147111$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
2827,1,529,45,1.260000," ","int((a*x+(a*x-b)^(1/2))^(1/2)/x/(a*x-b)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}+\frac{\left(1-2 \sqrt{-b}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}\right)}{2}+\frac{\sqrt{-b}\, \ln \left(\frac{-2 \sqrt{-b}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)+2 \sqrt{-\sqrt{-b}}\, \sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}}{\sqrt{a x -b}+\sqrt{-b}}\right)}{\sqrt{-\sqrt{-b}}}}{\sqrt{-b}}+\frac{\sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}+\frac{\left(1+2 \sqrt{-b}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}\right)}{2}-\left(-b \right)^{\frac{1}{4}} \ln \left(\frac{2 \sqrt{-b}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+2 \left(-b \right)^{\frac{1}{4}} \sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}}{\sqrt{a x -b}-\sqrt{-b}}\right)}{\sqrt{-b}}$&$529$\\ default&$-\frac{\sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}+\frac{\left(1-2 \sqrt{-b}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}\right)}{2}+\frac{\sqrt{-b}\, \ln \left(\frac{-2 \sqrt{-b}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)+2 \sqrt{-\sqrt{-b}}\, \sqrt{\left(\sqrt{a x -b}+\sqrt{-b}\right)^{2}+\left(1-2 \sqrt{-b}\right) \left(\sqrt{a x -b}+\sqrt{-b}\right)-\sqrt{-b}}}{\sqrt{a x -b}+\sqrt{-b}}\right)}{\sqrt{-\sqrt{-b}}}}{\sqrt{-b}}+\frac{\sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}+\frac{\left(1+2 \sqrt{-b}\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}\right)}{2}-\left(-b \right)^{\frac{1}{4}} \ln \left(\frac{2 \sqrt{-b}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+2 \left(-b \right)^{\frac{1}{4}} \sqrt{\left(\sqrt{a x -b}-\sqrt{-b}\right)^{2}+\left(1+2 \sqrt{-b}\right) \left(\sqrt{a x -b}-\sqrt{-b}\right)+\sqrt{-b}}}{\sqrt{a x -b}-\sqrt{-b}}\right)}{\sqrt{-b}}$&$529$\\ \hline \end{longtable}"," ",0,"-1/(-b)^(1/2)*((((a*x-b)^(1/2)+(-b)^(1/2))^2+(1-2*(-b)^(1/2))*((a*x-b)^(1/2)+(-b)^(1/2))-(-b)^(1/2))^(1/2)+1/2*(1-2*(-b)^(1/2))*ln(1/2+(a*x-b)^(1/2)+(((a*x-b)^(1/2)+(-b)^(1/2))^2+(1-2*(-b)^(1/2))*((a*x-b)^(1/2)+(-b)^(1/2))-(-b)^(1/2))^(1/2))+(-b)^(1/2)/(-(-b)^(1/2))^(1/2)*ln((-2*(-b)^(1/2)+(1-2*(-b)^(1/2))*((a*x-b)^(1/2)+(-b)^(1/2))+2*(-(-b)^(1/2))^(1/2)*(((a*x-b)^(1/2)+(-b)^(1/2))^2+(1-2*(-b)^(1/2))*((a*x-b)^(1/2)+(-b)^(1/2))-(-b)^(1/2))^(1/2))/((a*x-b)^(1/2)+(-b)^(1/2))))+1/(-b)^(1/2)*((((a*x-b)^(1/2)-(-b)^(1/2))^2+(1+2*(-b)^(1/2))*((a*x-b)^(1/2)-(-b)^(1/2))+(-b)^(1/2))^(1/2)+1/2*(1+2*(-b)^(1/2))*ln(1/2+(a*x-b)^(1/2)+(((a*x-b)^(1/2)-(-b)^(1/2))^2+(1+2*(-b)^(1/2))*((a*x-b)^(1/2)-(-b)^(1/2))+(-b)^(1/2))^(1/2))-(-b)^(1/4)*ln((2*(-b)^(1/2)+(1+2*(-b)^(1/2))*((a*x-b)^(1/2)-(-b)^(1/2))+2*(-b)^(1/4)*(((a*x-b)^(1/2)-(-b)^(1/2))^2+(1+2*(-b)^(1/2))*((a*x-b)^(1/2)-(-b)^(1/2))+(-b)^(1/2))^(1/2))/((a*x-b)^(1/2)-(-b)^(1/2))))","B"
2828,0,0,236,180.000000," ","int((a*x+(a^2*x^2+b)^(1/2))^(1/2)*(c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2),x)","\[\int \sqrt{a x +\sqrt{a^{2} x^{2}+b}}\, \sqrt{c +\sqrt{a x +\sqrt{a^{2} x^{2}+b}}}\, dx\]"," ",0,"int((a*x+(a^2*x^2+b)^(1/2))^(1/2)*(c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2),x)","F"
2829,0,0,242,180.000000," ","int(x^4*(a^2*x^4+b)^(1/2)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x)","\[\int x^{4} \sqrt{a^{2} x^{4}+b}\, \sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}\, dx\]"," ",0,"int(x^4*(a^2*x^4+b)^(1/2)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x)","F"
2830,0,0,143,180.000000," ","int((c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2)/(a^2*x^2+b)^(3/2)/(a*x+(a^2*x^2+b)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{c +\sqrt{a x +\sqrt{a^{2} x^{2}+b}}}}{\left(a^{2} x^{2}+b \right)^{\frac{3}{2}} \sqrt{a x +\sqrt{a^{2} x^{2}+b}}}\, dx\]"," ",0,"int((c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2)/(a^2*x^2+b)^(3/2)/(a*x+(a^2*x^2+b)^(1/2))^(1/2),x)","F"
2831,0,0,143,180.000000," ","int((c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2)/(a^2*x^2+b)^(3/2)/(a*x+(a^2*x^2+b)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{c +\sqrt{a x +\sqrt{a^{2} x^{2}+b}}}}{\left(a^{2} x^{2}+b \right)^{\frac{3}{2}} \sqrt{a x +\sqrt{a^{2} x^{2}+b}}}\, dx\]"," ",0,"int((c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2)/(a^2*x^2+b)^(3/2)/(a*x+(a^2*x^2+b)^(1/2))^(1/2),x)","F"
2832,0,0,222,0.065000," ","int(x^2/(a*x^2+b)/(x^3+x)^(1/3),x)","\[\int \frac{x^{2}}{\left(a \,x^{2}+b \right) \left(x^{3}+x \right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(x^2/(a*x^2+b)/(x^3+x)^(1/3),x)","F"
2833,1,5994,223,71.313000," ","int((x^6+1)/(x^4+x^2)^(1/3)/(x^6-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$5994$\\ \hline \end{longtable}"," ",0,"result too large to display","C"
2834,1,92,43,8.001000," ","int((3*x^4-2)^(1/2)*(3*x^4-1)/x^3/(3*x^8-3*x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\sqrt{3 x^{4}-2}}{2 x^{2}}-\frac{\sqrt{3}\, \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-16 \textit{\_Z} +16\right)}{\sum}\frac{\left(\textit{\_R}^{2}-8 \textit{\_R} +4\right) \ln \left(\left(\sqrt{3 x^{4}-2}-\sqrt{3}\, x^{2}\right)^{2}-\textit{\_R} \right)}{\textit{\_R}^{3}-3 \textit{\_R}^{2}+12 \textit{\_R} -4}\right)}{4}$&$92$\\ elliptic&$\frac{\sqrt{3 x^{4}-2}}{2 x^{2}}-\frac{\sqrt{3}\, \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-16 \textit{\_Z} +16\right)}{\sum}\frac{\left(\textit{\_R}^{2}-8 \textit{\_R} +4\right) \ln \left(\left(\sqrt{3 x^{4}-2}-\sqrt{3}\, x^{2}\right)^{2}-\textit{\_R} \right)}{\textit{\_R}^{3}-3 \textit{\_R}^{2}+12 \textit{\_R} -4}\right)}{4}$&$92$\\ default&$-\frac{\sqrt{3}\, \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+2 \textit{\_Z}^{3}-4 \textit{\_Z} +4\right)}{\sum}\frac{\left(-\textit{\_R}^{2}-\textit{\_R} +2\right) \ln \left(\sqrt{3 x^{4}-2}-\sqrt{3}\, x^{2}-\textit{\_R} \right)}{2 \textit{\_R}^{3}+3 \textit{\_R}^{2}-2}\right)}{2}-\frac{\sqrt{3}\, \ln \left(\sqrt{3 x^{4}-2}-\sqrt{3}\, x^{2}\right)}{2}-\frac{\sqrt{3}\, \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+4 \textit{\_Z} +4\right)}{\sum}\frac{\left(\textit{\_R}^{2}-\textit{\_R} -2\right) \ln \left(\sqrt{3 x^{4}-2}-\sqrt{3}\, x^{2}-\textit{\_R} \right)}{2 \textit{\_R}^{3}-3 \textit{\_R}^{2}+2}\right)}{2}-\frac{\left(3 x^{4}-2\right)^{\frac{3}{2}}}{4 x^{2}}+\frac{3 x^{2} \sqrt{3 x^{4}-2}}{4}-\frac{\ln \left(\sqrt{3}\, x^{2}+\sqrt{3 x^{4}-2}\right) \sqrt{3}}{2}$&$213$\\ trager&$\frac{\sqrt{3 x^{4}-2}}{2 x^{2}}+\frac{\RootOf \left(\textit{\_Z}^{2}+144 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2}-3\right) \ln \left(-\frac{-55296 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{4} x^{4} \RootOf \left(\textit{\_Z}^{2}+144 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2}-3\right)-720 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+144 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2}-3\right) x^{4}+1872 \sqrt{3 x^{4}-2}\, \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2} x^{2}+55296 \RootOf \left(\textit{\_Z}^{2}+144 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2}-3\right) \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{4}+39 \RootOf \left(\textit{\_Z}^{2}+144 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2}-3\right) x^{4}-47 x^{2} \sqrt{3 x^{4}-2}+1104 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+144 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2}-3\right)-26 \RootOf \left(\textit{\_Z}^{2}+144 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2}-3\right)}{144 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2} x^{4}-144 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2}+1}\right)}{4}-3 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right) \ln \left(\frac{-165888 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{5} x^{4}+9072 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{3} x^{4}+468 \sqrt{3 x^{4}-2}\, \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2} x^{2}+165888 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{5}+2 x^{2} \sqrt{3 x^{4}-2}-10224 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{3}+63 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)}{\left(1728 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{3} x^{2}+144 x^{2} \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2}-1728 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{3}-24 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right) x^{2}-144 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2}-3 x^{2}+24 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)+2\right) \left(1728 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{3} x^{2}-144 x^{2} \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2}-1728 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{3}-24 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right) x^{2}+144 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)^{2}+3 x^{2}+24 \RootOf \left(6912 \textit{\_Z}^{4}-144 \textit{\_Z}^{2}+1\right)-2\right)}\right)$&$730$\\ \hline \end{longtable}"," ",0,"1/2*(3*x^4-2)^(1/2)/x^2-1/4*3^(1/2)*sum((_R^2-8*_R+4)/(_R^3-3*_R^2+12*_R-4)*ln(((3*x^4-2)^(1/2)-3^(1/2)*x^2)^2-_R),_R=RootOf(_Z^4-4*_Z^3+24*_Z^2-16*_Z+16))","B"
2835,0,0,256,0.086000," ","int(1/(a^2*x^2-b*x)^(5/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x)","\[\int \frac{1}{\left(a^{2} x^{2}-b x \right)^{\frac{5}{2}} \left(a \,x^{2}+x \sqrt{a^{2} x^{2}-b x}\right)^{\frac{3}{2}}}\, dx\]"," ",0,"int(1/(a^2*x^2-b*x)^(5/2)/(a*x^2+x*(a^2*x^2-b*x)^(1/2))^(3/2),x)","F"
2836,0,0,237,0.125000," ","int((a-2*b+x)*(-b+x)/((-a+x)*(-b+x))^(1/3)/(a^4-b^2*d-2*(2*a^3-b*d)*x+(6*a^2-d)*x^2-4*a*x^3+x^4),x)","\[\int \frac{\left(a -2 b +x \right) \left(-b +x \right)}{\left(\left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{3}} \left(a^{4}-b^{2} d -2 \left(2 a^{3}-b d \right) x +\left(6 a^{2}-d \right) x^{2}-4 a \,x^{3}+x^{4}\right)}\, dx\]"," ",0,"int((a-2*b+x)*(-b+x)/((-a+x)*(-b+x))^(1/3)/(a^4-b^2*d-2*(2*a^3-b*d)*x+(6*a^2-d)*x^2-4*a*x^3+x^4),x)","F"
2837,0,0,237,0.039000," ","int((-1+x)*x*(1+(-2+k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(1-4*k*x+(6*k^2-b)*x^2+(-4*k^3+2*b)*x^3+(k^4-b)*x^4),x)","\[\int \frac{\left(-1+x \right) x \left(1+\left(-2+k \right) x \right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(1-4 k x +\left(6 k^{2}-b \right) x^{2}+\left(-4 k^{3}+2 b \right) x^{3}+\left(k^{4}-b \right) x^{4}\right)}\, dx\]"," ",0,"int((-1+x)*x*(1+(-2+k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(1-4*k*x+(6*k^2-b)*x^2+(-4*k^3+2*b)*x^3+(k^4-b)*x^4),x)","F"
2838,0,0,209,0.019000," ","int((x^3-1)^(2/3)*(x^6+4)/x^6/(x^6-4),x)","\[\int \frac{\left(x^{3}-1\right)^{\frac{2}{3}} \left(x^{6}+4\right)}{x^{6} \left(x^{6}-4\right)}\, dx\]"," ",0,"int((x^3-1)^(2/3)*(x^6+4)/x^6/(x^6-4),x)","F"
2839,0,0,227,0.042000," ","int((c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/6)/(a^2*x^2-b)^(1/2),x)","\[\int \frac{\left(c +\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}}\right)^{\frac{1}{6}}}{\sqrt{a^{2} x^{2}-b}}\, dx\]"," ",0,"int((c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/6)/(a^2*x^2-b)^(1/2),x)","F"
2840,0,0,246,0.156000," ","int((-b+x)*(a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^2)^(2/3)/(b*d-(a+d)*x+x^2),x)","\[\int \frac{\left(-b +x \right) \left(a b -2 b x +x^{2}\right)}{\left(x \left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{2}{3}} \left(b d -\left(a +d \right) x +x^{2}\right)}\, dx\]"," ",0,"int((-b+x)*(a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^2)^(2/3)/(b*d-(a+d)*x+x^2),x)","F"
2841,0,0,224,0.046000," ","int((c*x^4-d)/x/(a*x^3-b)^(1/3),x)","\[\int \frac{c \,x^{4}-d}{x \left(a \,x^{3}-b \right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((c*x^4-d)/x/(a*x^3-b)^(1/3),x)","F"
2842,0,0,257,0.173000," ","int((a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^2)^(1/3)/(b-(a*d+1)*x+d*x^2),x)","\[\int \frac{a b -2 b x +x^{2}}{\left(x \left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{3}} \left(b -\left(a d +1\right) x +d \,x^{2}\right)}\, dx\]"," ",0,"int((a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^2)^(1/3)/(b-(a*d+1)*x+d*x^2),x)","F"
2843,0,0,257,0.023000," ","int((-a*b^2+(4*a-b)*b*x-3*a*x^2+x^3)/(x*(-a+x)*(-b+x)^2)^(1/3)/(-a^2+(b^2*d+2*a)*x-(2*b*d+1)*x^2+d*x^3),x)","\[\int \frac{-a \,b^{2}+\left(4 a -b \right) b x -3 a \,x^{2}+x^{3}}{\left(x \left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{3}} \left(-a^{2}+\left(b^{2} d +2 a \right) x -\left(2 b d +1\right) x^{2}+d \,x^{3}\right)}\, dx\]"," ",0,"int((-a*b^2+(4*a-b)*b*x-3*a*x^2+x^3)/(x*(-a+x)*(-b+x)^2)^(1/3)/(-a^2+(b^2*d+2*a)*x-(2*b*d+1)*x^2+d*x^3),x)","F"
2844,0,0,253,0.022000," ","int((-4*a+b+3*x)*(-b^3+3*b^2*x-3*b*x^2+x^3)/((-a+x)*(-b+x)^2)^(2/3)/(b^4+a*d-(4*b^3+d)*x+6*b^2*x^2-4*b*x^3+x^4),x)","\[\int \frac{\left(-4 a +b +3 x \right) \left(-b^{3}+3 b^{2} x -3 b \,x^{2}+x^{3}\right)}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{2}{3}} \left(b^{4}+a d -\left(4 b^{3}+d \right) x +6 b^{2} x^{2}-4 b \,x^{3}+x^{4}\right)}\, dx\]"," ",0,"int((-4*a+b+3*x)*(-b^3+3*b^2*x-3*b*x^2+x^3)/((-a+x)*(-b+x)^2)^(2/3)/(b^4+a*d-(4*b^3+d)*x+6*b^2*x^2-4*b*x^3+x^4),x)","F"
2845,0,0,238,0.078000," ","int((a*x^4-b*x^3)^(1/4)/x/(c*x-d),x)","\[\int \frac{\left(a \,x^{4}-b \,x^{3}\right)^{\frac{1}{4}}}{x \left(c x -d \right)}\, dx\]"," ",0,"int((a*x^4-b*x^3)^(1/4)/x/(c*x-d),x)","F"
2846,0,0,239,0.070000," ","int((-a+x)*(-b+x)*(-2*a*b*x+(a+b)*x^2)/(x*(-a+x)*(-b+x))^(2/3)/(a^2*b^2*d-2*a*b*(a+b)*d*x+(a^2+4*a*b+b^2)*d*x^2-2*(a+b)*d*x^3+(-1+d)*x^4),x)","\[\int \frac{\left(-a +x \right) \left(-b +x \right) \left(-2 a b x +\left(a +b \right) x^{2}\right)}{\left(x \left(-a +x \right) \left(-b +x \right)\right)^{\frac{2}{3}} \left(a^{2} b^{2} d -2 a b \left(a +b \right) d x +\left(a^{2}+4 a b +b^{2}\right) d \,x^{2}-2 \left(a +b \right) d \,x^{3}+\left(-1+d \right) x^{4}\right)}\, dx\]"," ",0,"int((-a+x)*(-b+x)*(-2*a*b*x+(a+b)*x^2)/(x*(-a+x)*(-b+x))^(2/3)/(a^2*b^2*d-2*a*b*(a+b)*d*x+(a^2+4*a*b+b^2)*d*x^2-2*(a+b)*d*x^3+(-1+d)*x^4),x)","F"
2847,1,1415,231,32.677000," ","int((x^6+x^3+1)/(x^5+x^3)^(1/4)/(-x^6+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1415$\\ \hline \end{longtable}"," ",0,"1/24*RootOf(_Z^4+8)*ln(-(-RootOf(_Z^4+8)^3*(x^5+x^3)^(1/2)*x-2*(x^5+x^3)^(1/4)*RootOf(_Z^4+8)^2*x^2+RootOf(_Z^4+8)*x^4-2*RootOf(_Z^4+8)*x^3+4*(x^5+x^3)^(3/4)+RootOf(_Z^4+8)*x^2)/(1+x)^2/x^2)+1/24*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln(-((x^5+x^3)^(1/2)*RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x+2*(x^5+x^3)^(1/4)*RootOf(_Z^4+8)^2*x^2+RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^4-2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^3+4*(x^5+x^3)^(3/4)+RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^2)/(1+x)^2/x^2)+1/32*ln(-(RootOf(_Z^4+8)^3*x^4-2*RootOf(_Z^4+8)^3*x^3+8*(x^5+x^3)^(1/4)*RootOf(_Z^4+8)^2*x^2+RootOf(_Z^4+8)^3*x^2-16*(x^5+x^3)^(1/2)*RootOf(_Z^4+8)*x+16*(x^5+x^3)^(3/4))/x^2/(-1+x)^2)*RootOf(_Z^4+8)^3+1/32*ln(-(RootOf(_Z^4+8)^3*x^4-2*RootOf(_Z^4+8)^3*x^3+8*(x^5+x^3)^(1/4)*RootOf(_Z^4+8)^2*x^2+RootOf(_Z^4+8)^3*x^2-16*(x^5+x^3)^(1/2)*RootOf(_Z^4+8)*x+16*(x^5+x^3)^(3/4))/x^2/(-1+x)^2)*RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)-1/16*RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln((RootOf(_Z^4+8)^3*x^4-RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*x^4+2*RootOf(_Z^4+8)^3*x^3-2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*x^3+8*(x^5+x^3)^(1/4)*RootOf(_Z^4+8)*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^2+RootOf(_Z^4+8)^3*x^2-RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^2-8*(x^5+x^3)^(1/2)*RootOf(_Z^4+8)*x-8*RootOf(_Z^2+RootOf(_Z^4+8)^2)*(x^5+x^3)^(1/2)*x+16*(x^5+x^3)^(3/4))/x^2/(-1+x)^2)+1/6*ln((x^4+2*(x^5+x^3)^(3/4)+2*(x^5+x^3)^(1/2)*x+2*(x^5+x^3)^(1/4)*x^2+x^3+x^2)/x^2/(x^2-x+1))+1/48*RootOf(_Z^4+8)^3*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln((RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^3*x^4-2*RootOf(_Z^4+8)^3*(x^5+x^3)^(1/2)*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x+RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^3*x^3+RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^2*RootOf(_Z^4+8)^3+16*(x^5+x^3)^(3/4)-16*(x^5+x^3)^(1/4)*x^2)/x^2/(x^2-x+1))+1/8*ln((x^4*RootOf(_Z^4+8)^2-4*RootOf(_Z^4+8)^2*(x^5+x^3)^(1/2)*x+x^3*RootOf(_Z^4+8)^2+RootOf(_Z^4+8)^2*x^2+8*(x^5+x^3)^(3/4)-8*(x^5+x^3)^(1/4)*x^2)/x^2/(x^2+x+1))*RootOf(_Z^4+8)^2+1/8*ln((x^4*RootOf(_Z^4+8)^2-4*RootOf(_Z^4+8)^2*(x^5+x^3)^(1/2)*x+x^3*RootOf(_Z^4+8)^2+RootOf(_Z^4+8)^2*x^2+8*(x^5+x^3)^(3/4)-8*(x^5+x^3)^(1/4)*x^2)/x^2/(x^2+x+1))*RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)-1/4*RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)*ln(((x^5+x^3)^(1/4)*RootOf(_Z^4+8)^3*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^2+x^4*RootOf(_Z^4+8)^2-RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)*x^4-2*RootOf(_Z^4+8)^2*(x^5+x^3)^(1/2)*x-2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)*(x^5+x^3)^(1/2)*x-x^3*RootOf(_Z^4+8)^2+RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)*x^3+RootOf(_Z^4+8)^2*x^2-x^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)+8*(x^5+x^3)^(3/4))/x^2/(x^2+x+1))","C"
2848,1,1907,247,0.348000," ","int((-a-b*x+(a*k^2+b)*x^2)/((1-x)*x*(-k^2*x+1))^(1/2)/(k^2*x^2-2*x+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 \left(a \,k^{2}+b \right) \sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}\, \sqrt{\frac{-1+x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{4} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) a}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{2}}+\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) a}{\sqrt{-k^{2}+1}\, \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}-\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{\sqrt{-k^{2}+1}\, \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{\sqrt{-k^{2}+1}\, \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{2}}-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) a \,k^{2}}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{-1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) a}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{-1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{-1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{2}}-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{-1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) a}{\sqrt{-k^{2}+1}\, \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{-1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{\sqrt{-k^{2}+1}\, \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{-1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{\sqrt{-k^{2}+1}\, \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{2}}-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{-1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) a \,k^{2}}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}}{k^{2}}$&$1907$\\ elliptic&$-\frac{2 a \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right)}{k^{2} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticF \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{k^{4} \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) a}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{2}}-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{2}}+\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{4}}+\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) a}{\sqrt{-k^{2}+1}\, \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{2}}-\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{\sqrt{-k^{2}+1}\, \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{2}}+\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{\sqrt{-k^{2}+1}\, \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{4}}-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}-\frac{1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) a}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}+\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{-1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) a}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{2}}-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{-1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{2}}+\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{-1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{4}}-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{-1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) a}{\sqrt{-k^{2}+1}\, \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{2}}+\frac{\sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{-1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{\sqrt{-k^{2}+1}\, \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{2}}-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{-1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) b}{\sqrt{-k^{2}+1}\, \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}\, k^{4}}-\frac{2 \sqrt{-k^{2} x +1}\, \sqrt{-\frac{1}{\frac{1}{k^{2}}-1}+\frac{x}{\frac{1}{k^{2}}-1}}\, \sqrt{k^{2} x}\, \EllipticPi \left(\sqrt{-\left(x -\frac{1}{k^{2}}\right) k^{2}}, \frac{1}{k^{2} \left(\frac{1}{k^{2}}+\frac{-1+\sqrt{-k^{2}+1}}{k^{2}}\right)}, \sqrt{\frac{1}{k^{2} \left(\frac{1}{k^{2}}-1\right)}}\right) a}{\left(-k^{2}+1\right) \sqrt{k^{2} x^{3}-k^{2} x^{2}-x^{2}+x}}$&$2014$\\ \hline \end{longtable}"," ",0,"-2*(a*k^2+b)/k^4*(-(x-1/k^2)*k^2)^(1/2)*((-1+x)/(1/k^2-1))^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticF((-(x-1/k^2)*k^2)^(1/2),(1/k^2/(1/k^2-1))^(1/2))+1/k^2*(2/(-k^2+1)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-(1+(-k^2+1)^(1/2))/k^2),(1/k^2/(1/k^2-1))^(1/2))*a-2/(-k^2+1)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-(1+(-k^2+1)^(1/2))/k^2),(1/k^2/(1/k^2-1))^(1/2))*b+2/(-k^2+1)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-(1+(-k^2+1)^(1/2))/k^2),(1/k^2/(1/k^2-1))^(1/2))/k^2*b+2/(-k^2+1)^(1/2)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-(1+(-k^2+1)^(1/2))/k^2),(1/k^2/(1/k^2-1))^(1/2))*a-1/(-k^2+1)^(1/2)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-(1+(-k^2+1)^(1/2))/k^2),(1/k^2/(1/k^2-1))^(1/2))*b+2/(-k^2+1)^(1/2)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-(1+(-k^2+1)^(1/2))/k^2),(1/k^2/(1/k^2-1))^(1/2))/k^2*b-2/(-k^2+1)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2-(1+(-k^2+1)^(1/2))/k^2),(1/k^2/(1/k^2-1))^(1/2))*a*k^2+2/(-k^2+1)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+(-1+(-k^2+1)^(1/2))/k^2),(1/k^2/(1/k^2-1))^(1/2))*a-2/(-k^2+1)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+(-1+(-k^2+1)^(1/2))/k^2),(1/k^2/(1/k^2-1))^(1/2))*b+2/(-k^2+1)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+(-1+(-k^2+1)^(1/2))/k^2),(1/k^2/(1/k^2-1))^(1/2))/k^2*b-2/(-k^2+1)^(1/2)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+(-1+(-k^2+1)^(1/2))/k^2),(1/k^2/(1/k^2-1))^(1/2))*a+1/(-k^2+1)^(1/2)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+(-1+(-k^2+1)^(1/2))/k^2),(1/k^2/(1/k^2-1))^(1/2))*b-2/(-k^2+1)^(1/2)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+(-1+(-k^2+1)^(1/2))/k^2),(1/k^2/(1/k^2-1))^(1/2))/k^2*b-2/(-k^2+1)*(-k^2*x+1)^(1/2)*(-1/(1/k^2-1)+1/(1/k^2-1)*x)^(1/2)*(k^2*x)^(1/2)/(k^2*x^3-k^2*x^2-x^2+x)^(1/2)*EllipticPi((-(x-1/k^2)*k^2)^(1/2),1/k^2/(1/k^2+(-1+(-k^2+1)^(1/2))/k^2),(1/k^2/(1/k^2-1))^(1/2))*a*k^2)","C"
2849,1,1006,213,13.136000," ","int((x^8-2*x^4+1)/(x^4-1)^(1/4)/(2*x^8-2*x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-2 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \left(x^{4}-1\right)^{\frac{3}{4}} x -2 x^{3} \left(x^{4}-1\right)^{\frac{1}{4}}-\RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{8}+\frac{\ln \left(2 \left(x^{4}-1\right)^{\frac{3}{4}} x +2 x^{2} \sqrt{x^{4}-1}+2 x^{3} \left(x^{4}-1\right)^{\frac{1}{4}}+2 x^{4}-1\right)}{8}-\frac{\RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right) \ln \left(-\frac{\sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)^{3} x^{2}-\left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)^{2} x^{3}-\left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{4}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right) x^{4}+2 \left(x^{4}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+x^{4}-1}\right)}{16}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right) \ln \left(\frac{-\sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)^{3} x^{2}+\left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)^{2} x^{3}-\left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \left(x^{4}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right) x^{4}-2 \left(x^{4}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)}{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+x^{4}-1}\right)}{16}+\frac{\RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)^{3} \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)^{3} \RootOf \left(\textit{\_Z}^{2}+1\right)^{2} x^{4}+2 \RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)^{3} \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}+4 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)^{3} x^{4}+4 \RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}-1}\, x^{2}+4 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right) x^{2}+8 \left(x^{4}-1\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)^{3}-\RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)^{3}}{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-x^{4}+1}\right)}{32}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)^{3} \ln \left(-\frac{-\RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)^{3} \RootOf \left(\textit{\_Z}^{2}+1\right)^{2} x^{4}-4 \left(x^{4}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)^{2} x^{3}+\RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)^{3} x^{4}+4 \RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right) \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{x^{4}-1}\, x^{2}-4 \sqrt{x^{4}-1}\, \RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right) x^{2}+8 \left(x^{4}-1\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{2}+1\right) \RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)^{3}-\RootOf \left(\textit{\_Z}^{4}+4 \RootOf \left(\textit{\_Z}^{2}+1\right)\right)^{3}}{\RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-x^{4}+1}\right)}{32}$&$1006$\\ \hline \end{longtable}"," ",0,"1/8*RootOf(_Z^2+1)*ln(-2*RootOf(_Z^2+1)*(x^4-1)^(1/2)*x^2+2*RootOf(_Z^2+1)*x^4+2*(x^4-1)^(3/4)*x-2*x^3*(x^4-1)^(1/4)-RootOf(_Z^2+1))+1/8*ln(2*(x^4-1)^(3/4)*x+2*x^2*(x^4-1)^(1/2)+2*x^3*(x^4-1)^(1/4)+2*x^4-1)-1/16*RootOf(_Z^4+4*RootOf(_Z^2+1))*ln(-((x^4-1)^(1/2)*RootOf(_Z^4+4*RootOf(_Z^2+1))^3*x^2-(x^4-1)^(1/4)*RootOf(_Z^2+1)*RootOf(_Z^4+4*RootOf(_Z^2+1))^2*x^3-(x^4-1)^(1/4)*RootOf(_Z^4+4*RootOf(_Z^2+1))^2*x^3+RootOf(_Z^4+4*RootOf(_Z^2+1))*RootOf(_Z^2+1)*x^4+2*RootOf(_Z^2+1)*(x^4-1)^(3/4)*x-RootOf(_Z^4+4*RootOf(_Z^2+1))*x^4+2*(x^4-1)^(3/4)*x+RootOf(_Z^4+4*RootOf(_Z^2+1)))/(RootOf(_Z^2+1)*x^4+x^4-1))+1/16*RootOf(_Z^2+1)*RootOf(_Z^4+4*RootOf(_Z^2+1))*ln((-(x^4-1)^(1/2)*RootOf(_Z^4+4*RootOf(_Z^2+1))^3*x^2+(x^4-1)^(1/4)*RootOf(_Z^2+1)*RootOf(_Z^4+4*RootOf(_Z^2+1))^2*x^3-(x^4-1)^(1/4)*RootOf(_Z^4+4*RootOf(_Z^2+1))^2*x^3+RootOf(_Z^4+4*RootOf(_Z^2+1))*RootOf(_Z^2+1)*x^4+2*RootOf(_Z^2+1)*(x^4-1)^(3/4)*x-RootOf(_Z^4+4*RootOf(_Z^2+1))*x^4-2*(x^4-1)^(3/4)*x+RootOf(_Z^4+4*RootOf(_Z^2+1)))/(RootOf(_Z^2+1)*x^4+x^4-1))+1/32*RootOf(_Z^4+4*RootOf(_Z^2+1))^3*ln(-(RootOf(_Z^4+4*RootOf(_Z^2+1))^3*RootOf(_Z^2+1)^2*x^4+2*RootOf(_Z^4+4*RootOf(_Z^2+1))^3*RootOf(_Z^2+1)*x^4+4*(x^4-1)^(1/4)*RootOf(_Z^2+1)*RootOf(_Z^4+4*RootOf(_Z^2+1))^2*x^3+RootOf(_Z^4+4*RootOf(_Z^2+1))^3*x^4+4*RootOf(_Z^4+4*RootOf(_Z^2+1))*RootOf(_Z^2+1)*(x^4-1)^(1/2)*x^2+4*(x^4-1)^(1/2)*RootOf(_Z^4+4*RootOf(_Z^2+1))*x^2+8*(x^4-1)^(3/4)*x-RootOf(_Z^2+1)*RootOf(_Z^4+4*RootOf(_Z^2+1))^3-RootOf(_Z^4+4*RootOf(_Z^2+1))^3)/(RootOf(_Z^2+1)*x^4-x^4+1))-1/32*RootOf(_Z^2+1)*RootOf(_Z^4+4*RootOf(_Z^2+1))^3*ln(-(-RootOf(_Z^4+4*RootOf(_Z^2+1))^3*RootOf(_Z^2+1)^2*x^4-4*(x^4-1)^(1/4)*RootOf(_Z^2+1)*RootOf(_Z^4+4*RootOf(_Z^2+1))^2*x^3+RootOf(_Z^4+4*RootOf(_Z^2+1))^3*x^4+4*RootOf(_Z^4+4*RootOf(_Z^2+1))*RootOf(_Z^2+1)*(x^4-1)^(1/2)*x^2-4*(x^4-1)^(1/2)*RootOf(_Z^4+4*RootOf(_Z^2+1))*x^2+8*(x^4-1)^(3/4)*x+RootOf(_Z^2+1)*RootOf(_Z^4+4*RootOf(_Z^2+1))^3-RootOf(_Z^4+4*RootOf(_Z^2+1))^3)/(RootOf(_Z^2+1)*x^4-x^4+1))","C"
2850,0,0,245,0.012000," ","int((c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2),x)","\[\int \sqrt{c +\sqrt{a x +\sqrt{a^{2} x^{2}+b}}}\, dx\]"," ",0,"int((c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2),x)","F"
2851,0,0,230,0.044000," ","int(x^3/(x^2*(-a+x))^(1/3)/(-a^4+4*a^3*x-6*a^2*x^2+4*a*x^3+(-1+d)*x^4),x)","\[\int \frac{x^{3}}{\left(x^{2} \left(-a +x \right)\right)^{\frac{1}{3}} \left(-a^{4}+4 a^{3} x -6 a^{2} x^{2}+4 a \,x^{3}+\left(-1+d \right) x^{4}\right)}\, dx\]"," ",0,"int(x^3/(x^2*(-a+x))^(1/3)/(-a^4+4*a^3*x-6*a^2*x^2+4*a*x^3+(-1+d)*x^4),x)","F"
2852,0,0,214,0.047000," ","int((c+(a*x^2+x*(a^2*x^2-b)^(1/2))^(1/2))^(1/2)/(a^2*x^2-b)^(1/2),x)","\[\int \frac{\sqrt{c +\sqrt{a \,x^{2}+x \sqrt{a^{2} x^{2}-b}}}}{\sqrt{a^{2} x^{2}-b}}\, dx\]"," ",0,"int((c+(a*x^2+x*(a^2*x^2-b)^(1/2))^(1/2))^(1/2)/(a^2*x^2-b)^(1/2),x)","F"
2853,0,0,252,0.221000," ","int((-a*(a*b+a*c-2*b*c)+2*(a^2-b*c)*x+(-2*a+b+c)*x^2)/((-a+x)*(-b+x)*(-c+x))^(2/3)/(-b*c+a^2*d+(-2*a*d+b+c)*x+(-1+d)*x^2),x)","\[\int \frac{-a \left(a b +a c -2 b c \right)+2 \left(a^{2}-b c \right) x +\left(-2 a +b +c \right) x^{2}}{\left(\left(-a +x \right) \left(-b +x \right) \left(-c +x \right)\right)^{\frac{2}{3}} \left(-b c +a^{2} d +\left(-2 a d +b +c \right) x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((-a*(a*b+a*c-2*b*c)+2*(a^2-b*c)*x+(-2*a+b+c)*x^2)/((-a+x)*(-b+x)*(-c+x))^(2/3)/(-b*c+a^2*d+(-2*a*d+b+c)*x+(-1+d)*x^2),x)","F"
2854,0,0,243,0.056000," ","int(x^2*(-2*a*b+(a+b)*x)/(x*(-a+x)*(-b+x))^(1/3)/(-a^2*b^2+2*a*b*(a+b)*x-(a^2+4*a*b+b^2)*x^2+2*(a+b)*x^3+(-1+d)*x^4),x)","\[\int \frac{x^{2} \left(-2 a b +\left(a +b \right) x \right)}{\left(x \left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{3}} \left(-a^{2} b^{2}+2 a b \left(a +b \right) x -\left(a^{2}+4 a b +b^{2}\right) x^{2}+2 \left(a +b \right) x^{3}+\left(-1+d \right) x^{4}\right)}\, dx\]"," ",0,"int(x^2*(-2*a*b+(a+b)*x)/(x*(-a+x)*(-b+x))^(1/3)/(-a^2*b^2+2*a*b*(a+b)*x-(a^2+4*a*b+b^2)*x^2+2*(a+b)*x^3+(-1+d)*x^4),x)","F"
2855,1,1425,231,27.534000," ","int((x^6+1)/(x^5+x^3)^(1/4)/(-x^6+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$1425$\\ \hline \end{longtable}"," ",0,"-1/12*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln(((x^5+x^3)^(1/2)*RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x-2*(x^5+x^3)^(1/4)*RootOf(_Z^4+8)^2*x^2+RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^4-2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^3-4*(x^5+x^3)^(3/4)+RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^2)/(1+x)^2/x^2)+1/12*RootOf(_Z^4+8)*ln((RootOf(_Z^4+8)^3*(x^5+x^3)^(1/2)*x+2*(x^5+x^3)^(1/4)*RootOf(_Z^4+8)^2*x^2-RootOf(_Z^4+8)*x^4+2*RootOf(_Z^4+8)*x^3-RootOf(_Z^4+8)*x^2-4*(x^5+x^3)^(3/4))/(1+x)^2/x^2)+1/48*ln(-(RootOf(_Z^4+8)^3*x^4-2*RootOf(_Z^4+8)^3*x^3+8*(x^5+x^3)^(1/4)*RootOf(_Z^4+8)^2*x^2+RootOf(_Z^4+8)^3*x^2-16*(x^5+x^3)^(1/2)*RootOf(_Z^4+8)*x+16*(x^5+x^3)^(3/4))/x^2/(-1+x)^2)*RootOf(_Z^4+8)^3+1/48*ln(-(RootOf(_Z^4+8)^3*x^4-2*RootOf(_Z^4+8)^3*x^3+8*(x^5+x^3)^(1/4)*RootOf(_Z^4+8)^2*x^2+RootOf(_Z^4+8)^3*x^2-16*(x^5+x^3)^(1/2)*RootOf(_Z^4+8)*x+16*(x^5+x^3)^(3/4))/x^2/(-1+x)^2)*RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)-1/24*RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln((RootOf(_Z^4+8)^3*x^4-RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*x^4+2*RootOf(_Z^4+8)^3*x^3-2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^2*x^3+8*(x^5+x^3)^(1/4)*RootOf(_Z^4+8)*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^2+RootOf(_Z^4+8)^3*x^2-RootOf(_Z^4+8)^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^2-8*(x^5+x^3)^(1/2)*RootOf(_Z^4+8)*x-8*RootOf(_Z^2+RootOf(_Z^4+8)^2)*(x^5+x^3)^(1/2)*x+16*(x^5+x^3)^(3/4))/x^2/(-1+x)^2)-1/24*RootOf(_Z^4+8)^3*RootOf(_Z^2+RootOf(_Z^4+8)^2)*ln((-RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^3*x^4+2*RootOf(_Z^4+8)^3*(x^5+x^3)^(1/2)*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x-RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)^3*x^3-RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^2*RootOf(_Z^4+8)^3+16*(x^5+x^3)^(3/4)-16*(x^5+x^3)^(1/4)*x^2)/x^2/(x^2-x+1))+1/3*ln((x^4+2*(x^5+x^3)^(3/4)+2*(x^5+x^3)^(1/2)*x+2*(x^5+x^3)^(1/4)*x^2+x^3+x^2)/x^2/(x^2-x+1))+1/12*ln(-(-x^4*RootOf(_Z^4+8)^2+4*RootOf(_Z^4+8)^2*(x^5+x^3)^(1/2)*x-x^3*RootOf(_Z^4+8)^2-RootOf(_Z^4+8)^2*x^2-8*(x^5+x^3)^(3/4)+8*(x^5+x^3)^(1/4)*x^2)/x^2/(x^2+x+1))*RootOf(_Z^4+8)^2+1/12*ln(-(-x^4*RootOf(_Z^4+8)^2+4*RootOf(_Z^4+8)^2*(x^5+x^3)^(1/2)*x-x^3*RootOf(_Z^4+8)^2-RootOf(_Z^4+8)^2*x^2-8*(x^5+x^3)^(3/4)+8*(x^5+x^3)^(1/4)*x^2)/x^2/(x^2+x+1))*RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)-1/6*RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)*ln(((x^5+x^3)^(1/4)*RootOf(_Z^4+8)^3*RootOf(_Z^2+RootOf(_Z^4+8)^2)*x^2+x^4*RootOf(_Z^4+8)^2-RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)*x^4-2*RootOf(_Z^4+8)^2*(x^5+x^3)^(1/2)*x-2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)*(x^5+x^3)^(1/2)*x-x^3*RootOf(_Z^4+8)^2+RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)*x^3+RootOf(_Z^4+8)^2*x^2-x^2*RootOf(_Z^2+RootOf(_Z^4+8)^2)*RootOf(_Z^4+8)+8*(x^5+x^3)^(3/4))/x^2/(x^2+x+1))","C"
2856,1,526,256,0.307000," ","int((a^16*x^16+b^16)/(a^4*x^4-b^4)^(1/2)/(a^16*x^16-b^16),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\sqrt{2}\, \ln \left(\frac{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}-\frac{\left(a^{4} b^{4}\right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}}{x}+\sqrt{a^{4} b^{4}}}{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}+\frac{\left(a^{4} b^{4}\right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}}{x}+\sqrt{a^{4} b^{4}}}\right)}{32 \left(a^{4} b^{4}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}}{\left(a^{4} b^{4}\right)^{\frac{1}{4}} x}+1\right)}{16 \left(a^{4} b^{4}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}}{\left(a^{4} b^{4}\right)^{\frac{1}{4}} x}-1\right)}{16 \left(a^{4} b^{4}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, x}{4 \sqrt{a^{4} x^{4}-b^{4}}}+\frac{\ln \left(\frac{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}-\frac{\sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}\, \sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{2 x}+\frac{\sqrt{2}\, \sqrt{a^{4} b^{4}}}{2}}{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}+\frac{\sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}\, \sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{2 x}+\frac{\sqrt{2}\, \sqrt{a^{4} b^{4}}}{2}}\right)}{8 \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}+\frac{\arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{\sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}\, x}+1\right)}{4 \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}+\frac{\arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{\sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}\, x}-1\right)}{4 \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}\right) \sqrt{2}}{2}$&$526$\\ default&$\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{\sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}-\frac{b \left(\frac{a^{4} x^{3}-a^{3} b \,x^{2}+a^{2} b^{2} x -a \,b^{3}}{2 a^{2} b^{3} \sqrt{\left(x +\frac{b}{a}\right) \left(a^{4} x^{3}-a^{3} b \,x^{2}+a^{2} b^{2} x -a \,b^{3}\right)}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}-\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \left(\EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)-\EllipticE \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{8}+\frac{b \left(-\frac{a^{4} x^{3}+a^{3} b \,x^{2}+a^{2} b^{2} x +a \,b^{3}}{2 a^{2} b^{3} \sqrt{\left(x -\frac{b}{a}\right) \left(a^{4} x^{3}+a^{3} b \,x^{2}+a^{2} b^{2} x +a \,b^{3}\right)}}-\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \left(\EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)-\EllipticE \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{8}-\frac{b^{8} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{8} a^{8}+b^{8}\right)}{\sum}\frac{-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{6} a^{4}+b^{4} x^{2}\right) a^{4}}{b^{4} \sqrt{\underline{\hspace{1.25 ex}}\alpha^{4} a^{4}-b^{4}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4} a^{4}-b^{4}}}+\frac{2 \underline{\hspace{1.25 ex}}\alpha^{7} a^{8} \sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{6} a^{6}}{b^{6}}, \frac{\sqrt{\frac{a^{2}}{b^{2}}}}{\sqrt{-\frac{a^{2}}{b^{2}}}}\right)}{\sqrt{-\frac{a^{2}}{b^{2}}}\, b^{8} \sqrt{a^{4} x^{4}-b^{4}}}}{\underline{\hspace{1.25 ex}}\alpha^{7}}\right)}{16 a^{8}}-\frac{b^{4} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4} a^{4}+b^{4}\right)}{\sum}\frac{-\frac{\sqrt{2}\, \arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}\right) a^{4}}{\sqrt{-2 b^{4}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{\sqrt{-b^{4}}}+\frac{4 \underline{\hspace{1.25 ex}}\alpha^{3} a^{4} \sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}}{b^{2}}, \frac{\sqrt{\frac{a^{2}}{b^{2}}}}{\sqrt{-\frac{a^{2}}{b^{2}}}}\right)}{\sqrt{-\frac{a^{2}}{b^{2}}}\, b^{4} \sqrt{a^{4} x^{4}-b^{4}}}}{\underline{\hspace{1.25 ex}}\alpha^{3}}\right)}{32 a^{4}}-\frac{b^{2} \left(-\frac{\left(a^{4} x^{2}-a^{2} b^{2}\right) x}{2 b^{4} a^{2} \sqrt{\left(x^{2}+\frac{b^{2}}{a^{2}}\right) \left(a^{4} x^{2}-a^{2} b^{2}\right)}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{2 b^{2} \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \left(\EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)-\EllipticE \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)\right)}{2 b^{2} \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{4}$&$1190$\\ \hline \end{longtable}"," ",0,"1/2*(1/32/(a^4*b^4)^(1/4)*2^(1/2)*ln((1/2*(a^4*x^4-b^4)/x^2-(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x+(a^4*b^4)^(1/2))/(1/2*(a^4*x^4-b^4)/x^2+(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x+(a^4*b^4)^(1/2)))+1/16/(a^4*b^4)^(1/4)*2^(1/2)*arctan(1/(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x+1)+1/16/(a^4*b^4)^(1/4)*2^(1/2)*arctan(1/(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x-1)-1/4/(a^4*x^4-b^4)^(1/2)*2^(1/2)*x+1/8/(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*ln((1/2*(a^4*x^4-b^4)/x^2-1/2*(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x+1/2*2^(1/2)*(a^4*b^4)^(1/2))/(1/2*(a^4*x^4-b^4)/x^2+1/2*(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x+1/2*2^(1/2)*(a^4*b^4)^(1/2)))+1/4/(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*arctan(1/(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x+1)+1/4/(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*arctan(1/(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x-1))*2^(1/2)","B"
2857,0,0,126,0.075000," ","int((a^3*x^3-b^2*x^2)^(1/3)/(a*x^2+b),x)","\[\int \frac{\left(a^{3} x^{3}-b^{2} x^{2}\right)^{\frac{1}{3}}}{a \,x^{2}+b}\, dx\]"," ",0,"int((a^3*x^3-b^2*x^2)^(1/3)/(a*x^2+b),x)","F"
2858,0,0,126,0.004000," ","int((a^3*x^3-b^2*x^2)^(1/3)/(a*x^2+b),x)","\[\int \frac{\left(a^{3} x^{3}-b^{2} x^{2}\right)^{\frac{1}{3}}}{a \,x^{2}+b}\, dx\]"," ",0,"int((a^3*x^3-b^2*x^2)^(1/3)/(a*x^2+b),x)","F"
2859,1,515,260,0.279000," ","int((a^8*x^8+b^8+x^4)/(a^4*x^4-b^4)^(1/2)/(a^8*x^8-b^8),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}}{\left(a^{4} b^{4}\right)^{\frac{1}{4}} x}-1\right)}{8 \left(a^{4} b^{4}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \ln \left(\frac{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}-\frac{\left(a^{4} b^{4}\right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}}{x}+\sqrt{a^{4} b^{4}}}{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}+\frac{\left(a^{4} b^{4}\right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}}{x}+\sqrt{a^{4} b^{4}}}\right)}{16 \left(a^{4} b^{4}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}}{\left(a^{4} b^{4}\right)^{\frac{1}{4}} x}+1\right)}{8 \left(a^{4} b^{4}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}}{\left(a^{4} b^{4}\right)^{\frac{1}{4}} x}-1\right)}{16 a^{4} b^{4} \left(a^{4} b^{4}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \ln \left(\frac{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}-\frac{\left(a^{4} b^{4}\right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}}{x}+\sqrt{a^{4} b^{4}}}{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}+\frac{\left(a^{4} b^{4}\right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}}{x}+\sqrt{a^{4} b^{4}}}\right)}{32 a^{4} b^{4} \left(a^{4} b^{4}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}}{\left(a^{4} b^{4}\right)^{\frac{1}{4}} x}+1\right)}{16 a^{4} b^{4} \left(a^{4} b^{4}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, x}{2 \sqrt{a^{4} x^{4}-b^{4}}}-\frac{\sqrt{2}\, x}{4 a^{4} b^{4} \sqrt{a^{4} x^{4}-b^{4}}}\right) \sqrt{2}}{2}$&$515$\\ default&$\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{\sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}+\frac{\left(-2 a^{4} b^{4}-1\right) \left(\frac{a^{4} x^{3}-a^{3} b \,x^{2}+a^{2} b^{2} x -a \,b^{3}}{2 a^{2} b^{3} \sqrt{\left(x +\frac{b}{a}\right) \left(a^{4} x^{3}-a^{3} b \,x^{2}+a^{2} b^{2} x -a \,b^{3}\right)}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}-\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \left(\EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)-\EllipticE \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{8 a^{4} b^{3}}+\frac{\left(2 a^{4} b^{4}+1\right) \left(-\frac{a^{4} x^{3}+a^{3} b \,x^{2}+a^{2} b^{2} x +a \,b^{3}}{2 a^{2} b^{3} \sqrt{\left(x -\frac{b}{a}\right) \left(a^{4} x^{3}+a^{3} b \,x^{2}+a^{2} b^{2} x +a \,b^{3}\right)}}-\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \left(\EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)-\EllipticE \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{8 b^{3} a^{4}}+\frac{\left(-2 a^{4} b^{4}+1\right) \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4} a^{4}+b^{4}\right)}{\sum}\frac{-\frac{\sqrt{2}\, \arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}\right) a^{4}}{\sqrt{-2 b^{4}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{\sqrt{-b^{4}}}+\frac{4 \underline{\hspace{1.25 ex}}\alpha^{3} a^{4} \sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}}{b^{2}}, \frac{\sqrt{\frac{a^{2}}{b^{2}}}}{\sqrt{-\frac{a^{2}}{b^{2}}}}\right)}{\sqrt{-\frac{a^{2}}{b^{2}}}\, b^{4} \sqrt{a^{4} x^{4}-b^{4}}}}{\underline{\hspace{1.25 ex}}\alpha^{3}}\right)}{32 a^{8}}+\frac{\left(-2 a^{4} b^{4}-1\right) \left(-\frac{\left(a^{4} x^{2}-a^{2} b^{2}\right) x}{2 b^{4} a^{2} \sqrt{\left(x^{2}+\frac{b^{2}}{a^{2}}\right) \left(a^{4} x^{2}-a^{2} b^{2}\right)}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{2 b^{2} \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \left(\EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)-\EllipticE \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)\right)}{2 b^{2} \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{4 a^{4} b^{2}}$&$1031$\\ \hline \end{longtable}"," ",0,"1/2*(1/8/(a^4*b^4)^(1/4)*2^(1/2)*arctan(1/(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x-1)+1/16/(a^4*b^4)^(1/4)*2^(1/2)*ln((1/2*(a^4*x^4-b^4)/x^2-(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x+(a^4*b^4)^(1/2))/(1/2*(a^4*x^4-b^4)/x^2+(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x+(a^4*b^4)^(1/2)))+1/8/(a^4*b^4)^(1/4)*2^(1/2)*arctan(1/(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x+1)-1/16/a^4/b^4/(a^4*b^4)^(1/4)*2^(1/2)*arctan(1/(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x-1)-1/32/a^4/b^4/(a^4*b^4)^(1/4)*2^(1/2)*ln((1/2*(a^4*x^4-b^4)/x^2-(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x+(a^4*b^4)^(1/2))/(1/2*(a^4*x^4-b^4)/x^2+(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x+(a^4*b^4)^(1/2)))-1/16/a^4/b^4/(a^4*b^4)^(1/4)*2^(1/2)*arctan(1/(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x+1)-1/2/(a^4*x^4-b^4)^(1/2)*2^(1/2)*x-1/4/a^4/b^4/(a^4*x^4-b^4)^(1/2)*2^(1/2)*x)*2^(1/2)","A"
2860,0,0,126,0.067000," ","int((a^3*x^3-b^2*x^2)^(1/3)/(a*x^2-b),x)","\[\int \frac{\left(a^{3} x^{3}-b^{2} x^{2}\right)^{\frac{1}{3}}}{a \,x^{2}-b}\, dx\]"," ",0,"int((a^3*x^3-b^2*x^2)^(1/3)/(a*x^2-b),x)","F"
2861,0,0,126,0.004000," ","int((a^3*x^3-b^2*x^2)^(1/3)/(a*x^2-b),x)","\[\int \frac{\left(a^{3} x^{3}-b^{2} x^{2}\right)^{\frac{1}{3}}}{a \,x^{2}-b}\, dx\]"," ",0,"int((a^3*x^3-b^2*x^2)^(1/3)/(a*x^2-b),x)","F"
2862,0,0,257,0.049000," ","int((-b+x)/((-a+x)*(-b+x)^2)^(2/3)/(a-b*d+(-1+d)*x),x)","\[\int \frac{-b +x}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{2}{3}} \left(a -b d +\left(-1+d \right) x \right)}\, dx\]"," ",0,"int((-b+x)/((-a+x)*(-b+x)^2)^(2/3)/(a-b*d+(-1+d)*x),x)","F"
2863,0,0,255,0.047000," ","int((x^2-b)^(1/2)*(x^4+c)*(x+(x^2-b)^(1/2))^(1/2)/x,x)","\[\int \frac{\sqrt{x^{2}-b}\, \left(x^{4}+c \right) \sqrt{x +\sqrt{x^{2}-b}}}{x}\, dx\]"," ",0,"int((x^2-b)^(1/2)*(x^4+c)*(x+(x^2-b)^(1/2))^(1/2)/x,x)","F"
2864,1,568,262,0.258000," ","int(x^8/(a^4*x^4-b^4)^(1/2)/(a^16*x^16-b^16),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\sqrt{2}\, \ln \left(\frac{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}-\frac{\left(a^{4} b^{4}\right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}}{x}+\sqrt{a^{4} b^{4}}}{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}+\frac{\left(a^{4} b^{4}\right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}}{x}+\sqrt{a^{4} b^{4}}}\right)}{64 a^{8} b^{8} \left(a^{4} b^{4}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}}{\left(a^{4} b^{4}\right)^{\frac{1}{4}} x}+1\right)}{32 a^{8} b^{8} \left(a^{4} b^{4}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}}{\left(a^{4} b^{4}\right)^{\frac{1}{4}} x}-1\right)}{32 a^{8} b^{8} \left(a^{4} b^{4}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, x}{8 a^{8} b^{8} \sqrt{a^{4} x^{4}-b^{4}}}-\frac{\ln \left(\frac{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}-\frac{\sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}\, \sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{2 x}+\frac{\sqrt{2}\, \sqrt{a^{4} b^{4}}}{2}}{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}+\frac{\sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}\, \sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{2 x}+\frac{\sqrt{2}\, \sqrt{a^{4} b^{4}}}{2}}\right)}{16 a^{8} b^{8} \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}-\frac{\arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{\sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}\, x}+1\right)}{8 a^{8} b^{8} \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}-\frac{\arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{\sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}\, x}-1\right)}{8 a^{8} b^{8} \sqrt{\sqrt{2}\, \sqrt{a^{4} b^{4}}}}\right) \sqrt{2}}{2}$&$568$\\ default&$-\frac{\frac{a^{4} x^{3}-a^{3} b \,x^{2}+a^{2} b^{2} x -a \,b^{3}}{2 a^{2} b^{3} \sqrt{\left(x +\frac{b}{a}\right) \left(a^{4} x^{3}-a^{3} b \,x^{2}+a^{2} b^{2} x -a \,b^{3}\right)}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}-\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \left(\EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)-\EllipticE \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}}{16 b^{7} a^{8}}+\frac{-\frac{a^{4} x^{3}+a^{3} b \,x^{2}+a^{2} b^{2} x +a \,b^{3}}{2 a^{2} b^{3} \sqrt{\left(x -\frac{b}{a}\right) \left(a^{4} x^{3}+a^{3} b \,x^{2}+a^{2} b^{2} x +a \,b^{3}\right)}}-\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \left(\EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)-\EllipticE \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}}{16 b^{7} a^{8}}+\frac{\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{8} a^{8}+b^{8}\right)}{\sum}\frac{-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{6} a^{4}+b^{4} x^{2}\right) a^{4}}{b^{4} \sqrt{\underline{\hspace{1.25 ex}}\alpha^{4} a^{4}-b^{4}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{\sqrt{\underline{\hspace{1.25 ex}}\alpha^{4} a^{4}-b^{4}}}+\frac{2 \underline{\hspace{1.25 ex}}\alpha^{7} a^{8} \sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{6} a^{6}}{b^{6}}, \frac{\sqrt{\frac{a^{2}}{b^{2}}}}{\sqrt{-\frac{a^{2}}{b^{2}}}}\right)}{\sqrt{-\frac{a^{2}}{b^{2}}}\, b^{8} \sqrt{a^{4} x^{4}-b^{4}}}}{\underline{\hspace{1.25 ex}}\alpha^{7}}}{32 a^{16}}-\frac{\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4} a^{4}+b^{4}\right)}{\sum}\frac{-\frac{\sqrt{2}\, \arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}\right) a^{4}}{\sqrt{-2 b^{4}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{\sqrt{-b^{4}}}+\frac{4 \underline{\hspace{1.25 ex}}\alpha^{3} a^{4} \sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}}{b^{2}}, \frac{\sqrt{\frac{a^{2}}{b^{2}}}}{\sqrt{-\frac{a^{2}}{b^{2}}}}\right)}{\sqrt{-\frac{a^{2}}{b^{2}}}\, b^{4} \sqrt{a^{4} x^{4}-b^{4}}}}{\underline{\hspace{1.25 ex}}\alpha^{3}}}{64 a^{12} b^{4}}-\frac{-\frac{\left(a^{4} x^{2}-a^{2} b^{2}\right) x}{2 b^{4} a^{2} \sqrt{\left(x^{2}+\frac{b^{2}}{a^{2}}\right) \left(a^{4} x^{2}-a^{2} b^{2}\right)}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{2 b^{2} \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \left(\EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)-\EllipticE \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)\right)}{2 b^{2} \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}}{8 a^{8} b^{6}}$&$1130$\\ \hline \end{longtable}"," ",0,"1/2*(1/64/a^8/b^8/(a^4*b^4)^(1/4)*2^(1/2)*ln((1/2*(a^4*x^4-b^4)/x^2-(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x+(a^4*b^4)^(1/2))/(1/2*(a^4*x^4-b^4)/x^2+(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x+(a^4*b^4)^(1/2)))+1/32/a^8/b^8/(a^4*b^4)^(1/4)*2^(1/2)*arctan(1/(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x+1)+1/32/a^8/b^8/(a^4*b^4)^(1/4)*2^(1/2)*arctan(1/(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x-1)-1/8/a^8/b^8/(a^4*x^4-b^4)^(1/2)*2^(1/2)*x-1/16/a^8/b^8/(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*ln((1/2*(a^4*x^4-b^4)/x^2-1/2*(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x+1/2*2^(1/2)*(a^4*b^4)^(1/2))/(1/2*(a^4*x^4-b^4)/x^2+1/2*(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x+1/2*2^(1/2)*(a^4*b^4)^(1/2)))-1/8/a^8/b^8/(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*arctan(1/(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x+1)-1/8/a^8/b^8/(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*arctan(1/(2^(1/2)*(a^4*b^4)^(1/2))^(1/2)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x-1))*2^(1/2)","B"
2865,0,0,238,0.085000," ","int(x^2/(a*x^2-b)/(x^3-x)^(1/3),x)","\[\int \frac{x^{2}}{\left(a \,x^{2}-b \right) \left(x^{3}-x \right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(x^2/(a*x^2-b)/(x^3-x)^(1/3),x)","F"
2866,0,0,224,0.055000," ","int((x^4+1)*(x+(x^2+1)^(1/2))^(1/2)/(x^4-1),x)","\[\int \frac{\left(x^{4}+1\right) \sqrt{x +\sqrt{x^{2}+1}}}{x^{4}-1}\, dx\]"," ",0,"int((x^4+1)*(x+(x^2+1)^(1/2))^(1/2)/(x^4-1),x)","F"
2867,0,0,257,0.166000," ","int((-a+x)*(-b+x)/((-a+x)*(-b+x)^2)^(2/3)/(-b^2+a^2*d+2*(-a*d+b)*x+(-1+d)*x^2),x)","\[\int \frac{\left(-a +x \right) \left(-b +x \right)}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{2}{3}} \left(-b^{2}+a^{2} d +2 \left(-a d +b \right) x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((-a+x)*(-b+x)/((-a+x)*(-b+x)^2)^(2/3)/(-b^2+a^2*d+2*(-a*d+b)*x+(-1+d)*x^2),x)","F"
2868,0,0,257,0.166000," ","int((a*b-(a+b)*x+x^2)/((-a+x)*(-b+x)^2)^(2/3)/(-b^2+a^2*d+2*(-a*d+b)*x+(-1+d)*x^2),x)","\[\int \frac{a b -\left(a +b \right) x +x^{2}}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{2}{3}} \left(-b^{2}+a^{2} d +2 \left(-a d +b \right) x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((a*b-(a+b)*x+x^2)/((-a+x)*(-b+x)^2)^(2/3)/(-b^2+a^2*d+2*(-a*d+b)*x+(-1+d)*x^2),x)","F"
2869,1,172,11,0.155000," ","int(x/(x^2-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 c \,\textit{\_Z}^{6}+\left(6 c^{2}-2 b \right) \textit{\_Z}^{4}-a^{2} \textit{\_Z}^{3}+\left(-4 c^{3}+4 b c \right) \textit{\_Z}^{2}+a^{2} c \textit{\_Z} +c^{4}-2 b \,c^{2}+b^{2}\right)}{\sum}\frac{\left(\textit{\_R}^{7}-3 c \,\textit{\_R}^{5}+\left(3 c^{2}-b \right) \textit{\_R}^{3}+c \left(-c^{2}+b \right) \textit{\_R} \right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{8 \textit{\_R}^{7}-24 c \,\textit{\_R}^{5}+24 \textit{\_R}^{3} c^{2}-8 \textit{\_R}^{3} b -3 \textit{\_R}^{2} a^{2}-8 \textit{\_R} \,c^{3}+8 \textit{\_R} b c +a^{2} c}\right)$&$172$\\ default&$4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 c \,\textit{\_Z}^{6}+\left(6 c^{2}-2 b \right) \textit{\_Z}^{4}-a^{2} \textit{\_Z}^{3}+\left(-4 c^{3}+4 b c \right) \textit{\_Z}^{2}+a^{2} c \textit{\_Z} +c^{4}-2 b \,c^{2}+b^{2}\right)}{\sum}\frac{\left(\textit{\_R}^{7}-3 c \,\textit{\_R}^{5}+\left(3 c^{2}-b \right) \textit{\_R}^{3}+c \left(-c^{2}+b \right) \textit{\_R} \right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{8 \textit{\_R}^{7}-24 c \,\textit{\_R}^{5}+24 \textit{\_R}^{3} c^{2}-8 \textit{\_R}^{3} b -3 \textit{\_R}^{2} a^{2}-8 \textit{\_R} \,c^{3}+8 \textit{\_R} b c +a^{2} c}\right)$&$172$\\ \hline \end{longtable}"," ",0,"4*sum((_R^7-3*c*_R^5+(3*c^2-b)*_R^3+c*(-c^2+b)*_R)/(8*_R^7-24*_R^5*c+24*_R^3*c^2-8*_R^3*b-3*_R^2*a^2-8*_R*c^3+8*_R*b*c+a^2*c)*ln((c+(a*x+b)^(1/2))^(1/2)-_R),_R=RootOf(_Z^8-4*c*_Z^6+(6*c^2-2*b)*_Z^4-a^2*_Z^3+(-4*c^3+4*b*c)*_Z^2+a^2*c*_Z+c^4-2*b*c^2+b^2))","B"
2870,1,172,11,0.152000," ","int(x/(x^2-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 c \,\textit{\_Z}^{6}+\left(6 c^{2}-2 b \right) \textit{\_Z}^{4}-a^{2} \textit{\_Z}^{3}+\left(-4 c^{3}+4 b c \right) \textit{\_Z}^{2}+a^{2} c \textit{\_Z} +c^{4}-2 b \,c^{2}+b^{2}\right)}{\sum}\frac{\left(\textit{\_R}^{7}-3 c \,\textit{\_R}^{5}+\left(3 c^{2}-b \right) \textit{\_R}^{3}+c \left(-c^{2}+b \right) \textit{\_R} \right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{8 \textit{\_R}^{7}-24 c \,\textit{\_R}^{5}+24 \textit{\_R}^{3} c^{2}-8 \textit{\_R}^{3} b -3 \textit{\_R}^{2} a^{2}-8 \textit{\_R} \,c^{3}+8 \textit{\_R} b c +a^{2} c}\right)$&$172$\\ default&$4 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 c \,\textit{\_Z}^{6}+\left(6 c^{2}-2 b \right) \textit{\_Z}^{4}-a^{2} \textit{\_Z}^{3}+\left(-4 c^{3}+4 b c \right) \textit{\_Z}^{2}+a^{2} c \textit{\_Z} +c^{4}-2 b \,c^{2}+b^{2}\right)}{\sum}\frac{\left(\textit{\_R}^{7}-3 c \,\textit{\_R}^{5}+\left(3 c^{2}-b \right) \textit{\_R}^{3}+c \left(-c^{2}+b \right) \textit{\_R} \right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{8 \textit{\_R}^{7}-24 c \,\textit{\_R}^{5}+24 \textit{\_R}^{3} c^{2}-8 \textit{\_R}^{3} b -3 \textit{\_R}^{2} a^{2}-8 \textit{\_R} \,c^{3}+8 \textit{\_R} b c +a^{2} c}\right)$&$172$\\ \hline \end{longtable}"," ",0,"4*sum((_R^7-3*c*_R^5+(3*c^2-b)*_R^3+c*(-c^2+b)*_R)/(8*_R^7-24*_R^5*c+24*_R^3*c^2-8*_R^3*b-3*_R^2*a^2-8*_R*c^3+8*_R*b*c+a^2*c)*ln((c+(a*x+b)^(1/2))^(1/2)-_R),_R=RootOf(_Z^8-4*c*_Z^6+(6*c^2-2*b)*_Z^4-a^2*_Z^3+(-4*c^3+4*b*c)*_Z^2+a^2*c*_Z+c^4-2*b*c^2+b^2))","B"
2871,0,0,268,0.166000," ","int((a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^2)^(1/3)/(b*d-(a+d)*x+x^2),x)","\[\int \frac{a b -2 b x +x^{2}}{\left(x \left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{3}} \left(b d -\left(a +d \right) x +x^{2}\right)}\, dx\]"," ",0,"int((a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^2)^(1/3)/(b*d-(a+d)*x+x^2),x)","F"
2872,0,0,266,0.020000," ","int((-a*b^2+(4*a-b)*b*x-3*a*x^2+x^3)/(x*(-a+x)*(-b+x)^2)^(1/3)/(-a^2*d+(2*a*d+b^2)*x-(2*b+d)*x^2+x^3),x)","\[\int \frac{-a \,b^{2}+\left(4 a -b \right) b x -3 a \,x^{2}+x^{3}}{\left(x \left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{3}} \left(-a^{2} d +\left(2 a d +b^{2}\right) x -\left(2 b +d \right) x^{2}+x^{3}\right)}\, dx\]"," ",0,"int((-a*b^2+(4*a-b)*b*x-3*a*x^2+x^3)/(x*(-a+x)*(-b+x)^2)^(1/3)/(-a^2*d+(2*a*d+b^2)*x-(2*b+d)*x^2+x^3),x)","F"
2873,0,0,240,0.045000," ","int((c*x^7-d)/x/(a*x^3-b)^(1/3),x)","\[\int \frac{c \,x^{7}-d}{x \left(a \,x^{3}-b \right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((c*x^7-d)/x/(a*x^3-b)^(1/3),x)","F"
2874,1,212,242,0.249000," ","int((c+(a*x+b)^(1/2))^(1/2)/(x-(a*x+b)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$4 \sqrt{c +\sqrt{a x +b}}+\frac{4 \left(a \sqrt{a^{2}+4 b}+c \sqrt{a^{2}+4 b}-a^{2}-a c -2 b \right) \arctan \left(\frac{2 \sqrt{c +\sqrt{a x +b}}}{\sqrt{2 \sqrt{a^{2}+4 b}-2 a -4 c}}\right)}{\sqrt{a^{2}+4 b}\, \sqrt{2 \sqrt{a^{2}+4 b}-2 a -4 c}}+\frac{4 \left(a \sqrt{a^{2}+4 b}+c \sqrt{a^{2}+4 b}+a^{2}+a c +2 b \right) \arctan \left(\frac{2 \sqrt{c +\sqrt{a x +b}}}{\sqrt{-2 \sqrt{a^{2}+4 b}-2 a -4 c}}\right)}{\sqrt{a^{2}+4 b}\, \sqrt{-2 \sqrt{a^{2}+4 b}-2 a -4 c}}$&$212$\\ default&$4 \sqrt{c +\sqrt{a x +b}}+\frac{4 \left(a \sqrt{a^{2}+4 b}+c \sqrt{a^{2}+4 b}-a^{2}-a c -2 b \right) \arctan \left(\frac{2 \sqrt{c +\sqrt{a x +b}}}{\sqrt{2 \sqrt{a^{2}+4 b}-2 a -4 c}}\right)}{\sqrt{a^{2}+4 b}\, \sqrt{2 \sqrt{a^{2}+4 b}-2 a -4 c}}+\frac{4 \left(a \sqrt{a^{2}+4 b}+c \sqrt{a^{2}+4 b}+a^{2}+a c +2 b \right) \arctan \left(\frac{2 \sqrt{c +\sqrt{a x +b}}}{\sqrt{-2 \sqrt{a^{2}+4 b}-2 a -4 c}}\right)}{\sqrt{a^{2}+4 b}\, \sqrt{-2 \sqrt{a^{2}+4 b}-2 a -4 c}}$&$212$\\ \hline \end{longtable}"," ",0,"4*(c+(a*x+b)^(1/2))^(1/2)+4*(a*(a^2+4*b)^(1/2)+c*(a^2+4*b)^(1/2)-a^2-a*c-2*b)/(a^2+4*b)^(1/2)/(2*(a^2+4*b)^(1/2)-2*a-4*c)^(1/2)*arctan(2*(c+(a*x+b)^(1/2))^(1/2)/(2*(a^2+4*b)^(1/2)-2*a-4*c)^(1/2))+4*(a*(a^2+4*b)^(1/2)+c*(a^2+4*b)^(1/2)+a^2+a*c+2*b)/(a^2+4*b)^(1/2)/(-2*(a^2+4*b)^(1/2)-2*a-4*c)^(1/2)*arctan(2*(c+(a*x+b)^(1/2))^(1/2)/(-2*(a^2+4*b)^(1/2)-2*a-4*c)^(1/2))","A"
2875,1,3730,254,20.258000," ","int((1+x)/(1+2*x)/(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$3730$\\ \hline \end{longtable}"," ",0,"1/9*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*ln(-(-42103828584900*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(2/3)+634969321830*RootOf(_Z^3-100)*x^5-89275137943635*RootOf(_Z^3-100)-4839705196875*RootOf(_Z^3-100)*x^4-38562771008700*RootOf(_Z^3-100)*x^3-42047358750450*RootOf(_Z^3-100)*x^2+9059928128550*RootOf(_Z^3-100)*x-640746115263450*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)-34735564406250*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^4-276772977189000*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^3-301782583561500*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^2+65024976568500*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x+4557306050100*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^5+1235042290000*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x^4+172078407000*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x^4+13894225762500*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x^2+1935882078750*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x^2+1777529944800*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(2/3)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^2*x+21051914292450*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(2/3)*x-5052459430188*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(_Z^3-100)^2+154380286250*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x^5+21509800875*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x^5-3555059889600*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)*x^3+3555059889600*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)*x^2+28440479116800*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)*x+5094549446250*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x^3+709823428875*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x^3+16673070915000*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x+2323058494500*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x-421038285849*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(_Z^3-100)^2*x^3-3555059889600*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(2/3)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^2+421038285849*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(_Z^3-100)^2*x^2+3368306286792*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(_Z^3-100)^2*x-42660718675200*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100))/(1+2*x)/(3+x)^4)-1/50*ln((-21887249427900*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(2/3)+72330055488*RootOf(_Z^3-100)*x^5-26059162803786*RootOf(_Z^3-100)-2316822089850*RootOf(_Z^3-100)*x^4-14985883371420*RootOf(_Z^3-100)*x^3-22444920343620*RootOf(_Z^3-100)*x^2-9561129209820*RootOf(_Z^3-100)*x-640746115263450*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)-56966325626250*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^4-368474867221500*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^3-551878647286500*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^2-235090299901500*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x+1778460897600*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^5-1235042290000*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x^4-50229205200*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x^4-13894225762500*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x^2-565078558500*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x^2+1777529944800*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(2/3)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^2*x+10943624713950*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(2/3)*x-2626469931348*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(_Z^3-100)^2-154380286250*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x^5-6278650650*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x^5-3555059889600*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)*x^3+3555059889600*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)*x^2+28440479116800*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)*x-5094549446250*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x^3-207195471450*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x^3-16673070915000*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x-678094270200*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x-218872494279*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(_Z^3-100)^2*x^3-3555059889600*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(2/3)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^2+218872494279*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(_Z^3-100)^2*x^2+1750979954232*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(_Z^3-100)^2*x-42660718675200*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100))/(1+2*x)/(3+x)^4)*RootOf(_Z^3-100)-1/9*ln((-21887249427900*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(2/3)+72330055488*RootOf(_Z^3-100)*x^5-26059162803786*RootOf(_Z^3-100)-2316822089850*RootOf(_Z^3-100)*x^4-14985883371420*RootOf(_Z^3-100)*x^3-22444920343620*RootOf(_Z^3-100)*x^2-9561129209820*RootOf(_Z^3-100)*x-640746115263450*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)-56966325626250*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^4-368474867221500*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^3-551878647286500*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^2-235090299901500*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x+1778460897600*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*x^5-1235042290000*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x^4-50229205200*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x^4-13894225762500*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x^2-565078558500*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x^2+1777529944800*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(2/3)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^2*x+10943624713950*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(2/3)*x-2626469931348*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(_Z^3-100)^2-154380286250*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x^5-6278650650*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x^5-3555059889600*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)*x^3+3555059889600*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)*x^2+28440479116800*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)*x-5094549446250*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x^3-207195471450*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x^3-16673070915000*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)^2*RootOf(_Z^3-100)^2*x-678094270200*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^3*x-218872494279*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(_Z^3-100)^2*x^3-3555059889600*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(2/3)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100)^2+218872494279*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(_Z^3-100)^2*x^2+1750979954232*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(_Z^3-100)^2*x-42660718675200*(x^5+9*x^4+28*x^3+36*x^2+27*x+27)^(1/3)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)*RootOf(_Z^3-100))/(1+2*x)/(3+x)^4)*RootOf(81*RootOf(_Z^3-100)^2+450*_Z*RootOf(_Z^3-100)+2500*_Z^2)","C"
2876,0,0,131,0.076000," ","int((a*x^3-b*x)/(2*a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{a \,x^{3}-b x}{\left(2 a \,x^{3}-b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a*x^3-b*x)/(2*a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
2877,0,0,131,0.001000," ","int((a*x^3-b*x)/(2*a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{a \,x^{3}-b x}{\left(2 a \,x^{3}-b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a*x^3-b*x)/(2*a*x^3-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
2878,0,0,131,0.074000," ","int((a*x^3+b*x)/(2*a*x^3+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{a \,x^{3}+b x}{\left(2 a \,x^{3}+b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a*x^3+b*x)/(2*a*x^3+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
2879,0,0,258,0.038000," ","int(x*(-b+x)*(a*b+(-2*a+b)*x)/(x*(-a+x)*(-b+x))^(1/3)/(-a^4+4*a^3*x+(b^2*d-6*a^2)*x^2+2*(-b*d+2*a)*x^3+(-1+d)*x^4),x)","\[\int \frac{x \left(-b +x \right) \left(a b +\left(-2 a +b \right) x \right)}{\left(x \left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{3}} \left(-a^{4}+4 a^{3} x +\left(b^{2} d -6 a^{2}\right) x^{2}+2 \left(-b d +2 a \right) x^{3}+\left(-1+d \right) x^{4}\right)}\, dx\]"," ",0,"int(x*(-b+x)*(a*b+(-2*a+b)*x)/(x*(-a+x)*(-b+x))^(1/3)/(-a^4+4*a^3*x+(b^2*d-6*a^2)*x^2+2*(-b*d+2*a)*x^3+(-1+d)*x^4),x)","F"
2880,0,0,271,0.211000," ","int((-a*b-a*c+2*b*c+(2*a-b-c)*x)/((-a+x)*(-b+x)*(-c+x))^(1/3)/(-b*c+a^2*d+(-2*a*d+b+c)*x+(-1+d)*x^2),x)","\[\int \frac{-a b -a c +2 b c +\left(2 a -b -c \right) x}{\left(\left(-a +x \right) \left(-b +x \right) \left(-c +x \right)\right)^{\frac{1}{3}} \left(-b c +a^{2} d +\left(-2 a d +b +c \right) x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((-a*b-a*c+2*b*c+(2*a-b-c)*x)/((-a+x)*(-b+x)*(-c+x))^(1/3)/(-b*c+a^2*d+(-2*a*d+b+c)*x+(-1+d)*x^2),x)","F"
2881,0,0,257,0.019000," ","int(x*(-a*b+x^2)/(x^2*(-a+x)*(-b+x))^(1/3)/(a^2*b^2-2*a*b*(a+b)*x+(a^2+4*a*b+b^2-d)*x^2-2*(a+b)*x^3+x^4),x)","\[\int \frac{x \left(-a b +x^{2}\right)}{\left(x^{2} \left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{3}} \left(a^{2} b^{2}-2 a b \left(a +b \right) x +\left(a^{2}+4 a b +b^{2}-d \right) x^{2}-2 \left(a +b \right) x^{3}+x^{4}\right)}\, dx\]"," ",0,"int(x*(-a*b+x^2)/(x^2*(-a+x)*(-b+x))^(1/3)/(a^2*b^2-2*a*b*(a+b)*x+(a^2+4*a*b+b^2-d)*x^2-2*(a+b)*x^3+x^4),x)","F"
2882,1,475,233,0.281000," ","int((a^6*x^6-b^6)/(a^2*x^3-b^2*x)^(1/2)/(a^6*x^6+b^6),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{b \sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{2 \left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}-b^{2} x}}-\frac{2 b^{2} \left(-\frac{i \sqrt{1+\frac{a x}{b}}\, \sqrt{2-\frac{2 a x}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, -\frac{b}{a \left(-\frac{i b}{a}-\frac{b}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a^{2} x^{3}-b^{2} x}\, \left(-\frac{i b}{a}-\frac{b}{a}\right)}+\frac{i \sqrt{1+\frac{a x}{b}}\, \sqrt{2-\frac{2 a x}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, -\frac{b}{a \left(-\frac{b}{a}+\frac{i b}{a}\right)}, \frac{\sqrt{2}}{2}\right)}{2 a^{2} \sqrt{a^{2} x^{3}-b^{2} x}\, \left(-\frac{b}{a}+\frac{i b}{a}\right)}\right)}{3}-\frac{\sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4} a^{4}-\textit{\_Z}^{2} a^{2} b^{2}+b^{4}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+2 b^{2}\right) \underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha  a -b \right) \sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{\left(x -\frac{b}{a}\right) a}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticPi \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, -\frac{a^{2} \underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha  a -b \right)}{b^{3}}, \frac{\sqrt{2}}{2}\right)}{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-b^{2}\right) \sqrt{x \left(a^{2} x^{2}-b^{2}\right)}}\right)}{3 b}$&$475$\\ elliptic&$\frac{b \sqrt{1+\frac{a x}{b}}\, \sqrt{2-\frac{2 a x}{b}}\, \sqrt{-\frac{a x}{b}}\, \EllipticF \left(\sqrt{\frac{\left(x +\frac{b}{a}\right) a}{b}}, \frac{\sqrt{2}}{2}\right)}{a \sqrt{a^{2} x^{3}-b^{2} x}}+\frac{b \sqrt{2}\, \sqrt{\frac{a x +b}{b}}\, \sqrt{-\frac{a x -b}{b}}\, \sqrt{-\frac{a x}{b}}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{2} \textit{\_Z}^{2}+b^{2}\right)}{\sum}\EllipticPi \left(\sqrt{\frac{a x +b}{b}}, -\frac{\underline{\hspace{1.25 ex}}\alpha  a -b}{2 b}, \frac{\sqrt{2}}{2}\right)\right)}{6 a \sqrt{x \left(a^{2} x^{2}-b^{2}\right)}}-\frac{b^{2} \sqrt{2}\, \sqrt{\frac{a x +b}{b}}\, \sqrt{-\frac{a x -b}{b}}\, \sqrt{-\frac{a x}{b}}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{2} \textit{\_Z}^{2}+b^{2}\right)}{\sum}\frac{\EllipticPi \left(\sqrt{\frac{a x +b}{b}}, -\frac{\underline{\hspace{1.25 ex}}\alpha  a -b}{2 b}, \frac{\sqrt{2}}{2}\right)}{\underline{\hspace{1.25 ex}}\alpha}\right)}{6 a^{2} \sqrt{x \left(a^{2} x^{2}-b^{2}\right)}}-\frac{\sqrt{2}\, \sqrt{\frac{a x +b}{b}}\, \sqrt{-\frac{a x -b}{b}}\, \sqrt{-\frac{a x}{b}}\, a^{3} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4} a^{4}-\textit{\_Z}^{2} a^{2} b^{2}+b^{4}\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha^{4} \EllipticPi \left(\sqrt{\frac{a x +b}{b}}, -\frac{a^{2} \underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha  a -b \right)}{b^{3}}, \frac{\sqrt{2}}{2}\right)}{2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-b^{2}}\right)}{3 b \sqrt{x \left(a^{2} x^{2}-b^{2}\right)}}+\frac{\sqrt{2}\, \sqrt{\frac{a x +b}{b}}\, \sqrt{-\frac{a x -b}{b}}\, \sqrt{-\frac{a x}{b}}\, a^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4} a^{4}-\textit{\_Z}^{2} a^{2} b^{2}+b^{4}\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha^{3} \EllipticPi \left(\sqrt{\frac{a x +b}{b}}, -\frac{a^{2} \underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha  a -b \right)}{b^{3}}, \frac{\sqrt{2}}{2}\right)}{2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-b^{2}}\right)}{3 \sqrt{x \left(a^{2} x^{2}-b^{2}\right)}}+\frac{2 b \sqrt{2}\, \sqrt{\frac{a x +b}{b}}\, \sqrt{-\frac{a x -b}{b}}\, \sqrt{-\frac{a x}{b}}\, a \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4} a^{4}-\textit{\_Z}^{2} a^{2} b^{2}+b^{4}\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \EllipticPi \left(\sqrt{\frac{a x +b}{b}}, -\frac{a^{2} \underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha  a -b \right)}{b^{3}}, \frac{\sqrt{2}}{2}\right)}{2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-b^{2}}\right)}{3 \sqrt{x \left(a^{2} x^{2}-b^{2}\right)}}-\frac{2 b^{2} \sqrt{2}\, \sqrt{\frac{a x +b}{b}}\, \sqrt{-\frac{a x -b}{b}}\, \sqrt{-\frac{a x}{b}}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4} a^{4}-\textit{\_Z}^{2} a^{2} b^{2}+b^{4}\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \EllipticPi \left(\sqrt{\frac{a x +b}{b}}, -\frac{a^{2} \underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha  a -b \right)}{b^{3}}, \frac{\sqrt{2}}{2}\right)}{2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-b^{2}}\right)}{3 \sqrt{x \left(a^{2} x^{2}-b^{2}\right)}}$&$847$\\ \hline \end{longtable}"," ",0,"b/a*((x+b/a)/b*a)^(1/2)*(-2*(x-b/a)/b*a)^(1/2)*(-a*x/b)^(1/2)/(a^2*x^3-b^2*x)^(1/2)*EllipticF(((x+b/a)/b*a)^(1/2),1/2*2^(1/2))-2/3*b^2*(-1/2*I/a^2*(1+a*x/b)^(1/2)*(2-2*a*x/b)^(1/2)*(-a*x/b)^(1/2)/(a^2*x^3-b^2*x)^(1/2)/(-I*b/a-b/a)*EllipticPi(((x+b/a)/b*a)^(1/2),-b/a/(-I*b/a-b/a),1/2*2^(1/2))+1/2*I/a^2*(1+a*x/b)^(1/2)*(2-2*a*x/b)^(1/2)*(-a*x/b)^(1/2)/(a^2*x^3-b^2*x)^(1/2)/(-b/a+I*b/a)*EllipticPi(((x+b/a)/b*a)^(1/2),-b/a/(-b/a+I*b/a),1/2*2^(1/2)))-1/3/b*2^(1/2)*sum((-_alpha^2*a^2+2*b^2)*_alpha/(2*_alpha^2*a^2-b^2)*(_alpha*a-b)*((x+b/a)/b*a)^(1/2)*(-(x-b/a)/b*a)^(1/2)*(-a*x/b)^(1/2)/(x*(a^2*x^2-b^2))^(1/2)*EllipticPi(((x+b/a)/b*a)^(1/2),-a^2*_alpha^2*(_alpha*a-b)/b^3,1/2*2^(1/2)),_alpha=RootOf(_Z^4*a^4-_Z^2*a^2*b^2+b^4))","C"
2883,0,0,238,0.063000," ","int((x^4+1)^(1/2)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4-1),x)","\[\int \frac{\sqrt{x^{4}+1}\, \sqrt{x^{2}+\sqrt{x^{4}+1}}}{x^{4}-1}\, dx\]"," ",0,"int((x^4+1)^(1/2)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4-1),x)","F"
2884,0,0,116,0.093000," ","int(x^4/(1-x*(x^2+1)^(1/2)*(x-(x^2+1)^(1/2))^(1/2)),x)","\[\int \frac{x^{4}}{1-x \sqrt{x^{2}+1}\, \sqrt{x -\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int(x^4/(1-x*(x^2+1)^(1/2)*(x-(x^2+1)^(1/2))^(1/2)),x)","F"
2885,0,0,240,0.075000," ","int((x^2+(x^4+1)^(1/2))^(1/2)/(1+x)^2/(x^4+1)^(1/2),x)","\[\int \frac{\sqrt{x^{2}+\sqrt{x^{4}+1}}}{\left(1+x \right)^{2} \sqrt{x^{4}+1}}\, dx\]"," ",0,"int((x^2+(x^4+1)^(1/2))^(1/2)/(1+x)^2/(x^4+1)^(1/2),x)","F"
2886,0,0,275,0.022000," ","int((-b+x)*(a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^2)^(1/3)/(-b^2*d+2*b*d*x-(-a^2+d)*x^2-2*a*x^3+x^4),x)","\[\int \frac{\left(-b +x \right) \left(a b -2 b x +x^{2}\right)}{\left(x \left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{3}} \left(-b^{2} d +2 b d x -\left(-a^{2}+d \right) x^{2}-2 a \,x^{3}+x^{4}\right)}\, dx\]"," ",0,"int((-b+x)*(a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^2)^(1/3)/(-b^2*d+2*b*d*x-(-a^2+d)*x^2-2*a*x^3+x^4),x)","F"
2887,1,249,230,0.434000," ","int((a^8*x^8+b^8)/(a^4*x^4-b^4)^(1/2)/(a^8*x^8-b^8),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\sqrt{2}\, \ln \left(\frac{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}-\frac{\left(a^{4} b^{4}\right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}}{x}+\sqrt{a^{4} b^{4}}}{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}+\frac{\left(a^{4} b^{4}\right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}}{x}+\sqrt{a^{4} b^{4}}}\right)}{16 \left(a^{4} b^{4}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}}{\left(a^{4} b^{4}\right)^{\frac{1}{4}} x}+1\right)}{8 \left(a^{4} b^{4}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}}{\left(a^{4} b^{4}\right)^{\frac{1}{4}} x}-1\right)}{8 \left(a^{4} b^{4}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, x}{2 \sqrt{a^{4} x^{4}-b^{4}}}\right) \sqrt{2}}{2}$&$249$\\ default&$\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{\sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}-\frac{b \left(\frac{a^{4} x^{3}-a^{3} b \,x^{2}+a^{2} b^{2} x -a \,b^{3}}{2 a^{2} b^{3} \sqrt{\left(x +\frac{b}{a}\right) \left(a^{4} x^{3}-a^{3} b \,x^{2}+a^{2} b^{2} x -a \,b^{3}\right)}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}-\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \left(\EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)-\EllipticE \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{4}+\frac{b \left(-\frac{a^{4} x^{3}+a^{3} b \,x^{2}+a^{2} b^{2} x +a \,b^{3}}{2 a^{2} b^{3} \sqrt{\left(x -\frac{b}{a}\right) \left(a^{4} x^{3}+a^{3} b \,x^{2}+a^{2} b^{2} x +a \,b^{3}\right)}}-\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \left(\EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)-\EllipticE \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{4}-\frac{b^{4} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4} a^{4}+b^{4}\right)}{\sum}\frac{-\frac{\sqrt{2}\, \arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}\right) a^{4}}{\sqrt{-2 b^{4}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{\sqrt{-b^{4}}}+\frac{4 \underline{\hspace{1.25 ex}}\alpha^{3} a^{4} \sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}}{b^{2}}, \frac{\sqrt{\frac{a^{2}}{b^{2}}}}{\sqrt{-\frac{a^{2}}{b^{2}}}}\right)}{\sqrt{-\frac{a^{2}}{b^{2}}}\, b^{4} \sqrt{a^{4} x^{4}-b^{4}}}}{\underline{\hspace{1.25 ex}}\alpha^{3}}\right)}{16 a^{4}}-\frac{b^{2} \left(-\frac{\left(a^{4} x^{2}-a^{2} b^{2}\right) x}{2 b^{4} a^{2} \sqrt{\left(x^{2}+\frac{b^{2}}{a^{2}}\right) \left(a^{4} x^{2}-a^{2} b^{2}\right)}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{2 b^{2} \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \left(\EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)-\EllipticE \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)\right)}{2 b^{2} \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{2}$&$981$\\ \hline \end{longtable}"," ",0,"1/2*(1/16/(a^4*b^4)^(1/4)*2^(1/2)*ln((1/2*(a^4*x^4-b^4)/x^2-(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x+(a^4*b^4)^(1/2))/(1/2*(a^4*x^4-b^4)/x^2+(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x+(a^4*b^4)^(1/2)))+1/8/(a^4*b^4)^(1/4)*2^(1/2)*arctan(1/(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x+1)+1/8/(a^4*b^4)^(1/4)*2^(1/2)*arctan(1/(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x-1)-1/2/(a^4*x^4-b^4)^(1/2)*2^(1/2)*x)*2^(1/2)","A"
2888,1,902,220,0.229000," ","int(1/(x^2-1)^(1/2)/(x^(1/2)+(x^2-1)^(1/2))^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{6 \sqrt{5}\, \arctanh \left(\frac{2+2 \sqrt{5}+2 \left(\sqrt{5}+1\right) \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}{\sqrt{2+2 \sqrt{5}}\, \sqrt{4 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)^{2}+4 \left(\sqrt{5}+1\right) \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)+2+2 \sqrt{5}}}\right)}{25 \sqrt{2+2 \sqrt{5}}}-\frac{6 \sqrt{5}\, \arctan \left(\frac{2-2 \sqrt{5}+2 \left(-\sqrt{5}+1\right) \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)}{\sqrt{-2+2 \sqrt{5}}\, \sqrt{4 \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)^{2}+4 \left(-\sqrt{5}+1\right) \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)+2-2 \sqrt{5}}}\right)}{25 \sqrt{-2+2 \sqrt{5}}}-\frac{\sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)^{2}+\left(-\sqrt{5}+1\right) \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)+\frac{1}{2}-\frac{\sqrt{5}}{2}}}{5 \left(\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)}+\frac{2 \arctan \left(\frac{2-2 \sqrt{5}+2 \left(-\sqrt{5}+1\right) \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)}{\sqrt{-2+2 \sqrt{5}}\, \sqrt{4 \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)^{2}+4 \left(-\sqrt{5}+1\right) \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)+2-2 \sqrt{5}}}\right) \sqrt{5}}{5 \left(\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{-2+2 \sqrt{5}}}-\frac{6 \arctan \left(\frac{2-2 \sqrt{5}+2 \left(-\sqrt{5}+1\right) \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)}{\sqrt{-2+2 \sqrt{5}}\, \sqrt{4 \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)^{2}+4 \left(-\sqrt{5}+1\right) \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)+2-2 \sqrt{5}}}\right)}{5 \left(\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \sqrt{-2+2 \sqrt{5}}}+\frac{\sqrt{5}\, \sqrt{\left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)^{2}+\left(-\sqrt{5}+1\right) \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)+\frac{1}{2}-\frac{\sqrt{5}}{2}}}{5 \left(\frac{1}{2}-\frac{\sqrt{5}}{2}\right) \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)}-\frac{\sqrt{\left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)^{2}+\left(\sqrt{5}+1\right) \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)+\frac{1}{2}+\frac{\sqrt{5}}{2}}}{5 \left(\frac{1}{2}+\frac{\sqrt{5}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}+\frac{6 \arctanh \left(\frac{2+2 \sqrt{5}+2 \left(\sqrt{5}+1\right) \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}{\sqrt{2+2 \sqrt{5}}\, \sqrt{4 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)^{2}+4 \left(\sqrt{5}+1\right) \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)+2+2 \sqrt{5}}}\right)}{5 \left(\frac{1}{2}+\frac{\sqrt{5}}{2}\right) \sqrt{2+2 \sqrt{5}}}+\frac{2 \arctanh \left(\frac{2+2 \sqrt{5}+2 \left(\sqrt{5}+1\right) \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}{\sqrt{2+2 \sqrt{5}}\, \sqrt{4 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)^{2}+4 \left(\sqrt{5}+1\right) \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)+2+2 \sqrt{5}}}\right) \sqrt{5}}{5 \left(\frac{1}{2}+\frac{\sqrt{5}}{2}\right) \sqrt{2+2 \sqrt{5}}}-\frac{\sqrt{5}\, \sqrt{\left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)^{2}+\left(\sqrt{5}+1\right) \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)+\frac{1}{2}+\frac{\sqrt{5}}{2}}}{5 \left(\frac{1}{2}+\frac{\sqrt{5}}{2}\right) \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}+\frac{2 \sqrt{x}}{5 \left(x -\frac{1}{2}-\frac{\sqrt{5}}{2}\right)}-\frac{4 \arctanh \left(\frac{2 \sqrt{x}}{\sqrt{2+2 \sqrt{5}}}\right)}{5 \sqrt{2+2 \sqrt{5}}}-\frac{8 \arctanh \left(\frac{2 \sqrt{x}}{\sqrt{2+2 \sqrt{5}}}\right) \sqrt{5}}{25 \sqrt{2+2 \sqrt{5}}}+\frac{2 \sqrt{x}}{5 \left(x -\frac{1}{2}+\frac{\sqrt{5}}{2}\right)}+\frac{4 \arctan \left(\frac{2 \sqrt{x}}{\sqrt{-2+2 \sqrt{5}}}\right)}{5 \sqrt{-2+2 \sqrt{5}}}-\frac{8 \arctan \left(\frac{2 \sqrt{x}}{\sqrt{-2+2 \sqrt{5}}}\right) \sqrt{5}}{25 \sqrt{-2+2 \sqrt{5}}}$&$902$\\ \hline \end{longtable}"," ",0,"-6/25*5^(1/2)/(2+2*5^(1/2))^(1/2)*arctanh(2*(1+5^(1/2)+(5^(1/2)+1)*(x-1/2-1/2*5^(1/2)))/(2+2*5^(1/2))^(1/2)/(4*(x-1/2-1/2*5^(1/2))^2+4*(5^(1/2)+1)*(x-1/2-1/2*5^(1/2))+2+2*5^(1/2))^(1/2))-6/25*5^(1/2)/(-2+2*5^(1/2))^(1/2)*arctan(2*(1-5^(1/2)+(-5^(1/2)+1)*(x-1/2+1/2*5^(1/2)))/(-2+2*5^(1/2))^(1/2)/(4*(x-1/2+1/2*5^(1/2))^2+4*(-5^(1/2)+1)*(x-1/2+1/2*5^(1/2))+2-2*5^(1/2))^(1/2))-1/5/(1/2-1/2*5^(1/2))/(x-1/2+1/2*5^(1/2))*((x-1/2+1/2*5^(1/2))^2+(-5^(1/2)+1)*(x-1/2+1/2*5^(1/2))+1/2-1/2*5^(1/2))^(1/2)+2/5/(1/2-1/2*5^(1/2))/(-2+2*5^(1/2))^(1/2)*arctan(2*(1-5^(1/2)+(-5^(1/2)+1)*(x-1/2+1/2*5^(1/2)))/(-2+2*5^(1/2))^(1/2)/(4*(x-1/2+1/2*5^(1/2))^2+4*(-5^(1/2)+1)*(x-1/2+1/2*5^(1/2))+2-2*5^(1/2))^(1/2))*5^(1/2)-6/5/(1/2-1/2*5^(1/2))/(-2+2*5^(1/2))^(1/2)*arctan(2*(1-5^(1/2)+(-5^(1/2)+1)*(x-1/2+1/2*5^(1/2)))/(-2+2*5^(1/2))^(1/2)/(4*(x-1/2+1/2*5^(1/2))^2+4*(-5^(1/2)+1)*(x-1/2+1/2*5^(1/2))+2-2*5^(1/2))^(1/2))+1/5*5^(1/2)/(1/2-1/2*5^(1/2))/(x-1/2+1/2*5^(1/2))*((x-1/2+1/2*5^(1/2))^2+(-5^(1/2)+1)*(x-1/2+1/2*5^(1/2))+1/2-1/2*5^(1/2))^(1/2)-1/5/(1/2+1/2*5^(1/2))/(x-1/2-1/2*5^(1/2))*((x-1/2-1/2*5^(1/2))^2+(5^(1/2)+1)*(x-1/2-1/2*5^(1/2))+1/2+1/2*5^(1/2))^(1/2)+6/5/(1/2+1/2*5^(1/2))/(2+2*5^(1/2))^(1/2)*arctanh(2*(1+5^(1/2)+(5^(1/2)+1)*(x-1/2-1/2*5^(1/2)))/(2+2*5^(1/2))^(1/2)/(4*(x-1/2-1/2*5^(1/2))^2+4*(5^(1/2)+1)*(x-1/2-1/2*5^(1/2))+2+2*5^(1/2))^(1/2))+2/5/(1/2+1/2*5^(1/2))/(2+2*5^(1/2))^(1/2)*arctanh(2*(1+5^(1/2)+(5^(1/2)+1)*(x-1/2-1/2*5^(1/2)))/(2+2*5^(1/2))^(1/2)/(4*(x-1/2-1/2*5^(1/2))^2+4*(5^(1/2)+1)*(x-1/2-1/2*5^(1/2))+2+2*5^(1/2))^(1/2))*5^(1/2)-1/5*5^(1/2)/(1/2+1/2*5^(1/2))/(x-1/2-1/2*5^(1/2))*((x-1/2-1/2*5^(1/2))^2+(5^(1/2)+1)*(x-1/2-1/2*5^(1/2))+1/2+1/2*5^(1/2))^(1/2)+2/5*x^(1/2)/(x-1/2-1/2*5^(1/2))-4/5/(2+2*5^(1/2))^(1/2)*arctanh(2*x^(1/2)/(2+2*5^(1/2))^(1/2))-8/25/(2+2*5^(1/2))^(1/2)*arctanh(2*x^(1/2)/(2+2*5^(1/2))^(1/2))*5^(1/2)+2/5*x^(1/2)/(x-1/2+1/2*5^(1/2))+4/5/(-2+2*5^(1/2))^(1/2)*arctan(2*x^(1/2)/(-2+2*5^(1/2))^(1/2))-8/25/(-2+2*5^(1/2))^(1/2)*arctan(2*x^(1/2)/(-2+2*5^(1/2))^(1/2))*5^(1/2)","B"
2889,0,0,249,0.060000," ","int((a*x^2+b)/(c*x^2+d)/(x^3+x)^(1/3),x)","\[\int \frac{a \,x^{2}+b}{\left(c \,x^{2}+d \right) \left(x^{3}+x \right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a*x^2+b)/(c*x^2+d)/(x^3+x)^(1/3),x)","F"
2890,0,0,277,0.023000," ","int(x^3*(4*a*b-3*(a+b)*x+2*x^2)/(x^2*(-a+x)*(-b+x))^(2/3)/(-a*b+(a+b)*x-x^2+d*x^4),x)","\[\int \frac{x^{3} \left(4 a b -3 \left(a +b \right) x +2 x^{2}\right)}{\left(x^{2} \left(-a +x \right) \left(-b +x \right)\right)^{\frac{2}{3}} \left(-a b +\left(a +b \right) x -x^{2}+d \,x^{4}\right)}\, dx\]"," ",0,"int(x^3*(4*a*b-3*(a+b)*x+2*x^2)/(x^2*(-a+x)*(-b+x))^(2/3)/(-a*b+(a+b)*x-x^2+d*x^4),x)","F"
2891,0,0,136,0.005000," ","int((a*x^3+b*x)/(2*a*x^3+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{a \,x^{3}+b x}{\left(2 a \,x^{3}+b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a*x^3+b*x)/(2*a*x^3+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
2892,1,232,11,0.081000," ","int(1/((-1+2*x)^(1/2)*(4+3*x)+(1+x)*(-3+4*x)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-8 \left(\munderset{\textit{\_R} =\RootOf \left(7 \textit{\_Z}^{6}+131 \textit{\_Z}^{4}+677 \textit{\_Z}^{2}+625\right)}{\sum}\frac{\textit{\_R}^{2} \ln \left(\sqrt{-3+4 x}-\textit{\_R} \right)}{21 \textit{\_R}^{5}+262 \textit{\_R}^{3}+677 \textit{\_R}}\right)+8 \left(\munderset{\textit{\_R} =\RootOf \left(7 \textit{\_Z}^{6}+55 \textit{\_Z}^{4}+109 \textit{\_Z}^{2}+9\right)}{\sum}\frac{\textit{\_R}^{2} \ln \left(\sqrt{-1+2 x}-\textit{\_R} \right)}{21 \textit{\_R}^{5}+110 \textit{\_R}^{3}+109 \textit{\_R}}\right)-2 \left(\munderset{\textit{\_R} =\RootOf \left(7 \textit{\_Z}^{6}+131 \textit{\_Z}^{4}+677 \textit{\_Z}^{2}+625\right)}{\sum}\frac{\left(\textit{\_R}^{4}+3 \textit{\_R}^{2}\right) \ln \left(\sqrt{-3+4 x}-\textit{\_R} \right)}{21 \textit{\_R}^{5}+262 \textit{\_R}^{3}+677 \textit{\_R}}\right)+3 \left(\munderset{\textit{\_R} =\RootOf \left(7 \textit{\_Z}^{6}+55 \textit{\_Z}^{4}+109 \textit{\_Z}^{2}+9\right)}{\sum}\frac{\left(\textit{\_R}^{4}+\textit{\_R}^{2}\right) \ln \left(\sqrt{-1+2 x}-\textit{\_R} \right)}{21 \textit{\_R}^{5}+110 \textit{\_R}^{3}+109 \textit{\_R}}\right)$&$232$\\ \hline \end{longtable}"," ",0,"-8*sum(_R^2/(21*_R^5+262*_R^3+677*_R)*ln((-3+4*x)^(1/2)-_R),_R=RootOf(7*_Z^6+131*_Z^4+677*_Z^2+625))+8*sum(_R^2/(21*_R^5+110*_R^3+109*_R)*ln((-1+2*x)^(1/2)-_R),_R=RootOf(7*_Z^6+55*_Z^4+109*_Z^2+9))-2*sum((_R^4+3*_R^2)/(21*_R^5+262*_R^3+677*_R)*ln((-3+4*x)^(1/2)-_R),_R=RootOf(7*_Z^6+131*_Z^4+677*_Z^2+625))+3*sum((_R^4+_R^2)/(21*_R^5+110*_R^3+109*_R)*ln((-1+2*x)^(1/2)-_R),_R=RootOf(7*_Z^6+55*_Z^4+109*_Z^2+9))","B"
2893,1,338,169,0.992000," ","int((e*x+f)/(g*x+h)/(d+(c+(a*x+b)^(1/2))^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\frac{8 e \left(\frac{\left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{7}{2}}}{7}-\frac{3 \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{5}{2}} d}{5}+d^{2} \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{3}{2}}-\frac{c \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{3}{2}}}{3}-d^{3} \sqrt{d +\sqrt{c +\sqrt{a x +b}}}+c d \sqrt{d +\sqrt{c +\sqrt{a x +b}}}\right)}{g}-\frac{a \left(\munderset{\textit{\_R} =\RootOf \left(g \,\textit{\_Z}^{8}-4 d g \,\textit{\_Z}^{6}+\left(6 d^{2} g -2 c g \right) \textit{\_Z}^{4}+\left(-4 d^{3} g +4 c d g \right) \textit{\_Z}^{2}+d^{4} g -2 c \,d^{2} g +c^{2} g +a h -b g \right)}{\sum}\frac{\left(\textit{\_R}^{6} \left(e h -f g \right)+3 d \left(-e h +f g \right) \textit{\_R}^{4}+\left(3 d^{2} e h -3 d^{2} f g -c e h +c f g \right) \textit{\_R}^{2}-d^{3} e h +d^{3} f g +c d e h -c d f g \right) \ln \left(\sqrt{d +\sqrt{c +\sqrt{a x +b}}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5} d +3 \textit{\_R}^{3} d^{2}-\textit{\_R}^{3} c -\textit{\_R} \,d^{3}+\textit{\_R} c d}\right)}{g^{2}}}{a}$&$338$\\ default&$\frac{\frac{8 e \left(\frac{\left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{7}{2}}}{7}-\frac{3 \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{5}{2}} d}{5}+d^{2} \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{3}{2}}-\frac{c \left(d +\sqrt{c +\sqrt{a x +b}}\right)^{\frac{3}{2}}}{3}-d^{3} \sqrt{d +\sqrt{c +\sqrt{a x +b}}}+c d \sqrt{d +\sqrt{c +\sqrt{a x +b}}}\right)}{g}-\frac{a \left(\munderset{\textit{\_R} =\RootOf \left(g \,\textit{\_Z}^{8}-4 d g \,\textit{\_Z}^{6}+\left(6 d^{2} g -2 c g \right) \textit{\_Z}^{4}+\left(-4 d^{3} g +4 c d g \right) \textit{\_Z}^{2}+d^{4} g -2 c \,d^{2} g +c^{2} g +a h -b g \right)}{\sum}\frac{\left(\textit{\_R}^{6} \left(e h -f g \right)+3 d \left(-e h +f g \right) \textit{\_R}^{4}+\left(3 d^{2} e h -3 d^{2} f g -c e h +c f g \right) \textit{\_R}^{2}-d^{3} e h +d^{3} f g +c d e h -c d f g \right) \ln \left(\sqrt{d +\sqrt{c +\sqrt{a x +b}}}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5} d +3 \textit{\_R}^{3} d^{2}-\textit{\_R}^{3} c -\textit{\_R} \,d^{3}+\textit{\_R} c d}\right)}{g^{2}}}{a}$&$338$\\ \hline \end{longtable}"," ",0,"2/a*(4*e/g*(1/7*(d+(c+(a*x+b)^(1/2))^(1/2))^(7/2)-3/5*(d+(c+(a*x+b)^(1/2))^(1/2))^(5/2)*d+d^2*(d+(c+(a*x+b)^(1/2))^(1/2))^(3/2)-1/3*c*(d+(c+(a*x+b)^(1/2))^(1/2))^(3/2)-d^3*(d+(c+(a*x+b)^(1/2))^(1/2))^(1/2)+c*d*(d+(c+(a*x+b)^(1/2))^(1/2))^(1/2))-1/2*a/g^2*sum((_R^6*(e*h-f*g)+3*d*(-e*h+f*g)*_R^4+(3*d^2*e*h-3*d^2*f*g-c*e*h+c*f*g)*_R^2-d^3*e*h+d^3*f*g+c*d*e*h-c*d*f*g)/(_R^7-3*_R^5*d+3*_R^3*d^2-_R^3*c-_R*d^3+_R*c*d)*ln((d+(c+(a*x+b)^(1/2))^(1/2))^(1/2)-_R),_R=RootOf(g*_Z^8-4*d*g*_Z^6+(6*d^2*g-2*c*g)*_Z^4+(-4*d^3*g+4*c*d*g)*_Z^2+d^4*g-2*c*d^2*g+c^2*g+a*h-b*g)))","A"
2894,0,0,268,0.038000," ","int((x^2+1)^(3/2)*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2),x)","\[\int \left(x^{2}+1\right)^{\frac{3}{2}} \sqrt{x +\sqrt{x^{2}+1}}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^2+1)^(3/2)*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2),x)","F"
2895,0,0,259,0.131000," ","int((a-5*b+4*x)*(-a^3+3*a^2*x-3*a*x^2+x^3)/((-a+x)*(-b+x))^(2/3)/(b-a^5*d-(-5*a^4*d+1)*x-10*a^3*d*x^2+10*a^2*d*x^3-5*a*d*x^4+d*x^5),x)","\[\int \frac{\left(a -5 b +4 x \right) \left(-a^{3}+3 a^{2} x -3 a \,x^{2}+x^{3}\right)}{\left(\left(-a +x \right) \left(-b +x \right)\right)^{\frac{2}{3}} \left(b -a^{5} d -\left(-5 a^{4} d +1\right) x -10 a^{3} d \,x^{2}+10 a^{2} d \,x^{3}-5 a d \,x^{4}+d \,x^{5}\right)}\, dx\]"," ",0,"int((a-5*b+4*x)*(-a^3+3*a^2*x-3*a*x^2+x^3)/((-a+x)*(-b+x))^(2/3)/(b-a^5*d-(-5*a^4*d+1)*x-10*a^3*d*x^2+10*a^2*d*x^3-5*a*d*x^4+d*x^5),x)","F"
2896,1,3515,274,121.567000," ","int((3*x^4-3*x^3+2*x^2-2*x+2)*(x^6-x^4-x^3-x)^(1/3)/(1+x)/(x^3-2*x^2+2*x-1)/(x^5-x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$3515$\\ \hline \end{longtable}"," ",0,"RootOf(_Z^3-2)*ln((17352778151361340*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^3*x^5+77595076881412992*RootOf(_Z^3-2)^4*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*x^5-17352778151361340*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^3*x^3-77595076881412992*RootOf(_Z^3-2)^4*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*x^3-99778474370327705*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^3*x^2-446171692068124704*RootOf(_Z^3-2)^4*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*x^2+164851392437932730*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)*x^5+737153230373423424*RootOf(_Z^3-2)^2*x^5-17352778151361340*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^3+202095364609360356*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*(x^6-x^4-x^3-x)^(2/3)-77595076881412992*RootOf(_Z^3-2)^4*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)-164851392437932730*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)*x^3-737153230373423424*RootOf(_Z^3-2)^2*x^3-355731952102907470*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)*x^2-1590699076068966336*RootOf(_Z^3-2)^2*x^2-695401143134438700*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*(x^6-x^4-x^3-x)^(1/3)*x+808381458437441424*RootOf(_Z^3-2)*(x^6-x^4-x^3-x)^(1/3)*x-164851392437932730*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)+2199183744706318824*(x^6-x^4-x^3-x)^(2/3)-737153230373423424*RootOf(_Z^3-2)^2)/(1+x)^2/(-1+x)/(x^2-x+1))-ln(-(19398769220353248*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^3*x^5+17352778151361340*RootOf(_Z^3-2)^4*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*x^5-19398769220353248*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^3*x^3-17352778151361340*RootOf(_Z^3-2)^4*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*x^3-111542923017031176*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^3*x^2-99778474370327705*RootOf(_Z^3-2)^4*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*x^2-106693230711942864*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)*x^5-95440279832487370*RootOf(_Z^3-2)^2*x^5-19398769220353248*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^3+101047682304680178*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*(x^6-x^4-x^3-x)^(2/3)-17352778151361340*RootOf(_Z^3-2)^4*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)+106693230711942864*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)*x^3+95440279832487370*RootOf(_Z^3-2)^2*x^3-48496923050883120*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)*x^2-43381945378403350*RootOf(_Z^3-2)^2*x^2+549795936176579706*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*(x^6-x^4-x^3-x)^(1/3)*x+404190729218720712*RootOf(_Z^3-2)*(x^6-x^4-x^3-x)^(1/3)*x+106693230711942864*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)-695401143134438700*(x^6-x^4-x^3-x)^(2/3)+95440279832487370*RootOf(_Z^3-2)^2)/(1+x)^2/(-1+x)/(x^2-x+1))*RootOf(_Z^3-2)-1/2*ln(-(19398769220353248*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^3*x^5+17352778151361340*RootOf(_Z^3-2)^4*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*x^5-19398769220353248*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^3*x^3-17352778151361340*RootOf(_Z^3-2)^4*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*x^3-111542923017031176*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^3*x^2-99778474370327705*RootOf(_Z^3-2)^4*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*x^2-106693230711942864*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)*x^5-95440279832487370*RootOf(_Z^3-2)^2*x^5-19398769220353248*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^3+101047682304680178*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*(x^6-x^4-x^3-x)^(2/3)-17352778151361340*RootOf(_Z^3-2)^4*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)+106693230711942864*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)*x^3+95440279832487370*RootOf(_Z^3-2)^2*x^3-48496923050883120*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)*x^2-43381945378403350*RootOf(_Z^3-2)^2*x^2+549795936176579706*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*(x^6-x^4-x^3-x)^(1/3)*x+404190729218720712*RootOf(_Z^3-2)*(x^6-x^4-x^3-x)^(1/3)*x+106693230711942864*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)-695401143134438700*(x^6-x^4-x^3-x)^(2/3)+95440279832487370*RootOf(_Z^3-2)^2)/(1+x)^2/(-1+x)/(x^2-x+1))*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)-1/4*RootOf(_Z^3-2)^2*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*ln((19913269584084711108*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^4*x^5-19913269584084711108*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^4*x^3-114501300108487088871*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^4*x^2-228558878565540724252*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*x^5-19913269584084711108*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^4+228558878565540724252*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*x^3+273745215983433009056*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*(x^6-x^4-x^3-x)^(2/3)-273745215983433009056*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*(x^6-x^4-x^3-x)^(1/3)*x-184259984450515346428*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*x^2-1052102477935949135520*x^5+228558878565540724252*RootOf(_Z^3-2)^2*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)+1052102477935949135520*x^3+2603562618888822787984*(x^6-x^4-x^3-x)^(2/3)-2603562618888822787984*x*(x^6-x^4-x^3-x)^(1/3)+771541817153029366048*x^2+1052102477935949135520)/(x^5-x^3-1))+1/4*ln((19913269584084711108*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^4*x^5-19913269584084711108*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^4*x^3-114501300108487088871*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^4*x^2+387865035238218413116*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*x^5-19913269584084711108*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^4-387865035238218413116*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*x^3-273745215983433009056*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*(x^6-x^4-x^3-x)^(2/3)+273745215983433009056*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*(x^6-x^4-x^3-x)^(1/3)*x-731750416417381364540*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*x^2+180745349671569139216*x^5-387865035238218413116*RootOf(_Z^3-2)^2*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)-180745349671569139216*x^3+1508581754955090751760*(x^6-x^4-x^3-x)^(2/3)-1508581754955090751760*x*(x^6-x^4-x^3-x)^(1/3)-323439046780702670176*x^2-180745349671569139216)/(x^5-x^3-1))*RootOf(_Z^3-2)^2*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)+ln((19913269584084711108*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^4*x^5-19913269584084711108*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^4*x^3-114501300108487088871*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^4*x^2+387865035238218413116*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*x^5-19913269584084711108*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)^2*RootOf(_Z^3-2)^4-387865035238218413116*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*x^3-273745215983433009056*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*(x^6-x^4-x^3-x)^(2/3)+273745215983433009056*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*(x^6-x^4-x^3-x)^(1/3)*x-731750416417381364540*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)*RootOf(_Z^3-2)^2*x^2+180745349671569139216*x^5-387865035238218413116*RootOf(_Z^3-2)^2*RootOf(4*RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+_Z^2)-180745349671569139216*x^3+1508581754955090751760*(x^6-x^4-x^3-x)^(2/3)-1508581754955090751760*x*(x^6-x^4-x^3-x)^(1/3)-323439046780702670176*x^2-180745349671569139216)/(x^5-x^3-1))","C"
2897,0,0,252,0.067000," ","int(1/(a*x-b)/(a^3*x^3-b^2*x^2)^(1/3),x)","\[\int \frac{1}{\left(a x -b \right) \left(a^{3} x^{3}-b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(a*x-b)/(a^3*x^3-b^2*x^2)^(1/3),x)","F"
2898,0,0,283,0.017000," ","int((-b+x)*(-4*a+b+3*x)/((-a+x)*(-b+x)^2)^(1/3)/(b^4+a*d-(4*b^3+d)*x+6*b^2*x^2-4*b*x^3+x^4),x)","\[\int \frac{\left(-b +x \right) \left(-4 a +b +3 x \right)}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{3}} \left(b^{4}+a d -\left(4 b^{3}+d \right) x +6 b^{2} x^{2}-4 b \,x^{3}+x^{4}\right)}\, dx\]"," ",0,"int((-b+x)*(-4*a+b+3*x)/((-a+x)*(-b+x)^2)^(1/3)/(b^4+a*d-(4*b^3+d)*x+6*b^2*x^2-4*b*x^3+x^4),x)","F"
2899,1,273,236,0.252000," ","int(x^4/(a^4*x^4-b^4)^(1/2)/(a^8*x^8-b^8),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(-\frac{\sqrt{2}\, \ln \left(\frac{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}-\frac{\left(a^{4} b^{4}\right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}}{x}+\sqrt{a^{4} b^{4}}}{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}+\frac{\left(a^{4} b^{4}\right)^{\frac{1}{4}} \sqrt{a^{4} x^{4}-b^{4}}}{x}+\sqrt{a^{4} b^{4}}}\right)}{32 a^{4} b^{4} \left(a^{4} b^{4}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}}{\left(a^{4} b^{4}\right)^{\frac{1}{4}} x}+1\right)}{16 a^{4} b^{4} \left(a^{4} b^{4}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}}{\left(a^{4} b^{4}\right)^{\frac{1}{4}} x}-1\right)}{16 a^{4} b^{4} \left(a^{4} b^{4}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, x}{4 a^{4} b^{4} \sqrt{a^{4} x^{4}-b^{4}}}\right) \sqrt{2}}{2}$&$273$\\ default&$-\frac{\frac{a^{4} x^{3}-a^{3} b \,x^{2}+a^{2} b^{2} x -a \,b^{3}}{2 a^{2} b^{3} \sqrt{\left(x +\frac{b}{a}\right) \left(a^{4} x^{3}-a^{3} b \,x^{2}+a^{2} b^{2} x -a \,b^{3}\right)}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}-\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \left(\EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)-\EllipticE \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}}{8 b^{3} a^{4}}+\frac{-\frac{a^{4} x^{3}+a^{3} b \,x^{2}+a^{2} b^{2} x +a \,b^{3}}{2 a^{2} b^{3} \sqrt{\left(x -\frac{b}{a}\right) \left(a^{4} x^{3}+a^{3} b \,x^{2}+a^{2} b^{2} x +a \,b^{3}\right)}}-\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \left(\EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)-\EllipticE \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}}{8 b^{3} a^{4}}+\frac{\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4} a^{4}+b^{4}\right)}{\sum}\frac{-\frac{\sqrt{2}\, \arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}+x^{2}\right) a^{4}}{\sqrt{-2 b^{4}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{\sqrt{-b^{4}}}+\frac{4 \underline{\hspace{1.25 ex}}\alpha^{3} a^{4} \sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}}{b^{2}}, \frac{\sqrt{\frac{a^{2}}{b^{2}}}}{\sqrt{-\frac{a^{2}}{b^{2}}}}\right)}{\sqrt{-\frac{a^{2}}{b^{2}}}\, b^{4} \sqrt{a^{4} x^{4}-b^{4}}}}{\underline{\hspace{1.25 ex}}\alpha^{3}}}{32 a^{8}}-\frac{-\frac{\left(a^{4} x^{2}-a^{2} b^{2}\right) x}{2 b^{4} a^{2} \sqrt{\left(x^{2}+\frac{b^{2}}{a^{2}}\right) \left(a^{4} x^{2}-a^{2} b^{2}\right)}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{2 b^{2} \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \left(\EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)-\EllipticE \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)\right)}{2 b^{2} \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}}{4 a^{4} b^{2}}$&$921$\\ \hline \end{longtable}"," ",0,"1/2*(-1/32/a^4/b^4/(a^4*b^4)^(1/4)*2^(1/2)*ln((1/2*(a^4*x^4-b^4)/x^2-(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x+(a^4*b^4)^(1/2))/(1/2*(a^4*x^4-b^4)/x^2+(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x+(a^4*b^4)^(1/2)))-1/16/a^4/b^4/(a^4*b^4)^(1/4)*2^(1/2)*arctan(1/(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x+1)-1/16/a^4/b^4/(a^4*b^4)^(1/4)*2^(1/2)*arctan(1/(a^4*b^4)^(1/4)*(a^4*x^4-b^4)^(1/2)/x-1)-1/4/a^4/b^4/(a^4*x^4-b^4)^(1/2)*2^(1/2)*x)*2^(1/2)","A"
2900,0,0,249,180.000000," ","int(1/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3),x)","\[\int \frac{1}{\sqrt{a^{2} x^{2}-b}\, \sqrt{a x +\sqrt{a^{2} x^{2}-b}}\, \left(c +\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3),x)","F"
2901,0,0,52,0.055000," ","int((x^2+1)^2*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1),x)","\[\int \frac{\left(x^{2}+1\right)^{2} \sqrt{x^{2}+\sqrt{x^{4}+1}}}{\sqrt{x^{4}+1}\, \left(x^{4}+x^{2}-1\right)}\, dx\]"," ",0,"int((x^2+1)^2*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1),x)","F"
2902,0,0,52,0.004000," ","int((x^2+1)^2*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1),x)","\[\int \frac{\left(x^{2}+1\right)^{2} \sqrt{x^{2}+\sqrt{x^{4}+1}}}{\sqrt{x^{4}+1}\, \left(x^{4}+x^{2}-1\right)}\, dx\]"," ",0,"int((x^2+1)^2*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1),x)","F"
2903,0,0,60,0.072000," ","int(x^2*(a*x^4+b*x^3)^(1/4)/(a*x^4-b),x)","\[\int \frac{x^{2} \left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}}{a \,x^{4}-b}\, dx\]"," ",0,"int(x^2*(a*x^4+b*x^3)^(1/4)/(a*x^4-b),x)","F"
2904,0,0,60,0.004000," ","int(x^2*(a*x^4+b*x^3)^(1/4)/(a*x^4-b),x)","\[\int \frac{x^{2} \left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}}{a \,x^{4}-b}\, dx\]"," ",0,"int(x^2*(a*x^4+b*x^3)^(1/4)/(a*x^4-b),x)","F"
2905,0,0,59,0.044000," ","int((x^2+1)*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","\[\int \frac{\left(x^{2}+1\right) \sqrt{x +\sqrt{x^{2}+1}}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right)^{2}}\, dx\]"," ",0,"int((x^2+1)*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","F"
2906,0,0,59,0.005000," ","int((x^2+1)*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","\[\int \frac{\left(x^{2}+1\right) \sqrt{x +\sqrt{x^{2}+1}}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right)^{2}}\, dx\]"," ",0,"int((x^2+1)*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","F"
2907,0,0,272,0.032000," ","int(x^3*(-b+x)*(2*a*b-3*a*x+x^2)/(x^2*(-a+x)*(-b+x))^(1/3)/(-a^4+4*a^3*x-6*a^2*x^2+4*a*x^3+(b^2*d-1)*x^4-2*b*d*x^5+d*x^6),x)","\[\int \frac{x^{3} \left(-b +x \right) \left(2 a b -3 a x +x^{2}\right)}{\left(x^{2} \left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{3}} \left(-a^{4}+4 a^{3} x -6 a^{2} x^{2}+4 a \,x^{3}+\left(b^{2} d -1\right) x^{4}-2 b d \,x^{5}+d \,x^{6}\right)}\, dx\]"," ",0,"int(x^3*(-b+x)*(2*a*b-3*a*x+x^2)/(x^2*(-a+x)*(-b+x))^(1/3)/(-a^4+4*a^3*x-6*a^2*x^2+4*a*x^3+(b^2*d-1)*x^4-2*b*d*x^5+d*x^6),x)","F"
2908,1,8453,237,178.671000," ","int((x^3+1)^(2/3)*(x^6-1)/x^6/(2*x^6-2*x^3-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$8453$\\ trager&$\text{Expression too large to display}$&$11228$\\ \hline \end{longtable}"," ",0,"result too large to display","C"
2909,0,0,241,0.063000," ","int((x^4+1)/(x^4-1)/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{x^{4}+1}{\left(x^{4}-1\right) \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^4+1)/(x^4-1)/(x+(x^2+1)^(1/2))^(1/2),x)","F"
2910,0,0,92,0.008000," ","int((2*a*x+b)*(a*x^4+b*x^3)^(1/4)/(a*x+x^2-b),x)","\[\int \frac{\left(2 a x +b \right) \left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}}{a x +x^{2}-b}\, dx\]"," ",0,"int((2*a*x+b)*(a*x^4+b*x^3)^(1/4)/(a*x+x^2-b),x)","F"
2911,0,0,92,0.004000," ","int((2*a*x+b)*(a*x^4+b*x^3)^(1/4)/(a*x+x^2-b),x)","\[\int \frac{\left(2 a x +b \right) \left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}}{a x +x^{2}-b}\, dx\]"," ",0,"int((2*a*x+b)*(a*x^4+b*x^3)^(1/4)/(a*x+x^2-b),x)","F"
2912,1,2469,254,52.737000," ","int(x^3/(x^4-x^2)^(1/3)/(x^6+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2469$\\ \hline \end{longtable}"," ",0,"1/4*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*ln((8763000*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3*x^4+347184*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2*x^4-37242750*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3*x^2-1475532*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2*x^2+50416182*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*(x^4-x^2)^(2/3)-8402697*(x^4-x^2)^(1/3)*RootOf(_Z^3+4)^2*x^2+4019850*(x^4-x^2)^(1/3)*RootOf(_Z^3+4)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^2-3286125*RootOf(_Z^3+4)*x^4-130194*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^4+8763000*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3+347184*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2+8402697*RootOf(_Z^3+4)^2*(x^4-x^2)^(1/3)-4019850*(x^4-x^2)^(1/3)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)-3651250*RootOf(_Z^3+4)*x^2-144660*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^2-36290688*(x^4-x^2)^(2/3)-3286125*RootOf(_Z^3+4)-130194*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2))/(x^2+1)^2)+1/24*RootOf(_Z^3+4)*ln(-(57864*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3*x^4+52578000*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2*x^4-245922*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3*x^2-223456500*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2*x^2+50416182*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*(x^4-x^2)^(2/3)-8402697*(x^4-x^2)^(1/3)*RootOf(_Z^3+4)^2*x^2-54436032*(x^4-x^2)^(1/3)*RootOf(_Z^3+4)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^2-16877*RootOf(_Z^3+4)*x^4-15335250*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^4+57864*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^3+52578000*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^2+8402697*RootOf(_Z^3+4)^2*(x^4-x^2)^(1/3)+54436032*(x^4-x^2)^(1/3)*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)+188058*RootOf(_Z^3+4)*x^2+170878500*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^2+2679900*(x^4-x^2)^(2/3)-16877*RootOf(_Z^3+4)-15335250*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2))/(x^2+1)^2)-1/4*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*ln((-445572*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^4*x^4+1893681*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^4*x^2+469206*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*x^4-1692009*(x^4-x^2)^(1/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^2-445572*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^4+1692009*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*(x^4-x^2)^(2/3)-3126621*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*x^2+1692009*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*(x^4-x^2)^(1/3)+700430*x^4-783690*(x^4-x^2)^(1/3)*x^2+469206*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2+783690*(x^4-x^2)^(2/3)-840516*x^2+783690*(x^4-x^2)^(1/3)+700430)/(x^4-x^2+1))+1/4*ln(-(445572*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^4*x^4-1893681*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^4*x^2-124890*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*x^4-1692009*(x^4-x^2)^(1/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^2+445572*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^4+1692009*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*(x^4-x^2)^(2/3)-601713*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*x^2+1692009*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*(x^4-x^2)^(1/3)-815202*x^4+1911696*(x^4-x^2)^(1/3)*x^2-124890*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2-1911696*(x^4-x^2)^(2/3)+2083294*x^2-1911696*(x^4-x^2)^(1/3)-815202)/(x^4-x^2+1))*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2-1/6*ln(-(445572*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^4*x^4-1893681*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^4*x^2-124890*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*x^4-1692009*(x^4-x^2)^(1/3)*RootOf(_Z^3+4)^2*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*x^2+445572*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)^2*RootOf(_Z^3+4)^4+1692009*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*(x^4-x^2)^(2/3)-601713*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*x^2+1692009*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2*(x^4-x^2)^(1/3)-815202*x^4+1911696*(x^4-x^2)^(1/3)*x^2-124890*RootOf(RootOf(_Z^3+4)^2+6*_Z*RootOf(_Z^3+4)+36*_Z^2)*RootOf(_Z^3+4)^2-1911696*(x^4-x^2)^(2/3)+2083294*x^2-1911696*(x^4-x^2)^(1/3)-815202)/(x^4-x^2+1))","C"
2913,0,0,184,0.158000," ","int(x^4*(a^2*x^2+b)^(1/2)/(x^2-(a*x-(a^2*x^2+b)^(1/2))^(1/2)),x)","\[\int \frac{x^{4} \sqrt{a^{2} x^{2}+b}}{x^{2}-\sqrt{a x -\sqrt{a^{2} x^{2}+b}}}\, dx\]"," ",0,"int(x^4*(a^2*x^2+b)^(1/2)/(x^2-(a*x-(a^2*x^2+b)^(1/2))^(1/2)),x)","F"
2914,0,0,301,0.008000," ","int((x^2-1)/((a*x+b)/(c*x+d))^(1/4),x)","\[\int \frac{x^{2}-1}{\left(\frac{a x +b}{c x +d}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((x^2-1)/((a*x+b)/(c*x+d))^(1/4),x)","F"
2915,1,23,241,0.229000," ","int((a*x^4-b)/(a*x^4+b)^(1/2)/(a*x^4-c^2*x^2+b),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$-\frac{\arctanh \left(\frac{\sqrt{a \,x^{4}+b}}{x c}\right)}{c}$&$23$\\ default&$\frac{\sqrt{1-\frac{i \sqrt{a}\, x^{2}}{\sqrt{b}}}\, \sqrt{1+\frac{i \sqrt{a}\, x^{2}}{\sqrt{b}}}\, \EllipticF \left(x \sqrt{\frac{i \sqrt{a}}{\sqrt{b}}}, i\right)}{\sqrt{\frac{i \sqrt{a}}{\sqrt{b}}}\, \sqrt{a \,x^{4}+b}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{4}-c^{2} \textit{\_Z}^{2}+b \right)}{\sum}\frac{\left(c^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-2 b \right) \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{2} a +a \,x^{2}+c^{2}\right)}{\sqrt{c^{2} \underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{a \,x^{4}+b}}\right)}{\sqrt{c^{2} \underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{2 \underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2} a -c^{2}\right) \sqrt{1-\frac{i \sqrt{a}\, x^{2}}{\sqrt{b}}}\, \sqrt{1+\frac{i \sqrt{a}\, x^{2}}{\sqrt{b}}}\, \EllipticPi \left(x \sqrt{\frac{i \sqrt{a}}{\sqrt{b}}}, \frac{i \left(\underline{\hspace{1.25 ex}}\alpha^{2} a -c^{2}\right)}{\sqrt{b}\, \sqrt{a}}, \frac{\sqrt{-\frac{i \sqrt{a}}{\sqrt{b}}}}{\sqrt{\frac{i \sqrt{a}}{\sqrt{b}}}}\right)}{\sqrt{\frac{i \sqrt{a}}{\sqrt{b}}}\, b \sqrt{a \,x^{4}+b}}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2} a -c^{2}\right)}\right)}{4}$&$297$\\ \hline \end{longtable}"," ",0,"-1/c*arctanh((a*x^4+b)^(1/2)/x/c)","A"
2916,1,4208,254,62.239000," ","int((x^2+1)*(x^6+x^4-x^2-1)^(1/3)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$4208$\\ \hline \end{longtable}"," ",0,"(1/4*x^2+7/12)*(x^6+x^4-x^2-1)^(1/3)-1/18*ln((-3512538612846350307808910800426120825077702305535079176113120464327428721518261731293967309748584316363213250560*x^20-67463892896780779234287648106041671369479318690212268342862504291743786612860389474681240476732543769808465113280*x^10+52679274774128937965344261265866250201276341121710369582430706980165796549239620007340698525251375371432562462080*x^6-14842283170367790226271482519764753425385942246466594065004761265496645063655774074048616341442669901500132596640*x^2+25508815338424088146757744263919025400673839142208728799803283638455703435896773308395878117326105007475243014720*x^8-3168543061057415052959185013903006086433610993967145387041722593555876414455706773748203553112968312965706401920*x^4-37293035310101636179328899559738961728311492960880432101889227389127684085673615291145454107760869705383124782720*x^12+20308862540464149811959881796093130698045026694957500163400751522254901546072938198037121655858979748076366572000*x^16+227301629008012301219413888300366503111029103977518483328887338705710723800891977193038268394989033284635197440*x^22-105950737744652866109736701522073162038786339261033388687618276313152072076044081900441699051617881374822771744*RootOf(_Z^2-3*_Z+9)^2-7445856372466336854641029537910891590528702926351860620242168685456838651089235799706964314361158444717196964000*x^18+36845794808838101650418331878779754402173337753205441679778798531429467975539636026732604490663769881326936977280*x^14-1728234831861090488217212360767601944408207712369299366538851705805363716660761007508541756785266377307461120*RootOf(_Z^2-3*_Z+9)^2*x^20+224134332318525289242814385295113591319229581186654058705830711949163533042428320093257366022070686015644160256*RootOf(_Z^2-3*_Z+9)*x^20-227820312028461981261179993675765526859625653654076442414344854731483758892476378477927296930316902381704726944*RootOf(_Z^2-3*_Z+9)^2*x^18+4562775803811176534203966521074620977311715237629578169381148712639461641887259054801573531089260096766833508965*RootOf(_Z^2-3*_Z+9)*x^18-157371588493610719968021732034115870103824952728228979060711916734377234896010179391669030890348444781341186968*RootOf(_Z^2-3*_Z+9)^2*x^2-5795107455482578238360842925578031416094181580439765880762242397840431141994976475846878104799239434550402137691*(x^6+x^4-x^2-1)^(1/3)+513649750555857432060310710939014156141821862591649149294203833248919221585602339311128396436564803925869700744*RootOf(_Z^2-3*_Z+9)^2*x^4+2033163967592154275892919033624114738730308660420986201184417481603593384538050149404769453388726186368301897929*RootOf(_Z^2-3*_Z+9)-9193010031607746136970126518396493949441476076167971661739921327538899396363574019691055378089041752706561426748*RootOf(_Z^2-3*_Z+9)*x^4+3683695096475897610351694027889566062517145439831607612428056055950525372377410259872484493372890760959350593469*RootOf(_Z^2-3*_Z+9)*x^2-118029977669068878547173266180289406813797199347038718923725511276532167697353926644133555470000415498520655336*RootOf(_Z^2-3*_Z+9)^2*x^16+1038672995877658212545741789320720128963634579406193290393786127901474384966249198077337251380107829074391296785*RootOf(_Z^2-3*_Z+9)*x^16+832533794574288042612432172954213552978476256754426867711197977643644510653542809975329944871627044231262816952*RootOf(_Z^2-3*_Z+9)^2*x^14-17202370452837787386916050877788767541976970849258256958722581676491156787566332925254352152845292057983719786748*RootOf(_Z^2-3*_Z+9)*x^14+539260172409068885261871916627336836655698491788345631350709633707926541940978967859535590747972466777838171672*RootOf(_Z^2-3*_Z+9)^2*x^12-7788733073958092892868289822246443424296216042743174927212605232037232845339712694542281310564018108708145607948*RootOf(_Z^2-3*_Z+9)*x^12-1194998862699794078156671494935157472747352890409401624360016957722442857317469154624237588332876603846718564904*RootOf(_Z^2-3*_Z+9)^2*x^10+25491195463702601559996234899141786761834368971317393902234023486044813784606843889084575979060865302180044306118*RootOf(_Z^2-3*_Z+9)*x^10-827223395203132555499472387816103042224566428656373080868507710594503215419933856518257741683848952815735002520*RootOf(_Z^2-3*_Z+9)^2*x^8+13686162122139038122591498520403702808165552828866118129635489155942065657591173633969807503783177933294272154478*RootOf(_Z^2-3*_Z+9)*x^8+734568961181009693081090842027790235236061831561822796823050584688256958145456684088253229521481298561282151336*RootOf(_Z^2-3*_Z+9)^2*x^6-16284180807552717499830048715981395933118256313635826613749627795103496084858602642441238512835822887986622489068*RootOf(_Z^2-3*_Z+9)*x^6-250724791237633947371238466335096433126968954915691020604021865219983208011963048751208451920878440597983657984*x^22*RootOf(_Z^2-3*_Z+9)+13065584982779970369933265350152861272227587878637674099348283923255326923544899530573190982718362854541492224*x^22*RootOf(_Z^2-3*_Z+9)^2+227041718091639138023788601993492479834624339730172740449889393984220482919452380920352532710315558059996020736*(x^6+x^4-x^2-1)^(1/3)*x^20+227273650843916557827255777004777768623816992948384615601004339519725071999838827996968815411775871398717685760*(x^6+x^4-x^2-1)^(2/3)*x^18-3589334681910956758107082906248128297876447144145117282823441491903519226405841352495706393107757746880009913856*(x^6+x^4-x^2-1)^(1/3)*x^18-3664709091410540732215780004856765331779396547958006182948065243717059636706830377742475135227919173014792139520*(x^6+x^4-x^2-1)^(2/3)*x^16-6147233452912926825619586652877390387334673609385824426667424170516899309120612733209452613695717423677031662545*(x^6+x^4-x^2-1)^(1/3)*x^16-4818486743271061974263639633130894090461168742385084074699886773854105299329059450210146369494839832931248474255*(x^6+x^4-x^2-1)^(2/3)*x^14+20829579031661897295286173116493967427650773115291271835100401450783556756498939824644823901487630494097112371406*(x^6+x^4-x^2-1)^(1/3)*x^14+20805548482123289627244844583716773183990207566002820728313098229206653099801707602401705096857911760459384830455*(x^6+x^4-x^2-1)^(2/3)*x^12+27098769649345548976229687230714951473640888369965349112690332094547887985365438509506156300704367364362269922894*(x^6+x^4-x^2-1)^(1/3)*x^12+17683824139507740839809462020607190265021728765858365347469901325658071574525384854299308914992445434870729901465*(x^6+x^4-x^2-1)^(2/3)*x^10-38255142578164215758552935749842846956040922957619237530263974387037684411357540032584351701707403040842096631498*(x^6+x^4-x^2-1)^(1/3)*x^10-35515774945673969825025519589866526086610407388029555745331198509949954455824911764672973180213590964705817034665*(x^6+x^4-x^2-1)^(2/3)*x^8-43129228731945250568021143202653314723112540166556051758911376711925651031495820697092037040034913162764345335620*(x^6+x^4-x^2-1)^(1/3)*x^8-22010526566918642917002049817431397487293881501535188513231129494692736478955841764686305119447634467743985967045*(x^6+x^4-x^2-1)^(2/3)*x^6+27691040152357647927882654724046506800784337856759629132706257673648057362886310612733855330017327442395755181674*(x^6+x^4-x^2-1)^(1/3)*x^6+22282392587913985582760451408384059704037745422407710560621249442771675314467701575124931799611647558420598052205*(x^6+x^4-x^2-1)^(2/3)*x^4+27741323864347090190833569827267607173069112640050765276863909889524618708019498461407008289710688747826153894946*(x^6+x^4-x^2-1)^(1/3)*x^4+33681107160086945536486599885619985432111060617970800638471726610804630147108011933383077276787142000206588928*RootOf(_Z^2-3*_Z+9)^2*(x^6+x^4-x^2-1)^(2/3)+8867793798484777400111310575746488838381608637112713031415736606456487180242048422204040528504096897795083152955*(x^6+x^4-x^2-1)^(2/3)*x^2-397598482420532510559844300662311382756412651044467429429562386258261287328984805904109018271807865483226514432*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)-72130243600887911741079570933816184250259183614011975044172715538668848562802529415171670677513534202100154400*RootOf(_Z^2-3*_Z+9)^2*(x^6+x^4-x^2-1)^(1/3)-6680576332500850033423336305582184374514510876921901091056155147716664787928889606613471772094295499514120305006*(x^6+x^4-x^2-1)^(1/3)*x^2+1635147324220587738836563140853892378904647724289366932739933592854296317110664721844999581824966705367527298249*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)-45742748085033471029289083755717489945013482738881131277259999641950860727670581720337832012634565135618336504*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)^2*x^14+19237970928913342884506573809228139046023320189768249610068068913082958677232334363430695268039669105680144128*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)^2*x^12-304110342643905302544182706523867674901048954639644136777621861073064762346776946253523531848729946126776294898*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)*x^14-1491570632667120400800660042684106825335078769909688724317547969474419636217055218705357480570631772129383813032*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)*x^12+747799115677575031501549410875188643157838665964203388908716264240803336462876330925066352910568048461972969584*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)^2*x^12+648840380994234664285584158472594508158918429635132209773469110953601770221005959327794291970247505778306297088*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)^2*x^10-15147174575419323292539859764030875922455256056524610415349021012661946284368396286157419920882612168688363652522*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)*x^12-12804150466163519737353663731265294410006995443448674910589953355586731283142440352126234253684887550371699959096*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)*x^10+248041345977258994396262776074676557817456187515963023720574784954736919244449623878970025634046185092640116152*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)^2*x^10+38319445579411087815837238531239274918416306268448835241709691427254323566226476623568657519495491020770318848*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)^2*x^8-2438733310903095643597973091805002578015302273695093364598729364478906406784984364723173077048313642610449601146*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)*x^10+1248240262273376141127564564632657814450477334242796450033232825964319404182957366277641820669509201945651436336*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)*x^8-962066514787838066117525012798857360300465954096752313501398264039449246339858374959464685544135500769994145888*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)^2*x^8-701403943135908753695868088749970444920331170482957149125792786258853975207479643477680020321297409350492717568*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)^2*x^6+19939670241257081682720981770389592483335446582124467453151852407810974666175972723497203806125322509796223599372*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)*x^8+14000105723426297843512275850525466765834379700748641854500703411278363273574670587522498039521909735445222598608*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)*x^6-334097605465860615749839314237637573137744842067561004733464049538657639168698635892248283622500014406074946952*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)^2*x^6-81734200534172030116591477828010819585159171789846885029553899862643425501639507949357691590394654458397076736*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)^2*x^4+4589336792075648214428958941713913209482965377931724801502653438967698799571228280103847070662815581473679798282*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)*x^6+269157993749983118700707779572149683501270616575429323110041419665900310642775519987912531757517554234285505528*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)*x^4+492490457495758816365689561537614040611702962698657261323925687574929088077001582289880842562287652092262132592*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)^2*x^4+248786970078759110852029031505060660915484707027364420942256957370537632319332317841545391955027452627838740736*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)^2*x^2-10517220107999747891133254365826085392465137874007611211863642551578254598342611139762478455670657687479892737222*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)*x^4-5023970427584527465442259737664117896590240365592567662303457406123464615563450593296528006047296031051132361752*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)*x^2+137650322902905626706204584524619525498727913931219433284449235206819894092147961641724008197485359787558578888*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)^2*x^2-2149602460161390679728522041623358264492309108600025711629350553581579254925044027602054501631263986490444953758*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)*x^2+13036705992071841125974900204944636463738169628932591557237401176423077936718277722496998128865754496248250368*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)^2*x^20+13062476297880443326360141872865224106981797764289466574027950680368032278983438508787696206805789311661768704*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)^2*x^18-250638154265509559639363370899471758701500700166575772977689216979486461051483183326979873359320615523103932416*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)*x^20-250715465182935366240519095903233521631231584572646398028060865491321324078278665685851967593140719969344487424*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)*x^18-6105938493178187470330659875568845164358162766305410673152263972675326681179896769875437691101374606010260224*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)^2*x^18-10433361617327115031604628942906894985526425902229155479988068606169796564204732074846373572597383653334261760*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)^2*x^16+308004598083241645028425214076195615712833644553166844569018832684982219427988839399259115517041224525926675200*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)*x^18+391220785754868088189677929771155926080144395909301867489557676832608067809535649078064715007941302148057001728*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)*x^16-219384143940587364281600986154701600613487046706594042923160666405764420814886815424575356874776829345893900896*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)^2*x^16-210470049208246211088188909166334662343528162797300881827277697675050707417568384587643754600992249924881769472*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)^2*x^14+4345110548657409555341638905350828519168939009835091447364537273073546955418264944829029937613850487299545048219*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)*x^16+4103077348624613368553497783528584308053848610524803103267975346432428177909631414509445552637996516349239085312*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)*x^14-3953139815812989501011593885186751609572610974780255817076000799217627642942799293398006013886194030281821204795*(x^6+x^4-x^2-1)^(2/3)-1843222122522690816838783816715012737729315460920965580731006106095910839347379047415854650788900250821225188640)/x^18/(x^2+1))+1/54*RootOf(_Z^2-3*_Z+9)*ln((3417991875066354421873963556729150820007548700204627190428992216133173269052463239027877821270084783203403816960*x^20+2088955396301134975249584996784389865855271945340288410716144460388179311157012425720771087195304958955601396160*x^10-12493127802820157771114270981473357329614478176576219428968550092950767952070926262998238023556083371253950992000*x^6+6232937937287364468276046879668749430280367000495617512361734660164868876406996996868731838303971833387926397600*x^2-70763818877222587930629541422358033730526247473591512047945873886560891135326464310745816054040674869417029440320*x^8+31268837871264287979022557546481009893988689989916760823530383827771228334539401534971334459441823959483118394240*x^4+66794402355835169184888137364883826735383143317464906723705481179901027183673351870886966208954949057573440042880*x^12-26765941834971260536652579014409090078832822909038280414915248886891446761961138282805954736308911703196903162080*x^16+487478801599834469677809456214392359170510086459477468769097978351090032407865030264514830644335607369726689280*x^22-538078034944597987996558178700277852042979524632310330419955194556095789456104546843470851991672534671310880736*RootOf(_Z^2-3*_Z+9)^2-5017535121105366136556307892916082536212968865107895357632409493260373991117455951749800910348352155720540564320*x^18+8699725347028586242851805467762625461535032320226105778320561805932774698752163201949070568477380861313289041280*x^14-8776958254805119060110259161117954174497748435458699042808731426889686557316849244279179185270237307115809280*RootOf(_Z^2-3*_Z+9)^2*x^20-920380997199176122846491770696906154516511275351996236203449915212643647791708375938560866338313374184079495424*RootOf(_Z^2-3*_Z+9)*x^20-1157000965035060573316301943082787153889448989841451999571719387348206534686044927239491061370739831000266109536*RootOf(_Z^2-3*_Z+9)^2*x^18+5551826574760912635939195837686018575470494565036647294682250646198468362248981903284391943747760108195232849573*RootOf(_Z^2-3*_Z+9)*x^18-799222326293103253142582227976551240463461185712990637899624372746931230353853940294984802791729118342237279592*RootOf(_Z^2-3*_Z+9)^2*x^2-302276791695308688716011438169504483995123546386338643485627558861012233294693679356682268642107637328284856347*(x^6+x^4-x^2-1)^(1/3)+2608605228356017337502286237125208489142075803624974788093425192775008769534808189713663926488863601242731631736*RootOf(_Z^2-3*_Z+9)^2*x^4+3032990698251717967602998964153277382282808747344261998867281029906577139790570774129897125767443706775159477257*RootOf(_Z^2-3*_Z+9)-18075006737028269833796713567739788112345573818365277821700771103715884509786567513414781675259955327423325122596*RootOf(_Z^2-3*_Z+9)*x^4+1133934351899277294355613205230968642112214914815048171125342085692437375553714056074566787933854815486018233365*RootOf(_Z^2-3*_Z+9)*x^2-599423277276165646418681980299261635495957935550825753466774195905306189623557193885736786802214246181538965784*RootOf(_Z^2-3*_Z+9)^2*x^16+9606563674527538422455081662249548601466517284377837271927692556369026802527900179080254830406410483644463718137*RootOf(_Z^2-3*_Z+9)*x^16+4228079556077566167750916421106050876322453751404633960966508726507715786489990437655967283921834149395428962888*RootOf(_Z^2-3*_Z+9)^2*x^14-17604677518124452006696022848180335370219886185737011615029175012204481488523092229311385841056204545727694349652*RootOf(_Z^2-3*_Z+9)*x^14+2738669499339101448689154506166537053018929325609929326628874120822444913392325096556187976051369683465530190568*RootOf(_Z^2-3*_Z+9)^2*x^12-28435753342009275965378719860659041826123501673199773607728970057547128947407893081259329941305083727565777773892*RootOf(_Z^2-3*_Z+9)*x^12-6068883081797944172847557739426762694321985636798596145878467467983735731760683850815814566060149930692488514776*RootOf(_Z^2-3*_Z+9)^2*x^10+21209880410169507667109692082074851054973886318309092892248591126081425442268765616638272851663800504321354812686*RootOf(_Z^2-3*_Z+9)*x^10-4201110331330034087152949518677120105536812274830602835591780094750517640072254032631735362395547698511130155880*RootOf(_Z^2-3*_Z+9)^2*x^8+34792431562270503099636261831074738258333936034094169569678590653012186389773526834663639630078522697986076960358*RootOf(_Z^2-3*_Z+9)*x^8+3730558480075521439611130300682531194948589606786416109117189069446746219317731509727575715111328923680785789784*RootOf(_Z^2-3*_Z+9)^2*x^6-9916097989736302496882019196073572784205244760091618413624292676721802559731923835843732816419351201884792371060*RootOf(_Z^2-3*_Z+9)*x^6-374020970155905526154041822356101969033789553432937154562343006233913904710616693580993822520835221157601411072*x^22*RootOf(_Z^2-3*_Z+9)+66354462862536337507535995151487012314610099947695209467094529083055868210761434631377153354984374995943161856*x^22*RootOf(_Z^2-3*_Z+9)^2-80054321743429866447584053256085241935087568922892661967093483133367231611235187179337340336356703372941721600*(x^6+x^4-x^2-1)^(1/3)*x^20-407310458023965550957060233849135779307041580890949379316926700830926609724146222481497821506394184704359858176*(x^6+x^4-x^2-1)^(2/3)*x^18-534348626550573788386384870703054263786130155563577182674656641503475708555065314582712059074175882426756436736*(x^6+x^4-x^2-1)^(1/3)*x^18-2584946988701880502931187876029459608408701193350162979799284830674763602356066019181898352357471719450629490176*(x^6+x^4-x^2-1)^(2/3)*x^16+965195764294458837269192022060755952021766074312939377420896838950511736289707250933773618739078035123999170799*(x^6+x^4-x^2-1)^(1/3)*x^16+5596514859728562231603153534957846872608623624013617298658539986367722867641719332029396497010219466792532856433*(x^6+x^4-x^2-1)^(2/3)*x^14+3831514642946625708532341797148866896507534576332699731280465926527676930783918811760749774679475181528366445638*(x^6+x^4-x^2-1)^(1/3)*x^14+16503978322482148510803423619947505959399181137981668801851066941001140819245632955556508912558373466022354688511*(x^6+x^4-x^2-1)^(2/3)*x^12-2281077498981007065601060483008659859818182113487698167622781970246948309075404433952031625726431973121771180258*(x^6+x^4-x^2-1)^(1/3)*x^12-14889063830034706393681271746935342391568991697771469496338736742519706342912882568129245218329989664239613302031*(x^6+x^4-x^2-1)^(2/3)*x^10-8513155830460730782976949674443319037826512760900201399299764548645507348692696471057893694284181989991943906434*(x^6+x^4-x^2-1)^(1/3)*x^10-31426179148639141611300290749187399168993228628885126878056112809211707331180001376227929800529603939681929856025*(x^6+x^4-x^2-1)^(2/3)*x^8+1577580519553074716908632057750136008632908242201943782281653612422136763972389033496184533856691490742595543452*(x^6+x^4-x^2-1)^(1/3)*x^8+13677155115137071830271964935395268805926277066364122708138845662812667564900853206582068816226418054437247370667*(x^6+x^4-x^2-1)^(2/3)*x^6+7553232804848157486627979702788261709983120518720568786029400348863831537302897975806937044651867253260060083826*(x^6+x^4-x^2-1)^(1/3)*x^6+22354258764356386667813251446648411378275124726025376564685388603005585416881272563544450170570648330997880878165*(x^6+x^4-x^2-1)^(2/3)*x^4+122195889543763431165886270663515539975263591362571560676997355461127852461643953307689514537571254819155811954*(x^6+x^4-x^2-1)^(1/3)*x^4+33681107160086945536486599885619985432111060617970800638471726610804630147108011933383077276787142000206588928*RootOf(_Z^2-3*_Z+9)^2*(x^6+x^4-x^2-1)^(2/3)-3965034753559972998547207353700318903149750096418710167014322995579067975574312497111634962042544121707765265677*(x^6+x^4-x^2-1)^(2/3)*x^2+195511839460010837340924701348591470163746287336642625598732026593433506446336734303810554611085013481986980864*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)+439332554284273702458217982887536332718498552661739375481846531094873008996897524604641271192796741217266183200*RootOf(_Z^2-3*_Z+9)^2*(x^6+x^4-x^2-1)^(1/3)-2335679429811927259217932578750597389996467499508964688031400290650076832096648064677484633544540095506973418294*(x^6+x^4-x^2-1)^(1/3)*x^2+397314091505374570189054980395286254458453984652667908676023059379518141319225329889520542655482318592035033097*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)+278610986916623173515132435975089606922140707529315237716917816281213877466061415279682076779952695214163614712*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)^2*x^14+19237970928913342884506573809228139046023320189768249610068068913082958677232334363430695268039669105680144128*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)^2*x^12-7916254215558935698728655598023743766485053609235013052016000598030679800080842599215001026873638612415049977450*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)*x^14+1376142807093640343493620599828737991058938848771079226657139555995921884153661212524773308962393757495302948264*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)*x^12-4554712131571200184411855008580509982084822476598188768165710958896173014890522923788743801353239560336567267952*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)^2*x^12+648840380994234664285584158472594508158918429635132209773469110953601770221005959327794291970247505778306297088*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)^2*x^10+6874610525297809322330317514795445384514353971032060100326504304561633058938384927639378362556633704941530738310*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)*x^12+8911108180198111751640158780429727361053484865637881651949138689865120661816404596159468501863402515701862176568*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)*x^10-1510775961041631862689389329465137527946145988260201586623419953054399366205289216701853632746967472443281296056*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)^2*x^10+38319445579411087815837238531239274918416306268448835241709691427254323566226476623568657519495491020770318848*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)^2*x^8+18028166113778077824107934899900391242637780846534906341119975676373303660135063199270588209045508652888463113790*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)*x^10-1478156935749842668022587995820093463960975171853489461483490974527845345580316226019053765786482148070273349424*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)*x^8+5859776956692641907779316917081021912881672711300508368913847384388890838382397981039179309148382168133479892064*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)^2*x^8-701403943135908753695868088749970444920331170482957149125792786258853975207479643477680020321297409350492717568*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)^2*x^6-6089120837126356399016811388755199578508902607339764794275278041309803243668162168965252970732581952455640335316*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)*x^8-9791682064610845321337067318025644096312392677850898959745946693725239422329792726656417917594125279342266293200*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)*x^6+2034929414653595176462922522199029242243590341545299349770687135546556575944255010343138189337534874225158328456*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)^2*x^6-81734200534172030116591477828010819585159171789846885029553899862643425501639507949357691590394654458397076736*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)^2*x^4-16337427777810916685932503750658836046405451503091790774414539446471661766300964476284111195552547146692284886782*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)*x^6+221247209455049061998841087395915234009684414163651987067281979509960242367061527708233617784850372516096954888*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)*x^4-2999672257443738988326963419219579363546091485152482969222066567899919349985908358374535363268201437643351467376*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)^2*x^4+248786970078759110852029031505060660915484707027364420942256957370537632319332317841545391955027452627838740736*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)^2*x^2+1229380190036130017133435666515711154783679130203165599350006803249672411515563668190912520921237686598122834922*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)*x^4+3531248607111972800330085548633753931097332123428381136649915661900238821647456686247255654317131315284099917336*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)*x^2-838403767129994295338628604766566272664982622214229658151045426059270616671383165856459118295662646321142341064*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)^2*x^2+5155021047598983110608945003067618852662635234076980971325202366370493128266889918032373303510875851497476194858*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)*x^2-79404270067923552803544451567777643318438460306914072987224947053779879259468915295311553028280751052891029504*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)^2*x^20+13062476297880443326360141872865224106981797764289466574027950680368032278983438508787696206805789311661768704*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)^2*x^18+201642355482773135780628521320336012734988443230815746816757246695868710615410785413308142568000997294085832704*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)*x^20+172340607395652706282358244666042176989340797986909598583893161409113130404378034633125790352305984099373875200*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)*x^18+37190191251171939940657203627268108541460812577686072774892164533043667733142459187354038695226157744103471872*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)^2*x^18-10433361617327115031604628942906894985526425902229155479988068606169796564204732074846373572597383653334261760*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)^2*x^16+1066556504737268537136064044907531904841358788683064643930347211784016092225646716293547035210269985242995441664*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)*x^18-328620616050905398000050156113714556166985840495926934609629265195589288424307256628986473572357000228051431168*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)*x^16+1336230012755711247195522206968991900445244409273207481467340295613252535023391194066631691078626448101065467488*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)^2*x^16-210470049208246211088188909166334662343528162797300881827277697675050707417568384587643754600992249924881769472*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)^2*x^14-2617764652451253559224840695078617040731303164810796430949028162551417764474629784070470272628304024448534217637*(x^6+x^4-x^2-1)^(1/3)*RootOf(_Z^2-3*_Z+9)*x^16-2840257053375136102024364328530576333992679633740997812304309160382123933404221106983583025032043016799948468480*(x^6+x^4-x^2-1)^(2/3)*RootOf(_Z^2-3*_Z+9)*x^14-4842805298633804522862747388203105888952849382351920899618442418495169833605781603709885373210533348729641447739*(x^6+x^4-x^2-1)^(2/3)-3953036831680566870117870105286146389006577314119127891237155131727319914441958611279358308600713493593977683680)/x^18/(x^2+1))","C"
2917,0,0,276,0.041000," ","int((-a/b^2+a^2*x^2/b^2)^(1/2)*(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/3),x)","\[\int \sqrt{-\frac{a}{b^{2}}+\frac{a^{2} x^{2}}{b^{2}}}\, \left(a \,x^{2}+b x \sqrt{-\frac{a}{b^{2}}+\frac{a^{2} x^{2}}{b^{2}}}\right)^{\frac{1}{3}}\, dx\]"," ",0,"int((-a/b^2+a^2*x^2/b^2)^(1/2)*(a*x^2+b*x*(-a/b^2+a^2*x^2/b^2)^(1/2))^(1/3),x)","F"
2918,0,0,265,0.092000," ","int((a*x^2-b)/(c*x^2-d)/(x^3-x)^(1/3),x)","\[\int \frac{a \,x^{2}-b}{\left(c \,x^{2}-d \right) \left(x^{3}-x \right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a*x^2-b)/(c*x^2-d)/(x^3-x)^(1/3),x)","F"
2919,0,0,263,0.064000," ","int(1/(a*x+b)/(a^3*x^3-b^3)^(1/3),x)","\[\int \frac{1}{\left(a x +b \right) \left(a^{3} x^{3}-b^{3}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(a*x+b)/(a^3*x^3-b^3)^(1/3),x)","F"
2920,1,187,28,0.245000," ","int((a^12*x^12-b^12)/(a^4*x^4+b^4)^(1/2)/(a^12*x^12+b^12),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(-\frac{\sqrt{2}\, x}{3 \sqrt{a^{4} x^{4}+b^{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{a^{4} x^{4}+b^{4}}}{x \sqrt{\sqrt{3}\, \sqrt{a^{4} b^{4}}}}\right)}{3 \sqrt{\sqrt{3}\, \sqrt{a^{4} b^{4}}}}-\frac{\sqrt{2}\, \ln \left(\frac{\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{2 x}+\frac{\sqrt{2}\, \sqrt{\sqrt{3}\, \sqrt{a^{4} b^{4}}}}{2}}{\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{2 x}-\frac{\sqrt{2}\, \sqrt{\sqrt{3}\, \sqrt{a^{4} b^{4}}}}{2}}\right)}{6 \sqrt{\sqrt{3}\, \sqrt{a^{4} b^{4}}}}\right) \sqrt{2}}{2}$&$187$\\ default&$\frac{\sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, i\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}+b^{4}}}-\frac{b^{4} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{8} a^{8}-\textit{\_Z}^{4} a^{4} b^{4}+b^{8}\right)}{\sum}\frac{\left(-a^{4} \underline{\hspace{1.25 ex}}\alpha^{4}+2 b^{4}\right) \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{6} a^{4}+\underline{\hspace{1.25 ex}}\alpha^{2} b^{4}+b^{4} x^{2}\right) a^{4}}{b^{4} \sqrt{a^{4} \underline{\hspace{1.25 ex}}\alpha^{4}+b^{4}}\, \sqrt{a^{4} x^{4}+b^{4}}}\right)}{\sqrt{a^{4} \underline{\hspace{1.25 ex}}\alpha^{4}+b^{4}}}+\frac{2 a^{4} \underline{\hspace{1.25 ex}}\alpha^{3} \left(a^{4} \underline{\hspace{1.25 ex}}\alpha^{4}-b^{4}\right) \sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, \frac{i \underline{\hspace{1.25 ex}}\alpha^{2} \left(a^{4} \underline{\hspace{1.25 ex}}\alpha^{4}-b^{4}\right) a^{2}}{b^{6}}, \frac{\sqrt{-\frac{i a^{2}}{b^{2}}}}{\sqrt{\frac{i a^{2}}{b^{2}}}}\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, b^{8} \sqrt{a^{4} x^{4}+b^{4}}}\right)}{\underline{\hspace{1.25 ex}}\alpha^{3} \left(2 a^{4} \underline{\hspace{1.25 ex}}\alpha^{4}-b^{4}\right)}\right)}{12 a^{4}}-\frac{2 b^{4} \left(\frac{x}{2 b^{4} \sqrt{\left(x^{4}+\frac{b^{4}}{a^{4}}\right) a^{4}}}+\frac{\sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, i\right)}{2 b^{4} \sqrt{\frac{i a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}+b^{4}}}\right)}{3}$&$467$\\ \hline \end{longtable}"," ",0,"1/2*(-1/3/(a^4*x^4+b^4)^(1/2)*2^(1/2)*x+1/3*2^(1/2)/(3^(1/2)*(a^4*b^4)^(1/2))^(1/2)*arctan((a^4*x^4+b^4)^(1/2)/x/(3^(1/2)*(a^4*b^4)^(1/2))^(1/2))-1/6*2^(1/2)/(3^(1/2)*(a^4*b^4)^(1/2))^(1/2)*ln((1/2*(a^4*x^4+b^4)^(1/2)*2^(1/2)/x+1/2*2^(1/2)*(3^(1/2)*(a^4*b^4)^(1/2))^(1/2))/(1/2*(a^4*x^4+b^4)^(1/2)*2^(1/2)/x-1/2*2^(1/2)*(3^(1/2)*(a^4*b^4)^(1/2))^(1/2))))*2^(1/2)","B"
2921,1,431,308,0.448000," ","int((a*x^2+b*x+c)^(5/2)/(b*x+c),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\sqrt{a \,x^{2}+b x +c}\, \left(384 a^{4} b^{4} x^{4}-480 a^{4} b^{3} c \,x^{3}+1008 a^{3} b^{5} x^{3}+640 a^{4} b^{2} c^{2} x^{2}+48 a^{3} b^{4} c \,x^{2}+744 a^{2} b^{6} x^{2}-960 a^{4} b \,c^{3} x -80 a^{3} b^{3} c^{2} x +1308 a^{2} b^{5} c x +30 a \,b^{7} x +1920 a^{4} c^{4}+160 a^{3} b^{2} c^{3}+24 a^{2} b^{4} c^{2}+390 b^{6} c a -45 b^{8}\right)}{1920 a^{2} b^{5}}-\frac{a^{\frac{5}{2}} \ln \left(\frac{\frac{b}{2}+a x}{\sqrt{a}}+\sqrt{a \,x^{2}+b x +c}\right) c^{5}}{b^{6}}+\frac{5 \ln \left(\frac{\frac{b}{2}+a x}{\sqrt{a}}+\sqrt{a \,x^{2}+b x +c}\right) c^{2}}{16 \sqrt{a}}-\frac{15 b^{2} \ln \left(\frac{\frac{b}{2}+a x}{\sqrt{a}}+\sqrt{a \,x^{2}+b x +c}\right) c}{128 a^{\frac{3}{2}}}+\frac{3 b^{4} \ln \left(\frac{\frac{b}{2}+a x}{\sqrt{a}}+\sqrt{a \,x^{2}+b x +c}\right)}{256 a^{\frac{5}{2}}}-\frac{a^{3} c^{6} \ln \left(\frac{\frac{2 a \,c^{2}}{b^{2}}-\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+2 \sqrt{\frac{a \,c^{2}}{b^{2}}}\, \sqrt{\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}}}{x +\frac{c}{b}}\right)}{b^{7} \sqrt{\frac{a \,c^{2}}{b^{2}}}}$&$431$\\ default&$\frac{\frac{\left(\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}\right)^{\frac{5}{2}}}{5}-\frac{\left(2 a c -b^{2}\right) \left(\frac{\left(2 a \left(x +\frac{c}{b}\right)-\frac{2 a c -b^{2}}{b}\right) \left(\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}\right)^{\frac{3}{2}}}{8 a}+\frac{3 \left(\frac{4 a^{2} c^{2}}{b^{2}}-\frac{\left(2 a c -b^{2}\right)^{2}}{b^{2}}\right) \left(\frac{\left(2 a \left(x +\frac{c}{b}\right)-\frac{2 a c -b^{2}}{b}\right) \sqrt{\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}}}{4 a}+\frac{\left(\frac{4 a^{2} c^{2}}{b^{2}}-\frac{\left(2 a c -b^{2}\right)^{2}}{b^{2}}\right) \ln \left(\frac{-\frac{2 a c -b^{2}}{2 b}+a \left(x +\frac{c}{b}\right)}{\sqrt{a}}+\sqrt{\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}}\right)}{8 a^{\frac{3}{2}}}\right)}{16 a}\right)}{2 b}+\frac{a \,c^{2} \left(\frac{\left(\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}\right)^{\frac{3}{2}}}{3}-\frac{\left(2 a c -b^{2}\right) \left(\frac{\left(2 a \left(x +\frac{c}{b}\right)-\frac{2 a c -b^{2}}{b}\right) \sqrt{\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}}}{4 a}+\frac{\left(\frac{4 a^{2} c^{2}}{b^{2}}-\frac{\left(2 a c -b^{2}\right)^{2}}{b^{2}}\right) \ln \left(\frac{-\frac{2 a c -b^{2}}{2 b}+a \left(x +\frac{c}{b}\right)}{\sqrt{a}}+\sqrt{\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}}\right)}{8 a^{\frac{3}{2}}}\right)}{2 b}+\frac{a \,c^{2} \left(\sqrt{\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}}-\frac{\left(2 a c -b^{2}\right) \ln \left(\frac{-\frac{2 a c -b^{2}}{2 b}+a \left(x +\frac{c}{b}\right)}{\sqrt{a}}+\sqrt{\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}}\right)}{2 b \sqrt{a}}-\frac{a \,c^{2} \ln \left(\frac{\frac{2 a \,c^{2}}{b^{2}}-\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+2 \sqrt{\frac{a \,c^{2}}{b^{2}}}\, \sqrt{\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}}}{x +\frac{c}{b}}\right)}{b^{2} \sqrt{\frac{a \,c^{2}}{b^{2}}}}\right)}{b^{2}}\right)}{b^{2}}}{b}$&$881$\\ \hline \end{longtable}"," ",0,"1/1920*(a*x^2+b*x+c)^(1/2)*(384*a^4*b^4*x^4-480*a^4*b^3*c*x^3+1008*a^3*b^5*x^3+640*a^4*b^2*c^2*x^2+48*a^3*b^4*c*x^2+744*a^2*b^6*x^2-960*a^4*b*c^3*x-80*a^3*b^3*c^2*x+1308*a^2*b^5*c*x+30*a*b^7*x+1920*a^4*c^4+160*a^3*b^2*c^3+24*a^2*b^4*c^2+390*a*b^6*c-45*b^8)/a^2/b^5-a^(5/2)/b^6*ln((1/2*b+a*x)/a^(1/2)+(a*x^2+b*x+c)^(1/2))*c^5+5/16/a^(1/2)*ln((1/2*b+a*x)/a^(1/2)+(a*x^2+b*x+c)^(1/2))*c^2-15/128/a^(3/2)*b^2*ln((1/2*b+a*x)/a^(1/2)+(a*x^2+b*x+c)^(1/2))*c+3/256/a^(5/2)*b^4*ln((1/2*b+a*x)/a^(1/2)+(a*x^2+b*x+c)^(1/2))-a^3/b^7*c^6/(a*c^2/b^2)^(1/2)*ln((2*a*c^2/b^2-(2*a*c-b^2)/b*(x+c/b)+2*(a*c^2/b^2)^(1/2)*((x+c/b)^2*a-(2*a*c-b^2)/b*(x+c/b)+a*c^2/b^2)^(1/2))/(x+c/b))","A"
2922,0,0,98,0.010000," ","int((x^4-a*x^2-b)*(a*x^4+b*x^2)^(1/4)/(a*x^4+b),x)","\[\int \frac{\left(x^{4}-a \,x^{2}-b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}{a \,x^{4}+b}\, dx\]"," ",0,"int((x^4-a*x^2-b)*(a*x^4+b*x^2)^(1/4)/(a*x^4+b),x)","F"
2923,0,0,98,0.003000," ","int((x^4-a*x^2-b)*(a*x^4+b*x^2)^(1/4)/(a*x^4+b),x)","\[\int \frac{\left(x^{4}-a \,x^{2}-b \right) \left(a \,x^{4}+b \,x^{2}\right)^{\frac{1}{4}}}{a \,x^{4}+b}\, dx\]"," ",0,"int((x^4-a*x^2-b)*(a*x^4+b*x^2)^(1/4)/(a*x^4+b),x)","F"
2924,1,161,61,0.181000," ","int((1+x)^(1/2)*(x^2-1)/(x^2+1)/(x+(1+x)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\sqrt{1+x}\, \sqrt{x +\sqrt{1+x}}-\frac{3 \sqrt{x +\sqrt{1+x}}}{2}+\frac{7 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{4}+\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)}{\sum}\frac{\left(2 \textit{\_R}^{5}-\textit{\_R}^{4}+4 \textit{\_R}^{3}-2 \textit{\_R}^{2}+2 \textit{\_R} -1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+5 \textit{\_R}^{4}+10 \textit{\_R}^{3}-18 \textit{\_R}^{2}+10 \textit{\_R} -1}\right)$&$161$\\ default&$\sqrt{1+x}\, \sqrt{x +\sqrt{1+x}}-\frac{3 \sqrt{x +\sqrt{1+x}}}{2}+\frac{7 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{4}+\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)}{\sum}\frac{\left(2 \textit{\_R}^{5}-\textit{\_R}^{4}+4 \textit{\_R}^{3}-2 \textit{\_R}^{2}+2 \textit{\_R} -1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+5 \textit{\_R}^{4}+10 \textit{\_R}^{3}-18 \textit{\_R}^{2}+10 \textit{\_R} -1}\right)$&$161$\\ \hline \end{longtable}"," ",0,"(1+x)^(1/2)*(x+(1+x)^(1/2))^(1/2)-3/2*(x+(1+x)^(1/2))^(1/2)+7/4*ln(1/2+(1+x)^(1/2)+(x+(1+x)^(1/2))^(1/2))+sum((2*_R^5-_R^4+4*_R^3-2*_R^2+2*_R-1)/(_R^7-3*_R^5+5*_R^4+10*_R^3-18*_R^2+10*_R-1)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^8-4*_Z^6+8*_Z^5+20*_Z^4-48*_Z^3+40*_Z^2-8*_Z+1))","B"
2925,1,161,61,0.171000," ","int((1+x)^(1/2)*(x^2-1)/(x^2+1)/(x+(1+x)^(1/2))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\sqrt{1+x}\, \sqrt{x +\sqrt{1+x}}-\frac{3 \sqrt{x +\sqrt{1+x}}}{2}+\frac{7 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{4}+\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)}{\sum}\frac{\left(2 \textit{\_R}^{5}-\textit{\_R}^{4}+4 \textit{\_R}^{3}-2 \textit{\_R}^{2}+2 \textit{\_R} -1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+5 \textit{\_R}^{4}+10 \textit{\_R}^{3}-18 \textit{\_R}^{2}+10 \textit{\_R} -1}\right)$&$161$\\ default&$\sqrt{1+x}\, \sqrt{x +\sqrt{1+x}}-\frac{3 \sqrt{x +\sqrt{1+x}}}{2}+\frac{7 \ln \left(\frac{1}{2}+\sqrt{1+x}+\sqrt{x +\sqrt{1+x}}\right)}{4}+\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{6}+8 \textit{\_Z}^{5}+20 \textit{\_Z}^{4}-48 \textit{\_Z}^{3}+40 \textit{\_Z}^{2}-8 \textit{\_Z} +1\right)}{\sum}\frac{\left(2 \textit{\_R}^{5}-\textit{\_R}^{4}+4 \textit{\_R}^{3}-2 \textit{\_R}^{2}+2 \textit{\_R} -1\right) \ln \left(\sqrt{x +\sqrt{1+x}}-\sqrt{1+x}-\textit{\_R} \right)}{\textit{\_R}^{7}-3 \textit{\_R}^{5}+5 \textit{\_R}^{4}+10 \textit{\_R}^{3}-18 \textit{\_R}^{2}+10 \textit{\_R} -1}\right)$&$161$\\ \hline \end{longtable}"," ",0,"(1+x)^(1/2)*(x+(1+x)^(1/2))^(1/2)-3/2*(x+(1+x)^(1/2))^(1/2)+7/4*ln(1/2+(1+x)^(1/2)+(x+(1+x)^(1/2))^(1/2))+sum((2*_R^5-_R^4+4*_R^3-2*_R^2+2*_R-1)/(_R^7-3*_R^5+5*_R^4+10*_R^3-18*_R^2+10*_R-1)*ln((x+(1+x)^(1/2))^(1/2)-(1+x)^(1/2)-_R),_R=RootOf(_Z^8-4*_Z^6+8*_Z^5+20*_Z^4-48*_Z^3+40*_Z^2-8*_Z+1))","B"
2926,1,886,64,0.255000," ","int((-x^2+(2*x^2+1)^(1/2)+(2*x^2+1)^(5/2))/(x^2-x*(2*x^2+1)^(3/2)),x)","\[\frac{x \left(2 x^{2}+1\right)^{\frac{3}{2}}}{40}-\frac{\sqrt{2 x^{2}+1}\, x}{20}-\frac{\sqrt{2}\, x^{2}}{20}-\frac{\sqrt{2}}{320}-\frac{\sqrt{2}\, x^{4}}{10}-\frac{\sqrt{2}\, x}{10}-\frac{\sqrt{2 x^{2}+1}}{10}-\frac{\arctan \left(x \right)}{5}+\frac{\ln \left(x^{2}+1\right)}{5}-2 \ln \left(x \right)-x^{2}+\frac{4 \arctan \left(\frac{2 \left(-\sqrt{2}\, x +\sqrt{2 x^{2}+1}\right)^{2}}{-2+2 \sqrt{2}}\right) \sqrt{2}}{5 \left(-2+2 \sqrt{2}\right)}-\frac{3 \ln \left(\left(-\sqrt{2}\, x +\sqrt{2 x^{2}+1}\right)^{4}+2 \sqrt{2}+3\right)}{20}+\frac{4 \arctan \left(\frac{2 \left(-\sqrt{2}\, x +\sqrt{2 x^{2}+1}\right)^{2}}{2+2 \sqrt{2}}\right) \sqrt{2}}{5 \left(2+2 \sqrt{2}\right)}+\frac{4 \arctan \left(\frac{2 \left(-\sqrt{2}\, x +\sqrt{2 x^{2}+1}\right)^{2}}{2+2 \sqrt{2}}\right)}{5 \left(2+2 \sqrt{2}\right)}-\frac{4 \arctan \left(\frac{2 \left(-\sqrt{2}\, x +\sqrt{2 x^{2}+1}\right)^{2}}{-2+2 \sqrt{2}}\right)}{5 \left(-2+2 \sqrt{2}\right)}+\frac{3 \ln \left(\left(-\sqrt{2}\, x +\sqrt{2 x^{2}+1}\right)^{4}+3-2 \sqrt{2}\right)}{20}+\frac{\sqrt{2}\, \ln \left(-\sqrt{2}\, x +\sqrt{2 x^{2}+1}\right)}{8}+\frac{3 \ln \left(8 x^{4}+4 x^{2}+1\right)}{20}-\frac{2 \arctan \left(4 x^{2}+1\right)}{5}-\frac{3 \ln \left(\sqrt{2}+2 \sqrt{\sqrt{2}-1}\, \sqrt{2}\, x +4 x^{2}\right) \sqrt{\sqrt{2}-1}}{40}+\frac{3 \ln \left(-2 \sqrt{\sqrt{2}-1}\, \sqrt{2}\, x +4 x^{2}+\sqrt{2}\right) \sqrt{\sqrt{2}-1}}{40}-\frac{3 x^{3} \sqrt{2 x^{2}+1}}{20}+\frac{\sqrt{2}}{320 \left(-\sqrt{2}\, x +\sqrt{2 x^{2}+1}\right)^{4}}-\frac{\ln \left(\sqrt{2}+2 \sqrt{\sqrt{2}-1}\, \sqrt{2}\, x +4 x^{2}\right) \sqrt{2}\, \sqrt{\sqrt{2}-1}}{40}+\frac{\arctan \left(\frac{2 \sqrt{2}\, \sqrt{\sqrt{2}-1}+8 x}{2 \sqrt{2+2 \sqrt{2}}}\right) \sqrt{2}}{20 \sqrt{2+2 \sqrt{2}}}+\frac{\ln \left(-2 \sqrt{\sqrt{2}-1}\, \sqrt{2}\, x +4 x^{2}+\sqrt{2}\right) \sqrt{2}\, \sqrt{\sqrt{2}-1}}{40}+\frac{\arctan \left(\frac{-2 \sqrt{2}\, \sqrt{\sqrt{2}-1}+8 x}{2 \sqrt{2+2 \sqrt{2}}}\right) \sqrt{2}}{20 \sqrt{2+2 \sqrt{2}}}+\frac{\arctan \left(\sqrt{2 x^{2}+1}\right)}{5}+\frac{1}{-10 \sqrt{2}\, x +10 \sqrt{2 x^{2}+1}}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(2 \textit{\_Z}^{4}+2 \textit{\_Z}^{2}+25\right)}{\sum}\textit{\_R} \ln \left(35 \left(-\sqrt{2}\, x +\sqrt{2 x^{2}+1}\right)^{2}+\left(4 \textit{\_R}^{3}-26 \textit{\_R} \right) \left(-\sqrt{2}\, x +\sqrt{2 x^{2}+1}\right)+35\right)\right)}{20}+\frac{2 \arctanh \left(\frac{x}{\sqrt{2 x^{2}+1}}\right)}{5}-\frac{\left(\munderset{\textit{\_R} =\RootOf \left(8 \textit{\_Z}^{4}+28 \textit{\_Z}^{2}+25\right)}{\sum}\textit{\_R} \ln \left(5 \left(-\sqrt{2}\, x +\sqrt{2 x^{2}+1}\right)^{2}+\left(-24 \textit{\_R}^{3}-44 \textit{\_R} \right) \left(-\sqrt{2}\, x +\sqrt{2 x^{2}+1}\right)+5\right)\right)}{10}-\frac{3 \sqrt{2}\, \arcsinh \left(\sqrt{2}\, x \right)}{8}+\frac{\arctan \left(\frac{-2 \sqrt{2}\, \sqrt{\sqrt{2}-1}+8 x}{2 \sqrt{2+2 \sqrt{2}}}\right)}{5 \sqrt{2+2 \sqrt{2}}}+\frac{\arctan \left(\frac{2 \sqrt{2}\, \sqrt{\sqrt{2}-1}+8 x}{2 \sqrt{2+2 \sqrt{2}}}\right)}{5 \sqrt{2+2 \sqrt{2}}}\]"," ",0,"1/40*x*(2*x^2+1)^(3/2)-1/20*(2*x^2+1)^(1/2)*x-1/20*2^(1/2)*x^2-1/320*2^(1/2)-1/10*2^(1/2)*x^4-1/10*2^(1/2)*x-1/10*(2*x^2+1)^(1/2)-1/5*arctan(x)+1/5*ln(x^2+1)-2*ln(x)-x^2+1/20*sum(_R*ln(35*(-2^(1/2)*x+(2*x^2+1)^(1/2))^2+(4*_R^3-26*_R)*(-2^(1/2)*x+(2*x^2+1)^(1/2))+35),_R=RootOf(2*_Z^4+2*_Z^2+25))+4/5/(-2+2*2^(1/2))*arctan(2*(-2^(1/2)*x+(2*x^2+1)^(1/2))^2/(-2+2*2^(1/2)))*2^(1/2)-3/20*ln((-2^(1/2)*x+(2*x^2+1)^(1/2))^4+2*2^(1/2)+3)+4/5/(2+2*2^(1/2))*arctan(2*(-2^(1/2)*x+(2*x^2+1)^(1/2))^2/(2+2*2^(1/2)))*2^(1/2)+4/5/(2+2*2^(1/2))*arctan(2*(-2^(1/2)*x+(2*x^2+1)^(1/2))^2/(2+2*2^(1/2)))-4/5/(-2+2*2^(1/2))*arctan(2*(-2^(1/2)*x+(2*x^2+1)^(1/2))^2/(-2+2*2^(1/2)))+2/5*arctanh(x/(2*x^2+1)^(1/2))+3/20*ln((-2^(1/2)*x+(2*x^2+1)^(1/2))^4+3-2*2^(1/2))-3/8*2^(1/2)*arcsinh(2^(1/2)*x)+1/8*2^(1/2)*ln(-2^(1/2)*x+(2*x^2+1)^(1/2))+3/20*ln(8*x^4+4*x^2+1)-2/5*arctan(4*x^2+1)-3/40*ln(2^(1/2)+2*(2^(1/2)-1)^(1/2)*2^(1/2)*x+4*x^2)*(2^(1/2)-1)^(1/2)+3/40*ln(-2*(2^(1/2)-1)^(1/2)*2^(1/2)*x+4*x^2+2^(1/2))*(2^(1/2)-1)^(1/2)-3/20*x^3*(2*x^2+1)^(1/2)+1/320*2^(1/2)/(-2^(1/2)*x+(2*x^2+1)^(1/2))^4-1/40*ln(2^(1/2)+2*(2^(1/2)-1)^(1/2)*2^(1/2)*x+4*x^2)*2^(1/2)*(2^(1/2)-1)^(1/2)+1/20/(2+2*2^(1/2))^(1/2)*arctan(1/2*(2*2^(1/2)*(2^(1/2)-1)^(1/2)+8*x)/(2+2*2^(1/2))^(1/2))*2^(1/2)+1/40*ln(-2*(2^(1/2)-1)^(1/2)*2^(1/2)*x+4*x^2+2^(1/2))*2^(1/2)*(2^(1/2)-1)^(1/2)+1/20/(2+2*2^(1/2))^(1/2)*arctan(1/2*(-2*2^(1/2)*(2^(1/2)-1)^(1/2)+8*x)/(2+2*2^(1/2))^(1/2))*2^(1/2)+1/10/(-2^(1/2)*x+(2*x^2+1)^(1/2))-1/10*sum(_R*ln(5*(-2^(1/2)*x+(2*x^2+1)^(1/2))^2+(-24*_R^3-44*_R)*(-2^(1/2)*x+(2*x^2+1)^(1/2))+5),_R=RootOf(8*_Z^4+28*_Z^2+25))+1/5*arctan((2*x^2+1)^(1/2))+1/5/(2+2*2^(1/2))^(1/2)*arctan(1/2*(-2*2^(1/2)*(2^(1/2)-1)^(1/2)+8*x)/(2+2*2^(1/2))^(1/2))+1/5/(2+2*2^(1/2))^(1/2)*arctan(1/2*(2*2^(1/2)*(2^(1/2)-1)^(1/2)+8*x)/(2+2*2^(1/2))^(1/2))","B"
2927,0,0,311,0.011000," ","int((x^3-b)*(x^3+b)*(x^3-c)/(a*x^2+x^3)^(1/3),x)","\[\int \frac{\left(x^{3}-b \right) \left(x^{3}+b \right) \left(x^{3}-c \right)}{\left(a \,x^{2}+x^{3}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((x^3-b)*(x^3+b)*(x^3-c)/(a*x^2+x^3)^(1/3),x)","F"
2928,0,0,300,0.026000," ","int(x*(-a+x)*(-b+x)*(a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^2)^(2/3)/(-b^2+2*b*x-(-a^2*d+1)*x^2-2*a*d*x^3+d*x^4),x)","\[\int \frac{x \left(-a +x \right) \left(-b +x \right) \left(a b -2 b x +x^{2}\right)}{\left(x \left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{2}{3}} \left(-b^{2}+2 b x -\left(-a^{2} d +1\right) x^{2}-2 a d \,x^{3}+d \,x^{4}\right)}\, dx\]"," ",0,"int(x*(-a+x)*(-b+x)*(a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^2)^(2/3)/(-b^2+2*b*x-(-a^2*d+1)*x^2-2*a*d*x^3+d*x^4),x)","F"
2929,0,0,101,0.012000," ","int((x^4-a*x^2-b)*(a*x^4-b*x^2)^(1/4)/(a*x^4+b),x)","\[\int \frac{\left(x^{4}-a \,x^{2}-b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}{a \,x^{4}+b}\, dx\]"," ",0,"int((x^4-a*x^2-b)*(a*x^4-b*x^2)^(1/4)/(a*x^4+b),x)","F"
2930,0,0,101,0.005000," ","int((x^4-a*x^2-b)*(a*x^4-b*x^2)^(1/4)/(a*x^4+b),x)","\[\int \frac{\left(x^{4}-a \,x^{2}-b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}{a \,x^{4}+b}\, dx\]"," ",0,"int((x^4-a*x^2-b)*(a*x^4-b*x^2)^(1/4)/(a*x^4+b),x)","F"
2931,1,520,47,0.635000," ","int((a^2*x^2+a*b*c-b^2*x)/(a*x^2+b*x+c)^(1/2)/(b*x^2+c),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{a^{\frac{3}{2}} \ln \left(\frac{\frac{b}{2}+a x}{\sqrt{a}}+\sqrt{a \,x^{2}+b x +c}\right)}{b}-\frac{\left(a \,b^{2} c -\sqrt{-b c}\, b^{2}-a^{2} c \right) \ln \left(\frac{-\frac{2 \left(-\sqrt{-b c}\, b +a c -b c \right)}{b}+\frac{\sqrt{-b c}\, \left(-\sqrt{-b c}\, b +2 a c \right) \left(x -\frac{\sqrt{-b c}}{b}\right)}{b c}+2 \sqrt{-\frac{-\sqrt{-b c}\, b +a c -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-b c}}{b}\right)^{2} a +\frac{\sqrt{-b c}\, \left(-\sqrt{-b c}\, b +2 a c \right) \left(x -\frac{\sqrt{-b c}}{b}\right)}{b c}-\frac{-\sqrt{-b c}\, b +a c -b c}{b}}}{x -\frac{\sqrt{-b c}}{b}}\right)}{2 \sqrt{-b c}\, b \sqrt{-\frac{-\sqrt{-b c}\, b +a c -b c}{b}}}-\frac{\left(-a \,b^{2} c -\sqrt{-b c}\, b^{2}+a^{2} c \right) \ln \left(\frac{-\frac{2 \left(\sqrt{-b c}\, b +a c -b c \right)}{b}-\frac{\sqrt{-b c}\, \left(\sqrt{-b c}\, b +2 a c \right) \left(x +\frac{\sqrt{-b c}}{b}\right)}{b c}+2 \sqrt{-\frac{\sqrt{-b c}\, b +a c -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-b c}}{b}\right)^{2} a -\frac{\sqrt{-b c}\, \left(\sqrt{-b c}\, b +2 a c \right) \left(x +\frac{\sqrt{-b c}}{b}\right)}{b c}-\frac{\sqrt{-b c}\, b +a c -b c}{b}}}{x +\frac{\sqrt{-b c}}{b}}\right)}{2 \sqrt{-b c}\, b \sqrt{-\frac{\sqrt{-b c}\, b +a c -b c}{b}}}$&$520$\\ \hline \end{longtable}"," ",0,"a^(3/2)/b*ln((1/2*b+a*x)/a^(1/2)+(a*x^2+b*x+c)^(1/2))-1/2*(a*b^2*c-(-b*c)^(1/2)*b^2-a^2*c)/(-b*c)^(1/2)/b/(-(-(-b*c)^(1/2)*b+a*c-b*c)/b)^(1/2)*ln((-2*(-(-b*c)^(1/2)*b+a*c-b*c)/b+(-b*c)^(1/2)/b/c*(-(-b*c)^(1/2)*b+2*a*c)*(x-(-b*c)^(1/2)/b)+2*(-(-(-b*c)^(1/2)*b+a*c-b*c)/b)^(1/2)*((x-(-b*c)^(1/2)/b)^2*a+(-b*c)^(1/2)/b/c*(-(-b*c)^(1/2)*b+2*a*c)*(x-(-b*c)^(1/2)/b)-(-(-b*c)^(1/2)*b+a*c-b*c)/b)^(1/2))/(x-(-b*c)^(1/2)/b))-1/2*(-a*b^2*c-(-b*c)^(1/2)*b^2+a^2*c)/(-b*c)^(1/2)/b/(-((-b*c)^(1/2)*b+a*c-b*c)/b)^(1/2)*ln((-2*((-b*c)^(1/2)*b+a*c-b*c)/b-(-b*c)^(1/2)/b/c*((-b*c)^(1/2)*b+2*a*c)*(x+(-b*c)^(1/2)/b)+2*(-((-b*c)^(1/2)*b+a*c-b*c)/b)^(1/2)*((x+(-b*c)^(1/2)/b)^2*a-(-b*c)^(1/2)/b/c*((-b*c)^(1/2)*b+2*a*c)*(x+(-b*c)^(1/2)/b)-((-b*c)^(1/2)*b+a*c-b*c)/b)^(1/2))/(x+(-b*c)^(1/2)/b))","B"
2932,0,0,101,0.018000," ","int((x^4+a*x^2+b)*(a*x^4-b*x^2)^(1/4)/(a*x^4-b),x)","\[\int \frac{\left(x^{4}+a \,x^{2}+b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}{a \,x^{4}-b}\, dx\]"," ",0,"int((x^4+a*x^2+b)*(a*x^4-b*x^2)^(1/4)/(a*x^4-b),x)","F"
2933,0,0,101,0.005000," ","int((x^4+a*x^2+b)*(a*x^4-b*x^2)^(1/4)/(a*x^4-b),x)","\[\int \frac{\left(x^{4}+a \,x^{2}+b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}{a \,x^{4}-b}\, dx\]"," ",0,"int((x^4+a*x^2+b)*(a*x^4-b*x^2)^(1/4)/(a*x^4-b),x)","F"
2934,0,0,272,0.102000," ","int((-1+(-1+2*k)*x)*(x^2-2*x+1)/((1-x)*x*(-k*x+1))^(1/3)/(-b+4*b*x+(1-6*b)*x^2+(4*b-2*k)*x^3+(k^2-b)*x^4),x)","\[\int \frac{\left(-1+\left(-1+2 k \right) x \right) \left(x^{2}-2 x +1\right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(-b +4 b x +\left(1-6 b \right) x^{2}+\left(4 b -2 k \right) x^{3}+\left(k^{2}-b \right) x^{4}\right)}\, dx\]"," ",0,"int((-1+(-1+2*k)*x)*(x^2-2*x+1)/((1-x)*x*(-k*x+1))^(1/3)/(-b+4*b*x+(1-6*b)*x^2+(4*b-2*k)*x^3+(k^2-b)*x^4),x)","F"
2935,0,0,263,0.092000," ","int(1/(a*x+b)/(a^2*x^3+b^2*x)^(1/4),x)","\[\int \frac{1}{\left(a x +b \right) \left(a^{2} x^{3}+b^{2} x \right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(a*x+b)/(a^2*x^3+b^2*x)^(1/4),x)","F"
2936,0,0,97,0.013000," ","int((a*x^4-b)*(a*x^4-b*x^2)^(1/4)/(x^4-a*x^2-b),x)","\[\int \frac{\left(a \,x^{4}-b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}{x^{4}-a \,x^{2}-b}\, dx\]"," ",0,"int((a*x^4-b)*(a*x^4-b*x^2)^(1/4)/(x^4-a*x^2-b),x)","F"
2937,0,0,97,0.005000," ","int((a*x^4-b)*(a*x^4-b*x^2)^(1/4)/(x^4-a*x^2-b),x)","\[\int \frac{\left(a \,x^{4}-b \right) \left(a \,x^{4}-b \,x^{2}\right)^{\frac{1}{4}}}{x^{4}-a \,x^{2}-b}\, dx\]"," ",0,"int((a*x^4-b)*(a*x^4-b*x^2)^(1/4)/(x^4-a*x^2-b),x)","F"
2938,0,0,303,0.020000," ","int((-b+x)*(-4*a+b+3*x)/((-a+x)*(-b+x)^2)^(1/3)/(a+b^4*d-(4*b^3*d+1)*x+6*b^2*d*x^2-4*b*d*x^3+d*x^4),x)","\[\int \frac{\left(-b +x \right) \left(-4 a +b +3 x \right)}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{3}} \left(a +b^{4} d -\left(4 b^{3} d +1\right) x +6 b^{2} d \,x^{2}-4 b d \,x^{3}+d \,x^{4}\right)}\, dx\]"," ",0,"int((-b+x)*(-4*a+b+3*x)/((-a+x)*(-b+x)^2)^(1/3)/(a+b^4*d-(4*b^3*d+1)*x+6*b^2*d*x^2-4*b*d*x^3+d*x^4),x)","F"
2939,0,0,90,180.000000," ","int((c*x^2+d)*(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)/(e*x^2+f),x)","\[\int \frac{\left(c \,x^{2}+d \right) \sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}{e \,x^{2}+f}\, dx\]"," ",0,"int((c*x^2+d)*(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)/(e*x^2+f),x)","F"
2940,0,0,14,0.040000," ","int((x^2+1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1),x)","\[\int \frac{\left(x^{2}+1\right) \sqrt{x^{2}+\sqrt{x^{4}+1}}}{\sqrt{x^{4}+1}\, \left(x^{4}+x^{2}-1\right)}\, dx\]"," ",0,"int((x^2+1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1),x)","F"
2941,0,0,14,0.005000," ","int((x^2+1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1),x)","\[\int \frac{\left(x^{2}+1\right) \sqrt{x^{2}+\sqrt{x^{4}+1}}}{\sqrt{x^{4}+1}\, \left(x^{4}+x^{2}-1\right)}\, dx\]"," ",0,"int((x^2+1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1),x)","F"
2942,1,2140,265,73.110000," ","int((-x^4+1)/(x^4+x^2+1)/(x^5-x^3)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2140$\\ \hline \end{longtable}"," ",0,"1/6*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*ln(-108*(16*x^4*RootOf(_Z^8+2187)^8*RootOf(_Z^2+RootOf(_Z^8+2187)^2)-24*x^3*RootOf(_Z^8+2187)^8*RootOf(_Z^2+RootOf(_Z^8+2187)^2)-16*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)^8*x^2-54*(x^5-x^3)^(1/2)*RootOf(_Z^8+2187)^6*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*x-162*(x^5-x^3)^(1/4)*RootOf(_Z^8+2187)^6*x^2+1350*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)^4*x^4+243*x^3*RootOf(_Z^8+2187)^4*RootOf(_Z^2+RootOf(_Z^8+2187)^2)+8100*(x^5-x^3)^(3/4)*RootOf(_Z^8+2187)^4-1350*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)^4*x^2-24300*(x^5-x^3)^(1/2)*RootOf(_Z^8+2187)^2*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*x-72900*(x^5-x^3)^(1/4)*RootOf(_Z^8+2187)^2*x^2+28431*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*x^4+56862*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*x^3-39366*(x^5-x^3)^(3/4)-28431*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*x^2)/x^2/(x*RootOf(_Z^8+2187)^4-2*RootOf(_Z^8+2187)^4-135*x-108)/(x*RootOf(_Z^8+2187)^4-2*RootOf(_Z^8+2187)^4-81*x))+1/6*RootOf(_Z^8+2187)*ln(-108*(16*RootOf(_Z^8+2187)^9*x^4-24*RootOf(_Z^8+2187)^9*x^3-16*RootOf(_Z^8+2187)^9*x^2+54*(x^5-x^3)^(1/2)*RootOf(_Z^8+2187)^7*x+162*(x^5-x^3)^(1/4)*RootOf(_Z^8+2187)^6*x^2+1350*RootOf(_Z^8+2187)^5*x^4+243*RootOf(_Z^8+2187)^5*x^3+8100*(x^5-x^3)^(3/4)*RootOf(_Z^8+2187)^4-1350*RootOf(_Z^8+2187)^5*x^2+24300*(x^5-x^3)^(1/2)*RootOf(_Z^8+2187)^3*x+72900*(x^5-x^3)^(1/4)*RootOf(_Z^8+2187)^2*x^2+28431*RootOf(_Z^8+2187)*x^4+56862*RootOf(_Z^8+2187)*x^3-39366*(x^5-x^3)^(3/4)-28431*RootOf(_Z^8+2187)*x^2)/x^2/(x*RootOf(_Z^8+2187)^4-2*RootOf(_Z^8+2187)^4-135*x-108)/(x*RootOf(_Z^8+2187)^4-2*RootOf(_Z^8+2187)^4-81*x))+1/13122*RootOf(_Z^8+2187)^7*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*ln(-108*(26*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^11*x^4-39*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^11*x^3-26*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)^11*x^2+243*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^7*x^4-4050*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^7*x^3-243*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^7*x^2+4374*(x^5-x^3)^(1/2)*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^6*x+13122*(x^5-x^3)^(1/4)*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)^5*x^2-52488*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^3*x^4-104976*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)^3*x^3+656100*(x^5-x^3)^(3/4)*RootOf(_Z^8+2187)^4+52488*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^3*x^2-1968300*(x^5-x^3)^(1/2)*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^2*x-5904900*(x^5-x^3)^(1/4)*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)*x^2+3188646*(x^5-x^3)^(3/4))/x^2/(x*RootOf(_Z^8+2187)^4-2*RootOf(_Z^8+2187)^4+81*x)/(x*RootOf(_Z^8+2187)^4-2*RootOf(_Z^8+2187)^4+135*x+108))+1/6*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*ln(-108*(-16*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^8*x^4+24*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^8*x^3+16*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^8*x^2-54*(x^5-x^3)^(1/2)*RootOf(_Z^8+2187)^5*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*x-162*(x^5-x^3)^(1/4)*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)^5*x^2+1350*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^4*x^4+243*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^4*x^3+8100*(x^5-x^3)^(3/4)*RootOf(_Z^8+2187)^4-1350*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^4*x^2+24300*(x^5-x^3)^(1/2)*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)*x+72900*(x^5-x^3)^(1/4)*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)*x^2-28431*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*x^4-56862*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*x^3+39366*(x^5-x^3)^(3/4)+28431*RootOf(_Z^2+RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*x^2)/x^2/(x*RootOf(_Z^8+2187)^4-2*RootOf(_Z^8+2187)^4+81*x)/(x*RootOf(_Z^8+2187)^4-2*RootOf(_Z^8+2187)^4+135*x+108))","C"
2943,0,0,269,0.040000," ","int((a^2*x^2-b)^(1/2)/(a*x^2+x*(a^2*x^2-b)^(1/2))^(1/3),x)","\[\int \frac{\sqrt{a^{2} x^{2}-b}}{\left(a \,x^{2}+x \sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a^2*x^2-b)^(1/2)/(a*x^2+x*(a^2*x^2-b)^(1/2))^(1/3),x)","F"
2944,0,0,82,180.000000," ","int((a^2*x^2+b)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^2-b)/(a^2*x^4+b)^(1/2),x)","\[\int \frac{\left(a^{2} x^{2}+b \right) \sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}{\left(a^{2} x^{2}-b \right) \sqrt{a^{2} x^{4}+b}}\, dx\]"," ",0,"int((a^2*x^2+b)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^2-b)/(a^2*x^4+b)^(1/2),x)","F"
2945,0,0,82,180.000000," ","int((a^2*x^2+b)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^2-b)/(a^2*x^4+b)^(1/2),x)","\[\int \frac{\left(a^{2} x^{2}+b \right) \sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}{\left(a^{2} x^{2}-b \right) \sqrt{a^{2} x^{4}+b}}\, dx\]"," ",0,"int((a^2*x^2+b)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^2-b)/(a^2*x^4+b)^(1/2),x)","F"
2946,0,0,299,0.089000," ","int(x^3/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2)/(-x^6+1),x)","\[\int \frac{x^{3}}{\sqrt{a \,x^{4}+b \,x^{3}+c \,x^{2}+b x +a}\, \left(-x^{6}+1\right)}\, dx\]"," ",0,"int(x^3/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2)/(-x^6+1),x)","F"
2947,0,0,342,0.032000," ","int((2*p*x^3-q)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)*(b*x^6+a*(p*x^3+q)^6)/x^9,x)","\[\int \frac{\left(2 p \,x^{3}-q \right) \sqrt{p^{2} x^{6}+2 p q \,x^{3}-2 p q \,x^{2}+q^{2}}\, \left(b \,x^{6}+a \left(p \,x^{3}+q \right)^{6}\right)}{x^{9}}\, dx\]"," ",0,"int((2*p*x^3-q)*(p^2*x^6+2*p*q*x^3-2*p*q*x^2+q^2)^(1/2)*(b*x^6+a*(p*x^3+q)^6)/x^9,x)","F"
2948,0,0,342,0.043000," ","int((p*x^3-2*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)*(b*x^12+a*(p*x^3+q)^6)/x^17,x)","\[\int \frac{\left(p \,x^{3}-2 q \right) \sqrt{p^{2} x^{6}-2 x^{4} p q +2 p q \,x^{3}+q^{2}}\, \left(b \,x^{12}+a \left(p \,x^{3}+q \right)^{6}\right)}{x^{17}}\, dx\]"," ",0,"int((p*x^3-2*q)*(p^2*x^6-2*p*q*x^4+2*p*q*x^3+q^2)^(1/2)*(b*x^12+a*(p*x^3+q)^6)/x^17,x)","F"
2949,1,191,11,0.197000," ","int((p*x^4-q)*(p*x^4+q)^(1/2)/(b*x^4+a*(p*x^4+q)^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(\frac{\ln \left(\frac{\frac{p \,x^{4}+q}{2 x^{2}}-\frac{\left(\frac{b}{a}\right)^{\frac{1}{4}} \sqrt{p \,x^{4}+q}\, \sqrt{2}}{2 x}+\frac{\sqrt{\frac{b}{a}}}{2}}{\frac{p \,x^{4}+q}{2 x^{2}}+\frac{\left(\frac{b}{a}\right)^{\frac{1}{4}} \sqrt{p \,x^{4}+q}\, \sqrt{2}}{2 x}+\frac{\sqrt{\frac{b}{a}}}{2}}\right)}{4 a \left(\frac{b}{a}\right)^{\frac{1}{4}}}+\frac{\arctan \left(\frac{\sqrt{p \,x^{4}+q}\, \sqrt{2}}{\left(\frac{b}{a}\right)^{\frac{1}{4}} x}+1\right)}{2 a \left(\frac{b}{a}\right)^{\frac{1}{4}}}+\frac{\arctan \left(\frac{\sqrt{p \,x^{4}+q}\, \sqrt{2}}{\left(\frac{b}{a}\right)^{\frac{1}{4}} x}-1\right)}{2 a \left(\frac{b}{a}\right)^{\frac{1}{4}}}\right) \sqrt{2}}{2}$&$191$\\ elliptic&$\frac{\left(\frac{\ln \left(\frac{\frac{p \,x^{4}+q}{2 x^{2}}-\frac{\left(\frac{b}{a}\right)^{\frac{1}{4}} \sqrt{p \,x^{4}+q}\, \sqrt{2}}{2 x}+\frac{\sqrt{\frac{b}{a}}}{2}}{\frac{p \,x^{4}+q}{2 x^{2}}+\frac{\left(\frac{b}{a}\right)^{\frac{1}{4}} \sqrt{p \,x^{4}+q}\, \sqrt{2}}{2 x}+\frac{\sqrt{\frac{b}{a}}}{2}}\right)}{4 a \left(\frac{b}{a}\right)^{\frac{1}{4}}}+\frac{\arctan \left(\frac{\sqrt{p \,x^{4}+q}\, \sqrt{2}}{\left(\frac{b}{a}\right)^{\frac{1}{4}} x}+1\right)}{2 a \left(\frac{b}{a}\right)^{\frac{1}{4}}}+\frac{\arctan \left(\frac{\sqrt{p \,x^{4}+q}\, \sqrt{2}}{\left(\frac{b}{a}\right)^{\frac{1}{4}} x}-1\right)}{2 a \left(\frac{b}{a}\right)^{\frac{1}{4}}}\right) \sqrt{2}}{2}$&$191$\\ \hline \end{longtable}"," ",0,"1/2*(1/4/a/(b/a)^(1/4)*ln((1/2*(p*x^4+q)/x^2-1/2*(b/a)^(1/4)*(p*x^4+q)^(1/2)*2^(1/2)/x+1/2*(b/a)^(1/2))/(1/2*(p*x^4+q)/x^2+1/2*(b/a)^(1/4)*(p*x^4+q)^(1/2)*2^(1/2)/x+1/2*(b/a)^(1/2)))+1/2/a/(b/a)^(1/4)*arctan(1/(b/a)^(1/4)*(p*x^4+q)^(1/2)*2^(1/2)/x+1)+1/2/a/(b/a)^(1/4)*arctan(1/(b/a)^(1/4)*(p*x^4+q)^(1/2)*2^(1/2)/x-1))*2^(1/2)","B"
2950,0,0,277,0.091000," ","int((a*x-3*b)/(-a^2*x^2+b^2)^(1/3)/(a^2*x^2+3*b^2),x)","\[\int \frac{a x -3 b}{\left(-a^{2} x^{2}+b^{2}\right)^{\frac{1}{3}} \left(a^{2} x^{2}+3 b^{2}\right)}\, dx\]"," ",0,"int((a*x-3*b)/(-a^2*x^2+b^2)^(1/3)/(a^2*x^2+3*b^2),x)","F"
2951,1,494,64,0.031000," ","int((x+(2*x^5+5*x^4+8*x^3+7*x^2+4*x+1)^(1/2))/(1-(2*x^5+5*x^4+8*x^3+7*x^2+4*x+1)^(1/2)),x)","\[-\frac{4 \left(\munderset{\textit{\_R} =\RootOf \left(\sqrt{2 x^{5}+5 x^{4}+8 x^{3}+7 x^{2}+4 x +1}\, \textit{\_Z}^{5}-4 \sqrt{1+2 x}\, x^{2}+3 \sqrt{2 x^{5}+5 x^{4}+8 x^{3}+7 x^{2}+4 x +1}\, \textit{\_Z} -4 \sqrt{1+2 x}\, x -4 \sqrt{1+2 x}\right)}{\sum}\frac{\textit{\_R} \left(\textit{\_R}^{2}+1\right) \ln \left(\sqrt{1+2 x}-\textit{\_R} \right)}{5 \textit{\_R}^{4}+3}\right) \sqrt{1+2 x}\, x^{2}+4 \left(\munderset{\textit{\_R} =\RootOf \left(\sqrt{2 x^{5}+5 x^{4}+8 x^{3}+7 x^{2}+4 x +1}\, \textit{\_Z}^{5}-4 \sqrt{1+2 x}\, x^{2}+3 \sqrt{2 x^{5}+5 x^{4}+8 x^{3}+7 x^{2}+4 x +1}\, \textit{\_Z} -4 \sqrt{1+2 x}\, x -4 \sqrt{1+2 x}\right)}{\sum}\frac{\textit{\_R} \left(\textit{\_R}^{2}+1\right) \ln \left(\sqrt{1+2 x}-\textit{\_R} \right)}{5 \textit{\_R}^{4}+3}\right) \sqrt{1+2 x}\, x +2 x \sqrt{2 x^{5}+5 x^{4}+8 x^{3}+7 x^{2}+4 x +1}+4 \sqrt{1+2 x}\, \left(\munderset{\textit{\_R} =\RootOf \left(\sqrt{2 x^{5}+5 x^{4}+8 x^{3}+7 x^{2}+4 x +1}\, \textit{\_Z}^{5}-4 \sqrt{1+2 x}\, x^{2}+3 \sqrt{2 x^{5}+5 x^{4}+8 x^{3}+7 x^{2}+4 x +1}\, \textit{\_Z} -4 \sqrt{1+2 x}\, x -4 \sqrt{1+2 x}\right)}{\sum}\frac{\textit{\_R} \left(\textit{\_R}^{2}+1\right) \ln \left(\sqrt{1+2 x}-\textit{\_R} \right)}{5 \textit{\_R}^{4}+3}\right)+\sqrt{2 x^{5}+5 x^{4}+8 x^{3}+7 x^{2}+4 x +1}}{2 \sqrt{2 x^{5}+5 x^{4}+8 x^{3}+7 x^{2}+4 x +1}}\]"," ",0,"-1/2*(4*sum(_R*(_R^2+1)*ln((1+2*x)^(1/2)-_R)/(5*_R^4+3),_R=RootOf((2*x^5+5*x^4+8*x^3+7*x^2+4*x+1)^(1/2)*_Z^5-4*(1+2*x)^(1/2)*x^2+3*(2*x^5+5*x^4+8*x^3+7*x^2+4*x+1)^(1/2)*_Z-4*(1+2*x)^(1/2)*x-4*(1+2*x)^(1/2)))*(1+2*x)^(1/2)*x^2+4*sum(_R*(_R^2+1)*ln((1+2*x)^(1/2)-_R)/(5*_R^4+3),_R=RootOf((2*x^5+5*x^4+8*x^3+7*x^2+4*x+1)^(1/2)*_Z^5-4*(1+2*x)^(1/2)*x^2+3*(2*x^5+5*x^4+8*x^3+7*x^2+4*x+1)^(1/2)*_Z-4*(1+2*x)^(1/2)*x-4*(1+2*x)^(1/2)))*(1+2*x)^(1/2)*x+2*x*(2*x^5+5*x^4+8*x^3+7*x^2+4*x+1)^(1/2)+4*(1+2*x)^(1/2)*sum(_R*(_R^2+1)*ln((1+2*x)^(1/2)-_R)/(5*_R^4+3),_R=RootOf((2*x^5+5*x^4+8*x^3+7*x^2+4*x+1)^(1/2)*_Z^5-4*(1+2*x)^(1/2)*x^2+3*(2*x^5+5*x^4+8*x^3+7*x^2+4*x+1)^(1/2)*_Z-4*(1+2*x)^(1/2)*x-4*(1+2*x)^(1/2)))+(2*x^5+5*x^4+8*x^3+7*x^2+4*x+1)^(1/2))/(2*x^5+5*x^4+8*x^3+7*x^2+4*x+1)^(1/2)","B"
2952,0,0,305,0.023000," ","int(x^3*(4*a*b-3*(a+b)*x+2*x^2)/(x^2*(-a+x)*(-b+x))^(2/3)/(-a*b*d+(a+b)*d*x-d*x^2+x^4),x)","\[\int \frac{x^{3} \left(4 a b -3 \left(a +b \right) x +2 x^{2}\right)}{\left(x^{2} \left(-a +x \right) \left(-b +x \right)\right)^{\frac{2}{3}} \left(-a b d +\left(a +b \right) d x -d \,x^{2}+x^{4}\right)}\, dx\]"," ",0,"int(x^3*(4*a*b-3*(a+b)*x+2*x^2)/(x^2*(-a+x)*(-b+x))^(2/3)/(-a*b*d+(a+b)*d*x-d*x^2+x^4),x)","F"
2953,1,2401,276,59.645000," ","int(x^3/(x^4+x^2)^(1/3)/(x^6-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2401$\\ \hline \end{longtable}"," ",0,"1/4*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*ln((-1051752*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^4+7172976*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^4+4469946*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^2-30485148*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^2+34713150*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*(x^4+x^2)^(2/3)-5785525*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^2*x^2-20043774*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^2+1095575*RootOf(_Z^3-4)*x^4-7471850*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^4-1051752*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3+7172976*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2-5785525*RootOf(_Z^3-4)^2*(x^4+x^2)^(1/3)-20043774*(x^4+x^2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)+9378122*RootOf(_Z^3-4)*x^2-63959036*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^2+9779584*(x^4+x^2)^(2/3)+1095575*RootOf(_Z^3-4)-7471850*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(-1+x)^2/(1+x)^2)+1/24*RootOf(_Z^3-4)*ln(-(3586488*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^4-18931536*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^4-15242574*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3*x^2+80459028*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2*x^2+104139450*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*(x^4+x^2)^(2/3)-17356575*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^2*x^2-44008128*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^2+6126917*RootOf(_Z^3-4)*x^4-32341374*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^4+3586488*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^3-18931536*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^2-17356575*RootOf(_Z^3-4)^2*(x^4+x^2)^(1/3)-44008128*(x^4+x^2)^(1/3)*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)+21817802*RootOf(_Z^3-4)*x^2-115166844*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^2+40087548*(x^4+x^2)^(2/3)+6126917*RootOf(_Z^3-4)-32341374*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2))/(-1+x)^2/(1+x)^2)-1/6*ln((545052*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^4*x^4-2316471*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^4*x^2-1675418*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*x^4-8496*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^2*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^2+545052*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^4+6133350*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*(x^4+x^2)^(2/3)-9707954*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*x^2-8496*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*(x^4+x^2)^(1/3)-2481800*x^4+4083236*(x^4+x^2)^(1/3)*x^2-1675418*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2+5664*(x^4+x^2)^(2/3)-7842488*x^2+4083236*(x^4+x^2)^(1/3)-2481800)/(x^2+x+1)/(x^2-x+1))+1/6*ln(-(-348396*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^4*x^4+1480683*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^4*x^2-2279546*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*x^4-6124854*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^2*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^2-348396*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^4+6133350*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*(x^4+x^2)^(2/3)-1068656*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*x^2-6124854*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*(x^4+x^2)^(1/3)-2878888*x^4+5664*(x^4+x^2)^(1/3)*x^2-2279546*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2+4083236*(x^4+x^2)^(2/3)-6154864*x^2+5664*(x^4+x^2)^(1/3)-2878888)/(x^2+x+1)/(x^2-x+1))+1/4*ln(-(-348396*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^4*x^4+1480683*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^4*x^2-2279546*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*x^4-6124854*(x^4+x^2)^(1/3)*RootOf(_Z^3-4)^2*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*x^2-348396*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)^2*RootOf(_Z^3-4)^4+6133350*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*(x^4+x^2)^(2/3)-1068656*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*x^2-6124854*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2*(x^4+x^2)^(1/3)-2878888*x^4+5664*(x^4+x^2)^(1/3)*x^2-2279546*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2+4083236*(x^4+x^2)^(2/3)-6154864*x^2+5664*(x^4+x^2)^(1/3)-2878888)/(x^2+x+1)/(x^2-x+1))*RootOf(RootOf(_Z^3-4)^2+6*_Z*RootOf(_Z^3-4)+36*_Z^2)*RootOf(_Z^3-4)^2","C"
2954,0,0,105,0.074000," ","int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x^2+1)^(1/2),x)","\[\int \frac{\sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right)^{2} \sqrt{x^{2}+1}}\, dx\]"," ",0,"int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x^2+1)^(1/2),x)","F"
2955,0,0,105,0.004000," ","int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x^2+1)^(1/2),x)","\[\int \frac{\sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right)^{2} \sqrt{x^{2}+1}}\, dx\]"," ",0,"int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x^2+1)^(1/2),x)","F"
2956,0,0,105,0.068000," ","int((x^2+1)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","\[\int \frac{\sqrt{x^{2}+1}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right)^{2}}\, dx\]"," ",0,"int((x^2+1)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","F"
2957,0,0,105,0.005000," ","int((x^2+1)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","\[\int \frac{\sqrt{x^{2}+1}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right)^{2}}\, dx\]"," ",0,"int((x^2+1)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","F"
2958,0,0,105,0.003000," ","int((x^2+1)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","\[\int \frac{\sqrt{x^{2}+1}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right)^{2}}\, dx\]"," ",0,"int((x^2+1)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","F"
2959,1,555,330,0.433000," ","int((a*x^2+b*x+c)^(5/2)/(b*x+c)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(48 a^{3} x^{3} b^{3}-128 a^{3} b^{2} c \,x^{2}+136 a^{2} b^{4} x^{2}+288 a^{3} b \,c^{2} x -200 a^{2} b^{3} c x +118 a \,b^{5} x -768 a^{3} c^{3}+400 a^{2} b^{2} c^{2}+28 a \,b^{4} c +15 b^{6}\right) \sqrt{a \,x^{2}+b x +c}}{192 a \,b^{5}}+\frac{5 a^{\frac{5}{2}} \ln \left(\frac{\frac{b}{2}+a x}{\sqrt{a}}+\sqrt{a \,x^{2}+b x +c}\right) c^{4}}{b^{6}}-\frac{5 a^{\frac{3}{2}} \ln \left(\frac{\frac{b}{2}+a x}{\sqrt{a}}+\sqrt{a \,x^{2}+b x +c}\right) c^{3}}{2 b^{4}}+\frac{5 \ln \left(\frac{\frac{b}{2}+a x}{\sqrt{a}}+\sqrt{a \,x^{2}+b x +c}\right) c}{16 \sqrt{a}}-\frac{5 b^{2} \ln \left(\frac{\frac{b}{2}+a x}{\sqrt{a}}+\sqrt{a \,x^{2}+b x +c}\right)}{128 a^{\frac{3}{2}}}-\frac{a^{2} c^{4} \sqrt{\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}}}{b^{6} \left(x +\frac{c}{b}\right)}+\frac{5 a^{3} c^{5} \ln \left(\frac{\frac{2 a \,c^{2}}{b^{2}}-\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+2 \sqrt{\frac{a \,c^{2}}{b^{2}}}\, \sqrt{\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}}}{x +\frac{c}{b}}\right)}{b^{7} \sqrt{\frac{a \,c^{2}}{b^{2}}}}-\frac{5 a^{2} c^{4} \ln \left(\frac{\frac{2 a \,c^{2}}{b^{2}}-\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+2 \sqrt{\frac{a \,c^{2}}{b^{2}}}\, \sqrt{\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}}}{x +\frac{c}{b}}\right)}{2 b^{5} \sqrt{\frac{a \,c^{2}}{b^{2}}}}$&$555$\\ default&$\frac{-\frac{b^{2} \left(\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}\right)^{\frac{7}{2}}}{a \,c^{2} \left(x +\frac{c}{b}\right)}-\frac{5 \left(2 a c -b^{2}\right) b \left(\frac{\left(\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}\right)^{\frac{5}{2}}}{5}-\frac{\left(2 a c -b^{2}\right) \left(\frac{\left(2 a \left(x +\frac{c}{b}\right)-\frac{2 a c -b^{2}}{b}\right) \left(\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}\right)^{\frac{3}{2}}}{8 a}+\frac{3 \left(\frac{4 a^{2} c^{2}}{b^{2}}-\frac{\left(2 a c -b^{2}\right)^{2}}{b^{2}}\right) \left(\frac{\left(2 a \left(x +\frac{c}{b}\right)-\frac{2 a c -b^{2}}{b}\right) \sqrt{\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}}}{4 a}+\frac{\left(\frac{4 a^{2} c^{2}}{b^{2}}-\frac{\left(2 a c -b^{2}\right)^{2}}{b^{2}}\right) \ln \left(\frac{-\frac{2 a c -b^{2}}{2 b}+a \left(x +\frac{c}{b}\right)}{\sqrt{a}}+\sqrt{\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}}\right)}{8 a^{\frac{3}{2}}}\right)}{16 a}\right)}{2 b}+\frac{a \,c^{2} \left(\frac{\left(\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}\right)^{\frac{3}{2}}}{3}-\frac{\left(2 a c -b^{2}\right) \left(\frac{\left(2 a \left(x +\frac{c}{b}\right)-\frac{2 a c -b^{2}}{b}\right) \sqrt{\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}}}{4 a}+\frac{\left(\frac{4 a^{2} c^{2}}{b^{2}}-\frac{\left(2 a c -b^{2}\right)^{2}}{b^{2}}\right) \ln \left(\frac{-\frac{2 a c -b^{2}}{2 b}+a \left(x +\frac{c}{b}\right)}{\sqrt{a}}+\sqrt{\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}}\right)}{8 a^{\frac{3}{2}}}\right)}{2 b}+\frac{a \,c^{2} \left(\sqrt{\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}}-\frac{\left(2 a c -b^{2}\right) \ln \left(\frac{-\frac{2 a c -b^{2}}{2 b}+a \left(x +\frac{c}{b}\right)}{\sqrt{a}}+\sqrt{\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}}\right)}{2 b \sqrt{a}}-\frac{a \,c^{2} \ln \left(\frac{\frac{2 a \,c^{2}}{b^{2}}-\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+2 \sqrt{\frac{a \,c^{2}}{b^{2}}}\, \sqrt{\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}}}{x +\frac{c}{b}}\right)}{b^{2} \sqrt{\frac{a \,c^{2}}{b^{2}}}}\right)}{b^{2}}\right)}{b^{2}}\right)}{2 a \,c^{2}}+\frac{6 b^{2} \left(\frac{\left(2 a \left(x +\frac{c}{b}\right)-\frac{2 a c -b^{2}}{b}\right) \left(\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}\right)^{\frac{5}{2}}}{12 a}+\frac{5 \left(\frac{4 a^{2} c^{2}}{b^{2}}-\frac{\left(2 a c -b^{2}\right)^{2}}{b^{2}}\right) \left(\frac{\left(2 a \left(x +\frac{c}{b}\right)-\frac{2 a c -b^{2}}{b}\right) \left(\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}\right)^{\frac{3}{2}}}{8 a}+\frac{3 \left(\frac{4 a^{2} c^{2}}{b^{2}}-\frac{\left(2 a c -b^{2}\right)^{2}}{b^{2}}\right) \left(\frac{\left(2 a \left(x +\frac{c}{b}\right)-\frac{2 a c -b^{2}}{b}\right) \sqrt{\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}}}{4 a}+\frac{\left(\frac{4 a^{2} c^{2}}{b^{2}}-\frac{\left(2 a c -b^{2}\right)^{2}}{b^{2}}\right) \ln \left(\frac{-\frac{2 a c -b^{2}}{2 b}+a \left(x +\frac{c}{b}\right)}{\sqrt{a}}+\sqrt{\left(x +\frac{c}{b}\right)^{2} a -\frac{\left(2 a c -b^{2}\right) \left(x +\frac{c}{b}\right)}{b}+\frac{a \,c^{2}}{b^{2}}}\right)}{8 a^{\frac{3}{2}}}\right)}{16 a}\right)}{24 a}\right)}{c^{2}}}{b^{2}}$&$1378$\\ \hline \end{longtable}"," ",0,"1/192/a*(48*a^3*b^3*x^3-128*a^3*b^2*c*x^2+136*a^2*b^4*x^2+288*a^3*b*c^2*x-200*a^2*b^3*c*x+118*a*b^5*x-768*a^3*c^3+400*a^2*b^2*c^2+28*a*b^4*c+15*b^6)*(a*x^2+b*x+c)^(1/2)/b^5+5/b^6*a^(5/2)*ln((1/2*b+a*x)/a^(1/2)+(a*x^2+b*x+c)^(1/2))*c^4-5/2/b^4*a^(3/2)*ln((1/2*b+a*x)/a^(1/2)+(a*x^2+b*x+c)^(1/2))*c^3+5/16/a^(1/2)*ln((1/2*b+a*x)/a^(1/2)+(a*x^2+b*x+c)^(1/2))*c-5/128*b^2/a^(3/2)*ln((1/2*b+a*x)/a^(1/2)+(a*x^2+b*x+c)^(1/2))-1/b^6*a^2*c^4/(x+c/b)*((x+c/b)^2*a-(2*a*c-b^2)/b*(x+c/b)+a*c^2/b^2)^(1/2)+5/b^7*a^3*c^5/(a*c^2/b^2)^(1/2)*ln((2*a*c^2/b^2-(2*a*c-b^2)/b*(x+c/b)+2*(a*c^2/b^2)^(1/2)*((x+c/b)^2*a-(2*a*c-b^2)/b*(x+c/b)+a*c^2/b^2)^(1/2))/(x+c/b))-5/2/b^5*a^2*c^4/(a*c^2/b^2)^(1/2)*ln((2*a*c^2/b^2-(2*a*c-b^2)/b*(x+c/b)+2*(a*c^2/b^2)^(1/2)*((x+c/b)^2*a-(2*a*c-b^2)/b*(x+c/b)+a*c^2/b^2)^(1/2))/(x+c/b))","A"
2960,0,0,267,0.115000," ","int((x^4+1)^2/(x^4-1)^2/(x^2+(x^4+1)^(1/2))^(1/2),x)","\[\int \frac{\left(x^{4}+1\right)^{2}}{\left(x^{4}-1\right)^{2} \sqrt{x^{2}+\sqrt{x^{4}+1}}}\, dx\]"," ",0,"int((x^4+1)^2/(x^4-1)^2/(x^2+(x^4+1)^(1/2))^(1/2),x)","F"
2961,1,214,301,0.130000," ","int((a*x+(a*x-b)^(1/2))^(1/2)/(1+(a*x-b)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{2}+\frac{\left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{4}-2 \sqrt{\left(1+\sqrt{a x -b}\right)^{2}+b -\sqrt{a x -b}-1}+\ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(1+\sqrt{a x -b}\right)^{2}+b -\sqrt{a x -b}-1}\right)+2 \sqrt{b}\, \ln \left(\frac{2 b -\sqrt{a x -b}-1+2 \sqrt{b}\, \sqrt{\left(1+\sqrt{a x -b}\right)^{2}+b -\sqrt{a x -b}-1}}{1+\sqrt{a x -b}}\right)}{a}$&$214$\\ default&$\frac{\frac{\left(2 \sqrt{a x -b}+1\right) \sqrt{a x +\sqrt{a x -b}}}{2}+\frac{\left(4 b -1\right) \ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{a x +\sqrt{a x -b}}\right)}{4}-2 \sqrt{\left(1+\sqrt{a x -b}\right)^{2}+b -\sqrt{a x -b}-1}+\ln \left(\frac{1}{2}+\sqrt{a x -b}+\sqrt{\left(1+\sqrt{a x -b}\right)^{2}+b -\sqrt{a x -b}-1}\right)+2 \sqrt{b}\, \ln \left(\frac{2 b -\sqrt{a x -b}-1+2 \sqrt{b}\, \sqrt{\left(1+\sqrt{a x -b}\right)^{2}+b -\sqrt{a x -b}-1}}{1+\sqrt{a x -b}}\right)}{a}$&$214$\\ \hline \end{longtable}"," ",0,"2/a*(1/4*(2*(a*x-b)^(1/2)+1)*(a*x+(a*x-b)^(1/2))^(1/2)+1/8*(4*b-1)*ln(1/2+(a*x-b)^(1/2)+(a*x+(a*x-b)^(1/2))^(1/2))-((1+(a*x-b)^(1/2))^2+b-(a*x-b)^(1/2)-1)^(1/2)+1/2*ln(1/2+(a*x-b)^(1/2)+((1+(a*x-b)^(1/2))^2+b-(a*x-b)^(1/2)-1)^(1/2))+b^(1/2)*ln((2*b-(a*x-b)^(1/2)-1+2*b^(1/2)*((1+(a*x-b)^(1/2))^2+b-(a*x-b)^(1/2)-1)^(1/2))/(1+(a*x-b)^(1/2))))","A"
2962,0,0,120,0.010000," ","int((a*x^2+b*x)*(a*x^4+b*x^3)^(1/4)/(a*x+x^2-b),x)","\[\int \frac{\left(a \,x^{2}+b x \right) \left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}}{a x +x^{2}-b}\, dx\]"," ",0,"int((a*x^2+b*x)*(a*x^4+b*x^3)^(1/4)/(a*x+x^2-b),x)","F"
2963,0,0,120,0.005000," ","int((a*x^2+b*x)*(a*x^4+b*x^3)^(1/4)/(a*x+x^2-b),x)","\[\int \frac{\left(a \,x^{2}+b x \right) \left(a \,x^{4}+b \,x^{3}\right)^{\frac{1}{4}}}{a x +x^{2}-b}\, dx\]"," ",0,"int((a*x^2+b*x)*(a*x^4+b*x^3)^(1/4)/(a*x+x^2-b),x)","F"
2964,1,187,57,0.309000," ","int((a^10*x^10-b^10)/(a^4*x^4+b^4)^(1/2)/(a^10*x^10+b^10),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{4 \arctan \left(\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{x \sqrt{-a^{2} b^{2}+\sqrt{5}\, \sqrt{a^{4} b^{4}}}}\right)}{5 \sqrt{-a^{2} b^{2}+\sqrt{5}\, \sqrt{a^{4} b^{4}}}}+\frac{4 \arctan \left(\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{x \sqrt{-a^{2} b^{2}-\sqrt{5}\, \sqrt{a^{4} b^{4}}}}\right)}{5 \sqrt{-a^{2} b^{2}-\sqrt{5}\, \sqrt{a^{4} b^{4}}}}+\frac{\arctan \left(\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{2 x a b}\right)}{5 a b}\right) \sqrt{2}}{2}$&$187$\\ default&$\frac{\sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, i\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}+b^{4}}}-\frac{b^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{8} \textit{\_Z}^{8}-a^{6} b^{2} \textit{\_Z}^{6}+a^{4} b^{4} \textit{\_Z}^{4}-a^{2} b^{6} \textit{\_Z}^{2}+b^{8}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{6} a^{6}+2 \underline{\hspace{1.25 ex}}\alpha^{4} a^{4} b^{2}-3 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b^{4}+4 b^{6}\right) \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{6} a^{6}+\underline{\hspace{1.25 ex}}\alpha^{4} a^{4} b^{2}-\underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b^{4}+a^{2} b^{4} x^{2}+b^{6}\right) a^{2}}{b^{4} \sqrt{a^{4} \underline{\hspace{1.25 ex}}\alpha^{4}+b^{4}}\, \sqrt{a^{4} x^{4}+b^{4}}}\right)}{\sqrt{a^{4} \underline{\hspace{1.25 ex}}\alpha^{4}+b^{4}}}+\frac{2 a^{2} \underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{6} a^{6}-\underline{\hspace{1.25 ex}}\alpha^{4} a^{4} b^{2}+\underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b^{4}-b^{6}\right) \sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, \frac{i \left(\underline{\hspace{1.25 ex}}\alpha^{6} a^{6}-\underline{\hspace{1.25 ex}}\alpha^{4} a^{4} b^{2}+\underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b^{4}-b^{6}\right)}{b^{6}}, \frac{\sqrt{-\frac{i a^{2}}{b^{2}}}}{\sqrt{\frac{i a^{2}}{b^{2}}}}\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, b^{8} \sqrt{a^{4} x^{4}+b^{4}}}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(4 \underline{\hspace{1.25 ex}}\alpha^{6} a^{6}-3 \underline{\hspace{1.25 ex}}\alpha^{4} a^{4} b^{2}+2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b^{4}-b^{6}\right)}\right)}{10 a^{2}}-\frac{2 \sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, i, \frac{\sqrt{-\frac{i a^{2}}{b^{2}}}}{\sqrt{\frac{i a^{2}}{b^{2}}}}\right)}{5 \sqrt{\frac{i a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}+b^{4}}}$&$577$\\ \hline \end{longtable}"," ",0,"1/2*(4/5/(-a^2*b^2+5^(1/2)*(a^4*b^4)^(1/2))^(1/2)*arctan((a^4*x^4+b^4)^(1/2)*2^(1/2)/x/(-a^2*b^2+5^(1/2)*(a^4*b^4)^(1/2))^(1/2))+4/5/(-a^2*b^2-5^(1/2)*(a^4*b^4)^(1/2))^(1/2)*arctan((a^4*x^4+b^4)^(1/2)*2^(1/2)/x/(-a^2*b^2-5^(1/2)*(a^4*b^4)^(1/2))^(1/2))+1/5/a/b*arctan(1/2*(a^4*x^4+b^4)^(1/2)*2^(1/2)/x/a/b))*2^(1/2)","B"
2965,1,187,57,0.272000," ","int((a^10*x^10-b^10)/(a^4*x^4+b^4)^(1/2)/(a^10*x^10+b^10),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{4 \arctan \left(\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{x \sqrt{-a^{2} b^{2}+\sqrt{5}\, \sqrt{a^{4} b^{4}}}}\right)}{5 \sqrt{-a^{2} b^{2}+\sqrt{5}\, \sqrt{a^{4} b^{4}}}}+\frac{4 \arctan \left(\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{x \sqrt{-a^{2} b^{2}-\sqrt{5}\, \sqrt{a^{4} b^{4}}}}\right)}{5 \sqrt{-a^{2} b^{2}-\sqrt{5}\, \sqrt{a^{4} b^{4}}}}+\frac{\arctan \left(\frac{\sqrt{a^{4} x^{4}+b^{4}}\, \sqrt{2}}{2 x a b}\right)}{5 a b}\right) \sqrt{2}}{2}$&$187$\\ default&$\frac{\sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, i\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}+b^{4}}}-\frac{b^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a^{8} \textit{\_Z}^{8}-a^{6} b^{2} \textit{\_Z}^{6}+a^{4} b^{4} \textit{\_Z}^{4}-a^{2} b^{6} \textit{\_Z}^{2}+b^{8}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{6} a^{6}+2 \underline{\hspace{1.25 ex}}\alpha^{4} a^{4} b^{2}-3 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b^{4}+4 b^{6}\right) \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{6} a^{6}+\underline{\hspace{1.25 ex}}\alpha^{4} a^{4} b^{2}-\underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b^{4}+a^{2} b^{4} x^{2}+b^{6}\right) a^{2}}{b^{4} \sqrt{a^{4} \underline{\hspace{1.25 ex}}\alpha^{4}+b^{4}}\, \sqrt{a^{4} x^{4}+b^{4}}}\right)}{\sqrt{a^{4} \underline{\hspace{1.25 ex}}\alpha^{4}+b^{4}}}+\frac{2 a^{2} \underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{6} a^{6}-\underline{\hspace{1.25 ex}}\alpha^{4} a^{4} b^{2}+\underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b^{4}-b^{6}\right) \sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, \frac{i \left(\underline{\hspace{1.25 ex}}\alpha^{6} a^{6}-\underline{\hspace{1.25 ex}}\alpha^{4} a^{4} b^{2}+\underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b^{4}-b^{6}\right)}{b^{6}}, \frac{\sqrt{-\frac{i a^{2}}{b^{2}}}}{\sqrt{\frac{i a^{2}}{b^{2}}}}\right)}{\sqrt{\frac{i a^{2}}{b^{2}}}\, b^{8} \sqrt{a^{4} x^{4}+b^{4}}}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(4 \underline{\hspace{1.25 ex}}\alpha^{6} a^{6}-3 \underline{\hspace{1.25 ex}}\alpha^{4} a^{4} b^{2}+2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2} b^{4}-b^{6}\right)}\right)}{10 a^{2}}-\frac{2 \sqrt{1-\frac{i a^{2} x^{2}}{b^{2}}}\, \sqrt{1+\frac{i a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{\frac{i a^{2}}{b^{2}}}, i, \frac{\sqrt{-\frac{i a^{2}}{b^{2}}}}{\sqrt{\frac{i a^{2}}{b^{2}}}}\right)}{5 \sqrt{\frac{i a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}+b^{4}}}$&$577$\\ \hline \end{longtable}"," ",0,"1/2*(4/5/(-a^2*b^2+5^(1/2)*(a^4*b^4)^(1/2))^(1/2)*arctan((a^4*x^4+b^4)^(1/2)*2^(1/2)/x/(-a^2*b^2+5^(1/2)*(a^4*b^4)^(1/2))^(1/2))+4/5/(-a^2*b^2-5^(1/2)*(a^4*b^4)^(1/2))^(1/2)*arctan((a^4*x^4+b^4)^(1/2)*2^(1/2)/x/(-a^2*b^2-5^(1/2)*(a^4*b^4)^(1/2))^(1/2))+1/5/a/b*arctan(1/2*(a^4*x^4+b^4)^(1/2)*2^(1/2)/x/a/b))*2^(1/2)","B"
2966,0,0,297,0.010000," ","int((a*x^2+b)*(x^3+x)^(1/3)/(c*x^2+d),x)","\[\int \frac{\left(a \,x^{2}+b \right) \left(x^{3}+x \right)^{\frac{1}{3}}}{c \,x^{2}+d}\, dx\]"," ",0,"int((a*x^2+b)*(x^3+x)^(1/3)/(c*x^2+d),x)","F"
2967,0,0,12,0.050000," ","int(x^2*(a*x^3+b)*(2*a*p*x^3+3*a*q-b*p)/(p*x^3+q)^(2/3)/(b^3*c+d*q+(3*a*b^2*c+d*p)*x^3+3*a^2*b*c*x^6+a^3*c*x^9),x)","\[\int \frac{x^{2} \left(a \,x^{3}+b \right) \left(2 a p \,x^{3}+3 a q -b p \right)}{\left(p \,x^{3}+q \right)^{\frac{2}{3}} \left(b^{3} c +d q +\left(3 a \,b^{2} c +d p \right) x^{3}+3 a^{2} b c \,x^{6}+a^{3} c \,x^{9}\right)}\, dx\]"," ",0,"int(x^2*(a*x^3+b)*(2*a*p*x^3+3*a*q-b*p)/(p*x^3+q)^(2/3)/(b^3*c+d*q+(3*a*b^2*c+d*p)*x^3+3*a^2*b*c*x^6+a^3*c*x^9),x)","F"
2968,0,0,310,0.216000," ","int((a*b+a*c-2*b*c+(-2*a+b+c)*x)/((-a+x)*(-b+x)*(-c+x))^(1/3)/(a^2-b*c*d+(b*d+c*d-2*a)*x+(1-d)*x^2),x)","\[\int \frac{a b +a c -2 b c +\left(-2 a +b +c \right) x}{\left(\left(-a +x \right) \left(-b +x \right) \left(-c +x \right)\right)^{\frac{1}{3}} \left(a^{2}-b c d +\left(b d +c d -2 a \right) x +\left(1-d \right) x^{2}\right)}\, dx\]"," ",0,"int((a*b+a*c-2*b*c+(-2*a+b+c)*x)/((-a+x)*(-b+x)*(-c+x))^(1/3)/(a^2-b*c*d+(b*d+c*d-2*a)*x+(1-d)*x^2),x)","F"
2969,0,0,323,0.017000," ","int((-2+x)*(x^2-x+1)/x^3/(x^2+x-1)/((2*x^2-x+1)/(3*x^2-x+1))^(1/3),x)","\[\int \frac{\left(-2+x \right) \left(x^{2}-x +1\right)}{x^{3} \left(x^{2}+x -1\right) \left(\frac{2 x^{2}-x +1}{3 x^{2}-x +1}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((-2+x)*(x^2-x+1)/x^3/(x^2+x-1)/((2*x^2-x+1)/(3*x^2-x+1))^(1/3),x)","F"
2970,0,0,307,0.044000," ","int(x^3*(9*a*x^4+5*b)/(a*x^5+b*x)^(1/4)/(a*x^9+b*x^5+1),x)","\[\int \frac{x^{3} \left(9 a \,x^{4}+5 b \right)}{\left(a \,x^{5}+b x \right)^{\frac{1}{4}} \left(a \,x^{9}+b \,x^{5}+1\right)}\, dx\]"," ",0,"int(x^3*(9*a*x^4+5*b)/(a*x^5+b*x)^(1/4)/(a*x^9+b*x^5+1),x)","F"
2971,0,0,215,0.068000," ","int((x^2+1)^(1/2)*(x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1),x)","\[\int \frac{\sqrt{x^{2}+1}\, \left(x^{4}+1\right) \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{-x^{4}+1}\, dx\]"," ",0,"int((x^2+1)^(1/2)*(x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1),x)","F"
2972,0,0,215,0.005000," ","int((x^2+1)^(1/2)*(x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1),x)","\[\int \frac{\sqrt{x^{2}+1}\, \left(x^{4}+1\right) \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{-x^{4}+1}\, dx\]"," ",0,"int((x^2+1)^(1/2)*(x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1),x)","F"
2973,1,305,30,0.329000," ","int((a^12*x^12+b^12)/(a^4*x^4-b^4)^(1/2)/(a^12*x^12-b^12),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(-\frac{\sqrt{2}\, x}{3 \sqrt{a^{4} x^{4}-b^{4}}}+\frac{\ln \left(\frac{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}-\frac{\sqrt{\sqrt{3}\, \sqrt{a^{4} b^{4}}}\, \sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{2 x}+\frac{\sqrt{3}\, \sqrt{a^{4} b^{4}}}{2}}{\frac{a^{4} x^{4}-b^{4}}{2 x^{2}}+\frac{\sqrt{\sqrt{3}\, \sqrt{a^{4} b^{4}}}\, \sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{2 x}+\frac{\sqrt{3}\, \sqrt{a^{4} b^{4}}}{2}}\right)}{6 \sqrt{\sqrt{3}\, \sqrt{a^{4} b^{4}}}}+\frac{\arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{\sqrt{\sqrt{3}\, \sqrt{a^{4} b^{4}}}\, x}+1\right)}{3 \sqrt{\sqrt{3}\, \sqrt{a^{4} b^{4}}}}+\frac{\arctan \left(\frac{\sqrt{a^{4} x^{4}-b^{4}}\, \sqrt{2}}{\sqrt{\sqrt{3}\, \sqrt{a^{4} b^{4}}}\, x}-1\right)}{3 \sqrt{\sqrt{3}\, \sqrt{a^{4} b^{4}}}}\right) \sqrt{2}}{2}$&$305$\\ default&$\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{\sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}-\frac{b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}-\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha  a +2 b \right) \left(-\frac{\arctanh \left(\frac{\left(\underline{\hspace{1.25 ex}}\alpha  a -b \right) a b \left(a \,x^{2}+b \underline{\hspace{1.25 ex}}\alpha  \right)}{\sqrt{-b^{3} \left(\underline{\hspace{1.25 ex}}\alpha  a +b \right)}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{\sqrt{-b^{3} \left(\underline{\hspace{1.25 ex}}\alpha  a +b \right)}}+\frac{2 a \left(\underline{\hspace{1.25 ex}}\alpha  a -b \right) \sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, \frac{\underline{\hspace{1.25 ex}}\alpha  a}{b}, \frac{\sqrt{\frac{a^{2}}{b^{2}}}}{\sqrt{-\frac{a^{2}}{b^{2}}}}\right)}{\sqrt{-\frac{a^{2}}{b^{2}}}\, b^{2} \sqrt{a^{4} x^{4}-b^{4}}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  a -b}\right)}{12 a}-\frac{b \left(\frac{a^{4} x^{3}-a^{3} b \,x^{2}+a^{2} b^{2} x -a \,b^{3}}{2 a^{2} b^{3} \sqrt{\left(x +\frac{b}{a}\right) \left(a^{4} x^{3}-a^{3} b \,x^{2}+a^{2} b^{2} x -a \,b^{3}\right)}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}-\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \left(\EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)-\EllipticE \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{6}+\frac{b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{2} a^{2}+\textit{\_Z} a b +b^{2}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha  a -2 b \right) \left(\frac{\arctanh \left(\frac{\left(\underline{\hspace{1.25 ex}}\alpha  a +b \right) a b \left(a \,x^{2}-b \underline{\hspace{1.25 ex}}\alpha  \right)}{\sqrt{b^{3} \left(\underline{\hspace{1.25 ex}}\alpha  a -b \right)}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{\sqrt{b^{3} \left(\underline{\hspace{1.25 ex}}\alpha  a -b \right)}}+\frac{2 a \left(\underline{\hspace{1.25 ex}}\alpha  a +b \right) \sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, -\frac{\underline{\hspace{1.25 ex}}\alpha  a}{b}, \frac{\sqrt{\frac{a^{2}}{b^{2}}}}{\sqrt{-\frac{a^{2}}{b^{2}}}}\right)}{\sqrt{-\frac{a^{2}}{b^{2}}}\, b^{2} \sqrt{a^{4} x^{4}-b^{4}}}\right)}{2 \underline{\hspace{1.25 ex}}\alpha  a +b}\right)}{12 a}+\frac{b \left(-\frac{a^{4} x^{3}+a^{3} b \,x^{2}+a^{2} b^{2} x +a \,b^{3}}{2 a^{2} b^{3} \sqrt{\left(x -\frac{b}{a}\right) \left(a^{4} x^{3}+a^{3} b \,x^{2}+a^{2} b^{2} x +a \,b^{3}\right)}}-\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \left(\EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)-\EllipticE \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)\right)}{2 b \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{6}-\frac{b^{2} \left(-\frac{\left(a^{4} x^{2}-a^{2} b^{2}\right) x}{2 b^{4} a^{2} \sqrt{\left(x^{2}+\frac{b^{2}}{a^{2}}\right) \left(a^{4} x^{2}-a^{2} b^{2}\right)}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)}{2 b^{2} \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}+\frac{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \left(\EllipticF \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)-\EllipticE \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, i\right)\right)}{2 b^{2} \sqrt{-\frac{a^{2}}{b^{2}}}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{3}-\frac{b^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4} a^{4}-\textit{\_Z}^{2} a^{2} b^{2}+b^{4}\right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+2 b^{2}\right) \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+a^{2} x^{2}-b^{2}\right) a^{2}}{\sqrt{b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-2 b^{2}\right)}\, \sqrt{a^{4} x^{4}-b^{4}}}\right)}{\sqrt{b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-2 b^{2}\right)}}+\frac{2 a^{2} \underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-b^{2}\right) \sqrt{\frac{a^{2} x^{2}}{b^{2}}+1}\, \sqrt{1-\frac{a^{2} x^{2}}{b^{2}}}\, \EllipticPi \left(x \sqrt{-\frac{a^{2}}{b^{2}}}, \frac{\underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-b^{2}}{b^{2}}, \frac{\sqrt{\frac{a^{2}}{b^{2}}}}{\sqrt{-\frac{a^{2}}{b^{2}}}}\right)}{\sqrt{-\frac{a^{2}}{b^{2}}}\, b^{4} \sqrt{a^{4} x^{4}-b^{4}}}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-b^{2}\right)}\right)}{12 a^{2}}$&$1496$\\ \hline \end{longtable}"," ",0,"1/2*(-1/3/(a^4*x^4-b^4)^(1/2)*2^(1/2)*x+1/6/(3^(1/2)*(a^4*b^4)^(1/2))^(1/2)*ln((1/2*(a^4*x^4-b^4)/x^2-1/2*(3^(1/2)*(a^4*b^4)^(1/2))^(1/2)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x+1/2*3^(1/2)*(a^4*b^4)^(1/2))/(1/2*(a^4*x^4-b^4)/x^2+1/2*(3^(1/2)*(a^4*b^4)^(1/2))^(1/2)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x+1/2*3^(1/2)*(a^4*b^4)^(1/2)))+1/3/(3^(1/2)*(a^4*b^4)^(1/2))^(1/2)*arctan(1/(3^(1/2)*(a^4*b^4)^(1/2))^(1/2)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x+1)+1/3/(3^(1/2)*(a^4*b^4)^(1/2))^(1/2)*arctan(1/(3^(1/2)*(a^4*b^4)^(1/2))^(1/2)*(a^4*x^4-b^4)^(1/2)*2^(1/2)/x-1))*2^(1/2)","B"
2974,0,0,17,180.000000," ","int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^4+b)^(1/2)/(c*x^4+d),x)","\[\int \frac{\sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}{\sqrt{a^{2} x^{4}+b}\, \left(c \,x^{4}+d \right)}\, dx\]"," ",0,"int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^4+b)^(1/2)/(c*x^4+d),x)","F"
2975,0,0,17,180.000000," ","int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^4+b)^(1/2)/(c*x^4+d),x)","\[\int \frac{\sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}{\sqrt{a^{2} x^{4}+b}\, \left(c \,x^{4}+d \right)}\, dx\]"," ",0,"int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^4+b)^(1/2)/(c*x^4+d),x)","F"
2976,1,203,58,0.178000," ","int(x/(x-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{2 \left(-2 a^{3} \sqrt{c +\sqrt{a x +b}}-a^{2} \left(c +\sqrt{a x +b}\right)-\frac{2 a \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}-\frac{\left(c +\sqrt{a x +b}\right)^{2}}{2}+c \left(c +\sqrt{a x +b}\right)+2 a \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-a \,\textit{\_Z}^{3}-2 c \,\textit{\_Z}^{2}+a c \textit{\_Z} +c^{2}-b \right)}{\sum}\frac{\left(a \left(-a^{2}-c \right) \textit{\_R}^{3}+\left(-a^{2} c -b \right) \textit{\_R}^{2}+a \left(a^{2} c +c^{2}-b \right) \textit{\_R} +a^{2} c^{2}-a^{2} b \right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-3 \textit{\_R}^{2} a -4 \textit{\_R} c +a c}\right)\right)}{a}$&$203$\\ default&$-\frac{2 \left(-2 a^{3} \sqrt{c +\sqrt{a x +b}}-a^{2} \left(c +\sqrt{a x +b}\right)-\frac{2 a \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}-\frac{\left(c +\sqrt{a x +b}\right)^{2}}{2}+c \left(c +\sqrt{a x +b}\right)+2 a \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-a \,\textit{\_Z}^{3}-2 c \,\textit{\_Z}^{2}+a c \textit{\_Z} +c^{2}-b \right)}{\sum}\frac{\left(a \left(-a^{2}-c \right) \textit{\_R}^{3}+\left(-a^{2} c -b \right) \textit{\_R}^{2}+a \left(a^{2} c +c^{2}-b \right) \textit{\_R} +a^{2} c^{2}-a^{2} b \right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-3 \textit{\_R}^{2} a -4 \textit{\_R} c +a c}\right)\right)}{a}$&$203$\\ \hline \end{longtable}"," ",0,"-2/a*(-2*a^3*(c+(a*x+b)^(1/2))^(1/2)-a^2*(c+(a*x+b)^(1/2))-2/3*a*(c+(a*x+b)^(1/2))^(3/2)-1/2*(c+(a*x+b)^(1/2))^2+c*(c+(a*x+b)^(1/2))+2*a*sum((a*(-a^2-c)*_R^3+(-a^2*c-b)*_R^2+a*(a^2*c+c^2-b)*_R+a^2*c^2-a^2*b)/(4*_R^3-3*_R^2*a-4*_R*c+a*c)*ln((c+(a*x+b)^(1/2))^(1/2)-_R),_R=RootOf(_Z^4-_Z^3*a-2*_Z^2*c+_Z*a*c+c^2-b)))","B"
2977,1,203,58,0.153000," ","int(x/(x-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{2 \left(-2 a^{3} \sqrt{c +\sqrt{a x +b}}-a^{2} \left(c +\sqrt{a x +b}\right)-\frac{2 a \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}-\frac{\left(c +\sqrt{a x +b}\right)^{2}}{2}+c \left(c +\sqrt{a x +b}\right)+2 a \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-a \,\textit{\_Z}^{3}-2 c \,\textit{\_Z}^{2}+a c \textit{\_Z} +c^{2}-b \right)}{\sum}\frac{\left(a \left(-a^{2}-c \right) \textit{\_R}^{3}+\left(-a^{2} c -b \right) \textit{\_R}^{2}+a \left(a^{2} c +c^{2}-b \right) \textit{\_R} +a^{2} c^{2}-a^{2} b \right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-3 \textit{\_R}^{2} a -4 \textit{\_R} c +a c}\right)\right)}{a}$&$203$\\ default&$-\frac{2 \left(-2 a^{3} \sqrt{c +\sqrt{a x +b}}-a^{2} \left(c +\sqrt{a x +b}\right)-\frac{2 a \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}-\frac{\left(c +\sqrt{a x +b}\right)^{2}}{2}+c \left(c +\sqrt{a x +b}\right)+2 a \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-a \,\textit{\_Z}^{3}-2 c \,\textit{\_Z}^{2}+a c \textit{\_Z} +c^{2}-b \right)}{\sum}\frac{\left(a \left(-a^{2}-c \right) \textit{\_R}^{3}+\left(-a^{2} c -b \right) \textit{\_R}^{2}+a \left(a^{2} c +c^{2}-b \right) \textit{\_R} +a^{2} c^{2}-a^{2} b \right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{4 \textit{\_R}^{3}-3 \textit{\_R}^{2} a -4 \textit{\_R} c +a c}\right)\right)}{a}$&$203$\\ \hline \end{longtable}"," ",0,"-2/a*(-2*a^3*(c+(a*x+b)^(1/2))^(1/2)-a^2*(c+(a*x+b)^(1/2))-2/3*a*(c+(a*x+b)^(1/2))^(3/2)-1/2*(c+(a*x+b)^(1/2))^2+c*(c+(a*x+b)^(1/2))+2*a*sum((a*(-a^2-c)*_R^3+(-a^2*c-b)*_R^2+a*(a^2*c+c^2-b)*_R+a^2*c^2-a^2*b)/(4*_R^3-3*_R^2*a-4*_R*c+a*c)*ln((c+(a*x+b)^(1/2))^(1/2)-_R),_R=RootOf(_Z^4-_Z^3*a-2*_Z^2*c+_Z*a*c+c^2-b)))","B"
2978,0,0,303,0.050000," ","int((-2*x+(1+k)*x^2)*(1-(1+k)*x+(a+k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(1-2*(1+k)*x+(k^2+4*k+1)*x^2-2*(k^2+k)*x^3+(k^2-b)*x^4),x)","\[\int \frac{\left(-2 x +\left(1+k \right) x^{2}\right) \left(1-\left(1+k \right) x +\left(a +k \right) x^{2}\right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{2}{3}} \left(1-2 \left(1+k \right) x +\left(k^{2}+4 k +1\right) x^{2}-2 \left(k^{2}+k \right) x^{3}+\left(k^{2}-b \right) x^{4}\right)}\, dx\]"," ",0,"int((-2*x+(1+k)*x^2)*(1-(1+k)*x+(a+k)*x^2)/((1-x)*x*(-k*x+1))^(2/3)/(1-2*(1+k)*x+(k^2+4*k+1)*x^2-2*(k^2+k)*x^3+(k^2-b)*x^4),x)","F"
2979,0,0,303,0.044000," ","int((-2+(1+k)*x)*(1-(1+k)*x+(a+k)*x^2)/((1-x)*x*(-k*x+1))^(1/3)/(1-(2+2*k)*x+(k^2+4*k+1)*x^2-2*(k^2+k)*x^3+(k^2-b)*x^4),x)","\[\int \frac{\left(-2+\left(1+k \right) x \right) \left(1-\left(1+k \right) x +\left(a +k \right) x^{2}\right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(1-\left(2+2 k \right) x +\left(k^{2}+4 k +1\right) x^{2}-2 \left(k^{2}+k \right) x^{3}+\left(k^{2}-b \right) x^{4}\right)}\, dx\]"," ",0,"int((-2+(1+k)*x)*(1-(1+k)*x+(a+k)*x^2)/((1-x)*x*(-k*x+1))^(1/3)/(1-(2+2*k)*x+(k^2+4*k+1)*x^2-2*(k^2+k)*x^3+(k^2-b)*x^4),x)","F"
2980,0,0,297,180.000000," ","int(1/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/6),x)","\[\int \frac{1}{\sqrt{a^{2} x^{2}-b}\, \sqrt{a x +\sqrt{a^{2} x^{2}-b}}\, \left(c +\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}}\right)^{\frac{1}{6}}}\, dx\]"," ",0,"int(1/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/6),x)","F"
2981,0,0,339,0.015000," ","int(x/(1+(a*x+(a^2*x^2-b)^(1/2))^(1/2))^(1/2),x)","\[\int \frac{x}{\sqrt{1+\sqrt{a x +\sqrt{a^{2} x^{2}-b}}}}\, dx\]"," ",0,"int(x/(1+(a*x+(a^2*x^2-b)^(1/2))^(1/2))^(1/2),x)","F"
2982,0,0,304,180.000000," ","int((c*x^2+d)*(a*x+(a^2*x^2-b)^(1/2))^(5/4)/(a^2*x^2-b)^(3/2),x)","\[\int \frac{\left(c \,x^{2}+d \right) \left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{5}{4}}}{\left(a^{2} x^{2}-b \right)^{\frac{3}{2}}}\, dx\]"," ",0,"int((c*x^2+d)*(a*x+(a^2*x^2-b)^(1/2))^(5/4)/(a^2*x^2-b)^(3/2),x)","F"
2983,0,0,315,0.010000," ","int((a*x^2-b)*(x^3-x)^(1/3)/(c*x^2-d),x)","\[\int \frac{\left(a \,x^{2}-b \right) \left(x^{3}-x \right)^{\frac{1}{3}}}{c \,x^{2}-d}\, dx\]"," ",0,"int((a*x^2-b)*(x^3-x)^(1/3)/(c*x^2-d),x)","F"
2984,0,0,315,0.041000," ","int((-a*b+(2*a-b)*x)*(a^2-2*a*x+x^2)/(x*(-a+x)*(-b+x))^(1/3)/(a^4*d-4*a^3*d*x+(6*a^2*d-b^2)*x^2+2*(-2*a*d+b)*x^3+(-1+d)*x^4),x)","\[\int \frac{\left(-a b +\left(2 a -b \right) x \right) \left(a^{2}-2 a x +x^{2}\right)}{\left(x \left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{3}} \left(a^{4} d -4 a^{3} d x +\left(6 a^{2} d -b^{2}\right) x^{2}+2 \left(-2 a d +b \right) x^{3}+\left(-1+d \right) x^{4}\right)}\, dx\]"," ",0,"int((-a*b+(2*a-b)*x)*(a^2-2*a*x+x^2)/(x*(-a+x)*(-b+x))^(1/3)/(a^4*d-4*a^3*d*x+(6*a^2*d-b^2)*x^2+2*(-2*a*d+b)*x^3+(-1+d)*x^4),x)","F"
2985,0,0,360,0.010000," ","int((d*x+b)/x^4/((a*x+b)/(c*x+d))^(1/4),x)","\[\int \frac{d x +b}{x^{4} \left(\frac{a x +b}{c x +d}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((d*x+b)/x^4/((a*x+b)/(c*x+d))^(1/4),x)","F"
2986,0,0,76,0.287000," ","int((e*x+f)/(d+c*x+(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)),x)","\[\int \frac{e x +f}{d +c x +\sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}\, dx\]"," ",0,"int((e*x+f)/(d+c*x+(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)),x)","F"
2987,1,2178,288,124.083000," ","int((x^6+1)/(x^5-x^3)^(1/4)/(-x^6+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\text{Expression too large to display}$&$2178$\\ trager&$\text{Expression too large to display}$&$2187$\\ \hline \end{longtable}"," ",0,"4/3*x/(x^3*(x^2-1))^(1/4)+1/19683*RootOf(_Z^8+2187)^7*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*ln(-108*(26*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^11*x^4-39*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^11*x^3-26*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^11*x^2+243*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^7*x^4-4050*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^7*x^3-243*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^7*x^2-4374*(x^5-x^3)^(1/2)*RootOf(_Z^8+2187)^6*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*x-13122*(x^5-x^3)^(1/4)*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)^5*x^2-52488*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^3*x^4-104976*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^3*x^3+656100*(x^5-x^3)^(3/4)*RootOf(_Z^8+2187)^4+52488*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^3*x^2+1968300*(x^5-x^3)^(1/2)*RootOf(_Z^8+2187)^2*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*x+5904900*(x^5-x^3)^(1/4)*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)*x^2+3188646*(x^5-x^3)^(3/4))/x^2/(x*RootOf(_Z^8+2187)^4-2*RootOf(_Z^8+2187)^4+81*x)/(x*RootOf(_Z^8+2187)^4-2*RootOf(_Z^8+2187)^4+135*x+108))+1/9*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*ln(-108*(-16*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^8*x^4+24*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^8*x^3+16*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^8*x^2+54*(x^5-x^3)^(1/2)*RootOf(_Z^8+2187)^5*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*x+162*(x^5-x^3)^(1/4)*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)^5*x^2+1350*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^4*x^4+243*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^4*x^3+8100*(x^5-x^3)^(3/4)*RootOf(_Z^8+2187)^4-1350*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)^4*x^2-24300*(x^5-x^3)^(1/2)*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*RootOf(_Z^8+2187)*x-72900*(x^5-x^3)^(1/4)*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)*x^2-28431*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*x^4-56862*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*x^3+39366*(x^5-x^3)^(3/4)+28431*RootOf(_Z^2-RootOf(_Z^8+2187)*RootOf(_Z^2+RootOf(_Z^8+2187)^2))*x^2)/x^2/(x*RootOf(_Z^8+2187)^4-2*RootOf(_Z^8+2187)^4+81*x)/(x*RootOf(_Z^8+2187)^4-2*RootOf(_Z^8+2187)^4+135*x+108))-1/9*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*ln(-108*(-16*x^4*RootOf(_Z^8+2187)^8*RootOf(_Z^2+RootOf(_Z^8+2187)^2)+24*x^3*RootOf(_Z^8+2187)^8*RootOf(_Z^2+RootOf(_Z^8+2187)^2)+16*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)^8*x^2+54*(x^5-x^3)^(1/2)*RootOf(_Z^8+2187)^6*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*x-162*(x^5-x^3)^(1/4)*RootOf(_Z^8+2187)^6*x^2-1350*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)^4*x^4-243*x^3*RootOf(_Z^8+2187)^4*RootOf(_Z^2+RootOf(_Z^8+2187)^2)+8100*(x^5-x^3)^(3/4)*RootOf(_Z^8+2187)^4+1350*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*RootOf(_Z^8+2187)^4*x^2+24300*(x^5-x^3)^(1/2)*RootOf(_Z^8+2187)^2*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*x-72900*(x^5-x^3)^(1/4)*RootOf(_Z^8+2187)^2*x^2-28431*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*x^4-56862*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*x^3-39366*(x^5-x^3)^(3/4)+28431*RootOf(_Z^2+RootOf(_Z^8+2187)^2)*x^2)/x^2/(x*RootOf(_Z^8+2187)^4-2*RootOf(_Z^8+2187)^4-135*x-108)/(x*RootOf(_Z^8+2187)^4-2*RootOf(_Z^8+2187)^4-81*x))-1/9*RootOf(_Z^8+2187)*ln(-108*(-16*RootOf(_Z^8+2187)^9*x^4+24*RootOf(_Z^8+2187)^9*x^3+16*RootOf(_Z^8+2187)^9*x^2-54*(x^5-x^3)^(1/2)*RootOf(_Z^8+2187)^7*x+162*(x^5-x^3)^(1/4)*RootOf(_Z^8+2187)^6*x^2-1350*RootOf(_Z^8+2187)^5*x^4-243*RootOf(_Z^8+2187)^5*x^3+8100*(x^5-x^3)^(3/4)*RootOf(_Z^8+2187)^4+1350*RootOf(_Z^8+2187)^5*x^2-24300*(x^5-x^3)^(1/2)*RootOf(_Z^8+2187)^3*x+72900*(x^5-x^3)^(1/4)*RootOf(_Z^8+2187)^2*x^2-28431*RootOf(_Z^8+2187)*x^4-56862*RootOf(_Z^8+2187)*x^3-39366*(x^5-x^3)^(3/4)+28431*RootOf(_Z^8+2187)*x^2)/x^2/(x*RootOf(_Z^8+2187)^4-2*RootOf(_Z^8+2187)^4-135*x-108)/(x*RootOf(_Z^8+2187)^4-2*RootOf(_Z^8+2187)^4-81*x))","C"
2988,0,0,348,180.000000," ","int((a^2*x^2-b)^(1/2)*(c*x^4+d)*(a*x+(a^2*x^2-b)^(1/2))^(1/2)/x^2,x)","\[\int \frac{\sqrt{a^{2} x^{2}-b}\, \left(c \,x^{4}+d \right) \sqrt{a x +\sqrt{a^{2} x^{2}-b}}}{x^{2}}\, dx\]"," ",0,"int((a^2*x^2-b)^(1/2)*(c*x^4+d)*(a*x+(a^2*x^2-b)^(1/2))^(1/2)/x^2,x)","F"
2989,0,0,134,0.069000," ","int((x^2+1)^(3/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","\[\int \frac{\left(x^{2}+1\right)^{\frac{3}{2}} \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right)^{2}}\, dx\]"," ",0,"int((x^2+1)^(3/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","F"
2990,0,0,134,0.004000," ","int((x^2+1)^(3/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","\[\int \frac{\left(x^{2}+1\right)^{\frac{3}{2}} \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right)^{2}}\, dx\]"," ",0,"int((x^2+1)^(3/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","F"
2991,0,0,134,0.005000," ","int((x^2+1)^(3/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","\[\int \frac{\left(x^{2}+1\right)^{\frac{3}{2}} \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right)^{2}}\, dx\]"," ",0,"int((x^2+1)^(3/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","F"
2992,0,0,52,0.036000," ","int((x^4+x^2+1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1),x)","\[\int \frac{\left(x^{4}+x^{2}+1\right) \sqrt{x^{2}+\sqrt{x^{4}+1}}}{\sqrt{x^{4}+1}\, \left(x^{4}+x^{2}-1\right)}\, dx\]"," ",0,"int((x^4+x^2+1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1),x)","F"
2993,0,0,52,0.004000," ","int((x^4+x^2+1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1),x)","\[\int \frac{\left(x^{4}+x^{2}+1\right) \sqrt{x^{2}+\sqrt{x^{4}+1}}}{\sqrt{x^{4}+1}\, \left(x^{4}+x^{2}-1\right)}\, dx\]"," ",0,"int((x^4+x^2+1)*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1),x)","F"
2994,0,0,351,180.000000," ","int((a^2*x^2-b)^(1/2)*(c*x^4+d)*(a*x+(a^2*x^2-b)^(1/2))^(1/2)/x,x)","\[\int \frac{\sqrt{a^{2} x^{2}-b}\, \left(c \,x^{4}+d \right) \sqrt{a x +\sqrt{a^{2} x^{2}-b}}}{x}\, dx\]"," ",0,"int((a^2*x^2-b)^(1/2)*(c*x^4+d)*(a*x+(a^2*x^2-b)^(1/2))^(1/2)/x,x)","F"
2995,0,0,84,180.000000," ","int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d),x)","\[\int \frac{\sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}{c \,x^{2}+d}\, dx\]"," ",0,"int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d),x)","F"
2996,0,0,84,180.000000," ","int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d),x)","\[\int \frac{\sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}{c \,x^{2}+d}\, dx\]"," ",0,"int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d),x)","F"
2997,0,0,335,0.048000," ","int(x^5*(10*a*x^3+7*b)/(a*x^6+b*x^3)^(1/4)/(a*x^10+b*x^7+1),x)","\[\int \frac{x^{5} \left(10 a \,x^{3}+7 b \right)}{\left(a \,x^{6}+b \,x^{3}\right)^{\frac{1}{4}} \left(a \,x^{10}+b \,x^{7}+1\right)}\, dx\]"," ",0,"int(x^5*(10*a*x^3+7*b)/(a*x^6+b*x^3)^(1/4)/(a*x^10+b*x^7+1),x)","F"
2998,1,1596,286,0.853000," ","int(x^4*(p*x^3-2*q)*(p*x^3+q)^(1/2)/(b*x^8+a*(p*x^3+q)^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,p^{4} \textit{\_Z}^{12}+4 a \,p^{3} q \,\textit{\_Z}^{9}+6 a \,p^{2} q^{2} \textit{\_Z}^{6}+b \,\textit{\_Z}^{8}+4 a p \,q^{3} \textit{\_Z}^{3}+a \,q^{4}\right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{6} p^{2}-\underline{\hspace{1.25 ex}}\alpha^{3} p q -2 q^{2}\right) \underline{\hspace{1.25 ex}}\alpha^{2} \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i p \left(2 x +\frac{-i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}+\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{p \left(x -\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{-3 \left(-q \,p^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i p \left(2 x +\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}+\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{2 \left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-q \,p^{2}\right)^{\frac{2}{3}} b \,q^{2}-3 i \left(-q \,p^{2}\right)^{\frac{1}{3}} p^{5} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5} a \,q^{2}-i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} q p b -i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  \,q^{2} p b +2 q \,p^{2} \left(a \,p^{5} \underline{\hspace{1.25 ex}}\alpha^{9}+3 a \,p^{4} q \,\underline{\hspace{1.25 ex}}\alpha^{6}+3 a \,p^{3} q^{2} \underline{\hspace{1.25 ex}}\alpha^{3}+b p \,\underline{\hspace{1.25 ex}}\alpha^{5}+a \,p^{2} q^{3}-b q \,\underline{\hspace{1.25 ex}}\alpha^{2}\right)-i \left(-q \,p^{2}\right)^{\frac{1}{3}} p^{3} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{7} b +i \left(-q \,p^{2}\right)^{\frac{2}{3}} p^{6} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{10} a +i \left(-q \,p^{2}\right)^{\frac{2}{3}} p^{3} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a \,q^{3}-\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{3} b p q +\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  b p \,q^{2}+3 \left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{8} a \,p^{6} q +3 \left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{7} a \,p^{5} q +3 \left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{5} a \,p^{5} q^{2}+3 \left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{4} a \,p^{4} q^{2}+i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, q^{2} b -3 i \left(-q \,p^{2}\right)^{\frac{1}{3}} p^{6} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{8} a q +3 i \left(-q \,p^{2}\right)^{\frac{2}{3}} p^{5} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{7} a q +3 i \left(-q \,p^{2}\right)^{\frac{2}{3}} p^{4} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{4} a \,q^{2}-i \left(-q \,p^{2}\right)^{\frac{1}{3}} p^{4} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a \,q^{3}+i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{4} q \,p^{2} b +\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{11} a \,p^{7}+\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{10} a \,p^{6}+\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{7} b \,p^{3}+\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{6} b \,p^{2}+\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a \,p^{4} q^{3}+\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  a \,p^{3} q^{3}-\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{4} b \,p^{2} q +i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{6} p^{2} b -i \left(-q \,p^{2}\right)^{\frac{1}{3}} p^{7} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{11} a \right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{3 i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{7} a \,p^{6} q^{2}+3 i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{4} a \,p^{5} q^{3}-i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{7} b \,p^{2}-3 q^{3} b p -2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, a \,p^{3} q^{4}+i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{10} a \,p^{7} q +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{6} b \,p^{3} q +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a \,p^{4} q^{4}-i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{11} a \,p^{6}+i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{4} b p q -3 i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{8} a \,p^{5} q -6 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{6} a \,p^{5} q^{2}-3 i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5} a \,p^{4} q^{2}-6 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} a \,p^{4} q^{3}-i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a \,p^{3} q^{3}-2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5} b \,p^{2} q +2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} b p \,q^{2}-2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{9} a \,p^{6} q -3 p^{3} \underline{\hspace{1.25 ex}}\alpha^{6} q b -3 p^{4} \underline{\hspace{1.25 ex}}\alpha  a \,q^{4}+3 \underline{\hspace{1.25 ex}}\alpha^{3} q^{2} p^{2} b -3 p^{7} \underline{\hspace{1.25 ex}}\alpha^{10} a q -9 p^{6} \underline{\hspace{1.25 ex}}\alpha^{7} a \,q^{2}-9 p^{5} \underline{\hspace{1.25 ex}}\alpha^{4} a \,q^{3}-3 \left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  \,q^{2} b -3 \underline{\hspace{1.25 ex}}\alpha^{11} p^{6} \left(-q \,p^{2}\right)^{\frac{2}{3}} a -3 \underline{\hspace{1.25 ex}}\alpha^{7} \left(-q \,p^{2}\right)^{\frac{2}{3}} p^{2} b -9 \underline{\hspace{1.25 ex}}\alpha^{5} p^{4} \left(-q \,p^{2}\right)^{\frac{2}{3}} a \,q^{2}-3 \underline{\hspace{1.25 ex}}\alpha^{2} p^{3} \left(-q \,p^{2}\right)^{\frac{2}{3}} a \,q^{3}+3 \underline{\hspace{1.25 ex}}\alpha^{4} \left(-q \,p^{2}\right)^{\frac{2}{3}} q p b -9 \underline{\hspace{1.25 ex}}\alpha^{8} p^{5} \left(-q \,p^{2}\right)^{\frac{2}{3}} a q +i \sqrt{3}\, b p \,q^{3}-i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} b \,p^{2} q^{2}-i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  b \,q^{2}}{2 p \,q^{3} b}, \sqrt{\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{p \left(-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right)}}\right)}{2 \left(-3 \underline{\hspace{1.25 ex}}\alpha^{9} a \,p^{4}-9 \underline{\hspace{1.25 ex}}\alpha^{6} a \,p^{3} q -9 \underline{\hspace{1.25 ex}}\alpha^{3} a \,p^{2} q^{2}-2 \underline{\hspace{1.25 ex}}\alpha^{5} b -3 a p \,q^{3}\right) \sqrt{p \,x^{3}+q}}\right)}{4 p^{2} q^{3} b}$&$1596$\\ elliptic&$\frac{i \sqrt{2}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,p^{4} \textit{\_Z}^{12}+4 a \,p^{3} q \,\textit{\_Z}^{9}+6 a \,p^{2} q^{2} \textit{\_Z}^{6}+b \,\textit{\_Z}^{8}+4 a p \,q^{3} \textit{\_Z}^{3}+a \,q^{4}\right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{6} p^{2}-\underline{\hspace{1.25 ex}}\alpha^{3} p q -2 q^{2}\right) \underline{\hspace{1.25 ex}}\alpha^{2} \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{2}\, \sqrt{\frac{i p \left(2 x +\frac{-i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}+\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{p \left(x -\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{-3 \left(-q \,p^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i p \left(2 x +\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}+\left(-q \,p^{2}\right)^{\frac{1}{3}}}{p}\right)}{2 \left(-q \,p^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-q \,p^{2}\right)^{\frac{2}{3}} b \,q^{2}-3 i \left(-q \,p^{2}\right)^{\frac{1}{3}} p^{5} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5} a \,q^{2}-i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} q p b -i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  \,q^{2} p b +2 q \,p^{2} \left(a \,p^{5} \underline{\hspace{1.25 ex}}\alpha^{9}+3 a \,p^{4} q \,\underline{\hspace{1.25 ex}}\alpha^{6}+3 a \,p^{3} q^{2} \underline{\hspace{1.25 ex}}\alpha^{3}+b p \,\underline{\hspace{1.25 ex}}\alpha^{5}+a \,p^{2} q^{3}-b q \,\underline{\hspace{1.25 ex}}\alpha^{2}\right)-i \left(-q \,p^{2}\right)^{\frac{1}{3}} p^{3} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{7} b +i \left(-q \,p^{2}\right)^{\frac{2}{3}} p^{6} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{10} a +i \left(-q \,p^{2}\right)^{\frac{2}{3}} p^{3} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a \,q^{3}-\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{3} b p q +\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha  b p \,q^{2}+3 \left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{8} a \,p^{6} q +3 \left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{7} a \,p^{5} q +3 \left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{5} a \,p^{5} q^{2}+3 \left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{4} a \,p^{4} q^{2}+i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, q^{2} b -3 i \left(-q \,p^{2}\right)^{\frac{1}{3}} p^{6} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{8} a q +3 i \left(-q \,p^{2}\right)^{\frac{2}{3}} p^{5} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{7} a q +3 i \left(-q \,p^{2}\right)^{\frac{2}{3}} p^{4} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{4} a \,q^{2}-i \left(-q \,p^{2}\right)^{\frac{1}{3}} p^{4} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a \,q^{3}+i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{4} q \,p^{2} b +\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{11} a \,p^{7}+\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{10} a \,p^{6}+\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{7} b \,p^{3}+\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha^{6} b \,p^{2}+\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{2} a \,p^{4} q^{3}+\left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  a \,p^{3} q^{3}-\left(-q \,p^{2}\right)^{\frac{1}{3}} \underline{\hspace{1.25 ex}}\alpha^{4} b \,p^{2} q +i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{6} p^{2} b -i \left(-q \,p^{2}\right)^{\frac{1}{3}} p^{7} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{11} a \right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}-\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right) \sqrt{3}\, p}{\left(-q \,p^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{3 i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{7} a \,p^{6} q^{2}+3 i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{4} a \,p^{5} q^{3}-i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{7} b \,p^{2}-3 q^{3} b p -2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, a \,p^{3} q^{4}+i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{10} a \,p^{7} q +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{6} b \,p^{3} q +i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  a \,p^{4} q^{4}-i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{11} a \,p^{6}+i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{4} b p q -3 i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{8} a \,p^{5} q -6 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{6} a \,p^{5} q^{2}-3 i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5} a \,p^{4} q^{2}-6 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} a \,p^{4} q^{3}-i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} a \,p^{3} q^{3}-2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{5} b \,p^{2} q +2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{2} b p \,q^{2}-2 i \left(-q \,p^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{9} a \,p^{6} q -3 p^{3} \underline{\hspace{1.25 ex}}\alpha^{6} q b -3 p^{4} \underline{\hspace{1.25 ex}}\alpha  a \,q^{4}+3 \underline{\hspace{1.25 ex}}\alpha^{3} q^{2} p^{2} b -3 p^{7} \underline{\hspace{1.25 ex}}\alpha^{10} a q -9 p^{6} \underline{\hspace{1.25 ex}}\alpha^{7} a \,q^{2}-9 p^{5} \underline{\hspace{1.25 ex}}\alpha^{4} a \,q^{3}-3 \left(-q \,p^{2}\right)^{\frac{2}{3}} \underline{\hspace{1.25 ex}}\alpha  \,q^{2} b -3 \underline{\hspace{1.25 ex}}\alpha^{11} p^{6} \left(-q \,p^{2}\right)^{\frac{2}{3}} a -3 \underline{\hspace{1.25 ex}}\alpha^{7} \left(-q \,p^{2}\right)^{\frac{2}{3}} p^{2} b -9 \underline{\hspace{1.25 ex}}\alpha^{5} p^{4} \left(-q \,p^{2}\right)^{\frac{2}{3}} a \,q^{2}-3 \underline{\hspace{1.25 ex}}\alpha^{2} p^{3} \left(-q \,p^{2}\right)^{\frac{2}{3}} a \,q^{3}+3 \underline{\hspace{1.25 ex}}\alpha^{4} \left(-q \,p^{2}\right)^{\frac{2}{3}} q p b -9 \underline{\hspace{1.25 ex}}\alpha^{8} p^{5} \left(-q \,p^{2}\right)^{\frac{2}{3}} a q +i \sqrt{3}\, b p \,q^{3}-i \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha^{3} b \,p^{2} q^{2}-i \left(-q \,p^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \underline{\hspace{1.25 ex}}\alpha  b \,q^{2}}{2 p \,q^{3} b}, \sqrt{\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{p \left(-\frac{3 \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}+\frac{i \sqrt{3}\, \left(-q \,p^{2}\right)^{\frac{1}{3}}}{2 p}\right)}}\right)}{2 \left(-3 \underline{\hspace{1.25 ex}}\alpha^{9} a \,p^{4}-9 \underline{\hspace{1.25 ex}}\alpha^{6} a \,p^{3} q -9 \underline{\hspace{1.25 ex}}\alpha^{3} a \,p^{2} q^{2}-2 \underline{\hspace{1.25 ex}}\alpha^{5} b -3 a p \,q^{3}\right) \sqrt{p \,x^{3}+q}}\right)}{4 p^{2} q^{3} b}$&$1596$\\ \hline \end{longtable}"," ",0,"1/4*I/p^2/q^3/b*2^(1/2)*sum((_alpha^6*p^2-_alpha^3*p*q-2*q^2)*_alpha^2/(-3*_alpha^9*a*p^4-9*_alpha^6*a*p^3*q-9*_alpha^3*a*p^2*q^2-2*_alpha^5*b-3*a*p*q^3)*(-q*p^2)^(1/3)*(1/2*I*p*(2*x+1/p*(-I*3^(1/2)*(-q*p^2)^(1/3)+(-q*p^2)^(1/3)))/(-q*p^2)^(1/3))^(1/2)*(p*(x-1/p*(-q*p^2)^(1/3))/(-3*(-q*p^2)^(1/3)+I*3^(1/2)*(-q*p^2)^(1/3)))^(1/2)*(-1/2*I*p*(2*x+1/p*(I*3^(1/2)*(-q*p^2)^(1/3)+(-q*p^2)^(1/3)))/(-q*p^2)^(1/3))^(1/2)/(p*x^3+q)^(1/2)*((-q*p^2)^(2/3)*b*q^2+I*(-q*p^2)^(2/3)*p^3*3^(1/2)*_alpha*a*q^3+I*(-q*p^2)^(1/3)*3^(1/2)*_alpha^4*q*p^2*b+3*I*(-q*p^2)^(2/3)*p^4*3^(1/2)*_alpha^4*a*q^2+2*q*p^2*(_alpha^9*a*p^5+3*_alpha^6*a*p^4*q+3*_alpha^3*a*p^3*q^2+_alpha^5*b*p+a*p^2*q^3-_alpha^2*b*q)-I*(-q*p^2)^(1/3)*p^4*3^(1/2)*_alpha^2*a*q^3-3*I*(-q*p^2)^(1/3)*p^6*3^(1/2)*_alpha^8*a*q+3*I*(-q*p^2)^(2/3)*p^5*3^(1/2)*_alpha^7*a*q-3*I*(-q*p^2)^(1/3)*p^5*3^(1/2)*_alpha^5*a*q^2-I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^3*q*p*b-I*(-q*p^2)^(1/3)*3^(1/2)*_alpha*q^2*p*b-(-q*p^2)^(2/3)*_alpha^3*b*p*q+(-q*p^2)^(1/3)*_alpha*b*p*q^2+3*(-q*p^2)^(1/3)*_alpha^8*a*p^6*q+3*(-q*p^2)^(2/3)*_alpha^7*a*p^5*q+3*(-q*p^2)^(1/3)*_alpha^5*a*p^5*q^2+3*(-q*p^2)^(2/3)*_alpha^4*a*p^4*q^2+(-q*p^2)^(1/3)*_alpha^11*a*p^7+(-q*p^2)^(2/3)*_alpha^10*a*p^6+(-q*p^2)^(1/3)*_alpha^7*b*p^3+(-q*p^2)^(2/3)*_alpha^6*b*p^2+(-q*p^2)^(1/3)*_alpha^2*a*p^4*q^3+(-q*p^2)^(2/3)*_alpha*a*p^3*q^3-(-q*p^2)^(1/3)*_alpha^4*b*p^2*q+I*(-q*p^2)^(2/3)*3^(1/2)*q^2*b+I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^6*p^2*b-I*(-q*p^2)^(1/3)*p^7*3^(1/2)*_alpha^11*a-I*(-q*p^2)^(1/3)*p^3*3^(1/2)*_alpha^7*b+I*(-q*p^2)^(2/3)*p^6*3^(1/2)*_alpha^10*a)*EllipticPi(1/3*3^(1/2)*(I*(x+1/2/p*(-q*p^2)^(1/3)-1/2*I*3^(1/2)/p*(-q*p^2)^(1/3))*3^(1/2)*p/(-q*p^2)^(1/3))^(1/2),-1/2/p*(-3*q^3*b*p+I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^4*b*p*q-3*I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^8*a*p^5*q-6*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha^6*a*p^5*q^2-3*I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^5*a*p^4*q^2-6*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha^3*a*p^4*q^3-I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^2*a*p^3*q^3-2*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha^5*b*p^2*q+2*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha^2*b*p*q^2-2*I*(-q*p^2)^(1/3)*3^(1/2)*_alpha^9*a*p^6*q+I*3^(1/2)*b*p*q^3-2*I*(-q*p^2)^(1/3)*3^(1/2)*a*p^3*q^4-3*p^3*_alpha^6*q*b-3*p^4*_alpha*a*q^4+3*_alpha^3*q^2*p^2*b-3*p^7*_alpha^10*a*q-9*p^6*_alpha^7*a*q^2-9*p^5*_alpha^4*a*q^3-3*(-q*p^2)^(2/3)*_alpha*q^2*b-3*_alpha^11*p^6*(-q*p^2)^(2/3)*a-3*_alpha^7*(-q*p^2)^(2/3)*p^2*b-9*_alpha^5*p^4*(-q*p^2)^(2/3)*a*q^2-3*_alpha^2*p^3*(-q*p^2)^(2/3)*a*q^3+3*_alpha^4*(-q*p^2)^(2/3)*q*p*b-9*_alpha^8*p^5*(-q*p^2)^(2/3)*a*q+I*3^(1/2)*_alpha^10*a*p^7*q+I*3^(1/2)*_alpha^6*b*p^3*q+I*3^(1/2)*_alpha*a*p^4*q^4-I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^11*a*p^6+3*I*3^(1/2)*_alpha^7*a*p^6*q^2+3*I*3^(1/2)*_alpha^4*a*p^5*q^3-I*(-q*p^2)^(2/3)*3^(1/2)*_alpha^7*b*p^2-I*3^(1/2)*_alpha^3*b*p^2*q^2-I*(-q*p^2)^(2/3)*3^(1/2)*_alpha*b*q^2)/q^3/b,(I*3^(1/2)/p*(-q*p^2)^(1/3)/(-3/2/p*(-q*p^2)^(1/3)+1/2*I*3^(1/2)/p*(-q*p^2)^(1/3)))^(1/2)),_alpha=RootOf(_Z^12*a*p^4+4*_Z^9*a*p^3*q+6*_Z^6*a*p^2*q^2+_Z^8*b+4*_Z^3*a*p*q^3+a*q^4))","C"
2999,0,0,187,0.034000," ","int((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^2,x)","\[\int \frac{\sqrt{x +\sqrt{x^{2}+1}}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(x^{2}+1\right)^{2}}\, dx\]"," ",0,"int((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^2,x)","F"
3000,0,0,187,0.004000," ","int((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^2,x)","\[\int \frac{\sqrt{x +\sqrt{x^{2}+1}}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(x^{2}+1\right)^{2}}\, dx\]"," ",0,"int((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^2,x)","F"
3001,0,0,61,0.045000," ","int((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","\[\int \frac{\sqrt{x +\sqrt{x^{2}+1}}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right)^{2}}\, dx\]"," ",0,"int((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","F"
3002,0,0,61,0.005000," ","int((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","\[\int \frac{\sqrt{x +\sqrt{x^{2}+1}}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right)^{2}}\, dx\]"," ",0,"int((x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","F"
3003,0,0,191,0.038000," ","int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(x^{2}+1\right)^{2} \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x)","F"
3004,0,0,191,0.004000," ","int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(x^{2}+1\right)^{2} \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x)","F"
3005,0,0,333,0.042000," ","int((1+(-2+k)*x)*(k^2*x^2-2*k*x+1)/((1-x)*x*(-k*x+1))^(1/3)/(b-4*b*k*x+(6*b*k^2-1)*x^2+(-4*b*k^3+2)*x^3+(b*k^4-1)*x^4),x)","\[\int \frac{\left(1+\left(-2+k \right) x \right) \left(k^{2} x^{2}-2 k x +1\right)}{\left(\left(1-x \right) x \left(-k x +1\right)\right)^{\frac{1}{3}} \left(b -4 b k x +\left(6 b \,k^{2}-1\right) x^{2}+\left(-4 b \,k^{3}+2\right) x^{3}+\left(b \,k^{4}-1\right) x^{4}\right)}\, dx\]"," ",0,"int((1+(-2+k)*x)*(k^2*x^2-2*k*x+1)/((1-x)*x*(-k*x+1))^(1/3)/(b-4*b*k*x+(6*b*k^2-1)*x^2+(-4*b*k^3+2)*x^3+(b*k^4-1)*x^4),x)","F"
3006,0,0,59,0.049000," ","int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right)^{2} \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x)","F"
3007,0,0,59,0.004000," ","int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right)^{2} \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x)","F"
3008,0,0,333,0.136000," ","int((a-2*b+x)*(a^2-2*a*x+x^2)/((-a+x)*(-b+x))^(1/3)/(-b^2+a^4*d+2*(-2*a^3*d+b)*x+(6*a^2*d-1)*x^2-4*a*d*x^3+d*x^4),x)","\[\int \frac{\left(a -2 b +x \right) \left(a^{2}-2 a x +x^{2}\right)}{\left(\left(-a +x \right) \left(-b +x \right)\right)^{\frac{1}{3}} \left(-b^{2}+a^{4} d +2 \left(-2 a^{3} d +b \right) x +\left(6 a^{2} d -1\right) x^{2}-4 a d \,x^{3}+d \,x^{4}\right)}\, dx\]"," ",0,"int((a-2*b+x)*(a^2-2*a*x+x^2)/((-a+x)*(-b+x))^(1/3)/(-b^2+a^4*d+2*(-2*a^3*d+b)*x+(6*a^2*d-1)*x^2-4*a*d*x^3+d*x^4),x)","F"
3009,0,0,180,0.049000," ","int((x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1)/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{\left(x^{4}+1\right) \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{4}+1\right) \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1)/(x+(x^2+1)^(1/2))^(1/2),x)","F"
3010,0,0,180,0.005000," ","int((x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1)/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{\left(x^{4}+1\right) \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{4}+1\right) \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1)/(x+(x^2+1)^(1/2))^(1/2),x)","F"
3011,1,268,321,0.293000," ","int((a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)/(x-(a*x+b)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{4 \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}+4 a \sqrt{c +\sqrt{a x +b}}+\frac{4 \left(a^{2} \sqrt{a^{2}+4 b}+a c \sqrt{a^{2}+4 b}+a^{3}+a^{2} c +b \sqrt{a^{2}+4 b}+3 a b +2 b c \right) \arctan \left(\frac{2 \sqrt{c +\sqrt{a x +b}}}{\sqrt{-2 \sqrt{a^{2}+4 b}-2 a -4 c}}\right)}{\sqrt{a^{2}+4 b}\, \sqrt{-2 \sqrt{a^{2}+4 b}-2 a -4 c}}+\frac{4 \left(a^{2} \sqrt{a^{2}+4 b}+a c \sqrt{a^{2}+4 b}-a^{3}-a^{2} c +b \sqrt{a^{2}+4 b}-3 a b -2 b c \right) \arctan \left(\frac{2 \sqrt{c +\sqrt{a x +b}}}{\sqrt{2 \sqrt{a^{2}+4 b}-2 a -4 c}}\right)}{\sqrt{a^{2}+4 b}\, \sqrt{2 \sqrt{a^{2}+4 b}-2 a -4 c}}$&$268$\\ default&$\frac{4 \left(c +\sqrt{a x +b}\right)^{\frac{3}{2}}}{3}+4 a \sqrt{c +\sqrt{a x +b}}+\frac{4 \left(a^{2} \sqrt{a^{2}+4 b}+a c \sqrt{a^{2}+4 b}+a^{3}+a^{2} c +b \sqrt{a^{2}+4 b}+3 a b +2 b c \right) \arctan \left(\frac{2 \sqrt{c +\sqrt{a x +b}}}{\sqrt{-2 \sqrt{a^{2}+4 b}-2 a -4 c}}\right)}{\sqrt{a^{2}+4 b}\, \sqrt{-2 \sqrt{a^{2}+4 b}-2 a -4 c}}+\frac{4 \left(a^{2} \sqrt{a^{2}+4 b}+a c \sqrt{a^{2}+4 b}-a^{3}-a^{2} c +b \sqrt{a^{2}+4 b}-3 a b -2 b c \right) \arctan \left(\frac{2 \sqrt{c +\sqrt{a x +b}}}{\sqrt{2 \sqrt{a^{2}+4 b}-2 a -4 c}}\right)}{\sqrt{a^{2}+4 b}\, \sqrt{2 \sqrt{a^{2}+4 b}-2 a -4 c}}$&$268$\\ \hline \end{longtable}"," ",0,"4/3*(c+(a*x+b)^(1/2))^(3/2)+4*a*(c+(a*x+b)^(1/2))^(1/2)+4*(a^2*(a^2+4*b)^(1/2)+a*c*(a^2+4*b)^(1/2)+a^3+a^2*c+b*(a^2+4*b)^(1/2)+3*a*b+2*b*c)/(a^2+4*b)^(1/2)/(-2*(a^2+4*b)^(1/2)-2*a-4*c)^(1/2)*arctan(2*(c+(a*x+b)^(1/2))^(1/2)/(-2*(a^2+4*b)^(1/2)-2*a-4*c)^(1/2))+4*(a^2*(a^2+4*b)^(1/2)+a*c*(a^2+4*b)^(1/2)-a^3-a^2*c+b*(a^2+4*b)^(1/2)-3*a*b-2*b*c)/(a^2+4*b)^(1/2)/(2*(a^2+4*b)^(1/2)-2*a-4*c)^(1/2)*arctan(2*(c+(a*x+b)^(1/2))^(1/2)/(2*(a^2+4*b)^(1/2)-2*a-4*c)^(1/2))","A"
3012,0,0,338,0.009000," ","int((1+x)/(-a*x+1)/((-b*x+1)/(c+x))^(1/4),x)","\[\int \frac{1+x}{\left(-a x +1\right) \left(\frac{-b x +1}{c +x}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((1+x)/(-a*x+1)/((-b*x+1)/(c+x))^(1/4),x)","F"
3013,0,0,349,0.044000," ","int(x^5*(9*a*x^2-7*b)/(a*x^5-b*x^3)^(1/4)/(a*x^9-b*x^7+1),x)","\[\int \frac{x^{5} \left(9 a \,x^{2}-7 b \right)}{\left(a \,x^{5}-b \,x^{3}\right)^{\frac{1}{4}} \left(a \,x^{9}-b \,x^{7}+1\right)}\, dx\]"," ",0,"int(x^5*(9*a*x^2-7*b)/(a*x^5-b*x^3)^(1/4)/(a*x^9-b*x^7+1),x)","F"
3014,1,24,301,0.212000," ","int((a*x^4+b)/(a*x^4-b)^(1/2)/(a*x^4+c^2*x^2-b),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\arctan \left(\frac{\sqrt{a \,x^{4}-b}}{x c}\right)}{c}$&$24$\\ default&$\frac{\sqrt{1+\frac{\sqrt{a}\, x^{2}}{\sqrt{b}}}\, \sqrt{1-\frac{\sqrt{a}\, x^{2}}{\sqrt{b}}}\, \EllipticF \left(x \sqrt{-\frac{\sqrt{a}}{\sqrt{b}}}, i\right)}{\sqrt{-\frac{\sqrt{a}}{\sqrt{b}}}\, \sqrt{a \,x^{4}-b}}-\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{4}+c^{2} \textit{\_Z}^{2}-b \right)}{\sum}\frac{\left(c^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-2 b \right) \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{2} a +a \,x^{2}-c^{2}\right)}{\sqrt{-c^{2} \underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{a \,x^{4}-b}}\right)}{\sqrt{-c^{2} \underline{\hspace{1.25 ex}}\alpha^{2}}}-\frac{2 \underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2} a +c^{2}\right) \sqrt{1+\frac{\sqrt{a}\, x^{2}}{\sqrt{b}}}\, \sqrt{1-\frac{\sqrt{a}\, x^{2}}{\sqrt{b}}}\, \EllipticPi \left(x \sqrt{-\frac{\sqrt{a}}{\sqrt{b}}}, -\frac{\underline{\hspace{1.25 ex}}\alpha^{2} a +c^{2}}{\sqrt{b}\, \sqrt{a}}, \frac{\sqrt{\frac{\sqrt{a}}{\sqrt{b}}}}{\sqrt{-\frac{\sqrt{a}}{\sqrt{b}}}}\right)}{\sqrt{-\frac{\sqrt{a}}{\sqrt{b}}}\, b \sqrt{a \,x^{4}-b}}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2} a +c^{2}\right)}\right)}{4}$&$288$\\ \hline \end{longtable}"," ",0,"1/c*arctan((a*x^4-b)^(1/2)/x/c)","A"
3015,0,0,363,0.023000," ","int(x*(-a+x)*(a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^2)^(1/3)/(-b^2+2*b*x+(a^2*d-1)*x^2-2*a*d*x^3+d*x^4),x)","\[\int \frac{x \left(-a +x \right) \left(a b -2 b x +x^{2}\right)}{\left(x \left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{3}} \left(-b^{2}+2 b x +\left(a^{2} d -1\right) x^{2}-2 a d \,x^{3}+d \,x^{4}\right)}\, dx\]"," ",0,"int(x*(-a+x)*(a*b-2*b*x+x^2)/(x*(-a+x)*(-b+x)^2)^(1/3)/(-b^2+2*b*x+(a^2*d-1)*x^2-2*a*d*x^3+d*x^4),x)","F"
3016,0,0,337,0.074000," ","int((a*x+b)/(a*x-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{a x +b}{\left(a x -b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a*x+b)/(a*x-b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
3017,0,0,82,180.000000," ","int((a^2*x^4+b)^(1/2)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^4-b),x)","\[\int \frac{\sqrt{a^{2} x^{4}+b}\, \sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}{a^{2} x^{4}-b}\, dx\]"," ",0,"int((a^2*x^4+b)^(1/2)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^4-b),x)","F"
3018,0,0,82,180.000000," ","int((a^2*x^4+b)^(1/2)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^4-b),x)","\[\int \frac{\sqrt{a^{2} x^{4}+b}\, \sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}{a^{2} x^{4}-b}\, dx\]"," ",0,"int((a^2*x^4+b)^(1/2)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(a^2*x^4-b),x)","F"
3019,0,0,369,0.046000," ","int(1/((-a+x)*(-b+x)^2)^(1/3)/(b-a*d+(-1+d)*x),x)","\[\int \frac{1}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{3}} \left(b -a d +\left(-1+d \right) x \right)}\, dx\]"," ",0,"int(1/((-a+x)*(-b+x)^2)^(1/3)/(b-a*d+(-1+d)*x),x)","F"
3020,0,0,378,0.024000," ","int((2*x^2-3*x-4)*(x^4-x^2+x+1)*((2*x^4-x^2+x+1)/(3*x^4-x^2+x+1))^(1/3)/x^5/(x^4+x^2-x-1),x)","\[\int \frac{\left(2 x^{2}-3 x -4\right) \left(x^{4}-x^{2}+x +1\right) \left(\frac{2 x^{4}-x^{2}+x +1}{3 x^{4}-x^{2}+x +1}\right)^{\frac{1}{3}}}{x^{5} \left(x^{4}+x^{2}-x -1\right)}\, dx\]"," ",0,"int((2*x^2-3*x-4)*(x^4-x^2+x+1)*((2*x^4-x^2+x+1)/(3*x^4-x^2+x+1))^(1/3)/x^5/(x^4+x^2-x-1),x)","F"
3021,0,0,345,0.074000," ","int((a*x-b)/(a*x+b)/(a^3*x^3-b^2*x^2)^(1/3),x)","\[\int \frac{a x -b}{\left(a x +b \right) \left(a^{3} x^{3}-b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a*x-b)/(a*x+b)/(a^3*x^3-b^2*x^2)^(1/3),x)","F"
3022,1,242,11,0.201000," ","int((p*x^4-q)*(p*x^4+q)^(1/2)/(c*x^4+b*x^2*(p*x^4+q)+a*(p*x^4+q)^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(\frac{\arctan \left(\frac{\sqrt{p \,x^{4}+q}\, \sqrt{2}\, a}{x \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) a}}\right)}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) a}}+\frac{\arctan \left(\frac{\sqrt{p \,x^{4}+q}\, \sqrt{2}\, a}{x \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) a}}\right) b}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) a}}-\frac{\arctanh \left(\frac{\sqrt{p \,x^{4}+q}\, \sqrt{2}\, a}{x \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) a}}\right)}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) a}}+\frac{\arctanh \left(\frac{\sqrt{p \,x^{4}+q}\, \sqrt{2}\, a}{x \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) a}}\right) b}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) a}}\right) \sqrt{2}}{2}$&$242$\\ elliptic&$\frac{\left(\frac{\arctan \left(\frac{\sqrt{p \,x^{4}+q}\, \sqrt{2}\, a}{x \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) a}}\right)}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) a}}+\frac{\arctan \left(\frac{\sqrt{p \,x^{4}+q}\, \sqrt{2}\, a}{x \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) a}}\right) b}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) a}}-\frac{\arctanh \left(\frac{\sqrt{p \,x^{4}+q}\, \sqrt{2}\, a}{x \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) a}}\right)}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) a}}+\frac{\arctanh \left(\frac{\sqrt{p \,x^{4}+q}\, \sqrt{2}\, a}{x \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) a}}\right) b}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) a}}\right) \sqrt{2}}{2}$&$242$\\ \hline \end{longtable}"," ",0,"1/2*(1/((b+(-4*a*c+b^2)^(1/2))*a)^(1/2)*arctan((p*x^4+q)^(1/2)*2^(1/2)/x*a/((b+(-4*a*c+b^2)^(1/2))*a)^(1/2))+1/(-4*a*c+b^2)^(1/2)/((b+(-4*a*c+b^2)^(1/2))*a)^(1/2)*arctan((p*x^4+q)^(1/2)*2^(1/2)/x*a/((b+(-4*a*c+b^2)^(1/2))*a)^(1/2))*b-1/((-b+(-4*a*c+b^2)^(1/2))*a)^(1/2)*arctanh((p*x^4+q)^(1/2)*2^(1/2)/x*a/((-b+(-4*a*c+b^2)^(1/2))*a)^(1/2))+1/(-4*a*c+b^2)^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*a)^(1/2)*arctanh((p*x^4+q)^(1/2)*2^(1/2)/x*a/((-b+(-4*a*c+b^2)^(1/2))*a)^(1/2))*b)*2^(1/2)","B"
3023,0,0,118,0.071000," ","int((x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(1/2)/(-x^4+1),x)","\[\int \frac{\left(x^{4}+1\right) \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\sqrt{x^{2}+1}\, \left(-x^{4}+1\right)}\, dx\]"," ",0,"int((x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(1/2)/(-x^4+1),x)","F"
3024,0,0,118,0.005000," ","int((x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(1/2)/(-x^4+1),x)","\[\int \frac{\left(x^{4}+1\right) \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\sqrt{x^{2}+1}\, \left(-x^{4}+1\right)}\, dx\]"," ",0,"int((x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(1/2)/(-x^4+1),x)","F"
3025,0,0,329,180.000000," ","int((x^6-x^3+1)/(x^4+x^2)^(1/3)/(x^6-1),x)","\[\int \frac{x^{6}-x^{3}+1}{\left(x^{4}+x^{2}\right)^{\frac{1}{3}} \left(x^{6}-1\right)}\, dx\]"," ",0,"int((x^6-x^3+1)/(x^4+x^2)^(1/3)/(x^6-1),x)","F"
3026,0,0,329,180.000000," ","int((x^6+x^3+1)/(x^4+x^2)^(1/3)/(x^6-1),x)","\[\int \frac{x^{6}+x^{3}+1}{\left(x^{4}+x^{2}\right)^{\frac{1}{3}} \left(x^{6}-1\right)}\, dx\]"," ",0,"int((x^6+x^3+1)/(x^4+x^2)^(1/3)/(x^6-1),x)","F"
3027,0,0,379,180.000000," ","int((a^2*x^2-b)^(1/2)*(a*x+(a^2*x^2-b)^(1/2))^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/2))^(1/2),x)","\[\int \frac{\sqrt{a^{2} x^{2}-b}\, \sqrt{a x +\sqrt{a^{2} x^{2}-b}}}{\sqrt{c +\sqrt{a x +\sqrt{a^{2} x^{2}-b}}}}\, dx\]"," ",0,"int((a^2*x^2-b)^(1/2)*(a*x+(a^2*x^2-b)^(1/2))^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/2))^(1/2),x)","F"
3028,0,0,318,0.040000," ","int((a*x^8-1)*(a*x^8+1)^(3/4)/(a^2*x^16+x^8+1),x)","\[\int \frac{\left(a \,x^{8}-1\right) \left(a \,x^{8}+1\right)^{\frac{3}{4}}}{a^{2} x^{16}+x^{8}+1}\, dx\]"," ",0,"int((a*x^8-1)*(a*x^8+1)^(3/4)/(a^2*x^16+x^8+1),x)","F"
3029,0,0,353,0.075000," ","int((a*x-b)/(a*x+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","\[\int \frac{a x -b}{\left(a x +b \right) \left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a*x-b)/(a*x+b)/(a^3*x^3+b^2*x^2)^(1/3),x)","F"
3030,0,0,327,0.081000," ","int(1/(x^2-1)^2/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{1}{\left(x^{2}-1\right)^{2} \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int(1/(x^2-1)^2/(x+(x^2+1)^(1/2))^(1/2),x)","F"
3031,1,487,52,0.411000," ","int((a*x^2+b*x+c)^(3/2)/(1-x*(a*x^2+b*x+c)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8} a -2 \sqrt{a}\, \textit{\_Z}^{7} b +\textit{\_Z}^{6} b^{2}+2 \sqrt{a}\, \textit{\_Z}^{5} b c +\left(-2 a \,c^{2}-2 b^{2} c -16 a^{2}\right) \textit{\_Z}^{4}+\left(32 a^{\frac{3}{2}} b +2 \sqrt{a}\, c^{2} b \right) \textit{\_Z}^{3}+\left(b^{2} c^{2}-24 a \,b^{2}\right) \textit{\_Z}^{2}+\left(-2 \sqrt{a}\, c^{3} b +8 \sqrt{a}\, b^{3}\right) \textit{\_Z} +a \,c^{4}-b^{4}\right)}{\sum}\frac{\left(2 a \left(\left(a c +b^{2}\right) \textit{\_R}^{5}+2 \left(a \,c^{2}+b^{2} c +2 a^{2}\right) \textit{\_R}^{3}+a \left(c^{3}+3 b^{2}\right) \textit{\_R} \right)+b \left(-a^{\frac{3}{2}} \textit{\_R}^{6}+\textit{\_R}^{4} \left(-6 a^{\frac{3}{2}} c -b^{2} \sqrt{a}\right)+\textit{\_R}^{2} \left(-12 a^{\frac{5}{2}}-5 a^{\frac{3}{2}} c^{2}\right)-a^{\frac{3}{2}} b^{2}\right)\right) \ln \left(\sqrt{a \,x^{2}+b x +c}-\sqrt{a}\, x -\textit{\_R} \right)}{4 \textit{\_R}^{7} a +3 \textit{\_R}^{5} b^{2}-4 \textit{\_R}^{3} a \,c^{2}-4 \textit{\_R}^{3} b^{2} c -32 \textit{\_R}^{3} a^{2}+\textit{\_R} \,b^{2} c^{2}-24 a \,b^{2} \textit{\_R} +b \left(-7 \textit{\_R}^{6} \sqrt{a}+5 c \,\textit{\_R}^{4} \sqrt{a}+48 \textit{\_R}^{2} a^{\frac{3}{2}}+3 c^{2} \textit{\_R}^{2} \sqrt{a}-\sqrt{a}\, c^{3}+4 b^{2} \sqrt{a}\right)}}{\sqrt{a}}+\sqrt{a}\, \ln \left(2 \left(-\sqrt{a}\, x +\sqrt{a \,x^{2}+b x +c}\right) \sqrt{a}-b \right)-\frac{a \,x^{2}}{2}-b x -\left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{4}+b \,\textit{\_Z}^{3}+c \,\textit{\_Z}^{2}-1\right)}{\sum}\frac{\left(\textit{\_R}^{3} a c +\textit{\_R}^{2} b c +\left(c^{2}+a \right) \textit{\_R} +b \right) \ln \left(x -\textit{\_R} \right)}{4 \textit{\_R}^{3} a +3 \textit{\_R}^{2} b +2 \textit{\_R} c}\right)$&$487$\\ \hline \end{longtable}"," ",0,"1/a^(1/2)*sum((2*a*((a*c+b^2)*_R^5+2*(a*c^2+b^2*c+2*a^2)*_R^3+a*(c^3+3*b^2)*_R)+b*(-a^(3/2)*_R^6+_R^4*(-6*a^(3/2)*c-b^2*a^(1/2))+_R^2*(-12*a^(5/2)-5*a^(3/2)*c^2)-a^(3/2)*b^2))/(4*_R^7*a+3*_R^5*b^2-4*_R^3*a*c^2-4*_R^3*b^2*c-32*_R^3*a^2+_R*b^2*c^2-24*a*b^2*_R+b*(-7*_R^6*a^(1/2)+5*c*_R^4*a^(1/2)+48*_R^2*a^(3/2)+3*c^2*_R^2*a^(1/2)-a^(1/2)*c^3+4*b^2*a^(1/2)))*ln((a*x^2+b*x+c)^(1/2)-a^(1/2)*x-_R),_R=RootOf(_Z^8*a-2*a^(1/2)*_Z^7*b+_Z^6*b^2+2*a^(1/2)*_Z^5*b*c+(-2*a*c^2-2*b^2*c-16*a^2)*_Z^4+(32*a^(3/2)*b+2*a^(1/2)*c^2*b)*_Z^3+(b^2*c^2-24*a*b^2)*_Z^2+(-2*a^(1/2)*c^3*b+8*a^(1/2)*b^3)*_Z+a*c^4-b^4))+a^(1/2)*ln(2*(-a^(1/2)*x+(a*x^2+b*x+c)^(1/2))*a^(1/2)-b)-1/2*a*x^2-b*x-sum((_R^3*a*c+_R^2*b*c+(c^2+a)*_R+b)/(4*_R^3*a+3*_R^2*b+2*_R*c)*ln(x-_R),_R=RootOf(_Z^4*a+_Z^3*b+_Z^2*c-1))","B"
3032,0,0,346,0.212000," ","int((-b+x)^2/((-a+x)*(-b+x)^2)^(2/3)/(-a^2+b^2*d+2*(-b*d+a)*x+(-1+d)*x^2),x)","\[\int \frac{\left(-b +x \right)^{2}}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{2}{3}} \left(-a^{2}+b^{2} d +2 \left(-b d +a \right) x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((-b+x)^2/((-a+x)*(-b+x)^2)^(2/3)/(-a^2+b^2*d+2*(-b*d+a)*x+(-1+d)*x^2),x)","F"
3033,0,0,361,0.078000," ","int((a*x+b)/(a*x-b)/(a^3*x^3-b^2*x^2)^(1/3),x)","\[\int \frac{a x +b}{\left(a x -b \right) \left(a^{3} x^{3}-b^{2} x^{2}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((a*x+b)/(a*x-b)/(a^3*x^3-b^2*x^2)^(1/3),x)","F"
3034,0,0,355,180.000000," ","int(1/(a*x+(a^2*x^2-b)^(1/2))^(1/3)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/3))^(1/4),x)","\[\int \frac{1}{\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{3}} \left(c +\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{3}}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(a*x+(a^2*x^2-b)^(1/2))^(1/3)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/3))^(1/4),x)","F"
3035,0,0,330,0.048000," ","int(x^4/(a*x^4-b)^(1/4)/(x^8+2*a*x^4-b),x)","\[\int \frac{x^{4}}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(x^{8}+2 a \,x^{4}-b \right)}\, dx\]"," ",0,"int(x^4/(a*x^4-b)^(1/4)/(x^8+2*a*x^4-b),x)","F"
3036,0,0,370,180.000000," ","int((c*x^2+d)*(a*x+(a^2*x^2-b)^(1/2))^(3/4)/(a^2*x^2-b)^(5/2),x)","\[\int \frac{\left(c \,x^{2}+d \right) \left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{3}{4}}}{\left(a^{2} x^{2}-b \right)^{\frac{5}{2}}}\, dx\]"," ",0,"int((c*x^2+d)*(a*x+(a^2*x^2-b)^(1/2))^(3/4)/(a^2*x^2-b)^(5/2),x)","F"
3037,1,2928,339,109.589000," ","int(x^2/(x^4+1)/(x^6-x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2928$\\ \hline \end{longtable}"," ",0,"1/4*RootOf(32*_Z^4+8*_Z^2+1)*ln((-230912*RootOf(32*_Z^4+8*_Z^2+1)^5*x^5+865920*RootOf(32*_Z^4+8*_Z^2+1)^5*x^3-27672*RootOf(32*_Z^4+8*_Z^2+1)^3*x^5+208080*(x^6-x^2)^(1/2)*RootOf(32*_Z^4+8*_Z^2+1)^3*x+230912*RootOf(32*_Z^4+8*_Z^2+1)^5*x+364448*RootOf(32*_Z^4+8*_Z^2+1)^3*x^3+5789*RootOf(32*_Z^4+8*_Z^2+1)*x^5+73984*(x^6-x^2)^(3/4)*RootOf(32*_Z^4+8*_Z^2+1)^2+43928*(x^6-x^2)^(1/4)*RootOf(32*_Z^4+8*_Z^2+1)^2*x^2+36992*(x^6-x^2)^(1/2)*RootOf(32*_Z^4+8*_Z^2+1)*x+27672*RootOf(32*_Z^4+8*_Z^2+1)^3*x+38042*RootOf(32*_Z^4+8*_Z^2+1)*x^3+5491*(x^6-x^2)^(3/4)-7514*(x^6-x^2)^(1/4)*x^2-5789*RootOf(32*_Z^4+8*_Z^2+1)*x)/(8*RootOf(32*_Z^4+8*_Z^2+1)^2*x^2-32*RootOf(32*_Z^4+8*_Z^2+1)^2+5*x^2-3)^2/x)-1/8*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*ln(-(-230912*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*RootOf(32*_Z^4+8*_Z^2+1)^4*x^5+865920*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*RootOf(32*_Z^4+8*_Z^2+1)^4*x^3-87784*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*RootOf(32*_Z^4+8*_Z^2+1)^2*x^5-208080*(x^6-x^2)^(1/2)*RootOf(32*_Z^4+8*_Z^2+1)^2*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*x+230912*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*RootOf(32*_Z^4+8*_Z^2+1)^4*x+68512*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*RootOf(32*_Z^4+8*_Z^2+1)^2*x^3-1725*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*x^5+147968*(x^6-x^2)^(3/4)*RootOf(32*_Z^4+8*_Z^2+1)^2+87856*(x^6-x^2)^(1/4)*RootOf(32*_Z^4+8*_Z^2+1)^2*x^2-15028*(x^6-x^2)^(1/2)*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*x+87784*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*RootOf(32*_Z^4+8*_Z^2+1)^2*x+1050*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*x^3+26010*(x^6-x^2)^(3/4)+36992*(x^6-x^2)^(1/4)*x^2+1725*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*x)/(8*RootOf(32*_Z^4+8*_Z^2+1)^2*x^2-32*RootOf(32*_Z^4+8*_Z^2+1)^2-3*x^2-5)^2/x)+ln(-(-192512*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*RootOf(32*_Z^4+8*_Z^2+1)^4*x^5+721920*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*RootOf(32*_Z^4+8*_Z^2+1)^4*x^3-122112*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*RootOf(32*_Z^4+8*_Z^2+1)^2*x^5+87856*(x^6-x^2)^(1/2)*RootOf(32*_Z^4+8*_Z^2+1)^2*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*x+192512*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*RootOf(32*_Z^4+8*_Z^2+1)^4*x+240592*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*RootOf(32*_Z^4+8*_Z^2+1)^2*x^3-19021*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*x^5+147968*(x^6-x^2)^(3/4)*RootOf(32*_Z^4+8*_Z^2+1)^2-87856*(x^6-x^2)^(1/4)*RootOf(32*_Z^4+8*_Z^2+1)^2*x^2+36992*(x^6-x^2)^(1/2)*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*x+122112*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*RootOf(32*_Z^4+8*_Z^2+1)^2*x+11578*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*x^3+26010*(x^6-x^2)^(3/4)-36992*(x^6-x^2)^(1/4)*x^2+19021*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*x)/(8*RootOf(32*_Z^4+8*_Z^2+1)^2*x^2-32*RootOf(32*_Z^4+8*_Z^2+1)^2-3*x^2-5)^2/x)*RootOf(32*_Z^4+8*_Z^2+1)^2*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)+1/8*ln(-(-192512*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*RootOf(32*_Z^4+8*_Z^2+1)^4*x^5+721920*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*RootOf(32*_Z^4+8*_Z^2+1)^4*x^3-122112*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*RootOf(32*_Z^4+8*_Z^2+1)^2*x^5+87856*(x^6-x^2)^(1/2)*RootOf(32*_Z^4+8*_Z^2+1)^2*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*x+192512*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*RootOf(32*_Z^4+8*_Z^2+1)^4*x+240592*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*RootOf(32*_Z^4+8*_Z^2+1)^2*x^3-19021*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*x^5+147968*(x^6-x^2)^(3/4)*RootOf(32*_Z^4+8*_Z^2+1)^2-87856*(x^6-x^2)^(1/4)*RootOf(32*_Z^4+8*_Z^2+1)^2*x^2+36992*(x^6-x^2)^(1/2)*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*x+122112*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*RootOf(32*_Z^4+8*_Z^2+1)^2*x+11578*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*x^3+26010*(x^6-x^2)^(3/4)-36992*(x^6-x^2)^(1/4)*x^2+19021*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)*x)/(8*RootOf(32*_Z^4+8*_Z^2+1)^2*x^2-32*RootOf(32*_Z^4+8*_Z^2+1)^2-3*x^2-5)^2/x)*RootOf(_Z^2+4*RootOf(32*_Z^4+8*_Z^2+1)^2+1)-2*RootOf(32*_Z^4+8*_Z^2+1)^3*ln((192512*RootOf(32*_Z^4+8*_Z^2+1)^5*x^5-721920*RootOf(32*_Z^4+8*_Z^2+1)^5*x^3-25856*RootOf(32*_Z^4+8*_Z^2+1)^3*x^5+87856*(x^6-x^2)^(1/2)*RootOf(32*_Z^4+8*_Z^2+1)^3*x-192512*RootOf(32*_Z^4+8*_Z^2+1)^5*x-120368*RootOf(32*_Z^4+8*_Z^2+1)^3*x^3+525*RootOf(32*_Z^4+8*_Z^2+1)*x^5+73984*(x^6-x^2)^(3/4)*RootOf(32*_Z^4+8*_Z^2+1)^2-43928*(x^6-x^2)^(1/4)*RootOf(32*_Z^4+8*_Z^2+1)^2*x^2-15028*(x^6-x^2)^(1/2)*RootOf(32*_Z^4+8*_Z^2+1)*x+25856*RootOf(32*_Z^4+8*_Z^2+1)^3*x+3450*RootOf(32*_Z^4+8*_Z^2+1)*x^3+5491*(x^6-x^2)^(3/4)+7514*(x^6-x^2)^(1/4)*x^2-525*RootOf(32*_Z^4+8*_Z^2+1)*x)/(8*RootOf(32*_Z^4+8*_Z^2+1)^2*x^2-32*RootOf(32*_Z^4+8*_Z^2+1)^2+5*x^2-3)^2/x)-1/4*RootOf(32*_Z^4+8*_Z^2+1)*ln((192512*RootOf(32*_Z^4+8*_Z^2+1)^5*x^5-721920*RootOf(32*_Z^4+8*_Z^2+1)^5*x^3-25856*RootOf(32*_Z^4+8*_Z^2+1)^3*x^5+87856*(x^6-x^2)^(1/2)*RootOf(32*_Z^4+8*_Z^2+1)^3*x-192512*RootOf(32*_Z^4+8*_Z^2+1)^5*x-120368*RootOf(32*_Z^4+8*_Z^2+1)^3*x^3+525*RootOf(32*_Z^4+8*_Z^2+1)*x^5+73984*(x^6-x^2)^(3/4)*RootOf(32*_Z^4+8*_Z^2+1)^2-43928*(x^6-x^2)^(1/4)*RootOf(32*_Z^4+8*_Z^2+1)^2*x^2-15028*(x^6-x^2)^(1/2)*RootOf(32*_Z^4+8*_Z^2+1)*x+25856*RootOf(32*_Z^4+8*_Z^2+1)^3*x+3450*RootOf(32*_Z^4+8*_Z^2+1)*x^3+5491*(x^6-x^2)^(3/4)+7514*(x^6-x^2)^(1/4)*x^2-525*RootOf(32*_Z^4+8*_Z^2+1)*x)/(8*RootOf(32*_Z^4+8*_Z^2+1)^2*x^2-32*RootOf(32*_Z^4+8*_Z^2+1)^2+5*x^2-3)^2/x)","C"
3038,1,2931,339,113.298000," ","int(x^2/(x^4+1)/(x^6-x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2931$\\ \hline \end{longtable}"," ",0,"-1/4*RootOf(32*_Z^4-8*_Z^2+1)*ln(-(-230912*RootOf(32*_Z^4-8*_Z^2+1)^5*x^5+865920*RootOf(32*_Z^4-8*_Z^2+1)^5*x^3+27672*RootOf(32*_Z^4-8*_Z^2+1)^3*x^5+208080*(x^6-x^2)^(1/2)*RootOf(32*_Z^4-8*_Z^2+1)^3*x+230912*RootOf(32*_Z^4-8*_Z^2+1)^5*x-364448*RootOf(32*_Z^4-8*_Z^2+1)^3*x^3+5789*RootOf(32*_Z^4-8*_Z^2+1)*x^5+73984*(x^6-x^2)^(3/4)*RootOf(32*_Z^4-8*_Z^2+1)^2-43928*(x^6-x^2)^(1/4)*RootOf(32*_Z^4-8*_Z^2+1)^2*x^2-36992*(x^6-x^2)^(1/2)*RootOf(32*_Z^4-8*_Z^2+1)*x-27672*RootOf(32*_Z^4-8*_Z^2+1)^3*x+38042*RootOf(32*_Z^4-8*_Z^2+1)*x^3-5491*(x^6-x^2)^(3/4)-7514*(x^6-x^2)^(1/4)*x^2-5789*RootOf(32*_Z^4-8*_Z^2+1)*x)/(8*RootOf(32*_Z^4-8*_Z^2+1)^2*x^2-32*RootOf(32*_Z^4-8*_Z^2+1)^2-5*x^2+3)^2/x)-1/8*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*ln((230912*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*RootOf(32*_Z^4-8*_Z^2+1)^4*x^5-865920*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*RootOf(32*_Z^4-8*_Z^2+1)^4*x^3-87784*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*RootOf(32*_Z^4-8*_Z^2+1)^2*x^5+208080*(x^6-x^2)^(1/2)*RootOf(32*_Z^4-8*_Z^2+1)^2*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*x-230912*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*RootOf(32*_Z^4-8*_Z^2+1)^4*x+68512*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*RootOf(32*_Z^4-8*_Z^2+1)^2*x^3+1725*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*x^5+147968*(x^6-x^2)^(3/4)*RootOf(32*_Z^4-8*_Z^2+1)^2-87856*(x^6-x^2)^(1/4)*RootOf(32*_Z^4-8*_Z^2+1)^2*x^2-15028*(x^6-x^2)^(1/2)*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*x+87784*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*RootOf(32*_Z^4-8*_Z^2+1)^2*x-1050*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*x^3-26010*(x^6-x^2)^(3/4)+36992*(x^6-x^2)^(1/4)*x^2-1725*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*x)/(8*RootOf(32*_Z^4-8*_Z^2+1)^2*x^2-32*RootOf(32*_Z^4-8*_Z^2+1)^2+3*x^2+5)^2/x)-ln(-(20168550173184*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*RootOf(32*_Z^4-8*_Z^2+1)^4*x^5-75632063149440*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*RootOf(32*_Z^4-8*_Z^2+1)^4*x^3-5372907862360*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*RootOf(32*_Z^4-8*_Z^2+1)^2*x^5-22189554285584*(x^6-x^2)^(1/2)*RootOf(32*_Z^4-8*_Z^2+1)^2*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*x-20168550173184*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*RootOf(32*_Z^4-8*_Z^2+1)^4*x-2619997860096*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*RootOf(32*_Z^4-8*_Z^2+1)^2*x^3-673887370171*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*x^5+661540638128*(x^6-x^2)^(3/4)*RootOf(32*_Z^4-8*_Z^2+1)^2+22189554285584*(x^6-x^2)^(1/4)*RootOf(32*_Z^4-8*_Z^2+1)^2*x^2+165385159532*(x^6-x^2)^(1/2)*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*x+5372907862360*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*RootOf(32*_Z^4-8*_Z^2+1)^2*x+410192312278*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*x^3+2608309126166*(x^6-x^2)^(3/4)-165385159532*(x^6-x^2)^(1/4)*x^2+673887370171*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*x)/(8*RootOf(32*_Z^4-8*_Z^2+1)^2*x^2-32*RootOf(32*_Z^4-8*_Z^2+1)^2+3*x^2+5)^2/x)*RootOf(32*_Z^4-8*_Z^2+1)^2*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)+1/8*ln(-(20168550173184*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*RootOf(32*_Z^4-8*_Z^2+1)^4*x^5-75632063149440*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*RootOf(32*_Z^4-8*_Z^2+1)^4*x^3-5372907862360*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*RootOf(32*_Z^4-8*_Z^2+1)^2*x^5-22189554285584*(x^6-x^2)^(1/2)*RootOf(32*_Z^4-8*_Z^2+1)^2*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*x-20168550173184*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*RootOf(32*_Z^4-8*_Z^2+1)^4*x-2619997860096*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*RootOf(32*_Z^4-8*_Z^2+1)^2*x^3-673887370171*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*x^5+661540638128*(x^6-x^2)^(3/4)*RootOf(32*_Z^4-8*_Z^2+1)^2+22189554285584*(x^6-x^2)^(1/4)*RootOf(32*_Z^4-8*_Z^2+1)^2*x^2+165385159532*(x^6-x^2)^(1/2)*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*x+5372907862360*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*RootOf(32*_Z^4-8*_Z^2+1)^2*x+410192312278*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*x^3+2608309126166*(x^6-x^2)^(3/4)-165385159532*(x^6-x^2)^(1/4)*x^2+673887370171*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)*x)/(8*RootOf(32*_Z^4-8*_Z^2+1)^2*x^2-32*RootOf(32*_Z^4-8*_Z^2+1)^2+3*x^2+5)^2/x)*RootOf(_Z^2+4*RootOf(32*_Z^4-8*_Z^2+1)^2-1)+2*RootOf(32*_Z^4-8*_Z^2+1)^3*ln(-(-192512*RootOf(32*_Z^4-8*_Z^2+1)^5*x^5+721920*RootOf(32*_Z^4-8*_Z^2+1)^5*x^3-25856*RootOf(32*_Z^4-8*_Z^2+1)^3*x^5-87856*(x^6-x^2)^(1/2)*RootOf(32*_Z^4-8*_Z^2+1)^3*x+192512*RootOf(32*_Z^4-8*_Z^2+1)^5*x-120368*RootOf(32*_Z^4-8*_Z^2+1)^3*x^3-525*RootOf(32*_Z^4-8*_Z^2+1)*x^5+73984*(x^6-x^2)^(3/4)*RootOf(32*_Z^4-8*_Z^2+1)^2+43928*(x^6-x^2)^(1/4)*RootOf(32*_Z^4-8*_Z^2+1)^2*x^2-15028*(x^6-x^2)^(1/2)*RootOf(32*_Z^4-8*_Z^2+1)*x+25856*RootOf(32*_Z^4-8*_Z^2+1)^3*x-3450*RootOf(32*_Z^4-8*_Z^2+1)*x^3-5491*(x^6-x^2)^(3/4)+7514*(x^6-x^2)^(1/4)*x^2+525*RootOf(32*_Z^4-8*_Z^2+1)*x)/(8*RootOf(32*_Z^4-8*_Z^2+1)^2*x^2-32*RootOf(32*_Z^4-8*_Z^2+1)^2-5*x^2+3)^2/x)-1/4*RootOf(32*_Z^4-8*_Z^2+1)*ln(-(-192512*RootOf(32*_Z^4-8*_Z^2+1)^5*x^5+721920*RootOf(32*_Z^4-8*_Z^2+1)^5*x^3-25856*RootOf(32*_Z^4-8*_Z^2+1)^3*x^5-87856*(x^6-x^2)^(1/2)*RootOf(32*_Z^4-8*_Z^2+1)^3*x+192512*RootOf(32*_Z^4-8*_Z^2+1)^5*x-120368*RootOf(32*_Z^4-8*_Z^2+1)^3*x^3-525*RootOf(32*_Z^4-8*_Z^2+1)*x^5+73984*(x^6-x^2)^(3/4)*RootOf(32*_Z^4-8*_Z^2+1)^2+43928*(x^6-x^2)^(1/4)*RootOf(32*_Z^4-8*_Z^2+1)^2*x^2-15028*(x^6-x^2)^(1/2)*RootOf(32*_Z^4-8*_Z^2+1)*x+25856*RootOf(32*_Z^4-8*_Z^2+1)^3*x-3450*RootOf(32*_Z^4-8*_Z^2+1)*x^3-5491*(x^6-x^2)^(3/4)+7514*(x^6-x^2)^(1/4)*x^2+525*RootOf(32*_Z^4-8*_Z^2+1)*x)/(8*RootOf(32*_Z^4-8*_Z^2+1)^2*x^2-32*RootOf(32*_Z^4-8*_Z^2+1)^2-5*x^2+3)^2/x)","C"
3039,1,2857,339,99.300000," ","int((x^4-1)/(x^4+1)/(x^6-x^2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2857$\\ \hline \end{longtable}"," ",0,"1/4*RootOf(2*_Z^4-2*_Z^2+1)*ln(-(-12032*RootOf(2*_Z^4-2*_Z^2+1)^5*x^5+45120*RootOf(2*_Z^4-2*_Z^2+1)^5*x^3-6464*RootOf(2*_Z^4-2*_Z^2+1)^3*x^5-21964*(x^6-x^2)^(1/2)*RootOf(2*_Z^4-2*_Z^2+1)^3*x+12032*RootOf(2*_Z^4-2*_Z^2+1)^5*x-30092*RootOf(2*_Z^4-2*_Z^2+1)^3*x^3-525*RootOf(2*_Z^4-2*_Z^2+1)*x^5+36992*(x^6-x^2)^(3/4)*RootOf(2*_Z^4-2*_Z^2+1)^2+21964*(x^6-x^2)^(1/4)*RootOf(2*_Z^4-2*_Z^2+1)^2*x^2-15028*(x^6-x^2)^(1/2)*RootOf(2*_Z^4-2*_Z^2+1)*x+6464*RootOf(2*_Z^4-2*_Z^2+1)^3*x-3450*RootOf(2*_Z^4-2*_Z^2+1)*x^3-10982*(x^6-x^2)^(3/4)+15028*(x^6-x^2)^(1/4)*x^2+525*RootOf(2*_Z^4-2*_Z^2+1)*x)/(2*RootOf(2*_Z^4-2*_Z^2+1)^2*x^2-8*RootOf(2*_Z^4-2*_Z^2+1)^2-5*x^2+3)^2/x)-1/4*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*ln((-12032*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*RootOf(2*_Z^4-2*_Z^2+1)^4*x^5+45120*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*RootOf(2*_Z^4-2*_Z^2+1)^4*x^3+30528*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*RootOf(2*_Z^4-2*_Z^2+1)^2*x^5+21964*RootOf(2*_Z^4-2*_Z^2+1)^2*(x^6-x^2)^(1/2)*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*x+12032*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*RootOf(2*_Z^4-2*_Z^2+1)^4*x-60148*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*RootOf(2*_Z^4-2*_Z^2+1)^2*x^3-19021*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*x^5+36992*(x^6-x^2)^(3/4)*RootOf(2*_Z^4-2*_Z^2+1)^2+21964*(x^6-x^2)^(1/4)*RootOf(2*_Z^4-2*_Z^2+1)^2*x^2-36992*(x^6-x^2)^(1/2)*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*x-30528*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*RootOf(2*_Z^4-2*_Z^2+1)^2*x+11578*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*x^3-26010*(x^6-x^2)^(3/4)-36992*(x^6-x^2)^(1/4)*x^2+19021*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*x)/(2*RootOf(2*_Z^4-2*_Z^2+1)^2*x^2-8*RootOf(2*_Z^4-2*_Z^2+1)^2+3*x^2+5)^2/x)-1/2*RootOf(2*_Z^4-2*_Z^2+1)^2*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*ln((14432*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*RootOf(2*_Z^4-2*_Z^2+1)^4*x^5-54120*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*RootOf(2*_Z^4-2*_Z^2+1)^4*x^3-21946*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*RootOf(2*_Z^4-2*_Z^2+1)^2*x^5+52020*RootOf(2*_Z^4-2*_Z^2+1)^2*(x^6-x^2)^(1/2)*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*x-14432*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*RootOf(2*_Z^4-2*_Z^2+1)^4*x+17128*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*RootOf(2*_Z^4-2*_Z^2+1)^2*x^3+1725*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*x^5+36992*(x^6-x^2)^(3/4)*RootOf(2*_Z^4-2*_Z^2+1)^2-21964*(x^6-x^2)^(1/4)*RootOf(2*_Z^4-2*_Z^2+1)^2*x^2-15028*(x^6-x^2)^(1/2)*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*x+21946*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*RootOf(2*_Z^4-2*_Z^2+1)^2*x-1050*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*x^3-26010*(x^6-x^2)^(3/4)+36992*(x^6-x^2)^(1/4)*x^2-1725*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*x)/(2*RootOf(2*_Z^4-2*_Z^2+1)^2*x^2-8*RootOf(2*_Z^4-2*_Z^2+1)^2+3*x^2+5)^2/x)+1/4*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*ln((14432*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*RootOf(2*_Z^4-2*_Z^2+1)^4*x^5-54120*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*RootOf(2*_Z^4-2*_Z^2+1)^4*x^3-21946*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*RootOf(2*_Z^4-2*_Z^2+1)^2*x^5+52020*RootOf(2*_Z^4-2*_Z^2+1)^2*(x^6-x^2)^(1/2)*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*x-14432*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*RootOf(2*_Z^4-2*_Z^2+1)^4*x+17128*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*RootOf(2*_Z^4-2*_Z^2+1)^2*x^3+1725*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*x^5+36992*(x^6-x^2)^(3/4)*RootOf(2*_Z^4-2*_Z^2+1)^2-21964*(x^6-x^2)^(1/4)*RootOf(2*_Z^4-2*_Z^2+1)^2*x^2-15028*(x^6-x^2)^(1/2)*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*x+21946*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*RootOf(2*_Z^4-2*_Z^2+1)^2*x-1050*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*x^3-26010*(x^6-x^2)^(3/4)+36992*(x^6-x^2)^(1/4)*x^2-1725*RootOf(RootOf(2*_Z^4-2*_Z^2+1)^2+_Z^2-1)*x)/(2*RootOf(2*_Z^4-2*_Z^2+1)^2*x^2-8*RootOf(2*_Z^4-2*_Z^2+1)^2+3*x^2+5)^2/x)-1/2*RootOf(2*_Z^4-2*_Z^2+1)^3*ln(-(14432*RootOf(2*_Z^4-2*_Z^2+1)^5*x^5-54120*RootOf(2*_Z^4-2*_Z^2+1)^5*x^3-6918*RootOf(2*_Z^4-2*_Z^2+1)^3*x^5-52020*(x^6-x^2)^(1/2)*RootOf(2*_Z^4-2*_Z^2+1)^3*x-14432*RootOf(2*_Z^4-2*_Z^2+1)^5*x+91112*RootOf(2*_Z^4-2*_Z^2+1)^3*x^3-5789*RootOf(2*_Z^4-2*_Z^2+1)*x^5+36992*(x^6-x^2)^(3/4)*RootOf(2*_Z^4-2*_Z^2+1)^2-21964*(x^6-x^2)^(1/4)*RootOf(2*_Z^4-2*_Z^2+1)^2*x^2+36992*(x^6-x^2)^(1/2)*RootOf(2*_Z^4-2*_Z^2+1)*x+6918*RootOf(2*_Z^4-2*_Z^2+1)^3*x-38042*RootOf(2*_Z^4-2*_Z^2+1)*x^3-10982*(x^6-x^2)^(3/4)-15028*(x^6-x^2)^(1/4)*x^2+5789*RootOf(2*_Z^4-2*_Z^2+1)*x)/(2*RootOf(2*_Z^4-2*_Z^2+1)^2*x^2-8*RootOf(2*_Z^4-2*_Z^2+1)^2-5*x^2+3)^2/x)+1/4*RootOf(2*_Z^4-2*_Z^2+1)*ln(-(14432*RootOf(2*_Z^4-2*_Z^2+1)^5*x^5-54120*RootOf(2*_Z^4-2*_Z^2+1)^5*x^3-6918*RootOf(2*_Z^4-2*_Z^2+1)^3*x^5-52020*(x^6-x^2)^(1/2)*RootOf(2*_Z^4-2*_Z^2+1)^3*x-14432*RootOf(2*_Z^4-2*_Z^2+1)^5*x+91112*RootOf(2*_Z^4-2*_Z^2+1)^3*x^3-5789*RootOf(2*_Z^4-2*_Z^2+1)*x^5+36992*(x^6-x^2)^(3/4)*RootOf(2*_Z^4-2*_Z^2+1)^2-21964*(x^6-x^2)^(1/4)*RootOf(2*_Z^4-2*_Z^2+1)^2*x^2+36992*(x^6-x^2)^(1/2)*RootOf(2*_Z^4-2*_Z^2+1)*x+6918*RootOf(2*_Z^4-2*_Z^2+1)^3*x-38042*RootOf(2*_Z^4-2*_Z^2+1)*x^3-10982*(x^6-x^2)^(3/4)-15028*(x^6-x^2)^(1/4)*x^2+5789*RootOf(2*_Z^4-2*_Z^2+1)*x)/(2*RootOf(2*_Z^4-2*_Z^2+1)^2*x^2-8*RootOf(2*_Z^4-2*_Z^2+1)^2-5*x^2+3)^2/x)","C"
3040,0,0,338,0.045000," ","int((a*x^4-b)^(3/4)/(x^8+2*a*x^4-b),x)","\[\int \frac{\left(a \,x^{4}-b \right)^{\frac{3}{4}}}{x^{8}+2 a \,x^{4}-b}\, dx\]"," ",0,"int((a*x^4-b)^(3/4)/(x^8+2*a*x^4-b),x)","F"
3041,0,0,240,0.033000," ","int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(5/2),x)","\[\int \frac{\sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(x^{2}+1\right)^{\frac{5}{2}}}\, dx\]"," ",0,"int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(5/2),x)","F"
3042,0,0,240,0.004000," ","int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(5/2),x)","\[\int \frac{\sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(x^{2}+1\right)^{\frac{5}{2}}}\, dx\]"," ",0,"int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(x^2+1)^(5/2),x)","F"
3043,1,264,39,0.226000," ","int(x^2*(a*x+b)^(1/2)/(x^2-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{2 \left(-\frac{\left(c +\sqrt{a x +b}\right)^{3}}{3}+c \left(c +\sqrt{a x +b}\right)^{2}-c^{2} \left(c +\sqrt{a x +b}\right)-2 a^{2} \sqrt{c +\sqrt{a x +b}}+2 a^{2} \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 c \,\textit{\_Z}^{6}+\left(6 c^{2}-2 b \right) \textit{\_Z}^{4}-a^{2} \textit{\_Z}^{3}+\left(-4 c^{3}+4 b c \right) \textit{\_Z}^{2}+a^{2} c \textit{\_Z} +c^{4}-2 b \,c^{2}+b^{2}\right)}{\sum}\frac{\left(-\textit{\_R}^{6} c +\left(3 c^{2}-2 b \right) \textit{\_R}^{4}-\textit{\_R}^{3} a^{2}+c \left(-3 c^{2}+4 b \right) \textit{\_R}^{2}+a^{2} c \textit{\_R} +c^{4}-2 b \,c^{2}+b^{2}\right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{8 \textit{\_R}^{7}-24 c \,\textit{\_R}^{5}+24 \textit{\_R}^{3} c^{2}-8 \textit{\_R}^{3} b -3 \textit{\_R}^{2} a^{2}-8 \textit{\_R} \,c^{3}+8 \textit{\_R} b c +a^{2} c}\right)\right)}{a}$&$264$\\ default&$-\frac{2 \left(-\frac{\left(c +\sqrt{a x +b}\right)^{3}}{3}+c \left(c +\sqrt{a x +b}\right)^{2}-c^{2} \left(c +\sqrt{a x +b}\right)-2 a^{2} \sqrt{c +\sqrt{a x +b}}+2 a^{2} \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 c \,\textit{\_Z}^{6}+\left(6 c^{2}-2 b \right) \textit{\_Z}^{4}-a^{2} \textit{\_Z}^{3}+\left(-4 c^{3}+4 b c \right) \textit{\_Z}^{2}+a^{2} c \textit{\_Z} +c^{4}-2 b \,c^{2}+b^{2}\right)}{\sum}\frac{\left(-\textit{\_R}^{6} c +\left(3 c^{2}-2 b \right) \textit{\_R}^{4}-\textit{\_R}^{3} a^{2}+c \left(-3 c^{2}+4 b \right) \textit{\_R}^{2}+a^{2} c \textit{\_R} +c^{4}-2 b \,c^{2}+b^{2}\right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{8 \textit{\_R}^{7}-24 c \,\textit{\_R}^{5}+24 \textit{\_R}^{3} c^{2}-8 \textit{\_R}^{3} b -3 \textit{\_R}^{2} a^{2}-8 \textit{\_R} \,c^{3}+8 \textit{\_R} b c +a^{2} c}\right)\right)}{a}$&$264$\\ \hline \end{longtable}"," ",0,"-2/a*(-1/3*(c+(a*x+b)^(1/2))^3+c*(c+(a*x+b)^(1/2))^2-c^2*(c+(a*x+b)^(1/2))-2*a^2*(c+(a*x+b)^(1/2))^(1/2)+2*a^2*sum((-_R^6*c+(3*c^2-2*b)*_R^4-_R^3*a^2+c*(-3*c^2+4*b)*_R^2+a^2*c*_R+c^4-2*b*c^2+b^2)/(8*_R^7-24*_R^5*c+24*_R^3*c^2-8*_R^3*b-3*_R^2*a^2-8*_R*c^3+8*_R*b*c+a^2*c)*ln((c+(a*x+b)^(1/2))^(1/2)-_R),_R=RootOf(_Z^8-4*c*_Z^6+(6*c^2-2*b)*_Z^4-a^2*_Z^3+(-4*c^3+4*b*c)*_Z^2+a^2*c*_Z+c^4-2*b*c^2+b^2)))","B"
3044,1,264,39,0.200000," ","int(x^2*(a*x+b)^(1/2)/(x^2-(a*x+b)^(1/2)*(c+(a*x+b)^(1/2))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{2 \left(-\frac{\left(c +\sqrt{a x +b}\right)^{3}}{3}+c \left(c +\sqrt{a x +b}\right)^{2}-c^{2} \left(c +\sqrt{a x +b}\right)-2 a^{2} \sqrt{c +\sqrt{a x +b}}+2 a^{2} \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 c \,\textit{\_Z}^{6}+\left(6 c^{2}-2 b \right) \textit{\_Z}^{4}-a^{2} \textit{\_Z}^{3}+\left(-4 c^{3}+4 b c \right) \textit{\_Z}^{2}+a^{2} c \textit{\_Z} +c^{4}-2 b \,c^{2}+b^{2}\right)}{\sum}\frac{\left(-\textit{\_R}^{6} c +\left(3 c^{2}-2 b \right) \textit{\_R}^{4}-\textit{\_R}^{3} a^{2}+c \left(-3 c^{2}+4 b \right) \textit{\_R}^{2}+a^{2} c \textit{\_R} +c^{4}-2 b \,c^{2}+b^{2}\right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{8 \textit{\_R}^{7}-24 c \,\textit{\_R}^{5}+24 \textit{\_R}^{3} c^{2}-8 \textit{\_R}^{3} b -3 \textit{\_R}^{2} a^{2}-8 \textit{\_R} \,c^{3}+8 \textit{\_R} b c +a^{2} c}\right)\right)}{a}$&$264$\\ default&$-\frac{2 \left(-\frac{\left(c +\sqrt{a x +b}\right)^{3}}{3}+c \left(c +\sqrt{a x +b}\right)^{2}-c^{2} \left(c +\sqrt{a x +b}\right)-2 a^{2} \sqrt{c +\sqrt{a x +b}}+2 a^{2} \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-4 c \,\textit{\_Z}^{6}+\left(6 c^{2}-2 b \right) \textit{\_Z}^{4}-a^{2} \textit{\_Z}^{3}+\left(-4 c^{3}+4 b c \right) \textit{\_Z}^{2}+a^{2} c \textit{\_Z} +c^{4}-2 b \,c^{2}+b^{2}\right)}{\sum}\frac{\left(-\textit{\_R}^{6} c +\left(3 c^{2}-2 b \right) \textit{\_R}^{4}-\textit{\_R}^{3} a^{2}+c \left(-3 c^{2}+4 b \right) \textit{\_R}^{2}+a^{2} c \textit{\_R} +c^{4}-2 b \,c^{2}+b^{2}\right) \ln \left(\sqrt{c +\sqrt{a x +b}}-\textit{\_R} \right)}{8 \textit{\_R}^{7}-24 c \,\textit{\_R}^{5}+24 \textit{\_R}^{3} c^{2}-8 \textit{\_R}^{3} b -3 \textit{\_R}^{2} a^{2}-8 \textit{\_R} \,c^{3}+8 \textit{\_R} b c +a^{2} c}\right)\right)}{a}$&$264$\\ \hline \end{longtable}"," ",0,"-2/a*(-1/3*(c+(a*x+b)^(1/2))^3+c*(c+(a*x+b)^(1/2))^2-c^2*(c+(a*x+b)^(1/2))-2*a^2*(c+(a*x+b)^(1/2))^(1/2)+2*a^2*sum((-_R^6*c+(3*c^2-2*b)*_R^4-_R^3*a^2+c*(-3*c^2+4*b)*_R^2+a^2*c*_R+c^4-2*b*c^2+b^2)/(8*_R^7-24*_R^5*c+24*_R^3*c^2-8*_R^3*b-3*_R^2*a^2-8*_R*c^3+8*_R*b*c+a^2*c)*ln((c+(a*x+b)^(1/2))^(1/2)-_R),_R=RootOf(_Z^8-4*c*_Z^6+(6*c^2-2*b)*_Z^4-a^2*_Z^3+(-4*c^3+4*b*c)*_Z^2+a^2*c*_Z+c^4-2*b*c^2+b^2)))","B"
3045,0,0,403,180.000000," ","int((a^2*x^2+b)^(1/2)*(a*x+(a^2*x^2+b)^(1/2))^(1/2)*(c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2),x)","\[\int \sqrt{a^{2} x^{2}+b}\, \sqrt{a x +\sqrt{a^{2} x^{2}+b}}\, \sqrt{c +\sqrt{a x +\sqrt{a^{2} x^{2}+b}}}\, dx\]"," ",0,"int((a^2*x^2+b)^(1/2)*(a*x+(a^2*x^2+b)^(1/2))^(1/2)*(c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2),x)","F"
3046,0,0,338,0.047000," ","int(x^4/(a*x^4+b)^(1/4)/(2*x^8+2*a*x^4+b),x)","\[\int \frac{x^{4}}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(2 x^{8}+2 a \,x^{4}+b \right)}\, dx\]"," ",0,"int(x^4/(a*x^4+b)^(1/4)/(2*x^8+2*a*x^4+b),x)","F"
3047,1,47,324,0.206000," ","int(x^4*(p*x^4-q)*(p*x^4+q)^(1/2)/(b*x^8+a*(p*x^4+q)^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(\munderset{\textit{\_R} =\RootOf \left(16 \textit{\_Z}^{8} a +b \right)}{\sum}\frac{\ln \left(\frac{\sqrt{p \,x^{4}+q}\, \sqrt{2}}{2 x}-\textit{\_R} \right)}{\textit{\_R}^{5}}\right) \sqrt{2}}{64 a}$&$47$\\ elliptic&$\frac{\left(\munderset{\textit{\_R} =\RootOf \left(16 \textit{\_Z}^{8} a +b \right)}{\sum}\frac{\ln \left(\frac{\sqrt{p \,x^{4}+q}\, \sqrt{2}}{2 x}-\textit{\_R} \right)}{\textit{\_R}^{5}}\right) \sqrt{2}}{64 a}$&$47$\\ \hline \end{longtable}"," ",0,"1/64/a*sum(1/_R^5*ln(1/2*(p*x^4+q)^(1/2)*2^(1/2)/x-_R),_R=RootOf(16*_Z^8*a+b))*2^(1/2)","C"
3048,1,17220,271,12.283000," ","int(1/(-3*x^10+x^9-9*x^7+3*x^6-9*x^4+3*x^3-3*x+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$17220$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
3049,0,0,346,0.046000," ","int((a*x^4+b)^(3/4)/(2*x^8+2*a*x^4+b),x)","\[\int \frac{\left(a \,x^{4}+b \right)^{\frac{3}{4}}}{2 x^{8}+2 a \,x^{4}+b}\, dx\]"," ",0,"int((a*x^4+b)^(3/4)/(2*x^8+2*a*x^4+b),x)","F"
3050,0,0,197,180.000000," ","int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x+d)/(a^2*x^4+b)^(1/2),x)","\[\int \frac{\sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}{\left(c x +d \right) \sqrt{a^{2} x^{4}+b}}\, dx\]"," ",0,"int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x+d)/(a^2*x^4+b)^(1/2),x)","F"
3051,0,0,197,180.000000," ","int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x+d)/(a^2*x^4+b)^(1/2),x)","\[\int \frac{\sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}{\left(c x +d \right) \sqrt{a^{2} x^{4}+b}}\, dx\]"," ",0,"int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x+d)/(a^2*x^4+b)^(1/2),x)","F"
3052,1,1195,116,1.017000," ","int(1/(a*x^2+b*x+c)^(1/2)/(a^3*b^3*x^3+c^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{4 a b \ln \left(\frac{\frac{2 c \left(a \,b^{2}-b^{2}+c \right)}{a \,b^{2}}+\frac{\left(b^{2}-2 c \right) \left(x +\frac{c}{a b}\right)}{b}+2 \sqrt{\frac{c \left(a \,b^{2}-b^{2}+c \right)}{a \,b^{2}}}\, \sqrt{\left(x +\frac{c}{a b}\right)^{2} a +\frac{\left(b^{2}-2 c \right) \left(x +\frac{c}{a b}\right)}{b}+\frac{c \left(a \,b^{2}-b^{2}+c \right)}{a \,b^{2}}}}{x +\frac{c}{a b}}\right)}{\left(3 a b c +\sqrt{-3 a^{2} b^{2} c^{2}}\right) \left(-3 a b c +\sqrt{-3 a^{2} b^{2} c^{2}}\right) \sqrt{\frac{c \left(a \,b^{2}-b^{2}+c \right)}{a \,b^{2}}}}-\frac{2 a b \sqrt{2}\, \ln \left(\frac{\frac{2 a^{2} b^{3} c +a \,b^{3} c -a b \,c^{2}-\sqrt{-3 a^{2} b^{2} c^{2}}\, b^{2}-\sqrt{-3 a^{2} b^{2} c^{2}}\, c}{a^{2} b^{3}}+\frac{\left(a \,b^{3}+a b c -\sqrt{-3 a^{2} b^{2} c^{2}}\right) \left(x +\frac{-a b c +\sqrt{-3 a^{2} b^{2} c^{2}}}{2 a^{2} b^{2}}\right)}{a \,b^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a^{2} b^{3} c +a \,b^{3} c -a b \,c^{2}-\sqrt{-3 a^{2} b^{2} c^{2}}\, b^{2}-\sqrt{-3 a^{2} b^{2} c^{2}}\, c}{a^{2} b^{3}}}\, \sqrt{4 \left(x +\frac{-a b c +\sqrt{-3 a^{2} b^{2} c^{2}}}{2 a^{2} b^{2}}\right)^{2} a +\frac{4 \left(a \,b^{3}+a b c -\sqrt{-3 a^{2} b^{2} c^{2}}\right) \left(x +\frac{-a b c +\sqrt{-3 a^{2} b^{2} c^{2}}}{2 a^{2} b^{2}}\right)}{a \,b^{2}}+\frac{4 a^{2} b^{3} c +2 a \,b^{3} c -2 a b \,c^{2}-2 \sqrt{-3 a^{2} b^{2} c^{2}}\, b^{2}-2 \sqrt{-3 a^{2} b^{2} c^{2}}\, c}{a^{2} b^{3}}}}{2}}{x +\frac{-a b c +\sqrt{-3 a^{2} b^{2} c^{2}}}{2 a^{2} b^{2}}}\right)}{\left(-3 a b c +\sqrt{-3 a^{2} b^{2} c^{2}}\right) \sqrt{-3 a^{2} b^{2} c^{2}}\, \sqrt{\frac{2 a^{2} b^{3} c +a \,b^{3} c -a b \,c^{2}-\sqrt{-3 a^{2} b^{2} c^{2}}\, b^{2}-\sqrt{-3 a^{2} b^{2} c^{2}}\, c}{a^{2} b^{3}}}}-\frac{2 a b \sqrt{2}\, \ln \left(\frac{\frac{2 a^{2} b^{3} c +a \,b^{3} c -a b \,c^{2}+\sqrt{-3 a^{2} b^{2} c^{2}}\, b^{2}+\sqrt{-3 a^{2} b^{2} c^{2}}\, c}{a^{2} b^{3}}+\frac{\left(a \,b^{3}+a b c +\sqrt{-3 a^{2} b^{2} c^{2}}\right) \left(x -\frac{a b c +\sqrt{-3 a^{2} b^{2} c^{2}}}{2 a^{2} b^{2}}\right)}{a \,b^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a^{2} b^{3} c +a \,b^{3} c -a b \,c^{2}+\sqrt{-3 a^{2} b^{2} c^{2}}\, b^{2}+\sqrt{-3 a^{2} b^{2} c^{2}}\, c}{a^{2} b^{3}}}\, \sqrt{4 \left(x -\frac{a b c +\sqrt{-3 a^{2} b^{2} c^{2}}}{2 a^{2} b^{2}}\right)^{2} a +\frac{4 \left(a \,b^{3}+a b c +\sqrt{-3 a^{2} b^{2} c^{2}}\right) \left(x -\frac{a b c +\sqrt{-3 a^{2} b^{2} c^{2}}}{2 a^{2} b^{2}}\right)}{a \,b^{2}}+\frac{4 a^{2} b^{3} c +2 a \,b^{3} c -2 a b \,c^{2}+2 \sqrt{-3 a^{2} b^{2} c^{2}}\, b^{2}+2 \sqrt{-3 a^{2} b^{2} c^{2}}\, c}{a^{2} b^{3}}}}{2}}{x -\frac{a b c +\sqrt{-3 a^{2} b^{2} c^{2}}}{2 a^{2} b^{2}}}\right)}{\left(3 a b c +\sqrt{-3 a^{2} b^{2} c^{2}}\right) \sqrt{-3 a^{2} b^{2} c^{2}}\, \sqrt{\frac{2 a^{2} b^{3} c +a \,b^{3} c -a b \,c^{2}+\sqrt{-3 a^{2} b^{2} c^{2}}\, b^{2}+\sqrt{-3 a^{2} b^{2} c^{2}}\, c}{a^{2} b^{3}}}}$&$1195$\\ \hline \end{longtable}"," ",0,"4*a*b/(3*a*b*c+(-3*a^2*b^2*c^2)^(1/2))/(-3*a*b*c+(-3*a^2*b^2*c^2)^(1/2))/(c*(a*b^2-b^2+c)/a/b^2)^(1/2)*ln((2*c*(a*b^2-b^2+c)/a/b^2+(b^2-2*c)/b*(x+c/a/b)+2*(c*(a*b^2-b^2+c)/a/b^2)^(1/2)*((x+c/a/b)^2*a+(b^2-2*c)/b*(x+c/a/b)+c*(a*b^2-b^2+c)/a/b^2)^(1/2))/(x+c/a/b))-2*a*b/(-3*a*b*c+(-3*a^2*b^2*c^2)^(1/2))/(-3*a^2*b^2*c^2)^(1/2)*2^(1/2)/(1/a^2/b^3*(2*a^2*b^3*c+a*b^3*c-a*b*c^2-(-3*a^2*b^2*c^2)^(1/2)*b^2-(-3*a^2*b^2*c^2)^(1/2)*c))^(1/2)*ln((1/a^2/b^3*(2*a^2*b^3*c+a*b^3*c-a*b*c^2-(-3*a^2*b^2*c^2)^(1/2)*b^2-(-3*a^2*b^2*c^2)^(1/2)*c)+(a*b^3+a*b*c-(-3*a^2*b^2*c^2)^(1/2))/a/b^2*(x+1/2*(-a*b*c+(-3*a^2*b^2*c^2)^(1/2))/a^2/b^2)+1/2*2^(1/2)*(1/a^2/b^3*(2*a^2*b^3*c+a*b^3*c-a*b*c^2-(-3*a^2*b^2*c^2)^(1/2)*b^2-(-3*a^2*b^2*c^2)^(1/2)*c))^(1/2)*(4*(x+1/2*(-a*b*c+(-3*a^2*b^2*c^2)^(1/2))/a^2/b^2)^2*a+4*(a*b^3+a*b*c-(-3*a^2*b^2*c^2)^(1/2))/a/b^2*(x+1/2*(-a*b*c+(-3*a^2*b^2*c^2)^(1/2))/a^2/b^2)+2/a^2/b^3*(2*a^2*b^3*c+a*b^3*c-a*b*c^2-(-3*a^2*b^2*c^2)^(1/2)*b^2-(-3*a^2*b^2*c^2)^(1/2)*c))^(1/2))/(x+1/2*(-a*b*c+(-3*a^2*b^2*c^2)^(1/2))/a^2/b^2))-2*a*b/(3*a*b*c+(-3*a^2*b^2*c^2)^(1/2))/(-3*a^2*b^2*c^2)^(1/2)*2^(1/2)/(1/a^2/b^3*(2*a^2*b^3*c+a*b^3*c-a*b*c^2+(-3*a^2*b^2*c^2)^(1/2)*b^2+(-3*a^2*b^2*c^2)^(1/2)*c))^(1/2)*ln((1/a^2/b^3*(2*a^2*b^3*c+a*b^3*c-a*b*c^2+(-3*a^2*b^2*c^2)^(1/2)*b^2+(-3*a^2*b^2*c^2)^(1/2)*c)+(a*b^3+a*b*c+(-3*a^2*b^2*c^2)^(1/2))/a/b^2*(x-1/2*(a*b*c+(-3*a^2*b^2*c^2)^(1/2))/a^2/b^2)+1/2*2^(1/2)*(1/a^2/b^3*(2*a^2*b^3*c+a*b^3*c-a*b*c^2+(-3*a^2*b^2*c^2)^(1/2)*b^2+(-3*a^2*b^2*c^2)^(1/2)*c))^(1/2)*(4*(x-1/2*(a*b*c+(-3*a^2*b^2*c^2)^(1/2))/a^2/b^2)^2*a+4*(a*b^3+a*b*c+(-3*a^2*b^2*c^2)^(1/2))/a/b^2*(x-1/2*(a*b*c+(-3*a^2*b^2*c^2)^(1/2))/a^2/b^2)+2/a^2/b^3*(2*a^2*b^3*c+a*b^3*c-a*b*c^2+(-3*a^2*b^2*c^2)^(1/2)*b^2+(-3*a^2*b^2*c^2)^(1/2)*c))^(1/2))/(x-1/2*(a*b*c+(-3*a^2*b^2*c^2)^(1/2))/a^2/b^2))","B"
3053,0,0,166,180.000000," ","int((c*x^2-d)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d),x)","\[\int \frac{\left(c \,x^{2}-d \right) \sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}{c \,x^{2}+d}\, dx\]"," ",0,"int((c*x^2-d)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d),x)","F"
3054,0,0,166,180.000000," ","int((c*x^2-d)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d),x)","\[\int \frac{\left(c \,x^{2}-d \right) \sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}{c \,x^{2}+d}\, dx\]"," ",0,"int((c*x^2-d)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d),x)","F"
3055,1,402,422,0.236000," ","int(((a*x^5+2*a*x^3-x^4+a*x-2*x^2-1)/(a*x^5-2*a*x^3+x^4+a*x-2*x^2+1))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(a x +1\right) \sqrt{\frac{\left(x^{2}+1\right)^{2} \left(a x -1\right)}{\left(x^{2}-1\right)^{2} \left(a x +1\right)}}\, \left(x^{2}-1\right)}{a \left(x^{2}+1\right)}+\frac{\left(-\frac{\ln \left(\frac{a^{2} x}{\sqrt{a^{2}}}+\sqrt{a^{2} x^{2}-1}\right)}{\sqrt{a^{2}}}+\frac{\ln \left(\frac{2 a^{2}-2+2 a^{2} \left(-1+x \right)+2 \sqrt{a^{2}-1}\, \sqrt{a^{2} \left(-1+x \right)^{2}+2 a^{2} \left(-1+x \right)+a^{2}-1}}{-1+x}\right)}{\sqrt{a^{2}-1}}-\frac{\ln \left(\frac{2 a^{2}-2+2 a^{2} \left(-1+x \right)+2 \sqrt{a^{2}-1}\, \sqrt{a^{2} \left(-1+x \right)^{2}+2 a^{2} \left(-1+x \right)+a^{2}-1}}{-1+x}\right) a}{\sqrt{a^{2}-1}}-\frac{\ln \left(\frac{2 a^{2}-2-2 a^{2} \left(1+x \right)+2 \sqrt{a^{2}-1}\, \sqrt{a^{2} \left(1+x \right)^{2}-2 a^{2} \left(1+x \right)+a^{2}-1}}{1+x}\right) a}{\sqrt{a^{2}-1}}-\frac{\ln \left(\frac{2 a^{2}-2-2 a^{2} \left(1+x \right)+2 \sqrt{a^{2}-1}\, \sqrt{a^{2} \left(1+x \right)^{2}-2 a^{2} \left(1+x \right)+a^{2}-1}}{1+x}\right)}{\sqrt{a^{2}-1}}\right) \sqrt{\frac{\left(x^{2}+1\right)^{2} \left(a x -1\right)}{\left(x^{2}-1\right)^{2} \left(a x +1\right)}}\, \sqrt{\left(a x +1\right) \left(a x -1\right)}\, \left(x^{2}-1\right)}{\left(x^{2}+1\right) \left(a x -1\right)}$&$402$\\ default&$-\frac{\sqrt{\frac{a \,x^{5}+2 a \,x^{3}-x^{4}+a x -2 x^{2}-1}{a \,x^{5}-2 a \,x^{3}+x^{4}+a x -2 x^{2}+1}}\, \left(x^{2}-1\right) \left(a x +1\right) \left(\ln \left(\frac{-2 a^{2} x +2 \sqrt{a^{2}-1}\, \sqrt{a^{2} x^{2}-1}-2}{1+x}\right) \sqrt{a^{2}}\, \sqrt{a^{2}-1}\, a^{2}+\ln \left(\frac{2 a^{2} x +2 \sqrt{a^{2}-1}\, \sqrt{a^{2} x^{2}-1}-2}{-1+x}\right) \sqrt{a^{2}}\, \sqrt{a^{2}-1}\, a^{2}+\ln \left(\frac{-2 a^{2} x +2 \sqrt{a^{2}-1}\, \sqrt{a^{2} x^{2}-1}-2}{1+x}\right) \sqrt{a^{2}}\, \sqrt{a^{2}-1}\, a -\ln \left(\frac{2 a^{2} x +2 \sqrt{a^{2}-1}\, \sqrt{a^{2} x^{2}-1}-2}{-1+x}\right) \sqrt{a^{2}}\, \sqrt{a^{2}-1}\, a -\ln \left(\frac{a^{2} x +\sqrt{a^{2}}\, \sqrt{\left(a x +1\right) \left(a x -1\right)}}{\sqrt{a^{2}}}\right) a^{3}+2 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a^{3}-2 \sqrt{a^{2}}\, \sqrt{a^{2} x^{2}-1}\, a^{2}+\sqrt{a^{2}}\, \sqrt{\left(a x +1\right) \left(a x -1\right)}\, a^{2}-a \ln \left(\frac{a^{2} x +\sqrt{a^{2}}\, \sqrt{\left(a x +1\right) \left(a x -1\right)}}{\sqrt{a^{2}}}\right)+\sqrt{a^{2}}\, \sqrt{\left(a x +1\right) \left(a x -1\right)}\right)}{\left(x^{2}+1\right) \sqrt{\left(a x +1\right) \left(a x -1\right)}\, \left(-1+a \right) \left(1+a \right) a \sqrt{a^{2}}}$&$475$\\ \hline \end{longtable}"," ",0,"1/a*(a*x+1)*((x^2+1)^2*(a*x-1)/(x^2-1)^2/(a*x+1))^(1/2)/(x^2+1)*(x^2-1)+(-ln(a^2*x/(a^2)^(1/2)+(a^2*x^2-1)^(1/2))/(a^2)^(1/2)+1/(a^2-1)^(1/2)*ln((2*a^2-2+2*a^2*(-1+x)+2*(a^2-1)^(1/2)*(a^2*(-1+x)^2+2*a^2*(-1+x)+a^2-1)^(1/2))/(-1+x))-1/(a^2-1)^(1/2)*ln((2*a^2-2+2*a^2*(-1+x)+2*(a^2-1)^(1/2)*(a^2*(-1+x)^2+2*a^2*(-1+x)+a^2-1)^(1/2))/(-1+x))*a-1/(a^2-1)^(1/2)*ln((2*a^2-2-2*a^2*(1+x)+2*(a^2-1)^(1/2)*(a^2*(1+x)^2-2*a^2*(1+x)+a^2-1)^(1/2))/(1+x))*a-1/(a^2-1)^(1/2)*ln((2*a^2-2-2*a^2*(1+x)+2*(a^2-1)^(1/2)*(a^2*(1+x)^2-2*a^2*(1+x)+a^2-1)^(1/2))/(1+x)))*((x^2+1)^2*(a*x-1)/(x^2-1)^2/(a*x+1))^(1/2)*((a*x+1)*(a*x-1))^(1/2)/(x^2+1)/(a*x-1)*(x^2-1)","A"
3056,1,17124,318,117.771000," ","int((1+x)/(x^2-3)/(x^2+1)^(1/3),x)","\[\text{output too large to display}\]"," ",0,"result too large to display","C"
3057,1,4195,354,93.094000," ","int((-x^4+1)/(x^4+1)/(x^5-x^3)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$4195$\\ \hline \end{longtable}"," ",0,"-1/32*ln((-16*RootOf(_Z^8+128)^9*x^4-3072*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x^2-56*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^4*x^4-800*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^4*x^3+56*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^4*x^2+26*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^8*x^2+400*(x^5-x^3)^(1/2)*RootOf(_Z^8+128)^6*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x+56*RootOf(_Z^8+128)^5*x^3+400*RootOf(_Z^8+128)^5*x^2-400*RootOf(_Z^8+128)^5*x^4+4096*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x^3+3072*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x^4-2496*RootOf(_Z^8+128)*x^4-3328*RootOf(_Z^8+128)*x^3+2496*RootOf(_Z^8+128)*x^2+24*RootOf(_Z^8+128)^9*x^3+16*RootOf(_Z^8+128)^9*x^2-26*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^8*x^4+39*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^8*x^3+1792*(x^5-x^3)^(3/4)-28*(x^5-x^3)^(1/2)*RootOf(_Z^8+128)^7*x+56*(x^5-x^3)^(1/4)*RootOf(_Z^8+128)^6*x^2+3200*(x^5-x^3)^(1/2)*RootOf(_Z^8+128)^3*x-6400*(x^5-x^3)^(1/4)*RootOf(_Z^8+128)^2*x^2+448*(x^5-x^3)^(1/2)*RootOf(_Z^8+128)^2*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x+1600*RootOf(_Z^8+128)^4*(x^5-x^3)^(3/4))/x^2/(2*RootOf(_Z^8+128)^4*x^2-3*RootOf(_Z^8+128)^4*x-2*RootOf(_Z^8+128)^4-24*x^2-32*x+24))*RootOf(_Z^8+128)^4*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)-1/4*ln((-16*RootOf(_Z^8+128)^9*x^4-3072*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x^2-56*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^4*x^4-800*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^4*x^3+56*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^4*x^2+26*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^8*x^2+400*(x^5-x^3)^(1/2)*RootOf(_Z^8+128)^6*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x+56*RootOf(_Z^8+128)^5*x^3+400*RootOf(_Z^8+128)^5*x^2-400*RootOf(_Z^8+128)^5*x^4+4096*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x^3+3072*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x^4-2496*RootOf(_Z^8+128)*x^4-3328*RootOf(_Z^8+128)*x^3+2496*RootOf(_Z^8+128)*x^2+24*RootOf(_Z^8+128)^9*x^3+16*RootOf(_Z^8+128)^9*x^2-26*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^8*x^4+39*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^8*x^3+1792*(x^5-x^3)^(3/4)-28*(x^5-x^3)^(1/2)*RootOf(_Z^8+128)^7*x+56*(x^5-x^3)^(1/4)*RootOf(_Z^8+128)^6*x^2+3200*(x^5-x^3)^(1/2)*RootOf(_Z^8+128)^3*x-6400*(x^5-x^3)^(1/4)*RootOf(_Z^8+128)^2*x^2+448*(x^5-x^3)^(1/2)*RootOf(_Z^8+128)^2*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x+1600*RootOf(_Z^8+128)^4*(x^5-x^3)^(3/4))/x^2/(2*RootOf(_Z^8+128)^4*x^2-3*RootOf(_Z^8+128)^4*x-2*RootOf(_Z^8+128)^4-24*x^2-32*x+24))*RootOf(_Z^8+128)+1/4*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*ln(-(-4*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^8*x^4+6*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^8*x^3+4*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^8*x^2-100*(x^5-x^3)^(1/2)*RootOf(_Z^8+128)^7*x+7*(x^5-x^3)^(1/2)*RootOf(_Z^8+128)^6*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x-14*(x^5-x^3)^(1/4)*RootOf(_Z^8+128)^6*x^2-200*(x^5-x^3)^(1/4)*RootOf(_Z^8+128)^5*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x^2+100*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^4*x^4-14*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^4*x^3+400*RootOf(_Z^8+128)^4*(x^5-x^3)^(3/4)-100*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^4*x^2+112*(x^5-x^3)^(1/2)*RootOf(_Z^8+128)^3*x+800*(x^5-x^3)^(1/2)*RootOf(_Z^8+128)^2*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x-1600*(x^5-x^3)^(1/4)*RootOf(_Z^8+128)^2*x^2+224*(x^5-x^3)^(1/4)*RootOf(_Z^8+128)*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x^2-624*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x^4-832*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x^3-448*(x^5-x^3)^(3/4)+624*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x^2)/x^2/(2*RootOf(_Z^8+128)^4*x^2-3*RootOf(_Z^8+128)^4*x-2*RootOf(_Z^8+128)^4+24*x^2+32*x-24))-1/4*RootOf(_Z^8+128)*ln((-4*RootOf(_Z^8+128)^9*x^4+6*RootOf(_Z^8+128)^9*x^3+4*RootOf(_Z^8+128)^9*x^2+7*(x^5-x^3)^(1/2)*RootOf(_Z^8+128)^7*x-14*(x^5-x^3)^(1/4)*RootOf(_Z^8+128)^6*x^2-100*RootOf(_Z^8+128)^5*x^4+14*RootOf(_Z^8+128)^5*x^3+400*RootOf(_Z^8+128)^4*(x^5-x^3)^(3/4)+100*RootOf(_Z^8+128)^5*x^2-800*(x^5-x^3)^(1/2)*RootOf(_Z^8+128)^3*x+1600*(x^5-x^3)^(1/4)*RootOf(_Z^8+128)^2*x^2-624*RootOf(_Z^8+128)*x^4-832*RootOf(_Z^8+128)*x^3+448*(x^5-x^3)^(3/4)+624*RootOf(_Z^8+128)*x^2)/x^2/(2*RootOf(_Z^8+128)^4*x^2-3*RootOf(_Z^8+128)^4*x-2*RootOf(_Z^8+128)^4-24*x^2-32*x+24))+1/32*ln(-(26*RootOf(_Z^8+128)^9*x^4-2496*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x^2-400*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^4*x^4+56*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^4*x^3+400*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^4*x^2-16*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^8*x^2-28*(x^5-x^3)^(1/2)*RootOf(_Z^8+128)^6*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x-800*RootOf(_Z^8+128)^5*x^3+56*RootOf(_Z^8+128)^5*x^2-56*RootOf(_Z^8+128)^5*x^4+3328*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x^3+2496*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x^4-3072*RootOf(_Z^8+128)*x^4-4096*RootOf(_Z^8+128)*x^3+3072*RootOf(_Z^8+128)*x^2-39*RootOf(_Z^8+128)^9*x^3-26*RootOf(_Z^8+128)^9*x^2+16*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^8*x^4-24*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^8*x^3-1792*(x^5-x^3)^(3/4)+56*(x^5-x^3)^(1/4)*RootOf(_Z^8+128)^6*x^2+6400*(x^5-x^3)^(1/4)*RootOf(_Z^8+128)^2*x^2-3200*(x^5-x^3)^(1/2)*RootOf(_Z^8+128)^2*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x+800*(x^5-x^3)^(1/4)*RootOf(_Z^8+128)^5*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x^2-896*(x^5-x^3)^(1/4)*RootOf(_Z^8+128)*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x^2+1600*RootOf(_Z^8+128)^4*(x^5-x^3)^(3/4))/x^2/(2*RootOf(_Z^8+128)^4*x^2-3*RootOf(_Z^8+128)^4*x-2*RootOf(_Z^8+128)^4+24*x^2+32*x-24))*RootOf(_Z^8+128)^5-1/4*ln(-(26*RootOf(_Z^8+128)^9*x^4-2496*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x^2-400*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^4*x^4+56*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^4*x^3+400*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^4*x^2-16*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^8*x^2-28*(x^5-x^3)^(1/2)*RootOf(_Z^8+128)^6*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x-800*RootOf(_Z^8+128)^5*x^3+56*RootOf(_Z^8+128)^5*x^2-56*RootOf(_Z^8+128)^5*x^4+3328*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x^3+2496*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x^4-3072*RootOf(_Z^8+128)*x^4-4096*RootOf(_Z^8+128)*x^3+3072*RootOf(_Z^8+128)*x^2-39*RootOf(_Z^8+128)^9*x^3-26*RootOf(_Z^8+128)^9*x^2+16*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^8*x^4-24*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*RootOf(_Z^8+128)^8*x^3-1792*(x^5-x^3)^(3/4)+56*(x^5-x^3)^(1/4)*RootOf(_Z^8+128)^6*x^2+6400*(x^5-x^3)^(1/4)*RootOf(_Z^8+128)^2*x^2-3200*(x^5-x^3)^(1/2)*RootOf(_Z^8+128)^2*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x+800*(x^5-x^3)^(1/4)*RootOf(_Z^8+128)^5*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x^2-896*(x^5-x^3)^(1/4)*RootOf(_Z^8+128)*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)*x^2+1600*RootOf(_Z^8+128)^4*(x^5-x^3)^(3/4))/x^2/(2*RootOf(_Z^8+128)^4*x^2-3*RootOf(_Z^8+128)^4*x-2*RootOf(_Z^8+128)^4+24*x^2+32*x-24))*RootOf(-_Z*RootOf(_Z^8+128)^5-8*RootOf(_Z^8+128)^2+8*_Z^2)","C"
3058,0,0,354,180.000000," ","int((x^8-1)/(x^6-x^2)^(1/4)/(x^8+1),x)","\[\int \frac{x^{8}-1}{\left(x^{6}-x^{2}\right)^{\frac{1}{4}} \left(x^{8}+1\right)}\, dx\]"," ",0,"int((x^8-1)/(x^6-x^2)^(1/4)/(x^8+1),x)","F"
3059,0,0,354,180.000000," ","int((x^8-1)/(x^6-x^2)^(1/4)/(x^8+1),x)","\[\int \frac{x^{8}-1}{\left(x^{6}-x^{2}\right)^{\frac{1}{4}} \left(x^{8}+1\right)}\, dx\]"," ",0,"int((x^8-1)/(x^6-x^2)^(1/4)/(x^8+1),x)","F"
3060,0,0,386,180.000000," ","int((a*x+(a^2*x^2-b)^(1/2))^(1/3)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/3))^(1/4),x)","\[\int \frac{\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{3}}}{\left(c +\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{3}}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a*x+(a^2*x^2-b)^(1/2))^(1/3)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/3))^(1/4),x)","F"
3061,0,0,345,0.051000," ","int((a*x+b^2)/(a*x-b^2)/(b+(a*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{a x +b^{2}}{\left(a x -b^{2}\right) \sqrt{b +\sqrt{a \,x^{2}+b^{2}}}}\, dx\]"," ",0,"int((a*x+b^2)/(a*x-b^2)/(b+(a*x^2+b^2)^(1/2))^(1/2),x)","F"
3062,0,0,358,0.042000," ","int((a*x^4-b)^(3/4)/(2*x^8-2*a*x^4+b),x)","\[\int \frac{\left(a \,x^{4}-b \right)^{\frac{3}{4}}}{2 x^{8}-2 a \,x^{4}+b}\, dx\]"," ",0,"int((a*x^4-b)^(3/4)/(2*x^8-2*a*x^4+b),x)","F"
3063,0,0,166,180.000000," ","int((c*x^2-d)/(c*x^2+d)/(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x)","\[\int \frac{c \,x^{2}-d}{\left(c \,x^{2}+d \right) \sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}\, dx\]"," ",0,"int((c*x^2-d)/(c*x^2+d)/(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x)","F"
3064,0,0,166,180.000000," ","int((c*x^2-d)/(c*x^2+d)/(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x)","\[\int \frac{c \,x^{2}-d}{\left(c \,x^{2}+d \right) \sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}\, dx\]"," ",0,"int((c*x^2-d)/(c*x^2+d)/(a*x^2+(a^2*x^4+b)^(1/2))^(1/2),x)","F"
3065,0,0,358,0.043000," ","int(x^4/(a*x^4-b)^(1/4)/(2*x^8-2*a*x^4+b),x)","\[\int \frac{x^{4}}{\left(a \,x^{4}-b \right)^{\frac{1}{4}} \left(2 x^{8}-2 a \,x^{4}+b \right)}\, dx\]"," ",0,"int(x^4/(a*x^4-b)^(1/4)/(2*x^8-2*a*x^4+b),x)","F"
3066,0,0,375,0.042000," ","int(x^3*(6*a*x-5*b)/(a*x^2-b*x)^(1/4)/(a*x^6-b*x^5+c),x)","\[\int \frac{x^{3} \left(6 a x -5 b \right)}{\left(a \,x^{2}-b x \right)^{\frac{1}{4}} \left(a \,x^{6}-b \,x^{5}+c \right)}\, dx\]"," ",0,"int(x^3*(6*a*x-5*b)/(a*x^2-b*x)^(1/4)/(a*x^6-b*x^5+c),x)","F"
3067,0,0,373,0.165000," ","int((-a+x)/((-a+x)*(-b+x)^2)^(1/3)/(-b^2+a^2*d+2*(-a*d+b)*x+(-1+d)*x^2),x)","\[\int \frac{-a +x}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{3}} \left(-b^{2}+a^{2} d +2 \left(-a d +b \right) x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((-a+x)/((-a+x)*(-b+x)^2)^(1/3)/(-b^2+a^2*d+2*(-a*d+b)*x+(-1+d)*x^2),x)","F"
3068,0,0,356,0.048000," ","int((2*x^8-a*x^4+b)/(a*x^4+b)^(1/4)/(x^8-2*a*x^4-b),x)","\[\int \frac{2 x^{8}-a \,x^{4}+b}{\left(a \,x^{4}+b \right)^{\frac{1}{4}} \left(x^{8}-2 a \,x^{4}-b \right)}\, dx\]"," ",0,"int((2*x^8-a*x^4+b)/(a*x^4+b)^(1/4)/(x^8-2*a*x^4-b),x)","F"
3069,0,0,437,0.043000," ","int((a^2*x^2-b)^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/2))^(1/2),x)","\[\int \frac{\sqrt{a^{2} x^{2}-b}}{\sqrt{c +\sqrt{a x +\sqrt{a^{2} x^{2}-b}}}}\, dx\]"," ",0,"int((a^2*x^2-b)^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/2))^(1/2),x)","F"
3070,1,5476,424,20.443000," ","int((1+x)/(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+522*x^2+189*x+27)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$5476$\\ \hline \end{longtable}"," ",0,"result too large to display","C"
3071,1,51,387,0.220000," ","int((k^2*x^4-1)/((-x^2+1)*(-k^2*x^2+1))^(1/2)/(k^2*x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\arctan \left(\frac{\sqrt{\left(-x^{2}+1\right) \left(-k^{2} x^{2}+1\right)}\, \sqrt{2}}{x \sqrt{2 k^{2}+2}}\right) \sqrt{2}}{\sqrt{2 k^{2}+2}}$&$51$\\ default&$\frac{\sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \EllipticF \left(x , k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}-\frac{\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(k^{2} \textit{\_Z}^{4}+1\right)}{\sum}\frac{-\frac{\arctanh \left(\frac{\left(2 k^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-k^{2}-1\right) \left(\underline{\hspace{1.25 ex}}\alpha^{2} k^{4}+k^{4} x^{2}-2 k^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+6 k^{2} x^{2}+\underline{\hspace{1.25 ex}}\alpha^{2}-4 k^{2}+x^{2}-4\right)}{2 \left(k^{4}+6 k^{2}+1\right) \sqrt{-k^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}\right)}{\sqrt{-k^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-\underline{\hspace{1.25 ex}}\alpha^{2}}}+\frac{2 \sqrt{-x^{2}+1}\, \sqrt{-k^{2} x^{2}+1}\, \underline{\hspace{1.25 ex}}\alpha^{3} k^{2} \EllipticPi \left(x , -k^{2} \underline{\hspace{1.25 ex}}\alpha^{2}, k\right)}{\sqrt{k^{2} x^{4}-k^{2} x^{2}-x^{2}+1}}}{\underline{\hspace{1.25 ex}}\alpha^{3}}}{4 k^{2}}$&$269$\\ \hline \end{longtable}"," ",0,"1/(2*k^2+2)^(1/2)*arctan(((-x^2+1)*(-k^2*x^2+1))^(1/2)*2^(1/2)/x/(2*k^2+2)^(1/2))*2^(1/2)","A"
3072,-1,0,353,180.000000," ","int((1+2*x)/(x^2-1)^(1/3)/(x^2+3),x,method=_RETURNVERBOSE)","\text{hanged}"," ",0,"int((1+2*x)/(x^2-1)^(1/3)/(x^2+3),x,method=_RETURNVERBOSE)","F"
3073,0,0,373,0.120000," ","int(x/(1-(1-(1-1/x)^(1/2))^(1/2))^(1/2),x)","\[\int \frac{x}{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}}\, dx\]"," ",0,"int(x/(1-(1-(1-1/x)^(1/2))^(1/2))^(1/2),x)","F"
3074,1,2950,372,277.559000," ","int((x^6-x^2)^(1/4)*(x^8-x^4+1)/x^4/(x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2950$\\ risch&$\text{Expression too large to display}$&$7288$\\ \hline \end{longtable}"," ",0,"2/5*(x^4-1)*(x^6-x^2)^(1/4)/x^3-3/8*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*ln((-80530636800*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^4*x^5+301989888000*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^4*x^3-54812672*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^5+123109376*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*(x^6-x^2)^(1/2)*x+80530636800*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^4*x+249937920*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^3+3157*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^5+303038464*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*(x^6-x^2)^(3/4)+179929088*(x^6-x^2)^(1/4)*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*x^2+26010*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*(x^6-x^2)^(1/2)*x+54812672*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x+20746*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^3+10982*(x^6-x^2)^(3/4)-15028*(x^6-x^2)^(1/4)*x^2-3157*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x)/(16384*x^2*RootOf(134217728*_Z^4+16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+5*x^2-3)^2/x)+48*RootOf(134217728*_Z^4+16384*_Z^2+1)*ln(-(-5153960755200*RootOf(134217728*_Z^4+16384*_Z^2+1)^5*x^5+19327352832000*RootOf(134217728*_Z^4+16384*_Z^2+1)^5*x^3+2249719808*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*x^5-7879000064*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*(x^6-x^2)^(1/2)*x+5153960755200*RootOf(134217728*_Z^4+16384*_Z^2+1)^5*x-11277434880*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*x^3+553472*RootOf(134217728*_Z^4+16384*_Z^2+1)*x^5+151519232*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*(x^6-x^2)^(3/4)+89964544*(x^6-x^2)^(1/4)*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*x^2+702848*RootOf(134217728*_Z^4+16384*_Z^2+1)*(x^6-x^2)^(1/2)*x-2249719808*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*x-336896*RootOf(134217728*_Z^4+16384*_Z^2+1)*x^3+13005*(x^6-x^2)^(3/4)+18496*(x^6-x^2)^(1/4)*x^2-553472*RootOf(134217728*_Z^4+16384*_Z^2+1)*x)/(16384*x^2*RootOf(134217728*_Z^4+16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4+16384*_Z^2+1)^2-3*x^2-5)^2/x)+6144*ln(-(443992244224*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^4*x^5-1664970915840*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^4*x^3+929792*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^5+151519232*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*(x^6-x^2)^(1/2)*x-443992244224*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^4*x-248225792*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^3-1316*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^5-151519232*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*(x^6-x^2)^(3/4)+89964544*(x^6-x^2)^(1/4)*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*x^2+5491*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*(x^6-x^2)^(1/2)*x-929792*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x-8648*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^3-5491*(x^6-x^2)^(3/4)-7514*(x^6-x^2)^(1/4)*x^2+1316*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x)/(16384*x^2*RootOf(134217728*_Z^4+16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+5*x^2-3)^2/x)*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)+3/8*ln(-(443992244224*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^4*x^5-1664970915840*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^4*x^3+929792*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^5+151519232*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*(x^6-x^2)^(1/2)*x-443992244224*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^4*x-248225792*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^3-1316*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^5-151519232*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*(x^6-x^2)^(3/4)+89964544*(x^6-x^2)^(1/4)*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*x^2+5491*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*(x^6-x^2)^(1/2)*x-929792*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x-8648*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^3-5491*(x^6-x^2)^(3/4)-7514*(x^6-x^2)^(1/4)*x^2+1316*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x)/(16384*x^2*RootOf(134217728*_Z^4+16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+5*x^2-3)^2/x)*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)+786432*ln((2013442932919576297472*RootOf(134217728*_Z^4+16384*_Z^2+1)^5*x^5-7550410998448411115520*RootOf(134217728*_Z^4+16384*_Z^2+1)^5*x^3+929534195592069120*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*x^5+86709454520713216*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*(x^6-x^2)^(1/2)*x-2013442932919576297472*RootOf(134217728*_Z^4+16384*_Z^2+1)^5*x-2375895659744067584*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*x^3+101113373438848*RootOf(134217728*_Z^4+16384*_Z^2+1)*x^5+677417613443072*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*(x^6-x^2)^(3/4)-22722103588438016*(x^6-x^2)^(1/4)*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*x^2-166931784074624*RootOf(134217728*_Z^4+16384*_Z^2+1)*(x^6-x^2)^(1/2)*x-929534195592069120*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*x-61547270788864*RootOf(134217728*_Z^4+16384*_Z^2+1)*x^3-1304154563083*(x^6-x^2)^(3/4)-82692579766*(x^6-x^2)^(1/4)*x^2-101113373438848*RootOf(134217728*_Z^4+16384*_Z^2+1)*x)/(16384*x^2*RootOf(134217728*_Z^4+16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4+16384*_Z^2+1)^2-3*x^2-5)^2/x)*RootOf(134217728*_Z^4+16384*_Z^2+1)^3+48*ln((2013442932919576297472*RootOf(134217728*_Z^4+16384*_Z^2+1)^5*x^5-7550410998448411115520*RootOf(134217728*_Z^4+16384*_Z^2+1)^5*x^3+929534195592069120*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*x^5+86709454520713216*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*(x^6-x^2)^(1/2)*x-2013442932919576297472*RootOf(134217728*_Z^4+16384*_Z^2+1)^5*x-2375895659744067584*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*x^3+101113373438848*RootOf(134217728*_Z^4+16384*_Z^2+1)*x^5+677417613443072*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*(x^6-x^2)^(3/4)-22722103588438016*(x^6-x^2)^(1/4)*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*x^2-166931784074624*RootOf(134217728*_Z^4+16384*_Z^2+1)*(x^6-x^2)^(1/2)*x-929534195592069120*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*x-61547270788864*RootOf(134217728*_Z^4+16384*_Z^2+1)*x^3-1304154563083*(x^6-x^2)^(3/4)-82692579766*(x^6-x^2)^(1/4)*x^2-101113373438848*RootOf(134217728*_Z^4+16384*_Z^2+1)*x)/(16384*x^2*RootOf(134217728*_Z^4+16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4+16384*_Z^2+1)^2-3*x^2-5)^2/x)*RootOf(134217728*_Z^4+16384*_Z^2+1)","C"
3075,1,2950,372,0.000000," ","int((x^6-x^2)^(1/4)*(x^8-x^4+1)/x^4/(x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2950$\\ risch&$\text{Expression too large to display}$&$7288$\\ \hline \end{longtable}"," ",0,"2/5*(x^4-1)*(x^6-x^2)^(1/4)/x^3-3/8*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*ln((-80530636800*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^4*x^5+301989888000*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^4*x^3-54812672*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^5+123109376*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*(x^6-x^2)^(1/2)*x+80530636800*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^4*x+249937920*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^3+3157*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^5+303038464*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*(x^6-x^2)^(3/4)+179929088*(x^6-x^2)^(1/4)*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*x^2+26010*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*(x^6-x^2)^(1/2)*x+54812672*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x+20746*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^3+10982*(x^6-x^2)^(3/4)-15028*(x^6-x^2)^(1/4)*x^2-3157*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x)/(16384*x^2*RootOf(134217728*_Z^4+16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+5*x^2-3)^2/x)+48*RootOf(134217728*_Z^4+16384*_Z^2+1)*ln(-(-5153960755200*RootOf(134217728*_Z^4+16384*_Z^2+1)^5*x^5+19327352832000*RootOf(134217728*_Z^4+16384*_Z^2+1)^5*x^3+2249719808*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*x^5-7879000064*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*(x^6-x^2)^(1/2)*x+5153960755200*RootOf(134217728*_Z^4+16384*_Z^2+1)^5*x-11277434880*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*x^3+553472*RootOf(134217728*_Z^4+16384*_Z^2+1)*x^5+151519232*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*(x^6-x^2)^(3/4)+89964544*(x^6-x^2)^(1/4)*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*x^2+702848*RootOf(134217728*_Z^4+16384*_Z^2+1)*(x^6-x^2)^(1/2)*x-2249719808*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*x-336896*RootOf(134217728*_Z^4+16384*_Z^2+1)*x^3+13005*(x^6-x^2)^(3/4)+18496*(x^6-x^2)^(1/4)*x^2-553472*RootOf(134217728*_Z^4+16384*_Z^2+1)*x)/(16384*x^2*RootOf(134217728*_Z^4+16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4+16384*_Z^2+1)^2-3*x^2-5)^2/x)+6144*ln(-(443992244224*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^4*x^5-1664970915840*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^4*x^3+929792*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^5+151519232*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*(x^6-x^2)^(1/2)*x-443992244224*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^4*x-248225792*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^3-1316*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^5-151519232*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*(x^6-x^2)^(3/4)+89964544*(x^6-x^2)^(1/4)*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*x^2+5491*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*(x^6-x^2)^(1/2)*x-929792*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x-8648*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^3-5491*(x^6-x^2)^(3/4)-7514*(x^6-x^2)^(1/4)*x^2+1316*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x)/(16384*x^2*RootOf(134217728*_Z^4+16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+5*x^2-3)^2/x)*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)+3/8*ln(-(443992244224*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^4*x^5-1664970915840*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^4*x^3+929792*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^5+151519232*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*(x^6-x^2)^(1/2)*x-443992244224*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*RootOf(134217728*_Z^4+16384*_Z^2+1)^4*x-248225792*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^3-1316*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^5-151519232*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*(x^6-x^2)^(3/4)+89964544*(x^6-x^2)^(1/4)*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*x^2+5491*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*(x^6-x^2)^(1/2)*x-929792*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x-8648*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x^3-5491*(x^6-x^2)^(3/4)-7514*(x^6-x^2)^(1/4)*x^2+1316*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)*x)/(16384*x^2*RootOf(134217728*_Z^4+16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+5*x^2-3)^2/x)*RootOf(_Z^2+16384*RootOf(134217728*_Z^4+16384*_Z^2+1)^2+2)+786432*ln((2013442932919576297472*RootOf(134217728*_Z^4+16384*_Z^2+1)^5*x^5-7550410998448411115520*RootOf(134217728*_Z^4+16384*_Z^2+1)^5*x^3+929534195592069120*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*x^5+86709454520713216*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*(x^6-x^2)^(1/2)*x-2013442932919576297472*RootOf(134217728*_Z^4+16384*_Z^2+1)^5*x-2375895659744067584*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*x^3+101113373438848*RootOf(134217728*_Z^4+16384*_Z^2+1)*x^5+677417613443072*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*(x^6-x^2)^(3/4)-22722103588438016*(x^6-x^2)^(1/4)*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*x^2-166931784074624*RootOf(134217728*_Z^4+16384*_Z^2+1)*(x^6-x^2)^(1/2)*x-929534195592069120*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*x-61547270788864*RootOf(134217728*_Z^4+16384*_Z^2+1)*x^3-1304154563083*(x^6-x^2)^(3/4)-82692579766*(x^6-x^2)^(1/4)*x^2-101113373438848*RootOf(134217728*_Z^4+16384*_Z^2+1)*x)/(16384*x^2*RootOf(134217728*_Z^4+16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4+16384*_Z^2+1)^2-3*x^2-5)^2/x)*RootOf(134217728*_Z^4+16384*_Z^2+1)^3+48*ln((2013442932919576297472*RootOf(134217728*_Z^4+16384*_Z^2+1)^5*x^5-7550410998448411115520*RootOf(134217728*_Z^4+16384*_Z^2+1)^5*x^3+929534195592069120*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*x^5+86709454520713216*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*(x^6-x^2)^(1/2)*x-2013442932919576297472*RootOf(134217728*_Z^4+16384*_Z^2+1)^5*x-2375895659744067584*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*x^3+101113373438848*RootOf(134217728*_Z^4+16384*_Z^2+1)*x^5+677417613443072*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*(x^6-x^2)^(3/4)-22722103588438016*(x^6-x^2)^(1/4)*RootOf(134217728*_Z^4+16384*_Z^2+1)^2*x^2-166931784074624*RootOf(134217728*_Z^4+16384*_Z^2+1)*(x^6-x^2)^(1/2)*x-929534195592069120*RootOf(134217728*_Z^4+16384*_Z^2+1)^3*x-61547270788864*RootOf(134217728*_Z^4+16384*_Z^2+1)*x^3-1304154563083*(x^6-x^2)^(3/4)-82692579766*(x^6-x^2)^(1/4)*x^2-101113373438848*RootOf(134217728*_Z^4+16384*_Z^2+1)*x)/(16384*x^2*RootOf(134217728*_Z^4+16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4+16384*_Z^2+1)^2-3*x^2-5)^2/x)*RootOf(134217728*_Z^4+16384*_Z^2+1)","C"
3076,1,2950,372,246.156000," ","int((x^6-x^2)^(1/4)*(x^8+x^4+1)/x^4/(x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2950$\\ risch&$\text{Expression too large to display}$&$7288$\\ \hline \end{longtable}"," ",0,"2/5*(x^4-1)*(x^6-x^2)^(1/4)/x^3-1/8*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*ln((80530636800*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*RootOf(134217728*_Z^4-16384*_Z^2+1)^4*x^5-301989888000*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*RootOf(134217728*_Z^4-16384*_Z^2+1)^4*x^3-54812672*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^5-80530636800*RootOf(134217728*_Z^4-16384*_Z^2+1)^4*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x-123109376*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*(x^6-x^2)^(1/2)*x+249937920*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^3-3157*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^5-303038464*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(3/4)+179929088*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(1/4)*x^2+54812672*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x+26010*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*(x^6-x^2)^(1/2)*x-20746*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^3+10982*(x^6-x^2)^(3/4)+15028*(x^6-x^2)^(1/4)*x^2+3157*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x)/(16384*x^2*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-5*x^2+3)^2/x)+16*RootOf(134217728*_Z^4-16384*_Z^2+1)*ln(-(5153960755200*RootOf(134217728*_Z^4-16384*_Z^2+1)^5*x^5-19327352832000*RootOf(134217728*_Z^4-16384*_Z^2+1)^5*x^3+2249719808*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x^5-5153960755200*RootOf(134217728*_Z^4-16384*_Z^2+1)^5*x+7879000064*(x^6-x^2)^(1/2)*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x-11277434880*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x^3-553472*RootOf(134217728*_Z^4-16384*_Z^2+1)*x^5-151519232*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(3/4)+89964544*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(1/4)*x^2-2249719808*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x+702848*(x^6-x^2)^(1/2)*RootOf(134217728*_Z^4-16384*_Z^2+1)*x+336896*RootOf(134217728*_Z^4-16384*_Z^2+1)*x^3+13005*(x^6-x^2)^(3/4)-18496*(x^6-x^2)^(1/4)*x^2+553472*RootOf(134217728*_Z^4-16384*_Z^2+1)*x)/(16384*x^2*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4-16384*_Z^2+1)^2+3*x^2+5)^2/x)-2048*ln((443992244224*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*RootOf(134217728*_Z^4-16384*_Z^2+1)^4*x^5-1664970915840*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*RootOf(134217728*_Z^4-16384*_Z^2+1)^4*x^3-929792*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^5-443992244224*RootOf(134217728*_Z^4-16384*_Z^2+1)^4*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x+151519232*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*(x^6-x^2)^(1/2)*x+248225792*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^3-1316*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^5-151519232*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(3/4)-89964544*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(1/4)*x^2+929792*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x-5491*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*(x^6-x^2)^(1/2)*x-8648*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^3+5491*(x^6-x^2)^(3/4)-7514*(x^6-x^2)^(1/4)*x^2+1316*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x)/(16384*x^2*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-5*x^2+3)^2/x)*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)+1/8*ln((443992244224*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*RootOf(134217728*_Z^4-16384*_Z^2+1)^4*x^5-1664970915840*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*RootOf(134217728*_Z^4-16384*_Z^2+1)^4*x^3-929792*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^5-443992244224*RootOf(134217728*_Z^4-16384*_Z^2+1)^4*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x+151519232*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*(x^6-x^2)^(1/2)*x+248225792*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^3-1316*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^5-151519232*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(3/4)-89964544*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(1/4)*x^2+929792*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x-5491*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*(x^6-x^2)^(1/2)*x-8648*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^3+5491*(x^6-x^2)^(3/4)-7514*(x^6-x^2)^(1/4)*x^2+1316*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x)/(16384*x^2*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-5*x^2+3)^2/x)*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)-262144*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*ln(-(56831007260672*RootOf(134217728*_Z^4-16384*_Z^2+1)^5*x^5-213116277227520*RootOf(134217728*_Z^4-16384*_Z^2+1)^5*x^3-13755744256*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x^5-56831007260672*RootOf(134217728*_Z^4-16384*_Z^2+1)^5*x-19394461696*(x^6-x^2)^(1/2)*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x+20257439744*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x^3+663872*RootOf(134217728*_Z^4-16384*_Z^2+1)*x^5-151519232*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(3/4)-89964544*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(1/4)*x^2+13755744256*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x+1664640*(x^6-x^2)^(1/2)*RootOf(134217728*_Z^4-16384*_Z^2+1)*x-404096*RootOf(134217728*_Z^4-16384*_Z^2+1)*x^3+13005*(x^6-x^2)^(3/4)+18496*(x^6-x^2)^(1/4)*x^2-663872*RootOf(134217728*_Z^4-16384*_Z^2+1)*x)/(16384*x^2*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4-16384*_Z^2+1)^2+3*x^2+5)^2/x)+16*RootOf(134217728*_Z^4-16384*_Z^2+1)*ln(-(56831007260672*RootOf(134217728*_Z^4-16384*_Z^2+1)^5*x^5-213116277227520*RootOf(134217728*_Z^4-16384*_Z^2+1)^5*x^3-13755744256*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x^5-56831007260672*RootOf(134217728*_Z^4-16384*_Z^2+1)^5*x-19394461696*(x^6-x^2)^(1/2)*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x+20257439744*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x^3+663872*RootOf(134217728*_Z^4-16384*_Z^2+1)*x^5-151519232*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(3/4)-89964544*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(1/4)*x^2+13755744256*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x+1664640*(x^6-x^2)^(1/2)*RootOf(134217728*_Z^4-16384*_Z^2+1)*x-404096*RootOf(134217728*_Z^4-16384*_Z^2+1)*x^3+13005*(x^6-x^2)^(3/4)+18496*(x^6-x^2)^(1/4)*x^2-663872*RootOf(134217728*_Z^4-16384*_Z^2+1)*x)/(16384*x^2*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4-16384*_Z^2+1)^2+3*x^2+5)^2/x)","C"
3077,1,2950,372,0.000000," ","int((x^6-x^2)^(1/4)*(x^8+x^4+1)/x^4/(x^4+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2950$\\ risch&$\text{Expression too large to display}$&$7288$\\ \hline \end{longtable}"," ",0,"2/5*(x^4-1)*(x^6-x^2)^(1/4)/x^3-1/8*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*ln((80530636800*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*RootOf(134217728*_Z^4-16384*_Z^2+1)^4*x^5-301989888000*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*RootOf(134217728*_Z^4-16384*_Z^2+1)^4*x^3-54812672*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^5-80530636800*RootOf(134217728*_Z^4-16384*_Z^2+1)^4*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x-123109376*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*(x^6-x^2)^(1/2)*x+249937920*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^3-3157*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^5-303038464*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(3/4)+179929088*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(1/4)*x^2+54812672*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x+26010*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*(x^6-x^2)^(1/2)*x-20746*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^3+10982*(x^6-x^2)^(3/4)+15028*(x^6-x^2)^(1/4)*x^2+3157*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x)/(16384*x^2*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-5*x^2+3)^2/x)+16*RootOf(134217728*_Z^4-16384*_Z^2+1)*ln(-(5153960755200*RootOf(134217728*_Z^4-16384*_Z^2+1)^5*x^5-19327352832000*RootOf(134217728*_Z^4-16384*_Z^2+1)^5*x^3+2249719808*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x^5-5153960755200*RootOf(134217728*_Z^4-16384*_Z^2+1)^5*x+7879000064*(x^6-x^2)^(1/2)*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x-11277434880*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x^3-553472*RootOf(134217728*_Z^4-16384*_Z^2+1)*x^5-151519232*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(3/4)+89964544*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(1/4)*x^2-2249719808*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x+702848*(x^6-x^2)^(1/2)*RootOf(134217728*_Z^4-16384*_Z^2+1)*x+336896*RootOf(134217728*_Z^4-16384*_Z^2+1)*x^3+13005*(x^6-x^2)^(3/4)-18496*(x^6-x^2)^(1/4)*x^2+553472*RootOf(134217728*_Z^4-16384*_Z^2+1)*x)/(16384*x^2*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4-16384*_Z^2+1)^2+3*x^2+5)^2/x)-2048*ln((443992244224*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*RootOf(134217728*_Z^4-16384*_Z^2+1)^4*x^5-1664970915840*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*RootOf(134217728*_Z^4-16384*_Z^2+1)^4*x^3-929792*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^5-443992244224*RootOf(134217728*_Z^4-16384*_Z^2+1)^4*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x+151519232*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*(x^6-x^2)^(1/2)*x+248225792*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^3-1316*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^5-151519232*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(3/4)-89964544*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(1/4)*x^2+929792*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x-5491*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*(x^6-x^2)^(1/2)*x-8648*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^3+5491*(x^6-x^2)^(3/4)-7514*(x^6-x^2)^(1/4)*x^2+1316*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x)/(16384*x^2*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-5*x^2+3)^2/x)*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)+1/8*ln((443992244224*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*RootOf(134217728*_Z^4-16384*_Z^2+1)^4*x^5-1664970915840*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*RootOf(134217728*_Z^4-16384*_Z^2+1)^4*x^3-929792*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^5-443992244224*RootOf(134217728*_Z^4-16384*_Z^2+1)^4*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x+151519232*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*(x^6-x^2)^(1/2)*x+248225792*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^3-1316*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^5-151519232*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(3/4)-89964544*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(1/4)*x^2+929792*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x-5491*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*(x^6-x^2)^(1/2)*x-8648*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x^3+5491*(x^6-x^2)^(3/4)-7514*(x^6-x^2)^(1/4)*x^2+1316*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)*x)/(16384*x^2*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-5*x^2+3)^2/x)*RootOf(_Z^2+16384*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-2)-262144*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*ln(-(56831007260672*RootOf(134217728*_Z^4-16384*_Z^2+1)^5*x^5-213116277227520*RootOf(134217728*_Z^4-16384*_Z^2+1)^5*x^3-13755744256*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x^5-56831007260672*RootOf(134217728*_Z^4-16384*_Z^2+1)^5*x-19394461696*(x^6-x^2)^(1/2)*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x+20257439744*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x^3+663872*RootOf(134217728*_Z^4-16384*_Z^2+1)*x^5-151519232*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(3/4)-89964544*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(1/4)*x^2+13755744256*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x+1664640*(x^6-x^2)^(1/2)*RootOf(134217728*_Z^4-16384*_Z^2+1)*x-404096*RootOf(134217728*_Z^4-16384*_Z^2+1)*x^3+13005*(x^6-x^2)^(3/4)+18496*(x^6-x^2)^(1/4)*x^2-663872*RootOf(134217728*_Z^4-16384*_Z^2+1)*x)/(16384*x^2*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4-16384*_Z^2+1)^2+3*x^2+5)^2/x)+16*RootOf(134217728*_Z^4-16384*_Z^2+1)*ln(-(56831007260672*RootOf(134217728*_Z^4-16384*_Z^2+1)^5*x^5-213116277227520*RootOf(134217728*_Z^4-16384*_Z^2+1)^5*x^3-13755744256*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x^5-56831007260672*RootOf(134217728*_Z^4-16384*_Z^2+1)^5*x-19394461696*(x^6-x^2)^(1/2)*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x+20257439744*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x^3+663872*RootOf(134217728*_Z^4-16384*_Z^2+1)*x^5-151519232*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(3/4)-89964544*RootOf(134217728*_Z^4-16384*_Z^2+1)^2*(x^6-x^2)^(1/4)*x^2+13755744256*RootOf(134217728*_Z^4-16384*_Z^2+1)^3*x+1664640*(x^6-x^2)^(1/2)*RootOf(134217728*_Z^4-16384*_Z^2+1)*x-404096*RootOf(134217728*_Z^4-16384*_Z^2+1)*x^3+13005*(x^6-x^2)^(3/4)+18496*(x^6-x^2)^(1/4)*x^2-663872*RootOf(134217728*_Z^4-16384*_Z^2+1)*x)/(16384*x^2*RootOf(134217728*_Z^4-16384*_Z^2+1)^2-65536*RootOf(134217728*_Z^4-16384*_Z^2+1)^2+3*x^2+5)^2/x)","C"
3078,0,0,416,0.006000," ","int((a^3*x^3+b^2*x^2)^(1/3)/(a*x-b),x)","\[\int \frac{\left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}{a x -b}\, dx\]"," ",0,"int((a^3*x^3+b^2*x^2)^(1/3)/(a*x-b),x)","F"
3079,0,0,445,180.000000," ","int((a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/2))^(1/2),x)","\[\int \frac{\sqrt{a^{2} x^{2}-b}}{\sqrt{a x +\sqrt{a^{2} x^{2}-b}}\, \sqrt{c +\sqrt{a x +\sqrt{a^{2} x^{2}-b}}}}\, dx\]"," ",0,"int((a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/2))^(1/2),x)","F"
3080,0,0,486,0.019000," ","int((x^2-3)*(x^6+x^4-2*x^2+1)/x^10/((b*x^3+a*x^2-a)/(d*x^3+c*x^2-c))^(1/4),x)","\[\int \frac{\left(x^{2}-3\right) \left(x^{6}+x^{4}-2 x^{2}+1\right)}{x^{10} \left(\frac{b \,x^{3}+a \,x^{2}-a}{d \,x^{3}+c \,x^{2}-c}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((x^2-3)*(x^6+x^4-2*x^2+1)/x^10/((b*x^3+a*x^2-a)/(d*x^3+c*x^2-c))^(1/4),x)","F"
3081,0,0,178,0.030000," ","int((x^4+1)*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1),x)","\[\int \frac{\left(x^{4}+1\right) \sqrt{x +\sqrt{x^{2}+1}}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{-x^{4}+1}\, dx\]"," ",0,"int((x^4+1)*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1),x)","F"
3082,0,0,178,0.000000," ","int((x^4+1)*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1),x)","\[\int \frac{\left(x^{4}+1\right) \sqrt{x +\sqrt{x^{2}+1}}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{-x^{4}+1}\, dx\]"," ",0,"int((x^4+1)*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1),x)","F"
3083,0,0,457,0.016000," ","int((a^2*x^2+b)^(1/2)*(c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2),x)","\[\int \sqrt{a^{2} x^{2}+b}\, \sqrt{c +\sqrt{a x +\sqrt{a^{2} x^{2}+b}}}\, dx\]"," ",0,"int((a^2*x^2+b)^(1/2)*(c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2),x)","F"
3084,1,146,506,0.438000," ","int(((x^6-13*x^5+65*x^4-150*x^3+135*x^2+27*x-81)^3)^(1/2)/(-1+x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(1146880 x^{8}-23296000 x^{7}+199009280 x^{6}-910869760 x^{5}+2304529024 x^{4}-2700564848 x^{3}-508033624 x^{2}+4423205098 x -1245336401\right) \sqrt{\left(x^{2}-x -1\right)^{3} \left(-3+x \right)^{12}}}{10321920 \left(x^{2}-x -1\right) \left(-3+x \right)^{6}}+\frac{\left(-\frac{19451047 \ln \left(-\frac{1}{2}+x +\sqrt{x^{2}-x -1}\right)}{65536}+64 \arctan \left(\frac{-3+x}{2 \sqrt{\left(-1+x \right)^{2}-2+x}}\right)\right) \sqrt{\left(x^{2}-x -1\right)^{3} \left(-3+x \right)^{12}}}{\left(x^{2}-x -1\right)^{\frac{3}{2}} \left(-3+x \right)^{6}}$&$146$\\ default&$\frac{\sqrt{\left(x^{6}-13 x^{5}+65 x^{4}-150 x^{3}+135 x^{2}+27 x -81\right)^{3}}\, \left(2293760 x^{4} \left(x^{2}-x -1\right)^{\frac{5}{2}}-42004480 x^{3} \left(x^{2}-x -1\right)^{\frac{5}{2}}+316303360 x^{2} \left(x^{2}-x -1\right)^{\frac{5}{2}}-1235724800 x \left(x^{2}-x -1\right)^{\frac{5}{2}}+2535627008 \left(x^{2}-x -1\right)^{\frac{5}{2}}-2156202720 x \left(x^{2}-x -1\right)^{\frac{3}{2}}+1518503280 \left(x^{2}-x -1\right)^{\frac{3}{2}}+4373181540 x \sqrt{x^{2}-x -1}-3507796530 \sqrt{x^{2}-x -1}-6127079805 \ln \left(-\frac{1}{2}+x +\sqrt{x^{2}-x -1}\right)+1321205760 \arctan \left(\frac{-3+x}{2 \sqrt{x^{2}-x -1}}\right)\right)}{20643840 \left(-3+x \right)^{6} \left(x^{2}-x -1\right)^{\frac{3}{2}}}$&$205$\\ trager&$\frac{\left(1146880 x^{8}-23296000 x^{7}+199009280 x^{6}-910869760 x^{5}+2304529024 x^{4}-2700564848 x^{3}-508033624 x^{2}+4423205098 x -1245336401\right) \sqrt{x^{18}-39 x^{17}+702 x^{16}-7717 x^{15}+57735 x^{14}-309774 x^{13}+1221371 x^{12}-3554163 x^{11}+7498953 x^{10}-10819710 x^{9}+8764767 x^{8}+592677 x^{7}-10219851 x^{6}+9880866 x^{5}-885735 x^{4}-4704237 x^{3}+2480058 x^{2}+531441 x -531441}}{10321920 \left(-3+x \right)^{6} \left(x^{2}-x -1\right)}+\frac{19451047 \ln \left(-\frac{-729+2187 x -486 x^{2}-4077 x^{3}+5886 x^{4}-3897 x^{5}+1466 x^{6}-323 x^{7}+39 x^{8}-2 x^{9}+2 \sqrt{x^{18}-39 x^{17}+702 x^{16}-7717 x^{15}+57735 x^{14}-309774 x^{13}+1221371 x^{12}-3554163 x^{11}+7498953 x^{10}-10819710 x^{9}+8764767 x^{8}+592677 x^{7}-10219851 x^{6}+9880866 x^{5}-885735 x^{4}-4704237 x^{3}+2480058 x^{2}+531441 x -531441}}{\left(x^{2}-x -1\right) \left(-3+x \right)^{6}}\right)}{65536}+64 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}+1\right) x^{9}+22 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{8}-209 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{7}+1113 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{6}-3591 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{5}+6993 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{4}-7371 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{3}+2187 \RootOf \left(\textit{\_Z}^{2}+1\right) x^{2}+2916 \RootOf \left(\textit{\_Z}^{2}+1\right) x +2 \sqrt{x^{18}-39 x^{17}+702 x^{16}-7717 x^{15}+57735 x^{14}-309774 x^{13}+1221371 x^{12}-3554163 x^{11}+7498953 x^{10}-10819710 x^{9}+8764767 x^{8}+592677 x^{7}-10219851 x^{6}+9880866 x^{5}-885735 x^{4}-4704237 x^{3}+2480058 x^{2}+531441 x -531441}-2187 \RootOf \left(\textit{\_Z}^{2}+1\right)}{\left(-1+x \right) \left(x^{2}-x -1\right) \left(-3+x \right)^{6}}\right)$&$534$\\ \hline \end{longtable}"," ",0,"1/10321920/(x^2-x-1)*(1146880*x^8-23296000*x^7+199009280*x^6-910869760*x^5+2304529024*x^4-2700564848*x^3-508033624*x^2+4423205098*x-1245336401)*((x^2-x-1)^3*(-3+x)^12)^(1/2)/(-3+x)^6+(-19451047/65536*ln(-1/2+x+(x^2-x-1)^(1/2))+64*arctan(1/2*(-3+x)/((-1+x)^2-2+x)^(1/2)))*((x^2-x-1)^3*(-3+x)^12)^(1/2)/(x^2-x-1)^(3/2)/(-3+x)^6","A"
3085,0,0,162,0.017000," ","int((x^4+x^2+1)^2*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1)^2,x)","\[\int \frac{\left(x^{4}+x^{2}+1\right)^{2} \sqrt{x^{2}+\sqrt{x^{4}+1}}}{\sqrt{x^{4}+1}\, \left(x^{4}+x^{2}-1\right)^{2}}\, dx\]"," ",0,"int((x^4+x^2+1)^2*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1)^2,x)","F"
3086,0,0,162,0.001000," ","int((x^4+x^2+1)^2*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1)^2,x)","\[\int \frac{\left(x^{4}+x^{2}+1\right)^{2} \sqrt{x^{2}+\sqrt{x^{4}+1}}}{\sqrt{x^{4}+1}\, \left(x^{4}+x^{2}-1\right)^{2}}\, dx\]"," ",0,"int((x^4+x^2+1)^2*(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2)/(x^4+x^2-1)^2,x)","F"
3087,1,60,369,0.183000," ","int((p*x^4-q)*(p*x^4+q)^(1/2)/x^2/(a*p*x^4+b*x^2+a*q),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(\frac{\sqrt{p \,x^{4}+q}\, \sqrt{2}}{a x}-\frac{b \sqrt{2}\, \arctan \left(\frac{\sqrt{p \,x^{4}+q}\, a}{x \sqrt{a b}}\right)}{a \sqrt{a b}}\right) \sqrt{2}}{2}$&$60$\\ risch&$\frac{\sqrt{p \,x^{4}+q}}{a x}-\frac{b \left(\frac{\sqrt{1-\frac{i \sqrt{p}\, x^{2}}{\sqrt{q}}}\, \sqrt{1+\frac{i \sqrt{p}\, x^{2}}{\sqrt{q}}}\, \EllipticF \left(x \sqrt{\frac{i \sqrt{p}}{\sqrt{q}}}, i\right)}{a \sqrt{\frac{i \sqrt{p}}{\sqrt{q}}}\, \sqrt{p \,x^{4}+q}}+\frac{\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a p \,\textit{\_Z}^{4}+b \,\textit{\_Z}^{2}+a q \right)}{\sum}\frac{\left(-\underline{\hspace{1.25 ex}}\alpha^{2} b -2 a q \right) \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{2} a p +a p \,x^{2}-b \right)}{a \sqrt{-\frac{b \,\underline{\hspace{1.25 ex}}\alpha^{2}}{a}}\, \sqrt{p \,x^{4}+q}}\right)}{\sqrt{-\frac{b \,\underline{\hspace{1.25 ex}}\alpha^{2}}{a}}}+\frac{2 \underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2} a p +b \right) \sqrt{1-\frac{i \sqrt{p}\, x^{2}}{\sqrt{q}}}\, \sqrt{1+\frac{i \sqrt{p}\, x^{2}}{\sqrt{q}}}\, \EllipticPi \left(x \sqrt{\frac{i \sqrt{p}}{\sqrt{q}}}, \frac{i \left(\underline{\hspace{1.25 ex}}\alpha^{2} a p +b \right)}{\sqrt{p}\, \sqrt{q}\, a}, \frac{\sqrt{-\frac{i \sqrt{p}}{\sqrt{q}}}}{\sqrt{\frac{i \sqrt{p}}{\sqrt{q}}}}\right)}{\sqrt{\frac{i \sqrt{p}}{\sqrt{q}}}\, a q \sqrt{p \,x^{4}+q}}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2} a p +b \right)}}{4 a}\right)}{a}$&$332$\\ default&$-\frac{-\frac{\sqrt{p \,x^{4}+q}}{x}+\frac{2 i \sqrt{p}\, \sqrt{q}\, \sqrt{1-\frac{i \sqrt{p}\, x^{2}}{\sqrt{q}}}\, \sqrt{1+\frac{i \sqrt{p}\, x^{2}}{\sqrt{q}}}\, \left(\EllipticF \left(x \sqrt{\frac{i \sqrt{p}}{\sqrt{q}}}, i\right)-\EllipticE \left(x \sqrt{\frac{i \sqrt{p}}{\sqrt{q}}}, i\right)\right)}{\sqrt{\frac{i \sqrt{p}}{\sqrt{q}}}\, \sqrt{p \,x^{4}+q}}}{a}+\frac{-\frac{b \sqrt{1-\frac{i \sqrt{p}\, x^{2}}{\sqrt{q}}}\, \sqrt{1+\frac{i \sqrt{p}\, x^{2}}{\sqrt{q}}}\, \EllipticF \left(x \sqrt{\frac{i \sqrt{p}}{\sqrt{q}}}, i\right)}{a \sqrt{\frac{i \sqrt{p}}{\sqrt{q}}}\, \sqrt{p \,x^{4}+q}}+\frac{2 i \sqrt{p}\, \sqrt{q}\, \sqrt{1-\frac{i \sqrt{p}\, x^{2}}{\sqrt{q}}}\, \sqrt{1+\frac{i \sqrt{p}\, x^{2}}{\sqrt{q}}}\, \left(\EllipticF \left(x \sqrt{\frac{i \sqrt{p}}{\sqrt{q}}}, i\right)-\EllipticE \left(x \sqrt{\frac{i \sqrt{p}}{\sqrt{q}}}, i\right)\right)}{\sqrt{\frac{i \sqrt{p}}{\sqrt{q}}}\, \sqrt{p \,x^{4}+q}}+\frac{b \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a p \,\textit{\_Z}^{4}+b \,\textit{\_Z}^{2}+a q \right)}{\sum}\frac{\left(\underline{\hspace{1.25 ex}}\alpha^{2} b +2 a q \right) \left(-\frac{\arctanh \left(\frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(-\underline{\hspace{1.25 ex}}\alpha^{2} a p +a p \,x^{2}-b \right)}{a \sqrt{-\frac{b \,\underline{\hspace{1.25 ex}}\alpha^{2}}{a}}\, \sqrt{p \,x^{4}+q}}\right)}{\sqrt{-\frac{b \,\underline{\hspace{1.25 ex}}\alpha^{2}}{a}}}+\frac{2 \underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2} a p +b \right) \sqrt{1-\frac{i \sqrt{p}\, x^{2}}{\sqrt{q}}}\, \sqrt{1+\frac{i \sqrt{p}\, x^{2}}{\sqrt{q}}}\, \EllipticPi \left(x \sqrt{\frac{i \sqrt{p}}{\sqrt{q}}}, \frac{i \left(\underline{\hspace{1.25 ex}}\alpha^{2} a p +b \right)}{\sqrt{p}\, \sqrt{q}\, a}, \frac{\sqrt{-\frac{i \sqrt{p}}{\sqrt{q}}}}{\sqrt{\frac{i \sqrt{p}}{\sqrt{q}}}}\right)}{\sqrt{\frac{i \sqrt{p}}{\sqrt{q}}}\, a q \sqrt{p \,x^{4}+q}}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2} a p +b \right)}\right)}{4 a}}{a}$&$528$\\ \hline \end{longtable}"," ",0,"1/2*(1/a*(p*x^4+q)^(1/2)*2^(1/2)/x-b/a*2^(1/2)/(a*b)^(1/2)*arctan((p*x^4+q)^(1/2)/x*a/(a*b)^(1/2)))*2^(1/2)","A"
3088,0,0,438,0.007000," ","int((a^3*x^3+b^2*x^2)^(1/3)/(a*x+b),x)","\[\int \frac{\left(a^{3} x^{3}+b^{2} x^{2}\right)^{\frac{1}{3}}}{a x +b}\, dx\]"," ",0,"int((a^3*x^3+b^2*x^2)^(1/3)/(a*x+b),x)","F"
3089,0,0,412,180.000000," ","int((a^2*x^2-b)^(3/2)*(a*x+(a^2*x^2-b)^(1/2))^(1/4)/x,x)","\[\int \frac{\left(a^{2} x^{2}-b \right)^{\frac{3}{2}} \left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}}}{x}\, dx\]"," ",0,"int((a^2*x^2-b)^(3/2)*(a*x+(a^2*x^2-b)^(1/2))^(1/4)/x,x)","F"
3090,0,0,386,0.016000," ","int((a*x^2+b^2)*(b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2-b^2),x)","\[\int \frac{\left(a \,x^{2}+b^{2}\right) \sqrt{b +\sqrt{a \,x^{2}+b^{2}}}}{a \,x^{2}-b^{2}}\, dx\]"," ",0,"int((a*x^2+b^2)*(b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2-b^2),x)","F"
3091,0,0,424,180.000000," ","int((c*x^4+d)/x/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/4),x)","\[\int \frac{c \,x^{4}+d}{x \sqrt{a^{2} x^{2}-b}\, \left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((c*x^4+d)/x/(a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/4),x)","F"
3092,0,0,421,180.000000," ","int((a^2*x^2-b)^(3/2)*(a*x+(a^2*x^2-b)^(1/2))^(1/4)/x^2,x)","\[\int \frac{\left(a^{2} x^{2}-b \right)^{\frac{3}{2}} \left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}}}{x^{2}}\, dx\]"," ",0,"int((a^2*x^2-b)^(3/2)*(a*x+(a^2*x^2-b)^(1/2))^(1/4)/x^2,x)","F"
3093,0,0,451,0.036000," ","int((b-x)/((-a+x)*(-b+x)^2)^(1/3)/(a^2-b^2*d-2*(-b*d+a)*x+(1-d)*x^2),x)","\[\int \frac{b -x}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{3}} \left(a^{2}-b^{2} d -2 \left(-b d +a \right) x +\left(1-d \right) x^{2}\right)}\, dx\]"," ",0,"int((b-x)/((-a+x)*(-b+x)^2)^(1/3)/(a^2-b^2*d-2*(-b*d+a)*x+(1-d)*x^2),x)","F"
3094,0,0,451,0.033000," ","int((-b+x)/((-a+x)*(-b+x)^2)^(1/3)/(-a^2+b^2*d+2*(-b*d+a)*x+(-1+d)*x^2),x)","\[\int \frac{-b +x}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{3}} \left(-a^{2}+b^{2} d +2 \left(-b d +a \right) x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((-b+x)/((-a+x)*(-b+x)^2)^(1/3)/(-a^2+b^2*d+2*(-b*d+a)*x+(-1+d)*x^2),x)","F"
3095,0,0,394,0.019000," ","int((a*x^2+b^2)/(a*x^2-b^2)/(b+(a*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{a \,x^{2}+b^{2}}{\left(a \,x^{2}-b^{2}\right) \sqrt{b +\sqrt{a \,x^{2}+b^{2}}}}\, dx\]"," ",0,"int((a*x^2+b^2)/(a*x^2-b^2)/(b+(a*x^2+b^2)^(1/2))^(1/2),x)","F"
3096,0,0,452,0.013000," ","int(1/((-a+x)*(-b+x)^2)^(1/3)/(a-b*d+(-1+d)*x),x)","\[\int \frac{1}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{3}} \left(a -b d +\left(-1+d \right) x \right)}\, dx\]"," ",0,"int(1/((-a+x)*(-b+x)^2)^(1/3)/(a-b*d+(-1+d)*x),x)","F"
3097,0,0,173,180.000000," ","int((a^2*x^4+b)^(1/2)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d),x)","\[\int \frac{\sqrt{a^{2} x^{4}+b}\, \sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}{c \,x^{2}+d}\, dx\]"," ",0,"int((a^2*x^4+b)^(1/2)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d),x)","F"
3098,0,0,173,180.000000," ","int((a^2*x^4+b)^(1/2)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d),x)","\[\int \frac{\sqrt{a^{2} x^{4}+b}\, \sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}{c \,x^{2}+d}\, dx\]"," ",0,"int((a^2*x^4+b)^(1/2)*(a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x^2+d),x)","F"
3099,0,0,439,0.010000," ","int((x^2+(x^4+1)^(1/2))^(1/2)/(a*x+1),x)","\[\int \frac{\sqrt{x^{2}+\sqrt{x^{4}+1}}}{a x +1}\, dx\]"," ",0,"int((x^2+(x^4+1)^(1/2))^(1/2)/(a*x+1),x)","F"
3100,0,0,357,0.069000," ","int(1/(_C4+((_C1*x+_C0)/(_C3*x+_C2))^(1/2)*_C5)^(1/2)/(_C7*x+_C6),x)","\[\int \frac{1}{\sqrt{\textit{\_C4} +\sqrt{\frac{\textit{\_C1} x +\textit{\_C0}}{\textit{\_C3} x +\textit{\_C2}}}\, \textit{\_C5}}\, \left(\textit{\_C7} x +\textit{\_C6} \right)}\, dx\]"," ",0,"int(1/(_C4+((_C1*x+_C0)/(_C3*x+_C2))^(1/2)*_C5)^(1/2)/(_C7*x+_C6),x)","F"
3101,0,0,483,0.032000," ","int((-b+x)/((-a+x)*(-b+x)^2)^(1/3)/(-b^2+a^2*d+2*(-a*d+b)*x+(-1+d)*x^2),x)","\[\int \frac{-b +x}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{3}} \left(-b^{2}+a^{2} d +2 \left(-a d +b \right) x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((-b+x)/((-a+x)*(-b+x)^2)^(1/3)/(-b^2+a^2*d+2*(-a*d+b)*x+(-1+d)*x^2),x)","F"
3102,0,0,418,0.024000," ","int((a*x^2+b^2)^2/(a*x^2-b^2)^2/(b+(a*x^2+b^2)^(1/2))^(1/2),x)","\[\int \frac{\left(a \,x^{2}+b^{2}\right)^{2}}{\left(a \,x^{2}-b^{2}\right)^{2} \sqrt{b +\sqrt{a \,x^{2}+b^{2}}}}\, dx\]"," ",0,"int((a*x^2+b^2)^2/(a*x^2-b^2)^2/(b+(a*x^2+b^2)^(1/2))^(1/2),x)","F"
3103,1,239,14,0.128000," ","int((a*x+(a*x-b)^(1/2))^(1/2)/(a*x-b)^(1/2)/(a^2*x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}+4 b \,\textit{\_Z}^{6}-8 b \,\textit{\_Z}^{5}+\left(6 b^{2}+2 b +16\right) \textit{\_Z}^{4}+\left(-16 b^{2}-32\right) \textit{\_Z}^{3}+\left(4 b^{3}+20 b^{2}+24\right) \textit{\_Z}^{2}+\left(-8 b^{3}-8 b^{2}-8\right) \textit{\_Z} +b^{4}+2 b^{3}+b^{2}+1\right)}{\sum}\frac{\left(2 \textit{\_R}^{5}-5 \textit{\_R}^{4}+4 \left(1+b \right) \textit{\_R}^{3}+\left(-6 b -1\right) \textit{\_R}^{2}+2 b \left(1+b \right) \textit{\_R} -b^{2}\right) \ln \left(\sqrt{a x +\sqrt{a x -b}}-\sqrt{a x -b}-\textit{\_R} \right)}{\textit{\_R}^{7}+3 \textit{\_R}^{5} b -5 \textit{\_R}^{4} b +3 \textit{\_R}^{3} b^{2}+\textit{\_R}^{3} b -6 \textit{\_R}^{2} b^{2}+\textit{\_R} \,b^{3}+8 \textit{\_R}^{3}+5 \textit{\_R} \,b^{2}-b^{3}-12 \textit{\_R}^{2}-b^{2}+6 \textit{\_R} -1}}{2 a}$&$239$\\ default&$-\frac{\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}+4 b \,\textit{\_Z}^{6}-8 b \,\textit{\_Z}^{5}+\left(6 b^{2}+2 b +16\right) \textit{\_Z}^{4}+\left(-16 b^{2}-32\right) \textit{\_Z}^{3}+\left(4 b^{3}+20 b^{2}+24\right) \textit{\_Z}^{2}+\left(-8 b^{3}-8 b^{2}-8\right) \textit{\_Z} +b^{4}+2 b^{3}+b^{2}+1\right)}{\sum}\frac{\left(2 \textit{\_R}^{5}-5 \textit{\_R}^{4}+4 \left(1+b \right) \textit{\_R}^{3}+\left(-6 b -1\right) \textit{\_R}^{2}+2 b \left(1+b \right) \textit{\_R} -b^{2}\right) \ln \left(\sqrt{a x +\sqrt{a x -b}}-\sqrt{a x -b}-\textit{\_R} \right)}{\textit{\_R}^{7}+3 \textit{\_R}^{5} b -5 \textit{\_R}^{4} b +3 \textit{\_R}^{3} b^{2}+\textit{\_R}^{3} b -6 \textit{\_R}^{2} b^{2}+\textit{\_R} \,b^{3}+8 \textit{\_R}^{3}+5 \textit{\_R} \,b^{2}-b^{3}-12 \textit{\_R}^{2}-b^{2}+6 \textit{\_R} -1}}{2 a}$&$239$\\ \hline \end{longtable}"," ",0,"-1/2/a*sum((2*_R^5-5*_R^4+4*(1+b)*_R^3+(-6*b-1)*_R^2+2*b*(1+b)*_R-b^2)/(_R^7+3*_R^5*b-5*_R^4*b+3*_R^3*b^2+_R^3*b-6*_R^2*b^2+_R*b^3+8*_R^3+5*_R*b^2-b^3-12*_R^2-b^2+6*_R-1)*ln((a*x+(a*x-b)^(1/2))^(1/2)-(a*x-b)^(1/2)-_R),_R=RootOf(_Z^8+4*b*_Z^6-8*b*_Z^5+(6*b^2+2*b+16)*_Z^4+(-16*b^2-32)*_Z^3+(4*b^3+20*b^2+24)*_Z^2+(-8*b^3-8*b^2-8)*_Z+b^4+2*b^3+b^2+1))","B"
3104,0,0,183,0.034000," ","int((x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1),x)","\[\int \frac{\left(x^{4}+1\right) \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{-x^{4}+1}\, dx\]"," ",0,"int((x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1),x)","F"
3105,0,0,183,0.000000," ","int((x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1),x)","\[\int \frac{\left(x^{4}+1\right) \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{-x^{4}+1}\, dx\]"," ",0,"int((x^4+1)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^4+1),x)","F"
3106,0,0,323,0.025000," ","int((x^2+1)^(5/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","\[\int \frac{\left(x^{2}+1\right)^{\frac{5}{2}} \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right)^{2}}\, dx\]"," ",0,"int((x^2+1)^(5/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","F"
3107,0,0,323,0.000000," ","int((x^2+1)^(5/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","\[\int \frac{\left(x^{2}+1\right)^{\frac{5}{2}} \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right)^{2}}\, dx\]"," ",0,"int((x^2+1)^(5/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","F"
3108,0,0,480,0.017000," ","int((x^4+1)^(1/2)/(1+x)^3/(x^2+(x^4+1)^(1/2))^(1/2),x)","\[\int \frac{\sqrt{x^{4}+1}}{\left(1+x \right)^{3} \sqrt{x^{2}+\sqrt{x^{4}+1}}}\, dx\]"," ",0,"int((x^4+1)^(1/2)/(1+x)^3/(x^2+(x^4+1)^(1/2))^(1/2),x)","F"
3109,0,0,465,0.107000," ","int(x^2/(1-(1-(1-1/x)^(1/2))^(1/2))^(1/2),x)","\[\int \frac{x^{2}}{\sqrt{1-\sqrt{1-\sqrt{1-\frac{1}{x}}}}}\, dx\]"," ",0,"int(x^2/(1-(1-(1-1/x)^(1/2))^(1/2))^(1/2),x)","F"
3110,0,0,514,0.030000," ","int((x^2+1)*(a*x^2-b*x-a)/x^2/(c*x^2+d*x-c)/((-_C0*x+x^2-1)/(-_C1*x+x^2-1))^(1/3),x)","\[\int \frac{\left(x^{2}+1\right) \left(a \,x^{2}-b x -a \right)}{x^{2} \left(c \,x^{2}+d x -c \right) \left(\frac{-\textit{\_C0} x +x^{2}-1}{-\textit{\_C1} x +x^{2}-1}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int((x^2+1)*(a*x^2-b*x-a)/x^2/(c*x^2+d*x-c)/((-_C0*x+x^2-1)/(-_C1*x+x^2-1))^(1/3),x)","F"
3111,0,0,257,0.026000," ","int((x^2+1)^2*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{\left(x^{2}+1\right)^{2} \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right)^{2} \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^2+1)^2*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x)","F"
3112,0,0,257,0.000000," ","int((x^2+1)^2*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x)","\[\int \frac{\left(x^{2}+1\right)^{2} \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right)^{2} \sqrt{x +\sqrt{x^{2}+1}}}\, dx\]"," ",0,"int((x^2+1)^2*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x)","F"
3113,0,0,257,0.022000," ","int((x^2+1)^2*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","\[\int \frac{\left(x^{2}+1\right)^{2} \sqrt{x +\sqrt{x^{2}+1}}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right)^{2}}\, dx\]"," ",0,"int((x^2+1)^2*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","F"
3114,0,0,257,0.000000," ","int((x^2+1)^2*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","\[\int \frac{\left(x^{2}+1\right)^{2} \sqrt{x +\sqrt{x^{2}+1}}\, \sqrt{1+\sqrt{x +\sqrt{x^{2}+1}}}}{\left(-x^{2}+1\right)^{2}}\, dx\]"," ",0,"int((x^2+1)^2*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)","F"
3115,0,0,598,0.009000," ","int(x^2/(1+(a*x+(a^2*x^2-b)^(1/2))^(1/2))^(1/2),x)","\[\int \frac{x^{2}}{\sqrt{1+\sqrt{a x +\sqrt{a^{2} x^{2}-b}}}}\, dx\]"," ",0,"int(x^2/(1+(a*x+(a^2*x^2-b)^(1/2))^(1/2))^(1/2),x)","F"
3116,0,0,590,0.006000," ","int((x/(a*x^7-3*a*x^5+x^6+3*a*x^3-3*x^4-a*x+3*x^2-1))^(1/3),x)","\[\int \left(\frac{x}{a \,x^{7}-3 a \,x^{5}+x^{6}+3 a \,x^{3}-3 x^{4}-a x +3 x^{2}-1}\right)^{\frac{1}{3}}\, dx\]"," ",0,"int((x/(a*x^7-3*a*x^5+x^6+3*a*x^3-3*x^4-a*x+3*x^2-1))^(1/3),x)","F"
3117,0,0,590,180.000000," ","int((a^2*x^2-b)^(1/2)*(a*x+(a^2*x^2-b)^(1/2))^(1/3)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/3))^(1/4),x)","\[\int \frac{\sqrt{a^{2} x^{2}-b}\, \left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{3}}}{\left(c +\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{3}}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a^2*x^2-b)^(1/2)*(a*x+(a^2*x^2-b)^(1/2))^(1/3)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/3))^(1/4),x)","F"
3118,0,0,529,180.000000," ","int((a*x+(a^2*x^2-b)^(1/2))^(1/6)/x^3/(a^2*x^2-b)^(1/2),x)","\[\int \frac{\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{6}}}{x^{3} \sqrt{a^{2} x^{2}-b}}\, dx\]"," ",0,"int((a*x+(a^2*x^2-b)^(1/2))^(1/6)/x^3/(a^2*x^2-b)^(1/2),x)","F"
3119,0,0,425,0.110000," ","int(x^2*(_C3*x^2-_C4)*((_C3*x^2+_C0*x+_C4)/(_C3*x^2+_C1*x+_C4))^(1/4)/(_C3*x^2+_C4-x)/(_C3*x^2+_C4+x)/(_C3^2*x^4+2*_C3*_C4*x^2+_C4^2+x^2),x)","\[\int \frac{x^{2} \left(\textit{\_C3} \,x^{2}-\textit{\_C4} \right) \left(\frac{\textit{\_C3} \,x^{2}+\textit{\_C0} x +\textit{\_C4}}{\textit{\_C3} \,x^{2}+\textit{\_C1} x +\textit{\_C4}}\right)^{\frac{1}{4}}}{\left(\textit{\_C3} \,x^{2}+\textit{\_C4} -x \right) \left(\textit{\_C3} \,x^{2}+\textit{\_C4} +x \right) \left(\textit{\_C3}^{2} x^{4}+2 \textit{\_C3} \textit{\_C4} \,x^{2}+\textit{\_C4}^{2}+x^{2}\right)}\, dx\]"," ",0,"int(x^2*(_C3*x^2-_C4)*((_C3*x^2+_C0*x+_C4)/(_C3*x^2+_C1*x+_C4))^(1/4)/(_C3*x^2+_C4-x)/(_C3*x^2+_C4+x)/(_C3^2*x^4+2*_C3*_C4*x^2+_C4^2+x^2),x)","F"
3120,0,0,569,180.000000," ","int(1/(a*x+(a^2*x^2-b)^(1/2))^(1/4)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3),x)","\[\int \frac{1}{\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}} \left(c +\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(a*x+(a^2*x^2-b)^(1/2))^(1/4)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3),x)","F"
3121,0,0,575,0.005000," ","int(1/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3),x)","\[\int \frac{1}{\left(c +\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}}\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(1/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3),x)","F"
3122,0,0,680,0.005000," ","int(((a*x^9-4*a*x^7+x^8+6*a*x^5-4*x^6-4*a*x^3+6*x^4+a*x-4*x^2+1)/(b*x-c))^(1/4),x)","\[\int \left(\frac{a \,x^{9}-4 a \,x^{7}+x^{8}+6 a \,x^{5}-4 x^{6}-4 a \,x^{3}+6 x^{4}+a x -4 x^{2}+1}{b x -c}\right)^{\frac{1}{4}}\, dx\]"," ",0,"int(((a*x^9-4*a*x^7+x^8+6*a*x^5-4*x^6-4*a*x^3+6*x^4+a*x-4*x^2+1)/(b*x-c))^(1/4),x)","F"
3123,0,0,595,0.004000," ","int((c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3),x)","\[\int \left(c +\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}}\right)^{\frac{1}{3}}\, dx\]"," ",0,"int((c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3),x)","F"
3124,0,0,556,180.000000," ","int((a*x+(a^2*x^2-b)^(1/2))^(1/4)/x/(a^2*x^2-b)^(3/2),x)","\[\int \frac{\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}}}{x \left(a^{2} x^{2}-b \right)^{\frac{3}{2}}}\, dx\]"," ",0,"int((a*x+(a^2*x^2-b)^(1/2))^(1/4)/x/(a^2*x^2-b)^(3/2),x)","F"
3125,0,0,225,0.045000," ","int(x*(2*_C3*x^3-_C4)/(_C3*x^3+_C4-x)/((_C3*x^3+_C0*x+_C4)/(_C3*x^3+_C1*x+_C4))^(1/3)/(_C3^2*x^6+2*_C3*_C4*x^3+_C3*x^4+_C4^2+_C4*x+x^2),x)","\[\int \frac{x \left(2 \textit{\_C3} \,x^{3}-\textit{\_C4} \right)}{\left(\textit{\_C3} \,x^{3}+\textit{\_C4} -x \right) \left(\frac{\textit{\_C3} \,x^{3}+\textit{\_C0} x +\textit{\_C4}}{\textit{\_C3} \,x^{3}+\textit{\_C1} x +\textit{\_C4}}\right)^{\frac{1}{3}} \left(\textit{\_C3}^{2} x^{6}+2 \textit{\_C3} \textit{\_C4} \,x^{3}+\textit{\_C3} \,x^{4}+\textit{\_C4}^{2}+\textit{\_C4} x +x^{2}\right)}\, dx\]"," ",0,"int(x*(2*_C3*x^3-_C4)/(_C3*x^3+_C4-x)/((_C3*x^3+_C0*x+_C4)/(_C3*x^3+_C1*x+_C4))^(1/3)/(_C3^2*x^6+2*_C3*_C4*x^3+_C3*x^4+_C4^2+_C4*x+x^2),x)","F"
3126,0,0,633,180.000000," ","int((c*x-d)*(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)/(c*x+d),x)","\[\int \frac{\left(c x -d \right) \sqrt{a x +\sqrt{a^{2} x^{2}+b^{2}}}}{c x +d}\, dx\]"," ",0,"int((c*x-d)*(a*x+(a^2*x^2+b^2)^(1/2))^(1/2)/(c*x+d),x)","F"
3127,0,0,669,0.007000," ","int((x/(a*x^7-3*a*x^5+x^6+3*a*x^3-3*x^4-a*x+3*x^2-1))^(1/3)/x^3,x)","\[\int \frac{\left(\frac{x}{a \,x^{7}-3 a \,x^{5}+x^{6}+3 a \,x^{3}-3 x^{4}-a x +3 x^{2}-1}\right)^{\frac{1}{3}}}{x^{3}}\, dx\]"," ",0,"int((x/(a*x^7-3*a*x^5+x^6+3*a*x^3-3*x^4-a*x+3*x^2-1))^(1/3)/x^3,x)","F"
3128,1,8156,11,0.739000," ","int(1/(a*b*c-(a*b*x+c)^2*(a*x^2+b*x+c)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$8156$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
3129,0,0,580,180.000000," ","int((a*x+(a^2*x^2-b)^(1/2))^(1/4)/x^2/(a^2*x^2-b)^(3/2),x)","\[\int \frac{\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}}}{x^{2} \left(a^{2} x^{2}-b \right)^{\frac{3}{2}}}\, dx\]"," ",0,"int((a*x+(a^2*x^2-b)^(1/2))^(1/4)/x^2/(a^2*x^2-b)^(3/2),x)","F"
3130,0,0,280,0.044000," ","int((x^2-1)*(_C4+((_C1*x+_C0)/(_C3*x+_C2))^(1/2)*_C5)^(1/2)/(x^2+1),x)","\[\int \frac{\left(x^{2}-1\right) \sqrt{\textit{\_C4} +\sqrt{\frac{\textit{\_C1} x +\textit{\_C0}}{\textit{\_C3} x +\textit{\_C2}}}\, \textit{\_C5}}}{x^{2}+1}\, dx\]"," ",0,"int((x^2-1)*(_C4+((_C1*x+_C0)/(_C3*x+_C2))^(1/2)*_C5)^(1/2)/(x^2+1),x)","F"
3131,0,0,687,0.011000," ","int((a^2*x^2-b)^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/3))^(1/4),x)","\[\int \frac{\sqrt{a^{2} x^{2}-b}}{\left(c +\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{3}}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a^2*x^2-b)^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/3))^(1/4),x)","F"
3132,0,0,695,180.000000," ","int((a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/3)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/3))^(1/4),x)","\[\int \frac{\sqrt{a^{2} x^{2}-b}}{\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{3}} \left(c +\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{3}}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a^2*x^2-b)^(1/2)/(a*x+(a^2*x^2-b)^(1/2))^(1/3)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/3))^(1/4),x)","F"
3133,1,91,623,0.140000," ","int((a*x^4+b)*(a*x^4-c*x^2-b)^(1/2)/(a*x^4-b)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline elliptic&$\frac{\left(-\frac{\sqrt{a \,x^{4}-c \,x^{2}-b}\, \sqrt{2}}{4 x \left(\frac{a \,x^{4}-c \,x^{2}-b}{2 x^{2}}+\frac{c}{2}\right)}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{a \,x^{4}-c \,x^{2}-b}}{x \sqrt{c}}\right)}{2 \sqrt{c}}\right) \sqrt{2}}{2}$&$91$\\ default&$2 b \left(-\frac{x \sqrt{a \,x^{4}-c \,x^{2}-b}}{4 b \left(a \,x^{4}-b \right)}-\frac{\sqrt{4+\frac{2 \left(c +\sqrt{4 a b +c^{2}}\right) x^{2}}{b}}\, \sqrt{4-\frac{2 \left(-c +\sqrt{4 a b +c^{2}}\right) x^{2}}{b}}\, \EllipticF \left(\frac{x \sqrt{-\frac{2 \left(c +\sqrt{4 a b +c^{2}}\right)}{b}}}{2}, \frac{\sqrt{-4+\frac{2 c \left(-c +\sqrt{4 a b +c^{2}}\right)}{b a}}}{2}\right)}{8 b \sqrt{-\frac{2 \left(c +\sqrt{4 a b +c^{2}}\right)}{b}}\, \sqrt{a \,x^{4}-c \,x^{2}-b}}-\frac{\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{4}-b \right)}{\sum}\frac{\left(-c \,\underline{\hspace{1.25 ex}}\alpha^{2}-b \right) \left(-\frac{\arctanh \left(\frac{2 a \,x^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-c \,\underline{\hspace{1.25 ex}}\alpha^{2}-c \,x^{2}-2 b}{2 \sqrt{-c \,\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{a \,x^{4}-c \,x^{2}-b}}\right)}{\sqrt{-c \,\underline{\hspace{1.25 ex}}\alpha^{2}}}-\frac{a \sqrt{2}\, \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{2+\frac{c \,x^{2}}{b}+\frac{x^{2} \sqrt{4 a b +c^{2}}}{b}}\, \sqrt{2+\frac{c \,x^{2}}{b}-\frac{x^{2} \sqrt{4 a b +c^{2}}}{b}}\, \EllipticPi \left(\sqrt{-\frac{c +\sqrt{4 a b +c^{2}}}{2 b}}\, x , \frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(c -\sqrt{4 a b +c^{2}}\right)}{2 b}, \frac{\sqrt{2}\, \sqrt{\frac{-c +\sqrt{4 a b +c^{2}}}{b}}}{2 \sqrt{-\frac{c +\sqrt{4 a b +c^{2}}}{2 b}}}\right)}{b \sqrt{-\frac{c +\sqrt{4 a b +c^{2}}}{b}}\, \sqrt{a \,x^{4}-c \,x^{2}-b}}\right)}{\underline{\hspace{1.25 ex}}\alpha^{3}}}{16 a b}\right)+\frac{\sqrt{4+\frac{2 \left(c +\sqrt{4 a b +c^{2}}\right) x^{2}}{b}}\, \sqrt{4-\frac{2 \left(-c +\sqrt{4 a b +c^{2}}\right) x^{2}}{b}}\, \EllipticF \left(\frac{x \sqrt{-\frac{2 \left(c +\sqrt{4 a b +c^{2}}\right)}{b}}}{2}, \frac{\sqrt{-4+\frac{2 c \left(-c +\sqrt{4 a b +c^{2}}\right)}{b a}}}{2}\right)}{2 \sqrt{-\frac{2 \left(c +\sqrt{4 a b +c^{2}}\right)}{b}}\, \sqrt{a \,x^{4}-c \,x^{2}-b}}-\frac{c \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(a \,\textit{\_Z}^{4}-b \right)}{\sum}\frac{-\frac{\arctanh \left(\frac{2 a \,x^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-c \,\underline{\hspace{1.25 ex}}\alpha^{2}-c \,x^{2}-2 b}{2 \sqrt{-c \,\underline{\hspace{1.25 ex}}\alpha^{2}}\, \sqrt{a \,x^{4}-c \,x^{2}-b}}\right)}{\sqrt{-c \,\underline{\hspace{1.25 ex}}\alpha^{2}}}-\frac{a \sqrt{2}\, \underline{\hspace{1.25 ex}}\alpha^{3} \sqrt{2+\frac{c \,x^{2}}{b}+\frac{x^{2} \sqrt{4 a b +c^{2}}}{b}}\, \sqrt{2+\frac{c \,x^{2}}{b}-\frac{x^{2} \sqrt{4 a b +c^{2}}}{b}}\, \EllipticPi \left(\sqrt{-\frac{c +\sqrt{4 a b +c^{2}}}{2 b}}\, x , \frac{\underline{\hspace{1.25 ex}}\alpha^{2} \left(c -\sqrt{4 a b +c^{2}}\right)}{2 b}, \frac{\sqrt{2}\, \sqrt{\frac{-c +\sqrt{4 a b +c^{2}}}{b}}}{2 \sqrt{-\frac{c +\sqrt{4 a b +c^{2}}}{2 b}}}\right)}{b \sqrt{-\frac{c +\sqrt{4 a b +c^{2}}}{b}}\, \sqrt{a \,x^{4}-c \,x^{2}-b}}}{\underline{\hspace{1.25 ex}}\alpha}\right)}{8 a}$&$899$\\ \hline \end{longtable}"," ",0,"1/2*(-1/4*(a*x^4-c*x^2-b)^(1/2)*2^(1/2)/x/(1/2*(a*x^4-c*x^2-b)/x^2+1/2*c)+1/2*2^(1/2)/c^(1/2)*arctan((a*x^4-c*x^2-b)^(1/2)/x/c^(1/2)))*2^(1/2)","A"
3134,0,0,683,0.017000," ","int((-a-b*c+(1+c)*x)/((-a+x)*(-b+x)^2)^(2/3)/(a-b*d+(-1+d)*x),x)","\[\int \frac{-a -b c +\left(1+c \right) x}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{2}{3}} \left(a -b d +\left(-1+d \right) x \right)}\, dx\]"," ",0,"int((-a-b*c+(1+c)*x)/((-a+x)*(-b+x)^2)^(2/3)/(a-b*d+(-1+d)*x),x)","F"
3135,0,0,687,0.026000," ","int((-a-b*c+(1+c)*x)/(-b+x)/((-a+x)*(-b+x)^2)^(1/3)/(a-b*d+(-1+d)*x),x)","\[\int \frac{-a -b c +\left(1+c \right) x}{\left(-b +x \right) \left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{3}} \left(a -b d +\left(-1+d \right) x \right)}\, dx\]"," ",0,"int((-a-b*c+(1+c)*x)/(-b+x)/((-a+x)*(-b+x)^2)^(1/3)/(a-b*d+(-1+d)*x),x)","F"
3136,0,0,694,180.000000," ","int((c*x^2+d)*(a*x+(a^2*x^2-b)^(1/2))^(5/4)/x/(a^2*x^2-b)^(5/2),x)","\[\int \frac{\left(c \,x^{2}+d \right) \left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{5}{4}}}{x \left(a^{2} x^{2}-b \right)^{\frac{5}{2}}}\, dx\]"," ",0,"int((c*x^2+d)*(a*x+(a^2*x^2-b)^(1/2))^(5/4)/x/(a^2*x^2-b)^(5/2),x)","F"
3137,0,0,578,0.069000," ","int(1/(_C4+((_C1*x+_C0)/(_C3*x+_C2))^(1/2)*_C5)^(1/2)/(_C7*x+_C6)^2,x)","\[\int \frac{1}{\sqrt{\textit{\_C4} +\sqrt{\frac{\textit{\_C1} x +\textit{\_C0}}{\textit{\_C3} x +\textit{\_C2}}}\, \textit{\_C5}}\, \left(\textit{\_C7} x +\textit{\_C6} \right)^{2}}\, dx\]"," ",0,"int(1/(_C4+((_C1*x+_C0)/(_C3*x+_C2))^(1/2)*_C5)^(1/2)/(_C7*x+_C6)^2,x)","F"
3138,0,0,731,0.015000," ","int(((-b*x+1)/(c+x))^(1/6)*(d*x^2+1)/(b*x+1)/(c*x+1),x)","\[\int \frac{\left(\frac{-b x +1}{c +x}\right)^{\frac{1}{6}} \left(d \,x^{2}+1\right)}{\left(b x +1\right) \left(c x +1\right)}\, dx\]"," ",0,"int(((-b*x+1)/(c+x))^(1/6)*(d*x^2+1)/(b*x+1)/(c*x+1),x)","F"
3139,0,0,835,180.000000," ","int((a^2*x^2-b)^(1/2)*(a*x+(a^2*x^2-b)^(1/2))^(3/4)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(2/3),x)","\[\int \frac{\sqrt{a^{2} x^{2}-b}\, \left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{3}{4}}}{\left(c +\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}}\right)^{\frac{2}{3}}}\, dx\]"," ",0,"int((a^2*x^2-b)^(1/2)*(a*x+(a^2*x^2-b)^(1/2))^(3/4)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(2/3),x)","F"
3140,0,0,773,0.065000," ","int((_C7*x+_C6)/(_C4+((_C1*x+_C0)/(_C3*x+_C2))^(1/2)*_C5)^(1/2),x)","\[\int \frac{\textit{\_C7} x +\textit{\_C6}}{\sqrt{\textit{\_C4} +\sqrt{\frac{\textit{\_C1} x +\textit{\_C0}}{\textit{\_C3} x +\textit{\_C2}}}\, \textit{\_C5}}}\, dx\]"," ",0,"int((_C7*x+_C6)/(_C4+((_C1*x+_C0)/(_C3*x+_C2))^(1/2)*_C5)^(1/2),x)","F"
3141,0,0,1020,0.011000," ","int((a^2*x^2-b)^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(2/3),x)","\[\int \frac{\sqrt{a^{2} x^{2}-b}}{\left(c +\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}}\right)^{\frac{2}{3}}}\, dx\]"," ",0,"int((a^2*x^2-b)^(1/2)/(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(2/3),x)","F"
3142,0,0,1138,180.000000," ","int((a^2*x^2+b)^(3/2)*(a*x+(a^2*x^2+b)^(1/2))^(1/2)*(c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2),x)","\[\int \left(a^{2} x^{2}+b \right)^{\frac{3}{2}} \sqrt{a x +\sqrt{a^{2} x^{2}+b}}\, \sqrt{c +\sqrt{a x +\sqrt{a^{2} x^{2}+b}}}\, dx\]"," ",0,"int((a^2*x^2+b)^(3/2)*(a*x+(a^2*x^2+b)^(1/2))^(1/2)*(c+(a*x+(a^2*x^2+b)^(1/2))^(1/2))^(1/2),x)","F"
3143,0,0,1051,180.000000," ","int((a^2*x^2-b)^(1/2)*(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3)/(a*x+(a^2*x^2-b)^(1/2))^(1/4),x)","\[\int \frac{\sqrt{a^{2} x^{2}-b}\, \left(c +\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}}\right)^{\frac{1}{3}}}{\left(a x +\sqrt{a^{2} x^{2}-b}\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int((a^2*x^2-b)^(1/2)*(c+(a*x+(a^2*x^2-b)^(1/2))^(1/4))^(1/3)/(a*x+(a^2*x^2-b)^(1/2))^(1/4),x)","F"
3144,1,1250,125,0.267000," ","int((a^2*x^2+a*b*c-b^2*x)/(a*x^2+b*x+c)^(1/2)/(b*x^2+c)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(-a \,b^{2} c -\sqrt{-b c}\, b^{2}+a^{2} c \right) \left(\frac{b \sqrt{\left(x +\frac{\sqrt{-b c}}{b}\right)^{2} a -\frac{\sqrt{-b c}\, \left(\sqrt{-b c}\, b +2 a c \right) \left(x +\frac{\sqrt{-b c}}{b}\right)}{b c}-\frac{\sqrt{-b c}\, b +a c -b c}{b}}}{\left(\sqrt{-b c}\, b +a c -b c \right) \left(x +\frac{\sqrt{-b c}}{b}\right)}+\frac{\sqrt{-b c}\, \left(\sqrt{-b c}\, b +2 a c \right) \ln \left(\frac{-\frac{2 \left(\sqrt{-b c}\, b +a c -b c \right)}{b}-\frac{\sqrt{-b c}\, \left(\sqrt{-b c}\, b +2 a c \right) \left(x +\frac{\sqrt{-b c}}{b}\right)}{b c}+2 \sqrt{-\frac{\sqrt{-b c}\, b +a c -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-b c}}{b}\right)^{2} a -\frac{\sqrt{-b c}\, \left(\sqrt{-b c}\, b +2 a c \right) \left(x +\frac{\sqrt{-b c}}{b}\right)}{b c}-\frac{\sqrt{-b c}\, b +a c -b c}{b}}}{x +\frac{\sqrt{-b c}}{b}}\right)}{2 c \left(\sqrt{-b c}\, b +a c -b c \right) \sqrt{-\frac{\sqrt{-b c}\, b +a c -b c}{b}}}\right)}{4 c \,b^{2}}+\frac{\left(-a \,b^{2} c +\sqrt{-b c}\, b^{2}+a^{2} c \right) \left(\frac{b \sqrt{\left(x -\frac{\sqrt{-b c}}{b}\right)^{2} a +\frac{\sqrt{-b c}\, \left(-\sqrt{-b c}\, b +2 a c \right) \left(x -\frac{\sqrt{-b c}}{b}\right)}{b c}-\frac{-\sqrt{-b c}\, b +a c -b c}{b}}}{\left(-\sqrt{-b c}\, b +a c -b c \right) \left(x -\frac{\sqrt{-b c}}{b}\right)}-\frac{\sqrt{-b c}\, \left(-\sqrt{-b c}\, b +2 a c \right) \ln \left(\frac{-\frac{2 \left(-\sqrt{-b c}\, b +a c -b c \right)}{b}+\frac{\sqrt{-b c}\, \left(-\sqrt{-b c}\, b +2 a c \right) \left(x -\frac{\sqrt{-b c}}{b}\right)}{b c}+2 \sqrt{-\frac{-\sqrt{-b c}\, b +a c -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-b c}}{b}\right)^{2} a +\frac{\sqrt{-b c}\, \left(-\sqrt{-b c}\, b +2 a c \right) \left(x -\frac{\sqrt{-b c}}{b}\right)}{b c}-\frac{-\sqrt{-b c}\, b +a c -b c}{b}}}{x -\frac{\sqrt{-b c}}{b}}\right)}{2 c \left(-\sqrt{-b c}\, b +a c -b c \right) \sqrt{-\frac{-\sqrt{-b c}\, b +a c -b c}{b}}}\right)}{4 c \,b^{2}}-\frac{a \left(b^{2}+a \right) \ln \left(\frac{-\frac{2 \left(-\sqrt{-b c}\, b +a c -b c \right)}{b}+\frac{\sqrt{-b c}\, \left(-\sqrt{-b c}\, b +2 a c \right) \left(x -\frac{\sqrt{-b c}}{b}\right)}{b c}+2 \sqrt{-\frac{-\sqrt{-b c}\, b +a c -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-b c}}{b}\right)^{2} a +\frac{\sqrt{-b c}\, \left(-\sqrt{-b c}\, b +2 a c \right) \left(x -\frac{\sqrt{-b c}}{b}\right)}{b c}-\frac{-\sqrt{-b c}\, b +a c -b c}{b}}}{x -\frac{\sqrt{-b c}}{b}}\right)}{4 \sqrt{-b c}\, b \sqrt{-\frac{-\sqrt{-b c}\, b +a c -b c}{b}}}+\frac{a \left(b^{2}+a \right) \ln \left(\frac{-\frac{2 \left(\sqrt{-b c}\, b +a c -b c \right)}{b}-\frac{\sqrt{-b c}\, \left(\sqrt{-b c}\, b +2 a c \right) \left(x +\frac{\sqrt{-b c}}{b}\right)}{b c}+2 \sqrt{-\frac{\sqrt{-b c}\, b +a c -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-b c}}{b}\right)^{2} a -\frac{\sqrt{-b c}\, \left(\sqrt{-b c}\, b +2 a c \right) \left(x +\frac{\sqrt{-b c}}{b}\right)}{b c}-\frac{\sqrt{-b c}\, b +a c -b c}{b}}}{x +\frac{\sqrt{-b c}}{b}}\right)}{4 \sqrt{-b c}\, b \sqrt{-\frac{\sqrt{-b c}\, b +a c -b c}{b}}}$&$1250$\\ \hline \end{longtable}"," ",0,"1/4*(-a*b^2*c-(-b*c)^(1/2)*b^2+a^2*c)/c/b^2*(1/((-b*c)^(1/2)*b+a*c-b*c)*b/(x+(-b*c)^(1/2)/b)*((x+(-b*c)^(1/2)/b)^2*a-(-b*c)^(1/2)/b/c*((-b*c)^(1/2)*b+2*a*c)*(x+(-b*c)^(1/2)/b)-((-b*c)^(1/2)*b+a*c-b*c)/b)^(1/2)+1/2*(-b*c)^(1/2)/c*((-b*c)^(1/2)*b+2*a*c)/((-b*c)^(1/2)*b+a*c-b*c)/(-((-b*c)^(1/2)*b+a*c-b*c)/b)^(1/2)*ln((-2*((-b*c)^(1/2)*b+a*c-b*c)/b-(-b*c)^(1/2)/b/c*((-b*c)^(1/2)*b+2*a*c)*(x+(-b*c)^(1/2)/b)+2*(-((-b*c)^(1/2)*b+a*c-b*c)/b)^(1/2)*((x+(-b*c)^(1/2)/b)^2*a-(-b*c)^(1/2)/b/c*((-b*c)^(1/2)*b+2*a*c)*(x+(-b*c)^(1/2)/b)-((-b*c)^(1/2)*b+a*c-b*c)/b)^(1/2))/(x+(-b*c)^(1/2)/b)))+1/4*(-a*b^2*c+(-b*c)^(1/2)*b^2+a^2*c)/c/b^2*(1/(-(-b*c)^(1/2)*b+a*c-b*c)*b/(x-(-b*c)^(1/2)/b)*((x-(-b*c)^(1/2)/b)^2*a+(-b*c)^(1/2)/b/c*(-(-b*c)^(1/2)*b+2*a*c)*(x-(-b*c)^(1/2)/b)-(-(-b*c)^(1/2)*b+a*c-b*c)/b)^(1/2)-1/2*(-b*c)^(1/2)/c*(-(-b*c)^(1/2)*b+2*a*c)/(-(-b*c)^(1/2)*b+a*c-b*c)/(-(-(-b*c)^(1/2)*b+a*c-b*c)/b)^(1/2)*ln((-2*(-(-b*c)^(1/2)*b+a*c-b*c)/b+(-b*c)^(1/2)/b/c*(-(-b*c)^(1/2)*b+2*a*c)*(x-(-b*c)^(1/2)/b)+2*(-(-(-b*c)^(1/2)*b+a*c-b*c)/b)^(1/2)*((x-(-b*c)^(1/2)/b)^2*a+(-b*c)^(1/2)/b/c*(-(-b*c)^(1/2)*b+2*a*c)*(x-(-b*c)^(1/2)/b)-(-(-b*c)^(1/2)*b+a*c-b*c)/b)^(1/2))/(x-(-b*c)^(1/2)/b)))-1/4*a*(b^2+a)/(-b*c)^(1/2)/b/(-(-(-b*c)^(1/2)*b+a*c-b*c)/b)^(1/2)*ln((-2*(-(-b*c)^(1/2)*b+a*c-b*c)/b+(-b*c)^(1/2)/b/c*(-(-b*c)^(1/2)*b+2*a*c)*(x-(-b*c)^(1/2)/b)+2*(-(-(-b*c)^(1/2)*b+a*c-b*c)/b)^(1/2)*((x-(-b*c)^(1/2)/b)^2*a+(-b*c)^(1/2)/b/c*(-(-b*c)^(1/2)*b+2*a*c)*(x-(-b*c)^(1/2)/b)-(-(-b*c)^(1/2)*b+a*c-b*c)/b)^(1/2))/(x-(-b*c)^(1/2)/b))+1/4*a*(b^2+a)/(-b*c)^(1/2)/b/(-((-b*c)^(1/2)*b+a*c-b*c)/b)^(1/2)*ln((-2*((-b*c)^(1/2)*b+a*c-b*c)/b-(-b*c)^(1/2)/b/c*((-b*c)^(1/2)*b+2*a*c)*(x+(-b*c)^(1/2)/b)+2*(-((-b*c)^(1/2)*b+a*c-b*c)/b)^(1/2)*((x+(-b*c)^(1/2)/b)^2*a-(-b*c)^(1/2)/b/c*((-b*c)^(1/2)*b+2*a*c)*(x+(-b*c)^(1/2)/b)-((-b*c)^(1/2)*b+a*c-b*c)/b)^(1/2))/(x+(-b*c)^(1/2)/b))","B"
3145,0,0,1034,0.024000," ","int((a*x^2+b^2)^2*(b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2-b^2)^2,x)","\[\int \frac{\left(a \,x^{2}+b^{2}\right)^{2} \sqrt{b +\sqrt{a \,x^{2}+b^{2}}}}{\left(a \,x^{2}-b^{2}\right)^{2}}\, dx\]"," ",0,"int((a*x^2+b^2)^2*(b+(a*x^2+b^2)^(1/2))^(1/2)/(a*x^2-b^2)^2,x)","F"
3146,0,0,863,180.000000," ","int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x+d)^2/(a^2*x^4+b)^(1/2),x)","\[\int \frac{\sqrt{a \,x^{2}+\sqrt{a^{2} x^{4}+b}}}{\left(c x +d \right)^{2} \sqrt{a^{2} x^{4}+b}}\, dx\]"," ",0,"int((a*x^2+(a^2*x^4+b)^(1/2))^(1/2)/(c*x+d)^2/(a^2*x^4+b)^(1/2),x)","F"
3147,0,0,1080,0.026000," ","int((-b-a*c+(1+c)*x)/(-a+x)/((-a+x)*(-b+x)^2)^(1/3)/(b-a*d+(-1+d)*x),x)","\[\int \frac{-b -a c +\left(1+c \right) x}{\left(-a +x \right) \left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{3}} \left(b -a d +\left(-1+d \right) x \right)}\, dx\]"," ",0,"int((-b-a*c+(1+c)*x)/(-a+x)/((-a+x)*(-b+x)^2)^(1/3)/(b-a*d+(-1+d)*x),x)","F"
3148,0,0,1265,0.034000," ","int((-a-b*c+(1+c)*x)/((-a+x)*(-b+x)^2)^(1/3)/(-a^2+b^2*d+2*(-b*d+a)*x+(-1+d)*x^2),x)","\[\int \frac{-a -b c +\left(1+c \right) x}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{3}} \left(-a^{2}+b^{2} d +2 \left(-b d +a \right) x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((-a-b*c+(1+c)*x)/((-a+x)*(-b+x)^2)^(1/3)/(-a^2+b^2*d+2*(-b*d+a)*x+(-1+d)*x^2),x)","F"
3149,0,0,1301,0.036000," ","int((-b-a*c+(1+c)*x)/((-a+x)*(-b+x)^2)^(1/3)/(-b^2+a^2*d+2*(-a*d+b)*x+(-1+d)*x^2),x)","\[\int \frac{-b -a c +\left(1+c \right) x}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{1}{3}} \left(-b^{2}+a^{2} d +2 \left(-a d +b \right) x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((-b-a*c+(1+c)*x)/((-a+x)*(-b+x)^2)^(1/3)/(-b^2+a^2*d+2*(-a*d+b)*x+(-1+d)*x^2),x)","F"
3150,0,0,1081,0.071000," ","int((_C9*x+_C8)/(_C4+((_C1*x+_C0)/(_C3*x+_C2))^(1/2)*_C5)^(1/2)/(_C7*x+_C6),x)","\[\int \frac{\textit{\_C9} x +\textit{\_C8}}{\sqrt{\textit{\_C4} +\sqrt{\frac{\textit{\_C1} x +\textit{\_C0}}{\textit{\_C3} x +\textit{\_C2}}}\, \textit{\_C5}}\, \left(\textit{\_C7} x +\textit{\_C6} \right)}\, dx\]"," ",0,"int((_C9*x+_C8)/(_C4+((_C1*x+_C0)/(_C3*x+_C2))^(1/2)*_C5)^(1/2)/(_C7*x+_C6),x)","F"
3151,0,0,1409,0.037000," ","int((-b+x)*(-a-b*c+(1+c)*x)/((-a+x)*(-b+x)^2)^(2/3)/(-a^2+b^2*d+2*(-b*d+a)*x+(-1+d)*x^2),x)","\[\int \frac{\left(-b +x \right) \left(-a -b c +\left(1+c \right) x \right)}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{2}{3}} \left(-a^{2}+b^{2} d +2 \left(-b d +a \right) x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((-b+x)*(-a-b*c+(1+c)*x)/((-a+x)*(-b+x)^2)^(2/3)/(-a^2+b^2*d+2*(-b*d+a)*x+(-1+d)*x^2),x)","F"
3152,0,0,1444,0.037000," ","int((-b+x)*(-b-a*c+(1+c)*x)/((-a+x)*(-b+x)^2)^(2/3)/(-b^2+a^2*d+2*(-a*d+b)*x+(-1+d)*x^2),x)","\[\int \frac{\left(-b +x \right) \left(-b -a c +\left(1+c \right) x \right)}{\left(\left(-a +x \right) \left(-b +x \right)^{2}\right)^{\frac{2}{3}} \left(-b^{2}+a^{2} d +2 \left(-a d +b \right) x +\left(-1+d \right) x^{2}\right)}\, dx\]"," ",0,"int((-b+x)*(-b-a*c+(1+c)*x)/((-a+x)*(-b+x)^2)^(2/3)/(-b^2+a^2*d+2*(-a*d+b)*x+(-1+d)*x^2),x)","F"
3153,1,384279,1896,0.550000," ","int((x^2-c*x^2*((a*x+b)/(c*x+d))^(3/2))/(a-b*((a*x+b)/(c*x+d))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$384279$\\ \hline \end{longtable}"," ",0,"result too large to display","B"
3154,0,0,2305,0.083000," ","int((_C7*x+_C6)^2/(_C4+((_C1*x+_C0)/(_C3*x+_C2))^(1/2)*_C5)^(1/2),x)","\[\int \frac{\left(\textit{\_C7} x +\textit{\_C6} \right)^{2}}{\sqrt{\textit{\_C4} +\sqrt{\frac{\textit{\_C1} x +\textit{\_C0}}{\textit{\_C3} x +\textit{\_C2}}}\, \textit{\_C5}}}\, dx\]"," ",0,"int((_C7*x+_C6)^2/(_C4+((_C1*x+_C0)/(_C3*x+_C2))^(1/2)*_C5)^(1/2),x)","F"